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189600 | https://byjus.com/maths/monomial/ | A monomial is a polynomial, which has only one term. A monomial is an algebraic expression with a single term but can have multiple variables and a higher degree too. For example, 9x3yz is a single term, where 9 is the coefficient, x, y, z are the variables and 3 is the degree of monomial. Similar to polynomial, we can perform different operations, such as addition, subtraction, multiplication and division on monomials. In this article, we are going to learn the monomial definition, different arithmetic operations performed on monomials and examples in detail.
| |
| Table of Contents: Definition Examples Parts of Monomial Monomial Degree Factorization of Monomial Monomial Operations Monomial, Binomial and Trinomial Problems Practice Questions FAQs |
What is a Monomial?
A monomial is a type of polynomial, having only a non-zero single term. Monomial consists of only a single term which makes it easy to do the operation of addition, subtraction and multiplication. It consists of either only one variable or one coefficient or product of a variable and a coefficient with exponents as whole numbers, which represent only one term. Whereas binomial and trinomial are also considered to be polynomial, which consists of two and three terms respectively. It cannot have a variable in the denominator.
Examples of Monomial
Let us consider some of the variables and examples:
p – One variable and degree is one.
5p2 – with 5 as coefficient and degree as two.
p3q – with two variables (p and q) and degree as 4 (i.e., 3+1).
-6ty – t and y are two variables with coefficient -6.
Let us consider x3+3x2+4x+12 as a polynomial, where x3, 3x2, 4x and 12 are single terms and called monomials.
Parts of Monomial Expression
The different parts present in the monomial expression are:
Variable: The letters present in the monomial expression.
Coefficient: The number which is multiplied by the variable in the expression
Degree: The sum of the exponents present in the expression
Literal part: The alphabets which are present along with the exponent value in the expression
Example: 4xy2 is a monomial expression.
the coefficient is 4
Variables are x and y
The degree of the monomial expression = 1+2 = 3
The literal part is xy2
Like, 4x is a monomial example, as it denotes a single term. In the same way, 23, 4x2, 5xy, etc., are all examples of monomials. But 23+x, 4x + y, 5xy-2 are not monomials, as they don’t fulfil the conditions.
Degree of Monomial
The degree of a monomial expression or the monomial degree can be found by adding the exponents of the variables in the expression. While calculating the monomial degree, it includes the exponent values of the variables and it also includes the implicit exponent of 1 for the variables, which usually does not appear in the expression.
For example, 2xy3. In this, the exponent value of 1 is not visible in the expression. Thus, the degree of the expression is 1+3 = 4. In case, the monomial expression is a constant value. The degree of the non-zero constant is given as 0.
The degree of the monomial expression is also called the order of the monomial.
Factorization of Monomial
Like factoring a number, the monomial expression can also be factored. For example, the factorization of 15 is 3×5. The monomial expression can be expressed in the same way. Now, consider a monomial expression, 24a3. First, factor the coefficient of the variable, (i.e) 24. The number 24 is factored as 2×2×2×3. Similarly, a3 is factored as a×a×a.
Therefore, the factorization of the monomial 24a3 is 2×2×2×3×a×a×a.
Operations on Monomial
The arithmetic operations which are performed on the monomial expression are addition, subtraction, multiplication and division.
Addition of two monomials
Subtraction of two monomials
Multiplication of two monomials
Division of two monomials
Addition of Two Monomials
The addition of two monomials with the same literal part will result in a monomial expression
For example, the addition of 4ab + 6ab is 10 ab.
Subtraction of Two Monomials
The subtraction of two monomials with a similar literal part will result in a monomial expression
For example, the subtraction of 10xyz – 3xyz is 7xyz.
Multiplication of Two Monomials
The multiplication of two monomials will also result in monomial
For example, the product of 3x2y and 4z is 12x2yz
While multiplying two monomials with the same variables, then add the exponent value of the variables.
For example, the product of a3 and a4 is given as
(a3)(a4) = a3+4 = a7.
Division of Two Monomials
While dividing two monomials with the same variables, subtract the exponent value of the variables.
For example, the division of a9 by a3 is given as
(a9) / (a3) = a9-3 = a6.
Difference Between Monomial, Binomial and Trinomial
| | | |
---
| Monomial | Binomial | Trinomial |
| A monomial is an expression with a single term. | A binomial is a polynomial or algebraic expression, which has a maximum of two non-zero terms. | A trinomial is a polynomial or algebraic expression, which has a maximum of three non-zero terms. |
| Examples: 2x, 4y, 6z, 2x2, 7xyz, etc., are monomials | Example: 2x2 + y, 10p + 7q2, a + b, 2x2y2 + 9, are all binomials | Example: 2x2 + y + z, r + 10p + 7q2, a + b + c, 2x2y2 + 9 + z, are all trinomials |
Now hopefully, we have got the basic difference between Monomial, Binomial and Trinomial. Let us solve some problems based on monomial.
Important Facts of Monomials
The multiplication of two monomial will also result in the monomial.
The sum or difference of two monomials might not result in a monomial.
An expression having a single term with a negative exponent cannot be considered as a monomial. (i.e) A monomial cannot have variables with negative exponents.
Related Articles
Binomial
Degree of a Polynomial
Factorization of Polynomials
Multiplying Polynomials
Solved Problems on Monomials
Example 1:
Identify which of the following is a Monomial.
3ab
4b+c
6x2+2y
a+b+c2
Solution:
3ab is a Monomial
Whereas 4b+c and 6x2+2y are binomials and a+b+c2 is a trinomial.
And all of these equations are called a polynomial.
Example 2:
Find the factorization of the monomial 10y3.
Solution:
Given monomial: 10y3.
First, factorize the coefficient of the variable, y. (i.e.)10.
Hence, 10 can be factorized as 2×5.
y3 can be factorized as y × y × y.
Therefore, the factorization of the monomial 10y3 is 2×5×y×y×y.
Monomial Practice Questions
Categorize the following expressions into monomials, binomials and trinomials.
(a) 2x+3y
(b) 4m3
(c) 2x2+3m-2
(d) -2y3
Factorize the monomial expression 64x2y.
Frequently Asked Questions on Monomials
Q1
Define monomial, binomial and trinomial
A monomial is an expression with only one term. Example. 3x.
A binomial is an expression with two terms. Example 2x+3y
A trinomial is an expression with three terms. Example x+2y+3z
Q2
What is meant by the degree of a monomial?
The degree of a monomial is defined as the sum of the exponents of the variables present in the monomial term.
Q3
What are the different arithmetic operations performed on monomials?
The different arithmetic operations performed on monomials are addition, subtraction, multiplication and division.
Q4
Can we get a monomial term while adding two monomials?
If two monomials with the same literal parts are added, the sum should be a monomial. But, if we add two monomials with different literal parts, the result should be a binomial.
Q5
How to identify the monomial expression?
The monomial expression should not have an addition or subtraction operator. A monomial can be a constant term or else, the variables with coefficients and exponents.
Learn about the different types of algebraic expressions with us and download BYJU’S – The Learning App for interactive videos.
Test your knowledge on Monomials
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189601 | http://www.hanlonmath.com/pdfFiles/resource_1109.pdf | Derivation – Sum of Arithmetic Series Arithmetic Sequence is a sequence in which every term after the first is obtained by adding a constant, called the common difference (d). To find the nth term of a an arithmetic sequence, we know an = a1 + (n – 1)d The first term is a1, second term is a1 + d, third term is a1 + 2d, etc This leads up to finding the sum of the arithmetic series, Sn, by starting with the first term and successively adding the common difference. 1st 2nd 3rd nth Sn = a1 + (a1 + d) + (a1 + 2d) + … + [a1 + (n–1)d] We could have also started with the nth term and successively subtracted the common difference, so Sn = an + (an – d) + (an– 2d) + … + [an – (n–1)d] You could find the sum of the arithmetic sequence either way. However, if you looked at that, you might see that if you added those two equations together, terms add out. Sn = a1 + (a1 + d) + (a1 + 2d) + … + [a1 + (n–1)d] Sn = an + (an – d) + (an – 2d) + … + [an – (n–1)d] 2Sn = (a1 + an) + (a1 + an) + (a1 + an) + … + [a1 + an] Notice all the d terms added out. So 2Sn = n (a1 + an) Sn = n(a1+an) 2 Sn = n 2(a1 +an) By substituting an = a1 + (n – 1)d into the last formula, we have Sn = n 2 [a1 + a1 + (n – 1)d] Simplifying Sn = n 2 [2 a1 + (n – 1)d] These two formulas allow us to find the sum of an arithmetic series quickly. |
189602 | https://sfent.com/wp-content/uploads/2022/07/TypeDegreeConfiguration.pdf | Audiology Information Series © ASHA 2015 10802 AUDIOLOGY Information Series When describing hearing loss, we generally look at three aspects: type of hearing loss, degree of hearing loss, and configuration of hearing loss.
TYPES OF HEARING LOSS There are three basic types of hearing loss: conductive, sensorineural, and mixed.
m Conductive hearing loss occurs when sound is not sent easily through the outer ear canal to the eardrum and the tiny bones (ossicles) of the middle ear. Conductive hearing loss makes sounds softer and less easy to hear. This type of hearing loss can often be corrected medically or surgically. Some possible causes of conductive hearing loss are: • Fluid in the middle ear from colds or allergies • Ear infection (otitis media) • Poor eustachian tube function • Hole in the eardrum • Too much earwax (cerumen) • Swimmer’s ear (external otitis) • Foreign body in the ear canal • Malformation of the outer ear, ear canal, or middle ear m Sensorineural hearing loss (SNHL) happens when there is damage to the inner ear (cochlea) or to the nerve pathways from the inner ear to the brain. Most of the time, SNHL cannot be medically or surgically corrected. This is the most common type of permanent hearing loss.
SNHL reduces the ability to hear faint sounds. Even when speech is loud enough to hear, it may still be unclear or sound muffled.
Some possible causes of SNHL are: • Drugs that are toxic to hearing • Hearing loss that runs in the family (genetic or hereditary) • Aging • Head trauma • Malformation of the inner ear • Exposure to loud noise m Mixed hearing loss occurs when a conductive hearing loss happens in combination with an SNHL. In other words, there may be damage in the outer or middle ear and in the inner ear (cochlea) or auditory nerve. DEGREE OF HEARING LOSS Degree of hearing loss refers to the severity of the loss. The table below shows one of the more commonly used classification systems. The numbers are representative of the patient’s hearing loss range in decibels (dB HL). Source: Clark, J. G. (1981). Uses and abuses of hearing loss classification. Asha, 23, 493–500. CONFIGURATION OF HEARING LOSS The configuration, or shape, of the hearing loss refers to the degree and pattern of hearing loss across frequencies (tones) as illustrated in a graph called an audiogram. For example, a hearing loss that only affects the high tones would be described as a high-frequency loss. Its configuration would show good hearing in the low tones and poor hearing in the high tones. On the other hand, if only the low frequencies were affected, the configuration would show poorer hearing for low tones and better hearing for high tones. Some hearing Type, Degree, and Configuration of Hearing Loss Degree of hearing loss Hearing loss range (dB HL) Normal –10 to 15 Slight 16 to 25 Mild 26 to 40 Moderate 41 to 55 Moderately severe 56 to 70 Severe 71 to 90 Profound 91+ Compliments of American Speech-Language-Hearing Association 2200 Research Boulevard, Rockville, MD 20850 • 800-638-8255 For more information about hearing loss, hearing aids, or referral to an ASHA-certified audiologist, contact: 2200 Research Boulevard Rockville, MD 20850 800-638-8255 E-mail: actioncenter@asha.org Website: www.asha.org Audiology Information Series © ASHA 2015 10802 NOTES: For more information and to view the entire Audiology Information Series library, scan with your mobile device.
loss configurations are flat, indicating the same amount of hearing loss for low and high tones.
Other descriptors associated with hearing loss are: • Bilateral versus unilateral. Bilateral hearing loss means hearing loss in both ears. Unilateral hearing loss (UHL) means that hearing is normal in one ear but there is hearing loss in the other ear. The hearing loss can range from mild to very severe. UHL can occur in both adults and children. Approximately 1 out of every 10,000 children is born with UHL, and nearly 3% of school-age children have UHL. Children with UHL are at higher risk for having academic, speech-language, and social-emotional difficulties than their normal hearing peers. This may be because UHL is often not identified, and the children do not receive intervention. Below are some possible causes of UHL: o Hearing loss that runs in the family (genetic or hereditary) o An outer, middle, or inner ear abnormality o Syndromes such as Down and Usher syndrome o Illnesses or infections such as CMV, Rubella o Head injury o Exposure to loud noise o Traumatic brain injury (TBI) • Symmetrical versus asymmetrical. Symmetrical means the degree and configuration of hearing loss are the same in each ear. Asymmetrical means the degree and configuration are different in each ear.
• Progressive versus sudden hearing loss. Progressive means that hearing loss becomes worse over time. Sudden means that the loss happens quickly. Such a hearing loss requires immediate medical attention to determine its cause and treatment.
• Fluctuating versus stable hearing loss. Fluctuating means hearing loss that changes over time—sometimes getting better, sometimes getting worse. Stable hearing loss does not change over time and remains the same. |
189603 | https://cupcakephysics.com/relativity/2015/06/07/the-relativistic-doppler-shift.html | cupcake physics
June
7th,
2015
The Relativistic Doppler Shift
Introduction
Relativity is a weird and wonderful branch of physics. It is chock full of lasers, contracting objects, and terrible Star Trek references. But since it is so outlandish, it also contains many paradoxes. More often than not, these paradoxes come from the fact that we do not fully understand the rules of relativity, rather than an inconsistency of the theory itself.
Of course, a good way to make sure that you are on the right track is to check your work in a few different ways; since the theory of relativity ought to be self-consistent, there ought to be a few different ways to derive a common result. A bit of mathematical creativity will ensure that your calculations are correct and your assumptions are valid. It may even lead to a bit of deeper insight.
I offer three different derivations of the relativistic Doppler effect in this post. The first one is easy to understand, needing only the concept of time dilation and the basic tenants of special relativity. The second one is the textbook-derivation of the effect in one dimension. The final one is a derivation Doppler effect using the full Lorentz transformation in all four dimensions. It results in a surprising conclusion.
Derivation #1 - Time Dilation
The first derivation is quick and cute. Suppose an observer stands still (reference frame O) while a light source moves past him or her at some speed β=v/cβ=v/c in the +x direction (reference frame S). As the light source moves past the stationary observer (O), it radiates light in the -x direction. In reference frame S, the light has a wavelength of λλ and a frequency of fs=c/λfs=c/λ. We want to determine the frequency of light in reference frame O (fofo).
Start with the definition of time dilation.
to=tsγ
to=tsγ
In the equation above, toto is a time interval measured by the observer at rest while tsts is a time interval measured by the moving source. The time intervals toto and tsts will henceforth refer to the period of the light emitted by the source.
We know that frequency seen by the observer (fofo) is inversely proportional to the time-dilated period toto:
1fo=tsγ
1fo=tsγ
The expression for tsts is a bit more complicated. According to both reference frames, the light moves in the -x direction with a speed cc. Additionally, according to reference frame S, the observer in reference frame O moves in the -x direction with a speed of vv. Thus, reference frame S comes to the conclusion that the wavelength of light as seen in reference frame O must be a function of the speed of light cc and the speed of the observer vv:
λ+vts=cts
λ+vts=cts
λ=cts−vts=(c−v)ts
λ=cts−vts=(c−v)ts
Solving for tsts yields:
ts=λc−v=c/fsc−v=c(c−v)fs=1(1−β)fs
ts=λc−v=c/fsc−v=c(c−v)fs=1(1−β)fs
Plug your expression for tsts into the one for time dilation:
1fo=tsγ=1(1−β)fs1γ=1(1−β)fs√1−β2
1fo=tsγ=1(1−β)fs1γ=1(1−β)fs1−β2−−−−−√
Simplifying the ββ terms yields:
1fo=√1−β21−β1fs=√(1+β)(1−β)1−β1fs=√1+β1−β1fs
1fo=1−β2−−−−−√1−β1fs=(1+β)(1−β)−−−−−−−−−−−√1−β1fs=1+β1−β−−−−−√1fs
We usually write the ratio of the frequencies.
fsfo=√1+β1−β
fsfo=1+β1−β−−−−−√
Derivation #2 - One Dimensional Lorentz Transformations
This is the textbook method to getting an expression for the relativistic Doppler effect. Just to keep everything simple, we will assume that our rest frame and the frame of the source coincide at time t=0t=0. This means that the reference frames cross at (0,0). We can use the Lorentz transformations to translate position and time in the observer’s frame of reference (t,x) to position and time to the source’s frame of reference (t’,x’).
t′=γ(t−βx)
t′=γ(t−βx)
x′=γ(x−βt)
For example, if an event occurs at (T,0) in the observer’s frame of reference, then it occurs at (γT,−γβT) in the source’s frame of reference. We can reverse the direction of motion (β) and rearrange the equations above to translate position and time in the source frame of reference (t’, x’) to position and time in the observer’s frame of reference (t,x):
t=γ(t′+βx′)x=γ(x′+βt′)
Suppose that the moving source emits a light wave at a spacetime coordinate of (T,0) in the source reference frame. According to the observer, that event occured at the spacetime coordinate (γT,γβT). Thus, that wave will reach the observer at time:
t=γT+γβT=γT(1+β)=T1+β√1−β2
We can simplify this expression:
t=T1+β√1−β2=T1+β√(1+β)(1−β)=T√1+β1−βtT=√1+β1−β
We finish the derivation by noting that t=1/fo and T=1/fs:
fsfo=√1+β1−β
Derivation #3 - Tensor Formalism
I know what you are thinking. Those two derivations above were a piece of cake. Let’s up the difficulty! Bring on the tensors!
Our source is going to travel along the +x axis with a constant velocity of β. A general Lorentz transformation Λ for a given reference frame moving at a constant velocity is given by:
Λ00=γΛ0i=Λi0=−γβiΛij=(γ−1)βiβjβ2+δij
In our case, since βy=βz=0 and βx=β:
Λ=[γ−γβ00−γβγ0000100001]
The source emits a photon with energy hfs that travels along the -x axis. The four vectors of the photon in the source and observer reference frames are:
xμ=[hfo−hfo00]x′μ=[hfs−hfs00]
Let’s solve for the four vector of the photon in the reference frame of the observer:
x′μ=Λxμ[hfs−hfs00]=[γ−γβ00−γβγ0000100001][hfo−hfo00]=[γhfo+γβhfo−γβhfo−γhfo00]=γ(1+β)[hfo−hfo00]
We have seen that γ(1+β) term before from above:
[hfs−hfs00]=(√1+β1−β)[hfo−hfo00]
Again! We see the same ratio of βs that relates the frequency seen by the observer and the frequency seen by the source.
Let’s try something a little different. Suppose the photon is not directed along the x-axis. Instead, it is directed along the z-axes:
xμ=[hfs00−hfs]
Once again, the source travels along the +x axis with a constant velocity of β. Then:
x′μ=[γ−γβ00−γβγ0000100001][hfs00−hfs]=[γhfs−γβhfs0−hfs]≠[hfo00−hfo]
We see something kind of strange. There does not seem to be any change in momentum along the z-direction, as expected. However, the transformation created a component of momentum along the x-direction!
In the non-relativistic case, if you are traveling at 90 degrees with respect to the motion of the source you do not see any Doppler shift. However, when you are moving at relativistic speeds, you see a Doppler shift perpendicular to the motion of the source; note the non-zero component along the x-direction. This is called the transverse Doppler effect.
Conclusion
There we have it! Three derivations of the relativistic effect, all of them yielding the same answer. As a bonus, the final derivation yielded both the Doppler effect and the transverse Doppler effect.
Until next week!
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189604 | https://www.ck12.org/flexi/math-grade-7/probability-of-compound-events/a-pair-of-standard-dice-are-rolled-find-the-probability-of-rolling-a-sum-of-2-with-these-dice-lesspgreaterlessmathgreaterpleft(d_1plusd_22right)less-by-mathgreaterless-by-pgreater-lesspgreaterless-by-pgreater-be-sure-to-reduce/ | Flexi answers - A pair of standard dice are rolled. Find the probability of rolling a sum of 2 with these dice. @$\begin{align}P\left(D_{1}+D_{2}=2\right)=\end{align}@$□ Be sure to reduce. | CK-12 Foundation
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Questionless-by-mathgreaterless-by-pgreater-lesspgreaterless-by-pgreater-be-sure-to-reduce/ "A pair of standard dice are rolled. Find the probability of rolling a sum of 2 with these dice.
@$\begin{align}P\left(D_{1}+D_{2}=2\right)=\end{align}@$
□
Be sure to reduce.")
A pair of standard dice are rolled. Find the probability of rolling a sum of 2 with these dice.
P(D 1+D 2=2)=
□
Be sure to reduce.
Flexi Says:
The sum of 2 can only be achieved if both dice show a 1. There are 6 possible outcomes for each die, so there are 6×6=36 total possible outcomes.
The event of both dice showing a 1 is only one outcome.
So, the probability of rolling a sum of 2 is 1 36.
Therefore, the probability of rolling a sum of 2 with these dice is 1 36.
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What happens when you roll two pairs of dice once?What is the difference between classical and empirical probability?In Abby's figurine collection, 2/6 of the figurines are monkeys and 1/6 of the figurines are mice. What fraction of the figurines in Abby's collection are either monkeys or mice?
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189605 | https://stackoverflow.com/questions/59432096/simple-combinatorics-number-of-ways-to-pair-up-elements | Skip to main content
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Simple combinatorics: Number of ways to pair up elements
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I am trying to solve this question:
It's the end of the year, and finally Rafael is graduating in his
Computing course. His classmates decided to celebrate the graduation
organizing a ball, where there would be live music, food and free
drinks. As all balls, the most expected moment is the one in which
everyone starts to dance in pairs.
The pairs will be formed between a boy and a girl, and as Rafael's
classmates are so shy, that they decided to plan ahead what the pairs
would be. There is only one problem: there are more boys than girls in
the class. This implies that, if everyone wants to dance at least
once, one or more girls will have to dance with more than one boy.
Rafael asked your help: in how many ways the pairs can be formed, in
such a way that all the boys dance exactly once, and all the girls
dance at least once
While there might be a mathematical closed-form solution, I am trying to solve it using dynamic programming. I am not quite able to come up with the recurrence. Could someone point me in the right direction?
algorithm
combinations
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combinatorics
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asked Dec 20, 2019 at 22:50
nz_21nz_21
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What did you try? Did you already solve the simple cases (0, 1, 2 boys/girls, equal number of boys and girls, just one more boy, ...) ?
– JohanC
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For the most part, "point me in the right direction" is not a Stack Overflow issue, especially without posting your work so far. "Can Someone Help Me?" is not a valid SO question. This usually suggests that what you need is time with a local tutor or walk through a tutorial, rather than Stack Overflow.
– Prune
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Instead, post some (pseudo-)code to show what you're working on already, a framework for your desire to do this as dynamic programming rather than the closed-form solution.
– Prune
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What is needed here is the number of surjective functions from a set of b elements to a set of g elements.
A general formula exists, not necessarily needed here.
A simple recursive formula can directly be obtained.
Let us assume we know the number of possibilities S(b, g) for b boys and g girls. Then a new boy arrived. We want to calculate S(b+1, g).
We have two possibilities:
Pair this new boy with a girl who has already at least one partner -> we get g S(b,g) possibilities
Pair this new boy with a girl in an exclusive way -> we get g S(b, g-1) possibilities
At the end, we get the recursive relationship
```
S(b, g) = g (S(b-1, g) + S(b-1, g-1))
```
When implementing the solution in a recursive way, we have to consider that:
```
S(b=g, g) = g!
S(b, 1) = 1
```
When implementing this solution, pay attention not calculating the same value several times, e.g. by using memoization.
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edited Dec 21, 2019 at 19:04
answered Dec 21, 2019 at 6:22
DamienDamien
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189606 | https://pubs.nctm.org/view/journals/at/1/4/article-p9.xml | Concrete Materials for Teaching Percentage in: The Arithmetic Teacher Volume 1 Issue 4 (1954)
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Concrete Materials for Teaching Percentage
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Eldon Hauck Seattle, Washington
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Volume/Issue: Volume 1: Issue 4
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Abstract/Excerpt
Many problems and difficulties in elementary school arithmetic can be resolved through: (1) better instructional methods, (2) more instructional materials (3) better instructional materials, (4) concrete materials for each basic phase of the subject, and most important (5) the know how in using materials in the classroom. Concrete materials for teaching and learning should have: (1) the property of being handled in such a way as to conduct a learning situation to the handler or observer, (2) the inherent structure to present to the learner a sequential pattern leading to the abstract, and (3) a specific relation and application to the subject being treated which, at the same time, gives an immediate experience into reality. Concrete materials will enable the child to participate in discovery and develop organization and insight.
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Article Information
Copyright: The National Council of Teachers of Mathematics, Inc. All rights reserved. 1954 Page Count: 4 Article Category: Research Article Print Publication Date: 01 Dec 1954 Online Publication Date: Dec 1954
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189607 | https://www.varsitytutors.com/practice/subjects/ap-calculus-bc/help/derivatives-of-parametric-polar-and-vector-functions | AP Calculus BC - Derivatives of Parametric, Polar, and Vector Functions | Practice Hub
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HomeAP Calculus BCLearn by ConceptDerivatives of Parametric, Polar, and Vector Functions
Derivatives of Parametric, Polar, and Vector Functions
Help Questions
AP Calculus BC › Derivatives of Parametric, Polar, and Vector Functions
Questions 1 - 10
1
Solve for if and .
None of the above
Explanation
We can determine that since the terms will cancel out in the division process.
Since and , we can use the Power Rule
for all to derive
and .
Thus:
.
2
What is the derivative of ?
Explanation
In order to find the derivative of a polar equation , we must first find the derivative of with respect to as follows:
We can then swap the given values of and into the equation of the derivative of an expression into polar form:
Using the trigonometric identity , we can deduce that . Swapping this into the denominator, we get:
3
Let
What is the derivative of ?
Explanation
To find the derivative of this vector, all we need to do is to differentiate each component with respect to t.
Use the Power Rule and the Chain Rule when differentiating.
is the derivative of the first component.
of the second component.
is the derivative of the last component . we obtain then:
4
Given that . We define its gradient as :
Let be given by:
What is the gradient of ?
Explanation
By definition, to find the gradient vector , we will have to find the gradient components. We know that the gradient components are that partial derivatives.
We know that in our case we have :
To see this, fix all other variables and assume that you have only as the only variable.
Now we apply the given defintion , i.e,
with :
this gives us the solution .
5
Find the derivative of the polar function .
Explanation
The derivative of a polar function is found using the formula
The only unknown piece is . Recall that the derivative of a constant is zero, and that
, so
Substiting this into the derivative formula, we find
6
Find the derivative of the following polar equation:
Explanation
Our first step in finding the derivative dy/dx of the polar equation is to find the derivative of r with respect to . This gives us:
Now that we know dr/d, we can plug this value into the equation for the derivative of an expression in polar form:
Simplifying the equation, we get our final answer for the derivative of r:
7
A particle moves around the xy plane such that its position as a function of time is given by the parametric function:
.
What is the slope, , of the particle's trajectory when ?
Explanation
Evaluate the slope as
.
We have
and
so
Evaluating this when gives
.
Remark: This curve is one example from family of curves called Lissajous figures, which can be observed on oscilloscopes.
8
Let .
We define the gradient of as:
Let .
Find the vector gradient.
![Image 112: cos(x_{1}+2x_{2}+\cdots nx_{n}) \quad 2cos(x_{1}+2x_{2}+\cdots nx_{n})\quad \cdots\quad ncos(x_{1}+2x_{2}+\cdots nx_{n})]
![Image 113: cos(x_{1}+2x_{2}+\cdots nx_{n}) \quad cos(x_{1}+2x_{2}+\cdots nx_{n})\quad \cdots\quad cos(x_{1}+2x_{2}+\cdots nx_{n})]
![Image 114: cos(x_{1}+2x_{2}+\cdots nx_{n}) \quad 2cos(x_{1}+2x_{2}+\cdots nx_{n})\quad \cdots\quad -ncos(x_{1}+2x_{2}+\cdots nx_{n})]
![Image 115: x_{1}cos(x_{1}+2x_{2}+\cdots nx_{n}) \quad 2cos(x_{1}+2x_{2}+\cdots nx_{n})\quad \cdots\quad ncos(x_{1}+2x_{2}+\cdots nx_{n})]
![Image 116: cos(x_{1}+2x_{2}+\cdots nx_{n}) \quad 2cos(x_{1}+x_{2}+\cdots nx_{n})\quad \cdots\quad ncos(x_{1}+2x_{2}+\cdots nx_{n})]
Explanation
We note first that :
Using the Chain Rule where is the only variable here.
Using the Chain Rule where is the only variable here.
Continuing in this fashion we have:
Again using the Chain Rule and assuming that is the variable and all the others are constant.
Now applying the given definition of the gradient we have the required result.
![Image 123: cos(x_{1}+2x_{2}+\cdots nx_{n}) \quad 2cos(x_{1}+2x_{2}+\cdots nx_{n})\quad \cdots\quad ncos(x_{1}+2x_{2}+\cdots nx_{n})]
9
Find the derivative of the following set of parametric equations:
Explanation
We start by taking the derivative of x and y with respect to t, as both of the equations are only in terms of this variable:
The problem asks us to find the derivative of the parametric equations, dy/dx, and we can see from the work below that the dt term is cancelled when we divide dy/dt by dx/dt, leaving us with dy/dx:
So now that we know dx/dt and dy/dt, all we must do to find the derivative of our parametric equations is divide dy/dt by dx/dt:
10
Find the first derivative of the polar function
.
Explanation
In general, the dervative of a function in polar coordinates can be written as
.
Therefore, we need to find , and then substitute into the derivative formula.
To find , the chain rule,
, is necessary.
We also need to know that
.
Therefore,
.
Substituting into the derivative formula yields
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189608 | https://www.webel.com.au/node/3553 | Skip to main content
Fun fact: The normal boiling point of water isn't exactly 100 °C (at least not since 2019 when the definition of the Kelvin scale was changed to use the Boltzmann constant and decoupled from the triple point of water)
Finally you can win those pointless bets at the pub with insistent victims who frantically grab their mobile phones to Google stuff to try to confirm what they think they already know, while bellowing "I'll prove it to you!"
The boiling point of water is no longer exactly 100 °C . The main reason is that in 2019 the definition of the kelvin scale (and resulting impact on the Celsius scale) was changed to be based on the Boltzmann constant, rather than depending on the solid-liquid-gas triple point of water.
And it's not just for any old water; after 2007 it was defined to be based on Vienna Standard Mean Ocean Water (VSMOW), a precisely defined water standard. I guess Austrians just love very precise things, so their water is more precise than water elsewhere.
And it also depends on exactly which calibration standard you use for your measurement equipment! If you trust Wikipedia:
Wikipedia: 'Precise measurements show that the boiling point of VSMOW water under one standard atmosphere of pressure is actually 373.1339 K (99.9839 °C) when adhering strictly to the two-point definition of thermodynamic temperature.'
Wikipedia: 'When calibrated to ITS-90, where one must interpolate between the defining points of gallium and indium, the boiling point of VSMOW water is about 10 mK less, about 99.974 °C.'
CoolProp seems to like the later, it gives 99.9743 °C at 1 atmosphere (101325 Pa).
And BTW the International Temperature "Scale" of 1990 is not a scale, it's an equipment calibration standard. But you probably won't be winning many bets at the pub with that one.
If your "I'll prove it to you" betting victim has had too much to drink, you can trick them by using the standard boiling point, which is defined at exactly 100,000 Pa (1 bar), instead of normal boiling point at atmospheric pressure 101, 325 Pa.
At 100,000 Pa, CoolProp gives a standard boiling point for water of 99.6059 °C.
Now everyone knows for sure that Standard Temperature and Pressure (STP) means at 1 atmosphere (exactly 101, 325 Pa), right? Well, not quite:
Wikipedia: 'In chemistry and in various industries, the reference pressure referred to in standard temperature and pressure (STP) was commonly 1 atm (101.325 kPa) but standards have since diverged; In 1982, the International Union of Pure and Applied Chemistry (IUPAC) recommended that for the purposes of specifying the physical properties of substances, standard pressure should be precisely 100 kPa (1 bar).'
And what about "1 atmosphere" anyway? Is the pressure of the atmosphere really conveniently exactly 101, 325 Pa? Well atmospheric pressure is defined to be exactly 101, 325 Pa. The actual 'pressure of the atmosphere' at sea-level varies above and below that according to location and countless weather influences.
Relates to
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189609 | https://www.gophysics.co.uk/virtual-physics-handbook-blog-format/2m78xrwmskpxak4-868sb | GCSE Physics Tutorial: Acceleration of Objects Falling Through Fluids and Terminal Velocity — GoPhysics
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GCSE Physics Tutorial: Acceleration of Objects Falling Through Fluids and Terminal Velocity
ForcesAcceleration
12 Aug
Written By Seb Cox
When objects fall through fluids (such as air or water), their motion is influenced by a combination of forces, including gravity and resistive forces. Understanding this interaction is crucial in explaining why objects eventually reach a maximum speed known as terminal velocity. In this tutorial, we'll explore how objects accelerate when falling through fluids and how terminal velocity is reached.
Initial Acceleration
When an object is dropped from a certain height, it initially accelerates due to the force of gravity. This acceleration is commonly referred to as free fall. However, as the object gains speed, it encounters resistive forces from the fluid it's moving through. These resistive forces are collectively known as drag.
Resultant Forces
As the object accelerates downward due to gravity, the drag force opposes its motion. Initially, the force of gravity is greater than the drag force, causing the object to accelerate. This results in an increasing velocity.
Terminal Velocity
As the object's velocity increases, the drag force also increases. Eventually, a point is reached where the drag force becomes equal in magnitude to the force of gravity. At this point, the net force acting on the object becomes zero, resulting in a constant velocity known as terminal velocity.
Factors Affecting Terminal Velocity
The terminal velocity of an object falling through a fluid depends on several factors:
Mass and Shape: Objects with larger cross-sectional areas and greater mass will experience higher drag forces, leading to lower terminal velocities.
Fluid Density: Objects falling through denser fluids will experience higher drag forces, leading to lower terminal velocities.
Fluid Viscosity: Viscous fluids create greater drag forces, causing lower terminal velocities.
Gravitational Force: In environments with different gravitational fields (e.g., on the Moon), terminal velocity will be different due to the change in gravitational force.
Summary
When objects fall through fluids, they initially accelerate due to the force of gravity. However, as they gain speed, the drag force from the fluid increases, eventually balancing the force of gravity. This results in a constant velocity known as terminal velocity. Factors such as object mass, shape, fluid density, and fluid viscosity influence terminal velocity. Understanding these concepts helps us explain and predict the behaviour of objects falling through fluids and their ultimate maximum speeds.
Looking for a more dynamic learning experience?
Explore our engaging video lessons and interactive animations that GoPhysics has to offer – your gateway to an immersive physics education!
Learn more
Seb Cox
Previous Previous GCSE Physics Tutorial: Drawing and Interpreting Velocity-Time Graphs for Objects with Terminal Velocity -------------------------------------------------------------------------------------------------------Next Next GCSE Physics Tutorial: Recording the Acceleration Due to Gravity on Earth -------------------------------------------------------------------------
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189610 | https://flexbooks.ck12.org/cbook/ck-12-interactive-middle-school-math-8-for-ccss/section/9.1/primary/lesson/properties-of-exponents-in-multiplication-expressions-msm8-ccss/ | Skip to content
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9.1
Properties of Exponents in Multiplication Expressions
Written by:Larame Spence | Sean Regan
Fact-checked by:The CK-12 Editorial Team
Last Modified: Aug 02, 2025
Lesson
Exponents Revisited
When a number is being multiplied by itself repeatedly, an exponent can be used to express this.
The exponent is the number which indicates how many times to multiply the base. The base is the number being multiplied. This expression can be written as a product of factors:
Writing exponents in expanded form will help understand the properties for exponent operations.
Product of Powers Property
In algebraic equations, there will be many instances where you will need to multiply terms with exponents. For example, you might need to multiply the term by To multiply these expressions, first look at a simpler example.
Use the interactive below to explore how to multiply exponents.
Progress
0 / 0
The rule for multiplying exponents with the same base is called the Product of a Power Property. The Product of Powers Property states that when multiplying two exponents with the same base, you can add the exponents and keep the base.
To simplify the product of and , you will keep the base and add the exponent. However, in the expression what is the exponent and what is the base? The exponent is 4, and the base is x. The number 2 is the coefficient. To include the 2 in the base, you will need to write it in parenthesis: . Since the coefficients are not part of the base or the exponent you will multiply them normally. This concept is easier to observe when written expanded form:
Now you can rearrange this using the commutative property as follows:
Power of a Product Property
A term can be a product of coefficients and variables. What would happen if you took a term to a power? Use the interactive below to help understand this concept.
The rule for raising a term to a power is called the Power of a Product Property. The Power of a Product Property states that If a term is being raised to an exponent, you can distribute the exponent to each factor.
Power of a Power Property
The final property has to do with raising a power to a power. This property will pop up in many places. You may find yourself having to simplify an expression like . To do this use the interactive below to explore the property.
Discussion Questions
What is the pattern for raising a power to a power?
Why does this work?
The rule for raising a power to a power is called the Power of a Power Property. The Power of a Power Property states that if an exponent is being raised to another exponent, you can multiply the exponents. You can use this property to solve a problem like . Before applying the property, first write the expression in expanded form.
To solve a problem like this, you will need to use two of three properties: you will need to distribute the exponent to the term which will involve taking a power to a power. You must first distribute the outer exponent to each factor in the term:
After distributing the exponent, you will need to simplify the power to a power to obtain the answer.
| |
| Summary |
| Exponents represent repeated multiplication. For example: Use exponent properties to simplify exponential expressions: + Product of Powers Property: + Power of a Product Property: + Power of a Power Property: |
Asked by Students
Here are the top questions that students are asking Flexi for this concept:
Overview
| |
| + Exponents represent repeated multiplication. For example: @$7^3=7\cdot7\cdot7\cdot@$ + Use exponent properties to simplify exponential expressions: - Product of Powers Property: @$a^m\times a^n=a^{m+n}@$ - Power of a Product Property: @$a^m\times a^n=a^{m+n}@$ - Power of a Power Property: @$(a^m)^n=a^{mn}@$ |
Vocabulary
Exponent
Expression
expanded form
operation
algebraic
Term
Property
Product of Powers Property
Coefficient
Power of a Product Property
factor
Pattern
Power of a Power Property
Test Your Knowledge
Question 1
Simplify: @$\begin{align}(-5x^2 y)(-2xy)^3\end{align}@$
a
@$\begin{align}40x^5y^4\end{align}@$
b
@$\begin{align}20x^4y^5\end{align}@$
c
@$\begin{align}30x^6y^3\end{align}@$
d
@$\begin{align}10x^3y^6\end{align}@$
Simplify the expression:
@$$\begin{align}\eqalign{
&& (-5x^2y)(-2xy)^3 \
&& (-5) \cdot x^2 \cdot y^1 \cdot (-2)^3 \cdot x^3 \cdot y^3 \
&& (-5) \cdot x^2 \cdot y^1 \cdot (-8) \cdot x^3 \cdot y^3 \
&& (-5) \cdot (-8) \cdot x^2 \cdot x^3 \cdot y^1 \cdot y^3 \
&& 40\cdot x^2 \cdot x^3 \cdot y^1 \cdot y^3 \
&& 40\cdot x^{2 + 3} \cdot y^{1 + 3} \
&& 40\cdot x^{5} \cdot y^{4} \
&& 40x^{5}y^{4}
}\end{align}@$$
Option A is the correct answer.
Question 2
Simplify the expression: @$\begin{align}y^2 \cdot y \cdot y^4\end{align}@$
a
@$\begin{align}y^5\end{align}@$
b
@$\begin{align}y^7\end{align}@$
c
@$\begin{align}y^3\end{align}@$
d
@$\begin{align}y^8\end{align}@$
Simplify the expression:
@$$\begin{align}\eqalign{
&& y^2 \cdot y \cdot y^4 \
&& y^2 \cdot y^1 \cdot y^4 \
&& y^{2 + 1 + 4} \
&& y^7
}\end{align}@$$
Option B is the correct answer.
Study Guide
Go to Study Guide
Asked by Students
Here are the top questions that students are asking Flexi for this concept:
Related Content
Properties of Exponents Study Guide
Product of Powers Property - Overview
Multiple Exponent Properties Involving Products - Overview
Product of Powers: A Sample Application
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189611 | https://courses.lumenlearning.com/ccbcmd-math/chapter/solutions-4/ | Solutions 4.1: Angles | Applied Algebra and Trigonometry
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Applied Algebra and Trigonometry
Chapter 4.1: Angles
Search for:
Solutions 4.1: Angles
Solutions to Try Its
1.
2.3 π 2 3 π 2
3.−135°
4.7 π 10 7 π 10
5.α=150∘α=150∘
6.β=60∘β=60∘
7.7 π 6 7 π 6
8.215 π 18=37.525 units 215 π 18=37.525 units
9.1.88
10.−3 π 2−3 π 2 rad/s
11.1655 kilometers per hour
Solutions to Odd-Numbered Exercises
1.
3.Whether the angle is positive or negative determines the direction. A positive angle is drawn in the counterclockwise direction, and a negative angle is drawn in the clockwise direction.
5.Linear speed is a measurement found by calculating distance of an arc compared to time. Angular speed is a measurement found by calculating the angle of an arc compared to time.
7.
9.
11.
13.
15.
17.240°
19.4 π 3 4 π 3
21.2 π 3 2 π 3
23.7 π 2≈11.00 in 2 7 π 2≈11.00 in 2
25.81 π 20≈12.72 cm 2 81 π 20≈12.72 cm 2
27.20°
29.60°
31.−75°
33.π 2 π 2 radians
35.−3 π−3 π radians
37.π π radians
39.5 π 6 5 π 6 radians
41.5.02 π 3≈5.26 5.02 π 3≈5.26 miles
43.25 π 9≈8.73 25 π 9≈8.73 centimeters
45.21 π 10≈6.60 21 π 10≈6.60 meters
47.104.7198 cm2
49.0.7697 in2
51.250°
53.320°
55.4 π 3 4 π 3
57.8 π 9 8 π 9
59.1320 rad 210.085 RPM
61.7 in./s, 4.77 RPM, 28.65 deg/s
63.1,809,557.37 mm/min=30.16 m/s 1,809,557.37 mm/min=30.16 m/s
65.5.76 5.76 miles
67.120∘120∘
69.794 miles per hour
71.2,234 miles per hour
73.11.5 inches
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189612 | https://www.ck12.org/flexi/cbse-math/length-conversion/how-many-meters-are-there-in-1-centimeter/ | How many meters are there in 1 centimeter?
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There are 0.01 meters in 1 centimeter.
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189613 | https://www.kgs.ku.edu/Hydro/GWtutor/Plume_Busters/remediate_refs/redox_chemistry.htm | | | | | |
Redox Chemistry Primer
A discussion of chemical principles is necessary to understand groundwater contamination problems. A variety of parameters are measured when a sample is collected for water analysis. The following is a short compilation and discussion of some of the more common terms and principles used in the Plume Busters discussion of chromium chemistry and groundwater.
Water is made up of hydrogen (H) and oxygen (O) atoms with a formula of: H2O. This means that for every oxygen atom there are two hydrogen atoms bound to it. Each of these atoms has an electrical charge associated with it, either positive or negative. In this case the hydrogen atoms have a positive charge (H+) when not associated with oxygen and the oxygen has a negative charge (O-2). The superscripted numbers to the right of the chemical symbol indicate the number of electrons gained or lost by chemical bonding. A positive number indicates that the hydrogen atom gave up an electron. A negative number indicates that the oxygen atom acquired two electrons, one from each hydrogen atom, in the chemical bonding process. The combination of atoms makes a molecule, which is bound together by the sharing of electrons with acquired electrons under the influence of the oxygen atom most of the time. When H2O is formed the positive and negative charges are balanced out and the charge on the molecule is neutral or zero.
Water, when it dissociates, forms H+ and OH-. A charged particle, such as (H+) or (OH-) is called an ion. The charge, whether positive or negative, is called the oxidation number, which represents the number of electrons gained, lost, or shared in a chemical reaction.
Redox reactions describe the movement of electrons from one ion to another. The term RedOx comes from the two processes that occur during a reaction: REDuction and OXidation. These reactions occur together, they cannot occur separately.
Oxidation is the term given to the process of gain/addition of electrons from another compound, ion, or atom. Because the oxidizing substance removes electrons from another substance, which are then added to itself, the oxidizing substance becomes “reduced” (more negative). And because it “accepts” electrons it is called an electron acceptor. The oxidation number becomes more negative.
Reduction is the term given to the process of loss/removal of electrons, which are given to another compound, atom, or ion. Because the reducing substance gives electrons to another substance it becomes “oxidized” itself (more positive). And because it “donates” electrons it is called an electron donor. The oxidation number becomes more positive.
The key terms involved in redox can be confusing. A mnemonic for remembering what occurs is OIL RIG: Oxidation Is Loss of electrons; Reduction Is Gain of electrons. As an example, an element that is oxidized loses electrons and becomes more positive; however, that element is referred to as the reducing agent. If you want to know, for example, what an oxidizing agent does in terms of electrons:
In contrast, a reducing agent:
The Figure below illustrates the process of RedOx reactions.
Adapted from:
Redox reactions are evaluated the equation in terms of which ions are reduced (gain electrons) and which are oxidized (lose electrons). This is done by writing half equations for each reaction and including the electrons in the equation. An example of a reaction is given below for iron.
Iron forms a number of different ions for example, Fe+2 and Fe+3. If you think about how these might be produced from iron metal, the 2+ ion will be formed by oxidation of the metal by removing two electrons:
Fe+0 ® Fe+2 + 2e-
The iron is now said to be in an oxidation state of +2. Removal of another electron gives the Fe3+ ion: Fe+2 ® Fe+3 + e-. The iron now has an oxidation state of +3.
Question:
Batteries make use of redox reactions to produce electricity. What makes this possible?
Oxidation/Reduction Potential (Eh)
Metal ions have strong and weak oxidizing/reducing potential. In order to evaluate redox reactions, the redox potential of a solution is measured and reported as Eh. The following site shows how the Eh values are determined experimentally. A hydrogen electrode is used as the reference to which all of the experiments are compared and has a voltage of zero.
The results are listed as voltage (or potential), which represents the driving force for “moving” the electrons from one location to another (for example, from a reducing agent to an oxidizing agent). The higher the voltage the more strongly the electrons will be moved through a solution. A positive cell potential (voltage) indicates a spontaneous electrochemical reaction. A negative cell potential (voltage) indicates a non-spontaneous reaction (the opposite reaction will, therefore, be spontaneous!).
Redox potential (voltage) is a measure of how easily a metal (or other ion) will give up electrons or retain electrons, not the likelihood for a specific oxidation or reduction reaction occurring. The chemical equations are written as half-reactions with the most reducing reactions, donating electrons, having an Eh value that is more negative and the most oxidizing reactions, receiving electrons, having an Eh value that is the more positive.
A list of Standard electrode potentials for various reactions is given at:
This table illustrates that Eh values that are very negative, such as for lithium (Li, Eh = -3.04), are strong reducing agents, that is, electrons are given up quickly and the oxidation number becomes more positive. On the other end of the chart, fluoride (F, Eh = +2.87) is a strong oxidizing agent meaning that it takes electrons and the oxidation number becomes more negative.
More negative values indicate reducing reactions occurring (loss of electrons; more positive ion results) and oxidizing reactions (gain of electrons; more negative ion results). Higher Eh positive values suggest that reaction is more likely to occur spontaneously without the need of extra energy.
The Eh value gives an indication of how likely a given redox reaction will occur. When the two equations are written in terms of electrons being donated or received the Eh value will indicate whether the reaction is likely to proceed. In the case of chromium the following reactions are listed in the Standard electrode potential table referred to above:
Cr2O72−(aq) + 14H++ 6e−→ 2Cr3+(aq) + 7H2O | +1.38 volts
Cr3+(aq) + 3e−→ Cr(s) | -0.74 volts
Cr3+(aq) + e−→ Cr2+(aq) | -0.42 volts
Based on the voltages, the chromium(+6) (Cr2O7-2) value is a spontaneous reaction if it is in the presence of a reducing agent (Eh = +1.38 v). The conversion of chromium(+3) to either a solid phase or to chromium(+2) is much less likely to happen based on the negative Eh potentials.
This suggests that chromium(+6) will be preferentially reduced to Chromium(+3) and then is not likely to be further transformed into a mobile form.
Redox reactions are the controlling chemistry for chromium conversion from Cr+6 to Cr +3. Chromium (+6) is an extremely mobile form and moves rapidly with ground water. Chromium is a very toxic chemical, especially in the Cr+6 form, to both human and environmental health. Reduction of chromium from its Cr+6 state to Cr +3 requires a substance that will give electrons to the chromium so it will become more stable and remain in the sediment rather than move with the groundwater.
In the In Situ Redox remediation method discussed in the Remediation section of Plume Busters, a reagent is injected into the aquifer through injection/withdrawal wells at a rate and duration necessary to treat the desired volume of aquifer sediments. This treatment volume plus the quantity of available iron in the sediments determines the quantity of reductive capacity generated in the barrier and the barrier’s productivity. The redox-altering reagent generally used is sodium dithionite (Na2S2O4). The dithionite ion is commonly known as hydrosulfite and is a strong reducing agent, particularly in strongly basic solutions.
Questions
Sodium dithionite is a reducing agent. What is a reducing agent?
What happens when chromium (+6) is reduced?
Measuring pH
Another parameter measured in groundwater is pH. This term means the “power of hydrogen” and is a measure of the quantity of hydrogen ions (H+) in a solution. pH is a measure of the acidity of a solution in terms of the amount of hydrogen (H+) present ( A solution has an acid pH if the value measured occurs between 0 and 7 meaning there is more H+ present. A solution has a basic pH if the value measured occurs between 7 and 14 meaning there are more OH- ions than H+ ions present in the solution. A neutral pH is considered 7 where there are equal numbers of H+ and OH- ions. A ph of 7.00 is generally the value measured for uncontaminated water.
The values of pH are on a log scale and represent a ten-fold decrease in H+ ion concentration measurement as one goes up the scale. This means that a shift in pH from 2 to 3 represents a 10-fold decrease in H+ concentration, and a shift from 2 to 4 represents a 100 (10 × 10)-fold decrease in H+ concentration. The figure below shows a color scale of the pH values of common substances listed to the left. One can see from the diagram that coffee is much more acidic than bleach. This means that there are more H+ ions in coffee than in bleach.
This also means there are more OH- ions in bleach than in coffee so bleach is more basic than coffee.
The pH of groundwater is useful to help determine if contamination has occurred. Because water generally has a pH around 6-8 a number higher or lower than that is a signal that there is something different about the water sample. It may suggest a contamination problem if the number is a low pH (3-5) indicating the system is more acidic and potentially has more dissolved metals or contaminants. The pH also helps to determine the type of reagents that may be needed to treat a specific contamination plume. |
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Algebra 1
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Rational Numbers on the Number Line
Rational Numbers on the Number Line
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Rational Numbers on the Number Line
Rational Numbers on a Number Line – Introduction
Understanding Rational Numbers – Definition
Rational Numbers on a Number Line – Example
Rational Numbers on a Number Line – Guided Practice
Rational Numbers on a Number Line – Summary
Rational Numbers on a Number Line – Frequently Asked Questions
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Basics on the topic Rational Numbers on the Number Line
Rational Numbers on a Number Line – Introduction
Working with rational numbers on a number line is a fundamental concept in mathematics. It enhances numerical fluency and paves the way for understanding more advanced math topics. Rational numbers include whole numbers, fractions, and decimals, and they can be positioned on a number line that extends infinitely in both directions.
Understanding Rational Numbers – Definition
A rational number is any number that can be written as a fraction, which means it is the quotient of two integers. The word rational comes from ratio, reflecting that these numbers represent a ratio of two quantities.
Rational numbers on a number line represent points that correspond to both whole numbers and fractions or decimals. A number line is a visual representation where these numbers are placed according to their value.
To get started, consider a number line as a horizontal line with evenly spaced divisions, each representing a unit or a fraction of a unit.
Where would you place the fraction 31 on a number line?
You would place 31 between 0 and 1, closer to 0 because it’s less than half of a unit.
On a number line that only shows whole numbers, where can we find the number 2.5?
Since 2.5 is halfway between 2 and 3, it would be placed right in the middle of these two whole numbers.
If the number line goes from 0 to 3, where is the number 45 located?
The number 45 , or 1.25, is a little past 1 since 44 equals 1. So 45 will be between 1 and 2, closer to 1.
Rational Numbers on a Number Line – Example
| Step | Description | Illustration Request |
---
| 1 | Identify the numerator and denominator: The fraction 54 has a numerator of 4 and a denominator of 5. The denominator tells us into how many equal parts the interval from 0 to 1 is divided. | An illustration showing a number line from 0 to 1, highlighting the concept of dividing the line based on the denominator. |
| 2 | Divide the number line: Imagine dividing the line into 5 equal sections between 0 and 1. | A detailed illustration of a number line from 0 to 1 divided into 5 equal parts, each part labeled. |
| 3 | Locate the number: Count four sections from 0. Here is where you'll place the dot for 54. | An illustration of a number line with a dot marking the position of 54, showing four parts from 0 highlighted or colored differently. |
Rational Numbers on a Number Line – Guided Practice
Let's practice placing a rational number on a number line.
Place the fraction 83 on a number line from 0 to 1.
First, divide the space between 0 and 1 into 8 equal parts. Then, count three parts from 0. Place a dot on the third division to represent 83.
On a number line from 0 to 2, where would you place the number 121?
First, find the whole number 1 on the number line. Then, divide the space between 1 and 2 in half and place a dot at the halfway mark to represent
On a number line from 0 to 2, where would you place the number 121.
On a number line from 0 to 2, where would you place the number 43?
First, find the whole number 1 on the number line as a midpoint between 0 and 2. Then, divide the segment from 0 to 1 into four equal parts. Place a dot at the third mark to represent 43.
On a number line from 0 to 10, where would you place the number 2.5?
Identify the segment between 0 and 10. Divide this segment into four equal parts to locate each 2.5 units. The first 2.5 falls exactly in the middle of 0 and 5. Place a dot there to represent 2.5.
On a number line from −1 to 1, where would you position the number −21?
Start by locating 0 as the central point between −1 and 1. Divide the segment between −1 and 0 into two equal parts. The position exactly halfway is −21. Mark this spot on the line.
On a number line from 0 to 5, where would you mark the number 4.25?
Begin by identifying whole numbers 4 and 5 on the line. To find 4.25, split the segment from 4 to 5 into four equal parts since each part represents 0.25. Place a dot at the first mark past 4 to denote 4.25.
Rational Numbers on a Number Line – Summary
Key Learnings from this Text:
Rational numbers include whole numbers, fractions, and decimals.
A number line is a tool that helps visualize and understand the position and magnitude of these numbers.
Placing a fraction on a number line involves dividing the interval into equal parts based on the denominator and locating the numeral based on the numerator.
Comparing and ordering rational numbers is easier with a number line, as their relative positions instantly indicate their size.
Operations like addition and subtraction of rational numbers can be visualized as movements along the number line.
Equivalent fractions occupy the same position on a number line, reinforcing the concept of equality among different representations.
Explore other content on our platform, such as interactive practice problems and videos, to deepen your understanding of rational numbers and their placement on a number line!
Rational Numbers on a Number Line – Frequently Asked Questions
What is a rational number on a number line?
A rational number on a number line is a point that corresponds to a value that can be expressed as a fraction or decimal, including whole numbers.
How do you place a fraction on a number line?
First, determine the space between two whole numbers that the fraction falls between. Then divide that space into equal parts according to the denominator and count the parts according to the numerator to place the fraction.
Can you show negative rational numbers on a number line?
Yes, negative rational numbers are placed to the left of zero on a number line.
How do you compare two rational numbers using a number line?
By placing both numbers on the number line, you can easily compare them. The number further to the right is the larger number.
How do you find equivalent rational numbers on a number line?
Equivalent rational numbers will be located at the same point on a number line even if they have different numerators and denominators.
What does it mean if two rational numbers are at the same position on a number line?
If two rational numbers are at the same position on a number line, they are equivalent and represent the same value.
Can decimals be placed on a number line?
Yes, decimals can be placed on a number line just like fractions, as they are also rational numbers.
How does a number line help with adding and subtracting rational numbers?
A number line can visualize adding by moving to the right for positive jumps and subtracting by moving to the left for negative jumps.
Are all points on a number line rational numbers?
Not all points on a number line are rational numbers; some points represent irrational numbers, which cannot be expressed as fractions.
What real-world scenarios can be represented using a number line?
Real-world scenarios like measuring distances, comparing weights, cooking with fractions of ingredients, and budgeting can all be represented using a number line.
Transcript Rational Numbers on the Number Line
Tim is feeling nervous. He is about to jump off the high dive at the local swimming pool. There he goes! How far above the water is he shortly after jumping?
Rational Numbers on the Number Line
To answer this question, we can look at the rational numbers on the number line. Let's see. The platform is 33 feet high. The tower is like a vertical number line. The surface of the water can be represented by 0, above we have positive numbers. Below the water we have the negative numbers.
Let's rotate the number line to a horizontal position to have a more precise look at how high Tim is above the water. As you can see at a first glance, Tim is somewhere between 20 and 30 feet above the water, or between 20 and 30 feet on the number line.
Fractions on the Number Line
To more accurately determine his location, we can zoom in to display a more detailed scale. Now you can see he is somewhere between 27 and 28 feet on the number line. Let's zoom in even more.
We can divide feet in to inches. As you know, there are 12 inches in 1 foot. So if you count from left to right on the number line, you land at 27 feet and 3 inches. This represents Tim's current location above the water.
In math, we often look at the number line without units. Instead of using inch notation, we can write our position on the number line as a fraction, with a value over twelve, because we divide one whole into 12 pieces. Here we are at 27 and 3 over twelve on the number line.
You can simplify this mixed number to 27 and 1 over 4, or 27 and one fourth. As you can see, our location on the number line between 27 and 28 remains the same. We have just changed the scale.
Decimals on the Number Line
We can represent 27 and one over four in yet another way, with a different scale: It can also be represented as a decimal: 27.25. If we display decimals on the number line, we divide our units into 10, 100 and so on. Here our number is exactly between 27.2 and 27.3. We can either zoom in more and divide tenths into hundreths, or we can assume the value is 27.25.
Negative Numbers on the Number Line
Let's get back to Tim. As he dives into the water, he is below 0 on the number line, where we have the negative numbers. We can use the negative numbers to represent how far Tim dived below the surface of the water. He dived somewhere between 0 and minus ten feet.
Let's take a closer look to figure out his exact depth. Now you can see, he dived somewhere between 6 and 7 feet below the surface, or between -6 and -7 feet on our number line. To be more accurate, let's zoom in even more.
We can divide feet into inches again. Now we count downwards, from -6 to -7. So Tim dived to -6 feet and 9 inches. Remember, you can also write this as a fraction: -6 and 9 over 12 feet, or simplified: -6 and 3 over 4. You can also write this mixed number as a decimal, which is: -6.75 feet.
Tim is happy that he overcame his fear. But wait, something is not right.
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Rational Numbers on the Number Line exercise
Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Rational Numbers on the Number Line.
Explain how far Tim is above the water shortly after jumping.
Hints
27′3′′ means 27 feet and 3 inches.
Decimals are divided in tenths and hundredths.
Solution
The position of Tim shortly after jumping can be represented by a vertical number line. The surface of the water is our zero point. Above the water, we have the positive numbers. Below the water, we have the negative numbers.
Tim's height right after jumping is 27′3′′ which means 27 feet and 3 inches. Because there are 12 inches in one foot, we can express his position on the number line. It is 27123, which can be simplified to 2741.
Alternatively his height can be transformed into decimal form: 2741=27.25.
### Determine the decimals and fractions which equal the given values.
Hints
There are 12 inches in 1 foot.
You can simplify fractions by finding the Greatest Common Factor of the numerator and denominator. Then, you divide both numbers by the Greatest Common Factor.
Fractions can be transformed in decimals by dividing the numerator by the denominator.
Solution
As you can see, there are several numbers that describe the same value. Feet can be converted to inches: There are 12 inches in 1 foot. So now we can express 6′′ as 126. If we want, we can simplify it by converting it to a decimal, too.
### Find the height of each jump in feet and inches.
Hints
You can convert a decimal into a fraction, too.
If we display decimals on the number line, we divide our units into tenths, hundredths and so on.
Therefore, 5.75 can be interpreted as 510075, which is a fraction that can be simplified.
Solution
Tommy, Richard, Lisa and Harry are jumping off the different diving boards at their local swimming pool. The height of the diving boards can be written as decimals on the number line as well as in feet and inches. Let's take a look:
Tommy: 22.25 ft.
22.25 ft. can be written as a fraction because decimals are divided in tenths and hundredths. So we have 2210025 ft. Because the Greatest Common Factor of 25 and 100 is 25, we can simplify the fraction to 41. 2241ft.. Since one foot consists of 12 inches, 2241ft.=22123 ft. So 22.25 ft. is the same as 22′3′′.Richard: 19.75 ft.
0.75 ft. is 43 ft. Multiplying the numerator and denominator by 3 makes the denominator 12, the number of inches in a foot. The number of inches is in the numerator, making our final conversion 19.75ft.=19′9′′.Lisa: 15.5 ft.
0.5 ft. is 21 ft. Multiplying the numerator and denominator by 6 makes the denominator 12, the number of inches in a foot. The number of inches is in the numerator, making our final conversion 15.5ft.=15′6′′.Harry: 12.5 ft.
Again, 0.5 ft. is 21 ft. Multiplying the numerator and denominator by 6 makes the denominator 12, the number of inches in a foot. The number of inches is in the numerator, making our final conversion 12.5ft.=12′6′′.
Convert the depths to see which diver dove deepest.
Hints
Convert the depths to the same unit of measure in order to compare more easily.
Every depth can be written as a fraction as well as in feet and inches.
Solution
We want to find out who dove the deepest. Therefore, we have to compare the different values. It is a good idea to convert all the depths so they're expressed in the same units. In the table you can see all conversions. We have ordered the list beginning with the smallest depth to the greatest.
6.25 ft.
6124 ft.
6′5′′
621 ft.
Identify the steps for converting height from fraction to decimal form.
Hints
There are 12 in 1 foot.
So in fraction form, 10 inches is 1210 of one foot.
The Greatest Common Factor of 10 and 12 is 2. So we can simplify the fraction to 12÷210÷2=65.
Solution
A distance given in feet and inches can be transformed into a decimal by following these simple steps:
We have to determine the distance in feet and inches.
We know that inches are smaller divisions of a foot. There are 12 inches in one foot.
This can be represented as a fraction. We put the inches in the numerator and the total number of inches in a foot, 12, in the denominator.
Finally, we divide the numerator by the denominator, getting the decimal.e.g. 65=5÷6=0.83
Find out which distances Marshall ran this week.
Hints
You can convert every single value given into a fraction or decimal, showing the distance in miles. Alternatively, you can express miles in feet.
One helpful conversion you should keep in mind is: 41 mile is 1320 ft.
Solution
Marshall seems to be a really good runner. Let's take a look at the distances he covered this week. To compare the distances Marshall ran, we should convert all the numbers we have been given into one form. Let's begin with his shortest distance.
Remember, when converting units:
feet×feetmiles=miles1. The distance of 37488 ft. can be transformed like this:
5280 ft.37488 ft.=7.1 mi.
2. The next distance is 7.2 miles, which is equal to:
7 mi.+0.2 mi.7 mi.+102 mi.7×5280 ft.+105280 ft.×236,960 ft.+1,056 ft.====38,016 ft.
3. The distance 72010 miles (7.5 miles in decimal form) can be converted to feet as follows:
7 mi.+2010 mi.7 mi.+21 mi.7×5280 ft.+25280 ft.36,960 ft.+2640 ft.====39600 ft.
4. The distance 753 miles can be transformed the same way:
7 mi.+53 mi.7×5280 ft.+55280 ft.×336,960 ft.+3168 ft.===40128 ft.
5. The last distance of 41712 ft. can be transformed into miles the following way:
41712 ft.÷5280=7.9 mi.
See? It's much easier to compare distances when they are all in the same unit of measurement. And it`s easier to label numbers on the number line when they are transformed into decimals or mixed fractions.
More videos and learning texts for the topic
Basic Arithmetic
Simplifying Variable Expressions
Evaluating Expressions
How to do Order of Operations?
Distributive Property
Adding Integers
Subtracting Integers
Multiplying and Dividing Integers
Types of Numbers
Transforming Terminating Decimals to Fractions and Vice...
Transforming Simple Repeating Decimals to Fractions and Vice...
Rational Numbers on the Number Line
Standard and Scientific Notation
Using Operations with Scientific Notations |
189615 | https://arizonaforensics.com/wp-content/uploads/2014/06/IQ-Meaning.pdf | DSM-V Intellectual Disability (Intellectual Developmental Disorder), Formerly Mental Retardation Mental retardation has been renamed Intellectual Development Disorder (IDD) in DSM-5 to reflect changes in U.S. federal law (Public Law 111-256), which replaced the term mental retardation with intellectual disability. The criteria for IDD has changed, and people with IDD are no longer categorized solely on the basis of IQ, although IQ must be at least two standard deviations from the mean (70 or less). IDD is characterized by deficits in cognitive abilities (e.g., problem solving, planning, reasoning, judgment) and adaptive functioning. Diagnostic criteria emphasize the importance of assessing both cognitive abilities and adaptive functioning. The severity level (mild, moderate, severe, or profound) of the intellectual disability is determined by the person's ability to meet developmental and sociocultural standards for independence and social responsibility, not by the IQ score. To help determine a diagnosis, a table listing IDD severity levels (mild, moderate, severe, or profound) across three different domains (conceptual, social, and practical) is included on pages 34– 36 of DSM-5. A great deal of comorbidity exists among the neurodevelopmental disorders. For example, children born with neurobehavioral disorder due to prenatal alcohol exposure (ND-PAE; formerly fetal alcohol syndrome) often develop mild intellectual developmental disorders (see Seligman & Reichenberg, 2012, p. 51). Global developmental delay is diagnosed if the severity level cannot be accurately determined. This diagnosis is restricted to children under the age of 5. If the degree of intellectual disability cannot be determined, unspecified intellectual disability would be the diagnosis. Reichenberg, Lourie W. (2013-11-18). DSM-5 Essentials: The Savvy Clinician's Guide to the Changes in Criteria (Kindle Locations 532-544). Wiley. Kindle Edition. Severity level: Mild Conceptual Domain Social Domain Practical Domain For preschool children, there may be no obvious conceptual differences. For school-age children and adults, there are difficulties in learning academic skills involving reading, writing, arithmetic, time, or money, with support needed in one or more areas to meet age-related expectations. In adults, abstract thinking, executive function (i.e., planning, strategizing, priority setting, and cognitive flexibility), and short-term memory, as well as functional use of academic skills (e.g., reading, money management), are impaired. There is a somewhat concrete approach to problems and solutions compared with age mates. Compared with typically developing age mates, the individual is immature in social interactions. For example, there may be difficulty in accurately perceiving peers' social cues. Communication, conversation, and language are more concrete or immature than expected for age. There may be difficulties regulating emotion and behavior in age-appropriate fashion; these difficulties are noticed by peers in social situations. There is a limited understanding of risk in social situations; social judgment is immature for age, and the person is at risk of being manipulated by others (gullibility). The individual may function age-appropriately in personal care. Individuals need some support with complex daily living tasks in comparison to peers. In adulthood, supports typically involve grocery shopping, transportation, home and childcare organizing, nutritious food preparation, and banking and money management. Recreational skills resemble those of age mates, although judgment related to well-being and organization around recreation require support. In adulthood, competitive employment is often seen in jobs that do not emphasize conceptual skills. Individuals generally need support to make health care decisions and legal decisions, and to learn to perform a skilled vocation competently. Support is typically needed to raise a family. Severity level: Moderate Conceptual Domain Social Domain Practical Domain All through development, the individual's conceptual skills lag markedly behind those of peers. For preschoolers, language and pre-academic skills develop slowly. For school-age children, progress in reading, writing, mathematics, and understanding of time and money occurs slowly across the school years and is markedly limited compared with that of peers. For adults, academic skill development is typically at an elementary level, and support is required for all use of academic skills in work and personal life. Ongoing assistance on a daily basis is needed to complete conceptual tasks of day-to-day life, and others may take over these responsibilities fully for the individual. The individual shows marketed differences from peers in social and communicative behavior cross development. Spoken language is typically a primary tool for social communication but is much less complex than that of peers. Capacity for relationships is evident in ties to family and friends, and the individual may have successful friendships across life and sometimes romantic relations in adulthood. However, individuals may not perceive or interpret social cues accurately. Social judgment and decision-making abilities are limited, and caretakers must assist the person with life decisions. Friendships with typically developing peers are often affected by communication or social limitations. Significant social and communicative support is needed in work settings for success. The individual can care for personal needs involving eating, dressing, elimination, and hygiene as an adult, although an extended period of teaching and time is needed for the individual to become independent in these areas, and reminders may be needed. Similarly, participation in all household tasks can be achieved by adulthood, although an extended period of teaching is needed, and ongoing supports will typically occur for adult level performance. Independent employment in jobs that require limited conceptual and communication skills can be achieved, but considerable support from coworkers, supervisors, and others is needed to manage social expectations, job complexities, and ancillary responsibilities such as scheduling, transportation, health benefits, and money management. A variety of recreational skills can be developed. These typically require additional supports and learning opportunities over an extended period of time. Maladapted behavior is present in a significant minority and causes social problems. Severity level: Severe Conceptual Domain Social Domain Practical Domain Attainment of conceptual skills is limited. The individual generally has little understanding written language or of concepts involving numbers, quantity, time, and money. Caretakers provide extensive supports for problem-solving throughout life. Spoken language is quite limited in terms of vocabulary and grammar. Speech may be single words or phrases and may be supplemented through augmentative means. Speech and communication are focused on the here and now within everyday events. Language is used for social communication more than for explanation. Individuals understand simple speech and gestural communication. Relationships The individual require support for all activities of daily living, including meals, dressing, bathing, and elimination. The individual requires supervision at all times. The individual cannot make responsible decisions regarding well-being of self or others. In adulthood, participation in tasks at home, recreation, and work requires ongoing support and assistance. Skill acquisition in all domains involves long-term teaching and with family members and familiar others are a source of pleasure and help. ongoing support. Maladaptive behavior, including self-injury, is present in a significant minority. Severity level: Profound Conceptual Domain Social Domain Practical Domain Conceptual skills generally involve the physical world rather than symbolic processes. The individual may use objects and goal directed fashion for self-care, work, and recreation. Certain Visio spatial skills, such as matching and sorting based on physical characteristics, may be acquired. However, co-occurring motor and sensory impairments may prevent functional use of objects. The individual has very limited understanding of symbolic communication in speech or gesture. He or she may understand some simple instructions or gestures. The individual expresses his or her own desires and emotions largely through nonverbal, non-symbolic communication. The individual enjoys relationships with well-known family members, caretakers, and familiar others, and initiates in response to social interactions through gestural and emotional cues. Co-occurring sensory and physical impairments may prevent many social activities. = = = = = = Can learn simple life skills and employment tasks with special education. May be employed in special settings, and achieve some independence. Often socially immature. Self-awareness - having an inner image of self, realizing that one is a person separate from the others around one - may exist from here on, but is not guaranteed to exist as it depends on more than intelligence alone. The most intelligent animals, such as some chimpanzees, bonobos, parrots, and dolphins, are in this range. Bonobo or chimpanzee I.Q. scores are sometimes even quoted as high as 80 or 90, but those are childhood age-peer scores that correspond to adult I.Q.'s of only just over 40. 50-69 - Mildly retarded Educable, can learn to care for oneself, employable in routinized jobs but require supervision. Might live alone but do best in supervised settings. Immature but with adequate social adjustment, usually no obvious physical anomalies. Moderate and mild retardation, contrary to the more severe forms, are typically not caused by brain damage but part of the normal variance of intelligence, and therefore largely genetic and inherited. This is important with regard to the question whether or not retarded persons should have children; For especially the moderate and mild forms of retardation, wherewith it physically is possible to have children, are the most likely to be inherited. Individuals with IQ values within 51 and 70 will graduate special school with enough time, effort and help of others. They are able to serve themselves, follow daily duties. This means a slight mental retardation (debility). There is almost 7% of these individuals in the population. = = = = = = |
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Two troops of ring-tail lemurs interacting in Madagascar, pen or pencil drawing by Sarah Landry, in Sociobiology: A New Synthesis, by E. O. Wilson, pp. 532-33, Harvard University Press, 1975 (author’s copy)
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E. O. Wilson
JUNE 10, 2024
Edward Osborne Wilson, an American biologist, entomologist, and ecologist, was born in Alabama on June 10, 1929. Wilson, who published his books ...
Scientist of the Day - E. O. Wilson
June 10, 2024
Two troops of ring-tail lemurs interacting in Madagascar, pen or pencil drawing by Sarah Landry, in Sociobiology: A New Synthesis, by E. O. Wilson, pp. 532-33, Harvard University Press, 1975 (author’s copy)
Edward Osborne Wilson, an American biologist, entomologist, and ecologist, was born in Alabama on June 10, 1929. Wilson, who published his books (and there were many of them) as E. O. Wilson, was the world's leading expert on ants. As a child, he was drawn to studying and collecting nature, and when he was blinded in one eye at the age of 7 in a fishing accident, he chose to concentrate on insects, which he could see quite well up close, with his one good eye. He attended the University of Alabama, then switched to Harvard for graduate work in entomology, where he ultimately joined the faculty, teaching there from 1956 to 1996. He was also curator of entomology at the Harvard Museum of Comparative Zoology from 1973 on, taking that position in the same year that Stephen Jay Gould, 12 years his junior, became curator of invertebrate zoology.
E. O. Wilson at the blackboard, photograph, ca 1975, New Scientist (newscientist.com)
Wilson made many trips to places like Polynesia and Central America to collect ant specimens, which he studied both in the field and back in the entomology lab at Harvard. He was especially interested in ant behavior and ant society, and its evolutionary origins. He worked for many years at Harvard with German entomologist Bert Hölldobler, and before Hölldobler left to go back to Würzburg to head his own lab, the two decided to write a book on ants. They first intended that it be a popular book for the general public, but Wilson realized that the two of them knew more about more species of ants than anyone else in the world, and so they decided to write the definitive book on ants, containing the sum total of their combined knowledge. They didn't waste a lot of time thinking of a catchy title; it was published in 1990 as The Ants. Amazingly, it won the Pulitzer Prize for general non-fiction, the second such prize Wilson was awarded.
Front dust jacket, Sociobiology: A New Synthesis, by E. O. Wilson, Harvard University Press, 1975 (author’s copy)
But the book for which Wilson is best known (and which did NOT win a Pulitzer Prize) was a hefty tome called Sociobiology: The New Synthesis, published in 1975. I own this book – I bought it in those pre-Amazon days from a local bookshop in Kansas City and somehow got it home, which was not easy, since it is fully a foot square and two inches thick and weighs in at 5 pounds. I did not read much of it at the time, but I remember being fascinated by many of the illustrations, which were often pencil or pen drawings, occasionally double-page, such as the troop of lemurs (first image). I found them quite striking, and still do. Pencil drawing is an under-appreciated scientific art form.
Distraction display of the female nighthawk, pen or pencil drawing by J. B. Clark, in Sociobiology: A New Synthesis, by E. O. Wilson, p. 122, Harvard University Press, 1975 (author’s copy)
The book is the study of animal social behavior and its genetic origins. Wilson discussed a variety of behaviors, such as altruism, and why the sacrifice of an individual’s personal genes might make evolutionary sense for those genes in the long run. The book begins, unsurprisingly, with social insects, but soon moves to other social animals, such as birds, primates, and, in the last chapter, humans.
Interior of the nest of Amitermes hastatus, a social termite of South Africa, pen or pencil drawing by Sarah Landry, in Sociobiology: A New Synthesis, by E. O. Wilson, p. 436, Harvard University Press, 1975 (author’s copy)
The word "Sociobiology" was not coined by Wilson, but he certainly made it popular, and controversial. Wilson argued that, even for humans, behavior is rooted in our genes, and nearly everything we do should be studied as a solution to an evolutionary problem. Unfortunately, evolutionary determinism can be used to justify, or at least explain, many unsavory aspects of human behavior, including racism. Consequently, Wilson's book was roundly condemned by many left-leaning biologists, including Stephen Jay Gould, working in the same museum as Wilson. Wilson defended his book, and denied that it included any support for racism, and he had many supporters, but the controversy has lingered to the present day, almost 50 years later. Even after Wilson’s death in 2021, some historians have been combing through his papers, determined to find evidence that Wilson, if not a racist in public, had racist sympathies in private. This seems an unfortunate exercise to me.
Portrait of E. O. Wilson in retirement, photograph, 2003, Harvard Magazine (harvardmagazine.com)
I prefer to form my opinions of Wilson from his books and his public persona, which is that of a well-spoken gentleman with a fascinating personal history. A series of video interviews, each less than 5 minutes long, was recorded around 2005 (I would guess) and can be found on YouTube, where Wilson talks about his childhood, or writing his book on ants, or on what it takes to be a good scientist. Here is one of them, about his discovery of fire ants in Alabama, and you can see the others, 15 in all, listed on the YouTube page, so you can take your pick if you want to watch more. There was also a PBS Nova program that I watched, Lord of the Ants, but I cannot now find it online. I do remember enjoying the charming and enthusiastic E.O. Wilson who came across in that program.
William B. Ashworth, Jr., Consultant for the History of Science, Linda Hall Library and Associate Professor emeritus, Department of History, University of Missouri-Kansas City. Comments or corrections are welcome; please direct toashworthw@umkc.edu.
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189617 | https://www.food-safety.com/articles/7535-preventing-foodborne-illness-outbreaks-caused-by-staphylococcus-aureus | Preventing Foodborne Illness Outbreaks Caused by Staphylococcus aureus | Food Safety
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Contamination ControlSanitation
Preventing Foodborne Illness Outbreaks Caused by Staphylococcus aureus
By Bảo Thy Vương Ph.D.
eclipse_images/E+ via Getty Images
February 8, 2022
In April 2021, an outbreak of foodborne illness sickened 84 people working at a garment company in Vietnam. Of those sickened, 29 were hospitalized with symptoms of abdominal pain, dizziness, and nausea. The other 55 workers, exhibiting milder symptoms of abdominal pain, were administered oral medication and a follow-up at the garment company's medical facility. Local authorities, together with the Department of Health and the Sub-Department of Food Safety and Hygiene, worked with the garment company's support staff to investigate the cause of the foodborne illness outbreak. The investigation found that the garment company had contracted a catering service to provide workers with daily meals. The company's own cafeteria also continued to offer snacks. On the day the workers became ill, they had eaten lunch between 11 a.m. and 12:30 p.m. and had a snack at 6 p.m. The catered lunch consisted of white rice, basa braised with bananas, tofu with tomato sauce, fried pickles, pumpkin soup, boiled chayote squash, and bean dessert. Food samples from the lunch tested positive for Staphylococcus aureus bacteria; however, mixing and cross-contamination of the lunch foods prevented the identification of a single food source of the S. aureus contamination. Due to timely medical treatment, all of the workers recovered within a few days.
Mechanism of an S. aureus Illness Outbreak
Foodborne illness outbreaks caused by S. aureus bacteria commonly occur due to unhygienic food handling practices.S. aureus bacteria have been found on the hands, noses, throats, and in the open wounds of food workers who directly handle unpackaged or packaged foods.
S. aureus is a spherical bacterium, clustered like a bunch of grapes (Figure 1). It is widely scattered in nature and usually parasitizes the skin and mucous membranes. It is often found on foods with high hand contact, such as pastries, sandwiches, salads, and sliced meats, as well as in foods rich in protein and fat, and foods high in water content or starch.
Figure 1.Staphylococcus aureus Bacteria as Seen under a Microscope
S. aureus is heat-resistant and cannot be destroyed by normal cooking methods. The bacterium multiplies rapidly at room temperature, directly producing toxins that cause symptoms of abdominal pain, nausea, vomiting, and/or diarrhea within 30 minutes to a few hours after ingestion. The toxin has a very high temperature tolerance; it can survive for one to two hours at 100 °C (212 °F). S. aureus can maintain its toxicity for more than two months at normal temperatures and does not change the smell or taste of food.
After contaminating food, S. aureus produces exotoxins within four to five hours. These toxins are not destroyed by digestive enzymes. When people consume food contaminated with S. aureus, the toxins quickly penetrate the lining of the stomach and intestines and enter the bloodstream. Symptoms of illness occur quickly, within six hours after eating contaminated food. The severity of the illness depends on the amount of food consumed, the amount of toxins present in the food, the individual's sensitivity to the toxins, and the present health of the individual. The symptoms usually last for a short time—up to eight hours—but it may take a couple of days to fully recover from illness caused by S. aureus toxins.
Preventing S. aureus Foodborne Illness
It is always necessary to ensure food hygiene and safety by properly cooking food, using only clean water in cooking operations, and sourcing food ingredients from clear and reputable suppliers. Attention should always be paid to proper food storage and handling. However, food contamination by S. aureus can be difficult to prevent because a cooking killstep is not applicable. The key lies in educating food handlers on proper procedures for avoiding contamination of food—especially those involving personal hygiene.
To prevent foodborne illness outbreaks associated with S. aureus, the following list of practices should be observed by all food handlers, especially in retail foodservice and catering operations:
People with sinusitis, nasopharyngitis, open sores or wounds, or acne on their hands should not be permitted to have direct contact with raw or cooked food, food ingredients, or food utensils
All food handlers must thoroughly wash their hands with soap and warm water before handling food and food utensils, especially after using the restroom, eating, smoking, or contacting other easily contaminated sources
No bare hand contact is permitted on ready-to-eat foods
All utensils and surfaces used in food processing must be dry, sanitized, clean, and free of clutter
Food utensils should not be shared between raw and cooked foods
No cross-contamination should be allowed to occur between food, especially after cooking
Proper cooling and hot/cold holding practices must be observed
The amount of time that food spends in the temperature danger zone (5 °C– 57 °C or 41 °F–135 °F) must be minimized.
Such control measures will go a long way toward helping prevent foodborne illness outbreaks associated with S. aureus bacteria in retail foodservice and catering operations.
KEYWORDS: killstepStaphylococcus aureus
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Bảo Thy Vương, Ph.D. is Head of the Health Sciences Faculty at Mekong University in Vietnam. Her research interests include food safety, public health, and nutrition.
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189618 | https://ui.adsabs.harvard.edu/abs/2021PhRvL.127k7204Z/abstract | Strain-Driven Dzyaloshinskii-Moriya Interaction for Room-Temperature Magnetic Skyrmions - Astrophysics Data System
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Strain-Driven Dzyaloshinskii-Moriya Interaction for Room-Temperature Magnetic Skyrmions
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Abstract
Dzyaloshinskii-Moriya interaction in magnets, which is usually derived from inversion symmetry breaking at interfaces or in noncentrosymmetric crystals, plays a vital role in chiral spintronics. Here we report that an emergent Dzyaloshinskii-Moriya interaction can be achieved in a centrosymmetric material, La 0.67 Sr 0.33 MnO 3 , by a graded strain. This strain-driven Dzyaloshinskii-Moriya interaction not only exhibits distinctive two coexisting nonreciprocities of spin-wave propagation in one system, but also brings about a robust room-temperature magnetic skyrmion lattice as well as a spiral lattice at zero magnetic field. Our results demonstrate the feasibility of investigating chiral spintronics in a large category of centrosymmetric magnetic materials.
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Physical Review Letters, Volume 127, Issue 11, article id.117204
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189619 | https://www.johndcook.com/blog/2022/04/05/cubic/ | Numerically finding roots of a cubic
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Numerically finding roots of a cubic
Posted on 5 April 2022 by John
The analog of the quadratic formula for cubic equations is cumbersome. A lot of people naturally say “Forget all that. If I need to find the roots of a cubic, I’ll just use a numerical method like Newton’s method.” Sounds good.
Where to start?
But how do you know where to look for the roots? You have to have some idea where a root is before you can use a numerical method.
For the bisection method, you have to know an interval where the polynomial changes sign. For Newton’s method, if you don’t start close enough, you diverge. In fact, you can make complex fractals by plotting the points where Newton’s method converges and diverges.
Cornelius Lanczos gives an elegant explanation of how to solve cubic equations at the beginning of his book Applied Analysis. His book was published in 1956, before the days of ubiquitous computers, and so he couldn’t say “Plot the function and scroll around until you can see roughly where the zeros are.”
Lanczos does a sequence of change of variables that reduce the problem to finding a unique root in the unit interval.
Setup
Let
f(x) = ax ³ + bx ² + cx + d
where the coefficients are all real numbers. We want to find all real values of x where f(x) = 0.
The main task is to find a root of f(x). Once we’ve found a root r, we can divide by (x – r) to reduce the problem to a quadratic.
Reduce to standard form
By a change of variables we can reduce the problem to finding a root of
x ³ + bx ² + cx − 1 = 0.
How? First of all, you can always make the leading coefficient 1 by dividing by a if necessary. Second, you can make the constant term negative by replacing x by a new variable equal to –x. Third, you can make the constant term -1 by replacing x with d−1/3 x.
We’ve divided by a and d above. How do we know they’re not zero? If they were zero, that would be good news because it would make things easier.
We assume a is not zero because otherwise we don’t have a cubic equation. And we assume d is not zero because otherwise we can factor out an x and we’re left with a quadratic equation.
Bracketing a root
After our changes of variable,
f(x) = x³ + bx ² + cx – 1.
So f(0) = -1 and f(x) goes to infinity as x goes to infinity, and this means f(x) must have at least one positive root.
Evaluate f(1). If f(1) = 0 then you’re very lucky because you’ve found your root.
If f(1) > 0 then there is a root in (0, 1) since the polynomial changes signs over the interval.
If f(1) < 0 then the function has a root in (1,∞) . In that case, replace x with 1/x and then the new polynomial has a root somewhere in (0, 1).
Uniqueness
If f(x) equals zero somewhere in the interval (0, 1), could it be zero at two or three places in the interval?
It cannot have just two roots in the interval because the sign is different at the two ends of the interval.
It also cannot have three roots in the interval. We know from Vieta’s formula that the product of the roots of f equals 1. It cannot have three roots in the interval (0, 1) because the product of three positive numbers less than 1 is less than 1.
If f(x) had a zero somewhere in (1,∞) before replacing x with 1/x, an analogous argument applies. It can’t have two zeros because it changes signs over the interval, and it can’t have three zeros in the interval because if three numbers are each greater than 1, their product is greater than 1.
In either case, possibly after replacing x with 1/x, we know f has a unique root in the interval (0, 1), and now we can apply a numerical method.
More general functions
This post looked at a very special function, a cubic polynomial with real coefficients, and showed that after a change of variables it has a unique root in an interval. The next post shows how to determine how many zeros a more general, complex-valued function has in a region of the complex plane.
Related posts
Rate of convergence for Newton’s method
Higher order, Newton-like methods
Solving Kepler’s equation
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189620 | https://mathbitsnotebook.com/Algebra1/FunctionGraphs/FNGFunctionTransVertical.html | | | | | | | | | | | | | | | | | | | | | | | | |
--- --- --- --- --- --- --- --- --- --- ---
| | | | | | | | | | | | | | | | | | | | | | | | --- --- --- --- --- --- --- --- --- --- --- | | | | | Functions: Vertical Shift MathBitsNotebook.com Topical Outline | Algebra 1 Outline | MathBits' Teacher Resources Terms of Use Contact Person: Donna Roberts | The transformations you have seen in the past can also be used to move and resize graphs of functions. | | | Translation: Vertical Shift: f (x) + k | | | | | | | | --- --- --- | | A function can be moved up (or down) by adding a constant to the y-value. (Remember: the y-value is also the f (x)-value.) This movement is called a vertical shift. It is movement along the y-axis. The constant value to be added is represented as "k" (x, f (x)) → (x, f (x) + k) | | | | | --- --- | | Vertical Shift:f (x) + k | | | • k > 0 slides straight up | | • k < 0 slides straight down | | • k = 0 no movement | | When dealing with "k", the sign (±) indicates the "direction" of the movement. The actual distance traveled is always positive, | k |, as distance and units of measurement are positive. | Given: f (x) = x2 and k = 4 A vertical shift, will add four to the outputs of f (x). Vertical Shift: f (x) + 4 = x2 + 4 The new function can be renamed: g (x) = x2 + 4 | Every point in a function graph will move up (or down) in a vertical shift. (x, y) → (x, y + k) A vertical shift deals with changing ONLY the y-values. | | | a) Graph . b) State the equation, g(x), that represents a vertical shift of k = -3 to f (x). c) Graph g(x). Describe how the graph of g(x) is formed. d) The point (1,1) is located on f (x). What will be the coordinates of this point after the vertical shift? e) State the domain and range of f (x) and g(x). | | Solutions: a) See graph b) g(x) = f (x) - 3 c) See graph. Every point of f (x) slides straight "down" 3 units, forming function g(x). The graph of g(x) is the function f (x) shifted "down" three units. d) The point will be (1, -2). The y-value changed by 3 units in the negative direction (down). e) Domain of f (x): [0,∞). Domain of g (x): [0,∞) Range of f (x): [0,∞). Range of g (x): [-3,∞) | | | | a) Graph f (x) = | x | + 3 using your knowledge of its parent function. b) Describe the transformation that has occurred in this problem from the parent function. c) The turning point for the parent function is located at (0,0). What are the coordinates of the turning point of f (x)? d) State the domain and range of the parent function and of f (x), | | Solutions: a) The parent function is the simplest absolute value function which is g(x) = | x | (You need to remember the graph of the parent function of absolute value.) b) The parent function, g(x), was transformed by a vertical shift of k = 3 to produce the function f (x). c) (0,3) d) Domain of f (x): (-∞,∞). Domain of g (x): (-∞,∞) Range of f (x): [3,∞). Range of g (x): [0,∞) | | | | This example combines reflection with vertical shift. Given the graph at the right showing functions f (x) and g(x) where f (x) is the vertical shift of g(x). a) Describe the parent function associated with these graphs. b) Describe the transformation(s) that occurred in this problem. c) Write an equation for f (x). d) State the coordinates of the maximum point of g(x). State the coordinates of the maximum point of f (x). e) State the domain and range of f (x) and g(x). | | Solutions: a) These graphs are a parabolas, so the parent function is y = x2. BUT, the parent function opens upward, and these "children" are opening downward. So, we will need to adjust the parent function to open downward, by reflecting it over the x-axis, to get g (x) = -x2. b) The reflected parent function, g(x), was then transformed by a vertical shift of k = 4 to produce the function f (x). c) f (x) = -x2 + 4 d) (0,0) and (0,4) e) Domain of f (x): (-∞,∞). Domain of g (x): (-∞,∞) Range of f (x): (-∞,4]. Range of g (x): (-∞,0] | S U M M A R Y | | | Translation of a Function: f (x) + k called a Vertical Shift | | Translation vertically (upward or downward) f (x) + k translates f (x) up or down | Changes occur "outside" the function(affecting only the y-values). | | Vertical Shift: This translation is a "slide" straight up or down. • if k > 0, the graph translates upward k units. • if k < 0, the graph translates downward k units. In the past, on a coordinate grid, you used the formula (x,y) → (x,y + k) to move a figure upward or downward. | | | --- | | Keeping in mind that now y = f (x), we can replace y with f (x) and get: (x, f (x)) → (x, f (x) + k). Remember, you are adding the value of k to the y-values of the function, where the y-values are now called f (x). | vertical shift | | | | | NOTE: The re-posting of materials (in part or whole) from this site to the Internet is copyright violation and is not considered "fair use" for educators. Please read the "Terms of Use". | Topical Outline | Algebra 1 Outline | MathBitsNotebook.com | MathBits' Teacher Resources Terms of Use Contact Person: Donna Roberts | | |
189621 | https://pubmed.ncbi.nlm.nih.gov/7556731/ | Progressive outer retinal necrosis (PORN) in AIDS patients: a different appearance of varicella-zoster retinitis - PubMed
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. 1995:9 ( Pt 3):271-6.
doi: 10.1038/eye.1995.53.
Progressive outer retinal necrosis (PORN) in AIDS patients: a different appearance of varicella-zoster retinitis
C E Pavesio1,S M Mitchell,K Barton,S D Schwartz,H M Towler,S Lightman
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Affiliation
1 Uveitis and Acquired Immunodeficiency Syndrome Clinics, Moorfields Eye Hospital, London, UK.
PMID: 7556731
DOI: 10.1038/eye.1995.53
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Case Reports
Progressive outer retinal necrosis (PORN) in AIDS patients: a different appearance of varicella-zoster retinitis
C E Pavesio et al. Eye (Lond).1995.
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. 1995:9 ( Pt 3):271-6.
doi: 10.1038/eye.1995.53.
Authors
C E Pavesio1,S M Mitchell,K Barton,S D Schwartz,H M Towler,S Lightman
Affiliation
1 Uveitis and Acquired Immunodeficiency Syndrome Clinics, Moorfields Eye Hospital, London, UK.
PMID: 7556731
DOI: 10.1038/eye.1995.53
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Retinal infections caused by the varicella-zoster virus (VZV) have been reported in immunocompetent and immunocompromised individuals. Two cases of a VZV-related retinitis are described with the characteristic features of the recently described progressive outer retinal necrosis (PORN) syndrome. Both patients suffered from the acquired immunodeficiency syndrome (AIDS) with greatly reduced peripheral blood CD4+ T lymphocyte counts, and presented with macular retinitis without vitritis. The disease was bilateral in one case and unilateral in the other. The clinical course was rapidly progressive with widespread retinal involvement and the development of rhegmatogenous retinal detachment with complete loss of vision in the affected eyes despite intensive intravenous antiviral therapy. VZV DNA was identified in vitreous biopsies, by molecular techniques based on the polymerase chain reaction (PCR), in both patients. At present, the use of very high-dose intravenous acyclovir may be the best therapeutic option in these patients for whom the visual prognosis is poor. Intravitreal antiviral drugs could also contribute to the management of these cases.
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189622 | https://texasgateway.org/resource/34-contingency-tables | 3.4 Contingency Tables
Resource ID: 6p9ejZPO@5
Grade Range: HS - 12
Introduction
Introduction
Introduction
A two-way table provides a way of portraying data that can facilitate calculating probabilities. When used to calculate probabilities, a two-way table is often called a contingency table. The table helps in determining conditional probabilities quite easily. The table displays sample values in relation to two different variables that may be dependent or contingent on one another. We used two-way tables in Chapters 1 and 2 to calculate marginal and conditional distributions. These tables organize data in a way that supports the calculation of relative frequency and, therefore, experimental (empirical) probability. Later on, we will use contingency tables again, but in another manner.
Example 3.20
Suppose a study of speeding violations and drivers who use cell phones produced the following fictional data:
| | Speeding Violation in the Last Year | No Speeding Violation in the Last Year | Total |
--- --- |
| Uses a cell phone while driving | 25 | 280 | 305 |
| Does not use a cell phone while driving | 45 | 405 | 450 |
| Total | 70 | 685 | 755 |
Table 3.3
The total number of people in the sample is 755. The row totals are 305 and 450. The column totals are 70 and 685. Notice that 305 + 450 = 755 and 70 + 685 = 755.
Calculate the following probabilities using the table:
Find P(Person uses a cell phone while driving).
Find P(Person had no violation in the last year).
Find P(Person had no violation in the last year and uses a cell phone while driving).
Find P(Person uses a cell phone while driving or person had no violation in the last year).
Find P(Person uses a cell phone while driving given person had a violation in the last year).
Find P(Person had no violation last year given person does not use a cell phone while driving).
Solution 3.20
a. This is the same as the marginal distribution (Section 1.2).
b. The marginal distribution is
c. Find the number of participants who satisfy both conditions.
d. To find this probability, you need to identify how many participants use a cell phone while driving OR have no violation in the past year OR both.
P (Person uses a cell phone while driving or had no violation in the last year)
e. This is a conditional probability. You are given that the person had no violation in the last year, so you need only consider the values in that column of data.
f. For this conditional probability, consider only values in the row labeled “Does not use a cell phone while driving.”
Try It 3.20
Table 3.4 shows the number of athletes who stretch before exercising and how many had injuries within the past year.
| | Injury in Past Year | No Injury in Past Year | Total |
--- --- |
| Stretches | 55 | 295 | 350 |
| Does not stretch | 231 | 219 | 450 |
| Total | 286 | 514 | 800 |
Table 3.4
What is P(Athlete stretches before exercising)?
What is P(Athlete stretches before exercising|no injury in the last year)?
Example 3.21
Table 3.5 shows a random sample of 100 hikers and the areas of hiking they prefer.
| Sex | The Coastline | Near Lakes and Streams | On Mountain Peaks | Total |
| Female | 18 | 16 | ___ | 45 |
| Male | ___ | ___ | 14 | 55 |
| Total | ___ | 41 | ___ | ___ |
Table 3.5 Hiking Area Preference
a. Complete the table.
Solution 3.21
a. There are 45 females in the sample; 18 prefer the coastline and 16 prefer hiking near lakes and streams. So, we know there are 45 − 18 − 16 = 11 female students who prefer hiking on mountain peaks.
Continue reasoning in this way to complete the table.
| Sex | The Coastline | Near Lakes and Streams | On Mountain Peaks | Total |
| Female | 18 | 16 | 11 | 45 |
| Male | 16 | 25 | 14 | 55 |
| Total | 34 | 41 | 25 | 100 |
Table 3.6 Hiking Area Preference
b. Are the events being female and preferring the coastline independent events?
Let F = being female and let C = preferring the coastline.
Find P(F AND C).
Find P(F)P(C).
Are these two numbers the same? If they are, then F and C are independent. If they are not, then F and C are not independent.
Solution 3.21
b.
P(F AND C) = = .18
P(F)P(C) = = (.45)(.34) = .153
P(F AND C) ≠ P(F)P(C), so the events F and C are not independent.
c. Find the probability that a person is male given that the person prefers hiking near lakes and streams. Let M = being male, and let L = prefers hiking near lakes and streams.
What word tells you this is a conditional?
Is the sample space for this problem all 100 hikers? If not, what is it?
Fill in the blanks and calculate the probability: P(_____|_____) = _____.
Solution 3.21
c.
The word given tells you that this is a conditional.
No, the sample space for this problem is the 41 hikers who prefer lakes and streams.
Find the conditional probability P(M|L). Because it is given that the person prefers hiking near lakes and streams, you need only consider the values in the column labeled "Near Lakes and Streams." P(M|L) =
d. Find the probability that a person is female or prefers hiking on mountain peaks. Let F = being female, and let P = prefers mountain peaks.
Find P(F).
Find P(P).
Find P(F AND P).
Find P(F OR P).
Solution 3.21
d.
P(F) =
P(P) =
P(F AND P) = =
P(F OR P) = P(F) + P(P) − P(F AND P) = + - =
Try It 3.21
Table 3.7 shows a random sample of 200 cyclists and the routes they prefer. Let M = males and H = hilly path.
| Gender | Lake Path | Hilly Path | Wooded Path | Total |
--- ---
| Female | 45 | 38 | 27 | 110 |
| Male | 26 | 52 | 12 | 90 |
| Total | 71 | 90 | 39 | 200 |
Table 3.7
Out of the males, what is the probability that the cyclist prefers a hilly path?
Are the events being male and preferring the hilly path independent events?
Example 3.22
Muddy Mouse lives in a cage with three doors. If Muddy goes out the first door, the probability that he gets caught by Alissa the cat is and the probability he is not caught is . If he goes out the second door, the probability he gets caught by Alissa is and the probability he is not caught is . The probability that Alissa catches Muddy coming out of the third door is and the probability she does not catch Muddy is . It is equally likely that Muddy will choose any of the three doors, so the probability of choosing each door is .
| Caught or Not | Door One | Door Two | Door Three | Total |
| Caught | | | | ____ |
| Not Caught | | | | ____ |
| Total | ____ | ____ | ____ | 1 |
Table 3.8 Door Choice
The first entry is P(Door One AND Caught).
The entry is P(Door One AND Not Caught).
Verify the remaining entries.
a. Complete the probability contingency table. Calculate the entries for the totals. Verify that the lower-right corner entry is 1.
Solution 3.22
a.
| Caught or Not | Door One | Door Two | Door Three | Total |
| Caught | | | | |
| Not Caught | | | | |
| Total | | | | 1 |
Table 3.9 Door Choice
b. What is the probability that Alissa does not catch Muddy?
Solution 3.22
b.
c. What is the probability that Muddy chooses Door One OR Door Two given that Muddy is caught by Alissa?
Solution 3.22
c. This is a conditional probability, so consider only probabilities in the row labeled "Caught." Choosing Door One and choosing Door Two are mutually exclusive, so
Use the formula for conditional probability
Example 3.23
Table 3.10 contains the number of crimes per 100,000 inhabitants from 2008 to 2011 in the United States.
| Year | Crime A | Crime B | Crime C | Crime D | Total |
| 2008 | 145.7 | 732.1 | 29.7 | 314.7 | |
| 2009 | 133.1 | 717.7 | 29.1 | 259.2 | |
| 2010 | 119.3 | 701 | 27.7 | 239.1 | |
| 2011 | 113.7 | 702.2 | 26.8 | 229.6 | |
| Total | | | | | |
Table 3.10 U.S. Crime Index Rates Per 100,000 Inhabitants 2008–2011
TOTAL each column and each row. Total data = 4,520.7.
Find P(2009 AND Crime A).
Find P(2010 AND Crime B).
Find P(2010 OR Crime B).
Find P(2011|Crime A).
Find P(Crime D|2008).
Solution 3.23
a. = .0294, b. = .1551, c. P(2010 OR Crime B) = P(2010) + P(Crime B) − P(2010 AND Crime B) = + − = .7165, d. = .2222, e. = .2575
Try It 3.23
Table 3.11 relates the weights and heights of a group of individuals participating in an observational study.
| Ages | Tall | Medium | Short | Totals |
--- ---
| Under 18 | 18 | 28 | 14 | |
| 18–50 | 20 | 51 | 28 | |
| 51+ | 12 | 25 | 9 | |
| Totals | | | | |
Table 3.11
Find the total for each row and column.
Find the probability that a randomly chosen individual from this group is tall.
Find the probability that a randomly chosen individual from this group is Under 18 and Tall.
Find the probability that a randomly chosen individual from this group is tall given that the individual is Under 18.
Find the probability that a randomly chosen individual from this group is Under 18 given that the individual is tall.
Find the probability a randomly chosen individual from this group is tall and age 51+.
Are the events under 18 and tall independent?
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Analysing Percentage Changes with Google Sheets Formulas and Conditional Formatting
Ant
Oct 12, 2023
4 min read
Updated: Oct 13, 2023
In the realm of data analysis and spreadsheet management, it's crucial to derive meaningful insights from numerical data. One common scenario involves tracking changes in values over time, such as comparing data from this month to the previous month. In this blog post, we'll explore a simple yet effective approach to visualise and understand these changes using Google Sheets formulas and conditional formatting.
The Formula: Percentage Change
To determine the percentage change, you need to calculate the difference (change) between the two numbers being compared:
Change = Original Number - New Number
Divide the change by the Original Number and multiply the result by 100 to convert this into a percentage.
% Change = (Change ÷ Original Number) × 100.
If the resulting value is negative, it signifies a percentage increase, whereas a positive answer would be a decrease.
When we use this within the Google Sheets formula, we take account of the increase or decrease separately with the initial IF statement, and the change is calculated using the absolute (ABS) function; more on that later.
To start, let's consider a scenario where you have two values, one from this month (let's say in cell C4 - this is the new number) and another from last month (in cell D4 - this is the original number). You want to visualize the percentage change between these two values along with an indicator of the direction of the change.
Here's a formula that achieves this:
=IF(C4 > D4, CHAR(9650), CHAR(9660)) & " " & ROUND(ABS(D4 - C4) / D4 100,0) & "%"
This formula has two components:
Arrow Symbol: It displays an upward-pointing triangle (▲) if the value in C4 is greater than D4, indicating an increase. Conversely, it shows a downward-pointing triangle (▼) if the value in C4 is less than D4, indicating a decrease.
Percentage Change: It calculates the percentage change between the two values, rounds it to the nearest whole number, and appends a percentage sign.
This formula gives you a quick visual cue about the direction and magnitude of the change.
Let's break down the formula step by step.
=IF(C4 >D4, CHAR(9650), CHAR(9660)): This part of the formula is an IF statement. It checks whether the value in cell C4 is greater than the value in cell D4. If this condition is true, it returns the character with Unicode value 9650 (▲, an upward-pointing triangle); otherwise, it returns the character with Unicode value 9660 (▼, a downward-pointing triangle). So, this part of the formula generates an arrow symbol pointing up or down based on whether the value in C4 is greater than D4.
&" ": This part concatenates a space character to the result obtained from the IF statement. This is done to separate the arrow symbol from the next part of the formula.
& ROUND(ABS(D4 - C4) / D4 100,0) &"%": This part calculates the percentage difference between the values in cells C4 (new number) and D4 (original number), takes the absolute value, rounds the result to 0 decimal places, and appends the percentage sign. Let's break it down further:
ABS(D4 - C4): This calculates the absolute difference between the values in cells C4 and D4. Disregarding any positive or negative values, just the absolute difference.
/ D4 100: This computes the percentage change by dividing the absolute difference by the value in cell D4 and multiplying by 100.
ROUND(..., 0): This rounds the result to 0 decimal places.
&"%": This concatenates the percentage sign to the rounded result.
Putting it all together, the formula displays an arrow (▲ or ▼) based on whether the value in C4 is greater than D4 or not, followed by a space and then the percentage difference between the values in cells C4 and D4.
For this specific case, with C4=521 and D4=452, the value in C4 (521) is greater than D4 (452). Therefore, the formula displays an upward-pointing triangle (▲), a space, and the percentage difference rounded to 0 decimal places (rounded to the nearest whole number), followed by the percentage sign.
Conditional Formatting: Adding Colour to the Mix
To enhance the visual impact, you can employ conditional formatting to change the colour of the text based on the direction of the change. In this case, I’ve opted for red text for a decrease (▼) and green text for an increase (▲).
Here are the conditional formatting rules:
For Red Text (Decrease):
=LEFT(E4, 1) = CHAR(9660)
For Green Text (Increase):
=LEFT(E4, 1) = CHAR(9650)
These rules check the first character of the cell containing the formula (E4 in this case) and apply the colour based on whether it starts with the downward-pointing triangle (▼) or the upward-pointing triangle (▲).
To find out how to apply Conditional formatting, check out the steps with the link and use the formatting rules above. You’ll need to create two separate rules for each colour.
Practical Application: Weekly Data Analysis
Now, let's apply this concept to a real-world scenario. Imagine you have a sheet where you track sales figures for a product or the number of calls and chats from a call centre each month. By applying the formula and conditional formatting, you can quickly identify products or agents with significant increases or decreases in metrics. This visual representation makes it easier to spot trends and anomalies, aiding in better decision-making.
This particular example is essentially the same as the original formula above, except the previous month is located on another sheet; therefore, a VLOOKUP formula is adopted to locate that figure:
VLOOKUP($B181,'Call Staging'!$B$333:$M$345,H$178,FALSE)
In this case, the column reference within the VLOOKUP also adopts a reference to a column number rather than an actual number. The reference H$178 is essentially the same as referencing column 4. This is the complete formula below; it's wrapped with an IFERROR function to ensure blank cells do not cause issues with # N/A and the ISBLANK function to return nothing if the lookup cell is empty.
=IFERROR(IF(ISBLANK($B181),"", IF(C181>VLOOKUP($B181,'Call Staging'!$B$333:$M$345,H$178,FALSE), CHAR(9650),CHAR(9660)) &" "& ROUND(ABS(VLOOKUP($B181,'Call Staging'!$B$333:$M$345,H$178,FALSE)-C181) / VLOOKUP($B181,'Call Staging'!$B$333:$M$345,H$178,FALSE)100,0) &"%"))
Conclusion
In conclusion, leveraging formulas and conditional formatting in Google Sheets provides a powerful tool for visualising and understanding changes in data over time. Whether you're tracking sales, expenses, or any other metric, this approach helps you make informed decisions based on a clear and concise representation of the data.
Remember, the key to effective data analysis is not just in the numbers but in the insights derived from them. Happy spreadsheeting!
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189624 | https://www.doubtnut.com/qna/27175 | Using vectors, find the value of lambda such that the points (lambda,-
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Using vectors, find the value of `lambda...
Using vectors, find the value of λ such that the points (λ,−10,3),(1,−1,3)a n d(3,5,3) are collinear.
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Let the given points be
A(λ,−10,3),B(1,−1,3)and C(3,5,3)
A B=(i−j+3 k)−(λ i−10 j+3 k)=(1−λ)i+9 j
A C=(3 i+5 j+3 k)−(λ i−10 j+3 k)=(3−λ)i+15 j
Since they are collinear
A B=K A C
(1−λ)i+9 j=K[(3−λ)i+15]
1−λ=K(3−λ)
and 9=15 K
1−λ=3 5(3−λ)
5−5 λ=9−3 λ
2 λ=−4
λ=−2
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189625 | https://www.sciencedirect.com/science/article/abs/pii/S2213260019301377 | Paediatric tuberculosis transmission outside the household: challenging historical paradigms to inform future public health strategies - ScienceDirect
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The Lancet Respiratory Medicine
Volume 7, Issue 6, June 2019, Pages 544-552
Personal View
Paediatric tuberculosis transmission outside the household: challenging historical paradigms to inform future public health strategies
Author links open overlay panel Leonardo Martinez PhD a†, Nathan C Lo PhD a b†, Olivia Cords MS a, Prof Philip C Hill MD c, Palwasha Khan PhD d, Prof Mark Hatherill MD e, Anna Mandalakas MD f, Alexander Kay MD f g, Julio Croda MD h i, Prof C Robert Horsburgh MD j k, Prof Heather J Zar PhD l, Jason R Andrews MD a
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Summary
Tuberculosis is a major cause of death and disability among children globally, yet children have been neglected in global tuberculosis control efforts. Historically, tuberculosis in children has been thought of as a family disease, and because of this, household contact tracing of children after identification of an adult tuberculosis case has been emphasised as the principal public health intervention. However, the population-level effect of household contact tracing is predicated on the assumption that most paediatric tuberculosis infections are acquired within the household. In this Personal View, we focus on accumulating scientific evidence indicating that the majority of Mycobacterium tuberculosis transmission to children in high-burden settings occurs in the community, outside of households in which a person has tuberculosis. We estimate the population-attributable fraction of M tuberculosis transmission to children due to household exposures to be between 10% and 30%. M tuberculosis transmission from the household was low (<30%) even in children younger than age 5 years. We propose that an effective public health response to childhood tuberculosis requires comprehensive, community-based interventions, such as active surveillance in select settings, rather than contact tracing alone. Importantly, the historical paradigm that most paediatric transmission occurs in households should be reconsidered on the basis of the scientific knowledge presented.
Introduction
Tuberculosis in children continues to pose a pressing public health challenge and remains one of the leading infectious causes of child morbidity and mortality globally.1, 2 Most paediatric tuberculosis deaths occur in low-income and middle-income countries, predominantly among children younger than 5 years, who often die without being diagnosed with tuberculosis.1, 3 Impressive strides have been made to address the tuberculosis epidemic in adults through mass implementation of directly observed therapy, development and adoption of novel diagnostics, such as GeneXpert, and the integration of tuberculosis and HIV care into health systems.4 However, progress in the prevention, early detection, and treatment of tuberculosis in young children has been more limited.
Historically, the global tuberculosis public health strategy has not addressed the disease burden in children for several reasons. Although children are more susceptible to primary progressive tuberculosis disease, they are considered to be relatively non-infectious since they are often unable to generate a forceful cough with sufficient bacteria to transmit infection, and therefore might not contribute substantially to ongoing transmission. This argument has made children with tuberculosis less important from a public health perspective. Because of poor sputum collection, paucibacillary disease, and non-specific clinical presentation, paediatric tuberculosis is more difficult to diagnose than adult tuberculosis.5 Furthermore, most public health interventions designed to address adult tuberculosis are not translatable to children. Because of the lack of emphasis on children within the global tuberculosis strategy, the incidence of tuberculosis infection, disease, and death were previously largely unknown. The paediatric tuberculosis burden has only recently been examined and is estimated to be much higher than previously thought.1, 6, 7
In 2014, WHO published guidelines for National Tuberculosis Programs to manage children with or exposed to tuberculosis, and emphasised the primary strategy of tuberculosis contact tracing.8 Under this strategy, when an adult with active tuberculosis disease is diagnosed, health workers visit the household to examine any child for disease and, in some programmes, provide preventive therapy to children who are latently infected with tuberculosis. Alternatively, adults diagnosed with tuberculosis are asked whether there are any sick contacts in the family, and are asked to bring them to the hospital. This strategy is often of lower diagnostic yield. The potential of household contact tracing to affect the paediatric tuberculosis burden is predicated on conventional wisdom that Mycobacterium tuberculosis transmission to children occurs from people living within the household (and not by those living in the general community).9, 10, 11, 12, 13 This hypothesis is based on the traditional assumption that children spend the vast majority of their time in the household with limited exposure to other adults and, consequently, their social network structure includes predominantly household members. Several recent reviews10, 11 and guidelines12, 13 have stated that M tuberculosis transmission to children is largely attributable to exposures from within the household. However, accumulating epidemiological evidence suggests that this assumption might not be the case in high-burden settings and that children are more often infected by those living outside the household.
Key messages
•The public health strategy of household contact tracing of children after identification of an adult tuberculosis case has been emphasised as the principal public health intervention for paediatric tuberculosis, and is predicated on the hypothesis that most children are infected with tuberculosis through a household contact
•We estimate that the population-attributable fraction of paediatric tuberculosis transmission due to household exposure is between 10% and 30%, which is substantially lower than previously thought
•At the population level, transmission from the household was low (<30%) even in children younger than 5 years
•This suggests that household contact tracing is unlikely to reach the majority of children with tuberculosis
•We propose that new public health strategies are necessary to address childhood tuberculosis and will require comprehensive, community-based interventions in addition to household contact tracing
To address the crucial and unaddressed public health challenge of paediatric tuberculosis, an improved scientific understanding of the routes of transmission is urgently needed to inform a more effective global public health strategy. However, the ideal public health strategy that will maximise impact and cost-effectiveness remains subject to a key epidemiological question—what proportion of M tuberculosis transmission in children occurs in households and is therefore avertible by household contact-based strategies? In this Personal View, we provide a summary of scientific evidence on the route of M tuberculosis transmission to children, to bring insight to this important question and outline potential future public health steps necessary to address this vulnerable, at-risk paediatric population.
Section snippets
Epidemiological evidence: investigating where paediatric tuberculosis transmission occurs
Despite the complexity in quantifying where M tuberculosis transmission occurs in children at the population level, understanding this key question is essential to design appropriate and effective public health programmes to detect, diagnose, and treat children with tuberculosis. 13 studies14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26 published between 2003 and 2018 that made use of diverse methodologies and designs shed light on this topic. This description is specific to the type of
Is household transmission more common for the youngest children?
On the basis of empirical evidence, we estimate that a minority of children with tuberculosis have household contact-based transmission. However, a key question remains whether the youngest children (aged <5 years) are more likely to acquire transmission from inside the household than older children who are more likely to go to school and acquire community exposures. Although this hypothesis remains plausible,18, 48 our data suggest that, even among these infants and young children, community
A comprehensive public health strategy: looking forward
There is a growing consensus that new public health strategies are needed to address the global burden of paediatric tuberculosis. Policy discussions have focused on household contact tracing on the basis of the assumption that it has a high population-level yield (because of the idea of predominant household routes of transmission) and since the home represents a defined infrastructure that can be visited by health-care workers.8, 49, 50 We support that household contact tracing is an
Conclusion
Over the past 10 years, the field of paediatric tuberculosis has moved towards household contact tracing because of its pragmatic nature and the belief that most paediatric tuberculosis infections occur in the household. Although we support household contact investigations as a component of the global strategy to address paediatric tuberculosis, a strategy primarily focused on this intervention will probably continue to miss most tuberculosis infections and cases among children. We believe that
Search strategy and selection criteria
We first searched for any previous narrative or systematic review that attempted to quantify the population-attributable fraction of tuberculosis transmission to children caused by household exposure. None were found. We did find several review articles attempting to quantify the percentage of adult tuberculosis transmission attributable to household exposure. All of these studies excluded children. We then searched MEDLINE and Google Scholar for articles published before Dec 1, 2018. We used
Recommended articles
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Cited by (65)
Global, regional, and national age-specific progress towards the 2020 milestones of the WHO End TB Strategy: a systematic analysis for the Global Burden of Disease Study 2021
2024, Lancet Infectious Diseases Citation Excerpt :
Despite these improvements, the burden of tuberculosis in children remains high, with an estimated 89 800 deaths in 2020. With recent evidence suggesting that most tuberculosis transmission among children occurs outside the household,62 integrating effective household contact-tracing programmes63,64 with community-based strategies (eg, routine or mass screening, targeted preventive therapy, and environmental interventions) will be particularly important for continued progress. While individuals aged 50 years and older constituted 37% of all tuberculosis incident cases and 58% of all tuberculosis deaths in 2020, these age groups have shown slow progress in reducing the tuberculosis burden since 2015. Show abstract Global evaluations of the progress towards the WHO End TB Strategy 2020 interim milestones on mortality (35% reduction) and incidence (20% reduction) have not been age specific. We aimed to assess global, regional, and national-level burdens of and trends in tuberculosis and its risk factors across five separate age groups, from 1990 to 2021, and to report on age-specific progress between 2015 and 2020. We used the Global Burden of Diseases, Injuries, and Risk Factors Study 2021 (GBD 2021) analytical framework to compute age-specific tuberculosis mortality and incidence estimates for 204 countries and territories (1990–2021 inclusive). We quantified tuberculosis mortality among individuals without HIV co-infection using 22 603 site-years of vital registration data, 1718 site-years of verbal autopsy data, 825 site-years of sample-based vital registration data, 680 site-years of mortality surveillance data, and 9 site-years of minimally invasive tissue sample (MITS) diagnoses data as inputs into the Cause of Death Ensemble modelling platform. Age-specific HIV and tuberculosis deaths were established with a population attributable fraction approach. We analysed all available population-based data sources, including prevalence surveys, annual case notifications, tuberculin surveys, and tuberculosis mortality, in DisMod-MR 2.1 to produce internally consistent age-specific estimates of tuberculosis incidence, prevalence, and mortality. We also estimated age-specific tuberculosis mortality without HIV co-infection that is attributable to the independent and combined effects of three risk factors (smoking, alcohol use, and diabetes). As a secondary analysis, we examined the potential impact of the COVID-19 pandemic on tuberculosis mortality without HIV co-infection by comparing expected tuberculosis deaths, modelled with trends in tuberculosis deaths from 2015 to 2019 in vital registration data, with observed tuberculosis deaths in 2020 and 2021 for countries with available cause-specific mortality data. We estimated 9·40 million (95% uncertainty interval [UI] 8·36 to 10·5) tuberculosis incident cases and 1·35 million (1·23 to 1·52) deaths due to tuberculosis in 2021. At the global level, the all-age tuberculosis incidence rate declined by 6·26% (5·27 to 7·25) between 2015 and 2020 (the WHO End TB strategy evaluation period). 15 of 204 countries achieved a 20% decrease in all-age tuberculosis incidence between 2015 and 2020, eight of which were in western sub-Saharan Africa. When stratified by age, global tuberculosis incidence rates decreased by 16·5% (14·8 to 18·4) in children younger than 5 years, 16·2% (14·2 to 17·9) in those aged 5–14 years, 6·29% (5·05 to 7·70) in those aged 15–49 years, 5·72% (4·02 to 7·39) in those aged 50–69 years, and 8·48% (6·74 to 10·4) in those aged 70 years and older, from 2015 to 2020. Global tuberculosis deaths decreased by 11·9% (5·77 to 17·0) from 2015 to 2020. 17 countries attained a 35% reduction in deaths due to tuberculosis between 2015 and 2020, most of which were in eastern Europe (six countries) and central Europe (four countries). There was variable progress by age: a 35·3% (26·7 to 41·7) decrease in tuberculosis deaths in children younger than 5 years, a 29·5% (25·5 to 34·1) decrease in those aged 5–14 years, a 15·2% (10·0 to 20·2) decrease in those aged 15–49 years, a 7·97% (0·472 to 14·1) decrease in those aged 50–69 years, and a 3·29% (–5·56 to 9·07) decrease in those aged 70 years and older. Removing the combined effects of the three attributable risk factors would have reduced the number of all-age tuberculosis deaths from 1·39 million (1·28 to 1·54) to 1·00 million (0·703 to 1·23) in 2020, representing a 36·5% (21·5 to 54·8) reduction in tuberculosis deaths compared to those observed in 2015. 41 countries were included in our analysis of the impact of the COVID-19 pandemic on tuberculosis deaths without HIV co-infection in 2020, and 20 countries were included in the analysis for 2021. In 2020, 50 900 (95% CI 49 700 to 52 400) deaths were expected across all ages, compared to an observed 45 500 deaths, corresponding to 5340 (4070 to 6920) fewer deaths; in 2021, 39 600 (38 300 to 41 100) deaths were expected across all ages compared to an observed 39 000 deaths, corresponding to 657 (–713 to 2180) fewer deaths. Despite accelerated progress in reducing the global burden of tuberculosis in the past decade, the world did not attain the first interim milestones of the WHO End TB Strategy in 2020. The pace of decline has been unequal with respect to age, with older adults (ie, those aged >50 years) having the slowest progress. As countries refine their national tuberculosis programmes and recalibrate for achieving the 2035 targets, they could consider learning from the strategies of countries that achieved the 2020 milestones, as well as consider targeted interventions to improve outcomes in older age groups. Bill & Melinda Gates Foundation.
### The risk of tuberculosis in children after close exposure: a systematic review and individual-participant meta-analysis
2020, Lancet Citation Excerpt :
Although preventive therapy and contact tracing are effective and have value in averting disease among children,3 most children are reached too late to prevent disease. Although cost-effectiveness analyses and implementation barriers should be assessed, earlier diagnosis of adult cases or community-wide screening approaches in children might be needed to improve prevention of tuberculosis in children.26 Third, we provide robust estimates of tuberculosis risk in children living with HIV infection or with a previous tuberculosis diagnosis. Show abstract Tens of millions of children are exposed to Mycobacterium tuberculosis globally every year; however, there are no contemporary estimates of the risk of developing tuberculosis in exposed children. The effectiveness of contact investigations and preventive therapy remains poorly understood. In this systematic review and meta-analysis, we investigated the development of tuberculosis in children closely exposed to a tuberculosis case and followed for incident disease. We restricted our search to cohort studies published between Jan 1, 1998, and April 6, 2018, in MEDLINE, Web of Science, BIOSIS, and Embase electronic databases. Individual-participant data and a pre-specified list of variables were requested from authors of all eligible studies. These included characteristics of the exposed child, the index case, and environmental characteristics. To be eligible for inclusion in the final analysis, a dataset needed to include: (1) individuals below 19 years of age; (2) follow-up for tuberculosis for a minimum of 6 months; (3) individuals with household or close exposure to an individual with tuberculosis; (4) information on the age and sex of the child; and (5) start and end follow-up dates. Studies assessing incident tuberculosis but without dates or time of follow-up were excluded. Our analysis had two primary aims: (1) estimating the risk of developing tuberculosis by time-period of follow-up, demographics (age, region), and clinical attributes (HIV, tuberculosis infection status, previous tuberculosis); and (2) estimating the effectiveness of preventive therapy and BCG vaccination on the risk of developing tuberculosis. We estimated the odds of prevalent tuberculosis with mixed-effects logistic models and estimated adjusted hazard ratios (HRs) for incident tuberculosis with mixed-effects Poisson regression models. The effectiveness of preventive therapy against incident tuberculosis was estimated through propensity score matching. The study protocol is registered with PROSPERO (CRD42018087022). In total, study groups from 46 cohort studies in 34 countries—29 (63%) prospective studies and 17 (37%) retrospective—agreed to share their data and were included in the final analysis. 137 647 tuberculosis-exposed children were evaluated at baseline and 130 512 children were followed for 429 538 person-years, during which 1299 prevalent and 999 incident tuberculosis cases were diagnosed. Children not receiving preventive therapy with a positive result for tuberculosis infection had significantly higher 2-year cumulative tuberculosis incidence than children with a negative result for tuberculosis infection, and this incidence was greatest among children below 5 years of age (19·0% [95% CI 8·4–37·4]). The effectiveness of preventive therapy was 63% (adjusted HR 0·37 [95% CI 0·30–0·47]) among all exposed children, and 91% (adjusted HR 0·09 [0·05–0·15]) among those with a positive result for tuberculosis infection. Among all children <5 years of age who developed tuberculosis, 83% were diagnosed within 90 days of the baseline visit. The risk of developing tuberculosis among exposed infants and young children is very high. Most cases occurred within weeks of contact investigation initiation and might not be preventable through prophylaxis. This suggests that alternative strategies for prevention are needed, such as earlier initiation of preventive therapy through rapid diagnosis of adult cases or community-wide screening approaches. National Institutes of Health.
### Challenges and controversies in childhood tuberculosis
2019, Lancet Show abstract Children bear a substantial burden of suffering when it comes to tuberculosis. Ironically, they are often left out of the scientific and public health advances that have led to important improvements in tuberculosis diagnosis, treatment, and prevention over the past decade. This Series paper describes some of the challenges and controversies in paediatric tuberculosis, including the epidemiology and treatment of tuberculosis in children. Two areas in which substantial challenges and controversies exist (ie, diagnosis and prevention) are explored in more detail. This Series paper also offers possible solutions for including children in all efforts to end tuberculosis, with a focus on ensuring that the proper financial and human resources are in place to best serve children exposed to, infected with, and sick from all forms of tuberculosis.
### The impact of COVID-19 on TB: A review of the data
2021, International Journal of Tuberculosis and Lung Disease
### The epidemiological importance of subclinical tuberculosis a critical reappraisal
2021, American Journal of Respiratory and Critical Care Medicine
### Duration of exposure among close contacts of patients with infectious tuberculosis and risk of latent tuberculosis infection
2020, Clinical Infectious Diseases
View all citing articles on Scopus
†
Contributed equally
View full text
© 2019 Elsevier Ltd. All rights reserved.
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1995 AIME Problems/Problem 13
Contents
[hide]
1 Problem
2 Solution
3 Solution 2
4 See also
Problem
Let be the integer closest to Find
Solution
When , . Thus there are values of for which . Expanding using the binomial theorem,
Thus, appears in the summation times, and the sum for each is then . From to , we get (either adding or using the sum of consecutive squares formula).
But this only accounts for terms, so we still have terms with . This adds to our summation, giving .
Solution 2
This is a pretty easy problem just to bash. Since the max number we can get is , we just need to test values for and . Then just do how many numbers there are times , which should be
See also
1995 AIME (Problems • Answer Key • Resources)
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Problem 12Followed by
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Inequality
The subject of mathematical inequalities is tied closely with optimization methods. While most of the subject of inequalities is often left out of the ordinary educational track, they are common in mathematics Olympiads.
Contents
[hide]
1 Overview
2 Solving Inequalities
2.1 Linear Inequalities
2.2 Polynomial Inequalities
2.3 Rational Inequalities
3 Complete Inequalities
4 List of Theorems
4.1 Introductory
4.2 Advanced
5 Problems
5.1 Introductory
5.2 Intermediate
5.3 Olympiad
6 Resources
6.1 Books
6.1.1 Intermediate
6.1.2 Olympiad
6.2 Articles
6.2.1 Olympiad
6.3 Classes
6.3.1 Olympiad
7 See also
Overview
Inequalities are arguably a branch of elementary algebra, and relate slightly to number theory. They deal with relations of variables denoted by four signs: .
For two numbers and :
if is greater than , that is, is positive.
if is smaller than , that is, is negative.
if is greater than or equal to , that is, is nonnegative.
if is less than or equal to , that is, is nonpositive.
Note that if and only if , , and vice versa. The same applies to the latter two signs: if and only if , , and vice versa.
Some properties of inequalities are:
If , then , where .
If , then , where .
If , then , where .
Solving Inequalities
In general, when solving inequalities, same quantities can be added or subtracted without changing the inequality sign, much like equations. However, when multiplying, dividing, or square rooting, we have to watch the sign. In particular, notice that although , we must have . In particular, when multiplying or dividing by negative quantities, we have to flip the sign. Complications can arise when the value multiplied can have varying signs depending on the variable.
We also have to be careful about the boundaries of the solutions. In the example , the value does not satisfy the inequality because the inequality is strict. However, in the example , the value satisfies the inequality because the inequality is nonstrict.
Solutions can be written in interval notation. Closed bounds use square brackets, while open bounds (and bounds at infinity) use parentheses. For instance, ![Image 49: $x \in 3,6)$ means .
Linear Inequalities
Linear inequalities can be solved much like linear equations to get implicit restrictions upon a variable. However, when multiplying/dividing both sides by negative numbers, we have to flip the sign.
Polynomial Inequalities
The first part of solving polynomial inequalities is much like solving polynomial equations -- bringing all the terms to one side and finding the roots.
Afterward, we have to consider bounds. We're comparing the sign of the polynomial with different inputs, so we could imagine a rough graph of the polynomial and how it passes through zeroes (since passing through zeroes could change the sign). Then we can find the appropriate bounds of the inequality.
Rational Inequalities
A more complex example is .
Here is a common mistake: The problem here is that we multiplied by as one of the last steps. We also kept the inequality sign in the same direction. However, we don't know if the quantity is negative or not; we can't assume that it is positive for all real . Thus, we may have to reverse the direction of the inequality sign if we are multiplying by a negative number. But, we don't know if the quantity is negative either.
A correct solution would be to move everything to the left side of the inequality, and form a common denominator. Then, it will be simple to find the solutions to the inequality by considering the sign (negativeness or positiveness) of the fraction as varies. We will start with an intuitive solution, and then a rule can be built for solving general fractional inequalities. To make things easier, we test positive integers. makes a good starting point, but does not solve the inequality. Nor does . Therefore, these two aren't solutions. Then we begin to test numbers such as , , and so on. All of these work. In fact, it's not difficult to see that the fraction will remain positive as gets larger and larger. But just where does , which causes a negative fraction at and , begin to cause a positive fraction? We can't just assume that is the switching point; this solution is not simply limited to integers. The numerator and denominator are big hints. Specifically, we examine that when (the numerator), then the fraction is , and begins to be positive for all higher values of . Solving the equation reveals that is the turning point. After more of this type of work, we realize that brings about division by , so it certainly isn't a solution. However, it also tells us that any value of that is less than brings about a fraction that has a negative numerator and denominator, resulting in a positive fraction and thus satisfying the inequality. No value between and (except itself) seems to be a solution. Therefore, we conclude that the solutions are the intervals ![Image 78: $(-\infty,-5)\cup\frac{3}{2},+\infty)$.
For the sake of better notation, define the "x-intercept" of a fractional inequality to be those values of that cause the numerator and/or the denominator to be .To develop a method for quicker solutions of fractional inequalities, we can simply consider the "x-intercepts" of the numerator and denominator. We graph them on the number line. Then, in every region of the number line, we test one point to see if the whole region is part of the solution. For example, in the example problem above, we see that we only had to test one value such as in the region , as well as one value in the region ![Image 83: $(-\infty,-5]$]( and ![Image 84: $\frac{3}{2},+\infty)$; then we see which regions are part of the solution set. This does indeed give the complete solution set.
One must be careful about the boundaries of the solutions. In the example problem, the value was a solution only because the inequality was nonstrict. Also, the value was not a solution because it would bring about division by . Similarly, any "x-intercept" of the numerator is a solution if and only if the inequality is nonstrict, and every "x-intercept" of the denominator is never a solution because we cannot divide by .
Complete Inequalities
A inequality that is true for all real numbers or for all positive numbers (or even for all complex numbers) is sometimes called a complete inequality. An example for real numbers is the so-called Trivial Inequality, which states that for any real , . Most inequalities of this type are only for positive numbers, and this type of inequality often has extremely clever problems and applications.
List of Theorems
Here are some of the more useful inequality theorems, as well as general inequality topics.
Introductory
Arithmetic Mean-Geometric Mean Inequality
Cauchy-Schwarz Inequality
Titu's Lemma
Chebyshev's Inequality
Geometric inequalities
Jensen's Inequality
Nesbitt's Inequality
Rearrangement Inequality
Power mean inequality
Triangle Inequality
Trivial inequality
Schur's Inequality
Advanced
Aczel's Inequality
Callebaut's Inequality
Carleman's Inequality
Hölder's inequality
Radon's Inequality
Homogenization
Isoperimetric inequalities
Maclaurin's Inequality
Muirhead's Inequality
Minkowski Inequality
Newton's Inequality
Ptolemy's Inequality
Can someone fix that Ptolemy's is in Advanced?
Problems
Introductory
Practice Problems on Alcumus
Inequalities (Prealgebra)
Solving Linear Inequalities (Algebra)
Quadratic Inequalities (Algebra)
Basic Rational Function Equations and Inequalities (Intermediate Algebra)
A tennis player computes her win ratio by dividing the number of matches she has won by the total number of matches she has played. At the start of a weekend, her win ratio is exactly . During the weekend, she plays four matches, winning three and losing one. At the end of the weekend, her win ratio is greater than . What's the largest number of matches she could've won before the weekend began? (1992 AIME Problems/Problem 3)
Intermediate
Practice Problems on Alcumus
Quadratic Inequalities (Algebra)
Advanced Rational Function Equations and Inequalities (Intermediate Algebra)
General Inequality Skills (Intermediate Algebra)
Advanced Inequalities (Intermediate Algebra)
Given that , and show that . (weblog_entry.php?t=172070 Source)
Olympiad
See also Category:Olympiad Inequality Problems
Let be positive real numbers. Prove that (2001 IMO Problems/Problem 2)
Resources
Books
Intermediate
Introduction to Inequalities
Geometric Inequalities
Olympiad
Advanced Olympiad Inequalities: Algebraic & Geometric Olympiad Inequalities by Alijadallah Belabess.
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189628 | https://www.youtube.com/watch?v=W7jYJTCjuko | Formulae for Permutation & Combination | Permutations and Combinations| Grade 11| Math| Khan Academy
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Posted: 17 Apr 2025
In this video, we look at the formula for permutations and combinations of r distinct objects out of n distinct objects. We look at a convenient way to find number of combinations. We then practice using the formulae and observe a few key results.
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! (
Timestamps:
0:00 Formula for permutations
1:55 Formula for combinations
3:05 A convenient way to find combinations
4:50 Practicing using the formula for combinations
6:50 Key observations and special results
8:00 Practicing using the formula for permutations
9:05 Key observations and special results
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Formula for permutations In the previous few videos, we've been solving problems of permutation and combination without explicitly using the formula. But let's dedicate this video to familiarize ourselves with the formula for both. Let's do this with an example. N A T U R E. Nature. It's a sixletter word. In how many ways can we make two letter words using the letters of the word nature? Here the repetition is not allowed. How do we do this? Well, we can do this in 6 5. That's 30 ways. The first letter can be picked in six ways. the next one in five. But if you have to write a formula for this, how do we go about it? We can say that this is equal to 6 5 4 3 2 1. Why stop at 5? We can go all the way to 1. Now we can divide this with 4 3 2 1 the product of these four numbers. So that's 6 factorial by 4 factorial. But we started with six letters in the word nature and we wanted to make a twoletter word. So let's try to find a formula with the numbers 6 and 2. We can do this by replacing four with 6 - 2. This is 6 factorial by 6 - 2 factorial. Now if you have to generalize in how many ways we can arrange our objects out of n given objects and we are assuming that all n objects are distinct. So how do we arrange our objects out of n objects? That's n factorial divided by n minus r factorial. And this is called the permutation of r objects out of n objects. And it's written as n p r. p stands for permutation. So the number of permutations of r objects out of n objects. That's equal to n factorial by n minus r factorial. What this formula gives is the number of ways to select and arrange r objects out of n. Here we are selecting and arranging two objects out of these six distinct objects. Now let's talk about selection only. In how Formula for combinations many ways can we select two distinct letters? So we have seen that we can figure this out by dividing select and arrange by arrange. So number of ways of selecting and arranging that's 6 factorial by 6 - 2 factorial. Now we divide this by number of ways of arranging two letters that's 2 factorial. So we divide this by 2 factorial. This gives us the number of ways of selecting two distinct letters out of these six letters. We can generalize this as well. We'll get the formula for combinations. This is denoted by N C R. C stands for combination. That's equal to N factorial by N minus R factorial. That's NPR. We divide this by R factorial. So there's an extra R factorial in the denominator. These are the number of ways of just selection. If we only select R objects out of N, this is what gives us the number of ways and these two are related. You can see that N CR the number of selections times R factorial number of ways of arranging each selection should give us the total number of arrangements that's NPR if you're selecting and arranging if you're doing both of them. So NCR R factorial that's equal to NPR. Now before we start A convenient way to find combinations practicing using these formula here's a convenient way to find NCR. If you look at NCR, the formula is n factorial by n - r factorial r factorial. Way too many factorials. We can simplify this. We can write n factorial as n n -1 n -2 and so on up to 1. Somewhere in this list there's n minus r as well. So we can write this n factorial as n n -1 n -2 dot dot till n minus r. And then we can continue from here n - r -1 -2 and so on up until 1. This is n factorial. Notice that this includes n minus r factorial. These terms in the blue, the product of these terms, that's n minus r factorial. That's in the denominator as well. So ncr is this numerator divided by n - r factorial r factorial. We can cancel this out. How many terms do we have in the numerator? Well, we're removing n minus r terms, which means we have r terms left in the numerator. So that's n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n minus one, n minus2 dot dot. we have r terms in the numerator divided by r terms in the denominator that's r factorial r1. So in both numerator and denominator we have r ter terms in the numerator we start with n and in the denominator we start with r. Now I personally use this version to figure out ncr and you can also see that this version resembles our select and arrange divided by arrange version. Here we are selecting and arranging the order matters. So the first letter can be picked in n ways. Then n minus 1, n minus2, so on. If we're selecting and arranging r, we have r ter terms in the numerator. And to arrange our terms, we have r factorial in the denominator. Now let's practice. We have 5 c2, 5 c 3, 5 Practicing using the formula for combinations c1, 5 c4. And we might as well find 5 c 0 and 5 c5. So let's figure these six out. Pause the video. Try them out. Okay. So 5 C2 that's selecting two things out of five. Select and arrange two things out of five that's 5 4. Divide by number of ways to arrange two that's 2 1 2 factorial. We can see that we have two terms in the numerator and two in the denominator. The numerator starts with 5 and the denominator starts with 2. 5 4 is 20 by 2 is 10. So this gives us 10. 5 C2 is equal to 10. 5 C3 three terms in the numerator three in the denominator this starts with five this starts with three 5 4 3 by 3 2 1 3 cancels out 2 cancels out with four we have 5 2 that's 10 both of these are 10 let's continue 5 C1 this means selecting one out of five that's five ways and we can see that this is 5 / 1 one term in the numerator one in the denominator this starts with five this starts with one 5 by 1 that's five ways. So number of ways of selecting four out of five that's 5 4 3 2 4 terms here divided by 4 3 2 1 four terms here 4 3 and 2 all cancel out we're left with just five so this is also equal to five let's skip this one for now what about 55 selecting all five things out of five well that can be done in only one way you select all of them and the formula also gives us the same five terms in the numerator and five in the denominator everything cancels out we're left with one. Now what about 5 C 0? In how many ways can we select 0 out of five? Now math says that this is equal to 1. Let's also use the formula to get that. This is 5 factorial by 5 - 0 factorial 0 factorial. Now 0 factorial is 1. 5 factorial cancels out. This is 1 by 1. Key observations and special results That's equal to 1. Now let's take note of some observations. There's one way of selecting nothing and there's one way of selecting everything. In general, we can say that n c0 is equal to n cn is equal to one. Both of them are equal to one. So if you have n distinct objects and you want to select all of them or if you want to select none of them, each of these tasks can be done in one way. Now there's one more observation. Notice that this is 10 and this is also 10. This is five. This is also five. Can you figure out the next observation? Here's what it is. Number of ways of selecting r things is same as number of ways of selecting n minus r things. Think about it. If there are five pens on the table and you select two and put them in your hand, this is exactly same as if there are five pens in your hand and you put down three on the table. This means both of them can be done in the same number of ways. Similarly, picking one pen out of five on the table is same as putting down four pens on the table out of five in your hand. In general, you have nr equals to n c n minus r. Now, let's also practice permutations. Here's the list. Practicing using the formula for permutations 5 p2, 5p 3, 5p1, 5p4, 5p 0, and 5p5. Pause the video. Try figuring these out. Okay. In permutations, the order matters. We're selecting and arranging. So selecting and arranging two out of five that's five 4. The first one can be picked in five ways. The second one can be picked in four. Here the order matters. 5 4 is 20. 5 P3 that's 5 4 3. That's 60. 5 P1 is just 5. 5 P 4 is 5 4 3 2. Four terms here. So that's 5 2 10. 4 3 is 12. That's 120. What about 5 P5? That's selecting and arranging all five. That can be done in 5 4 3 2 1 or 5 factorial ways. That's also 120. Now what about 5 P 0? In how many ways can we select and arrange 0 out of five? Now math tells us that this is equal to 1. The formula also gives us the same 5 P 0 that's 5 factorial by 5 minus 0 that's also 5 factorial. Both of these cancel out we get 1. So there's Key observations and special results one way of arranging nothing. There are n factorial ways of arranging everything. If you write this down, we have np0 that's equal to 1. npn that's always equal to n factorial. And there's also a connection between number of permutations and combinations. 5 c2 is 10. And we can multiply 10 with 2 factorial to get 20. That's 5 p2. Number of ways of arranging r things out of n. That's equal to number of ways of selecting r things times number of ways of arranging those r things. So this npr that's equal to ncr r factorial. |
189629 | https://www.sciencedirect.com/topics/mathematics/polar-axis | Polar Axis - an overview | ScienceDirect Topics
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Polar Axis
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The polar axis is defined as the reference line in polar coordinates from which angles are measured, typically aligned with the positive x-axis in Cartesian coordinates, allowing for the representation of points as (θ, r).
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Chapter
Multiple integrals in mechanical engineering
2020, Calculus for Engineering StudentsDeolinda M.L. Dias Rasteiro, ... Pablo Rodríguez-Gonzálvez
Polar coordinates and their relation with Cartesian coordinates
Observe Fig. 7.4. To define the position of a point P using polar coordinates it is necessary to consider:
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Figure 7.4. Polar representation.
•
a point O called the origin;
•
a line that starts at O and will be called polar axis.
The position, in polar coordinates, of P will be defined by the pair (ρ,θ), where ρ is the distance between O and P and θ is the angle formed by the polar axis and O˙P. By convention the polar coordinates of O are (0,θ). See Fig. 7.5.
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Figure 7.5. Polar and Cartesian coordinates.
Considering both system coordinates and letting the x-axis coincide with the polar axis we can deduce the following relations:
If (x,y) are the Cartesian coordinates of the point P at the referential XOY, then its polar coordinates in the polar system can be given using the following equalities:
ρ 2=x 2+y 2,tan(θ)=y x.
If (ρ,θ) are the polar coordinates P, then the Cartesian coordinates of P are
{x=ρ cosθ,y=ρ sinθ.
Remark
To change from Cartesian coordinates to polar coordinates one must have in consideration to which quadrant the point P belongs.
In a system of polar coordinates ρ=f(θ) represents a curve.
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Book 2020, Calculus for Engineering StudentsDeolinda M.L. Dias Rasteiro, ... Pablo Rodríguez-Gonzálvez
Chapter
Plotting in MATLAB®
2021, Programming Mathematics Using MATLAB®Lisa A. Oberbroeckling
3.6.2 Polar curves
We can plot polar equations as parametric equations using the conversion equations. Notice in Fig. 3.19(A) that the curve appears somewhat jagged. This is because we are connecting only 100 points for the curve. We can create a smoother curve, by increasing the number of points in our
command. Fig. 3.19(B) was created by defining .
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Figure 3.19. Polar curves. (A) Default
, (B) 300 elements.
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Instead of using the conversion equations, one can have MATLAB do the conversion using the command
. You can have a polar axis with the command (see Fig. 3.20). This command wants values for θ and r in polar coordinates. Note that the command is no longer advised to use.
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Figure 3.20. Polar curves. (A) With
(A) and (B) with .
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Book 2021, Programming Mathematics Using MATLAB®Lisa A. Oberbroeckling
Chapter
Multidimensional Problems
2014, Mathematics for Physical Science and EngineeringFrank E. Harris
Spherical Polar Coordinates
In spherical polar coordinates, the coordinates are r,θ,φ, where r is the distance from the origin, θ is the angle from the polar direction (on the Earth, colatitude, which is 90°- latitude), and φ the azimuthal angle (longitude). It is customary to align the polar direction with the Cartesian coordinatez and to measure φ from a zero (our Greenwich meridian) along the +x direction, with the direction of φ such that the +y direction is at φ=π/2 (90°). Therefore, points with a given value of r lie on a sphere of radius r centered at the origin and points of given θ lie on a cone with vertex at the origin, axis in the z direction and an opening angle of rotationθ. Points of given φ lie on a half-plane which extends from the polar axis to infinity in the direction given by φ. In order for coordinate sets and arbitrary spatial points to be unambiguously related, we need to restrict the range of r to 0≤r<∞, with θ in the range 0≤θ≤π and φ within 0≤φ<2 π. See Fig. 6.3.
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Figure 6.3. Spherical polar coordinates r,θ,φ.
The equations connecting the two sets of coordinates are
(6.16)3 x=r sin θ cos φ,r=x 2+y 2+z 2,y=r sin θ sin φ,cos θ=z x 2+y 2+z 2,z=r cos θ,tan φ=y x.
Notice that Eq. (6.16) gives formulas for cos θ and tan φ rather than for θ and φ. When we convert cos θ into θ we must use the principal value of the cos-1 function so as to obtain a result within the range 0≤θ≤π. For φ we must be even more careful, as the range for the principal value of tan-1 y/x is only of length π, while the range of φ is of length 2 π. We must choose the value of φ that is in the azimuthal quadrant consistent with the individual signs of x and y.
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Book 2014, Mathematics for Physical Science and EngineeringFrank E. Harris
Chapter
Vector Analysis
2013, Mathematical Methods for Physicists (Seventh Edition)George B. Arfken, ... Frank E. Harris
Spherical Polar Coordinates
Spherical polar coordinates were introduced as an initial example of a curvilinear coordinate system, and were illustrated in Fig. 3.19. We reiterate: The coordinates are labeled (r, θ, φ). Their ranges are
0≤r<∞,0≤θ≤π,0≤φ<2 π.
For r = 0, neither θ nor φ is well defined. Additionally, φ is ill-defined for θ = 0 and θ = π. The coordinate surfaces follow:
1
Concentric spheres centered at the origin,
r=(x 2+y 2+z 2)1/2=constant.
2
Right circular cones centered on the z (polar) axis with vertices at the origin,
θ=arccos z r= constant.
3
Half-planes through the z (polar) axis, at an angle φ measured from the x direction,
φ=arctan y x= constant.
The arctangent is double valued on the range of φ, and the correct value of φ must be determined by the individual signs of x and y.
Inverting the preceding equations, we can obtain
(3.152)x=r sin θ cos φ,y=r sin θ sin φ,z=r cos θ.
The coordinate vector r and a general vector V are expressed as
r=r e^r,V=V r e^r+V θ e^θ+V φ e^φ.
From Eq. (3.131), the scale factors for these coordinates are
(3.153)h r=1,h θ=r,h φ=r sin θ,
so the elements of displacement, area, and volume are
(3.154)d r=e^r d r+r e^θ d θ+r sin θ e^φ d φ,d σ=r 2 sin θ e^r d θ d φ+r sin θ e^θ d r d φ+r e^φ d r d θ,d τ=r 2 sin θ d ρ d θ d φ.
Frequently one encounters a need to perform a surface integration over the angles, in which case the angular dependence of dσ reduces to
(3.155)d Ω=sin θ d θ d φ,
where d Ω is called an element of solid angle, and has the property that its integral over all angles has the value
∫d Ω=4 π.
Note that for spherical polar coordinates, all three of the unit vectors have directions that depend on position, and this fact must be taken into account when expressions containing the unit vectors are differentiated.
The vector differential operators may now be evaluated, using Eqs. (3.138), (3.141), (3.142), and (3.143):
(3.156)∇ψ(r,θ,φ)=e^r∂ψ∂r+e^θ 1 r∂ψ∂θ+e^φ 1 r sin θ∂ψ∂φ,
(3.157)∇⋅V=1 r 2 sin θ sin θ∂∂r(r 2 V r)+r∂∂θ(sin θ V θ)+r∂V φ∂φ,
(3.158)∇2 ψ=1 r 2 sin θ sin θ∂∂r r 2∂ψ∂r+∂∂θ sin θ∂ψ∂θ+1 sin θ∂2 ψ∂φ 2,
(3.159)∇×V=1 r 2 sin θ e^r r e^θ r sin θ e^φ∂∂r∂∂θ∂∂φ V r r V θ r sin θ V φ.
Finally, again using Eq. (3.70), the components of the vector Laplacian∇2V in spherical polar coordinates can be shown to be
(3.160)∇2 V r=∇2 V r−2 r 2 V r−2 r 2 cot θ V θ−2 r 2∂V θ∂θ−2 r 2 sin θ∂V φ∂φ,∇2 V θ=∇2 V θ−1 r 2 sin 2 θ V θ+2 r 2∂V r∂θ−2 cos θ r 2 sin 2 θ∂V φ∂φ,∇2 V φ=∇2 V φ−1 r 2 sin 2 θ V φ+2 r 2 sin θ∂V r∂φ+2 cos θ r 2 sin 2 θ∂V φ∂φ.
Example 3.10.3
∇, ∇ ⋅, ∇ × for a Central Force
We can now easily derive some of the results previously obtained more laboriously in Cartesian coordinates:
From Eq. (3.156),
(3.161)∇f(r)=e^r d f d r,∇r n=e^r n r n−1.
Specializing to the Coulomb potential of a point charge at the origin, V = Ze/(4 π ε 0 r), so the electric field has the expected value E=−∇V=(Z e/4 π ε 0 r 2)e^r.
Taking next the divergence of a radial function, we have from Eq. (3.157),
(3.162)∇⋅e^r f(r)=2 r f(r)+d f d r,∇⋅(e^r r n)=(n+2)r n−1.
Specializing the above to the Coulomb force (n = −2), we have (except for r = 0) ∇ ⋅ r−2 = 0, which is consistent with Gauss' law.
Continuing now to the Laplacian, from Eq. (3.158) we have
(3.163)∇2 f(r)=2 r d f d r+d 2 f d r 2,∇2 r n=n(n+1)r n−2,
in contrast to the ordinary second derivative of r n involving n − 1.
Finally, from Eq. (3.159),
(3.164)∇×(e^r f(r))=0,
which confirms that central forces are irrotational.
Example 3.10.4
Magnetic Vector Potential
A single current loop in the xy-plane has a vector potential A that is a function only of r and θ, is entirely in the e^φ direction and is related to the current densityJ by the equation
μ 0 J=∇×B=∇×[∇×e^φ A φ(r,θ)].
In spherical polar coordinates this reduces to
μ 0 J=∇×1 r 2 sin θ e^r r e^θ r sin θ e^φ∂∂r∂∂θ∂∂φ 0 0 r sin θ A φ=∇×1 r 2 sin θ e^r∂∂θ(r sin θ A φ)−r e^θ∂∂r(r sin θ A φ).
Taking the curl a second time, we obtain
μ 0 J=1 r 2 sin θ e^r r e^θ r sin θ e^φ∂∂r∂∂θ∂∂φ 1 r sin θ∂∂θ(sin θ A φ)−1 r∂∂r(r A φ)0.
Expanding this determinant from the top down, we reach
(3.165)μ 0 J=−e^φ∂2 A φ∂r 2+2 r∂A φ∂r+1 r 2 sin θ∂∂θ sin θ∂A φ∂θ−1 r 2 sin 2 θ A φ.
Note that we get, in addition to ∇2 A φ, one more term: −A φ/r 2 sin 2 θ.
Example 3.10.5
Stokes' Theorem
As a final example, let's compute ∮B⋅d r for a closed loop, comparing the result with integrals ∫(∇×B)⋅d σ for two different surfaces having the same perimeter. We use spherical polar coordinates, taking B=e−r e^φ.
The loop will be a unit circle about the origin in the xy-plane; the line integral about it will be taken in a counterclockwise sense as viewed from positive z, so the normal to the surfaces it bounds will pass through the xy-plane in the direction of positive z. The surfaces we consider are (1) a circular disk bounded by the loop, and (3) a hemisphere bounded by the loop, with its surface in the region z< 0. See Fig. 3.24.
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Figure 3.24. Surfaces for Example 3.10.5: (left) S 1, disk; (right) S 2, hemisphere.
For the line integral, d r=r sin θ e^φ d φ, which reduces to d r=e^φ d φ since θ = π/2 and r = 1 on the entire loop. We then have
∮B⋅d r=∫φ=0 2 π e−1 e^φ⋅e^φ d φ=2 π e.
For the surface integrals, we need ∇ × B:
∇×B=1 r 2 sin θ∂∂θ(r sin θ e−r)e^r−r∂∂r(r sin θ e−r)e^θ=e−r cos θ r sin θ e^r−(1−r)e−r e^θ.
Taking first the disk, at all points of which θ = π/2, with integration range 0 ≤ r ≤ 1, and 0 ≤ φ< 2 π, we note that d σ=−e^θ r sin θ d r d φ=−e^θ r d r d φ. The minus sign arises because the positive normal is in the direction of decreasingθ. Then,
∫S 1−(∇×B)⋅e^θ r d r d φ=∫0 2 π d φ∫0 1 d r(1−r)e−r=2 π e.
For the hemisphere, defined by r = 1, π/2 ≤ θ<π, and 0 ≤ φ< 2 π, we have d σ=−e^r r 2 sin θ d θ d φ=−e^r sin θ d θ d φ (the normal is in the direction of decreasing r), and
∫S 2−(∇×B)⋅e^r sin θ d θ d φ=−∫π/2 π d θ e−1 cos θ∫0 2 π d φ=2 π e.
The results for both surfaces agree with that from the line integral of their common perimeter. Because ∇ × B is solenoidal, all the flux that passes through the disk in the xy-plane must continue through the hemispherical surface, and for that matter, through any surface with the same perimeter. That is why Stokes' theorem is indifferent to features of the surface other than its perimeter.
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Book 2013, Mathematical Methods for Physicists (Seventh Edition)George B. Arfken, ... Frank E. Harris
Chapter
Theory of Colloid and Interfacial Electric Phenomena
2006, Interface Science and Technology
2.Fundamental Equations
Consider a dilute suspension of identical spherical particles of radius a in a general electrolyte solution of volume V under an applied electric fieldE. Each particle moves with a velocity U. The origin of the spherical coordinate system(r,θ,φ) is held fixed at the center of one particle. The polar axis(θ≃0) is set parallel to E. Let the electrolyte be composed of N ionic mobile species of valence z i and drag coefficientλ i(i=1,2,⋯,N), and n∞ be the concentration (number density) of the i th ionic species in the electrolyte solution. The fundamental electrokinetic equations for the flow velocityu(r)=(u r,u θ,u φ) of the liquid at position r and that of the i th mobile ionic species v i(r) are the same as those for the electrophoresis problem developed in Chapter 3.
We consider the case where the applied field E is small so that we may assume that the electrical double layer around the particle is only slightly distorted due to the applied electric fieldE. Then we may express the electric potential ψ(r) at position r, the electrochemical potentialμ i(r) and the concentration (the number density) n i(r) of the i th ionic species, and the charge density ρ el(r) resulting from the mobile charged ionic species as
(5.1)ψ(r)=ψ(0)(r)+δ ψ(r)
(5.2)μ i(r)=μ i(0)(r)+δ μ i(r)
(5.3)n i(r)=n i(0)(r)+δ n i(r)
(5.4)ρ el(r)=ρ el(0)(r)+δ ρ el(r)
(5.5)ρ el(r)=∑i=1 N z i e n i(r)
where the quantities with superscript (0) refer to those at equilibrium, i.e., in the absence of E and δ ψ,δ μ i,δ n i, and δ ρ e l el are perturbation quantities. The ratio U/E (where U = |U| and E = |E|) is the electrophoretic mobility of the particles. As in Chapter 3, we can express u(r) and δ μ i(r) as
(5.6)u(r)=(u r,u θ,u φ)=(−2 r h E cos θ,1 r d d r(r h)E sin θ,0)
(5.7)δ μ i(r)=−z i e φ i(r)E cos θ,
where h(r) and φ i(r) are given by Eqs. (3.90) and (3.91), viz.,
(5.8)h(r)=∫a∞{-r 3 30+a 2 r 18-a 5 45 r 2+(r 9 a-1 6+a 2 18 r 2)x 3}G(x)d x+∫a r(r 3 30-r x 2 6+x 3 6-x 5 30 r 2)G(x)d x
(5.9)φ i(r)=r+a 3 2 r 2-1 3(r+a 3 2 r 2)∫a b d y d x(z i d φ i d x-2 λ i e h x)d x+1 3∫a r(r-x 3 r 2)d y d x(z i d φ i d x-2 λ i e h x)d x,
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Book series2006, Interface Science and Technology
Chapter
Multidimensional Problems
2014, Mathematics for Physical Science and EngineeringFrank E. Harris
6.3 Curvilinear Coordinate Systems
Cartesian coordinate systems have two great virtues: (1) they are uniform, with the local geometry identical at all points, and (2) they are orthogonal; in two dimensions, the lines of constant x are perpendicular to the lines of constant y. In three dimensions, the points of constant x are planes; they intersect the planes of constant y or constant z at right angles.
Despite these obvious advantages, many problems in physics are handled advan-tageously in other coordinate systems that may reflect some symmetry of the physical system under study. For example, the electric field of a point charge can be expected to take a simple form in a spherical polar coordinate system when the point charge is placed at the coordinate origin. The electrodynamics of a signal in a coaxial cable will be most easily treated in a circular cylindrical coordinate system. Before the widespread deployment of digital computers, still other coordinate systems were frequently introduced for the study of specific problems. Though the proliferation of computers has in recent years reduced the need to use exotic coordinate systems, the use of spherical polar and cylindrical coordinates remains important in physics.
Although the lines of constant coordinate values in curvilinear coordinates may not always be straight lines, it may still be that they intersect at right angles. See, for example, the diagram for 2-D polar coordinates, Fig. 6.2. Here the lines of constant r, though circles, cross the lines of constant θ at right angles, and for this reason the polar coordinates are identified as an orthogonal coordinate system. The orthogonality is most important when one discusses the behavior in the neighborhood of a coordinate point; the infinitesimal displacements that define derivatives in the different coordinate directions are orthogonal (and more independent than if that were not the case). Because of their usefulness and relative simplicity, we restrict further discussion here to the two orthogonal curvilinear systems that are used most frequently in physics and engineering.
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Figure 6.2. Plane polar coordinates r,θ.
Spherical Polar Coordinates
In spherical polar coordinates, the coordinates are r,θ,φ, where r is the distance from the origin, θ is the angle from the polar direction (on the Earth, colatitude, which is 90°- latitude), and φ the azimuthal angle (longitude). It is customary to align the polar direction with the Cartesian coordinatez and to measure φ from a zero (our Greenwich meridian) along the +x direction, with the direction of φ such that the +y direction is at φ=π/2 (90°). Therefore, points with a given value of r lie on a sphere of radius r centered at the origin and points of given θ lie on a cone with vertex at the origin, axis in the z direction and an opening angle of rotationθ. Points of given φ lie on a half-plane which extends from the polar axis to infinity in the direction given by φ. In order for coordinate sets and arbitrary spatial points to be unambiguously related, we need to restrict the range of r to 0≤r<∞, with θ in the range 0≤θ≤π and φ within 0≤φ<2 π. See Fig. 6.3.
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Figure 6.3. Spherical polar coordinates r,θ,φ.
The equations connecting the two sets of coordinates are
(6.16)3 x=r sin θ cos φ,r=x 2+y 2+z 2,y=r sin θ sin φ,cos θ=z x 2+y 2+z 2,z=r cos θ,tan φ=y x.
Notice that Eq. (6.16) gives formulas for cos θ and tan φ rather than for θ and φ. When we convert cos θ into θ we must use the principal value of the cos-1 function so as to obtain a result within the range 0≤θ≤π. For φ we must be even more careful, as the range for the principal value of tan-1 y/x is only of length π, while the range of φ is of length 2 π. We must choose the value of φ that is in the azimuthal quadrant consistent with the individual signs of x and y.
Circular Cylindrical Coordinates
Circular cylindrical coordinates use the plane polar coordinates ρ and φ (in place of x and y) and the z Cartesian coordinate. The variable ρ is the distance of a coordinate point from the z Cartesian axis, and φ is its azimuthal angle. The ranges of these coordinates are 0≤ρ<∞,0≤φ<2 π, and of course -∞<z<∞. Thus, points of given ρ lie on a cylinder about the z axis of radius ρ, points of given φ lie on a half-plane extending from the entire z axis to infinity in the φ direction, and points of given z lie on the plane with that value of z. See Fig. 6.4.
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Figure 6.4. Circular cylindrical coordinates ρ,φ,z.
The conversion formulas between circular cylindrical and Cartesian coordinates are
(6.17)3 x=ρ cos φ,ρ=x 2+y 2,y=ρ sin φ,tan φ=y x,z=z,z=z.
The coordinate φ has the same definition as for spherical polar coordinates, and, just as there, it must be identified as the value of tan-1 y/x consistent with the individual signs of x and y. We have used ρ (not r) as the coordinate denoting distance from the z axis; we are reserving r to always mean distance from the origin and will reserve ρ for the axial distance defined here.
Vectors in Curvilinear Coordinates
In Cartesian coordinates, a unit vector e ˆ x is of unit length and in the x direction. That is simple and straightforward because the “x direction” is everywhere the same direction. However, in spherical polar coordinates the “r direction” is surely not the same everywhere and we need to define it unambiguously. Because the direction associated with the change in a coordinate may depend upon the value of it (and the other coordinates), it is most useful to define the “r direction” and other directions as those generated by infinitesimal changes in the coordinate values.
Our definition of the “r direction” is that of a vector from (r,θ,φ) to (r+dr,θ,φ). The unit vector r ˆ or e ˆ r is then a vector in the “r direction” and of unit length.
Continuing with spherical polar coordinates, we now wish to consider a unit vector in the θ direction. This direction is that of an infinitesimal vector from (r,θ,φ) to (r,θ+d θ,φ), and it (and the corresponding unit vector θ ˆ or e ˆ θ) will be perpendicular to the unit vector r ˆ. The third unit vector, φ ˆ or e ˆ φ, will be perpendicular to r ˆ and θ ˆ, so our spherical polar coordinate system is orthogonal.
Observations similar to those of the preceding paragraph indicate that circular cylindrical coordinates also form an orthogonal system. The orthogonality is also apparent from drawings showing the intersections of contours of constant coordinate values.
The unit vectors can be used to decompose vectors into their components in curvilinear systems. However, it is important to notice that vector components cannot be combined (either for addition or for forming dot products) unless the vectors are associated with the same point in space. Violation of this rule would cause the same unit-vector symbol to have different meanings at different occurrences in a single expression, thereby surely causing errors.
If two vectors A and B are indeed associated with the same spatial point, then (using spherical polar coordinates as an example), they have respective component decompositions
A=A r r ˆ+A θ θ ˆ+A φ φ ˆ,B=B r r ˆ+B θ θ ˆ+B φ φ ˆ,
and (adding components)
A+B=(A r+B r)r ˆ+(A θ+B θ)θ ˆ+(A φ+B φ)φ ˆ.
Rewriting the above in a general notation in which A i refers to the component of A in the direction of the unit vector e ˆ i, we have
(6.18)A+B=(A 1+B 1)e ˆ 1+(A 2+B 2)e ˆ 2+(A 3+B 3)e ˆ 3.
Since we have restricted the discussion to orthogonal coordinate systems, we have
(6.19)e ˆ i·e ˆ j=δ ij,
and it is straightforward to compute the dot product A·B:
(6.20)A·B=(A 1 e ˆ 1+A 2 e ˆ 2+A 3 e ˆ 3)·(B 1 e ˆ 1+B 2 e ˆ 2+B 3 e ˆ 3)=A 1 B 1+A 2 B 2+A 3 B 3.
This is the same as the formula that applies in Cartesian coordinates.
Displacements in Curvilinear Coordinates
Here there are significant differences from Cartesian systems. In spherical polar coordinates, a unit change in the coordinate r produces a unit displacement (change in position) of a point, but a unit change in the coordinate θ produces a displacement whose magnitude depends upon the current value of r and (because the displacement is the chord of a circular arc and not the arc-length itself) the displacement is not even linear in the change in θ. Similar remarks apply to the displacement produced by a change in the coordinate φ, which depends on the current values of both r and θ. (This is so because the quantity controlling the relation between displacement and d φ is ρ, which is r sin θ.) We therefore choose to focus attention on the properties of infinitesimal displacements and their relations to the corresponding infinitesimal changes in the coordinate values.
An infinitesimal displacement specified by dx,dy,dz or alternatively given in terms of general curvilinear but orthogonal coordinates q 1,q 2,q 3 can be written
d r=x ˆ dx+y ˆ dy+z ˆ dz=h 1 q ˆ 1 dq 1+h 2 q ˆ 2 dq 2+h 3 q ˆ 3 dq 3.
The quantities h i are sometimes called scale factors, and are needed because a unit change in q i does not necessarily produce a unit change in displacement.
There are general methods for finding the scale factors from the equations defining the q i, but in the cases of interest here, the h i can be obtained easily. Taking cylindrical coordinates as our first example, we note that a change d ρ in ρ causes a displacement d ρ, so h ρ=1. However, if φ is changed an amount d φ, the result is a displacement (in the φ ˆ direction) of amount ρ d φ, showing that h φ=ρ. Finally, we have h z=1.
In spherical polar coordinates, h r=1, and h φ, which has the same meaning as in cylindrical coordinates, has the value h φ=ρ; if we express ρ in the spherical coordinates we get h φ=r sin θ. Finally, we note that h θ=r.
Summarizing, the above discussion corresponds to
(6.21)d r=r ˆ dr+r θ ˆ d θ+r sin θ φ ˆ d φ,spherical polar,
(6.22)=ρ ˆ d ρ+ρ φ ˆ d φ+z ˆ dz,cylindrical,
and for future use we list the scale factors explicitly:
(6.23)Spherical:h r=1,h θ=r,h φ=r sin θ;Cylindrical:h ρ=h z=1,h φ=ρ.
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Book 2014, Mathematics for Physical Science and EngineeringFrank E. Harris
Chapter
SUN–EARTH ASTRONOMICAL RELATIONSHIPS
1983, An Introduction to Solar RadiationMuhammad Iqbal
Publisher Summary
This chapter discusses the motion of the earth around sun and around its polar axis, the angle between the earth's equator and the plane containing the sun–earth orbital system. It presents the trigonometric equations relating the position of the sun to a horizontal or an inclined surface. The chapter focuses on the relevant astronomical relationships that do not require a prior knowledge of solar radiation. The earth revolves around the sun in an elliptical orbit with the sun at one of the foci. The amount of solar radiation reaching the earth is inversely proportional to the square of its distance from the sun. Solar time is based on the rotation of the earth about its polar axis and on its revolution around the sun. A solar day is the interval of time as the sun appears to complete one cycle about a stationary observer on earth. The solar day varies in length through the year. The chapter presents an overview of the calculation of the sun–earth distance, declination, and the equation of time.
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Book 1983, An Introduction to Solar RadiationMuhammad Iqbal
Chapter
Modern Astrodynamics
2006, Elsevier Astrodynamics SeriesCOLIN R. MCINNES, MATTHEW P. CARTMELL
7.5.2 Polar observer mission
It has been seen in Section 7.4 that solar sails may be used to generate artificial equilibrium solutions in the Sun–Earth three-body system. While in-plane equilibria have applications for missions such as Geostorm, out-of-plane equilibria may be utilised for continual, low-resolution imaging of the high latitude regions of the Earth. In fact, if the artificial Lagrange point is located high enough above or below the ecliptic plane, the solar sail may be stationed directly over the north pole, or indeed the south pole, during the summer solstice [24, 6]. The solar sail can be stationed directly over the north pole at the summer solstice, as shown in Figure 7.10, but will not remain over the pole during the entire year due to the tilt of the polar axis. From this unique vantage point a constant daylight view of the north pole is available at the summer solstice, however six months later at the winter solstice the polar regions are in permanent darkness. The volume of space accessible above L 1 is shown in Figure 7.11, along with the optimum Polar Observer mission design point. It is found that the required solar sail performance can be minimized by an appropriate selection of polar altitude. It can be shown that an equilibrium location some 3.8 million km (596 Earth radii) above the north pole will minimize demands on the solar sail performance. Closer equilibrium locations are possible using larger, or higher performance solar sails, or indeed selecting a less demanding viewing geometry.
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Fig. 7.10. Polar Observer mission concept.
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Fig. 7.11. Volume of space accessible out of ecliptic plane for sail loadings 12–17 gm−2.
Although the distance of the solar sail from the Earth is large for imaging purposes, there are potential applications for real-time, low-resolution images for continuous views of large scale polar weather systems along with Arctic ice and cloud coverage for global climate studies. Although such images can be acquired by assembling a mosaic of instrument swaths from a conventional polar orbiting satellite, many high latitude passes are required to form a complete image. High resolution is then possible, but the completed image is not acquired in real-time and so dynamic phenomena cannot be captured.
For a 30 cm aperture instrument stationed 3.8 million km from the Earth and operating at optical wavelengths, a minimum ground resolution of order 10 km is possible, which is suitable for synoptic imaging. In practice though, the actual resolution obtained will be degraded due to factors such as the pointing stability of the camera. Higher resolution is possible if an equilibrium location closer to the pole is selected, at the expense of increased demands on the solar sail performance. Other applications of these orbits include line-of-sight, low-bandwidth communications to high-latitude users, such as Arctic or Antarctic stations. Applications for continuous data links to Mars polar landers and surface rovers have also been explored for a solar sail stationed high above the poles of Mars. Again, the Polar Observer mission makes excellent use of solar sailing by delivering an extremely high effective specific impulse for a multi-year mission duration.
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Book series2006, Elsevier Astrodynamics SeriesCOLIN R. MCINNES, MATTHEW P. CARTMELL
Chapter
Theory of Colloid and Interfacial Electric Phenomena
2006, Interface Science and Technology
2.Basic Equations
Consider a spherical colloidal particle of radius a falling steadily with a velocity U SED (sedimentation velocity) in a liquid containing a general electrolyte in a gravitational fieldg. The origin of the spherical coordinate system (r, θ, φ) is held fixed at the center of the particle. The polar axis (θ = 0) is set parallel to g. Let the electrolyte be composed of N onic mobile species of valence z i and drag coefficient λ i(i=1,2,⋯,N), and n i∞ be the concentration (number density) of the i th ionic species in the electrolyte solution.
For the sedimentation problem, the Navier-Stokes equation (3.8) for the flow velocityu(r)=(u r,u θ,u φ) of the liquid at position r is replaced by
(6.1)η∇×∇×u+∇p+ρ el∇ψ−ρ o g=0.
which includes the body force ρ o g. In Eq. (6.1) ρ o is the mass density of the liquid. The other fundamental equations are given by the same as those for electroporesis, i.e., Eqs. (3.9)–(3.14).
The boundary conditions are the same as those for electrophoresis (Eqs. (3.20), (3.21), and (3.26)), viz.,
(6.2)u=0 at r=a
(6.3)u→−U S E D as r→∞
(6.4)v i·n|r=a+=0
Equation (6.2) corresponds to the assumption that the slipping plane (at which the liquid velocity u(r) relative to the particle becomes zero) coincide with the particle surface at r = a and Eq. (6.4) states that no ionic species can penetrate the particle surface. In addition to these boundary conditions, we must satisfy the constraint that in the stationary state the net force acting on the particle or an arbitrary volume enclosing the particle must be zero (this condition is given by Eq. (3.22) for the electrophoresis problem). Consider a large sphere S of radius r containing the particle (plus the electrical double layer around the particle) at its center. The radius r of S is taken to be sufficiently large so that the net electric charge within S is zero. There is then no electric force acting on S, and we need consider only hydrodynamic forceFH and the gravitational force Fg which must be zero,
(6.5)F g+F H=0.
The gravitational force Fg acting on the particle and the liquid within the unit cell is given by
(6.6)F g=4 3 π a 3 ρ P g+4 3 π(r 3−a 3)ρ o g
where ρ p is the mass density of the particle. The hydrodynamic force F H is given by (see Eq. (3.22))
(6.7)F H=g∫0 π(σ r r cos θ−σ r θ sin θ)d S·g g
where σ rr and σ rθ are the normal and tangential components of the stress, given by Eqs. (3.24) and (3.25).
We assume that the electrical double layer around the particle is only slightly distorted due to the gravitational field g (slow sedimentation). Then we may write
(6.8)n i(r)=n i(0)(r)+δ n i(r),
(6.9)ψ(r)=ψ(0)(r)+δ ψ(r),
(6.10)μ i(r)=μ i(0)+δ μ i(r),
where the quantities with superscript (0) refer to those at equilibrium, i.e., in the absence of g.The small quantities δn i(r), δψ(r), and δμ i(r) are related to each other by
(6.11)δ μ i=z i e δ ψ+k T δ n i n i(0)
By substituting Eqs. (6.8)–(6.11) into Eqs. (6.1) and (3.9)–(3.14) gives
(6.12)η∇×∇×∇×u=∑i=1 N∇δ n i×∇n i(0)
(6.13)∇·(n i(0)u−1 λ i n i(0)∇δ μ i)=0,
which are the same as those for the electrophoresis problem (Eqs. (3.51) and (3.46)).
Symmetry considerations permit us to write
(6.14)u(r)=(u r,u θ,u φ)=(−2 r h g cos θ,1 r d d r(r h)g sin θ,0)
(6.15)δ μ i(r)=−z i e φ i(r)g cos θ,
where g = |g|. Equations (6.12) and (6.13) can be rewritten in terms of h and ϕ i as
(6.16)L(L h)=G(r),
(6.17)L φ i=d y d r(z i d φ i d r−2 λ i e h r),
with
(6.18)G(r)=−e η r d y d r∑i=1 N z i 2 n i∞exp(−z i y)φ i,
where y=eψ(0)/kT is the scaled equilibrium potential.
In order to express Eq. (6.5) in terms of h(r), we obtain the asymptotic expression of u(r) and p(r) far from the particle. Since ρ el(r) ≈ 0 beyond the particle double layer,Eq. (6.1) becomes
(6.19)η∇×∇×u+∇p−ρ o g=0 as r→∞
and Eq. (6.12) tends to
(6.20)L(L h)=0
with the solution
(6.21)h(r)=D 0 r+D 1 r 2+D 2+D 3 r 2 as r→∞
where D 0 -D 3 are integration constants to be determined. From Eq. (6.3) it follows that D 0 = U SED/2 E (where U SED = |USED|) and D 3 = 0. Also, by integrating Eq. (6.19), we obtain
(6.22)p(r,θ)→−{η d d r(r L h)−ρ o r}g cos θ as r→∞
Substituting Eq. (6.21) into Eq. (6.22), we obtain the asymptotic form of P(r), viz.,
(6.23)p(r)→ρ o g r cos θ−2 D 2 η E cos θ r 2 as r→∞
By using Eqs. (6.21) and (6.23) and calculating FH (Eq. (6.5), we find that
(6.24)F H=−4 3 π r 3 ρ P g+8 π D 2 η g
It thus follows from Eqs. (6.5), (6.6), and (6.24) that D 2 must satisfy
(6.25)D 2=−a 3 6 η(ρ P−ρ o)
so that h(r) and u(r) must satisfy
(6.26)h(r)→U S E D 2 g r−a 3(ρ P−ρ o)6 η as r→∞
(6.27)u(r)→U S E D+a 3(ρ P−ρ o)6 η{g+(g·r¯)r¯r}as r→∞
where r¯=r/r.Eq. (6.27) serves as a boundary condition for u(r) and Eq. (6.3) is thus replaced by Eq. (6.27).
Finally the boundary condition for δμ i(r) far from the particle is derived from Eq. (6.11), viz.,
(6.28)δ μ i→0 as r→∞
where we have used the fact that δψ→0 and δn i→0 as r→∞.
The other boundary conditions (6.2), (6.4), and (6.28) become
(6.29)h=d h d r=0 at r=a
(6.30)d φ i d r|r=a=0,
(6.31)φ i(r)→0 as r→∞
Equation (6.16) subject to Eqs. (6.26) and (6.29) can be integrated formally to give
(6.32)ϕ i(r)=-1 3(r+a 3 2 r 2)∫a∞d y d x(z i d ϕ i d x-2 λ i e h x)d x+1 3∫a r(r-x 3 r 2)d y d x(z i d ϕ i d x-2 λ i e h x)d x
Similarly, by integrating of Eq. (6.17) subject to Eqs. (6.30) and (6.31), we obtain
(6.33)h(r)=∫a∞{−r 3 30+a 2 r 18−a 5 45 r 2+(r 9 a−1 6+a 2 18 r 2)x 3}G(x)d x+∫a r(r 3 30−r x 2 6+x 3 6−x 5 30 r 2)G(x)d x+a 2(ρ P−ρ o)9 η(r−3 a 2+a 2 2 r 2)
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Book series2006, Interface Science and Technology
Chapter
Multipole Fields
1980, Classical Electromagnetic Radiation (Second Edition)Jerry B. Marion, Mark A. Heald
Problems
2-1.
Show that the electric field on the polar axis of a dipole p is 2p/z 3, whereas that in the equatorial plane is −p/r 3. Use this elementary argument to show, by resolving the dipole into two components, that the field at an arbitrary point is
E(r,θ)=p(2 cos θ e r+sin θ e θ)r 3
2-2.
The magnetic field of the Earth is approximately that of a magnetic dipole. Calculate the magnetic dipole moment using the fact that the horizontal component of the Earth's field at the surface of the Earth is approximately 0.23 G at a magnetic latitude of 40°.
2-3.
Show that the electric dipole moment of a system of charges is independent of the choice of origin if the system has zero net charge.
2-4.
Show that the force on an electric dipole is F = (p · grad)E. Then consider the interaction of a charge q and a dipole p that are a distance r apart, with the dipole oriented perpendicular to the line between them. Calculate the (vector) force (a) on q due to p, and (b) on p due to q. If your results violate Newton's third law, try again.
2-5.
Show that a simple finite dipole (charges ±q located at z = ±l/2) has zero quadrupole moment with respect to its center as the origin.
2-6.
A charge q 1 = +2 e is located at the origin and a charge q 2 = − e is located at the point (x, y) = (1, 0). Calculate the potential at the points (0, 5) and (5, 0) in the following ways: (a) by a direct calculation of q/R for each charge, (b) by considering one term of a multipole expansion, (c) two terms, and (d) three terms. Discuss the difference in the rates of convergence toward the exact values for the two different field points.
2-7.
Compute the quadrupole tensor for the following distribution of charges:
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Diagonalize the tensor by a coordinate rotation and find the quadrupole moment.
2-8.
Find the expression for the electric field vector for the linear quadrupole in Fig. 2-4. Sketch some of the field lines.
2-9.
Derive the quadrupole potential for the charge distribution shown in Fig. 2-6. Find the expression for the corresponding electric field vector and sketch some of the field lines for the plane θ = π/2.
2-10.
A charge q is distributed uniformly along the line from z = − h to z = h Calculate the first three multipole moments of this charge distribution.
2-11.
Calculate the dipole and quadrupole moments of a uniformly charged ring of radius a which has total charge + q. Add a charge − q at the center of the ring and recompute the moments.
2-12.
The linear charge density on a ring of radius a is given by
ρ l=q a(cos φ−sin 2 φ)
Find the monopole, dipole, and quadrupole moments of the system and calculate the potential at an arbitrary point in space, accurate to terms in 1/r 3.
2-13.
Show that the quadrupole potential, Eqs. (2.31a), can be written in the form
Φ(4)=1 2 e r⋅{Q}⋅e r r 3
where {Q} is the quadrupole tensor of Eq. (2.33) [compare the final form of Eq. (2.23) for dipoles]. Further, show that for the special case of axial symmetry, with the scalar quadrupole moment Q defined as Q 33 in Eq. (2.38),
Φ(4)→1 2 Q r 3(3 2 cos 2 θ−1 2)
where θ is the polar angle measured from the symmetry axis.2-14.
Consider a collection of electric chargesq α that are in arbitrary motion within a certain specified finite region of space. Write the first term of the multipole expansion for the vector potential [Eqs. (2.41)] as
A(1)=1 c r Σ α q α u α
where u α is the velocity of the u α=r˙α. Calculate the average value of A(1) taken over the interval of time τ:
=1 τ∫0 τ A(1)d t
Show that <A(1)> approaches zero as τ becomes very large, in agreement with Eq. (2.44).
2-15.
Prove Eq. (2.48) by applying Stokes' theorem to the quantity r × k where k is an arbitrary constant vector. Verify the result explicitly for the case of a plane area bounded by a circle; let the origin of r be located (a) at the center of the circle and (b) at some point outside the circle but in the plane of the circle.
2-16.
Construct an appropriate definition for the magnetic dipole momentm of a collection of moving charges by modifying Eqs. (2.50a) for the case of discrete charges. If all of the charges have the same ratio of charge to mass, q/m, show that m is proportional to the (nonrelativistic) angular momentumL of the system. The proportionality constant, g ≡ q/2 mc, is called the gyromagnetic ratio. Using the center of mass as the origin, show that the gyromagnetic ratio for a system of two charges having different q/m ratios is
g=μ 2 c(q 1 m 1 2+q 2 m 2 2)
where μ = m 1 m 2/(m 1 + m 2) is the reduced mass.★2-17
Continue the development begun in Problem 2-14 by applying it to the second term in the expansion for A. Using the definition of the magnetic moment m of a collection of moving charges from Problem 2-16, show that
m total〉×e r r 2
in analogy with Eqs. (2.51a).2-18.
Calculate the quadrupole term A(4) in the expansion of the vector potential.
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Book 1980, Classical Electromagnetic Radiation (Second Edition)Jerry B. Marion, Mark A. Heald
Related terms:
Dipole Moment
Angular Momentum
Charge Distribution
Point Group
Spherical Harmonic
Electric Field
Current Loop
Perpendicularity
Spherical Polar Coordinate
sin θ
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# 5 ways to solve quadratic equations by factoring
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Quadratic equations can seem intimidating, but they don’t have to be!
Learning to solve equations by factoring is a powerful tool that can make math much easier and even a bit fun.
Learn to break it down step-by-step, so you can confidently tackle any quadratic equation that comes your way!
Essentials of Quadratic Equations
A quadratic equation is a polynomial equation of degree two, typically written in the form ax² + bx + c = 0, where a and b are coefficients, c is a constant, and a isn't zero.
Image courtesy of mathspace
Standard Form:
Factored Form:
Images created by the author using Google Slides
Solving Quadratics:
To solve quadratic equations, the goal is to get the equation into factored form and find what x is equal to. To get to factored form from standard form, you'll use a method called factoring.
Preparing to Factor
There are a few things to consider before you solve equations by factoring:
Always be to factor out the Greatest Common Factor, if there is one.
If a = 1, you can use the Sum-Product Method.
If a ≠ 1, you can use Decomposition.
There are special cases of Perfect Square Trinomials and Difference of Squares that have their own rules.
The Quadratic Formula will always give you the value of x if you're unable to factor.
Image created by the author using WordArt
1. Common Factoring
ALWAYS start any factoring method by finding the Greatest Common Factor (GCF) of the terms in the quadratic and pulling it out.
Step 1: Find the Greatest Common Factor. Check out How to Find the Greatest Common Factor if you need a refresher.
Step 2: Divide the terms by the GCF.
Step 3: Pull the GCF out of the expression and leave the divided terms in the brackets.
Example:
10x³ + 30x² + 55x
Images in this Byte were created by the author using Google Slides. To hear audio descriptions of these images, click play on the audio player below each image:
Quiz
Factor the GCF out from 8x² - 12x + 16:
2. Sum-Product Method when a = 1
The Sum-Product Method is all about finding two numbers (r and s) that add up b (the coefficient of x) and multiply to c (the constant term). This method can only be used when a = 1 in ax² + bx + c.
Step 1: Find all the pairs of numbers that multiply to c. This includes negative numbers.
Step 2: Determine which pair adds up to get b.
Step 3: Plug the pair (r and s) into (x + r)(x + s) = 0.
Step 4: Find the x values that make the expression true (i.e., where x + r = 0 and x + s = 0).
Example:
x² - 7x + 12
a = 1
b = -7
c = 12
Quiz
Solve x² + 2x - 8 using the Sum-Product method:
3. Decomposition Method when a ≠ 1
The process of decomposition is breaking up the middle term in the expression and using grouping to fully factor. Use this method when you have more complex quadratics, such as when a ≠ 1.
If you need a reminder on how to group expressions, check out Factor a Quadratic Equation by Grouping Terms.
Step 1: Find all the pairs of numbers that multiply to (a)(c).
Step 2: Determine which factor pair (r and s) adds to get b.
Step 3: Break the middle term of the expression (bx) into rx and sx.
Step 4: Group each half of the expression and factor out the GCFS.
Step 5: Factor the GCF bracket out of the expression.
Step 6: Set the expression equal to 0 and solve for x.
Example:
Let's look at 2x² + 7x + 5
a = 2
b = 7
c = 5
Quiz
Solve 7x² + 3x - 10 using decomposition.
4. Special Cases
Sometimes, quadratic equations fall into special categories that allow for quick and easy factoring. Recognizing these cases can save you time and effort!
Perfect Square Trinomials
Perfect Square Trinomials have two square terms (a² and b²) with the third term 2ab.
They follow the pattern:
a² + 2ab + b² = (a + b)²
a² - 2ab + b² = (a - b)²
Examples:
Difference of Squares
Difference of Squares have two square terms (a² and b²) separated by a minus sign.
They follow the pattern:
a² - b² = (a + b) (a - b)
Examples:
Quiz
Solve 4x² - 36.
5. Quadratic Formula
When solving equations by factoring gets tricky or when you can't find nice numbers to work with, the quadratic formula comes to the rescue! It allows you to find the solutions for any quadratic equation, no matter how complicated.
Step 1: Sub the values of a, b, and c into the quadratic formula.
Image courtesy of CUEMATH
Step 2: Solve for x.
Example:
5x² + 10x + 4
a = 5
b = 10
c = 4
The solution is x = -1.45, -0.55.
Quiz
Solve 6x² + 25x + 14 using the quadratic formula:
Take Action
It can be tricky to learn a new concept but the most important thing is to take it step by step and PRACTICE. Practice makes perfect!
Not that you know how to solve quadratic equations by factoring:
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StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing; 2025 Jan-.
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Treasure Island (FL): StatPearls Publishing; 2025 Jan-.
Neurofibromatosis
Cuong Le; Aby Thomas; Forshing Lui.
Author Information and Affiliations
Authors
Cuong Le1; Aby Thomas2; Forshing Lui3.
Affiliations
1 US Derm Partners
2 University of Mississippi Medical Center
3 CA Northstate Uni, College of Med
Last Update: May 4, 2025.
Continuing Education Activity
Neurofibromatosis is a group of autosomal dominant neurocutaneous disorders marked by a predisposition to tumor formation, particularly involving nerve sheaths. The 3 types—neurofibromatosis type 1 (NF1), type 2 (NF2), and schwannomatosis—are distinct clinical entities with differing genetic mutations and manifestations.
NF1 is characterized by the presence of neurofibromas, cafe-au-lait spots, freckling, optic gliomas, and bony dysplasias. Bilateral vestibular schwannomas and meningiomas are characteristic of NF2; however, neurofibromas do not occur in this syndrome. Therefore, the name NF2 is a misnomer, and a new and more accurate name for NF2-related schwannomatosis has been established based on an international consensus recommendation. Neurofibromatosis types 1 and 2 treatment involves clinical monitoring and medical intervention when appropriate. Schwannomatosis is the rarest form, marked by multiple peripheral and spinal schwannomas, often causing chronic pain. Vestibular involvement is uncommon, differentiating it from NF2.
This course explores the complexities surrounding this neurocutaneous disorder, including the differentiation between the types of neurofibromatosis and the underlying genetic etiologies. This activity for healthcare professionals is designed to enhance the learner's competence in identifying neurofibromatosis, performing the recommended evaluation, and implementing an appropriate interprofessional approach when managing this condition.
Objectives:
Identify the etiology of neurofibromatosis.
Differentiate the various types of neurofibromatosis.
Implement the appropriate management approach for a patient with neurofibromatosis.
Apply interprofessional team strategies to improve care coordination and outcomes for patients with neurofibromatosis.
Access free multiple choice questions on this topic.
Introduction
Neurofibromatosis is an autosomal dominant genetic neurocutaneous disorder characterized by excessive nerve sheath tumor predisposition, most prominent in the nervous system and skin. This neurocutaneous disorder has 3 distinct types of neurofibromatosis: type 1 (NF1), type 2 (NF2), and schwannomatosis. NF1 and NF2 are the most common, while schwannomatosis is rare (see Image. Neurofibromatosis).
Neurofibromatosis Type 1 and 2
NF1, or von Recklinghausen disease, is characterized by multiple body organs with multiple (≥6) cafe-au-lait macules (CALM), neurofibromas of any type or plexiform neurofibroma, axillary or inguinal freckling, hamartomatous Lisch nodules of the iris, optic pathway glioma, and disease-specific bony dysplasia. In addition to benign and malignant tumor development, patients also have greater risks of other musculoskeletal, cardiovascular, and nervous system abnormalities. NF1 is caused by a loss-of-function mutation in 1 allele of the NF1 gene, resulting in a 50% loss of function of neurofibromin, a tumor suppressor protein ubiquitously expressed. According to the National Neurofibromatosis Foundation International Database, approximately 20% of children aged 0 to 19 develop plexiform neurofibromas. Plexiform neurofibromas are benign peripheral nerve tumors with a plexiform growth pattern. They are diffuse growths involving multiple nerves and plexi with significant morbidity.
NF2 has an autosomal dominant inheritance pattern and is characterized by the development of bilateral vestibular schwannomas and meningiomas. Notably, neurofibromas do not occur in this syndrome; therefore, the name NF2 is a misnomer. An international consensus has recommended the new and more accurate name of NF2-related schwannomatosis. NF1 and NF2 treatment involves clinical monitoring and medical intervention when appropriate.
Schwanomatosis
Schwanomatosis is the rarest of the 3 types of neurofibromatosis, with an incidence of 0.58 cases per 1,000,000 people. The presence of multiple nonintradermal peripheral and spinal schwanomas characterizes it. Localized or diffuse chronic pain or asymptomatic masses are common presentations. Vestibular schwannoma is uncommon in this entity. Schwannomatosis is mostly sporadic. Approximately 15% to 25% of these patients have inherited this disorder. SMARCB1 and LZTR1 are the 2 most common gene mutations, either spontaneous or inherited with reduced penetrance. The newly revised names for these entities are SMARCB1-related schwannomatosis and LZTR1-related schwannomatosis. Due to its rarity, schwanomatosis will not be elaborated on in this activity.
Etiology
Neurofibromatosis Type 1
NF1 is caused by a loss-of-function mutation, either de novo or inherited, on the neurofibromin 1 (NF1) gene. Approximately half of all NF1 cases are inherited, while the other half result from de novo mutations. This gene, located on chromosome 17q11.2, encodes the protein neurofibromin. Neurofibromin is a tumor suppressor protein in the RAS/MAPK and mTOR pathways. RAS is a GDPase that activates the downstream mitogen-activated protein kinase (MAPK) and the mammalian target of rapamycin (mTOR) cell proliferation pathway.
Inadequate neurofibromin activity results in a higher risk of tumors, including malignant peripheral nerve sheath tumors (MPNST), optic pathway gliomas, and phaechromocytomas, among others. Mosaicism can occur, resulting in the segmental, generalized, or gonadal expression of the NF1 gene. The segmental NF1 gene has pigment changes, tumors, or both, and is limited to 1 or more body segments.
A diagnosis of mosaic NF1 should be considered if such lesions are present only on 1 side or in 1 body segment. The generalized NF1 gene appears similar to the classic NF1 gene but lacks the typical mutation associated with the classic NF1 gene. Gonadal NF1 gene mutations occur when the mutation affects only the ova or sperm. The NF1 gene has complete penetrance with highly variable expressivity.
Neurofibromatosis Type 2
A loss-of-function mutation of the NF2 gene causes NF2 and is located on chromosome 22q12, coding for the protein Merlin. Merlin is a cell membrane protein and a tumor suppressor that functions in the PI3kinase/Akt, Ras/MEK/ERK, and mTOR pathways.
Epidemiology
NF1 accounts for approximately 96% of all neurofibromatosis cases. The prevalence is 1 in 3,000 births and occurs equally among both genders and races. Approximately 50% of patients have a spontaneous mutation, while the other half have an inherited mutation. A penetrance of 100% with variable expressivity is noted.
NF2 accounts for approximately 3% of all cases and has a prevalence ranging from 1 in 33,000 to 1 in 87,410 births. No gender or racial predilection has been documented. NF2 presents with variable symptoms in different families. A more severe clinical presentation is associated with a frameshift or a nonsense mutation that results in a truncated protein.
Pathophysiology
Neurofibromatosis Type 1
NF1 is caused by a mutation of the NF1 gene, resulting in reduced function of its encoded protein, neurofibromin. Neurofibromin is a tumor suppressor protein involved in the downregulation of Ras signaling. The pathological hallmark of NF1 is a neurofibroma, a peripheral nerve sheath tumor that exhibits mixed nervous and fibrous components, including Schwann cells, fibroblasts, endothelial cells, mast cells, macrophages, neurons, and extracellular matrix. Cutaneous neurofibromas are present in nearly all patients with NF1, arising from dermal nerve terminals and typically developing around puberty, with their number increasing with age.
The other type of neurofibroma, plexiform neurofibroma, primarily arises from nerve plexuses in approximately 30% of patients with NF1. They grow along nerve fibers in an infiltrative fashion. Plexiform neurofibroma involves multiple nerve fascicles and has a rich vascular supply. It develops in patients younger than 5 years old and rapidly grows, resulting in significant pressure and distortion of surrounding structures. In addition to the uncontrolled proliferation of Schwann cells, NF1 also affects other cells of neurocrest origin, resulting in a variety of symptoms that affect various organ systems, including cafe-au-lait macules, axillary freckling, Lisch nodules, optic pathway glioma, and skeletal dysplasia.
Neurofibromatosis Type 2
NF2 is caused by loss-of-function mutations in the NF2 gene on chromosome 22q12.2, resulting in impaired function of the encoded protein Merlin, a tumor suppressor protein. NF2 is fully penetrant. The average age of symptom onset is approximately 22. NF2 vestibular schwannoma and other tumors develop following a 2-hit hypothesis. The initial hit involves germline inactivation of an NF2 allele, followed by somatic inactivation of the NF2 gene on the opposite chromosome.
Histopathology
Neurofibromatosis Type 1
Neurofibromas are benign tumors composed of mixed cell types, including Schwann cells, perineural cells, and fibroblasts. The tumors also contain mast cells, axonal processes, and a collagenous extracellular matrix. Plexiform neurofibromas are benign peripheral nerve tumors with a plexiform growth pattern. They are diffuse growths involving multiple nerves and plexi with significant morbidity due to their propensity to infiltrate surrounding structures. They also have a risk of transforming into MPNST.
Neurofibromatosis Type 2
Schwannomas are the primary pathological entities associated with NF2. They most commonly arise from the eighth cranial nerve. They are benign peripheral nerve sheath tumours composed of mature Schwann cells. They consist of spindle cells with mixed Antoni A and B cellular arrangements, verocay bodies, and hyalinised vessels.
History and Physical
Neurofibromatosis Type 1
NF1 has cutaneous and noncutaneous manifestations. CALMs are a component of the 7 diagnostic criteria for NF1. The lesions are sharply demarcated with a homogenous appearance. Axillary and groin freckling, also known as Crowe sign, is the most specific criterion for NF1.
Neurofibromas can occur anywhere on the body and can be cutaneous or internal. Dermal tumors are soft, dome-shaped tumors, but can also present as pedunculated, nodular, or plaque-like. Internal tumors are deeper and can occur around the eye, retroperitoneal, along with the gastrointestinal tract, or in the mediastinum. Additionally, neurofibromas often exhibit a buttonhole sign.
Plexiform neurofibromas are usually present from birth and are derived from the nerve sheaths (see Image. Solitary Giant Neurofibroma). They can feel like a "bag of worms." Cutaneous manifestations include scoliosis, long bone dysplasia, learning difficulties, and attention deficit hyperactivity disorder. Lisch nodules are a form of hyperpigmentation in the iris; however, they do not affect vision. Optic glioma is a tumor of the optic nerve and can affect vision, occuring in 15% of patients with neurofibromatoafe-au-latsis type 1. Patients also have generalized hyperpigmentation, blue-red, pseudoatrophic macules, juvenile xanthogranuloma, glomus tumor, melanoma, nevus anemicus, and pruritus. Patients are at increased risk for rhabdomyosarcoma, myeloid leukemia, and pheochromocytoma.
The manifestations of NF1 clinical features tend to progress with age. CALMs, bony dysplasia, and plexiform neurofibroma start during infancy. Learning deficits, ADHD, or autism spectrum disorder, and optic pathway glioma develop during early childhood. Skin freckling, Lisch nodules, and dermal and spinal neurofibromas appear and increase in number from late childhood to adolescence. MPNST and higher-grade gliomas develop in adulthood.
Neurofibromatosis Type 2
NF2 patients typically present with schwannomas and meningiomas (see Image. Neurofibromatosis Type 2). Bilateral vestibular schwannoma and unilateral vestibular schwannoma occur on the superior division of the eighth cranial nerve. This is the most common type, but can occur with any cranial nerve. Involvement of the facial nerve with the vestibular schwannoma can make surgical treatment difficult. These patients typically present with tinnitus, hearing loss, and balance difficulties. Patients who have the truncated protein were found to have the disease of onset at a younger age and a higher prevalence of tumors. Younger patients typically experience symptoms at an earlier age.
Evaluation
Diagnostic Criteria of Neurofibromatosis Type 1
An international consensus group revised the diagnostic criteria for NF1 in 2021, with the presence of 2 of the following being required for the diagnosis:
Presence of ≥6 CALMs >5 mm in prepubertal individuals and >15 mm in postpubertal individuals
Presence of ≥2 neurofibromas or ≥1 plexiform neurofibromas
Axillary or inguinal freckling
Optic pathway glioma
Presence of ≥2 iris Lisch nodules or choroidal abnormalities
Distinct bony lesions, including sphenoid dysplasia, anterolateral bowing of the tibia, or pseudoarthrosis of a long bone
First-degree relative with NF1, or heterozygous pathogenic NF1 variant allele fraction of 50% in apparently normal tissues, eg, white blood cells
Neuroimaging Manifestations of Neurofibromatosis Type 1
The following findings may be associated with NF!:
Nonenhancing T2/FLAIR hyperintense foci
Commonly known as unidentified bright objects or focal areas of signal intensity (see Image. Neurofibromatosis Type I MRI).
Locations
Basal ganglia
Thalami
Mesial temporal lobes
Internal capsule
Splenium
Brainstem
Cerebellar white matter
Pathology demonstrates areas of myelin vacuolization
Timeline
Typically appear around the age of 3
Increase in number and size until approximately 12 years
Gradually regress thereafter
Other lesions associated with NF1
Optic pathway gliomas (see Image. Optic Nerve Glioma)
Cerebral astrocytomas
Vascular dysplasia, eg, aneurysms, moyamoya vasculopathy
Dural ectasia
Sphenoid wing dysplasia
Peripheral and cranial manifestations
Cranial nerve schwannomas
Peripheral neurofibromas
Plexiform neurofibromas (see Image. Plexiform Neurofibroma)
Malignant peripheral nerve sheath tumors
Spinal manifestations
Posterior vertebral scalloping caused by dural ectasia or neurofibromas
Scoliosis
Lateral meningoceles
Differential diagnosis includes neurofibromatosis type 1-like syndrome, familial cafe-au-lait spots, and segmental neurofibromatosis type 1. The NF1-like syndrome was first described in 2007. Patients with an NF1-like syndrome exhibit cafe-au-lait spots, axillary freckling, and macrocephaly; however, they typically lack the NF1 genetic mutation, neurofibromas, and Lisch nodules. NF1-like syndrome is an autosomal dominant disorder resulting from a mutation in the SPRED1 gene located on chromosome 15. Familial cafe-au-lait spots are a disorder presenting only cafe-au-lait macules.
Neuroimaging Manifestations of Neurofibromatosis Type 2
A key feature of NF2 is the presence of bilateral acoustic schwannomas, also known as vestibular schwannomas (see Image. Neurofibromatosis Type 2 MRI). Other associated lesions include meningiomas, gliomas, neurofibromas, and schwannomas of different cranial nerves.
Bilateral vestibular schwannoma is pathognomic for NF2, but not all patients with this condition have bilateral schwannoma. The NIH has established the following diagnostic criteria for NF2:
Definitive NF2: Bilateral vestibular schwannoma (see Image. Bilateral Vestibular Schwannomas) or a first-degree relative with neurofibromatosis type 2 plus unilateral vestibular schwannoma in individuals younger than 30 or any 2 of the following:
Meningioma
Glioma
Schwannoma
Juvenile posterior subcapsular lenticular opacities/juvenile cortical cataract
Presumptive or probable NF2
Unilateral vestibular schwannoma in patients younger than 30 and 1 of the following:
Meningioma
Glioma
Schwannoma
Juvenile posterior subcapsular lenticular opacities/juvenile cortical cataract
Multiple meningiomas (2 or greater) plus unilateral vestibular schwannoma in patients younger than 30 years, or 1 of the following:
Glioma
Schwannoma
Juvenile posterior subcapsular lenticular opacities/juvenile cortical cataract
Treatment / Management
Neurofibromatosis Type 1
CALMs do not require treatment; similarly, neurofibromas are benign and typically do not need treatment. Surgical excision can be performed on symptomatic lesions; however, recurrence can still occur.
Plexiform neurofibromas are often disfiguring and can be difficult to remove due to their infiltrative growth pattern. Their growth may affect the airways, which require more specialized treatment, including a tracheotomy. The growth rate of plexiform neurofibromas remains relatively constant within a single individual, and its growth after adolescence is much slower. In most cases, treatment for plexiform neurofibromas aims to improve or prevent morbidity. Plexiform neurofibromas have malignant potential. An 8% to 13% risk that plexiform neurofibromas will develop into malignant peripheral nerve sheath tumors has been reported. Therefore, plexiform neurofibromas should be suspected if there is pain for more than 1 month, new neurologic deficits, a change of the neurofibroma from soft to hard, or a rapid increase in size. These malignancies are treated with wide local excision.
Imatinib, a tyrosine kinase inhibitor, has been shown to decrease the size of plexiform neurofibroma. The recent discovery of a MEK inhibitor (MEKi) targeting downstream RAS has shown promising results for patients with inoperable, symptomatic plexiform neurofibromas. Selumatinib, a MEKi treatment, results in a good partial response and a reduction in the size of the plexiform neurofibromas.
Monitoring for any neurologic changes and referral to a neurologist is paramount. These changes can be due to tumor development. Consistent ophthalmologic evaluation is recommended for observation of the development of optic gliomas. Chemotherapy is the treatment of choice for optic gliomas. Monitoring children for difficulty learning and behavioral issues. Counseling can be beneficial for patients to provide support regarding the autosomal dominant inheritance pattern of the disease.
Neurofibromatosis Type 2
Patients with neurofibromatosis type 2 require the assessment of their hearing. Ophthalmology evaluation, magnetic resonance imaging (MRI), audiology, and brainstem-evoked potentials are essential in managing these patients. Surgery is still the first-line treatment for symptomatic tumors, but these patients have a 44% recurrence rate.
Radiation can be used, but it increases the risk of malignant transformation. Bevacizumab, a VEGF inhibitor, is a monoclonal antibody that can be used to medically treat patients with NF2. It decreased tumor size in 53% of cases and improved hearing in 57% of cases. Patients with suspected NF2 should undergo an MRI of the head and spine, with particular attention to obtaining thin cuts through the internal auditory canals. Treatment is done if the tumor is compressing the brainstem or causing hearing loss.
Differential Diagnosis
The following differential diagnoses should be considered in patients with suspected NF1; therefore, genetic testing is helpful:
Noonan syndrome (PTPN11 mutations and RAS-MARK mutations, characterized by CALM, fundal changes, and hematological malignancies)
Legius syndrome (SPRED1 mutation, characterized by café-au-lait spots, skinfold freckles, learning issues, and macrocephaly)
Constitutional mismatch repair deficiency, characterized by CALM, skin freckling, Lisch nodules, and numerous tumors or cancers
McCune-Albright syndrome
The differential diagnosis for NF2 includes nonsyndromic schwannoma and meningiomas.
Prognosis
Neurofibromatosis Type 1
The clinical features of NF1 develop and progress with age from early infancy to adulthood. The prognosis depends on the clinical features. CALMs, dermal freckling, and dermal neurofibromas affect the patient's cosmetic appearance but generally do not impact their functions. Bony dysplasia and pseudoarthrosis may affect the patient's mobility. Optic pathway gliomas often require surgical treatment, which can affect vision. Plexiform neurofibromas may cause pain, airway and spinal cord compression, dysfigurement, and, rarely, vision impairment and malignant transformation.
Neurofibromatosis Type 2
Schwannomas and meningiomas are benign tumors and are generally amenable to neurosurgical therapies.
Complications
The complications associated with neurofibromatosis vary depending on the type, including:
NF1
Skeletal complications, including bony deformities, tibial dysplasia, and pseudoarthrosis
Neurological problems, eg, learning disabilities, attention deficit and hyperactivity disorders (ADHD), vision loss due to optic pathway glioma, and hearing loss
Cardiovascular conditions, eg, hypertension, congenital heart diseases, pheochromocytoma, and Moya-Moya disease
Increased risk of multiple cancers, including MPNST, breast cancers before the age of 50, and brain tumors
NF2:Hearing loss (primary complication)
Deterrence and Patient Education
Deterrence of neurofibromatosis is limited due to its genetic nature, but patient education plays a crucial role in early recognition, management, and family planning. Patients and families should be counseled on the autosomal dominant inheritance pattern, which carries a 50% risk of transmission to offspring. Genetic counseling is essential for affected individuals or those with a family history to make informed reproductive decisions.
Patient education should focus on recognizing early symptoms, such as café-au-lait macules, freckling, or changes in hearing, and emphasize the importance of regular monitoring for potential tumor development. Empowering patients with knowledge about their condition enhances adherence to follow-up care, improves outcomes, and supports psychosocial well-being.
Enhancing Healthcare Team Outcomes
Effective management of neurofibromatosis requires a highly coordinated interprofessional approach to deliver patient-centered care and improve long-term outcomes. Physicians and advanced practitioners, such as nurse practitioners and physician assistants, play a central role in recognizing clinical signs, initiating diagnostic evaluations, and coordinating ongoing surveillance for complications like CNS tumors, which may have a poor prognosis if not detected early. Regular follow-up by dermatologists, ophthalmologists, neurologists, and neurosurgeons is essential to monitor for neurocutaneous lesions, optic gliomas, vestibular schwannomas, and other tumor-related manifestations. Pediatricians are particularly critical in early detection and developmental monitoring of children, ensuring timely referral to specialists. Genetic counselors contribute by educating families about inheritance patterns, facilitating early diagnosis, and supporting decision-making for future pregnancies.
Nurses are integral in patient education, symptom monitoring, care navigation, and providing psychosocial support, especially as patients cope with the visible and potentially disfiguring aspects of neurofibromatosis. Pharmacists contribute to guiding safe and effective medication use, including newer therapies such as MEK inhibitors and VEGF inhibitors, as well as monitoring for adverse effects. Open and consistent communication among team members ensures timely sharing of clinical findings, promotes unified treatment planning, and reduces the risk of fragmented care. Leveraging electronic health records for shared documentation and coordinating care transitions enhances team performance and patient safety. Ultimately, a well-synchronized interprofessional strategy fosters trust, improves quality of life for patients with neurofibromatosis, and supports proactive, individualized care across the lifespan.
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Figure
Neurofibromatosis. Neurofibromatosis encompasses three distinct disorders: neurofibromatosis type 1 (NF1), neurofibromatosis type 2 (NF2), and schwannomatosis. DermNet New Zealand
Figure
Neurofibromatosis Type 2. Neurofibromatosis type 2 patients typically present with schwannomas and meningiomas. Contributed by S Verma, MBBS, DVD, FRCP, FAAD
Figure
Solitary Giant Neurofibroma. Plexiform neurofibromas are usually present from birth and are derived from the nerve sheaths. Contributed by S Munakomi, MD
Figure
Neurofibromatosis Type I MRI. T1, T2, and postcontrast T1W MR images (top row) showing prominent soft tissue involving right occipital scalp, demonstrating heterogenous T2 signal with postcontrast enhancement, likely representing a plexiform neurofibroma. (more...)
Figure
Optic Nerve Glioma. Postcontrast T1W axial and coronal MR images of the orbits demonstrating an enlarged and enhancing right optic nerve (arrows) in the intraorbital segment, consistent with right optic nerve glioma in this patient with type I neurofibromatosis. (more...)
Figure
Plexiform Neurofibroma. T2W and postcontrast T1W FS axial MR images showing enhancing mass within the right cavernous sinus extending from the cavernous sinus through the superior orbital fissure into the right orbit, resulting in marked proptosis of (more...)
Figure
Bilateral Vestibular Schwannomas. Postcontrast T1W coronal and sagittal MR images (top row) showing a large enhancing mass at the vertex in right para-midline position with dural base on the right parietal calvarium and interhemispheric falx. (more...)
Figure
Neurofibromatosis Type 2 MRI. Axial T1W MR images at cervical and lumbar levels showing masses centered in the neural foramen. Numerous smaller masses were also seen throughout the cervical, thoracic, and lumbar levels (not shown). Postcontrast sagittal (more...)
References
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: Disclosure: Cuong Le declares no relevant financial relationships with ineligible companies.
: Disclosure: Aby Thomas declares no relevant financial relationships with ineligible companies.
: Disclosure: Forshing Lui declares no relevant financial relationships with ineligible companies.
Copyright © 2025, StatPearls Publishing LLC.
This book is distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) ( ), which permits others to distribute the work, provided that the article is not altered or used commercially. You are not required to obtain permission to distribute this article, provided that you credit the author and journal.
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Le C, Thomas A, Lui F. Neurofibromatosis. [Updated 2025 May 4]. In: StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing; 2025 Jan-.
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189632 | https://planetmath.org/limitofdisplaystylefracax1xasxapproaches0 | limit of as approaches 0
Corollary.
For , we have
| |
| |
Proof.
Recall that . Thus,
| | |
--- |
| | |
| |
| |
Let . Then as . Therefore,
| | |
--- |
| | |
| |
| |
The formula from the corollary is useful for proving that . On the other hand, once this fact is known, the corollary is easily proven via l’Hôpital’s rule (
| | |
--- |
| | |
| |
| |
| | |
--- |
| Title | limit of as approaches 0 |
| Canonical name | LimitOfdisplaystylefracax1xAsXApproaches0 |
| Date of creation | 2013-03-22 17:40:21 |
| Last modified on | 2013-03-22 17:40:21 |
| Owner | Wkbj79 (1863) |
| Last modified by | Wkbj79 (1863) |
| Numerical id | 5 |
| Author | Wkbj79 (1863) |
| Entry type | Corollary |
| Classification | msc 32A05 | |
189633 | https://stackoverflow.com/questions/48496189/ | arrays - Binary to Decimal Converter with C - Stack Overflow
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Binary to Decimal Converter with C
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Asked 7 years, 8 months ago
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I am new at writing in C, and I am not quite understanding why this programme is resulting in a failure. I feel like it is a result of the method isTrue. The purpose of the method was to ensure that the string entered was an actual integer, but it doesn't seem to work there. I am not really sure why. I get some weird values returned for some reason.
```c
/ Program: binToDec.c
Author: Sayan Chatterjee
Date created:1/25/17
Description:
The goal of the programme is to convert each command-line string
that represents the binary number into its decimal equivalent
using the binary expansion method.
/
include
include
include
/Methods/
int strLen(char str);
int isTrue(char str);
int signedBinToDec(char str);
/Main Method/
int main(int argc, char argv)
{
/Declaration of Variables/
int binNum = 0;
int decNum = 0;
int i;
/Introduction to the Programme/
printf("Welcome to Binary Converter\n");
printf("Now converting binary numbers\n");
printf("...\n");
/Check to see any parameters/
if(argc > 1)
{
for(i = 1; i < argc; i++)
{
if(isTrue(argv[i] == 1))
{
if(strLen(argv[i] <= 8))
{
binNum = atoi(argv[i]);
decNum = signedBinToDec(binNum);
}
else
{
printf("You did not enter a 8-bit binary\n\a");
break;
}
break;
}
else
{
printf("You did not enter a proper binary number\n\a");
break;
}
}
/Printing of the Result/
printf("Conversion as follows: \n");
printf("%d\n", decNum);
}
else
{
printf("You did not enter any parameters. \a\n");
}
}
int strLen(char str)
{
int len = 0;
while(str[len] != '\0')
{
len++;
}
return len;
}
int isTrue(char str)
{
int index = 0;
if(str >= '0' && str <= '9')
{
return 1;
}
else
{
return 0;
}
}
int signedBinToDec(char str)
{
int i;
int len = strLen(str);
int powOf2 = 1;
int sum = 0;
for(i = len-1; i >= 0; i--)
{
if(i == 0)
{
powOf2 = powOf2 -1;
}
sum = (str[i]powOf2) + sum;
powOf2 = powOf2 2;
}
return sum;
}
```
c
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edited Jan 29, 2018 at 8:07
Sourav Ghosh
135k 17 17 gold badges 192 192 silver badges 271 271 bronze badges
asked Jan 29, 2018 at 7:17
Sayan ChatterjeeSayan Chatterjee
3 1 1 bronze badge
8
Question conent is good, but where is your research effort?Sourav Ghosh –Sourav Ghosh 2018-01-29 07:18:51 +00:00 Commented Jan 29, 2018 at 7:18
Welcome to Stack Overflow! Kindly show your research / debugging effort so far. Please read How to Ask page first.Sourav Ghosh –Sourav Ghosh 2018-01-29 07:18:57 +00:00 Commented Jan 29, 2018 at 7:18
You are comparing a pointer to a char. Needs moar dereference. You got a clean compile, no errors/warnings??Martin James –Martin James 2018-01-29 07:22:19 +00:00 Commented Jan 29, 2018 at 7:22
2 Please stop trying to write 'clever' code, with compound expressions/statements - you're not very good at it. Don't feel slighted - nobody is. SImplify you code until you can easily debug it. Use temp vars instead of compound expressions in brackets. printf moar stuff out. Learn how to use your debugger - don't write any more code at all until you can use your debugger to, at least, step, breakpoint and inspect variables.Martin James –Martin James 2018-01-29 07:30:06 +00:00 Commented Jan 29, 2018 at 7:30
1 Not directly related, but the name of the isTrue function is a very poor choice. Why not call it isDigit??Jabberwocky –Jabberwocky 2018-01-29 07:49:24 +00:00 Commented Jan 29, 2018 at 7:49
|Show 3 more comments
1 Answer 1
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The if statement
c
if( isTrue(argv[i] == 1) )
is very wrong. It is bad because of two cases
argv[i] == 1 is a comparison between a pointer and an int, which is illegal. This causes a constraint violation. According to C11, chapter §6.5.9, Equality operators
One of the following shall hold:
— both operands have arithmetic type;
— both operands are pointers to qualified or unqualified versions of compatible types;
— one operand is a pointer to an object type and the other is a pointer to a qualified or unqualified version of void; or
— one operand is a pointer and the other is a null pointer constant.
The result of the comparison, again, an int value, is being used as the function argument, whereas, the function is supposed to accept a char . An int and char are not compatible types.
It appears, you meant to write
c
if ( isTrue(argv[i]) == 1 )
as you need to compare the return value of isTrue call.
The same goes for strLen(argv[i] <= 8) and others.
That said, there are other problems.
isTrue() only checks for the value in index 0, for the passed argument, you need some sort of loop to check the entire string.
There are already well-known library functions like isDigit() which does the work pretty nicely, try to make use of them.
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edited Jan 29, 2018 at 7:54
answered Jan 29, 2018 at 7:20
Sourav GhoshSourav Ghosh
135k 17 17 gold badges 192 192 silver badges 271 271 bronze badges
4 Comments
Add a comment
Martin James
Martin JamesOver a year ago
I WILL use a compound statement. I WILL not use temporary boolean values. I WILL not simplify expressions that might be wrong. I WLL keep getting it wrong, over, and over, again :)
2018-01-29T07:25:17.043Z+00:00
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Sourav Ghosh
Sourav GhoshOver a year ago
@MartinJames Please don't make me lose my lunch. I'm done.
2018-01-29T07:26:46.71Z+00:00
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Martin James
Martin JamesOver a year ago
sorry - I hope you keep your lunch where it belongs:)
2018-01-29T07:32:18.15Z+00:00
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Sourav Ghosh
Sourav GhoshOver a year ago
@MartinJames Sure thing, off to lunch now, before anything else pops up :)
2018-01-29T07:34:22.683Z+00:00
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189634 | https://faculty.fiu.edu/~boydj/mathecon/math11.pdf | Linear Independence This section focuses on bases for vector spaces. We’ve seen one basis already, the standard basis for Rn.
It allowed us to write any linear transformation from Rn to Rm in terms of matrix multiplication.
Bases allow us to define the dimension of a vector space.
In the context of solutions to linear systems, the dimension is the number of free variables. It tells us what the solution set looks like.
Finally, the judicious choice of a basis can simplify linear systems, allowing easier interpretation of results. In a dynamic context, this allows us to better understand both short and long-run dynamics of the system.
2 MATH METHODS 11.1 Linear Combinations Let L be a line through the origin. We say L = {x : x = tx1} is the line generated by x1, or the line spanned by x1. It’s the set of all scalar multiples of x1. What if we have more than one generator? What do we get?
Let’s try it. Let x1, . . . , xk be vectors in a vector space V. A sum of the form t1x1 + t2x2 + · · · + tkxk = k X j=1 tjxj for tj ∈R is called a linear combination of x1, . . . , xk.
For a single xi, we get a line. For two, if they are co-linear, we still get a line. If there are not, we get a plane. If we’re working in R2, that’s all there is. If we’re in Rn for a larger n, there are more possibilities.
Since we are doing economics, there may be an awful lot of possibilities.
When dealing with consumers, each good or service needs its own index, leading to a very, very large number of goods, n. A single supermarket has many thousands of goods. Consumers potentially choose from vast numbers of goods.
LINEAR INDEPENDENCE 3 11.2 The Span of a Set We define the span of a set {x1, . . . , xk}, L x1, . . . , xk , as the set of linear combinations of the points x1, . . . , xk. In other words, L x1, . . . , xk = x : x = k X j=1 tjxj for some tj ∈R .
Theorem 11.2.1. Suppose x1, . . . , xk are vectors in V and x, y ∈ Lx1, . . . , xk . Then for α ∈F, αx + y ∈Lx1, . . . , xk , so the span is a vector subspace of V.
Proof. In this case there are si, ti ∈F with x = P i sixi and y = P i tixi. Then αx + y = P i(αsi + ti)xi is also in L x1, . . . , xk .
4 MATH METHODS 11.3 The Span of a Matrix When V = Rn, we can write the span using a matrix. Form an n × k matrix X from the vectors x1, . . . , xk ∈Rn by taking xj as the jth column of X, so X = x1 | x2 | · · · | xk .
Linear combinations of the x1, . . . , xk can be written Xt = k X j=1 tjxj = t1 x11 x21 .
.
.
xn1 + · · · + tk xk1 xk2 .
.
.
xkn .
Then L x1, . . . , xk = Xt : t ∈Rk .
When writing y = Xt, we can think of the tj as coordinates of y in the coordinate system X = x1, · · · , xk .
LINEAR INDEPENDENCE 5 11.4 Spanning Examples ◮Example 11.4.1: Standard Basis Vectors. If k = n and xj = ej, then the matrix formed from the standard basis vectors ej is the identity matrix and the coordinates of x are Ix = x, meaning that the j coordinate is just xj. ◭ Spans need not resemble the standard basis vectors.
◮Example 11.4.2: Span of Vectors. Consider the case of three vectors in R4 given by the columns of X = 1 1 0 0 1 1 1 1 1 1 0 0 .
Then L[x1, x2, x3] = t1 + t2 t2 + t3 t1 + t2 + t3 t1 : tj ∈R .
Since the rank of X is three, there are vectors cannot be written x = Xt.
These vectors are not in the span, showing that L[x1, x2, x3] is a proper subspace of R4. ◭ 6 MATH METHODS 11.5 When are Linear Combinations Unique?
Linear combinations allow us to write vectors in terms of a particular set of vectors. It lets us set up a coordinate system. Does a vector have a single set of coordinates? Or are there multiple ways to write it in terms of our of vectors?
Let X be an n × k matrix whose columns define a coordinate system and suppose x = Xt and x = Xt′, so t and t′ are both coordinates for x. When can we conclude that t = t′?
Alternately, when can we conclude that a vector has only one set of coordinates?
By subtracting, we find 0 = X(t −t′), so the question is really whether this homogeneous linear system has a unique solution.
By Corollary 7.29.1, this will have multiple solutions if and only if k > rank X, which is equivalent to saying there are free variables.
This is connected to the idea of linear dependence.
Linear Dependence. Non-zero vectors x1 . . . , xk are linearly dependent if there are t1, . . . , tk, not all zero, with Pk j=1 tjxj = 0.
In other words, the vectors are linearly dependent if and only if Xt = 0 has a non-zero solution t.
LINEAR INDEPENDENCE 7 11.6 Theorem on Linear Dependence Theorem 11.6.1. Suppose x1 . . . , xk are linearly dependent vectors. Then there is h so that xh = −1 th X j̸=h tjxj.
Proof. By linear dependence, we can find t1, . . . , tk, not all zero, with Pk j=1 tjxj = 0. Take h with th ̸= 0. Then thxh = − X j̸=h tjxj implying that xh is a linear combination of the other xj’s. Dividing by th, we obtain xh = −1 th X j̸=h tjxj.
8 MATH METHODS 11.7 Examples of Linear Dependence The vectors x1 = 1 1 1 !
, x2 = 6 6 0 !
, x3 = 0 0 7 !
are linearly dependent as 7x1 −(7/6)x2 −x3 = 0.
Another set of linearly dependent vectors is x1 = 1 0 , x2 = 1 √ 2 1 1 , x3 = 1 √ 2 1 −1 .
Here x1 −1 √ 2 x2 + x3 = 0.
LINEAR INDEPENDENCE 9 11.8 Linear Dependence and Independence Linear Independence. We call non-zero vectors x1, . . . , xk linearly inde-pendent if they are not linearly dependent.
Equivalently, a set of non-zero vectors X = {x1, . . . , xk} is linearly independent if Pk j=1 tjxj = 0 implies t1 = t2 = · · · = tk = 0. Linear independence implies there is at most one vector t with x = Xt where X is the matrix formed by setting the jth column of X equal to xj ∈X.
The vectors x1 = 1 1 0 !
, x2 = 0 1 1 !
, x3 = 1 0 1 !
are linearly independent.
Suppose Xt = t1x1 + t2x2 + t3x3 = t1 + t3 t1 + t2 t2 + t3 !
= 0 0 0 !
.
Then t1 = −t3, t1 = −t2, and t2 = −t3. Combining these, we find t = 0. Since the only linear combination of x1, x2, and x3 that is zero is the zero linear combination, the vector are linearly independent.
10 MATH METHODS 11.9 Orthogonal Vectors are Linearly Independent Orthogonal sets of vectors are automatically independent.
Theorem 11.9.1. Let B = {bi}k i=1 be a set of orthogonal vectors in an inner product space V. Then B is a linearly independent set.
Proof. Suppose there are real numbers ti with z = k X i=1 tibi = 0 Now consider 0 = z·bj = k X i=1 tibi !
·bj = k X i=1 tibi·bj !
= k X i=1 tiδij !
= tj for every j = 1, . . . , k. Since every tj = 0, the vectors must be linearly independent.
LINEAR INDEPENDENCE 11 11.10 Too Many Vectors Must Be Dependent If there are too many vectors, they must be linearly dependent.
Theorem 11.10.1. Suppose x1, . . . , xk are non-zero vectors in Rn with k > n. Then x1, . . . , xk are linearly dependent.
Proof. Consider the equation Xt = 0.
Since there are more vari-ables than equations, there is at least one free variable. It follows that Xt = 0 has infinitely many solutions, establishing linear dependence.
Alternatively, we could quote Corollary 7.26.1.
◮Example11.10.2: Morethan nVectors areLinearlyDependentin Rn. For example, suppose that in R3, we have x1 = 1 1 1 !
, x2 = 1 1 0 !
, x3 = 0 1 1 !
, and x4 = 1 0 1 !
.
These vectors are linearly dependent because there are too many of them. In fact, x1 is a linear combination of the others: x1 = (1/2)(x2 + x3 + x4). ◭ 12 MATH METHODS 11.11 Spanning Sets A second issue concerning coordinate systems is whether a given set of vectors is big enough to encompass all possible vectors as linear combi-nations. If so, every vector will have coordinates in our system. If not, there will be vectors outside the coordinate system.
Span. A set of non-zero vectors X = {x1, . . . , xk} ⊂V spans a vector space V if Pk j=1 tjxj = Xt = y has a solution for every y ∈V.
Equivalently, x1, . . . , xk span V if every vector in V is a linear combi-nation of x1, . . . , xk. If the vectors we are using to build a coordinate system span V, then every vector can be written using our coordinate system.
LINEAR INDEPENDENCE 13 11.12 Size of Spanning Sets in Rn Any set that spans Rn must contain at least n vectors.
Theorem 11.12.1. If X = {x1, . . . , xk} is a set of non-zero vectors that spans Rn, then k ≥n.
Proof. If X spans Rn, construct X from X as before. Then y = Xt always has a solution. Corollary 7.30.1 tells us that rank X = n, which implies k ≥n.
More generally, if V is a vector subspace of Rn, x1, . . . , xk span V if Xt = x has a solution for every x ∈V.
14 MATH METHODS 11.13 Examples of Spanning Sets The set x1 = 1 1 , x2 = 1 −1 , x3 = 1 0 spans R2. To see it, suppose x1 x2 = t1x1 + t2x2 + t3x3 = t1 + t2 + t3 t1 −t2 .
This system has infinitely many solutions.
t = x2 0 x1 −x2 !
and t′ = x2 + 1 1 x1 −x2 −2 !
are two of them. We can use the fact taht X 1 1 −2 !
= 0 to find others.
LINEAR INDEPENDENCE 15 11.14 Basis of a Vector Space Larger sets that span will involve some redundancy. Theorem 11.10.1 says they will be linearly dependent, so by Theorem 11.6.1 at least one can be written as a linear combination of the others. So every time it appears in a linear combination, it can be replaced. It is redundant. It is not needed to span the set.
This brings us to the concept of a basis. A basis is a set of vectors that is big enough to span, but small enough to be linearly independent.
Basis. A set of non-zero vectors {x1, . . . , xk} ⊂V are a basis for a vector space V if 1. x1, . . . , xk are linearly independent.
x1, . . . , xk span V.
Bases are ideal for building coordinate systems. They are neither too big nor too small. A basis is just right. We can write any vector as a linear combination of the basis vectors, and there is only one way to do it, only one set of coordinates for each vector.
Theorem 11.14.1. Every basis for Rn has exactly n elements.
Proof. Suppose x1, . . . , xk is a basis for Rn.
By Theorem 11.12.1, k ≥n, and by Theorem 11.10.1, k ≤n. Thus k = n.
16 MATH METHODS 11.15 Bases and Independent Sets II Theorem 11.15.1. Let B = {b1, . . . , bn} be a basis for a vector space V.
Suppose S ⊂V has m > n elements. Then the vectors in S are linearly dependent.
Proof. Let S be as described. We can write S = {x1, . . . , xm}. Since B is a basis for V, and S ⊂V, we can write each xi as a linear combination of the basis vectors B. That means there are aij, for i = 1, . . . , m and j = 1, . . . , n, with xi = n X j=1 aijbj.
To examine linear independence of the xi, we consider the equation m X i=1 tixi = 0.
We will show it has non-zero solutions. We start by rewriting it 0 = m X i=1 ti n X j=1 aijbj = n X j=1 m X i=1 tiaij !
bj.
Proof continues ...
LINEAR INDEPENDENCE 17 11.16 Bases and Independent Sets I Remainder of Proof. As the bj are linearly independent, this implies their coefficients are zero. That means m X i=1 tiai1 = 0, m X i=1 tiai2 = 0, . . . , m X i=1 tiain = 0.
We have n equations in m unknowns, which we can write in matrix form as ATt = 0. This homogeneous system not only has a solution, but must have infinitely many solutions because there are more unknowns (m) than equations (n). See Corollary 7.29.1. It follows that there are t1, . . . , tm, not all zero, with m X i=1 tixi = 0.
In other words, the {xi} must be linearly dependent.
18 MATH METHODS 11.17 The Dimension of a Vector Space An important consequence of Theorem 11.15.1 is that every basis of a vector space must be the same size, provided the size if finite. More precisely.
Basis Theorem. Suppose a vector space V has a basis B with n elements where n is finite. Then every other basis of that vector space must also have n elements.
Proof. Any other basis must be a linearly independent set, so by The-orem 11.15.1, it cannot have more than n elements.
If there was a basis with fewer than n elements, we could apply The-orem 11.15.1 to determine that B is not a linearly independent set, and so not a basis. This contradicts our hypothesis, so it is impossible. We conclude that any basis has exactly n elements.
The Basis Theorem lets us define the dimension of a vector space, at least when the dimension is finite.
Suppose a vector space V has a finite basis B. The Basis Theorem tells us that any basis for V will have the same number of elements as B.
Dimension. For vector spaces with a finite basis, we define the dimension of V as the number of elements of that basis.
By the Basis Theorem, the dimension does not depend on which basis we use. We denote the dimension of V by dim V.
LINEAR INDEPENDENCE 19 11.18 Is the Dimension of a Vector Space Always Finite?
Although we started with a basis with a finite number of elements, there are vector spaces with infinite bases. The arguments become trickier then, and we will not consider that case further other than to give an example.1 ◮Example 11.18.1: Attempted Basis for the Sequence Space. The se-quence space s contains infinite linearly independent sets.
For s, define the vectors ej, j = 1, 2, 3, . . . by (ej)i = δij.
Then e1 = (1, 0, 0, . . . ), e2 = (0, 1, 0, 0, . . . ), etc.
We now have an infinite set E = {e1, e2, e3, . . . } that seems like a possible basis.
The set E is linearly independent in s. However, E is not a basis for s because it does not span s. The problem is that linear combinations involve finite sums, and vectors such as (1, 1, 1, . . . ) cannot be written as a finite sum of the ej.2 ◭ 1 When the vector space is infinite, we have two choices. We can continue to use finite linear combinations (Hamel basis), or we can allow infinite linear combinations, infinite sums. If we use the metric we previously defined on s, it is possible to show that the partial sums Pn i=1 xiei converge to x ∈s for every x. This is an example of a Schauder basis.
The German mathematician George Hamel (1877–1954) is best known for the Hamel basis. He used the concept to show Cauchy’s functional equation, f(x+y) = f(x)+f(y) has a infinity of non-linear solutions if no regularity condition is imposed. These solutions are called Hamel functions, and relate the 3rd and 5th Hilbert problems. Hamel also worked on cryptography.
Juliusz Paweł Schauder (1899–1943) was a Polish mathematician who worked in functional analysis, partial differential equations, and mathematical physics. He was killed by the Gestapo.
Besides the Schauder basis, he is known for the Schauder Fixed Point Theorem and the Open Mapping Theorem (sometimes called the Banach-Schauder Theorem).
2 If we allow infinite sums, the standard basis vectors will do nicely, providing a (Schauder) basis. However, we need to learn more about limits, particularly limits in s, before attempting this.
Hamel bases do exist, but methods of showing that are non-constructive. In other words, don’t ask what they look like.
20 MATH METHODS 11.19 Testing for a Basis 9/15/22 We can use our various results on solving equations to construct a test to see if {b1, . . . , bn} form a basis for Rn. Item (4) of the theorem is the test.
Theorem 11.19.1. Let {b1, . . . , bn} be a collection of vectors in Rn. Form the n × n matrix B whose columns whose columns are the bj. Then the following are equivalent.
b1, . . . , bn are linearly independent 2. b1, . . . , bn span Rn 3. b1, . . . , bn form a basis for Rn 4. det B is non-zero Proof. (1) implies (2). Linear independence means Bx = 0 has at most one solution, so rank B = #cols = n by Corollary 7.30.1. As B is n × n, this is also the number of rows, so Bx = y always has a solution by Corollary 7.31.2, showing that the vectors span.
(2) implies (3). We do this by showing (2) implies (1). Just use the same arguments in the opposite order. Then the vectors {b1, . . . , bn} span and are linearly independent, so they are a basis.
(3) clearly implies (1) and (2). So (1), (2), and (3) are equivalent.
(1)-(3) are equivalent to (4). As we saw above, (1), (2), and (3) are equivalent to rank B = n = #cols = #rows, which is equivalent to B being non-singular (Corollary 7.32.1). Finally, det B is non-zero if and only B is non-singular, completing the proof.
LINEAR INDEPENDENCE 21 11.20 Finding an Orthonormal Basis If we have a basis B for an inner product space, we can use it to construct an orthonormal basis using the Gram-Schmidt method.3 Let B = {b1, . . . , bn} be a basis for an inner product space V. The Gram-Schmidt method first constructs an orthogonal basis from B, and then normalizes it to obtain an orthonormal basis. Define w1 = b1 w2 = b2 −w1·b2 w1·w1 w1, w3 = b3 −w1·b3 w1·w1 w1 −w2·b3 w2·w2 w2, etc.
· · · wn = bn − n X i=2 wi−1·bn wi−1·wi−1 wi−1 (11.20.1) We will show that the set W = {w1, . . . , wn} is an orthogonal basis.
3 The Gram-Schmidt method can be found on page 624 of Simon and Blume.
The Danish mathematician and actuary Jørgen Pedersen Gram (1850–1916). He’s known for his reformulation of the Riemann zeta function. The Gramian (Gram matrix) is used in the analysis of control system and in econometrics.
Erhard Schmidt (1876–1859) was a German mathematician from what is now Estonia.
He was a student of Hilbert and contributed to Zermelo’s proof of the Well-ordering Theorem using the Axiom of Choice. He’s also known for Hilbert-Schmidt operators.
22 MATH METHODS 11.21 The Gram-Schmidt Vectors are Orthogonal I Theorem 11.21.1. If B is a basis for the inner product space V, then W = {w1, . . . , wn} as defined by equation (11.20.1) is also a basis for V.
Proof. Each of the wi is defined in terms of the bj for j = 1, . . . , i, and thus in their span. Alternatively, we can use equation (11.20.1) to write the bi in terms of the wj for j = 1, . . . , i. This shows that B ⊂L[W]. It follows that V = L[B] ⊂L[W] = V.
By Theorem 11.9.1, orthogonal vectors are linearly independent. Since they span V, that will imply they are a basis for V. All that remains is to show that W is an orthogonal set of non-zero vectors.
Note that if any wi were zero, it would contradict the linear indepen-dence of B.
We show that the wi are orthogonal vectors by inductively showing all of the {w1, . . . , wI} are orthogonal for I = 1, . . . , n. In this I = 1 case this reduces to {w1} = {b1}, which is trivially an orthogonal set of vectors.
Proof continues ...
LINEAR INDEPENDENCE 23 11.22 The Gram-Schmidt Vectors are Orthogonal II Remainder of Proof. For the induction step, suppose the set {w1, . . . , wI} is orthogonal for some I < n. We must show adding wI+1 to the set maintains orthogonality. That means we need to show wI+1·wj = 0 for all j = 1, . . . , I.
Now wI+1·wj = bI+1·wj − I+1 X i=2 wi−1·bI+1 wi−1·wi−1 (wi−1·wj) = bI+1·wj − I+1 X i=2 wi−1·bI+1 wi−1·wi−1 δi−1,j(wj·wj) = bI+1·wj −wj·bI+1 = 0.
Because of the Kronecker delta, only the i−1 = j term remains of the sum in the third line. We have proved the induction step that {w1, . . . , wI+1} is an orthogonal set of vectors. It follows that W is an orthogonal set of vectors, and hence a basis.
We can form an orthonormal basis from W by defining vi = wi ∥wi∥.
Then {v1, . . . , vn} is an orthonormal basis derived from B.
24 MATH METHODS 11.23 Testing for Linear Independence NEW Theorem 11.19.1 gave us a determinant test for a basis. There’s also a determinant test for linear independence.
The matrix Y = XTX is a Gramian matrix. Suppose X is a k×m matrix and we write it as a row of k column vectors, X = x1 x2 · · · xk .
where each xi is a column vector. We can write yij = xi·xj, the hallmark of a Gramian matrix.4 Theorem 11.23.1. Let x1, . . . , xk be vectors in Rm. Form the matrix m×k matrix X = ( x1 · · · xk ). Then {x1, . . . , xk} is a linearly independent set if and only if the Gramian matrix Y = XTX is invertible. Equivalently, {x1, . . . , xk} is linearly independent if and only if the Gramian determinant det(XTX) is not zero.
Proof. Take any z ∈Rk and form the product zTXTXz = ∥Xz∥2 = k X j=1 zjxj 2 .
If the xj are not linearly independent, there will be a z ̸= 0 with Xz = 0, implying that XTX is not invertible.
If the xi are linearly independent, the norm will only be zero when z = 0. Then the expression zTYz is positive definite, implying that the square matrix Y is invertible.
It follows that {x1, . . . , xk} are linearly independent if and only if det Y = det(XTX) ̸= 0.
4 Gramian matrices often occur in econometrics, including the OLS estimator. They are named after Jørgen Pedersen Gram.
LINEAR INDEPENDENCE 25 11.24 Subspaces and Direct Sums We can define linear independence of subspaces in a manner similar to independence of vectors.
Independent Subspaces. Let W1, . . . , Wk be subspaces of a vector space V. The subspaces are linearly independent if wi ∈Wi for all i = 1, . . . , k and w1 + w2 + · · · + wk = 0 implies wi = 0 for all i = 1, . . . , k.
Now suppose W1, . . . , Wk are independent subspaces of V. The direct sum of W1, . . . , Wk is L W1, . . . , Wk . We write the direct sum as W1 ⊕· · · ⊕Wk.
By using a direct sum, we indicate there is a unique way to write any x ∈V as x = w1 + · · · + wk. This type of direct sum, where all of the Wk are contained in the vector space V, is known as an internal direct sum. It’s easily verified that dim W1 ⊕+ · · · + ⊕Wk = dim W1 + · · · + dim Wk.
◮Example 11.24.1: Direct Sum. In R3, consider the subspace W1 spanned by w1 = (1, 1, 1)T and the subspace W2 spanned by w2 = (1, 2, 1)T and w3 = (2, 1, 1)T. Because {w1, w2, w3} is a basis for R3, these are independent subspaces. We can now write R3 = W1 ⊕W2. ◭ 26 MATH METHODS 11.25 External Direct Sums Another type of direct sum is the external direct sum. Let W1, . . . , Wk be vector spaces, and consider V = {v = (w1, 0, . . . , 0) + · · · (0, . . . , 0, wk) : each wi ∈Wi}.
Defining vector sums and scalar products in the obvious way makes V a vector space, the external direct sum of W1, . . . , Wk, V = W1 ⊕W2 ⊕· · · ⊕Wk.
We can then write direct sums such as Rn = n times z }| { R ⊕R ⊕· · · ⊕R or like R6 = R3 ⊕R2 ⊕R.
The only real difference between internal and external direct sums is the starting point. Suppose V is the external direct sum defined in terms of spaces Wk. Setting ˆ W1 = (w1, 0, . . . , 0) : w1 ∈W1 , ˆ W2 = (0, w2, 0, . . . , 0) : w2 ∈W2 , .
.
.
ˆ Wk = (0, . . . , 0, wk) : wk ∈Wk allows to write V as the internal direct sum ˆ W1 ⊕· · · ⊕ˆ Wk.
LINEAR INDEPENDENCE 27 11.26 Direct Sums of Linear Transformations We can also define direct sums of linear transformations. Suppose V = W1 ⊕· · · ⊕Wk and that Ti: Wi →Wi are linear transformations for i = 1, . . . , k. We define their direct sum, T = T1 ⊕· · · ⊕Tk by T(w1 ⊕· · · ⊕wk) = T1(w1) ⊕· · · ⊕Tk(wk) for every w1 ⊕· · · ⊕wk ∈W1 ⊕· · · ⊕Wk.
It is easily verified that T is a linear transformation from V to V.
Now suppose each Ti is represented by a matrix Ai on Wi in some basis Wi. Now L[W1, . . . , Wk] is a basis for V and in that basis, the matrix A for T takes the block diagonal form A = A1 0 0 · · · 0 0 A2 0 · · · 0 0 0 A3 · · · 0 0 0 0 ...
0 0 0 0 · · · Ak where row block i has ni rows and column block i has ni columns, making the matrix n × n where n = n1 + · · · + nk.
Conversely, any block diagonal matrix can be regarded as a direct sum of matrices.
28 MATH METHODS 27. Subspaces Attached to a Matrix This chapter draws on Chapter 27 of Simon and Blume.
27.1 The Kernel of a Matrix We saw in Theorem 7.3.1 that the solution set of a linear system is not affected by row operations. When applied to homogeneous systems, that means the kernel is not affected by row operations either. In particular, its dimension is not affected.
We also saw in section 10.16 that the solution set to Ax = b is a translate of ker A, so the dimension of the kernel tells us what the solution set looks like in general. It is just a translate of the kernel.
So what is the dimension of the kernel?
SUBSPACES ATTACHED TO A MATRIX 29 27.2 Kernel Example Let’s look at an example. Suppose the reduced row-echelon form of the coefficient matrix is R = 1 1 0 1 1 1 0 0 1 1 0 1 .
There are two basic variables (x1 and x3) and four free variables (x2, x4, x5, and x6). Each of the free variable columns have been marked in red.
The reduced matrix now gives us two equations that define the kernel: 0 = x1 + x2 + x4 + x5 + x6 0 = x3 + x4 + x6.
(27.2.1) We can find a basis for the kernel by successively setting each of the free variables but one to zero. The non-zero variable can be anything we want. We choose +1. Then we use equations (27.2.1) to solve for the basic variables x1 and x3. Here are the results.
b2 = −1 1 0 0 0 0 , b4 = −1 0 −1 1 0 0 , b5 = −1 0 0 0 1 0 , b6 = −1 0 −1 0 0 1 .
We have labelled the vectors by which xi = +1.
Each vector bi is in the kernel, and they are all linearly independent.
This is clear because each row i = 2, 4, 5, 6 is non-zero only for one of the vectors. This happens because each vector is generated by considering a case where only one of the free variables is non-zero, which forces the corresponding row to be non-zero.
The result of all this is that dim ker A = #free vars.
30 MATH METHODS 27.3 The Dimension of the Kernel It’s nice to have a illustrative example, but it is no substitute for a proof.
Fortunately, all the proof needs is to add some words of explanation.
Theorem 27.3.1. Let A be an m × n matrix. Then dim ker A = #free vars.
Proof. Row reduce A to a reduced row-echelon form R. Both A and R will have the same kernel because elementary row operations do not affect the solution set.
Write down the homogeneous equations corresponding to the reduced row-echelon form R. For each free variable i, set xi = 1, all the other free variables to zero, and solve for the basic variables. This defines a vector bi for each free variable i.
Each bi solves the homogeneous equations, so bi ∈ker A. Suppose x ∈ker A. Then x solves the reduced row-echelon system for some values xi of the free variables. We can write x = X i∈free vars xibi showing that the bi span ker A.
As bi is the only one of the bj where row i is non-zero, the bj are linearly independent. It follows that they form a basis for ker A, so dim ker A = #free vars.
SUBSPACES ATTACHED TO A MATRIX 31 27.4 Fundamental Theorem of Linear Algebra Equation (7.19.2) tells us that the number of free variables and the num-ber of basic variables add to the number of variables (n). Combining that with Theorem 27.3.1, we obtain #basic vars = n −dim ker A.
Since rank A is the number of basic variables, we can sum this up as follows.
Fundamental Theorem of Linear Algebra. Let A be an m × n matrix.
Then n = rank A + dim ker A.
32 MATH METHODS 31. Transformations and Coordinates You’ll notice there’s no Chapter 31 in Simon and Blume. Some of this material is not in Simon and Blume, some is scattered in the text.
It’s often helpful to analyze vector space problems based on general considerations rather than being tied to a specific vector space charac-terized by a particular basis.
We can change bases of vector spaces regardless of whether we think of them as being subspaces of Rn or something else entirely. However, if two vector spaces have the same finite dimension there will always be a mapping that will allow us to treat them as identical, as far as all vector space constructions are concerned. In a sense, all finite dimensional real vector spaces can be thought of as Rn.
TRANSFORMATIONS AND COORDINATES 33 31.1 Isomorphic Vector Spaces So when are two vector spaces essentially the same? If only the vector space properties matter, the answer is that they are the same if they are isomorphic vector spaces.
Isomorphic Vector Spaces. Two vector spaces V and W over the same field F are isomorphic if there is a linear transformation T : V →W that is one-to-one and onto. Such a mapping is called a linear isomorphism.
The fact that the transformation is linear tells us that it preserves the vector space operations.
The fact that it is bijective means it has an inverse.
If two isomorphic vector spaces had different underlying fields, we would have difficultly making sense of T(αx) = αT(x) and T −1(αy) = αT −1(y). So we require they be based on the same field, the same set of scalars.
Isomorphism says nothing about how non-vector space structures relate in the two vector spaces. Isomorphism as vector spaces says nothing about whether one space has a norm or metric and the other does not.
Such questions require other concepts of isomorphism that preserve those structures, just as linear mappings preserve everything linear.
34 MATH METHODS 31.2 The Inverse of a Linear Isomorphism The inverse of a linear isomorphism is also a linear isomorphism.
Theorem 31.2.1. Suppose T : V →W is a linear isomorphism between vector spaces V and W. Then the inverse transformation T −1 exists and is also a linear isomorphism.
Proof. For any y ∈W, let T −1(y) denote the unique x ∈V with T(x) = y. Here such x exist because T maps onto W, and x is unique because T is one-to-one.
Now if x, y ∈W, then for any scalar α, T αT −1(x) + T −1(y) = αx + y, showing that T −1(αx + y) = αT −1(x) + T −1(y). In other words, T −1 is linear.
For every x ∈V, T −1 T(x) = x, showing that T −1 is onto. And if v, w ∈W and T −1(v) = T −1(w), then apply T to find v = w, showing that T −1 is one-to-one. Thus T −1 is a linear isomorphism from W to V.
One consequence is that if V and W are isomorphic via T, they are also isomorphic via T −1 (in the opposite direction). This means that anything in V is, from a vector space point of view, faithfully reproduced in W, and vice-versa.
TRANSFORMATIONS AND COORDINATES 35 31.3 Matrix Isomorphisms One important result is that a linear isomorphism T from Rn to Rm can be written T(x) = Ax, that m = n, and that A is invertible.
Theorem 31.3.1. Let T : Rn →Rm be a linear isomorphism. Then m = n and there is an invertible matrix A with T(x) = Ax for every x ∈V.
Proof. Let T be as above. Because the mapping is linear, we can use Theorem 10.6.1 to find an m × n matrix A with T(x) = Ax.
Since T is a linear isomorphism, it must be both one-to-one and onto.
The first requires that rank A = n by Corollary 7.29.1. By Corollary 7.31.2, the fact that T is onto tells us that rank A = m.
Combining these shows m = n = rank A, which means that A is non-singular, that it must be invertible.
Notice that T −1 can be written T −1(y) = A−1y for every y ∈W.
36 MATH METHODS 31.4 Isomorphic Vector Spaces have the Same Dimension In fact, any two isomorphic finite dimensional vector spaces, not just Rn, must have the same dimension.
Theorem 31.4.1. Let V and W be finite-dimensional vector spaces and T : V →W be an isomorphism. Then dim V = dim W.
Proof. Let V = {v1, . . . , vk} be a linearly independent set in V. I claim that {T(vj)}k j=1 is a linearly independent set in W. If not, there are tj, not all zero, with Pk j=1 tjT(vj) = 0. Applying T −1, we find Pk j=1 tjvj = 0, contradicting the fact that V is a linearly independent set.
Now let V be a basis for V.
Since T(V) is linearly independent in W, dim W ≥dim V. Consideration of the isomorphism T −1 shows that dim V ≥dim W, so dim V = dim W.
TRANSFORMATIONS AND COORDINATES 37 31.5 Same Dimension Implies Isomorphic Spaces It’s also easy to show that two vector spaces over a field F that have the same finite dimension are isomorphic. The key to the proof is to create an isomorphism by mapping basis elements of one to basis elements of the other.
Theorem 31.5.1. Let V and W be finite-dimensional vector spaces over the same field F. If dim V = dim W, there is an isomorphism T : V →W.
Proof. Suppose dim V = dim W = n. Let V = {v1, . . . , vn} be a basis for V and W = {w1, . . . , wn} be a basis for W.
Define T : V →W on the basis elements of V by T(vi) = wi. Since V is a basis, we may use linearity to define T on all of V. The resulting transformation T maps V into W. We will show it is bijective.
(1) The linear mapping T maps onto W (surjective).
To see that, consider x ∈W.
We can find xj with x = P j xjwj.
But then x = T P j xjvj . This shows that T maps onto W.
(2) The mapping T is one-to-one (injective). Suppose T(x) = T(y) for some x, y ∈V. Since V is a basis for V, we can write x = P j xjvj and y = P j yjvj. Applying T, we find P j xjwj = P j yjwj. As W is linearly independent, xj = yj for all j = 1, . . . , n, showing that x = y. It follows that T is an one-to-one.
By (1) and (2), T is an isomorphism.
One corollary is that any n-dimensional real vector space is isomorphic to Rn.
We can combine the last two theorems as follows: Theorem 31.5.2. Let V and W be finite-dimensional vector spaces. Then dim V = dim W if and only if there is an isomorphism T : V →W.
38 MATH METHODS 31.6 Isomorphism Example ◮Example 31.6.1: An Isomorphism. Let W = {x ∈R3 : x1+x2+x3 = 0}.
This is a two-dimensional subspace of R3 and should be isomorphic with R2. We start by finding a basis for W. The vectors b1 = 1 0 −1 !
, b2 = 0 1 −1 !
will do (as a linearly independent set in a two-dimensional space, they must be a basis).
Define T x1 x2 = x1b1 + x2b2 = x1 1 0 −1 !
x2 0 1 −1 !
= x1 x2 −x1 −x2 !
Because b1 and b2 are linearly independent, T is one-to-one, and be-cause bi spans W, it is onto. That makes it an isomorphism. The inverse map T −1: W →R2 projects onto R2. It is T −1 y1 y2 y3 !
= y1 y2 .
Notice we tossed y3. Keep in mind that the components of y must sum to zero by the definition of W, so on W, y3 = −y1 −y2. ◭ 31. TRANSFORMATIONS AND COORDINATES 39 31.7 Isometric Normed Spaces Normed spaces and inner product spaces have to meet higher standards for isomorphism because they have structure beyond their vector space structure that must be preserved.
Isometric Normed Spaces. An isomorphism T between normed spaces V, ∥· ∥1 and W, ∥· ∥2 is a vector space isomorphism between V and W that preserves the norm, ∥T(x)∥2 = ∥x∥1. Such isomorphisms are also called linear isometries or isometric isomorphisms.
Norm-preserving mappings are often linear. To state this more precisely, define the midpoint of two vectors x and y as (x + y)/2.
We state the following theorem of Mazur and Ulam without proof.1 Mazur-Ulam Theorem. Let V and W be normed spaces and T a mapping of V onto W with ∥Tx∥2 = ∥x∥1 and T(0) = 0. Then T maps midpoints to midpoints and is linear as a map over R.
This means that T is an isometric isomorphism between V and W. The result can fail in complex vector spaces.
You’ll notice that although T maps midpoints to midpoints, that is not generally true of ∥T∥. What happens is that T 1 2(x + y) = 1 2 T(x) + T(y) ≤1 2 ∥T(x)∥+ ∥T(y)∥ .
However, the triangle inequality is often strict, so T usually doesn’t map midpoints to midpoints.
1 Barry Mazur (1937–) is an American mathematician. He’s done work in a variety of fields, ranging from functional analysis (as here) to arithmetic geometry (Mazur Torsion Theorem), geometric topology (Eilenberg-Mazur Swindle), and knot theory. His work also contributed to Wiles’s proof of Fermat’s Last Theorem Stanisław Marcin Ulam (1909–1984) was a Polish-American mathematician and physicist. He was part of the Manhattan project, and his contributions to designing the Teller-Ulam design for the H-bomb made it actually work. He’s known for devel-oping the method of Monte-Carlo simulations and cellular automata. He also worked on using bombs to propel rockets, which turned into Project Orion, led by Ted Taylor and Freeman Dyson.
40 MATH METHODS 31.8 Isomorphic Inner Product Spaces Inner product spaces have an even higher standard to uphold for iso-morphism.
The inner product must be preserved, meaning that an-gles between vectors remain the same.
We will use the notation ⟨x, y⟩i, i = 1, 2, . . . to distinguish the inner products. Preserving the inner product means the norm is also preserved, so inner product space isomorphisms are always isometric.
Isomorphic Inner Product Spaces. An isomorphism T between inner prod-uct spaces V, ⟨·, ·⟩1 and W, ⟨·, ·⟩2 is a vector space isomorphism be-tween V and W that preserves the inner product, ⟨T(x), T(y)⟩2 = ⟨x, y⟩1.
Using less precise notation, we may write the inner product condition as T(x)·T(y) = x·y.
This notation is a bit dangerous as it leads to easy confusion of the two different inner products that are involved.
TRANSFORMATIONS AND COORDINATES 41 31.9 Characterizing Inner Product Isomorphisms Suppose T : Rn →Rn is an inner product isomorphism when both Rn’s have the Euclidean inner product. Such a mapping is also an isometry.
The image of the standard basis is not only a basis (guaranteed by the vector space isomorphism), but must be an orthonormal basis.
Theorem 31.9.1. Let T be an inner product isomorphism from Rm to Rm and suppose {b1, . . . , bm} is an orthonormal basis for Rm. Then {T(bi)} is also an orthonormal basis for Rm.
Proof. To see this, we compute T(bi)·T(bj) = bi·bj = δij.
Since T(bi)·T(bj) = δij for all i, j = 1, . . . , m, T(bi) is an orthonormal set.
In particular, Theorem 31.9.1 applies when we use the standard basis vectors in Rm. They are mapped to an orthonormal set. This means that T is either a rotation, or a rotation together with an reflection.
The following lemma is useful in inner product spaces.
Lemma 31.9.2. Let V be an inner product space and suppose x and x′ obey x·y = x′·y for every y ∈V. Then x = x′.
Proof. Now (x −x′)·y = 0 for every y ∈V. Set y = x −x′ to obtain ∥x −x′∥2 = 0. It follows that x = x′.
42 MATH METHODS 31.10 Automorphisms An automorphism on a vector space V is an isomorphism from V to itself, T : V →V. Here will will consider automorphisms that preserve the inner product on ℓn 2, Euclidean Rn.
Automorphisms are not quite as specialized as you might think. When we have a linear isomorphism, the two vector spaces involved have the same dimension, and the isometry makes them act like they are identical.
Actually requiring they be the same space is then a small additional step.
TRANSFORMATIONS AND COORDINATES 43 31.11 Characterizing Automorphisms on ℓn 2 Suppose a matrix A defines an automorphism on ℓn 2, then A−1 = AT.
Theorem 31.11.1. Let T be an automorphism on ℓn 2. Let A be any matrix representation of T. Then ATA = I.
Proof. Under these conditions (Ax)·(Ay) = x·y for all x, y ∈Rn.
Now x·y = (Ax)·(Ay) = (Ay)T(Ax) = (yTAT)(Ax) = yT (ATA)x = (ATA)x·y.
Since this holds for every y ∈Rn, Lemma 31.9.2 implies that ATAx = x.
This holds for every x, which implies ATA = I.
The result can also be written as A−1 = AT.
When the vector space is Cn, we use x·y = x∗y = Pn j=1 xjyj. In that case, we find that the inner product is preserved when the basis matrix U obeys U∗U = I. Such matrices are called unitary matrices and are the complex version of rotations and reflections. We can still use det U = ±1 to sort out which is which.
44 MATH METHODS 31.12 Automorphisms on ℓn 2: ATA = I Automorphsims on Rn can be represented by matrices with ATA = I.
Let ai, i = 1, . . . , n denote the columns of A. Then aT i is the ith row of AT, and aT i aj = ai ·aj = δij, showing that the columns form an orthonormal basis for Rn. Since A maps ei 7→ai, we have either a pure rotation of the coordinates, or a combination of a rotation and reflection.
In fact, the pure rotations all have det A = +1, while those involving reflections have det A = −1. As in R2, an even number of reflections amounts to a rotation. I think the main reason it is less clear in dimensions higher than 3 is that our intuition doesn’t work so well there. I’ll have more to say about this.
◮Example 31.12.1: A Reflection in R2. Reflections also obey ATA = I, but the determinant is −1. For example, reflecting in the horizontal axis maps (e1, e2) 7→(e1, −e2). The new basis matrix is B = 1 0 0 −1 which has determinant −1.
Notice that multiplying again by B returns us to our original coordinates.
This transformation can’t possibly be a rotation because the diagonal elements are not the same. We will see in section 31.14 that rotating R2 by an angle θ makes both diagonal elements of the basis matrix the same: cos θ. Also, rotations always have determinant +1, this has determinant −1. ◭ 31. TRANSFORMATIONS AND COORDINATES 45 31.13 Rotations and Reflections in Two Dimensions Let’s start with R2 and let T be an automorphism of R2. Equivalently, T is generated by a matrix A obeying ATA = I.
The fact that a1 = T(e1) is perpendicular to a2 = T(e2) means that a2 lies on the line perpendicular to a1. Since a2 is a unit vector, there are only two possible places to put it. One is a rotation. The other involves a reflection together with a rotation. This is illustrated in Figure 31.13.1.
Rotation e1 e2 a1 a2 45◦ 45◦ x1 x2 Rotation and Reflection e1 e2 a1 a2 a′ 2 45◦ 45◦ x1 x2 Figure 31.13.1: In the left panel the standard coordinate vectors are rotated counter-clockwise by 45◦. The dashed line is perpendicular to a1 and shows the line that a2 must lie in. Then a2 is the only unit vector on that line that is consistent with rotation. Using −a2 would require a combination of both rotation and reflection In the right panel, we make the opposite choice for a2, pointing downward along the 45◦line rather than upward.
This amounts to first making the rotation shown in the left panel. We then reflect the result about the dotted line through the origin defined by a1. This leaves a1 unchanged, but flips a2 (in gray) to a′ 2 (in red), yielding the new coordinates.
46 MATH METHODS 31.14 General Rotations in R2 I Consider a clockwise rotation of the canonical basis vectors in R2 by an angle θ < 0 (we use negative angles for clockwise rotations, positive for counter-clockwise). This rotates black vectors ei into the red ones bi.
Effect of Rotation by θ e1 e2 b1 b2 θ θ sin θ cos θ x1 x2 Figure 31.14.1: The standard basis vectors (in black) are rotated clockwise by an angle θ < 0. This yields the new basis vectors (in red). A little trigonometry gives us the coordinates in the old system.
Since bi is a unit vector, we can read the coordinates in terms of the sine and cosine of θ. Specifically, b1 = (cos θ, sin θ) and b2 = (−sin θ, cos θ).
TRANSFORMATIONS AND COORDINATES 47 31.15 General Rotations in R2 II As shown in the diagram, we have the following mapping: e1 = 1 0 7→ cos θ sin θ , e2 = 0 1 7→ −sin θ cos θ .
Note that the new vectors are still an orthonormal basis, as both vectors are rotated by the same angle. The new basis matrix is R(θ) = cos θ −sin θ sin θ cos θ , which has determinant cos2 θ + sin2 θ = 1, regardless of the angle θ.
Rotations always have a determinant of +1.
48 MATH METHODS 31.16 Example: A Rotation and its Inverse ◮Example 31.16.1: 45◦Rotation: Done and Undone. The matrix B = R(45◦) = 1 √ 2 1 −1 1 1 rotates the coordinates of R2 by 45◦, taking (1, 0)T to (1/ √ 2, 1/ √ 2)T and (0, 1)T to (−1/ √ 2, 1/ √ 2)T. Since this is a rotation, its transpose is also its inverse, and we have B−1 = R(−45◦) = BT = 1 √ 2 1 1 −1 1 .
Effect of B e1 e2 b1 b2 45◦ 45◦ x1 x2 Effect of BT e1 e2 bT 1 bT 2 45◦ 45◦ x1 x2 Figure 31.16.2: Here the standard coordinate axes are rotated counter-clockwise by 45◦in the left panel. Here b1 and b2 are the columns of B.
In the right panel, we have the inverse transformation where a 45◦clockwise rotation gives us the new coordinate axes. Here bT 1 and bT 2 are the columns of the matrix BT.
◭ 31. TRANSFORMATIONS AND COORDINATES 49 31.17 Rotations and Reflections in Three Dimensions In R3, T(e1) determines the perpendicular plane that the other T(ei) lie in. Once we know where T(e2) goes, there are only two choices for T(e3). One involves a rotation of {e1, e2, e3}, the other combines a reflection and rotation.
That the latter case is possible can be seen by letting your thumb, forefinger, and middle finger represent the basis vectors. Your right hand cannot be rotated to be a left hand, and vice-versa. However, a mirror can turn a right hand into a left hand, which is why a reflection might be needed.
In any Rn, there are two orientations of orthogonal axes. One that is a rotation of the standard axes, the other always involves a reflection.
50 MATH METHODS 31.18 The Orthogonal Group O(n) The rotations and reflections in Rn form a group, the orthogonal group in Rn, O(n). The pure rotations of are distinguished by having positive determinants. They also form a group, the special orthogonal group in Rn, SO(n).
The notations O(n, R) and SO(n, R) are used when its necessary to distinguish the real and complex cases.
Group. A group is a set G together with a binary operation (a, b) 7→ab that is associative and has an identity element e. Moreover, each element g ∈G has an inverse g−1 so that g−1g = gg−1 = e.
The group operation need not commute.
If it does commute, we call the group an abelian group.2 Groups are one of the fundamental concepts in modern algebra.
Groups sometimes involve the manipulations of physical objects. For example, the set of manipulations of Rubik’s Cube also forms a group.
The integers together with addition form an abelian group. The posi-tive real numbers under multiplication also form an abelian group. The invertible n × n matrices form a non-abelian group under matrix multi-plication.
As for O(n), it’s the set of n × n real matrices obeying ATA = I. The group operation for O(n) is matrix multiplication, which is associative. If A, B ∈O(n), the product AB is in O(n) because (AB)T(AB) = BT(ATA)B = BTB = I, and because I ∈O(n) is the identity element.
2 Named for Neils Henrik Abel (1802–1829), as is the Abel Prize, the mathematical equivalent of the Nobel. The Abel Prize was originally proposed in 1899, and in 1902, the King of Sweden and Norway was convinced to contribute to setting it up. However, politics intervened in the form of the 1905 dissolution of the union between Sweden and Norway. It wasn’t until 2001 that the Norwegian government actually set up the prize. A honorary Abel prize was given to Atle Selberg in 2002, with the first regular prize going to Jean-Pierre Serre in 2003. I’m not sure what the honorary prize was all about as Selberg had the mathematical accomplishments to get a regular prize. It did ensure that they started off with a Norwegian on the 200th anniversary of Abel’s birth.
Perhaps the regular funding was not available yet.
TRANSFORMATIONS AND COORDINATES 51 31.19 SO(2) is Abelian 9/20/22 First, we show SO(2) is abelian. Recall that the elements of SO(2) all have the form R(θi) = cos θi −sin θi sin θi cos θi .
Then R(θ1)R(θ2) = cos θ1 cos θ2 −sin θ1 sin θ2 −cos θ1 sin θ2 −cos θ2 sin θ1 sin θ1 cos θ2 + sin θ2 cos θ1 cos θ1 cos θ2 −sin θ1 sin θ2 = cos(θ1 + θ2) −sin(θ1 + θ2) sin(θ1 + θ2) cos(θ1 + θ2) = R(θ1 + θ2).
Then R1R2 = R(θ1 + θ2) = R2R1 for any θi, showing that all matrices in SO(2) commute.
52 MATH METHODS 31.20 SO(n) is Not Abelian when n > 2 For n > 2, SO(n) is non-abelian. It is enough to show it for n = 3, since the same rotations are available for n > 3 (holding the extra axes fixed).
To see that SO(3, R) is not Abelian, consider the rotations R1 = 0 1 0 −1 0 0 0 0 1 !
and R2 = 1 0 0 0 0 1 0 −1 0 !
These do not commute as R1R2 = 0 0 1 −1 0 0 0 −1 0 !
while R2R1 = 0 1 0 0 0 1 1 0 0 !
.
TRANSFORMATIONS AND COORDINATES 53 31.21 Bases and Coordinates We’ve used two sets of bases for several pages. It’s time to approach the different coordinate systems more systematically.
Let B = {b1, . . . , bn} be a basis for Rn. Define the basis matrix by lining up the basis vectors in order: B = b1 | b2 | · · · | bn .
By Theorem 11.19.1 (determinant test), B is invertible. Given a vector x ∈Rn, we find its vector of coordinates tB in the B basis by solving the equation x = BtB.
Because B is invertible, tB = B−1x.
This all applies to the standard basis E = {e1, . . . , en}. In that case, the basis matrix E is the n × n identity matrix. Nonetheless, we use a special name for it to emphasize that we are doing basis calculations.
Given a vector x, expressed in the standard coordinates, we find that tE = E−1x = Ix = x, meaning that the coordinates are what we think they are. (That’s a relief!) 54 MATH METHODS 31.22 Example: Coordinates in R3 Let’s see how this works in R3. The basis B = {b1, b2, b3}, defined by b1 = 1 2 3 !
, b2 = 2 0 2 !
, b3 = 1 1 1 !
, gives us the basis matrix B = 1 2 1 2 0 1 3 2 1 !
.
We now use the formula x = BtB To change from B coordinates to standard coordinates.
The vectors with coordinates tB = (1, 1, 0)T and t′ B = (1, 0, 3) yield the vectors x = BtB = (3, 2, 5)T and x′ = Bt′ B = (4, 5, 6) in standard coordinates.
Let’s see how it works the other way, going from standard basis E coordinates to B coordinates. For that, we use the formula tB = B−1x.
The inverse of B is B−1 = −1/2 0 1/2 1/4 −1/2 1/4 1 1 −1 !
.
The vector x = (3, 2, 1)T then has coordinates tB = B−1x = (−1, 0, 4)T in the basis B, meaning that x = −b1 + 4b3.
The vector x′ = (−1, −1, +5)T has coordinates t′ B = B−1x′ = (3, 3/2, −7) in the B basis, so that x′ = 3b1 + (3/2)b2 −7b3 = (−1, −1, +5) in the standard basis.
TRANSFORMATIONS AND COORDINATES 55 31.23 Changing Coordinate Systems Consider two different bases and coordinate systems, B = {b1, . . . , bn}, and B′ = {b′ 1, . . . , b′ n}, we form the corresponding basis matrices B and B′.
Given a vector x, we can write it in the two coordinate systems as x = BtB and x = B′tB′. Then BtB = B′tB′. Solving for tB and tB′, we derive the change of coordinates formulas: tB = B−1B′ tB′ and tB′ = (B′)−1B tB (31.23.1) Starting with the B′ coordinates, we multiply by B′ to get the actual vector x, and then multiply by B−1 to put it into the B coordinate system. Conversely, to convert the B coordinates to B′ coordinates, we reverse the process, multiplying first by B, and then by (B′)−1.
56 MATH METHODS 31.24 Example: Changing Coordinates in R2 To see how this works, suppose B = 1 1 0 1 and B′ = 1 2 2 1 are the basis matrices. Then B−1 = 1 −1 0 1 and (B′)−1 = 1 3 −1 2 2 −1 .
Consider the vector with B′ coordinates tB′ = (1, 4)T.
Using the formula, we obtain the B coordinates tB = 1 −1 0 1 1 2 2 1 1 4 = 3 6 .
Let’s check it. Now tB′ = (1, 4)T corresponds to x = 1 2 + 4 2 1 = 9 6 and x = 3 1 0 + 6 1 1 = 9 6 .
This shows that both expressions refer to the same vector x, whose standard coordinates are x = 9 6 .
TRANSFORMATIONS AND COORDINATES 57 31.25 Linear Transformations and Bases So how do these coordinate changes affect linear transformations? Take a linear transformation on Rn, T : Rn →Rn. As we saw in section 10.6, we can use the standard basis to represent this in matrix form, so that T(x) = Ax.
So what happens if we want to use a different basis? One reason to do such a thing would be to write the transformation in a more convenient form—one that is easier to calculate or interpret.
Let B be a basis matrix for B. We will write the matrix for T as AE when it is in standard (E) coordinates and AB when it is in B coordinates.
To find AB from AE, we start with B coordinates tB, then convert them to standard coordinates, x = BtB. Then we feed this to the matrix in standard coordinates, obtaining AEBtB.
As this is in standard coordinates, we have to convert the result back to the B coordinates. We do this by multiplying on the left by B−1. That gives us (B−1AEB)tB as the B coordinates of the transformed vector.
Thus AB = B−1AEB or BABB−1 = AE.
(31.25.2) is the matrix for T in B coordinates. The type of transformation used in equation (31.25.2) is sometimes called a similarity transformation.
58 MATH METHODS 31.26 Coordinate Change with Arbitrary Bases Things are a bit more complicated if we had originally used a basis other than the standard basis. If the transformation had been written in B′ coordinates, we would multiply by (B′)−1B to convert B coordinates to B′ coordinates, apply A, then convert back. The result is: AB = B−1B′ AB′ (B′)−1B .
Another way to write this that may make the method clearer is transform both matrices into standard coordinates: BABB−1 = AE = B′AB′(B′)−1.
TRANSFORMATIONS AND COORDINATES 59 31.27 Example: Linear Transformation Basis Change Suppose our new basis is B = 1 1 , 1 −1 with basis matrix B = 1 1 1 −1 .
This is an orthogonal basis since the vectors are perpendicular, but not orthonormal because they have length √ 2.
This means that B−1 = (1/2)BT.
Suppose our linear transformation T has matrix A = 1 2 3 1 1 3 in the standard basis.
To find its representation AB in the B basis, we first compute B−1 = 1 2 1 1 1 −1 .
Then our new transformation matrix is AB = B−1AB = 1 4 1 1 1 −1 3 1 1 3 1 1 1 −1 = 2 0 0 1 .
As you can see, the transformation has taken a particularly simple form: The transformed matrix AB is diagonal. This reflects the fact that T(b1) = 2b1 and T(b2) = b2. In Chapter 23, you will learn how we can sometimes find such a basis from the original matrix.
60 MATH METHODS 31.28 Example: Transformations with Complex Numbers Consider the matrix A = 0 1 −1 0 .
In section 8.38, we saw that A is a square root of −I, the negative of the identity matrix. It’s a bit like an imaginary number.
By using a complex basis, we can see just how true that is. There is a complex basis B where AB is purely imaginary in the weak sense that all of its non-zero elements are purely imaginary. Indeed, the non-zero elements are square roots of −1.
Consider the basis with basis matrix B = 1 √ 2 1 1 i −i .
It is a unitary matrix. Its inverse is its Hermitian conjugate B−1 = 1 √ 2 1 −i 1 i .
Now AB = B−1AB = 1 2 1 −i 1 i 0 1 −1 0 1 1 i −i = 1 2 1 −i 1 i i −i −1 −1 = i 0 0 −i revealing that the matrix A is more closely connected to the imaginary numbers than we first realized.
If you’ve had a comprehensive linear algebra course, you may have seen such transformations before.
If you had a differential equations class that covered linear differential systems, you may have seen them there too. As was true of the previous page, you will learn how find these transformations like this in Chapter 23.
TRANSFORMATIONS AND COORDINATES 61 31.29 The Dual Space In section 10.8, we defined linear functionals, linear functions from a real vector space Rn to R. More generally, let F = R or C. A linear function f from a finite-dimensional vector space V over F to F is called a linear functional. We saw earlier that any linear functional on Fn can be represented by a 1 × n matrix, a horizontal vector, a covector.3 The dual space of V is the set of all linear functionals on V and is denoted V∗.
Since the set of 1×n matrices is a vector space of dimension n = dim V, dim V∗= dim V.
The most common duality in economics involves prices and quantities.
We think of quantities x ∈Rn and prices p ∈(Rn)∗, writing px for cost.
Some problems are better studied using functions of quantity (e.g., utility, production), while others are better studied using dual functions of price (cost, expenditure, indirect utility).
3 When dealing with infinite-dimensional spaces, a distinction is made between linear functions from V to R, sometimes called linear forms and continuous linear functions from V to R, called linear functionals.
We are avoiding these technical issues by restricting ourselves to finite-dimensional spaces.
62 MATH METHODS 31.30 Duality and Bases To see how duality relates to bases, we treat a linear functional f as we can treat any other linear transformation. We represent it using a matrix by expressing x using the standard basis and using linearity of f to write: f(x) = f n X j=1 xjej = n X j=1 xjf(ej) = f(e1) · · · f(en) x1 .
.
.
xn !
.
(31.30.3) So any linear functional f on V defines a 1 × n matrix vf by vf = f(e1) · · · f(en) .
Reading equation (31.30.3) up from the bottom makes it clear that any 1 × n matrix defines a linear functional on V, and vice-versa. We can think of the linear functionals as 1 × n matrices.
In fact, if V is an inner product space, we can identify x ∈V with the dual element x∗since y 7→x·y = x∗y is a linear functional on V.
However, this mapping is only linear if V is a real vector space. If it is a complex vector space, the mapping is conjugate linear.
TRANSFORMATIONS AND COORDINATES 63 31.31 The Dual of a Basis Given a basis B = {b1, . . . , bn} for V, we can define a corresponding dual basis B∗for V∗by setting b∗ i(bj) = δij. The elements of the dual basis can be used to read the B coordinates of any vector. Just compute b∗ i(x) = b∗ i X j xjbj = X j xjb∗ i(bj) = X j xjδij = xi.
When the original basis the canonical basis, its dual basis, the standard or canonical dual basis is e∗ 1, . . . , e∗ n = eT 1, . . . , eT n .
This follows because e∗ i(ej) = eT i ej = δij as required.
This allows us to write any f ∈V∗as f = n X i=1 f(ei)e∗ i = f(e1), . . . , f(en).
64 MATH METHODS 31.32 Dual Bases are Bases It is easy to verify that the dual basis {b∗ i} is a basis for V∗.
Theorem 31.32.1. Let V be a finite-dimensional vector space and B be a basis for V. Then the dual basis of B is a basis for V∗ Proof. Let f be a linear functional on V and vf its matrix representation.
We write x in the basis B as x = P j xjbj. Then b∗ i(x) = n X j=1 xjb∗ i(bj) = n X j=1 xjδij = xi.
Now expand vfx = f(x): vfx = f(x) = f n X j=1 xjbj = n X j=1 xjf(bj) = n X j=1 f(bj)b∗ j (x).
This shows that f = vf = P j f(bj)b∗ j , meaning that B∗spans V∗.
Next, we consider linear independence. Suppose f = vf = Pn j=1 xjb∗ j = 0. Then for each bi, i = 1, . . . , n, 0 = f(bi) = vf(bi) = n X j=1 xjb∗ j (bi) = n X j=1 xjδij = xi.
But then xi = 0 for i = 1, . . . , n, showing that B∗is a linearly indepen-dent set, and therefore a basis for V∗.
TRANSFORMATIONS AND COORDINATES 65 31.33 Linear Functionals Separate Points in V The following lemma is similar to Lemma 31.9.2, but applies to any dual space and doesn’t require that V be an inner product space.
It tells us that V∗contains a rich collection of dual elements, rich enough to distinguish between the points of V.
Lemma 31.33.1. Let V be a finite-dimensional vector space. Suppose f(x) = f(y) for every f ∈V∗, then x = y Proof. Let B be a basis for V. We can write x = P j xjbj and y = P j yjbj. Since b∗ i ∈V∗, xi = b∗ i(x) = b∗ i(y) = yi for every i = 1, . . . , n.
Then x = y by linear independence of the bi.
66 MATH METHODS 31.34 The Dual Basis Matrix Although we have a formula for the dual basis, we still need to fully identify it. Since the dual basis consists of covectors (row vectors), we form the dual basis matrix ˆ B by stacking the rows.4 ˆ B = b∗ 1 b∗ 2 .
.
.
b∗ n .
Then the ij coordinate of ˆ BB is b∗ ibj = δij, meaning that ˆ BB = I.
The dual basis matrix is simply B−1, keeping in mind that we are using the rows of B−1, not the columns. We formalize this as the following theorem.
Theorem 31.34.1. Let B be a basis for an n-dimensional real vector space V and B = (b1, . . . , bn) be the basis matrix. Then the dual basis B∗= {b∗ 1, . . . , b∗ n} has basis matrix B−1.
4 I don’t use B∗because of potential confusion with the Hermitian conjugate.
TRANSFORMATIONS AND COORDINATES 67 31.35 Coordinate Change in the Dual Space Of course, to change coordinates, tB = B−1x in V. The dual space works a little differently as the basis matrix must multiply the coordinate vector on the right. Thus if we have a linear functional f defined by the covector vf in the standard basis, the coordinates in the basis B∗are t∗ B = vf(ˆ B)−1 = vfB. Since the coordinates vary directly with the basis matrix, the vector is called covariant. With ordinary vectors, we use the inverse of the basis matrix, and call them contravariant as a result.
It follows that t∗ B(tB) = vfB B−1x = vf BB−1 x = vfx = f(x), showing that f(x) is unaffected by this double change of coordinates, which is what we need.
68 MATH METHODS 31.36 Example: Gallons vs. Quarts ◮Example 31.36.1: Gallons vs. Quarts Again. Going back to section 10.1, this means if we measures milk in quarts rather than gallons, and milk is good k, then the coordinate change for quantities is given by B−1 = diag(1, . . . , 1, 4, 1, . . . , 1) where 4 is in the kth row. It follows that B = diag(1, . . . , 1, 1/4, 1, . . . , 1), so the corresponding (dual) price vector must be multiplied by 1/4. ◭ 31. TRANSFORMATIONS AND COORDINATES 69 31.37 Rotations and Reflections Rotations and reflections are a little different from the other transforma-tions of bases. For starters, B−1 = BT. Now when we apply B−1 = BT to the coordinates of a vector, we taking sums of the columns of BT.
When we apply B to a covector, we obtain sums of the rows of B, which are the columns of BT. The action is the same on both the vectors and covectors.
70 MATH METHODS 31.38 Rotations and Reflections: An Example Let’s see how this works with an orthonormal basis.
◮Example 31.38.1: 45◦Rotation and Duality. The matrix B = 1 √ 2 1 −1 1 1 rotates the coordinates of R2 by 45◦, mapping 1 0 7→1 √ 2 1 1 and 0 1 7→1 √ 2 −1 1 Since this is a rotation, its transpose is also its inverse, and we have B−1 = BT = 1 √ 2 1 1 −1 1 .
Now what happens to the dual basis? It is also rotated by 45◦as the covector (1, 0) 7→(1/ √ 2, 1/ √ 2) and (0, 1) 7→(−1/ √ 2, 1/ √ 2).
e1, e∗ 1 e2, e∗ 2 b1, b∗ 1 b2, b∗ 2 45◦ 45◦ x1 x2 Figure 31.38.2: Here the standard coordinate axes are rotated counter-clockwise by 45◦. The standard dual basis lines up with the standard basis itself. Because the new basis is an orthonormal basis, the dual basis must rotate to match.
◭ 32. Rn GEOMETRY PUZZLE: THE SETTING 71 32. Rn Geometry Puzzle: The Setting Consider a square with 2-foot sides. Divide that square into 4 quadrants, with sides of 1-foot each (left diagram). Then inscribe a circle into each of the 4 quadrants (right diagram).
Division into Quadrants Inscribed Circles Finally, inscribe a small circle in the middle of the circles (shown in red below).
Central Inscribed Circle 72 MATH METHODS 32.1 Rn Geometry Puzzle: The Question Suppose we try an analogous construction in R3, R4, . . . .
In R3, we start with a cube with 2-foot sides. We bisect each side with planes, inscribe the 1-foot spheres, then inscribe the red 2-sphere in the middle.
In R4, we have a tesseract with 2-foot sides, we bisect each side with 3-d hyperplanes, inscribe the 1-foot 3-spheres, then the red 3-sphere in the middle. We do this for each Rn with n ≥2.
Problem: What does the diameter of the red sphere converge to as n →∞?
(a) 0.
(b) 1.
(c) 2.
(d) ∞.
Rn GEOMETRY PUZZLE: THE SETTING 73 32.2 Rn Geometry Puzzle: The Answer As shown in the diagram, we draw the diagonal of the 2-foot square (cube, tesseract, etc.).
We are in Euclidean R2, so the diagonal has length L2 = √ 22 + 22 = 2 √ 2.
Main Diagonal In Rn, the length is Ln = 2√n. Examining the diagonal more closely, we find that after subtracting the diameter of 1-foot circles, we have 2√n −2. This includes both the diameter of the red circle and the part sticking out of the 1-foot circles at either end. By symmetry, the portion sticking out of the 1-foot circle has the same length as the radius, so the leftover portion (2√n −2) is 4 times the radius, or twice the diameter of the red circle.
That means the red circle has diameter dn = √n −1. When n = 2, d2 ≈.414. when n = 4, d4 = 2−1 = 1. When n = 9, d9 = 3−1 = 2.
At that point the red hypersphere in the middle touches the sides of the large enclosing box. For n > 9, the red hypersphere actually pokes out.
We can see now that the correct answer was (D) ∞. The inside gets much roomier as the number of dimensions increases, which allows the red hypersphere to partly escape the containment by the other hyperspheres.
November 10, 2022 Copyright c ⃝2022 by John H. Boyd III: Department of Economics, Florida In-ternational University, Miami, FL 33199 |
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Solving the “No friends” math puzzle with a python algorithm
Emmanuel Kwakye Nyantakyi
4 min readJun 12, 2021
Place each of the digits 1,2,3,4,5,6,7 and 8 in separate boxes so that boxes that share common corners do not contain successive digits.
I’m sure more than half of you reading this have tried solving the puzzle above. If you were able to, bravo! Keep reading to see an algorithm I wrote to help solve the puzzle. If you weren’t able to, don’t worry. Check out my solution and how I used it to develop a algorithm to help tackle the problem.
Solving the problem on paper
To really understand what I needed to do, I rephrased the problem in my own words. Basically, the problem is asking us to put each of the digits into separate boxes such that the digits in any two boxes that share at least one corner have a difference greater than 1 (that is, if x and y are neighbors, then |a-b| should be greater than 1). I called digits of boxes that share common corners neighbors and any two digits with a difference of 1 friends. By that definition, any two digits that have a difference greater than 1 are strangers.
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The next thing I did was classify the boxes into three different types depending on how many neighbors they have.
From figure 2, it can be seen that boxes A have three neighbors each, boxes B have four neighbors each and boxes C have 6 neighbors each. This means, for the right arrangement, boxes A, B and C should be surrounded by three, four and six strangers respectively. You might want to get a pencil and a paper at this point The next thing I did was find possible digits from the eight that could occupy the different boxes: this way I eliminated the digits till they had all been placed in a box. I started with boxes C because they are the most critical boxes. From the eight digits only 1 and 8 can have up to 6 strangers. And so I put 1 and 8 in the C boxes. It can be seen that the two Cs have only one friend and it turns out one C’s friend happens to be a stranger to the other C. This lead me to put the two digits(2 and 7) into boxes A, so that the friend of one C is behind the other C. So I put 2 behind 8 and 7 in front of 1. This left me with four more digits (3,4,5, and 6) to place in boxes B. At this stage, I just put any two digits who are strangers at the top such that the bottom two are also strangers. But I checked to make sure I did not make any friends in boxes B and boxes A neighbors. I ended up with {3,5} on top and {4,6} at the bottom.
After a careful look, one can notice that there are two more ways of arranging the digits to solve the problem:
The whole figure has a vertical line of symmetry. By interchanging all values on the left of that line of symmetry with the values on the right, you form a different solution.
Also, by switching the B_top values with the B_bottom values, you form another solution.
Writing an algorithm to solve the puzzle
Based on my reasoning above, I decided to write an algorithm that would do the sorting of the digits into different box types for me. I currently don’t have a pc so I had to write the code on my phone using Cocalc.. forgive the messy code;( . I wrote the code such that it should work for any 8 consecutive numbers which are ordered or not. I also altered the box types a bit to fit the code.
Code
Essentially, the code sorts out which pairs belong to which types of boxes, but the user ultimately decides which digit or number in the pair comes first in accordance with the rules of the puzzle.
It would be fascinating to see other ways of solving the puzzle in the comments sections.
Don’t forget to leave a like:)
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Coefficient of Skewness
Coefficient of skewness is one way to measure the skewness of a distribution. Skewness can be defined as a measure of the asymmetry of a probability distribution. If the curve of a normal distribution is distorted towards the left or right then it is known as a skewed distribution.
The most important measure of skewness is the coefficient of skewness that was given by Karl Pearson. It is also known as Pearson's coefficient of skewness. In this article, we will learn more about the coefficient of skewness, its formulas, how to calculate it, and see certain associated examples.
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| 1. | What is the Coefficient of Skewness? |
| 2. | Coefficient of Skewness Formula |
| 3. | How to Calculate Coefficient of Skewness? |
| 4. | FAQs on Coefficient of Skewness |
What is the Coefficient of Skewness?
The coefficient of skewness can be defined as a measure that is used to determine the strength and direction of the skewness of a sample distribution by using descriptive statistics such as the mean, median, or mode. The coefficient of skewness is used to compare a sample distribution to a normal one. If the value is very large it implies that there is a greater difference between the sample distribution as compared to a normal distribution.
Coefficient of Skewness Interpretation
Depending upon the value of the coefficient of skewness, the following inferences can be drawn about a distribution.
If the mean exceeds the mode and median (Mode < Median < Mean) then the distribution is positively skewed. In other words, if the coefficient of skewness is positive then the distribution is skewed to the right.
If the mode exceeds the median and mean (Mean < Median < Mode) then the distribution is negatively skewed. Thus, the coefficient of skewness will be negative and the distribution will be skewed to the left.
If the value of the mean, median, and mode are equal then the distribution is a normal distribution and the coefficient of skewness will be 0.
Coefficient of Skewness Formula
There are two formulas, that were developed by Karl Pearson, available to calculate the coefficient of skewness. One uses the mode while the other uses the mean. The Karl Pearson coefficient of skewness formulas are given below:
Using Mode
sk1 = (\frac{\overline{x}-Mode}{s})
Using Median
sk2 = (\frac{3(\overline{x}-Median)}{s})
where, (\overline{x}) is the mean and s is the standard deviation.
The first coefficient of skewness formula uses the mode. However, if there are not enough data points in the dataset then the mode is not considered to be a robust measure of central tendency. Furthermore, a dataset can have more than one mode. Thus, in most cases, researchers prefer using the second formula (with the median) to calculate the coefficient of skewness.
How to Calculate Coefficient of Skewness?
Depending upon the data available either of the two formulas can be used to calculate the coefficient of skewness. Suppose the mean of a data set is 60.5, the mode is 75, the median is 70 and the standard deviation is 10. The steps to calculate the coefficient of skewness are as follows:
Using Mode
Step 1: Subtract the mode from the mean. 60.5 - 75 = -14.5
Step 2: Divide this value by the standard deviation to get the coefficient of skewness. Thus, sk1 = -14.5 / 10 = -1.45.
Using Median
Step 1: Subtract the median from the mean. 60.5 - 70 = -9.5
Step 2: Multiply this value by 3. This gives -28.5.
Step 3: Divide the value from step 2 by the standard deviation to obtain the coefficient of skewness. Thus, sk2 = -28.5 / 10 = -2.85
Related Articles:
Data Collection Methods
Summary statistics
How to Find Median
Important Notes on Coefficient of Skewness
The coefficient of skewness is used to measure the extent and direction of skewness of a sample or distribution.
The coefficient of skewness can be positive, negative, or zero.
There are two formulas, given by Karl Pearson, that can be used to calculate the coefficient of skewness.
Examples on Coefficient of Skewness
Example 1: Calculate the second coefficient of skewness for the following data. 1, 2, 3, 4, 5, 6, 7, 8, 9, 9
Solution: Mean = 54 / 10 = 5.4
Variance = [(1 - 5.4)2 + (2 - 5.4)2 + (3 - 5.4)2 + (4 - 5.4)2 + (5 - 5.4)2 + (6 - 5.4)2 + (7 - 5.4)2 + (8 - 5.4)2 + (9 - 5.4)2 + (9 - 5.4)2] / 10 - 1 = 7.44
Standard Deviation = √7.44 = 2.73
Median = ((n/2)th term + (n/2 + 1)th term)/2
= [5 + 6] / 2
= 5.5
sk2 = (\frac{3(\overline{x}-Median)}{s})
= 5.4 - 5.5 / 2.73
= -0.11
Answer: sk2 = -0.11
2. Example 2: Calculate the first coefficient of skewness for the following data. 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 12, 12, 13
Solution: Mode = 9
Mean = 7.96
Standard Deviation = 2.98
sk1 = (\frac{\overline{x}-Mode}{s})
= (7.96 - 9) / 2.98
= -0.34
Answer: sk1 = -0.31
3. Example 3: If the coefficient of skewness of a distribution is 0.32, the standard deviation is 6.5 and the mean is 29.6 then find the mode of the distribution.
Solution: Using the formula for the first coefficient of skewness, the mode can be determined as follows:
sk1 = (\frac{\overline{x}-Mode}{s})
0.32 = (29.6 - mode) / 6.5
2.08 = 29.6 - mode
Mode = 27.52
Answer: 27.52
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FAQs on Coefficient of Skewness
What is the Meaning of Coefficient of Skewness?
The coefficient of skewness can be defined as a measure of skewness that indicates the strength and the direction of asymmetry in a probability distribution.
What is the Coefficient of Skewness Formula Using the Mode?
There are two formulas that can be used to calculate the coefficient of skewness. The Karl Pearson coefficient of skewness formula using the mode can be given as sk1 = (\frac{\overline{x}-Mode}{s}).
What is the Coefficient of Skewness Formula Using the Median?
The coefficient of skewness using the median is a more robust measure of skewness than the coefficient that is calculated using the mode. The coefficient of skewness formula is given as (\frac{3(\overline{x}-Median)}{s}).
What Does a Negative Coefficient of Skewness Indicate?
A negative coefficient of skewness indicates that the distribution is negatively skewed. In other words, the distribution is skewed to the left and the mean < median < mode.
What Does a Zero Coefficient of Skewness Indicate?
A zero coefficient of skewness indicates that the distribution is symmetric. An example of a distribution that has a 0 coefficient of skewness is a normal distribution.
How to Calculate the Coefficient of Skewness Using the Mode?
The steps to calculate the coefficient of skewness using the mode are as follows:
Subtract the mode from the mean.
Divide this value by the standard deviation to get the coefficient of skewness.
How to Calculate the Coefficient of Skewness Using the Median?
The steps to calculate the coefficient of skewness using the mode are as follows:
Subtract the median from the mean and multiply this value by 3.
Divide this value by the standard deviation to get the Karl Pearson coefficient of skewness.
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189637 | http://archive.computerhistory.org/resources/access/text/2013/04/102723421-05-01-acc.pdf | VoL I - No. 6 October 5, 1979 This letter is a condensation of recent newsletters and internal thinking from the industry research groups at DATAQUEST, Inc. Requests for amplification of our thoughts or for specific newsletters should be directed to the author. A list of recent DATAQUEST Research Newsletters appears at the end of this letter. SEMICONDUCTORS Some good news and a little bad news this month. Business is still good and we think that the trend will continue. Naturally, there is concern about the impact of large amounts of capacity increases on pricing next year, particularly key product areas like 16K RAMS where there are numerous suppliers. DATAQUEST has done a detailed analysis of supply and demand for 16K RAMS for next year. We project supply to increase to about 140 miUion parts in 1980, up from 68 million parts this year. We believe that real demand next year could exceed 155 million devices. In other words, the business should be basically sold-out next year and price declines should be orderly. The big risk, of course, is that demand is based on shipment expectations by the computer industry. If computer/mini-computer/peripheral demand holds up reasonably well in 1980, as we at DATAQUEST believe it will, then we believe that our semiconductor forecast will be accurate. Now for a little bad news—the Japanese are back. We understand that, in the European market, some Japanese suppliers are quoting prices more than 20 percent below equivalent U.S. prices on computer memory for mid-1980 delivery. It is an attempt by the Japanese to expand their position in Europe, where they have made very little penetration to date. We do not believe that the price cutting wiU necessarily spread to other products or other markets, but it is worth noting, once again, this longer term risk to the U.S. industry's longer term profitability. COMPUTERS It appears that Digital Equipment may be delaying several new commercial data processing products. The widely anticipated "COMET" (a lower end version of the VAX 11/780) was expected this fall, but may be delayed until March 1980, we understand. Furthermore, a new version of the PDP-11/34 with a commercial instruction set may be delayed six months, and a commercial version of the PDP-11/70 may be delayed indefinitely. There are several ways of interpreting the DEC decisions. One possibility is that the company may be rethinking its whole approach to the commercial data processing market. More probably, the company is holding off on new product announcements because of very strong demand for existing products and a disinclination to build backlogs or beef up production schedules beyond targeted levels. Copyright © 5 October 1979 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients. This information is not furnished in connection vuith a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities Member, New York Stock Exchange 19055 Pruneridge Avenue / Cupertino, California 95014 / (408)725-1200 With delivery dates starting to stretch out at the company, strong earnings gains in the June 1980 year seem almost assured. We are using $5.20 per share for fiscal 1980 versus $4.10 per share in fiscal 1979. Any disappointments that may occur over the next nine months would likely be in orders, since the general purpose minicomputer market may soften in early 1980. Introducing new commercial products next spring rather than this faU may prove to be very good timing for DEC, givii^ the company's product line a boost when it may need it more than it does now. IBM's Data Products Division (DPD) recently announced two low-cost terminals. The products are interesting, but the pricing on the products is more worthy of note. DPD is offering discounts of up to 20 percent on purchases over 100 units. This is the first time DPD has ever offered a volume discount. This offer reinforces our earlier Stated beliefs that discoimts at IBM may spread throughout its product line to meet selective competitive threats. PAPER AND FOREST PRODUCTS Industry order rates remained strong in almost all grades through the end of the third quarter with only spotty areas of weakness. Prices on almost all products were increased to offset the impact of higher oil prices, but because of baclimarily of modules and hybrids. Copyright© 31 December 1979 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generallv available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracv or completeness. It does not contain material provided to us in confidence by our clients This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO DATAQUEST's Preliminary Appendix B, wliich is scheduled for a January publication, will include preliminary sJiipment estimates by product type for all products for aU companies covered in our annual Appendix B - IWarket Share Estimate Worksheets. The final revision of Appendix B is scheduled for publication in May. It is significant to note that in the preliminary ranking, two of the top seven semiconductor suppliers are European companies, namely, Philips and Siemens. (In Japan, Hitachi and NEC are of comparable size.) IC Suppliers The preliminary DATA QUEST estimates for the 1979 leading U.S. and European IC suppliers are shown in Table 2. It is obvious in the 39.7 percent market share increase of the top U.S. And European IC suppliers' revenues that 1979 was a good year for IC growth. Texas Instruments was the leading merchant IC manufacturer, shipping an estimated $925 million in 1979. Motorola, National and Philips are in close rank for second place among IC suppliers at about $500 million each. However, one should note that in Table 2 the IC estimates for National and Motorola do not include estimates for hybrids and modules, which are $40 miUion and $10 million respectively. Table 2 demonstrates remarkable growth in the IC marketplace for all the listed companies. However, AMD, Mostek, and Motorola, in particular, stand out as having annual growths above 50 percent. Mostek's outstanding 68.0 percent growth has placed it eighth among U.S. IC suppliers with AMD not far beliind with its 57.6 percent growth in ICs. Also, Motorola's 50.8 percent growth has moved it into a tight third place ranking behind Texas Instruments and National. Discrete SuE^lias Table 3 shows the preliminary estimates fca" the 13 leading U.S. and European discrete suppliers in 1979. Overall growth in the 1979 discrete marketplace is reflected in the 16.0 percent growth in shipments of the 13 leading U.S. and European discrete suppliers. For General Instrument, this includes revenues of the optoelec-tronics division acquired in 1979 from Monsanto for both 1978 and 1979 ($27 million and $33 million, respectively). General Instrument and National both exlubited a healthy 30 percent growth in discretes. MOS Suppliers Preliminary estimates for the 1979 leading U.S. MOS suppliers are shown in Table 4. The high demand for MOS devices in 1979 is reflected in the 51.5 percent over 1978 MOS shipments by the 14 leading U.S. MOS suppliers. Clearly, this growth marks the MOS market segment once again as the fastest growth segment in the semiconductor marketplace. AMD, Fairchild, Mostek, Motorola, National, and Synertek all exhibit 1979 preliminary MOS revenue estimates that are up at least 51.0 percent over 1978 levels. Motorola and Natiaial stand out with their remarkable 88.1 percent and 84.6 percent growths, respectively. Mostek grew next fastest at 68.0 percent. Fairchild has moved into a tie with RCA for tenth place among U.S. MOS suppliers due to its healthy 56.9 percent increase in MOS revenues in 1979. It is also significant to note that Synertek has joined the leading 12 U.S. MOS suppliers with a 51.5 percent MOS growth. Mary EUen Hrouda James F. Riley Daniel L. Klesken - 2 -# Table 1 PRELIMINARY ESTIMATES 1979 WORLDWIDE SHIPMENTS BY LEADING U.S. AND EUROPEAN SEMICONDUCTOR SUPPLIERS (Millions of Dollars) ICs Discretes Other Total Texas lnstrum«its Motorola Philips (including Signetics) Natiotal Faireliild Intel Siemeis RCA Signetics Mostelc AMD 3 General Instrument ITT Sescosem General Electric AEG-Telefunken Harris AMI Intersil Hewlett-Packard International Rectifier Rockwell $925 $496 $490 $515 $330 $430 $150 $155 $250 $210 $208 $ 90 $ 85 $ 40 $ 3 $ 40 $115 $ 95 $ 85 See Note 4 -$ 70 $285 $424 $290 $ 65 $120 -$260 $115 ---$100 $100 $120 $126 $ 85 --$ 7 $ 85 $ 78 --$10 -$40 $20 ------$ 6 ---------L ~ $1 $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ ,210 920 780 620 470 430 410 270 250 210 208 196 185 160 129 125 115 95 92 85 78 70 Includes Optoelectronics 2 Consists primarily of liybrids and modules 3 Includes Optoelectronics Division, formerly Monsanto, having estimated 1979 revenues of $33 million 4 For Hewlett-Packard, captive IC production is not counted Source: DATAQUEST, Inc. December 1979 3 -Table 2 PRELIMINARY ESTIMATES WORLDWIDE SHIPMENTS BY LEADING U.S. AND EUROPEAN IC SUPPLIERS (MiUicais of Dollars) Texas Instrum^its NaticHial Motorola Philips (including Signetics) Intel Fairchild Signetics Mostek AMD RCA Siemens Harris General Instrumait Total IC Shipmaits of 13 Leading Companies 1978 $ 669 370 329 375 300 255 205 125 132 127 108 85 T5 $2,950 1979 $ 925 515 496 490 430 330 250 210 208 155 150 115 96 $4,120 Annual Growth Percent 38.3% 39.2 50.8 30.7 43.3 29.4 22.0 68.0 57.6 22.0 38.9 35.3 28.0 39.7% Source: DATAQUEST, toe. December 1979 _ 4 _ Table 3 PRELIMINARY ESTIMATES . 1979 WORLDWIDE SHIPMENTS BY LEADING U.S. AND EUROPEAN DISCRETE SUPPLIERS^ (Millions of Dollars) • # Motorola Philips Texas Instrumaits 2 Siemens Fairchild General Electric Sescosem RCA ITT 3 General Instrumait Hewlett-Pac l\ f. ^^1 RESEARCH A Subgidiarvo^A.C. Nielsen CQ. ^ INCORPORATED I ^ I ^ Z i W ^ 3 ^ H E I I 1 ^ H ^ 4 SIS Code: Vol. HI, Appendix C MAJOR SEBAICONDUCTOR USERS In January 1980, DATAQUEST will publish a new Notebook Service Section entitled "Estimated Merchant Marl\ C (0 3 o k. o a - " S • & Q. JZ (0 M ^« c 3 i ^ M o CO c o s s s 18 16 14 12 10 8 6 4 Soiirce: DATAQUIfST, Inc. but two suppliers are still actively pursuing business. Note that these shipment estimates for the 12-bit products have been restated since the last newsletter. Worldwide shipmeits of 16-bit microprocessors in the third quarter of 1979 were an estimated 160,000 units, up about 14 percent over estimated second quarter 1979 shipm^ts and up about 63 percent over estimated third quarter 1978 shipments. 1979 and 1980 will still be design-in years for most of the new 16-bit products; ther^ore, large (^lantity increments in microprocessor shipmaits are not expected for another year or so. Prices on the 16-bit micro(»'ocessors remain Hrm in the third and fourth quarter of 1979. The more mature TlVIS-9900 family is available for about $12 for the TMS-9980 model and about $2S for the 9900. Most of the newer 16-bit products command prices in the $70 to $100 range. Some of ^ e very new products, such as the Z8000 and the 68000 are priced in the $150 to $250 range because of the very limited quantities available. Daniel L. Klesken Lane Mascm - 4 -Table 1 ESTIMATED WORLDWIDE SHIPMENTS OF MOS MICROPROCESSORS Cniousaflds of Units) Company AMD AMI EFCIS^ Fairchild G«n«Fal Instruinant Harris Hitachi Hughes Intd IntenU Matshusita (Pmaionie) MOS Teehnolog; Mo«t^ Mottfftia National NEC RCA Rockwell 4 Sescosem Siemens Signetics Sdid SUte Seientifie Synertelc Texas Instruments zaog Total Microproeesscn Percent change from previous quarter MPU Products 8080A 8083 8048 ZSOOO S2000 8800 8802/6808 8800 F8 38T0 8800 6802/8808 no-i6so CP-1600 6100 HUCS-IO 6800 1802 4004 8008 8080A 8048/8021 8748 8089 8086 6100 MMUOO 6500 F8 Z80 3870 141000 8800 6801/6803 6802/6808 680S 680S 3870 68000 COPS 4004 IMP 8080A 8049 3C/HP PACE COM-4 8080A 8048/8049 8089 Z80 768 1802 PPS-1 6500 6500A 6800 8080A 8089 2890 8048 1802 8500 TMS 1000 TMS 8080A TMS 9900 Z8 Z80 ZSOOO Bits 8 3 8 16 4 8 8 8 8 8 8 8 8 16 12 4 8 8 4 8 8 8 8 8 IS 12 4 8 8 8 8 4 8 8 8 8 8 8 16 4 4 4 8 8 8 16 4 8 8 8 8 16 8 4 8 8 8 8 8 8 8 8 8 4 8 18 8 8 16 MOS Process N N N N N N N M M N H M N N C P&C N C P P N N N N N C N,P&C N N N N C M N K N N N N N&C P P N N P P N,pacc N N N N N C P N N N N K N N C N P&C M K N N N Qtr. 115 s^ 0 0 8 30 0 0 190 5 80 0 105 IS 5 110 20 10 40 25 180 ISO S 95 10 M/^ 60 39 60 75 9 190 0 69 0 0 19 0 675 35 20 100 0 100 25 529 90 S 5 S 0 85 67S 75 0 6 0 0 35 S 8 60 3,000 40 48 0 150 0 7,429 38.4% 1978 4(h -9iL 12S S 0 D 12 35 0 0 200 10 90 S 175 IS 7 120 25 12 35 22 190 170 25 125 13 4 N/A 60 45 80 209 19 160 0 90 0 0 40 0 860 30 20 100 0 100 29 600 60 15 29 25 0 90 650 60 0 7 0 0 45 S 10 70 3,200 35 S3 0 210 0 8,390 12.9% is'fa Total 43S S 0 0 29 130 0 0 630 23 270 S 490 60 22 410 70 35 159 103 705 480 30 350 24 15 N/A 225 160 260 350 20 970 0 180 0 0 70 0 2,325 130 80 375 0 335 86 l.SOO 305 15 30 30 0 325 2,275 S O S 0 25 0 0 125 3 22 680 9,400 135 185 0 550 0 25,798 1st Qtr. 135 15 S ^^^ 38 S 8 ISO 40 155 20 300 15 7 130 S O 12 35 20 190 210 S O 175 13 4 S O O 65 90 100 260 30 165 0 ISO 0 s 80 0 900 30 18 150 0 100 25 1,100 65 25 55 80 3 l i s 600 S O S 0 S 0 49 15 10 100 3,700 32 68 0 195 0 10,720 27.7% 1979 12nd .SiL 32S 40 S 1 S . -sao-30 10 10 200 so 155 45 950 20 7 150 100 14 32 18 200 300 75 260 15 4 800 70 125 120 300 75 175 S 240 0 2 125 0 1,100 26 15 175 0 140 25 1,300 90 160 75 80 S 115 1,100 60 S 0 3 3 90 30 11 120 5,000 25 80 S 250 1 15,443 44.1% 3rd Qtr. 33S 75 3 •X S V" -450- 7 •?-' 30 - = ^ - ' 10 12 275 120 1,250 20 8 175 125 15 28 IS 210 375 75 32S 19 S 1,000 80 125 125 425 90 215 3 275 3 8 125 S 1,500 20 10 200 S 160 25 2,300 106 350 120 60 S 12S 1,100 60 3 0 10 2 110 60 12 280 7,000 18 92 S 425 4 20,932 35.3% , o fejs l>l/3«^ r» -S s Sampling 2 EFCIS, a joint venture between Seseoaam and the French AEC, now handlea the MOS HPUs formerly hamaad by SaBcoaam, a Division of Thompson-CSF ' N / A Z Not Available 4 Seseosem is no longer shipping MOS MPtIs sine thee are now handled by EFCIS Soweet DATAQUEST, Hne. November 1979 - 5 -Table 2 ESTIMATED WORLDWIDE SHIPMENTS OF SINGLE-CHIP MICROCOMPUTERS (Thousands of Units) 1978 1979 Company MPU Products AMD AMI Fairchild General Instrument Hitachi Intel Matshushita Mostek Motorola National NEC Rockwell Signetics Texas Instruments Zilog Total Percent change from previous quarter 8048 S2000 3870 PIC-1650 HMCS-40 8048/8021 8748 MN1400 3870 141000 6801 680S 3870 COPS 8049 COM-4 8048/8049 PPS-4 6300/1 8048 TMS 1000 Z8 "1rd~ 9^ 0 8 5 105 110 150 ^2 N/A^ 75 5 0 0 15 675 0 525 S 675 0 S 3,000 0 5,353 55.7% 4th S^ 0 12 10 175 120 170 25 N/A 205 15 0 0 40 850 0 600 15 650 0 S 3,200 0 6,087 13.7% 1978 Total 0 29 23 450 410 480 30 N/A 350 20 0 0 70 2,325 0 1,500 15 2,275 0 S 9,400 0 17,377 1st SSL S^ 30 40 300 130 210 50 500 260 30 0 0 80 900 0 1,100 25 600 S 15 3,700 0 7,970 30.9% 2nd Str, S 330 50 950 150 300 75 800 300 75 S 0 125 1,100 0 1,300 160 1,100 S 30 5,000 s 11,845 48.6% 3rd — — gtr. 3 550 120 1,250 175 375 75 1,000 425 90 3 S 125 1,500 S 2,300 ^ ^ 3 5 0 9 1,100 3 60 7,000 S 16,504 39.3% S = Sampling ^N/A = : Not Available Source: DATAQUEST, Inc. November 1979 - 6 -Tables ESTIMATED WORLDWIDE SHIPMENTS OF 4-BIT MICROPROCESSORS (Thousands of Units) 1978 1979 Company AMI Hitachi Intel Matshushita Motorola Nati<»ial NEC Rockwell Texas Instruments Total V. Percent change from previous quarter MPU Products S20Q0 HMCS^O 4004 MN1400 141000 COPS 4004 IMP COM-4 PPS-4 TMS 1000 3rd Qtr. 8 110 40, N/A^ S 675 3S 20 525 675 3,000 5,093 55.5% 4th Qto, 12 120 35 N/A 15 850 30 20 600 650 3,200 5,532 8.6% 1978 Total 29 410 159 N/A 20 2,325 130 80 1,500 2,275 9,400 16,328 1st 9^, 30 130 35 500 30 900 . 30 18 1,100 600 3,700 7,073 27.9% 2nd s^ 330 150 32 800 75 1,100 26 15 1,300 1,100 5,000 9,928 40.4% 3rd 9tr, 550 175 28 1,000 90 1,500 20 10 2,300 1,100 7,000 13,773 38.7% N/A = Not Available Source: DATAQUEST, Inc. November 1979 - 7 -Table 4 ESTIMATED WOaLOWIOE SHIPMENTS OF 8-Bit MICEOPBOCESSORS CnMUtands of Units) 19T8 19T9 Companv AMD AMI EFCB FairctiUd General Instrument Hitachi Hushes Intel MOS Teehmdogy Mestek Motorola National NEC acA RoekweU Seaeosain Siemens Signetics SoUd SUte Scientific Synerteic Texas Instruments ZUog MPUProchicts 8080A 8089 8048 6800 8802/6808 6800 F8 3870 6800 6802/6808 PIC-16S0 6800 1802 8008 8080A 8048/8031 8748 808S 6S00 FB Z O O 3870 6800 6801/6803 6802/6808 6805 6800 3870 8080A 8049 SC/HP 8080A 8048/8049 808S Z80 1802 6500 6500A 6800 8080A 8085 2650 8048 1802 6500 TMS 8080A Z8 Z S O 3rd s^ " 1 ^ 0 30 0 0 190 5 80 0 105 20 10 25 180 190 9 95 60 35 80 75 150 0 65 0 0 15 100 0 100 90 S 5 9 85 75 0 6 0 0 35 S 8 60 40 0 ISO 4 til Str. 125 9 0 35 0 0 200 10 90 S 179 29 12 22 190 170 25 125 60 45 80 205 160 0 90 0 0 40 100 0 100 60 15 25 25 90 60 0 7 0 0 45 S 10 70 35 0 210 -•igrr Total 435 5 0 130 0 0 630 23 270 S 450 70 35 103 705 480 30 350 225 180 260 350 970 0 180 0 0 70 375 0 335 305 19 30 30 329 595 0 25 0 0 125 S 22 680 135 0 550 l5t Qtr. 135 IS 3 38 S 8 150 40 199 20 300 90 12 20 190 210 90 179 65 90 100 260 169 0 150 0 S 80 ISO 0 100 65 25 95 80 115 S O 0 0 S 0 45 IS 10 100 32 0 195 ind SEi 325 40 S 30 10 10 200 90 199 45 990 100 14 18 200 300 79 260 70 125 120 300 175 S 240 0 2 125 175 0 140 90 160 75 80 US 60 S 0 3 S 90 30 11 120 25 S 250 S r d Qtr. 335 75 3 30 10 12 279 120 159 100 1,250 129 19 19 210 375 75 325 80 125 125 425 215 3 279 S 8 125 200 S 160 109 390 120 60 125 60 3 0 10 2 110 60 12 280 18 S 425 Total Pereent ehange from previois qMTter S>SafflpUns 2,229 2,741 9,078 3,515 5,363 6,986 7.5% 23.09b 28.2% 52.6% 30.3% Sonrea: DATAQDEST, ihe. November 1979 - 8 -Tables ESTIMATED WORLDWIDE SHIPMENTS OF 12-Brr AND 16-BIT MICROPROCESSORS (Thousands of Units) 12rBit Products Company Harris Intersil MPU Pro<Jucts 6100 6100 3rd Qtr. 5 4 1978 4th atr^ 7 4 197ff Str, 22 15 - 1 s t Total 7 4 1979 2nd Qtr. 7 4 3rd 9 ^ 8 5 Total 11 37 11 11 13 Percent change from previous quarter 12.5% 22.2% 0% 0% 18.2% 16-Bit Products AMP General Instrument Intel Motorola National NEC Texas Instruments ZUog Total Percent change from previous quarter Z8000 CP-1600 8086 68000 PACE 768 TIVIS 9900 ZSOOO 0 15 10 0 25 0 48 Jl 98 22.1% 0 15 13 0 25 0 53 0 106 8.2% 0 60 24 0 86 0 185 0 355 0 15 13 0 25 S 68 0 S 20 15 0 25 S 80 1 S 20 19 S 25 S 92 4 121 141 160 14.2% 16.5% 13.5% S = Sampling Source: DATAQUEST, Mc. November 1979 - 9 -- - = MUH 1 l-ULIU 7 SECURITIES, INC. ^ B ^ H I 1 ^ H P ^ VoL I - No. 7 November 28, 1979 This letter is a condensaticm of recent newsletters and internal thinldng from the industry research groins at DATAQUEST, Inc. Requests for amplification of our thoughts or f OT ^ecific newletters should be directed to the author. A Ust of recent DATAQUEST Research Newletta's appears at the «id of this letter. COPYING & DUPUCATING "The most significant (tevelopm^t in copying at Xerox since the 914." That's how Dave Jc^genseh, our resident e:q)ert on such matters, described the recent new product announcemaits from Xerox. We will attempt to teU you why in lialf a p£^e. On two of the new products, the Models 8200 and 9500, Xerox has made a brealcthrough in imaging that has dramatically improved the quality of the copy. Furthermore, this was accomplished without introducing a new engine, which means that startup problems with the new machines should be minimal. We at DATAQU^T divide the copy and duplicating marlcet into six segments (Segment 1 the very low end. Segment 6 the high caid). In Segmait 5, Eastman Kodalc has had, i^ to now, the only product entry. The prime selling points of the El<taprint line have been copy quality and, because of the document feeder and finisher, high productivity . The 8200 appears equal to the Elctaprint 150 in price, better in productivity, and, based < M I initial copies from the 8200, its copy quality is actually superior. The 8200 should allow Xerox to malce serious inroads into Kodalc's dominance of Segment 5 in North America; moreover, the fact that Kodalc has not yet introduced its copiers abroad may now be an error without remedy. In Segmait 6, the high end, tlie competiticai is offset presses. One of the prime limitations to the penetration of the Xerox 9400 has been the superior copy quality of offset. The 9500, which will obsolete the 9400, offers equivalent or even superior copy quality to offset. Therefore, it may speed the displacement of offset presses and thus expand the growth of Xerox's copier business. The net results are first that tlie probability of our 12 percent growth forecast in Xerox's copy and duplicating revenues and earnings over the next four years being low rather than high has increased materially, and second that the strength of Kodalc and IBM as competitors has diminished significantly. It is stiU essential that Xerox malce some material progress in word processing/office of the future markets. Nevertheless, the rislc/reward potential in Xerox, in our opinion, has been materially upgraded as a result of the new product announce m^ts. Copyri^t © 30 November 1979 by DATAQUEST - Reproducticai Prohibited The content of ttiis report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to acciiracy or cofripleteness. It does not contain material provided to us in confidence by our clients, This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. Member, New York Stock Exchange 19055 Pruneridge Avenue / Cupertino, California 95014 / (408) 725-1200 i PAPER & FOREST PRODUCTS W e will comment «i two relevant issues this month—industry profitability in 1980 and our laiga term thesis on brown paper. W e have seen some scare stories in the press about sharp drops in profitability of the papar industry in 1980. W e don't agree. W e thinl< that people wiE be surprised at the Strength of overall paper demand next year relative to the decline in GNP. By our reading, us^ inventories are low and liquidaticm should not contribute to softening demand. Finally, prices Iiave ris^ so dramatically in 1979 tl^t even with some declines next year, average pricing should stiU be solidly above average 1979 levels. In linerboard, fac example, we are assuming a 7 p^cent avarage gain in price realizaticni in 1980, ^9-10 pacent cost increases and a 1-2 percent decline in shipmatts, which should result in a 5-10 p^cent drop in operating profits. In general, we continue to forecast only a 10 percent decline in industry proHts in 1980. W e have stated in the past that the brown pap^ sector of the industry appears to have excellent potential over the next 3-4 years because of tight supply/demand relaticxiships. In part, our projecticxis were based on some expected plant closings, and recent announcements by International Paper lend considerable support to our thesis. LP. has indicated that in the next three years, it may close or redeploy three southern mills that togetha" account for 3.5 percent of linerboard capacity and 4.5 percent of semi-chemical capacity. Taldng that much capacity off stream can turn a soft operating environment into a ti^t one all by itself. So, let us reiterate—if you want to play the papers, you should loolc first at companies with a strong brown pap^ exposure. Among the larger companies, this means (in ctescending ordor of exposure to brown paper) Union Camp, Great Northern, Nelcoosa, St. Regis, and Westvaco. Amcxig smaller companies with very hig^ brown paper exposure are Longview Fibre, Stone Container, and Southwest Forest. INSTRUMENTATION Some impressiois and comments after our first Instrumentation Industry Conference; DATAQUEST estimates test and measuremoit (ex ATE) industry growth to be 19 po'cent in 1979, slowing to 12 p^cent next year. On a five-year basis, we are looidi^ for 15 p^cent revenue growth. There is a potential problem here in terms of investo attitudes. One must recognize that the rate of growth in individual company results will vary around a 15 percent target in the future instead of the 20-25 percent target of the past. Business is stifl strong fca the individual companies, but (^rder gains are begiimit^ to moderate somewhat and published numbers should soai start to reflect our reduced growth expectations for 1980 and beycaid, as evidenced by the recently repOTted fourth qimrter at Hewlett-Paclcard. Automatic test equipment (ATE) is having another booming year—industry sales are estimated to rise 37 p^cent to $615 million this year. Once again we expect moderatiCHi in 1980, to 16 percent total ATE growth. Two factors malce this sector very different than the test and measurement marlcet. First, there is - 2 -1 absolutely no evidence of any moderation in order trends. Second, the potential variation from our growth forecast to 1980 is large in both directions. We came away from the conference with the impression that while the 1980 outlook for ATE may be subject to debate because of the economy, the five-year picture seems really clearcut: the use of electronics will proliferate, the need to test integrated circuits and boards will remain, and the alternatives to automatic testing will rapidly become obsolete. The 20 percent plus growth we forecast between 1979-1984 seems a very solid estimate to us. At the company presentaticMis, Tektronix indicated tlmt second quarter (November) orders may come close to a 20 percent year-to-year rate of gain (lower in instruments, hi^er in displays), but sales may fall below target because of an inability to catdi up to past shipment shortfalls in graphic displays. None of the projecticais causes us to change our $5.00 per share forecast for final 1980. Teradyne had a surprisingly strong third quarter and a $3.25 per share estimate in 1980 now seems very attainable (versus $2.45 per share in 1979). GenRad is progressing pretty much OTI target, with 19 percent growth likely in 1980 earnings (to $3.45 pec share vs. $2.85 pa: share) on top of 34 p^cent gains this year. COIVIPUTERS Now that the furor over the down qimrter at Data General has subsided, one can properly talk about the longo t^m implications for both the company and the industry. We are witnessing the evolution of the small computer industry away from tlie traditional markets (R&D, process control, product OEM) to the broadly defined commercial market. This does not mean that the toaditional sectors will not grow, but rather that the peak rates of growth here have probably already been realized and that the growth opportunities in the commercial area are greater. The commercial market necessitates a different type of product (greater software and service support instead of maximum hardware price/performance) and a different type of sell (mainframe-type salesman selling to an executive rather than engineer selling to engineer). Data General and to a lesser extent Digital Equipment have c«iented their products to the traditional markets and now must redeploy their assets to capitalize on the opportunities in commercial fields. One of the means to this end is increase the level of field service support and the unusually high (42 percent year-to-year) gain in field service people was perhaps the major contributing factor to the poor quarter at Data General. The transition of the small computer market is most obvious among the smaller participants. Those companies with a strong commercial data processing orientaticMi (Datapoint, Four Phase, Prime, Wang) are flourishing. Those with more traditional product lines (General Automation, Computer Automation, SEL, Modcomp) are having degrees of difficulty. Among the giants, Hewlett-Packard sacrificed market sliare during the mid-1970s to position itself squarely in commercial markets and is reaping the benefits—orders and revenues will be up over 50 p^cent in 1979. We believe the transitions that DEC and Data General are making is the correct one for each and slTort-term disappointments that may occur should be viewed within this proper longer-term course. - 3 -i WORD PROCESSING IBM has finally annoiuiced its entry into the shared resource segment of the word processing marlcet, presently dominated by Wang Laboratories. Initial orders fcff the product, called the 5520 Administrative System, are strong, but the real test of its capabilities will not come for a year. The Strength of the product is its communicaticMis capability. It will have the ablity to send messages to IBM's intelligent copier, its ink jet printer, and most of its other word processing products. However, this communication package will not be ready until November 1980. The word processing features of the 5520 are fairly Standard, with no special features and a price-per-workstation about 30 percent above that of Wang. Because the 5520 will be marketed by IBM's GSD, there will be a natural inclination to offer it to data processing managers. We view the product more as a D.P. than a W.P. oriaited seU, since eommunicatiais are its strongest feature. Our initial reaction (we have not yet seen the product) is that it presents no major threat to Wang. The fact that communicaticms on the 5520 is a year away gives Wang an additional advantage. Orders, revenues, and earnings momentum at Wang remain very strong. The most impressive aspect of business thus far in fiscal 1980 is that we sense that orders for Wang's small business computers Imve slowed quite a bit; yet overall orders are running over 80 per cent ahead of those a year ago, as the VS-100 line of larger minicomputers is aijoying outstanding success and is, along with word processing, taking up any slack. This situation is very important in assessing Wang's outlook over the next year. Small business comEHiters orders usually slow in a recession (and apparently are slowing already), while the VS-100 type of product should be relatively tmaffected, so the company is reducing the cyclical exposure of its computer line. We believe that earnings at Wang can approach $2.00 per share in fiscal 1980, versus $1.17 per share in fiscal 1979. CAPITAL EQUIPMENT A check with construction equipment dealers around the country indicates that demand is still good for middle-sized products, typically sold to commercial contractors and large home builders. The small end of the market is starting to weaken, reflecting residential housing trends, and the h i ^ end remains soft. Interestingly, some dealers in the K«ituclcy area indicate that after having waited quite a while, some large coal operators have finally been issued permits to mine coal and that they are starting to buy some equipment. At present, the large supply of used or repossessed machinery available is soaking up any demand. The dealCTS also indicate that hig^ interest rates have not deterred people from buying equipment—they are apparently passing on the costs to their customers. We are not as negative as some about the timing of a resurgence in coal equipment demand. Coal demand should increase about 12 percent in 1979 and another 4 percent in 1980, and this should allow a lot of excess coal supplies to be worked off. W e believe that demand for mid-sized equipment from coal operators could turn up as early as third quarter 1980, while demand for larger equipment - 4 -•UJ (draglines, etc.) m i ^ t start improving in early 1981. In our view, tlie best way of participating in a resurgence in coal equipment demand is via Caterpillar, because of its e2q)osure to the mid-range equipment area. The Strike presently affecting Caterpillar could turn out to have some real benefits tor the company. Its dealers are starting to swap among each other f O T badly needed machines and CAT should be running near capacity for at least part of 1980 to catdi up with dealer needs. We are estimating $6.50 per share fully diluted at Caterpillar tar both 1979 and 1980 and if the strUce extends into January, additiOTial earnings will be shifted into 1980. While it is very early to forecast, 1981 Shapes up as a potentially excellent year for CAT; earnings of over $8.00 per share seem attainable. InternatiOTial Harvester is also being struclc, but the disadvantages seem to outweigh the benefits in this case. HarvestOT needs to gain market sliare to capitalize cm its potential and being shut down while Deere is operating can only liurt IH in both the construction and farm markets. SEIVIICONDUCTORS Booldngs remain strong through October. The current slowdown in some sectors of the economy is having no negative impact on the semiconductor industry. Our forecast for 1980 U. S. semiconductor consumptiai, as presented at our recent conference, is f O T a 13 pa-cent gain, with integrated circuits growing 16.5 per cent and dfecretes gaining 4 per cent. We should <^uti '-^ ^ ^ s s = S^S' ^ S S S SS ^ S s » ^ ^ s S ==^s RcaBARL^H ^ K P I ^ ^ ^ r ^ " ' ^ A Subsidiary of A.C.Njelstn Cci. ^ INCORPORATED r M E W ^ ^ B 1 1 Bl-f SB Code: Vol. E, 7.8 DJSTRIBDTIOll IN THE 1980s DATAQUESTs Semiconductor Indus^y Service has just published a comprehen-sive report on distribution in the 1980s. This report analyzes the current trend toward distribution of subsystem components and gives market data from 1974 to 1979, projected to 1984, An Mstoric analysis of geographic market share is also given. Subscribers will find a detailed analysis in SIS Volume n, Sections 7.8 throi^h 7.9. Overview 4 Distributors' share of semiconductor consumption has remained relatively con-stant over time, as shown in Table 1, except for the recession year of 1975. In this year, many electronic equipment manufacturers cut back their commitments with their semiconductor vendors, and were later forced to make up these deHciencies with purchases throi^h distributors. Once distributors gained this portion of the semicon-ductor market, the gain was permanent. & i spite of the data menticmed above, most distributors feel that distributicm is increasing its share of market year-by-year. An explanation for this belief can be found in these facts: • Semiconductors represent an increasing share of the total components. We estimate this share will increase from 33 percent in 1974 to 41 percent in 1984. • As a result, semiconductors will represent an increasing share of distributor sales, from an estimated 28 percent in 1974 to 31 percent in 1984. In Other words, semiconductors are becoming increasingly important to dis-tributors, but distributors, since the recession of 1975, have not significantly increased their share of semiconductor sales. Manufacturers of non-semiconductor components seem to be increasingly turning to distribution. We estimate that distributors' share of total components distribution will increase from 26 percent in 1974 to 30 percent in 1984. As in the case of subsystem components, it appears that distributors are able to find customers that are Otherwise not available to components manufacturers. These customers are also buyers of other components like resistors and capacitors and, obviously, are currently customers of industrial electronic component distributors. Moreover, some of these customers buy subsystem components from systems distributors as well. A system Copyright © 28 November 1979 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of infornnation generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO distributor sells systems and subsystems but does not sell components. Table 2 shows how this marlcet is segmented and how it is projected to grow. Systems distributors normally sell systems to end users and subsystems components to systems integrators. However, as shown in the table, it is estimated that they sold $20 million of subsystem components to manufacturers in 1979. The advantage of the industrial subsystem components market is that the buyers of these units generally expect only a minimum of software and service support from their distributors. Since these units are reincorporated into some larger piece of "hardware" and then resold, the equipment manufacturer, himself, generally develops the software and service capability needed to support his product. Distributor overhead is reduced because these customers do not demand extensive software and service support. One successful distributor made quite a point of his belief that profits in this business could be higher than profits in components distribution. This situation is possible because the cost to process a line item tends to be independent of the price of the line item. Since subsystem components have higher line item prices than components, profits improve. Market Statistics IMlarket statistics are presented here. Table 3 indicates semiconductor resales by technology. Table 4 gives the ratio of these sales to the total North American market as given in Appendix A. These figures overstate the distributor share on a unit basis since resales are at distributor selling prices. Note that only 19.9 percent of MOS sales passed through distribution in 1978. This figure reflects that ROMs and custom LSI constitute a large fraction of MOS sales; since the customization of these products requires direct customer-to-vendor contact, there is no reason for manufacturers to use distributors. Howard Z. Bogert Mary Ellen Hrouda 4 V, - 2 -# Table 1 ESTIMATED DISTRIBUTOR SEMICONDUCTOR RESALES AS A PERCENTAGE OF NORTH AMERICAN SEMICONDUCTOR CONSUMPTION " « Distributor Sales Growth (shrinJcage) in North American Semiconductor Consumption 1974 1975 1976 1977 1978 1979 22.6% 26.1% 25.0% 24.5% 26.8% 27.0% 15.6% (20.1%) 30.0% 15.2% 22.6% 30.1% Source: DATAQUEST, Inc. November 1979 • Table 2 ESTIMATED NORTH AMERICAN INDUSTRIAL AND SYSTEMS DISTRIBUTORS SUBSYSTEM COMPONENTS RESALES TO MANUFACTURERS (Millions of Dollars) Industrial Electronic Distributor Sales Semiconductor Company Products Non-Semiconductor Company Products System Distributor Sales Non-Semiconductor Company Products Total 1978 1979 1984 $110 15 10 $135 Source: $150 40 20 $210 $460 275 50 $785 DATAQUEST, Inc November 1979 - 3 -Table 3 ESTIMATED NORTH AMERICAN INDUSTRIAL ELECTRONIC DISTRIBUTOR SEMICONDUCTOR RESALES % (Millions of Dollars) 1974 1975 1976 1977 1978 1979 1984 Total Semiconductor Integrated Circuits Bipolar Digital MOS Linear Discrete Optoelectronic Not Available $512.0 288.3 139.6 72.2 76.5 206.7 17.0 $472.0 255.7 98.6 80.7 76.4 193.2 23.1 $589.0 359.0 133.2 134.1 91.7 202.7 27.3 $664.0 417.0 150.9 152.3 113.8 215.2 31.8 $875.0 591.7 223.7 229.1 138.9 244.2 39.1 $1,120 N/A^ N/A N/A N/A N/A N/A $2,218 N/A N/A N/A N/A N/A N/A Table 4 Source: DATAQUEST, Inc. November 1979 • ESTIMATED NORTH AMERICAN INDUSTRIAL ELECTRONIC DISTRIBUTOR RESALES AS A PERCENTAGE OF NORTH AMERICAN CONSUMPTION Total Semiconductor Integrated Circuits Bipolar Digital MOS Linear Discrete Optoelectronic Not Available 1974 22.6% 22.9% 24.4% 16.3% 31.3% 23.7% 13.9% 1975 26.1% 25.1% 27.2% 18.7% 34.1% 29.1% 18.0% 1976 25.0% 25.3% 27.3% 20.3% 34.0% 25.6% 19.0% 1977 24.5% 23.3% 25.8% 18.0% 32.1% 26.2% 30.3% 1978 26.3% 25.7% 31.1% 19.9% 31.9% 27.9% 26.8% 1979 26.3% N/A^ N/A N/A N/A N/A N/A 1984 27.0% N/A N/A N/A N/A N/A N/A Source: DATAQUEST, Inc. ^kd November 1979 ^ P - 4 -i. EK-M- R E S E A R C H K r ^ ASubsidiarvof A.C.Nielsen Co. ^ INCORPORATED i N I ^ Z I f V ^ S L ^ H 1 1 i C ^ f SIS Code: Vol. I, 2.2 GOVERNMENT ISSUES AFFECTING THE SEMICONDUCTOR INDUSTRY SUMMARY This report provides a brief analysis of some of the current government issues which have an impact on the U.S. semiconductor industry. Some of these issues have been reported in earlier DATAQUEST newsletters; we will be following all of them in tlie coming months. • President Carter has signed a new export control law which could (1) reduce the scope of controls over the export of certain high technology items; (2) ensure that export license applications are processed in a timely manner; and (3) require the U.S. government to take foreign availability into account when imposing export controls or processing export license applications. • Congressman Charles Vanik (D-OH) has introduced legislation to provide tax incentives for corporate contributions to stimulate basic research. • The Commerce Department seeks legislation to protect confidential business information submitted to the government by U.S. exporters. • The VHSIC (Very High Speed Integrated Circuit) Program has been authorized by both the fuU House and Senate. Appropriation of funds for the program must wait for passage of the Defense Appropriation Bill, which is now being heard by the Joint House Senate Committee. EXPORT CONTROL LEGISLATION BECOMES LAW On September 29, 1979, President Carter signed into law S. 737, a bill to amend and extend the Export Administration Act of 1969 for four years. As finally approved by the Congress and signed by the President, S. 737 represents a generally positive step for high technology exporters. Over the past several years, exporters have been complaining that overly restrictive export controls and delays in the processing of export licenses have put them at a competitive disadvantage against their foreign competitors in the emerging markets of the People's Republic of China, the U.S.S.R., and the other socialist countries of eastern Europe. In this connection, the legislation would: • Reduce the scope of controls over the export of certain high technology products Copyright © 28 November 1979 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness, It does not contain material provided to us in confidence by our clients. This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities This firm and its parent andfor their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO • Ensure that export license applications are processed in a timely and expeditious manner • Require the U.S. Government to take into account the question of foreign availability when imposing export controls or when processing an export license application. High technology companies must be relieved that the final version of the legislation did not contain amendments sought by conservative members in both the House and the Senate. Those amendments would have given the Department of Defense virtual control over which technologies and products eould be exported to both Communist and free world destinations. It is generally recognized that the sweeping changes made in the Export Administration Act tJiis year by the Congress were essentially in response to the bad management and poor implementation of earlier law by the Department of Commerce and Other Federal agencies involved in the export licensing process. S. 737, necessarily, gives the Executive Branch a great deal of flexibility in determining how the general guidelines established by the Congress will be implemented. It can decide such matters as what constitutes a "militarily" critical teclinology or product; how foreign availability is to be established, and what items should be decontrolled. The direction of Federal rulemaldng in these and other areas will not be evident for several montlis; however, these decisions will indicate how much progress the exporters of high technology products have made in the two-year effort to modernize and Streamline U.S. export control procedures. One positive change that should emerge is that the export licensing process will become more open to aU exporters. The new law contains numerous requirements for the government to inform the exporters of the status of his export license application, and provides the exporter with legal rights to ensure that the Federal licensing agencies meet their obligations in the handling of export license applications. Following is a summary of the major provisions of the Export Administration Act. DATAQUEST has prepared this summary to assist companies in understanding the changes made to the Export Administration Act by S. 737. Summary of the Major Provisions of S. 737 Affecting U. S. Hij^ Technology Exporters Congressional Findings The biU S.737: • Recognizes that the ability of U.S. citizens to engage in international commerce is a fundamental concern of U.S. policy • Declares that uncertainty of export control policy can curtail the efforts of American business to the detriment of the overall attempt to improve the trade balance of the United States • Specifies that for the salce of U.S. national security, export controls must be applied to the export of goods and technologies which could significantly aid a potentially threatening foreign military power - 2 -Congressional Policy Statements It is the Congressional intent that the U.S. policy minimize uncertainti^'in its export control policy, and encourage trade with all countries. } It is the policy of the United States to use export controls only after full consideration of the impact on the U.S. economy and only to the extent necessary: • To restrict the export of goods and technology which would significantly contribute to the military potential of any country which would prove detrimiental to the national security interests of the United States • To further fundamental national security or foreign policy objectives when such export controls wiU clearly aid these objectives, and when they are properly administered General Provisions The bin establishes the following three types of export licenses: • A validated license • A qualified general license • A general license (Note: The new qualified general license is established for exports which are not subject to multilateral, i.e., COCOM (NATO countries minus Switzerland, plus Japan) control, but which are nevertheless subject to U.S. national security controls. The new license is intended to form a "precedent"—subject to appropriate end use controls—for the licensing of high technology products which are available from foreign sources.) Also expressed is the intent of Congress that qualified general licenses be used to the maximum extent possible. Validated licenses shall be used for those items monopolized by the United States or applied to items for which the U.S. is seeldng comparable controls by other countries. The President may not delegate any authority to any department or agency unless the Senate has confirmed its head. (Note; TTiis provision is expressly intended to prevent the National Security Council from getting involved in decisions on export license applications.) National Security Controls Whenever the Secretary of Commerce malces any revision regarding any goods or technologies, or revisions involving any countries or destinations affected by export controls imposed for national security purposes, such changes must be published in the Federal Register. The Secretary of Commerce will establish and maintain a list of all goods and technologies subject to export controls for national security purposes. The Secretary of Defense and other agencies will assist the Secretary of Commerce in identifying - 3 -those items which are to be included on the control list, and the Secretary of Defense must concur on these items. If the Secretary of Defense and the Secretary of Commerce fail to agree on an item(s) or technology(ies) to t>e included on the control list, the matter is to be referred to the President for resolution. The Secretary of Commerce is required to issue regulations providing for the review of the list of items controlled by multinational agreement not less frequently than every three years, and annually in the case of all other controls. The regulations are to provide interested parties with an opportunity to submit written data, views or arguments. The regulations also must require that an assessment be made of the availability of goods or technologies from sources outside the U.S. which are controlled for national security purposes. (Note: In requiring an annual review for U.S. unilateral export controls, the Congress expressed the hope and expectation that this would ensure more frequent review of the U.S. unilateral control list than is now provided despite the fact that the Administration argued that it was "continuously" reviewing the control list.) The Secretary of Commerce, in consultation with the Secretary of Defense, is directed to ensure that export controls imposed for national security are limited to militarily critical goods and technologies. Critical Technologies List The Secretary of Defense bears the primary responsibility for developing a list of militarily critical goods and technologies with primary emphasis given to; • Arrays of design and manufacturing know-how • Keystone manufacturing, inspection and test equipment • Goods accompanied by sophisticated operation, application or maintenance know-how The initial version of this list is to be published in the Federal Register by October 1, 1980. (Note; In its ConfCTence Report, the Congress indicated that the inclusion of this provision was intended to clarify the respective roles of the Secretary of Commerce and the Secretary of Defense in the control list maintenance and review process, but not to change fundamentally the current sharing of responsibilities of these two officials and their respective departments. The Secretary of Commerce will retain the responsibility for maintaining the export control list; it is made clear that it is the responsibility of the Secretary of Defense to identify critical goods and technologies for possible inclusion on the control list.) Foreign Availability The Secretary of Commerce will establish within the Commerce Department a capability to monitor and gather information on foreign availability. The Secretary of Commerce is directed to review, on a continuing basis, the availability of items and technologies from sources outside the U.S. which are controlled by the United States. If the Secretary properly determines that any such goods or technologies a^ available to controlled (i.e., Communist) destinations to - 4 -sufficiently malce U.S. requirements for validated licenses ineffective, he may not impose validated licensing requirements on those items unless the President deter-mines it to be a case of national security. When the President malplicant must be informed of the ^lecific cpestions raised and/op the negative recommendations made. The applicant must be accorded the opportunity to respond in writing to such question or recommendations before a final decision on the application is made. The applicant must be informed within five days of a decision to deny an application. Whenever he denies an application for national security or foreign policy purposes, the Secretary of Commerce will notify the applicant of the denial and explain what, if any, modifications or restrictions on the goods or technologies could be made to allow the application to be approved. Alternatively, the Secretary may indicate in the denial notice which licensing officers in the Department of Commerce are most familiar with the case. These licensing officers are to be made reasonably available to the applicant for consultation with regard to any modifications or restrictions which might lead to the approval of the license application. The Secretary of Commerce may extend the time periods described above if he determines that a particular application or set of applications is of sufficiently exceptional importance or complexity that additional time is required to review the application. If the Secretary makes such a determination, he is required to notify both the applicant and the Congress. Special Role for the Secretary of Defense The Secretary of Defense may review the proposed export of any goods or technologies which are controlled for national security purposes. He is directed to confirm in writing to the Secretary of Commerce the types of transactions lie wish^ to review. - 7 -The Secretary of Defense must carefuUy consider any application referred to him by the Secretary of Commerce and, within 30 days: • • Recommend to the President that he disapprove the proposed export, or • Recommend to the Secretary of Commerce that the export be approved subject to specified conditions, or • Recommend to the Secretary of Commerce that the application be approved The President may overrule any recommendation of the Secretary of Defense, but in those instances, the President must inform the Congress of his decision. COCOM Review of U.S. Export License Applications When applications are subject to COCOM review, the Secretary of Commerce wiU notify the applicant of U.S. approval of the application and the date of such approval, although a license may not be issued until COCOM approval is secured. If COCOM does not reach a determination on the application within 60 days after it is approved by the U.S. Government, the Secretary of Commerce is directed to issue the license unless he determines that such action would prove detrimental to U.S. national security interests. If the Secretary malces such a determination, he is required to notify the applicant and the Congress of his decision, the reasons for it, the reasons the COCOM review could not be completed within the 60-day period, and the actions being talcen by the U.S. Government to secure conclusion of COCOM review. These 60-day extensions may be repeated, but in each instance the Secretary is required to inform both the applicant and the Congress of all the factors listed in the initial extension. Legal Rights of an Applicant Whenever any action is not talcen on a license application within the time periods specified (except in those cases involving applications of exceptional importance or complexity where the applicant is notified), the applicant may file a petition with the Secretary of Commerce requesting compliance with the law. If, after 30 days, the processing of an application has not been brought into conformity with the provisions of the law, or if the application has been brought into conformity but the Secretary has not so notified the applicant, the applicant may bring an action in the appropriate U.S. District Court to require compliance with the law's requirements. Effective Dates i By October 1, 1980, the bill also requires the Department of Defense to publish an initial critical technologies list. • By July 1, 1980, the bill requires the Secretary of Commerce to establish procedures for handling of export license applications. « The biU extends the Export Administration Act, as amended, until September 30, 1983. - 8 -LEGISLATION TO STIMULATE BASIC RESEARCH INTRODUCTION IN THE HOUSE Legislation has been introduced in the House by Rep. Charles Vanik (D-OH) to enable companies to obtain tax. credits and deductions for corporate or business expaiditures, for directed basic research, or for exploratory research conducted by universiti^. The legislation, entitled the "Basic Research Revitalization Act of 1979," permits companies to establish segregrated Research Resources Funtte (entities similar to Domestic International Sales Corporations) to receive, accumulate, and distribute funds to qualified ^ante^. Research Resources Funds would be tax exempt and could accumulate funds for i^ to four years before disbursement. Under the terms of the legislation, companies would qualify for a 25 percent tax credit in the year in which funds «ire placed into the Research Resources Fund. In additi(»i to the credits, the legislation would permit tax deductions on a doUar-for-doUar be^is in the year in which funds are placed in the Fund. The combination of tax credits and deductions should provide the investor with a tax write-off amottnting to about 70 percent of every dollar put into a Research Resources Development Fund. The legislation was introduced just a week after L. J. Sevin, Chairman of the Board of Mostek Corporation, recommended to the Joint Economic Committee that Congress provide f O T tax credits for corporate contributions to universities to Stimulate industrial innovation. CONFIDENTIALITY OF SHIPPERS' EXPORT DECLARATIONS BEING THREATENED Confidential reports, containing 20 items of detailed information on every U.S. export transaction are in danger of public disclosure, unless corrective legislation is passed before June 30, 1980. These reports, known as Shippers' Export Declarations, must be filed by U.S. exporters for each shipment of merchandise valued at $251.00 or more exported from the U.S. They are the basis for compilation of official U.S. export Statistics. Twin Coast Newspapers, Inc., publisher of the "Journal of Commerce" has filed suit in the U.S. District Court to compel the U.S. Department of Commerce to release Shippers' Export Declarations under the provisions of the Freedom of Information Act. In an amendment to the Export Administration Act, recently signed into law by President Carter, the Congress provided that information obtained under the Act's authority, including Shippers' Export Declarations, on or before June 30, 1980, shall be deemed to be confidential and exempt from disclosure. If legislation is not passed to permanently exempt Shippers' Export Declarations before June 30, 1980, and if the courts rule in favor of Twin Coast Newspapers, the government will have to reveal the following types of information on individual export transactions: -9 -Mode of Transportation Exporter Ultimate Consignee Description of the Commodity Net Quantity Value of the Shipment Date of £xportati(xi The Department of Commerce has had legislation introduced in the House to clarify its authority to maintain the confidentiality of Shippers' Export Declarations permanently. Hearings on this legislation are expected later this month. VHSIC PROGRAM AUTHORIZED, AWAITS APPROPRIATIONS In our last DATAQUEST Newsletter, we published erroneous information as to the Status of the VHSIC program. Presently, the VHSIC program has been authorized by both the Senate and House. The VHSIC fHrogram legislation is a part of the Defense Appropriations bill presently being heard by the joint House-Senate Appropriations Committee. Since Senate and House versions were almost identical as authorized, it is expected that the monies will be appropriated as written, with $30 million for Fiscal Year 1980. If the Appropriations bill is peissed as expected, awards to participating companies would follow after January 1, 1980. Frederick L.Zieber Lane Mason - 1 0 -SIS Code: Vol. I, 2.8.6 DYNAMIC AND STATIC S A G S R A I V I AND EPROM SHIPBSENTS SUMMARY Worldwide sliipments of 16K dynamic MOS RAMs increased to an estimated 18.7 million units in the tliird quarter of 1979, up about 29 percent over an estimated 14.5 million units shipped in the second quarter of 1979. Demand continues to be extremely Strong such that prices tliat had been flat are now increasing slightly. Prices are in the $5.50 range for plastic paclcages and in the $6.50 range for liermetic packages. Most major suppliers of 16K RAMs are fuUy committed tlirough mid-1980. Worldwide shipments of 4K dynamic MOS RAMs continued to decline slowly in tlie third quarter of 1979, falling to an estimated 17.2 million units, down about 7 percent from estimated second quarter shipments. Prices remain firm in the $2 range and lead times are in the 15 to 25 week range as the unavailability of the 16K dynamic RAMs makes the 4K dynamic RAMs still desirable. Estimated third quarter shipments of slow 4K NMOS static RAMs reached an estimated 10.4 million units up about 22 percent over second quarter shipments. The 2147 type fast static RAM shipments were an estimated 965,000 units, down from estimated second quarter shipments of 1.3 million units. CMOS 4K static RAMs continue to increase dramatically in the third quarter, reaching an estimated 1.9 million units, up about 51 percent from 1.2 million units shipped in the second quarter of 1979. Worldwide shipments of 8K EPROMs in the third quarter were up slightly to an estimated 5.3 miUion units. This level is up about 9 percent over the second quarter shipments and prices remain in the $6 to $7 range. Shipments of 16K EPROMs continue to increase to an estimated 3.3 million units, up about 36 percent over estimated second quarter shipments of 2.5 million units. Prices had been in the mid-$20 range for most of the third quarter, but recently some softness has occurred with price quotes reaching $18 to $20 range for plastic parts. The two quantity suppliers of 32K EPROMs shipped an estimated 110,000 units in the third quarter. Hitachi has now begim sampling this part, also. DYNAMIC MOS RAMS 16K RAMs DATAQUEST estimates of worldwide 16K dynamic MOS RAM shipments are presented in Table 1. We estimate that the current suppliers of this device shipped an estimated 18.7 mfllion units in the third quarter of 1979 an increase of about 29 percent over estimated second quarter of 14.5 miUion units. Our estimates include 16K chips shipped in 2-chip hybrid packages as 32K dynamic RAMs. Copyright © 16 November 1979 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients. This information Is not furnished in connection with a sale or offer to sell securities or in connection wirh the solicitation of an offer t o buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from lime to time, have a long or short posItion ir^ the securities mentioned and may sell or buy such securitiesn 19055 Prunendge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO The demand for 16K dynamic RAMs appears to be increasing almost weekly as more users are committing their design to this product. Purchasing agents of major corporations are coming back into the market for increased quantities as new programs are being added to the list of 16K RAM users or as existing programs expand their usage. IBM's requirements appear to be increasing as well, and their actual demand may be as high as 12 to 14 million 32K RAMs in 1980, thereby putting increased pressures on this market. Most major suppliers are committed through the second quarter of 1980 and some as far as the third and fourth quarter of 1980. Most price quotations for first half delivery of high volume and high quality plastic parts are in the $5.50 to $5.80 range with prices for the second half of the year still remaining in the same range. There is some uncertainty about the second half of 1980 as suppliers are trying to evaluate the effect of higher interest rates euid t^hter money on the computer and industrial segments. If demand from this sector should soften, prices could fall in the second half of 1980. However, the present outlook is that prices will remain relatively firm into the second half of 1980 and perhaps even increase. Currently there is a very active spot market for 16K dynamic RAMs for those suppliers who have some additional supply. The spot market prices range from $1 to $3 above the long term contract pricing depending upon quantity and specifications. About 50 percent of the 16K RAMs shipped in the third quarter were in plastic packages. Some manufacturers are shipping as much as 75 percent of their product in the plastic packages, but others who have not been manufacturing the product for quite S O long currently have only about a third of their product in plastic. As the prices decline over the next couples of years, there will be an increased incentive for pressure on the suppliers to switch to plastic packages in order to maintain margins. 4K RAMs DATAQUEST estimates of 4K dynamic MOS RAM shipments are presented in Table 2. Quarterly shipments continued to decline in the third quarter of 1979 to an estimated 17.2 million units, down about 7 percent from estimated second quarter shipments. Although many suppliers are now de-emphasizing this product as they continue to shift capacity toward the 16K dynamic RAMs and other products, demand remains quite strong. Some products that had been scheduled for conversion to 16K dynamic RAMs are being forced to stay with the 4K dynamic because of the tight supply of 16K RAMs. Lead times remain in the 15 to 25 week range with prices in the $2 range for plastic and $2.50 range for CERDIP. 32KRAMS Mostek is the only supplier that is currently marketing a 32K dynamic MOS RAM into the merchant market. They shipped an estimated 30,000 units in the third quarter with prices stiE in the $17 to $20 range. The estimated shipments of 32K dynamic RAMs by Intel, Mostek, Motorola, and TI to IBM are included as 16K equivalents in Table 1. - 2 -64K RAMs In the third quarter of 1979, there were still only three suppliers sampling 64K RAlVIs: Fujitsu, Motorola, and Texas Instruments. We estimate that Motorola shipped about 3,000 samples in the quarter whereas Fujitsu and TI each shipped an estimated 1,000 units in the third quarter. We are stiU expecting additional suppliers to begin sampling before the end of 1979, but the extreme difficulty in making this device has slowed introductions. STATIC MOS RAMS 4KRAMS The growing importance of fast static NMOS RAMs and CMOS static RAMs has restilted in our splitting static MOS RAMs into three separate tables: slow NMOS Statics, fast NMOS statics, and CMOS statics. Table 3 presents our estimates of slow 4K NMOS Static RAM shipments in the third quarter of 1979. The industry shipped an estimated 10.4 million units on a worldwide basis. This is i^ about 22 percent over an estimated 8.5 million units shipped in the second quarter. The split between the lKx4 and the 4Kxl architecture is indicated in the table. In the third quarter, the lKx4 architecture represented 82 percent of the total as opposed to 73 percent in the second quarter and 67 percent in the first quarter. We expect the percentage of lKx4 devices to level off at aix>ut 85 to 90 percent of the total. Lead times for slow static RAMs remain in the 15 to 20 weelc range with pricing in the $3.50 to $4.50 range for the 2114-type device in plastic. Table 4 presents DATAQUEST's estimates of worldwide shipments of fast 2147 (4Kxl) Static RAMs. Third quarter shipments of 965,000 units were down from estimated shipments of 1.3 million units in the second quarter. Note that Intel shipments in the third quarter included an estimated 25,000 of the 2148 (lKx4) fast Static RAM. All other shipments in Table 4 are of the 2147-type. Two years after the introduction of the 2147, Intel is stiU by far the leading producer of the product. However, four other companies are shipping the device now and several othCTS are sampling. Prices for the 2147 are in the $18.00 to $21.00 range with lead times of 12 to 18 weeks. Table 5 presents our estimates of 4K CMOS static RAM shipments. Third quarter shipments were an estimated 1.9 million units, up about 51 percent from the estimated 1.2 million units shipped in the second quarter. Lead times on the devices are in the range of 12 to 16 weeks and prices are running from $10.00 to $13.00 for shipments in the fourth quarter of 1979. The split between the lKx4 and 4Kxl device is in favor of the lKx4 architecture which has 63 percent of the total units in the third quarter. SERAMs Mostek shipped an estimated 50,000 lKx8 slow static NMOS RAMs in the third quarter of 1979 and an estimated 5,000 8Kxl fast static in the same quarter. In the meantime, EMM continued to sample its lKx8 static RAM. Prices for these devices are in the $13.00 to $15.00 range. Other suppliers are expected to sample 8K as weU as 16K Statics in the coming quarters. - 3 -EPROMs 8K EPROMs Table 6 presents DATAQUEST's estimated worldwide shipments of 8K EPROMs. In the third quarter of 1979 an estimated 5.3 million units were shipped, up about 9 percent from second quarter shipments. Prices are remaining firm in the $6.00 to $7.00 range with some lower quantities $1.00 to $2.00 higher. Lead times are in the 12 to 16 week range. 16E EPROMs Table 7 presents our estimates of worldwide shipments of 16K EPROlVIs. In the third quarter, an estimated 3.3 million units were shipped, up from an estimated 2.4 million imits in the second quarter and up very dramatically from 465,000 imits in the third quarter of 1978. During most of the third quarter, prices remained relatively firm in the mid-$20.00 range. However, toward the end of the third quarter and in the early fourth quarter, prices dropped to the $18.00 to $22.00 range as more supply has become available. Lead times have shortened to off-the-shelf delivery up to 12 weel<s. 32E EPROMs Table 8 presents our estimates of worldwide shipments of 32K EPROlVIs. Third quarter shipments of 110,000 imits are up from an estimated 65,000 units in the second quarter. Prices are still in the $50.00 to $80.00 range for the limited quantities being shipped. Additional suppliers should be entering this marlcet within the next two or tJiree quarters. Daniel L. Klesken Lane Mason - 4 -Table I ESTIMATED WORLDWIDE SHIPMENTS OF 16K DYNAMIC MOS RAMS (Thousands of Units) Company AMD Fairchild Fujitsu Hitachi Intel Intersil ITT Matsushita Mostek Motorola National NEC Siemens Signetics Texas Instruments Toshiba Zilog Total Percent Change From Previous Quarter 1978 1979 3rd Qtr. 0 200 500 350 600 0 75 0 1,400 550 75 1,100 25 30 950 80 15 4th Qtr. S2 200 900 500 900 S 100 0 1,800 500 150 1,300 40 80 1,400 150 20 Year S 465 2,000 1,210 2,400 S 203 0 4,900 1,750 287 3,850 85 140 3,150 285 60 1st qtr. S 300 1,100 800 600 S 200 0 2,400 700 2nd Qtr. 5 400 1,300 1,400 700 5 300 0 3,600 1,200 3rd Qtr. 10 500 1,600 2,200, 950" 5 600 S 4,600 1,000 -^?06-^5o tj^W^S^ 1,000 1,700 65 75 1 iyf\nt\ •±, OsUU 225 20 2,200 100 40 l,««'2,200 550 50 3,200 250 50 1,800 900 50 5,950 8,040 20,785 45.1% 35.1% 10,235 14,500 18,715 27.3% 41.7% 29.1% Includes merchant market and internal shipments 2 hidicates sampling 3 Includes an estimated 50,000 5-volt only parts Source: DATAQUEST, Inc. November 1979 - 5 -Table 2 ESTIMATED WORLDWIDE SHIPMENTS OF 4K DYNAMIC MOS RAMS^ (Thousands of Units) 1978 1979 Company A A I ^ Fairchild Fujitsu Hitachi Intel Intersil ITT Mostek Motorola National NEC Signetics Texas Instruments Total Percent Change From Previous Quarter 3rd Qtr. 1,800 0 400 500 2,700 100 300 4,800 1,500 1,500 1,600 300 4,000 19,500 0.0% 4th Qtr. 2,200 0 300 450 2,300 100 800 4,200 1,900 1,700 1,350 300 3,800 19,400 (0.5%) Year 6,600 900 r9««-' 1,780 11,000 450 1,600 17,000 5,700 5,600 6,150 1,150 16,700 76,530 1st Qtr. 2,600 0 jtoo 200 350 1,700 100 1,100 3,800 1,500 2,000 1,350 300 3,600 18,600 (4.1%) 2nd qtr. 3,000 0 200 200 1,700 50 1,300 3,300 1,150 2,400 1,900 . 100 3,200 18,500 (0.5%) 3rd qtr. -aao^ 'h.ooo 0 200 200 1,500 50 1,300 3,400 1,800 2,000 1,300 50 2,700 d 17,206-- r^o ^.im) Includes merchant marlcet and internal shipnjents / ^ . / t ' / I ( ^-'^ '"J Source: DATAQUEST, Inc. November 1979 - 6 -Table 3 ESTIIMATED 1979 WORLDWIDE SHIPIVIENTS OF SLOW 4K NIVIOS STATIC RAMS (Thousands of Units) AMD AMI EMM Fairchild Fujitsu Hitachi Intel Intersil Maruman Matsushita Mosteic Motorola Nati(»ial NEC Synertek Texas Instruments Toshiba Zilog 1st Quarter lKx4 4Kxl 150 50 600 50 80 450 400 200 0 0 450 270 530 400 560 500 150 0 30 0 500 0 0 0 400 100 0 0 0 30 120 600 0 500 0 110 2nd Quarter lKx4 4Kxl 275 55 600 100 150 450 600 230 10 20 600 320 900 600 600 500 210 0 75 0 600 0 0 0 600 130 0 0 0 20 190 60 0 500 0 110 3rd Quarter lKx4 4Kxl 330 95 700 300 250 450 850 250 20 50 900 450 900 1,200 900 550 300 0 140 0 650 0 0 0 100 150 0 0 S 30 200 0 0 450 0 150 Total Percent Change From Previous Quarter 4,840 2,390 6,190 2,285 27.9% (4.4%) 8,495 1,870 37.2% (18.2%) Source: DATAQUEST, fiic. November 1979 - 7 -Table 4 ESTIMATED 1979 WORLDWIDE SHIPMENTS OF FAST 4K NMOS STATIC RAMS (Thousands of Units) AMI Fujitsu Hitachi Intel Motorola National NEC Toshiba Total Change From Previous Quarter Indicates Sampling ^Includes 25,000 2148 (lKx4) Devices 1st Qtr 830 2nd Qtr 3rd Qtr. 5 0 0 800 S 0 25 0 lOl S^ 0 1,200 10 10 70 0 5 15 ^2 650^ 20 25 250 S 1,300 56.6% 965 (25.8%) Source: DATAQUEST, Inc. November 1979 Table 5 ESTIMATED 1979 WORLDWIDE SHIPMENTS OF 4K CMOS STATIC RAMS (TTiousands of Units) Harris < Hitachi^ Motorola National NEC RCA Toshiba Total 1st Quarter lKx4 25 0 0 0 100 50 175 350 Change From Previous Quarter 1 T _ ^ I . . ^ „ OC nnn ^•, An T , „ 4Kxl 15 150 0 0 0 0 25 190 2nd Quarter lKx4 40 0 0 0 270 80 450 840 140% 4Kxl 30 325 0 0 0 0 50 405 113.1% 3rd Quarter lKx4 100 °2 S " ^ S 450 125 500 1,175 39.9% 4Kxl 100 500 0 S 0 0 100 700 72.8% Includes 25,000 6147 Fast CMOS Static RAMs in 2nd Quarter and 100,000 in 3rd Quarter 2 Indicates sampling Source: DATAQUEST, Inc. November 1979 - 8 -Table 6 ESTIMATED WORLDWIDE SHIPMENTS OF 8K EPROMS^ (Thousands of Units) 1978 1979 Company AMD Electronic Arrays Fairchild Fujitsu Intel Motorola National Signetics Texas Instruments Toshiba Total Percent Chaise from Previous Quarter 3rd qtr. 80 60 60 70 800 300 300 80 400 10 2,160 (5.9%) 4th 9tr^ 340 60 120 70 1,000 400 500 50 800 30 3,370 56.0% Year 485 200 280 280 3,400 1,020 1,250 280 2,100 40 9,335 1st Qtr. 600 75 160 70 1,100 700 600 0 800 50 4,155 23.3% 2nd Qtr, 700 100 200 50 1,400 750 800 0 800 100 4,900 17.9% 3rd gtr. 700 125 350 50 1,400 1,000 800 0 800 100 5,325 8.7% Includes merchant marl S " market in 1979: GenRad, through the acquisition of Futuredaita (former independent MDS supplier) and Hewlett-Packard. The - entry of Tektronix has contributed to the growth of the non-'semiconductor segment of the MDS market in 1978; and this market is expected to increase in market share through 1983, as GenRad, Hewlett-Packard, and other test instrument companies augment this market segment. MARKET FORECAST The microprocessor development system (MDS) market is expected to increase from an estimated $143 million in 1978 to an estimated $520 million in 1983, a compound annual growth rate of approximately 30 percent, as shown in Figure 1. Table 2 presents DATAQUEST's estimated sales by supplier type through 1983. Copyright©10 October 1979 by DATAQUEST - Reproduction Prohibited 'The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness It does not contain material provided to us in confidence by our clients This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO Table 1 ESTIMATED WORLDWIDE SALES OF MICROPROCESSOR DEVELOPMENT SYSTEMS, 1976-1978 (Millions of Dollars) Supplier Semiconductor Manufacturer (Single-vendor) Test Instrument Manufacturers and Others (Multi-vendor) Total 1976 $46.0 2.0 $48,0 1977 $82.0 8.0 $90.0 1978 $127.0 16.0 $143.0 Compound Annual Growth Rate 1976-1978 66.2% 182.8% 72.6% Source: DATAQUEST, Inc. Sales of development systems have grown rapidly during the past three years and are expected to continue to have good growth, although at a slower rate. The following factors should contribute to the MDS market growth through 1983: • Expanding electronics sales • Penetration of microprocessors into new products • Increasing complexity of new microprocessor devices • Replacement and/or upgrading of installed base However, there are other factors which may cause the growth of this market to be moderate. These factors are: • Multi-user systems are expected to lower per-terminal cost. • Universal systems (multi-vendor) sales are expected to grow at a faster rate than dedicated (single-vendor) systems, thus reducing total capital output for development systems. • Stand-alone in-circuit emulators (ICE) are expected to increase in usage, allowing an increase in the down-loading from existing MDSs to these units. • There is a vast installed base of development systems. -2-i 5 2 0 480 440 400 360 320 280 ^ 240 200 1 6 0 1 2 0 80 40 FIGURE 1 ESTIMATED WORLDWIDE SALES OF MICROPROCESSOR DEVELOPMENT SYSTEMS, 1976-1983 • ^1 ' >/^::ii:::: . . . . . . r •• - ^ f- r n ::: 1 • • • (Tiliiiiiiliiii; • • • • • • • • • ; . J^\\ \\\\\\\\\" •.•.•.•••.v.v.v •1 C^ s'^ .._ . ^ / ; ; • % A::::: ^'•'•y-•''.•:•.. 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• • • • • • • • • a « • • • • • • « . • • • • • • • • « « • • • • • • • • • • • • • • • • • • • • • • her Manufac " ^ ^ • • • • • • • •jt \ • • • . • •^^ • • • • • • • « • • • • • ( • « • • « • • • • • r 4 « « « « « « «!• • « • • • « • • • • • • • • • • • • a • [ • • • • • • • • « • • / :::::::::;:::::;::; :::::::::::::::;:: :::::::::::::;:;;:; ; ; : ; : : ; ; : • • : ;::;::;::;::::"::; ::::;:::::::::;;::: iClurers:::;:::: V ^ » • • • • ' '^^« • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •.•..•..•.. • • • • • • • « • • • • • • • • • • • • • A B « A > « 4 a « a 4 B « 4 4 • « « • • . • • • > • < • ' : > ' ' ! • ' • • ; : ' ! turers .:.:.:•:•:• • • • • • • • • • t i • • • • • • • . . . • • 1976 1977 1978 1979 1980 Year 1 9 8 1 1982 1983 Source: DATAQUEST Inc. - 3 -Table 2 ESTIMATED WORLDWIDE SALES OF MICROPROCESSOR DEVELOPMENT SYSTEMS BY SUPPLIER, 1978-1983 (Millions of Dollars) Compound Annuail Growth Rate Supplier 1978 1979 1980 1981 1982 1983 1978-1983 Semiconductor Manufacturer (Single-vendor) $127.0 $165.0 $195.0 $235.0 $275.0 $320.0 20.3% Test Instrument Manufacturers and Others (Multi-vendor) 16.0 35.0 65.0 110.0 155.0 200.0 65.7% Total $143.0 $200.0 $260.0 $345.0 $430.0 $520.0 29.5% Source: DATAQUEST, Inc. Factors causing the non-semiconductor segment to grow to an expected 38 percent in market share by 1983 are: • Test instrument manufacturers are currently prominent in research and development (R&D) labs in which micro-processors are being designed into new products; thus, engineers are familiar with the major companies, their equipment, and their service. • Test instrument manufacturers sell primarily through their own direct sales force and sales representatives; typically, both segments have personnel with technical backgrounds. This combined sales force penetrates the total engineering community, including the R&D labs. • Test instrument manufacturers provide a variety of emulators for the popular microprocessors. This availability gives the user flexibility in the choice of microprocessors to be used in new applications without purchasing additional stand-alone systems. The forecast for the next five years is based upon the assumption that each semiconductor manufacturer will continue to provide emulation only for those devices that it manufactures, either as the original or a second source. TRENDS There are trends in the microprocessor market that affect the MDS market and there are trends within the development systems market itself. The major trends that influence the market are: Limited Number of Microprocessor Families DATAQUEST expects the number of distinct microprocessor families (multi and single chip) to grow at a moderate rate because of the large cost and time involved in bringing out a new family. However, within a product family, we expect a proliferation of microprocessor and peripheral chips. Increasing Demand for Microprocessors DATAQUEST estimates the market for microprocessors will increase at a compound annual growth rate of 63 percent for the next 5 years, reaching a consumption level in 1983 which is expected to be 11.5 times as large as that of 1978. Increasing Complexity of Microprocessor Devices With the arrival of the 16-bit microprocessors, designers are experiencing, first hand, the complexity of these higher-end microprocessors. -5-Multiple Microprocessors in Applications The increased application of multiple microprocessors on a board is expected to force suppliers of development systems to support this type of microprocessor application. Multi-User System Configuration Another trend in program development systems is toward multi-terminal or multi-station systems. Such systems are similar to time-sharing, except that they are dedicated to microprocessor program development. Increased Software Orientation The trend is expected to continue toward high-level languages, particularly PASCAL. The use of hard disc storage is expected to be on the incline. Distributed Terminals DATAQUEST expects an increasing number of manufacturers to provide development systems with terminals dedicated to the integration of hardware and software (in-circuit emulation) and terminals dedicated to software development (text editing and assembly). COMPETITION The competitors of the 1978 MDS market were primarily semiconductor manufacturers, representing an estimated 89 percent of the market. Intel was by far the dominant force in this market with an estimated 47 percent in market share. The combination of Intel, Motorola, and National Semiconductor accounted for approximately 69 percent of the 1978 market, as shown in Table 3. The non-semiconductor MDS manufacturers are primarily Tektronix and GenRad/Futuredata which represent approximately 9 percent of the 1978 market. Tektronix is the leader in this market segment. With the entry of Hewlett-Packard and other test instrument manufacturers in the MDS market, this segment is expected to reach an estimated 38 percent in market share in 1983. Kenneth N. Neff Galen W. Wampler -6-Table 3 ESTIMATED WORLDWIDE SALES OF MICROPROCESSOR DEVELOPMENT SYSTEMS BY MANUFACTURER (Millions Of Dollars) 1976 1977 1978 Total $48.0 $90.0 5143.0 Source: DATAQUEST, Inc. 1^7? Intel Motorola Tektronix National Semiconductor Zilog Texas Instruments AMD Mostek GenRad/Futuredata Rockwell Fairchild Signetics AMI Others Subtotal Distributor's Mark--Up $20.0 6.0 0 4.4 1.2 0.9 0 0.8 0 0.8 1.0 1.0 1.2 3.7 $41.0 7.0 $35.0 12.0 4.0 5.0 3.0 3.0 1.5 1.5 1.0 2.0 1.0 1.5 1.7 5.3 $77.5 12.5 $ 57.0 19.0 10.0 7.5 5.0 5.0 4.5 2.8 2.5 2.0 1.0 1.0 0.5 6.2 $124.0 19.0 74 It 20 \ \ ^ ^ . ^ 1 J Am %^ i- 1/ -1-A B ^ s s = S^S "SS = ^^_^.i =s == = == ,£= = = -= ^ » l-<ba^/\l-ld-i " » — "" • " " " " " " • " " ' " " ' ° " — " SIS Code: VoL I, 4.12 # ADVANCED SCHOTTKY TTL SUMHAARY Advanced Schottky TTL, an iteration of Super Sehottlcy, is now being offered by Fairchild, Raytheon, and Texas Instruments. It offers improved speed/power characteristics over conventional Schottky. Fairchild has placed its emphasis on lower power while Raytheon and Texas Instruments have emphasized higher speeds. We expect that the higher speeds of Advanced Schottky will cause significant usage problems—especially at wire wraps and connectors. Interest in the new families is high, but no significant market has yet developed due to the newness of the product lines and the lack of alternate sources. BACKGROUND Advanced Schottky (AS) and Advanced Low Power Schottky (ALS) have been announced recently. These families originated from Super Schottky development programs sponsored by IBM's Federal Systems Division, but they are now pursuing different directions. The divergent directions, imcertainty about the future, and lack of alternate sources is causing confusion in the marketplace. Two of the AS product families (Fairchild and Raytheon) are intended to be direct retrofits for Schottky (S), but some questions about full compatibility do exist. Texas Instruments AS family is implemented with new circuits in new packages; hence, it is definitely intended for new designs and not for retrofitting. Texas Instruments ALS family should be pin-compatible with the existing low-power Schottky (LS) family, but will be faster and should consume less power. Key parameters for the Schottky families are shown in Table 1. Advanced Schottky takes advantage of modern oxide-isolated processing to offer the user a significantly improved speed/power product. Thus, we expect that major extensions of Schottky will soon be effected with oxide isolation only. Copyright © 21 September 1979 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness It does not contain material provided to us in confidence by our clients. This information is not furnished in connection with a s^le or offer to sed securities or m connection with thp solicitation of an offer to buy securities This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO Table 1 TYPICAL VALUES FOR KEY PARAMETERS OF TTL LOGIC FAMILIES I IS9 I Parameter Average Switching Delay (ns) Waveform Rise Time (ns) Waveform Fall Time (ns) Power Consumption (mW per gate) ^eed-Power (pJ) Oxide Isolated ? TTL 9 6-9 4-6 10 90 No H-TTL 6 4-6 2-3 22.5 135 No S-TTL 3 1.8-2.8 1.6-2.6 20 60 No Logic Family FCI AS 2.65 2.5 2.5 4 11 Yes RAY AS 1.5 2.1 1.9 20 30 No TI AS 1.5 2.3 1.8 20 30 Yes Source: LS TI ALS 5.0 4.0 9.5 5.0 6.0 5.0 2 1 10 4 No Yes DATAQUEST, Inc. September 1979 MANUFACTURERS Fairchild Fairchild's FAST (Fairchild Advanced Sehottky TTL) employs Isoplanar processing and was the first of the new families to be introduced. Fairchild's product is well specified and nine SSI and MSI devices are available. Fairchild's strategy was to introduce a retrofitable family with slightly improved performance and greatly reduced power consumption. Although Fairchild claims that significant usage problems are not expected to result from retrofitting existing S designs, we advise potential users to proceed with caution; history has shown us that retrofitting contains many unexpected problems. We expect FAST to be performance-competitive in MSI devices, since it appears to be the interface design that limits the speed in SSI devices. Raytheon Raytheon's AS family offers no improvement in power consumption, but is about twice as fast as conventional Schottky. To facilitate driving transmission lines and large capacitances, Raytheon has increased I (output short-circuit current) to a minimum of 125 mA. This tripling of the outpirt current capability wiU result in very sharp edge speeds under light load conditions. Furthermore, Raytheon sacrificed some noise margin by lowering the input low-threshold voltage to 0.7 volts. Raytheon's AS is fabricated with a high-performance, junction-isolation process. Raytheon promotes its family as being fully compatible with existing S devices and offers it in the same packages as S. Data sheets are available, but we understand that device samples are still in short supply. Texas Instrumoits Texas Instruments approach to this emerging market is more radical; it chose to serve the extremes of high speed and low power and to offer the h^h-performance family in new packages. It uses an oxide-isolated process for both the AS and the ALS products. Its AS line is twice as fast as its S family and it is making no claims about retrofitability; the new family is offered in new circuit functions and in new package configurations and retrofitting is impossible. AS is to be the vehicle for introducing new complex functions, which wiU be offered in three output configurations as appropriate. These are: 50-ohm line drivers, buffers for lines to 100 ohms, and S configurations. Texas Instruments philosophy on ALS is to double the AC performance over comparable devices in LS while saving about one-half of the power and retaining the same design rules. With a doubling of the AC performance, TI expects that many existing S designs wiU be converted to ALS. In this case, some consideration must also be given DC loading rules. Note that DATAQUEST is skeptical about direct replacement of any devices by faster devices. Data sheets and samples are available on some SSI devices. TI expects initial availability of MSI specifications and product in October. - 3 -other Manufacturers No Other manufacturer has yet announced an Advanced Schottky family. National has recently upgraded its LS family to match the performance of Fairchild's and Motorola's LS witli the noise margin offered by Signetics' LS. AMD expects to use an oxide-isolated process for higher performance MSI/LSI in tlie future, but does not intend to enter the Advanced Schottky marketplace per se. Signetics' position is similar to tliat of AMD in that it sees no need for either a new family or an oxide-isolated process at this time. It expects to make additions and selective replacements to its LS line with advanced junction-isolated processes. Motorola states that it too is watching the market and that it intends to follow the approach that is best accepted by the marketplace. It intends to announce a decision in 1979. Motorola is one of IBM's suppliers; therefore, it has the technology to supply AS product. USAGE PROBLEMS A prominent problem in the use of high-speed logic forms is reflections on the signal lines. Reflections are generated in improperly terminated lines; they become more persistent as the propagation delay and the signal rise time approach the same magnitude. Especially in the case of the Raytheon AS, we would expect that careful termination would be required for all signal paths longer than a couple of inches. Reflections are aggravated by the discontinuities associated with wire-wrapped open wiring and connectors. Circuit malfunctions result if the reflections cause false or delayed crossings of the logic thresholds; therefore, noise margins are of vital concern. With these considerations, there is concern that AS may require more costly interconnection techniques, such as twisted pairs or strip lines on mother boards. MARKET Table 2 presents DATAQUEST's estimates of worldwide TTL logic consumption. TTL logic is segmented into standard TTL logic and Schottky logic; Schottky logic is further segmented into Standard Schottky and low-power Schottky. As indicated in Table 2, low-power Schottky is expected to have the highest growth of the various segments, reaching almost $1.2 billion by 1983. The AS and ALS markets will eventually be segments of the low-power Schottky market but it is still premature to forecast markets for these emerging product lines. - 4 -Table 2 ESTIMATED WORLDWIDE TTL LOGIC CONSUMPTION (Millions of Dollars) 1978 1979 1980 1981 1982 1983 Standard TTL Logic Schottky TTL Logic Standard SchottJcy Low-Power Sehottky Total TTL Logic $485 363 214 149 $848 $ 540 585 290 295 $1,125 $ 550 730 310 420 $1,280 $ 535 975 345 630 $1,510 $ 510 1,265 375 890 $1,775 $ 490 1,585 405 1,180 $2,075 Source: DATAQUEST, Inc. September 1979 DATAQUEST found the greatest user interest in AS and ALS to be with manufacturers of minicomputers and military equipment. Competitive minicomputers must have very fast logic in their data paths to effect the required throughput. The power consumption of conventional high-speed logic results in troublesome power-density problems and the associated problems of power distribution and heat removal. Military equipment manufacturers are vitaUy concerned with the size and weight of power supplies and with the effects of internally generated heat in high ambient temperature environments. Speed/power improvements thus typically result in large cost savings in these, and other, systems. Thus, we expect AS to be especially popular in applications that demand maximum performance, and ALS and FAST to be especially popular in military systems and in minicomputer peripheral circuits. Many users are concerned that the present movements wiU cause existing product lines to become obsolete. For example, Texas Instruments has commented that it wiU produce no new circuit designs in conventional LS; some systems manufacturers project that some existing LS may be discontinued. It certainly follows that new designs must use the new technology if the manufacturer is to remain competitive in its market. Prices of Advanced Schottky devices are expected to be 20-30 percent higher than their conventional equivalents. Although we found significant interest and awareness of the new families, we found no committed designs. We expect that there will be few commitments until at least one of the major TTL manufacturers decides to become an alternate source. Williard T. Booth Frederick L. Zieber - 5 -" '-'fdp ^^ 1 lf\i #1111 i ^m.s R E S E A R C H ^ \ A Subsidiary of A.C.NIeteBn,Go. ^ INCORPORATED I ^ I E M W ^ D l M l B I 1 1 ^ S ^ ^ SIS Code: VoL I - 2.8.1 MOS MICROPROCESSOR SHIPMENTS SUMMARY Worldwide shipments of IVIOS microprocessors in the second quarter of 1979 were an estimated 15.4 million units, up atwut 44 percent over estimated first quarter sliipments and up about 184 percent over the second quarter of 1978. Shipments of 4-bit microprocessors were an estimated 9.9 million units, up about 40 percent over estimated first quarter shipments and represented about 64 percent of the total; shipments of 8-bit microprocessors were an estimated 5.4 million units, up about 53 percent over estimated first quarter shipments and represented about 35 percent of the total. The 16-bit products represented about 1 percent of second quarter 1979 total shipments, with an estimated 141,000 units which is vp about 17 percent over estimated first quarter shipments. During the second quarter, two new 16-bit microprocessors, the 432 and the Z8000, were sampled in limited quantities. Early In the third quarter a limited number of the 68000 microprocessor were sampled. Single-chip microcomputer shipments in the second quarter of 1979 were an estimated 11.8 million units, representing about 76 percent of the total second quarter microprocessor shipments. Demand for single-chip microcomputers continues to be extremely strong and greatly exceeds available supply. Lead times range from 15 to 30 weelocessors. Shipments of 12-bit microprocessors were an estimated 19,000 units in the second quarter, up about 6 percent from an estimated 18,000 units in the first quarter of 1979 and up 27 percent from an estimated 15,000 units in the second quarter of 1978. The 12-bit microprocessor marlcet seems unlil 'Indicates sampling Source: DATAQUEST, Inc. August 1979 5 -Table 2 ESTIMATED WORLDWIDE SHIPMENTS OF t^K DYNAMIC MOS RAMS (Thousands of Units) 1978 1979 Company AMD Fairchild Fujitsu Hitachi Intel Intersil ITT Mostek Motorola National NEC Signetics Texas Instruments Total Percent Change From Previous Quarter 3rd Qtr. 1,800 0 400 500 2,700 100 300 ^^,800 1,500 1,500 1,600 300 4,000 19,500 0.0% 4th Qtr. 2,200 0 300 450 2,300 100 800 4,200 1,900 1,700 1,350 300 3,800 19,400 (0.5%) Total 6,600 900 1,900 1,780 11,000 450 1,600 17,000 5,700 5,600 6,150 1,150 16,700 76,530 " 1st gtr^ 2,600 0 200 350 1,700 100 1,100 3,800 1,500 2,000 1,350 300 3,600 18,600 (4.1%) 2nd Qtr. 3,000 0 200 200 1,700 50 1,300 3,300 1,150 2,400 1,900 100 3,200 18,500 (0.5%) Includes merchant market and internal shipments Source: DATAQUEST, Inc. August 1979 f. able 3 ESTIMATED 1979 WORLDWIDE SHIPMENTS OF 'fK STATIC MOS RAMS (Thousands of Units) I I Company AMD AMI EMM Fairchild Fujitsu Harris Hitachi Intel Intersil Mostek Motorola National NEC RCA Signetics Synertek Texas Instruments Toshiba Ziiog Total Percent Change From Previous Quarter or Year IKxif 150 50 600 50 80 0 1^50 WO 200 it50 270 530 WO 0 0 560 500 150 0 ti,UO 1st Quarter itKxl 30 0 500 0 0 0 ^2 1,200 100 0 30 120 600 0 0 0 500 0 110 3,190 CMOS 0 0 0 0 0 W 150 0 0 0 0 0 100 50 0 0 0 200 0 5f0 Total 180 50 1,100 50 80 ' fO 600 1,600 300 ^50 300 650 1,100 50 S 560 1,000 350 110 8,570 3^.3% iKxtf 275 55 600 100 150 0 ^50 600 230 600 320 900 600 0 0 600 500 210 0 6,190 27.9% 2nd Quarter ifKxI 75 5 600 0 0 ° 1 25^ 1,800 130 30^ 200^ 130 0 0 0 500 0 , 110 3,605 13.0% CMOS 0 0 0 0 0 75 300 0 0 0 0 0 270 80 0 0 0 660 0 1,385 156.5% T6t;^ 350 60 1,200 100 150 75 775 2,if00 360 600 350 1,100 1,000 80 S 600 1,000 870 110 11,180 30A% 1 All CMOS 2U7 RAMs 'Includes 800,000 21f7s 'includes 1,200,000 2147s, of which 50,000 were the 21'f7 H series at 35ns ^Includes 10,000 21175 ^Includes 10,000 21'f7s Source: DATAQUEST, Inc. August 1979 Table ^ f ESTIMATED WORLDWIDE SHIPMENTS OF 8K EPROMS (Thousands of Units) 1 1978 1979 Company AMD Electronic Arrays Fairchild Fujitsu Intel Motorola National Signetics Texas Instruments Toshiba Total Percent Change from Previous Quarter 3rd QtTj. 80 60 60 70 800 300 300 80 'fOO 10 2,160 (5.9%) i^th Qtr. 3i^0 60 120 70 1,000 itOO 500 50 800 30 3,370 56.0% Total ^^85 200 280 280 B.ifOO 1,020 1,250 280 2,100 to 9,335 1st 2tr, 600 75 160 70 1,100 700 600 0 800 50 ^,155 23.3% 2nd Qtr. 700 100 200 50 1,400 750 800 0 800 100 1^,900 17.9% 1 Includes merchant market and internal shipments Source: DATAQUEST, Inc. August 1979 8 -Table 5 ESTIMATED WORLDWIDE SHIPMENTS OF 16K EPROMS (Thousands of Units) 1 Total Percent Change from Previous Quarter 1978 65 905 (28.5%) 91.6% 2,370 1979 Company Fairchild Fujitsu Hitachi Intel Mostek , Motorola National ^ Texas Instruments Toshiba 3rd qtr. 0 0 5 250 S 10 S 200 S ifth Qtr. 0 5 30 ^50 25 90 S 300 5 Total 0 5 35 1,350 25 100 S 850 5 1st Qtr. s2 70 125 550 90 160 5 WO 25 2nd Qtr. S 200 200 750 150 150 50 900 50 1,«5 57.5% 2,450 71.9% 1 Includes merchant market and internal shipments 'Indicates sampling About 10 percent represent parts having a 5 volt-only power supply About 40 percent represent parts having a 5 volt-only power supply Source: DATAQUEST, Inc. August 1979 - 9 Table 6 ESTIMATED WORLDWIDE SHIPMENTS OF 32K EPROMS (Thousands of Units) Company Intel Texas Instruments Total 1st 3tr. 5 _ 1 0 15 2nd Qtr. 30 35 65 Source: DATAQUE5T, Inc. August 1979 10-SIS Code: VoL II Newsletter INTEL ANALYSTS' MEETING Intel Corporation held a meeting for financial analysts on Friday, July 20, 1979, in Santa Clara, California. Tlie meetir^ was attended by several members of the DATAQUEST staff. We feel information discussed at the meeting may be of interest to our clients, and therefore pass on our rough notes from that meeting. Frederick L. Zieber Michael R. Weisberg James F. Riley Copyright © 3 August 1979 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness It does not contain material provided to us in confidence by our clients This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO INTEL ANALYSTS' MEETING Friday, July 20, 1979 - Santa Clara, CA (Rough Notes Prepared by DATAQUEST Staff) General - Gordon Moore 1. Second quarter revenues were better than expected at the beginning of the quarter: Better pricing; prices down, but not at normal rate. Better manufacturing efficiencies as a result of a slowing in Q3 1978 hiring. This slowing began in Q3 1978 and first showed up in the Q2 1979 revenue rate. Intel was successful in recruiting 800+ people in Q2 1979, and expects to add more in Q3 because of an increased headcount in overseas assembly plants. 2. Third quarter dollar revenue growth vs. Q2 should be about the same as Q2 vs. Ql dollar revenue growth. 3. MRl was in for 3 months in Q2 and only two months in Ql, but this was a small increment. 4. IBM contract wiU be in for 2 months in Q3 and and then die. Intel does not expect the same growth increment in Q4 revenues. 5. Capital spending this year will be closer to $110 million rather than $120 million as projected earlier. It is locked into two-thirds of that amount in 1980, or $70-75 million. 6. Debt outstanding should not go up in next two quarters, as it hasn't spent money as fast as originally projected. 7. Employee stock purchases have been an important contribution to Intel's ability to finance growth. This source contributed $12 million in cash in the first half of 1979. Current Business Trends - Ed Gelbach 1. Have seen no slowing; distributor business is stror^, and customers tell Intel that their business is strong. 2. Intel has seen lead times come in by 5-10 percent. 3. Dynamic RAMs: Pricing is firm, should stay that way through 1979 and then soften. Demand for 16K RAMs wiU exceed supply throughout 1980. - 2 Althoi^h it gets less attention, the 4K dynamic shortage is even greater. The Shifting of wafer allocations to 16K RAMs is the cause. 4. EPROMs: Prices should start to decline in the fourth quarter of 1979 and first quarter of 1980 as new entrants come into market. Last year, EPROM prices dropped by less than $1. 16K EPROM shortages continue. 8K business fluctuates - strong now. Delivery is 12-30 weeks. 5. Microprocessors: 8-35 weeks delivery. This is the strongest part of Intel's business right now. 6. Static RAMs: High-speed devices have good delivery, firm prices, but it is positioned to respond to changes in pricing. Low-speed device delivery is extended; pricing firm but can change overnight. 4-20 weeks delivery 7. Systems: The order rate has slowed, and Litel is now quoting 4-8 weeks as supply and demand are more closely matched. Design aids are at the lower end of the growth curve at Intel. Customers talk about universal systems and are waiting for the Hewlett-Packard announcement which could be impacting demand. Memory Components Operation - Ron Whittier 1. Standard memories: DEC, Data General add-in/add-on memory In 40, 1600, 7000, 3000 Series 90 2. Custom memories: Major custom programs, such as IBM contract - 3 -Intel has a standard BUS introduced at NCC in June which should simplify the design and reduce the cost of custom memories. Dynamic RAMs: Total RAM market: $800 million in 1979 rising to $2 billion by 1983, including IBM external buying. Dynamic RAMs half the business in 1979, going to $1 billion in 1980. Growth rates will accelerate in 1980 due to IBM, solid-state discs, heavy demand. Intel Unit Forecast (16K RAM Equivalent Parts) 16K 1979 52M 1980 TOM 1981 80M 1982 TOM 1983 48M 64K 1980 4M 1981 30M 1982 105M 1983 210M 5V16K 1980 lOM 1981 20M 1982 30M 1983 40M WiU support 3 power supply parts through 1980/1981 to a well-defined customer base—around 20 major customers. Increased emphasis on 5v only part. Forcing as much business here as possible. Demand is very good. - 4 -4. 64K RAMs: Expect only 1 million pieces in 1980. It wiU sample in the second half of 1979. Currently processing material. 5. Static RAlVIs: Half of marlcet now and should be half in 1983. The marlcet for slow 4K static RAMs should pealc in units in 1980/1981, but the fast 4K segment is expected to grow through 1982. 16K Static RAMs - projecting 1 million units in 1980. 4K Static RAMs (Millions of Units in Equivalent 4K) Low Cost Fast 1979 1980 1981 1982 1983 1979 1980 1981 1982 1983 4K 30 40 40 35 25 6 18 45 60 80 16] 0 6 40 120 200 0 0 3 16 48 9. Static RAM strategy: Will support 2114, 2141 market through 1981. Intends to introduce a slow 16K RAM in 1980. HMOS - 1 (2115A, 2125A, 2147, 2148). Competition should emerge in second half of 1979 Hitachi is the bluest near-term threat 2 HMOS n can now compete fuUy with bipolar T L. HMOS n 16K RAM introduction in 1980. Special Products (Nonvolatile Memory, Bipolar, Telecommunications) - George Schneer 1. DATAQUEST estimates: $250 million in 1979, $700 million in 1983 for total EPROM revenues. - 5 -2. Expect to continue to be synergistic with the growth in microprocessors and to maintain technological leadership. 3. Relative size vs. density: 32K EPROM 16K EPROM 8K EPROM 2K EPROM 1.4 1.3 1.2 1.0 4. Bipolar PROM has achieved a 4x increase in bits in the last 4 years with a 25% increase in die size. Marlcet is $143 million in 1979 going to $254 million in 1982 (excluding General Motors). Intel is piggy bacl<ing their technology on what is happening in MOB. Intel is #4 or #5 in bipolar PROM market now; hopes to be #2 in 1982. Intel's limit to improved bipolar market share is the commitment of capacity. 16K PROM - Mtel's is the fastest unit (only Signetics is shipping in volume). Questions and Answers 1. Is 1979 a replay of 1974? - In 1974, there was a qualitative change in the business before it was evidenced in the numbers. Also, field salesmen began getting more conservative and demand accelerated just before dropping off. None of these events has occurred yet. 2. Will order shortfall be the same as 1974? Gelbach thinks that it will. 3. (Gordon Moore) - No real reason to think that industry will react any differently in a recession this time than in past recessions. 4. Fully expect fast 2147 prices to be cut dramatically over the next year. Intel will move its business into the 2147H (using HMOS n) and the 16K static RAM as this happens. 5. Intel will suffer some in a recession. However, in 1974-1975, Intel had 1 "golden goose," now it has 5-10. 6. Intel intends to continue capacity expansion in 1980 on the same trend of line growth as in past few years. 7. Intel has these and many other contingency plans if demand softens: More business with auto industry Build up business with customers who need more parts in 1980 - 6 -Disc market Bubble memory market 8. The codec business is growing as planned—no better. There are two parts to the market, transmission and local distribution. The CMOS design is really suited only for the local distribution segment. Intel's whole package with filter seUs for $12-13. 9. Intel is seeing more competition from Japan in Europe than in the U.S., especially in dynamic RAMs. 10. Intel is willing to make the wafer commitment to be the #1 64K dynamic RAM producer. 11. Does Gordon Moore believe that Intel will keep 70-80 percent of the 16-bit micro market? Yes. Intel feels stronger with 8086 vs. Z8000 and 68000, than with 8080 VS. 6800. 12. If the Hitachi part (2147) is producible, it should be a stroi^ competitive part. Intel is watching Hitachi's progress closely. 13. Intel is shipping the majority of its 16K RAMs to only about 20 customers. 14. Commercial Division IBM add-on memory, slowed by IBM announcements. Smaller than at beginning of year - but not much smaller. 15. Disc - could be a significant lease business. 16. A new Fab building in Santa Clara will be occupied in November with first wafer Starts then. It replaces original facility. 17. Yields getting back to where they should be; no dramatic improvement. - 7 -. . J l S "^K S B B S S ^ r ' ^ B B S ^^1 RESEARCH A Subsidiary of A.C. Nielsen Co. ' ^ INCORPORATED I ^ I ^ S W W ^ 3 ^ H ^ ^ 1 1 I C F ^ SIS Code: VoL HI - 2.10 Integrated Circuit Packaging INTEGRATED CIRCmT PACKAGING DATAQUEST's Semiconductor Industry Service has just published a comprehensive report on integrated circuit paclcaging that analyzes paclcage consumption through 1982. Subscribers to the service will find a detailed analysis in SIS Volume I, Section 2.10 dated July 30, 1979. OVERVIEW Historical forces have influenced the choice of package technology and the choice of pin configuration and spacing. The increasing requirement for packages with more than 40 pins is creating demand for more compact packages than can be achieved with the traditional DIP (dual in-line package) configuration. This has led to the QUIP (quad in-line package), developed by Intel and 3M, and to the chip carrier. Sometimes these packages are leadless; often a socket is used to facilitate interconnection at the next level. The interconnection of integrated circuit packages is required if useful electronic equipment is to be constructed. Popular mounting techniques include flow-soldered printed circuit boards, electronic watch assembly, hybrid assembly, and flip-chip assembly. PACKAGING TRENDS The key package technologies are TO header, flatpack, ceramic DIP, CERDIP, plastic DIP, and chip carriers. Demand for CERDIP and chip carriers is seen as growing faster than total package requirements. Plastic DIPs now account for 80.7 percent of integrated circuit packages, though this share is forecast to fall to 79.5 percent in 1982; plastic technology is believed to be very active and subject to significant future technological chaise. In particular, copper alloy lead frames with interdigitation and silver plating are seen as cost^-eduction measures. (Interdigitated lead frames use less metal because the leads of one package occupy the space between the leads of the next package.) In addition, it is possible that thermoplastics will be substituted for thermosetting plastics in some applications. Current 1979 prices for the 14-pin DIP configurations are about 6.3 for plastic DIPS, 9.9 for CERDIP, 82 for ceramic DIPs, and 51 for the chip carrier. These prices help explain the popularity of plastic DIPs in low cost {^plications. These prices are for 500,000 units and up, but price adders for lower quantities are provided in the notebook section. In addition, the effect of variations in gold prices on package prices is given for CERDIP and ceramic pack^es. Copyright © 1 August 1979 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generaIIy available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness It does not contain material provided to us in confidence by our clients This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO We estimate that package consumption by U.S. companies accounts for roughly 73 percent of world IC manufacture on a dollar volume basis. The figures provided in this report include packages that are consumed by U.S. companies, but because of assembly yield losses, are less than the numbers shipped as finished IC units. PACKAGE CONSUMPTION Estimates of integrated circuit pacl<age consumption in this section use U.S.-based companies as a common basis for tables . However, there are features of this market which must be taken into account when using the data. Much assembly is accomplished outside the United States, these figures of necessity include packages and package materials that are consumed overseas. Once assembly is complete, many of the finished integrated circuits are sold into foreign markets. Although consumption of the packaged integrated circuits and package materials may occur overseas, most of the purchase commitments are made in the continental United States. Finally, packages sold are necessarily less than finished semiconductor components sold because of yield losses at assembly and test. Table I gives estimated integrated circuit package consumption by U.S. companies for 1978. On a unit-count basis, most pack^e requirements are presently being met by the plastic DIP. Nevertheless, some of the other package types offer lucrative markets to suppliers of pack^es and materials because of the higher unit selling prices. Table n shows the way in which package shipments are distributed by pin count among the various packe^e technologies. It is interestir^ to note that the CERDIP and plastic DIP show a heavier concentration in the low pin counts. This is probably due to the fact that most low-cost integrated circuits have low pin counts. Because of their low cost, these circuits generally employ the low-cost CERDIP and plastic technologies. The concentration of high pin counts for the ceramic DIP reflects the use of this package in LSI applications where pin count and circuit prices tend to be higher. Table HI presents forecasted unit IC package consumption by U.S. companies for 1978 through 1982. Unit consumption is expected to show a 15.2 percent compound annual growth rate through this period. A slightly greater growth rate is anticipated for t)oth the CERDIP and chip carrier, as indicated by their increasing share of unit consumption. Howard Z. Bogert - 2 -TABLE I ESTIMATED 1978 CONSUMPTION OF IC PACKAGES BY U.S. SEMICONDUCTOR COMPANIES Pacicage Type Plastic DIP CERDIP Ceramic DIP Flatpacl< TO Header Chip Carrier Millions Of Units 4,020 710 120 60 50 20 Unit Share (Percent) 80.7% 14.2 2.4 1.3 1.0 0.4 Total 4,980 100.0% Source: DATAQUEST, fiic. July 1979 - 3 -TABLE n ESTIMATED 1978 INTEGRATED CIRCUIT PACKAGE CONSUMPTION BY U.S. COMPANIES (Percent Share of Units by Pin Count) Pin Count 8 10 12 14 16 18 20 22 24 28 36 40 Chip Carrier — --5% 24 36 --32 2 1 -100% TO Header 55% 30 15 --------,^^_ 100% Flat-pack — 20% -28 19 --9 17 -7 -100% Ceramic DIP 5% --9 11 20 -21 12 12 -10 100% Source: Plastic CERDIP DIP 3% 12% 1 -31 33 45 24 6 8 1 1 5 8 7 9 1 4 -1 2 100% 100% DATAQUEST, Inc. July 1979 - 4 -TABLE m ESTIMATED U.S. INTEGRATED CIRCUIT PACKAGE CONSUMPTION BY YEAR Plastic DIP CERDIP Ceramic DIP Flatpack TO Header Chip CaiTier 1978 80.7% 14.2 2.4 1.3 1.0 .4 1979 80.9% 14.5 2.0 1.0 .9 .7 1980 79.7% 15.5 1.9 .8 .9 1.2 1981 79.8% 15.8 1.7 .6 .7 1.4 C 1982 79.5% 16.1 1.6 .6 .6 1.6 Compound Annual Growth in Units 14.2% 18.2% 2.8% (3.5%) .9% 62.1% Total 100.0% 100.0% 100.0% 100.0% 100.0% 14.6% Units (Millions) 4,980 5,781 6,400 7,454 8,598 Source: DATAQUEST, Inc. July 1979 - 5 -•'T' • » 1^ .. ^ ^ ! RESEARCH ASubsidiarvofA.C. Nielsen CD. ^ INCORPORATED | ^ | | S W ^ S ^ B C H I 1 ^ Z P 4 SIS Code: Vol. m Newsletters GENERAL INDUSTRY UPDATE SUMMARY The following points should be noted: • The U.S. economy is clearly in a downturn, if not a recession. GNP fell 3.3 percent in the second quarter of 1979. • TJie rapid growth of semiconductor demand can be expected to ease signifi-cantly by the fourth quarter of this year. • DATAQUEST believes special factors should mitigate the affects on the semiconductor industry, however, and a demand decline comparable to 1974 is not expected. We forecast only a leveling of semiconductor consumption and demand for a limited duration. • Extreme caution is nevertheless advisable; order rates should be closely scrutinized. U.S. semiconductor consumption for 1979 is expected to be about 26 percent higher than in 1978. This increase follows strong 1978 growth for U.S. semiconductor consumption of 22.6 percent over 1977. The extremely strong growth of semicon-ductor shipments in the fourth quarter of 1978, up about 11 percent over the previous quarter, and strong growth in the second quarter of this year, up about 11 percent from the first quarter, provide most of the momentum for annual 1979 growth. • Because the true extent of the economic downturn is unlcnown, and because the effect of that downturn on the semiconductor industry is questionable, extreme caution is nevertheless advised. Order rates should be examined closely in the short term for an indication of true demand. • Currently, the economic downturn has occurred in sectors of the economy not directly related to strong semiconductor usage. Capital expenditures for business equipment have remained strong, which is beneficial for the semiconductor industry. • Factors outside the semiconductor industry's normal relationship to the economy are expected to provide semiconductor demand in the remainder of 1979 and 1980. These factors include: the effects of inflation; new marl<ets including automotive, telecommunications, industrial products, and games; a strong military and aerospace marl<et; outside purchases by General Motors, IBM and Western Electric; and the lowering of the value of the dollar. We do not expect the industry to enter a period of significant negative growth in the foreseeable future. Copyright © 3 August 1979 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or completeness, It does not contain material provided to us in confidence by our clients. This information is not furnIshed i buy securities This firm and its parent and/or their officers, stockholders, or members of their families may, from time leleased by responsible individuals in the subjer connection with a sale or offer to sell securities to time, have a long or ';hort position in the secu t companies, but is not guaranteed as to accuracy or or m connection with the solicitation of an offer to rities mentioned and may sell or buv such securities 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO • Greatly aided by the gasoline crisis, the economy is now in a downturn, contrary to the expectations of most economists. Historically, the semi-conductor industry has followed the general economy by about two quarters. This activity occurred in 1967, 1971, and 1974, and the current extremely strong demand for semiconductors is expected to ease later this year. RECENT ECONOMIC TRENDS The U.S. economy declined markedly in the second quarter of 1979 after very slow growth in the first quarter. The economy was slowed by the inclement weather in the first quarter and by gasoline and oil problems in the second quarter. Thus, the economic slowdown has come somewhat earlier than expected. Additionally, witli the secondary and tertiary effects of the oil price increases, there is increasing concern that the slowing of the economy may turn into either a major recession or a prolor^ed downturn. A moderate prolonging of the downturn appears most likely, but the effects of inflation on economic indicators make all forecasts highly questionable. There are segments of the economy that show some strength, particularly business investment. Additionally, the gross economic distortions of 1973 and early 1974 are not apparent at this time. The following recent economic developments are noteworthy: • The Gross National Product (GNP) declined about 3.3 percent in real terms in the second quarter of 1979, following a growth of 1.1 percent in the first quarter of 1979. • Most forecasts for GNP growth in 1979 are in the 2 to 3 percent range. • Retail sales in recent months have declined considerably in both current and real dollars. Lead by a decline in automobile sales due to the gasoline crisis, decreased consumer spending has been the major factor in the economic downturn. Lai^e borrowings by consumers now are apparently being paid off. • Inflation has been at record levels in recent months, about 1 percent a month for retail goods. It is currently the major economic concern. • Industrial production has remained essentially level through the second quarter of this year. • The Index of Leading Indicators has declined moderately over the last several months. This pattern indicates a current and future economic Slowdown, but not a major downturn. • Money supply spurted considerably in the second quarter of this year after declining in the first quarter, indicating that further tightening of the money supply may occur. - 2 -• Capital expenditures for business equipment remain strong. Since the recession of 1975, capital expenditures recovered slowly and still remain below historic levels relative to GNP, Because of this shortfall, capital expenditures (and related semiconductor demand) are expected to be less affected by an economic slowdown. • Economic growth in Europe wiU probably be slower than anticipated because of higher oil prices. However, in 1979 the Eiaropean economies are expected to moderately out-perform the U.S. economy for the first time in several years. Increased inflation in Europe has clouded the long-term economic outloolc. • The Japanese economy currently remains strong. The slowdown of the economy is here. The problems with energy and inflation mal<e further forecasting questionable. It is lil<ely that these problems may prolong the downturn, if not amplify its magnitude, and the economy should be closely watched over the next several months for indications on how the downturn will develop. SEIVIICONDUCTOR INDUSTRY TRENDS U.S. semiconductor demand in the second quarter of 1979 remained extremely strong. Book-to-bill ratios have recently been runnii^ in the range of about 1.2 to 1. Indications are that bookings for early July still showed strength. The extremely Strong bookings resulted from a combination of heavy demand, an increase in long-term orders, and stable and increasing prices. Semiconductor shipments and consumption in the second quarter were up Significantly over the first quarter of 1979. DATAQUEST estimates that these shipments were about 11 percent above the previous quarter. It is increasingly clear that one factor in this increase in shipments is due to pricing. For most product lines, average selling prices (ASPs) have either remained stable or increased. Significantly, ASPs for MOS integrated circuits in the second quarter of 1979 were higher than in the fourth quarter of 1978. If future demand slackens, price adjustments could hold shipments level despite increasing unit sales. However, except for a small number of individual products, we do not foresee a repeat of major price/cost discrepancies that existed in 1974. However, a continuation of price increases could pose a serious problem for the industry. The rapid expansion of production for the industry has had concomitant cost control problems. Significantly, several manufacturers have had isolated yield busts during late 1978 and early 1979. The rapid expansion of the work force by hiring employees new to the industry has weakened normal process control. It is our belief that yields have not increased throughout the industry as might be expected under normal circumstances of more regulated growth. If demand eases, this problem should work itself out gradually during the next year. Reduced costs from higher yields wiU compensate for some price erosion and, as a result, profits are expected to be somewhat less affected. - 3 -The heavy semiconductor demand has produced several industry problems: device shortages, equipment shortages, price increases (as mentioned above), lack of personnel, and some double-ordering. None of these problems are at the 1974 level with the exception of the current scarcity of trained labor and engineering talent. In many cases, availability and training of personnel has been the pacing item in increasing capacity. We believe that management, so far, has been more cautious than in 1973 and 1974. As a result, excessive double-ordering of semiconductors and inventory accumulation appears to be more moderate. It is our perception that a strong demand for semiconductors is based on very real needs and usage, and is not an illusion created by an overheated economy. Significantly, inventory levels appear moderate. New applications, new companies using semiconductors, and the use of more semiconductors in old applications are major factors in the current strong semiconductor demand. This is a more positive situation than the industry has had entering past economic slowdowns. It is clear that the industry has been operating at capacity or in excess of comfortable capacity. The ability to increase capacity has been made more difficult by the increasing complexity of semiconductor manufacturing. IVIore complex facilities and equipment require longer lead times. More extensive planning is required for today's high-eost facilities. Furthermore, switching from small chips to larger, more complex devices, requires an increase in wafer fab capacity even though dollar shipments remain leveL Larger chips are more wafer-fab intensive. As a result, despite the rapid increase in capital expenditures of the industry in recent years, we estimate that the new facilities coming on stream are barely adequate for reasonable industry expansion. An over-capacity situation is not expected. SEMICONDUCTOR INDUSTRY FORECAST Table 1 gives our estimates for U.S. semiconductor consumption in doUars. We believe that in 1978, semiconductor consumption increased about 22.6 percent over 1977. For 1979, we expect semiconductor consumption to increase by about 26 percent over 1978. This increase from our previous forecast reflects the very strong performance by the industry in the second quarter of this year. Furthermore, the industry entered 1979 at a running rate significantly above the average for 1978. While integrated circuits account for the majority of the increase in semiconductor consumption, with an annual increase of an estimated 30.1 percent over 1978, the growth of discrete devices should also be significant, with an estimated growth of 16.9 percent. Our current estimates for 1979 U.S. semiconductor consumption by calendar quarter are shown in Table 2. We expect significantly slower growth in the second half of 1979 and the first half of 1980. It should be noted that the first and third quarters are seasonally lower in consumption than the second and fourth quarters. Reflecting the economy, semiconductor shipments in the fourth quarter of this year and the first quarter of 1980 should remain essentially level, with a resumption of growth, and increasing strength, beginning in the second quarter of 1980, We expect shipments for all of 1980 to be about 8 percent above shipments for 1979. - 4 -In forecasting for 1979, we have consistently noted that factors that do not have historical precedent or relate directly to the economy could have a major positive effect on semiconductor demand. Thus far, our reasoning has proved correct, and these factors have combined to make 1979 an exceptional year for the industry. It is increasii^ly apparent that the cumulative effects of inflation have made semicon-ductors, and products using semiconductors, the best buys in town and that circum-stance has spurred markets relating to the industry. We expect the following to continue to be positive elements of semiconductor demand in 1980 and beyond: • The cumulative effects of inflation • Major new markets—automotive, telecommunications, industrial products, and Others • The military, government, and aerospace markets • Outside purchases by the captive semiconductor manufacturers, especially General Motors, IBM, and Western Electric • Increased competitiveness because of the devalued dollar These factors are helping maintain semiconductor demand in the face of a weakening economy. The advent of VLSI continues to make semiconductors cost effective in new applications. Semiconductor design in manufacturing is an increas-ingly scarce resource. Although a leveling of demand is expected in the short term, the secular trend appears extremely positive. Frederick L. Zieber Lane Mason Ralph R. Shaddock - 5 -Table 1 ESTIMATED U.S. SEMICONDUCTOR CONSUMPTION (Dollars in Millions) Discrete Devices Integrated Circuits Total 1977 $ 926 1,784 $2,710 1978 $1,019 2,304 $3,323 Percent Increase 1977-78 10.0% 29.1% 22.6% 1979 $1,191 2,998 $4,189 Percent bicrease 1978-79 16.9% 30.1% 26.1% Source: DATAQUEST, Inc. August 1979 Table 2 ESTIMATED QUARTERLY U.S. SEMICONDUCTOR CONSUMPTION (Dollars in Millions) 1978 Discrete Devices Integrated Circuits Total Change From Previous Quarter or Year Discrete Devices Integrated Circuits Total Percent Change From Previous Quarter Percent Change From Previous Year Discrete Devices Integrated Circuits Total Percent Change From Previous Quarter 1st Qtr. $ 233 502 $ 735 0.4% 1st Qtr. $ 279 678 $ 957 3.0% 30.2% 1st Qtr. $ 292 777 $1,069 (2.2%) 2nd Qtr. $ 255 567 $ 822 11.8% 2nd Qtr. $ 309 755 $1,064 11.2% 29.4% 2nd Qtr. $ 294 797 $1,091 2.1% 3rd 2t£i $ 256 581 $ 837 1.8% 1979 3rd Qtr. $ 304 771 $1,075 1.0% 28.4% 1980 4th Str. $ 275 654 $ 929 11.0% 4th Qtr. $ 299 794 $1,093 1.7% 17.7% Total Year $1,019 2,304 $3,323 22.6% Total Year $1,191 2,998 $4,189 26.1% Source: DATAQUEST, Inc. August 1979 - 7 -r r^ k%.i RESEARCH ^ " " '" '' NEWSLETTER SIS Code: VoL m Newsletters GENERAL INDUSTRY UPDATE SUMMARY TTie following points should be noted: • The U.S. economy is clearly in a downturn, if not a recession. ON? fell 3.3 percent in the second quarter of 1979. • The rapid growth of semiconductor demand can be expected to ease signifi-cantly by the fourth quarter of this year. • DATAQUEST believes special factors should mitigate the affects on the semiconductor industry, however, and a demand decline comparable to 1974 is not expected. We forecast only a leveling of semiconductor consumption and demand for a limited duration. • Extreme caution is nevertheless advisable; order rates should be closely scrutinized. U.S. semiconductor consumption for 1979 is expected to be about 26 percent higher than in 1978. This increase follows strong 1978 growth for U.S. semiconductor consumption of 22.6 percent over 1977. The extremely strong growth of semicon-ductor shipments in the fourth quarter of 1978, up about 11 percent over the previous quarter, and strong growth in the second quarter of this year, up about 11 percent from the first quarter, provide most of the momentum for annual 1979 growth. • Because the true extent of the economic downturn is unJ<nown, and because the effect of that downturn on the semiconductor industry is questionable, extreme caution is nevertheless advised. Order rates should be examined closely in the short term for an indication of true demand. • Currently, the economic downturn has occurred in sectors of the economy not directly related to strong semiconductor u s ^ e . Capital expenditures for business equipment have remained strong, which is beneficial for the semiconductor industry. • Factors outside the semiconductor industry's normal relationship to the economy are expected to provide semiconductor demand in the remainder of 1979 and 1980. These factors include: the effects of inflation; new marJcets including automotive, telecommunications, industrial products, and games; a strong military and aerospace marl<et; outside purchases by General Motors, IBM and Western Electric; and the lowerirtg of the value of the dollar. We do not expect the industry to enter a period of significant negative growth in the foreseeable future. Copyright © 3 August 1979 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsiblG individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by nur clients. This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short posi'tion in the securities mentioned and may sell or buy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO • Greatly aided by the gasoline crisis, the economy is now in a downturn, contrary to the expectations of most economists. Historically, the semi-conductor industry has followed the general economy by about two quarters. ITiis activity occurred in 1967, 1971, and 1974, and the current extremely strong demand for semiconductors is expected to ease later this year. RECENT ECONOMIC TRENDS The U.S. economy declined markedly in the second quarter of 1979 after very slow growth in the first quarter. The economy was slowed by the inclement weather in the first quarter and by gasoline and oil problems in the second quarter. Thus, the economic slowdown has come somewhat earlier than expected. Additionally, with the secondary and tertiary effects of the oil price increases, there is increasing concern that the slowing of the economy may turn into either a major recession or a prolor^ed downturn. A moderate prolonging of the downturn appears most likely, but the effects of inflation on economic indicators make all forecasts highly questionable. There are segments of the economy that show some strength, particularly business investment. Additionally, the gross economic distortions of 1973 and early 1974 are not apparent at this time. The following recent economic developments are noteworthy: • The Gross National Product (GNP) declined about 3.3 percent in real terms in the second quarter of 1979, following a growth of 1.1 percent in the first quarter of 1979. • Most forecasts for GNP growth in 1979 are in the 2 to 3 percent range. • Retail sales in recent months have declined considerably in both current and real dollars. Lead by a decline in automobile sales due to the gasoline crisis, decreased consumer spending has been the major factor in the economic downturn. Large borrowings by consumers now are apparently being paid off. • Inflation has been at record levels in recent months, about 1 percent a month for retail goods. It is currently the major economic concern. • Industrial production has remained essentially level through the second quarter of this year. • The Index of Leading Indicators has declined moderately over the last several months. This pattern indicates a current and future economic slowdown, but not a major downturn. • Money supply spurted considerably in the second quarter of this year after declining in the first quarter, indicating that further tightening of the money supply may occur. - 2 -• Capital expenditures for business equipment remain strong. Since the recession of 1975, capital expenditures recovered slowly and stiU remain below historic levels relative to GNP. Because of this shortfall, capital expenditures (and related semiconductor demand) are expected to be less affected by an economic slowdown. • Economic growth in Europe will probably be slower than anticipated because of h^her oil prices. However, in 1979 the European economies are expected to moderately outperform the U.S. economy for the first time in several years. Increased inflation in Europe has clouded the long-term economic outloolc. • The Japanese economy currently remains strong. The slowdown of the economy is here. The problems with energy and inflation mal<e further forecasting questionable. It is lilcely that these problems may prolong the downturn, if not amplify its magnitude, and the economy should be closely watched over the next several months for indications on how the downturn will develop. SEIMICONDDCTOR INDUSTRY TRENDS U.S. semiconductor demand in the second quarter of 1979 remained extremely Strong. Bool<-to-biU ratios have recently been running in the range of about 1.2 to 1. Indications are that bookings for early July stiU showed strength. The extremely Strong boolcings resulted from a combination of heavy demand, an increase in long-term orders, and stable and increasing prices. Semiconductor shipments and consumption in the second quarter were up significantly over the first quarter of 1979. DATAQUEST estimates that these shipments were about 11 percent above the previous quarter. It is increasingly clear that one factor in this increase in shipments is due to pricing. For most product lines, average selling prices (ASPs) have either remained stable or increased. Significantly, ASPs for MOS integrated circuits in the second quarter of 1979 were higher than in the fourth quarter of 1978. If future demand slaclcens, price adjustments could hold Shipments level despite increasing unit sales. However, except for a small number of individual products, we do not foresee a repeat of major price/cost discrepancies that existed in 1974. However, a continuation of price increases could pose a serious problem for the industry. The rapid expansion of production for the industry has had concomitant cost control problems. Significantly, several manufacturers have had isolated yield busts during late 1978 and early 1979. The rapid expansion of the work force by hiring employees new to the industry has weakened normal process controL It is our belief that yields have not increased throughout the industry as might be expected under normal circumstances of more regulated growth. If demand eases, this problem should work itself out gradually during the next year. Reduced costs from higher yields will compensate for some price erosion and, as a result, profits are expected to be somewhat less affected. - 3 -The heavy semiconductor demand has produced several industry problems: device shortages, equipment shortages, price increases (as mentioned above), lack of personnel, and some double-ordering. JJone of these problems are at the 1974 level with the exception of the current scarcity of trained labor and engineering talent. In many cases, availability and training of personnel has been the pacing item in increasing capacity. We believe that management, so far, has been more cautious than in 1973 and 1974. As a result, excessive double-ordering of semiconductors and inventory accumulation appears to be more moderate. It is our perception that a strong demand for semiconductors is based on very real needs and usage, and is not an illusion created by an overheated economy. Significantly, inventory levels appear moderate. New applications, new companies using semiconductors, and the use of more semiconductors in old applications are major factors in the current strong semiconductor demand. This is a more positive situation than the industry has had entering past economic slowdowns. It is clear that the industry has been operating at capacity or in excess of comfortable capacity. The ability to increase capacity has been made more difficult by the increasing complexity of semiconductor manufacturing. More complex facilities and equipment require longer lead times. More extensive plannir^ is required for today's high-cost facilities. Furthermore, switching from small chips to larger, more complex devices, requires an increase in wafer fab capacity even though dollar shipments remain leveL Larger chips are more wafer-fab intensive. As a result, despite the rapid increase in capital expenditures of the industry in recent years, we estimate that the new facilities coming on stream are barely adequate for reasonable industry expansion. An over-capacity situation is not expected. SEMICONDUCTOR INDUSTRY FORECAST Table 1 gives our estimates for U.S. semiconductor consumption in doUars. We believe that in 1978, semiconductor consumption increased about 22.6 percent over 1977. For 1979, we expect semiconductor consumption to increase by about 26 percent over 1978. This increase from our previous forecast reflects the very strong performance by the industry in the second quarter of this year. Furthermore, the industry entered 1979 at a running rate significantly above the average for 1978. While integrated circuits account for the majority of the increase in semiconductor consumption, with an annual increase of an estimated 30.1 percent over 1978, the growth of discrete devices should also be significant, with an estimated growth of 16.9 percent. Our current estimates for 1979 U.S. semiconductor consumption by calendar quarter are shown in Table 2. We expect significantly slower growth in the second half of 1979 and the first half of 1980. It should be noted that the first and third quarters are seasonally lower in consumption than the second and fourth quarters. Reflecting the economy, semiconductor shipments in the fourth quarter of this year and the first quarter of 1980 should remain essentially level, with a resumption of growth, and increasing strength, beginning in the second quarter of 1980, We expect shipments for all of 1980 to be about 8 percent above shipments for 1979. - 4 -In forecasting for 1979, we have consistently noted that factors that do not have historical precedent or relate directly to the economy could have a major positive effect on semiconductor demand. Thus far, our reasoning has proved correct, and these factors have combined to make 1979 an exceptional year for the industry. It is increasingly apparent that the cumulative effects of inflation have made semicon-ductors, and products using semiconductors, the best buys in town and that circum-stance has spurred markets relating to the industry. We expect the following to continue to be positive elements of semiconductor demand in 1980 and beyond: The cumulative effects of inflation Major new markets—automotive, telecommunications, industrial products, and others The military, government, and aerospace markets Outside purchases by the captive semiconductor manufacturers, especially General Motors, IBM, and Western Electric Increased competitiveness because of the devalued dollar These factors are helping maintain semiconductor demand in the face of a weakening economy. The advent of VLSI continues to make semiconductors cost effective in new ^plications. Semiconductor design in manufacturir^ is an increas-ingly scarce resource. Although a leveling of demand is expected in the short term, the secular trend appears extremely positive. Frederick L. Zieber Lane Mason Ralph R. Shaddock - 5 -Table 1 ESTIMATED U.S. SEMICONDUCTOR CONSUMPTION (Dollars in Millions) Discrete Devices Integrated Circuits Total 1977 $ 926 1,784 $2,710 1978 $1,019 2,304 $3,323 Percent Increase 1977-78 10.0% 29.1% 22.6% 1979 $1,191 2,998 $4,189 Percent Increase 1978-79 16.9% 30,1% 26.1% Source: DATAQUEST, Inc, August 1979 Table 2 ESTIMATED QUARTERLY U.S. SEMICONDUCTOR CONSUMPTION (Dollars in Millions) 1978 Total Year Discrete Devices Integrated Circuits Total Change From Previous Quarter or Year 1st Qtr. ( 233 502 2nd Qtr. ( 253 567 3rd Qtr. i 256 581 $ 735 $ 822 $ 837 0.4% 11.8% 1.8% 4th Qtr. $ 275 654 $ 929 11.0% $1,019 2,304 $3,323 22.6% 1979 • Discrete Devices Integrated Circuits Total Percent Change From Previous Quarter Percent Change From Previous Year Discrete Devices Integrated Circuits Total Percent Change From Previous Quarter 1st Qtr. $ 279 678 $ 957 3.0% 30.2% 1st Qtr. $ 292 777 $1,069 (2.2%) 2nd Qtr. $ 309 755 $1,064 11.2% 29.4% 2nd Qtr. $ 294 797 $1,091 2.1% 3rd Qtr-$ 304 771 $1,075 1.0% 28.4% 1980 4th Qtr. $ 299 794 $1,093 1.7% 17.7% Total Year $1,191 2,998 $4,189 26.1% Source: DATAQUEST, Inc. August 1979 - 7 -SIS Code: VoL HI - 2.10 Integrated Circuit PacJcaging INTEGRATED CIRCUIT PACKAGING DATAQUEST's Semiconductor Industry Service has just published a comprehensive report on integrated circuit pacJcaging that analyzes package consumption through 1982. Subscribers to the service will find a detailed analysis in SIS Volume I, Section 2.10 dated July 30, 1979. OVERVIEW Historical forces have influenced the choice of package technology and the choice of pin configuration and spacing. The increasir^ requirement for pack^es with more than 40 pins is creating demand for more compact packages than can be achieved with the traditional DIP (dual in-line package) configuration. This has led to tlie QUIP (quad in-line package), developed by Intel and 3M, and to the cliip carrier. Sometimes these packages are leadless; often a socket is used to facilitate interconnection at the nextleveL The interconnection of integrated circuit packages is required if useful electronic equipment is to be constructed. Popular moimting techniques include flow-soldered printed circuit boards, electronic watcli assembly, hybrid assembly, and flip-chip assembly. PACKAGING TRENDS Tlie key package technologies are TO header, flatpack, ceramic DIP, CERDIP, plastic DIP, and chip carriers. Demand for CERDIP and chip carriers is seen as growing faster than total package requirements. Plastic DlPs now account for 80.7 percent of integrated circuit packages, though this share is forecast to fall to 79.5 percent in 1982; plastic technology is believed to be very active and subject to significant future technological change. In particular, copper alloy lead frames with interdigitation and silver plating are seen as cost-reduction measures. (Interdigitated lead frames use less metal because the leads of one package occupy the space between the leads of the next package.) In addition, it is possible that thermoplastics will be substituted for thermosetting plastics in some applications. Current 1979 prices for the 14-pin DIP configurations are about 6.3<t for plastic DIPS, 9.9 for CERDIP, 82<t: for ceramic DIPs, and 51 for the chip carrier. These prices help explain the popularity of plastic DIPs in low cost applications. These prices are for 500,000 units and up, but price adders for lower quantities are provided in the notebook section. In addition, the effect of variations in gold prices on package prices is given for CERDIP and ceramic packages. Copyright © 1 August 1979 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation amd analysis of information generally available to the public or released by responsible individuals in the subiecl companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities, This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO We estimate that package consumption by U.S. companies accounts for rouglily 73 percent of world IC manufacture on a dollar volume basis. The figures provided in this report include packages that are consumed by U.S. companies, but because of assembly yield losses, are less than the numbers shipped as finished IC units. PACKAGE CONSDMPTION Estimates of integrated circuit package consumption in this section use U.S.-based companies as a common basis for tables . However, there are features of this market which must be taken into account when using the data. IVluch assembly is accomplished outside the United States, these figures of necessity include packages and package materials that are consumed overseas. Once assembly is complete, many of the finished integrated circuits are sold into foreign markets. Although consumption of the packaged integrated circuits and package materials may occur overseas, most of the purchase commitments are made in the continental United States. Finally, packages sold are necessarily less than finished semiconductor components sold because of yield losses at assembly and test. Table I gives estimated integrated circuit package consumption by U.S. companies for 1978. On a unit-count basis, most package requirements are presently being met by the plastic DIP. Nevertheless, some of the other package types offer lucrative markets to suppliers of packages and materials because of the higher unit selling prices. Table n shows the way in which package shipments are distributed by pin count amoi^ the various package technologies. It is interesting to note that the CERDIP and plastic DIP show a heavier concentration in the low pin counts. This is probably due to the fact that most low-cost integrated circuits have low pin counts. Because of their low cost, these circuits generally employ the low-cost CERDIP and plastic technologies. The concentration of high pin counts for the ceramic DIP reflects the use of this package in LSI applications where pin count and circuit prices tend to be h^her. Table ni presents forecasted imit IC package consumption by U.S. companies for 1978 through 1982. Unit consumption is expected to show a 15.2 percent compound annual growth rate through this period. A slightly greater growth rate is anticipated for both the CERDIP and chip carrier, as indicated by their increasing share of unit consumption. Howard Z. Bogert - 2 -TABLE I ESTIMATED 1978 CONSUMPTION OF IC PACKAGES BY U.S. SEMICONDUCTOR COMPANIES Pacicage Type Plastic DIP CERDIP Ceramic DIP Flatpack TO Header Chip Carrier Millions of Units 4,020 710 120 60 50 20 Unit Share (PeEcent) 80.7% 14.2 2.4 1.3 1.0 0.4 Total 4,980 100.0% Source: DATAQUEST, fee July 1979 - 3 -TABLE n ESTIMATED 1978 INTEGRATED CIRCUIT PACKAGE CONSUMPTION BY U.S. COMPANIES (Percent Share of Units by Pin Count) Pin Count 8 10 12 14 16 18 20 22 24 28 36 40 Chip Carrier — --5% 24 36 --32 2 1 -100% TO Header 55% 30 15 ---------100% Flat-paclc — 20% -28 19 --9 17 -7 -100% Ceramic DIP 5% --9 11 20 -21 12 12 -10 100% Source; Plastic CERDIP DIP 3% 12% 1 -31 33 45 24 6 8 1 1 5 8 7 9 1 4 -1 -100% 100% DATAQUEST, Inc. July 1979 - 4 -Plastic DIP CERDIP Ceramic DIP Flatpack TO Header Chip Carrier Total TABLE m ESTIMATED U.S. INTEGRATED CIRCUIT PACKAGE CONSUMPTION BY YEAR 1978 80.7% 14.2 2.4 1.3 1.0 .4 1979 80.9% 14.5 2.0 1.0 .9 .7 1980 79.7% 15.5 1.9 .8 .9 1.2 1981 79.8% 15.8 1.7 .6 .7 1.4 1982 Compound Annual Growth in Units 79.5% 14.2% 16.1 1.6 .6 .6 1.6 18.2% 2.8% (3.5%) .9% 62.1% 100.0% 100.0% 100.0% 100.0% 100.0% 14.6% ' ^ Units (Millions) 4,980 5,781 6,400 7,454 8,598 Source: DATAQUEST, Inc. July 1979 - 5 -- . ry ^^^ i ^#^1 M\W MW i =—— — i J I SI— i\ ^^^^^^ ^ ^ ^ ^ ^ A SubsiiJiary of A.C. Nielsen Co. ' ^ INCORPORATED | ^ | ^ £ W W ^ 3 L ^ S I 1 ^ Z ^ ^ SIS Code: 8.08 National Semiconductor Corporation UPDATE ON NATIONAL SEMICONDUCTOR SUMMARY National Semiconductor Corporation (NSC) should continue to grow rapidly in fiscal 1980 (ending May 31), with sales increasing 28 percent to about $920 million and earnings growing 28 percent to $3.30 per share. The performance of the Semiconductor Division is expected to more than compensate for revenue and earnings declines in the Computer Systems Group, which has been hurt by the introduction of IBM's 4300 series. We perceive that the Company is currently reaping the rewards of a major commitment to improving its technological and manufacturing base in semiconductors. Important Company developments include: • The Company has tempered its computer thrust, and we believe' potential risks are limited. • National is presently in production with its first XMOS product (reduced minimum dimensions), the 2147 fast 4K static RAM. If successful, it will be the second company in the industry in production in this extremely profitable high-density sector. • Other major areas of technical effort include 16-bit and CMOS microprocessors, bipolar LSI, ECL, magnetic bubbles, and linear ICs. • National participated significantly in the General Motors business recently released. Depending upon performance, it could be' a major participant in this business. , • NSC has significantly upgraded its image with customers, and now ranks high in terms of meeting allocations, reliability, and delivery consistency. • We believe a substantial debt agreement in the current quarter will ease financial constraints. CORPORATE National's sales are expected to grow about 28 percent in fiscal 1980 to $920 million. An estimated breakout of revenues and earnings by major division is shown in Table 1. • . , Copyright © 20 July 1979 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generallv avaiIable to the public or released by responsible inidividuals in the subject companies, but is not guaranteed as to accuracy or compleieness It does not contain material provided to us in confidence by our clients This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to ^ u y securities This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO Due to its rapid growth and moderate margins, National has always been under-financed. Currently, the Company has more growth opportunities than it can finance internally. We believe the Company will take on a substantial debt agreement with a major insurance company this year; it does not currently plan to finance growth through the sale of equity or through further joint arrangements with foreign firms. We believe that the addition of Pierre Lamond to the Office of General IVlanager of the Semiconductor Division has had a major effect on National's organization and has been a catalyst in improving the Company's technological base. Margin Analysis We expect the contribution from the Computer Systems Group to decline from about $0.60 per share in fiscal 1979 to about $0.10 per share in fiscal 1980. Strong revenue growth and good margin expansion in semiconductors should more than offset this decline. Much of this expansion was already evident in fourth quarter operating rates. Paralleling the expected revenue increase, Company earnings are also expected to grow about 28 percent in fiscal 1980 to $3.30 per share. In fiscal 1980, DATAQUEST estimates that semiconductors should account for 90 percent of operating profits at National Semiconductor. If this situation occurs, concerns about its other businesses would properly diminish. SEMICONDUCTOR GROUP National has always been considered one of the top production houses in the semiconductor industry. Successful implementation of its development efforts in semiconductors would enhance its technological position as well and thereby greatly improve its potential margins in its basic business. National has made a substantial investment in component manufacturing and technology over the past two years and these efforts are starting to bear fruit. The most significant technical development may well be a 70-nanosecond 4K static RAM— NSC's first product with reduced dimensions. DATAQUEST believes this product is now entering a production mode, as discussed more fully in the section on memory. In the past two years, the Company has had a major program to upgrade manufacturing and reliability. This program has apparently been quite successful. In surveying major semiconductor users, we found that NSC ranked high in its ability to deliver product during the current shortage situation. This image has not always existed in the past, and it has important positive implications for future customer relations. The improved delivery ability is also indicative of increased control over production. NSC has been singularly successful in the past year in increasing integrated circuit production. Increased output in wafer fabrication has been provided primarily from Scotland and Utah. Increased efficiency and automation in overseas assembly has resulted in about a 40 percent increase in units produced with virtually no increase in overhead. The current attention to manufacturing costs supports our optimism for increased margins. - 2 -Table 1 National Semiconductor Corporation SALES AND EAHNINGS FORECASTS ^ (Dollars in Millions) I M I Semiconductors Computer Systems PCS Consumer Total General Coporate Expenses Interest Expense Pretax Income Tax Rate Net bicome Average Shares Outstanding (MiniarH) Earnings Per Share Sales $327 75 44 4B $494 1978 Operating Profits 935.9 9.0 2.0 0 $46.9 $ 4.3 t 1.9 $40.6 44.6% $23.5 13.1 $ 1.73 Operatii% Margins 10% 12 4 0 9.5% »,m i.«% Sales $497 125 53 45 $720^ ' 1979 (Estimate) Operating Profits $51.0 16.0 2.5 1.5 $73.0 $ 5.0 1 5.7 $62.3^ 4S.0% $34.3' 13.2^ $ 2.57^ Operating Margins 10% 14 5 4 10.2% 8.7% 4.8% Sales $730 75 70 _ 4 5 $920 1980 (Estimate) Operating Profits $87.5 4.0 4.0 1.5 $97.0 $ 6.0 $ 9.0 $82.0 46.0% $44.0 13.3 $ 3.30 Operating Margins 12.0% 6.0 6.0 4.0 10.5% 8.9% 4.8% ^Fiscal year ending May 31 The group sales Tigures for fiscal 1978 do not agree with those in our January 24,1979, newsletter on National Semiconductor. In prior newsletters we reported revenues based on the actual organization of groups at National, white in the above table we are conforming to numbers published by the Company in Its Annual Report. Actual Source: DATAQUEST, Inc. July 1979 DATAQUEST estimates a 48 percent gain in semiconductor shipments in fiscal 1979 over 1978 to $540 million (before intracompany eliminations), and we are forecasting a 43 percent gain in revenues to $770 million in fiscal 1980. This is more than our forecast of semiconductor industry growth over this period and reflects several factors. • National is starting fiscal 1980 with a much higher level of shipment capacity than a year ago. The Greenock, Scotland, fire cost National $40-50 million in lost revenues in fiscal 1979. Since it is using 4-inch wafers, the current potential dollar volume of the plant is higher than before the fire. • The Utah wafer fabrication facility can significantly expand capacity. • Because of rapid revenue growth in fiscal 1979, the Company is entering fiscal 1980 with operating rates significantly above 1979 levels. DATAQUEST estimates that National's semiconductor shipments in the fourth quarter of fiscal 1979 were at a $670 armual rate (after elim-inations). Our semiconductor forecast for fiscal 1980 therefore implies 10 percent average growth from present shipment levels. • New product introduction activities, in our opinion, justify an optimistic revenue forecast. Semiconductor margins should definitely trend higher in fiscal 1980, aided by good profit levels from Greenock and higher price realization from market strength and new products. Table 2 shows estimated Semiconductor Group revenues by major product type. A discussion of each sector of the group follows, with higlUights of new product development efforts. IVIemory This product area has been a source of intense concentration for National during the past few years, and the results of the Company's efforts are starting to become evident. DATAQUEST believes that National is now commencing volume production of its first product to use XIVIOS (3-3 i micron line geometry), a 70-nanosecond 2147 Static RAM. Shipments of the 2147-3 (55 nanoseconds) are expected by DATAQUEST in September. If the 2147 effort is successful. National would be the second company in the industry (after Intel) to put the 3-micron technology into production. It would open up lucrative markets to the Company, particularly if pricing on more standard memory products weakens in the coming year. For example. National is believed to have a single power supply 16K dynamic RAM in design that uses this process. Other new products of note include: • A target date of January 1980, for samples of a 64K dynamic RAM. This part will use a triple poly 3i micron line width process and is expected to produce a very small die. • A 4Kx8 quasi-Static RAM, similar to the Zilog part, should be available in October 1979. - 4 -Table 2 National Semiconductor Corporation ESTIIVIATED REVENUES OF THE SEiVIICONDUCTOR GROUP-1978-1980 Semiconductor Group: Memory M icroprocessors MOS LSI Total MOS Bipolar Digital Linear Hybrid Discrete 2 Special Products: Optoelectronics Modules Watch Modules Dynacraft Total Less: Intracompany Eliminations Net (Dollars in Millions) Fiscal . Year 1978^ $ 40 10 40 $ 90 $ 85 $ 87 $ 15 $ 27 $ 15 10 20 15 $364 (37) $327 Fiscal Year 1979 $ 80 20 45 $145 $120 $120 $ 30 $ 35 $ 20 20 30 20 $540 (43) $497 Fiscal Year 1980 $150 30 50 $230 $180 $170 $ 35 $ 35 $ 25 30 40 25 $770 (40) $730 -Fiscal year ending May 31 Includes Dynacraft - a change from previous format Source: DATAQUEST, Inc. July 1979 - 5 -• A 16K EPROM is currently being sampled. DATAQUEST expects National to be in production by the second quarter of fiscal 1980. • A 32K EPROlVr should be sampled in December 1979. • 2141 and 2142 4K statics are currently being sampled. Like Other suppliers. National is wafer fabrication limited. It is expected to divert wafer starts away from the lower priced commodity memories to newer parts, such as those listed above, which have higher selling prices. Microprocessors Progress in microprocessors has lagged behind other areas and National is now investii^ heavily to catch up. DATAQUEST estimates that the Company has about 50 professionals working on its 16-bit microprocessor project; the part will be called the NS-16000. We believe that this microprocessor will be able to utilize existing 8080 family software. In the meantime. National, which has supported the Intel 8080 family vigorously with a wide range of peripherals, wiU be adding products to its 8-bit line: an 8049 single-chip microcomputer (using XMOS processing) to be sampled in July; and an 8050 8-bit microcomputer to be sampled in August. In the fourth quarter. National is expected to sample a CMOS version of the 8048 microcomputer, which employs a liigh density process called P CIVIOS, presumably employing double-layered polysilicon. A CMOS version of the Z80, but with 5 percent of the power, is also expected within six months, including peripheral devices. Clearly, National is making a major commitment to CMOS LSI, a market currently in the formative stages. Shipments of IMP and PACE processors are believed to have leveled, while semiconductor microprocessor shipments continue to ramp. Demand for the COPS products are high, with backlogs exceeding six months. Linear National is currently the industry leader in the linear market. This market has paralleled the MOS market in growth in recent years. DATAQUEST expects NSC's Strong position to become even stronger in the future. Its current Bi-FET and linear CMOS products give the Company a strong product position, especially in the rapidly expanding data acquisition market. Its new analog-to-digital converters (A/Ds) are proving popular. Substantial product introductions are being made in this traditional area of National strength: • Adjustable 3 amp and 5 amp voltage regulators. The advantage here is that several products can take the place of 20 to 25 products specified at particular voltages. • A 10-bit digital-to-analog converter (DAC) is being shipped. • An 8-bit A/D microprocessor-compatible converter is currently going into production. - 6 -• The LM-10—the new Widlar amplifier—operating from 1.5 to 20 volts power supply, is receiving good acceptance in the marketplace. Bipolar Digital Revenues in this product area are expanding rapidly due to the coincidence of product Shortage in the market and rapidly expanding capacity at National. The Company has a full line (4-inch) devoted to LS TTL in Greenock, Scotland, and we understand that it is ramping its shipments at the rate of 10 percent per month. Significantly, the market leader—Texas Instruments—has recently raised prices for LSTTL. Product development has been at a high level, with effort increasingly being focused on large chips. Additionally, NSC has been mapping its entry into the ECL market. Significant new product developments are: • In a major new market entry, the Fairchild FIOOK will be second-sourced with a product offerii^ of 10 to 15 parts. • ECL—a 256x1 ECL RAM is now available. A IKxl R A I V I is currently being sampled. DATAQUEST anticipates a 4K RAIVI within six months. • 8K bipolar PROlVIs are now in production; DATAQUEST anticipates a 16K PROM by the end of the year. National is participating in the General Motors' PROM business wliich could be a large incremental piece of business for National in fiscal 1980. • DATAQUEST anticipates National introducing product in the bipolar RAM area in this next fiscal year. • Five new 2900 series parts are e3q)ected to be introduced this year. Other SemiconduetOT Products Other Semiconductor Group products at National cover a rather large business base. These include: Hybrids: National is building laser-trimmed active filters, sample and hold circuits, and fast-rise time amplifiers. Modules: Modules include LCD travel alarms, toys and games products, appliance controllers, trip computers, other automotive products, and transducers. Optoelectronics: The focus in optoelectronics is on higher efficiency lamps and digits, and intelligent displays (pioneered by Litronix). We are observing applications where combining optoelectronics and linear technology is producing displays such as bar graphs, etc Bubbles: A year ago. National launched a major effort into this area. Currently, the group has 20 plus professionals and support staff. The 256K-bit memory is expected to be sampled and go into board products as the year moves along. We expect to see sales in the fourth calendar quarter. We are looking for National to introduce a 1-megabit bubble memory in mid-1980 with appropriate support circuitry. - 7 -Dynacraft: This division has three major areas of business; gold-plated lead frames, epoxy powders, and wafer fabrication chemicals. The lead frame business is the largest segment of this group and has an estimated annual revenues of about $12-13 million. We believe that about 40 percent is absorbed internally into National. Telecommunications: A one-chip filter is announced for September, to be followed by a codec in December. COBIPUTER PRODUCTS GROUP DATAQUEST revenue projections for the Computer Products Group are shown in Table 3. The well-published difficulties relating to shipments of IBM plug-compatible computers mal {$ jjilllgna) ' 4_Bit e-Bit_ 16-Bit:; 16-Bit^ 32-Bit Total Hlcroprocessors + Pejflg^gid# and 1/0 ($ HiliiptwH 4-Bit 8-Bit-16-Bit, 16-Bit^ 32-Bit Total -N/A B Product not available ,Older products with direct addressing capability less than 128K bytes Newer products with direct addressing capability up to 8M bytes 0.4 4.0 0.2 N/A N/A 4 .
6 $ 4.00 $ 8.00 $40.00 $ $ $ : 0.4 7.6 0.39 0.01 N/A 8.4 3.00 6.00 J2.00 N/A $150.00 N/A $ 2 32 8 0 0 $ 42 $ 4 77 12 0 0 $ 93 $ 6 109 20 0 0 $ 135 $ $ $ $ $ $ N/A 1 46 12 2 0 61 2 110 18 3 0 1 3 3 3 156 30 5 0 194 0.3 13.5 0.75 0.07 N/A 14.62 $ 2.50 $ 4.75 $ 24.00 $105.00 N/A $ 1 64 18 7 0 $ 90 $ 2 154 27 18 0 $ 201 $ 3 218 45 25 0 $ 591 ] ' $ $ 0.2 L9.0 1.4 0.6 N/A il.J 2.10 3.90 $17.00 $70.00 $ T $ r $ T N/A 0 74 24 42 0 140 o 185 41 76 0 302 0 259 65 118 0 442 $ $ $ $ 0.15 25.0 3.2 1.8 0.01 30.16 1.85 3.30 12.00 45.00 $240.00 $ T $ r $ r 0 83 38 81 2 204 0 216 68 162 4 450 0 299 106 243 6 654 $ $ $ $ 0.10 31.0 5.0 3.6 0.1 39.8 1.65 2.90 8.00 32.00 $180.00 $ r $ r $ T " 0 90 40 115 18 263 0 243 80 242 40 C O S 0 333 120 357 58 668 $ $ $ N/A^ 35.0 7.0 7.5 0.3 49.8 N/A 2.65 6.00 21.00 $125.00 $ r $ T $ r 0 93 42 158 38 331 0 260 97 348 84 789 0 353 139 506 122 1,120 Source: DATAQUEST, Inc. June 1979 Table 3 ESTIMATED SINGLE-CHIP MICROCOMPUTER CONSUMPTION I as I Hlcrocoinputgrs (MllllonB of Dnlta) 4-Bit e-Bit 16-Bit Total ftywtagc s e l l i n g H t ^ 4-Bit e-6it 16-Bit Mcrpcomputerg t$ HilXlOht^ 4-Bit S-Bit 16-Bit Total Peripheral • » • I/O 4-Bit 8-Bit 16-Bit Total HicrocowputerB • • • Peripherala + l/O ( $ Millions) 4-Bit 8-Bit 16-Bit Total 1977 1978 1979 1980 1981 1982 3.8 17.4 42.1 81.5 121.2 156.5 12 $ 50 $ 115 $ 199 $ 253 0 $ 0 0 0 $ 1 0 0 : 5 _0 5 $ 12 0 11 1 0 13 2 312 0 18 3 15 21 12 $ 51 $ 120 $ 211 $ 268 1983 3.7 0.1 N/A 16.0 1.4 N/A 35.0 7.0 0.1 60.0 21.0 0.5 85.0 35.0 1.2 100.0 54.0 2.5 115.0 70.0 4.0 189.0 $ 2.80 $15.00 N/A $ 10 2 0 $ 2.25 $10.00 N/A $ 36 14 0 $ 1.70 $ 7.25 $40.00 S 60 51 4 $ 1.35 $ 5.00 $25.00 $ BI 105 13 $ 1.15 $ 3.80 $18.00 $ 98 133 22 $ 1.05 $ 3.25 $12.50 $ 105 176 31 $ 1.00 $ 2.85 $ 9.00 $ 115 200 36 $ 351 0 20 4 24 $ 10 2 0 $ 36 15 0 $ 60 56 4 $ 81 116 14 $ 98 146 24 $ 105 194 34 $ 115 220 40 333 $ 375 N/A Product not available Source: DATAQUEST, Inc. June 1979 Table 4 ESTIMATED MEMORY CCWgiBBPTION ASSOCIATED WITH MICROPROCESSORS (ttillions of Dollars) Microprocessor Memory Consumption 4-Bit 8-Bit, 16-Biti; le-Bit'' 32-Bit Total 1977 1978 1979 1980 1981 1982 1983 $ 4 $ 2 $ 2 $ 0 $ 0 $ 0 $ 130 40 0 0 188 62 4 0 270 90 20 0 318 130 95 0 365 185 220 8 395 230 390 72 420 265 640 152 $174 $256 $382 $543 $778 $1,087 $1,477 I •vl I Mieroeonputer Meifc6if» CansaWHftttori 4-Bit 8-Bit 16-Bit Total $ 0 $ 9 2 0 $ 11 3 $ II $ 14 S 0 14 5 19 .Older products with direct addressing c a p a b i l i t y less than 128K bytes Newer products with direct addressing c a p a b i l i t y up to 8 M bytes Source: DATAQUEST, Inc. June 1979 (% 1 ^ U s=^s RESEARCH A Subsidiary ot A.C. Nielsen Co. ~ INCORPORATED SIS Code: Newsletters June 11, 1979 ESTIMATED WORLDWIDE MOS MEMORY CONSUMPTION Summary DATAQUEST estimates that worldwide consumption of MOS memory will grow from $1,238 million in 1979 to $3.0 billion in 1983, a 25 percent compound annual growth rate. Furthermore, we expect consumption of MOS memory bits to grow from 2.8 trillion bits in 1979 to 21.2 trillion bits in 1983, representing a compound annual growth rate of 65 percent. Dynamic MOS RAM consumption in 1979 is estimated at $488 million and represents 39 percent of the total. We expect that dynamic RAMs will remain the largest segment of MOS memory, with an estimated total of $1,063 million in 1983. Static MOS RAMs are expected to be one Of the fastest growing segments of the market in the next five years, growing from an estimated $252 million in 1979 to $739 million in 1983, which represents a 31 percent compound annual growth rate. MOS ROMs are expected to grow at a 21 percent rate reaching $352 million in 1983, while MOS EPROMs are growing at an estimated 27 percent compound annual growth rate and are expected to reach $697 million by 1983. EEPROMs should reach $105 million by 1983, repre-senting a 37 percent compound annual growth rate. The future of CCDs remains a major question and shift registers have a declining market. Total MOS Memory Consumption DATAQUEST estimates of worldwide MOS memory consumption are pre-sented in Table 1. We estimate 1979 worldwide MOS memory consumption at $1,238 million, up 47 percent over an estimated $843 million in 1978. Dynamic and static MOS RAMs represent 60 percent of the MOS memory market and are expected to grow at compound annual growth rates of 21 and 31 percent respectively. MOS ROMs represent about 13 percent of the MOS memory market and are expected to grow at a 21 percent compound annual rate. MOS EPROMs are growing at a 27 percent compound annual rate and represent 21 percent of total MOS consump-tion. EEPROMs (electrically erasable PROMs) are expected to grow at 37 percent per year to about $105 million by 1983. It is still unclear whether CCD technology will produce a commercially viable device that Copyright © 11 June 1979 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or releasei:! by responsitjle individuals in ihc subject co completeness It does not contain material provided to us in confidence by our clients This information is not furnished in connection with a sale or offer to sell securities or i buy securities This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities ipai cor mer es, but I S not gutiranteed as to accuracy oi nection wiih the solicitation of an offer to tioned and may sell or buy such securities 19055 P r u n e r i d g e Ave. / C u p e r t i n o , CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO is four times denser than MOS RAMs in order to realize a significant price advantage over RAMs. At this time, it appears that there are too many other good opportunities for MOS memory suppliers to con-centrate on, hence the outlook for CCDs is not good. MOS Dynamic RAMs Table 2 represents DATAQUEST's estimates of worldwide MOS dynamic RAM consumption. Estimates of units, average selling prices, and total dollar revenues are included. The average selling price (ASP) represents an average for the entire year over all devices of that category. Therefore, the ASP for 16K dynamic RAMs represents the pricing for plastic and ceramic, high-speed and low-speed, and all quantities over a 12-month time frame. Consumption of 16K dynamic RAMs is expected to reach 60 million units in 1979 and continue to about 110 million units in 1980. Growth in 1979 and 1980 seems limited only by the available capacity as users are converting their production from 4K dynamic to 16K dynamic RAMs. Unit volume should continue to grow until peaking in 1981, the year in which we estimate that 8 million 64K dynamic RAMs will be con-sumed. We have listed separately the 5 volt only, sub-120ns 16K dynamic RAM since this is a new device with higher ASPs aimed at the cache and buffer memory markets. We expect this fast RAM to represent a $112 million market by 1982. The 32K dynamic RAMs listed in Table 2 include 32K hybrids which use two 16K chips, as well as partially good 64K dynamic RAMs that can be used as 32K chips. Mostek has introduced its hybrid 32K RAM, while Intel and Texas Instruments are shipping hybrid 32K RAMs to IBM. We also understand that manufacturers producing 64K RAMs will ship some 64K partials for special applications such as memory systems. The presence of IBM in the merchant market for 32K dynamic RAMs makes this device an important product for the next several years. We have included the estimated merchant market purchases by IBM in Table 2. MOS Static RAMs Table 3 presents DATAQUEST's estimates of static MOS RAM consumption. This market is expected to grow from $252 million in 1979 to $739 million in 1983, representing a 31 percent compound annual growth between 1979 and 1983. Consumption of slow IK static RAMs continues to decline, but the fast IK statics still represent a Strong market because of some recent product announcements. Static 4K RAMs are still climbing in unit and dollar volume. We expect the total dollar revenues from 4K static RAMs to peak in 1980 at $228 million, but further expect the fast 4K static unit and dollar volume to continue growing through 1982. The 8K and 16K static RAMs represent important markets, as suppliers are expected to - 2 -make important slow and fast product offerings at the both 8K and 16K level. It is still too early to tell about total user acceptance for 8K, 16K, and 32K RAMs. MOS ROMs Table 4 presents DATAQUEST's estimates of worldwide MOS ROM con-sumption. This market is expected to grow from $162 million in 1979 to $352 million in 1983, which represents a compound annual growth rate of 21 percent. In 1979 and 1980, the important ROM markets are at 16K and 32K bits, but the 64K bit ROM is getting an important start this year. We expect the dollar revenues to be fairly evenly dis-tributed among 16K, 32K, and 64K ROMs in 1980, after which the 64K ROM should be the largest revenue producer through 1983. widespread use of ROMs for program storage in microprocessor applications is adding greatly to the strength of the MOS ROM market. MOS EPROMs and EEPROMs Worldwide consumption of MOS EPROMs is expected to grow from $266 million in 1979 to $697 million by 1983 as shown in Table 5. Unit volume of 8K EPROMs is expected to peak in 1979 while 16K EPROM unit volume is expected to continue growing into 1981. In 1979, the first of the 32K and 64K EPROMs are expected to be available. Unit volumes for these devices should continue to grow well into the 1980s and not peak before the 1983-84 time frame. MOS EEPROMs are expected to be an increasingly important market over the next five years. Total consumption in 1979 is estimated at about $28 million growing to $105 million by 1983. Currently the product offerings are at IK, 4K, and 8K with higher density products expected within two years. This market is expected to experience good growth as additional suppliers and users are showing increased interest in these products. Note that these estimates do not include the substantial internal consumption from captive EEPROM facilities such as the one at NCR. CCDs Table 6 represents our estimate of worldwide CCD consumption. Note that our estimates have decreased substantially from the last issue of this newsletter on October 6, 1978. The 64K CCD market is now serviced actively by only one supplier; other previous suppliers have essentially dropped out of the market. Great uncertainty surrounds this market since CCD technology has not moved fast enough to produce commercial devices that are four times denser than MOS RAMs in order to offer significant price advantages. We believe that only a few suppliers will continue to support this market. Bit Consumption Table 7 presents our estimates of MOS memory bit consumption on a worldwide basis. Total bits consumed in 1979 are estimated at - 3 -Daniel L. Klesken Frederick L. Zieber Mary Ellen Hrouda - 4 -Table 1 ESTIMATED WORLDWIDE MOS M04ORY CONSUMPTION (Dollars in Millions) I ui I RAM Dynamic Static ROM EPROM EEPROM CCD ShiCt Register Total MOS Memory Percent Change From Previous Year 1977 $351 254 97 100 66 4 2 38 1978 $530 360 170 125 134 15 3 36 1979 $ 740 488 252 162 266 30 8 32 1980 $ 987 645 342 205 375 45 15 27 1981 $1,235 801 434 251 461 60 22 24 1982 $1,497 937 560 300 573 80 27 20 1983 $1,802 1,063 739 352 697 105 33 16 Compound Annual Growth Rate 1979-1983 25% 21% 31% 21% 27% 37% 43% (16%) $561 $843 $1,238 $1,654 $2,053 $2,497 $3,005 26% 25% 50% 47% 34% 24% 22% Source: 20% DATAQUEST, Inc. June 1979 Table 2 Value (S t f t W i t r i c t i r H S ) IK 4K 16K^ 16K; 32K^ 64K 25eK Totals ESTIMATED WORLDWIDE DYNAMIC MOB RAM CONSIIMPTION 1977 1978 1979 1980 1981 $254 $360 $488 $645 $801 1982 $ 937 1983 $ 20 200 34 0 0 0 0 $ 14 154 192 0 0 0 0 $ 4 117 345 6 12 4 0 $ 0 68 420 45 80 32 0 $ 0 38 390 71 126 176 0 $ 0 28 250 112 125 400 22 $ 0 12 158 120 90 520 163 $1,063 I o\ I Percent Change Vttm Previous Yeat Units (Millions) IK 4K 16K^ 16K^ 3 2 K - e4K 256K Average Selling Price IK 4K I6K, 16K' 32K-64K 256K 24% 42% 36% 32% 24% 17% 13% 8.0 57.1 2.0 N/A N/A N/A N/A $ 2.50 $ 3.50 $17.00 N/A N/A N/A N/A 6.5 76.8 20.8 N/A N/A N/A N/A $ 2.20 $ 2.00 $ 9.25 N/A N/A N/A N/A 2.0 65.0 60.0 0.4 0.8 0.04 N/A $ 2.00 $ 1.80 $ 5.75 $14.00 $15.00 $95.00 N/A N/A^ 45.0 105.0 5.0 8.0 0.8 N/A N/A $ 1.50 $ 4.00 $ 9.00 $10.00 $40.00 N/A N/A 30.0 130.0 $ $ $ $ $ 15.0 18.0 8.0 0.001 N/A 1.25 3.00 4.75 7.00 22.00 $150.00 ] $ $ $ $ $ N/A 25.0 too.o 40.0 25.0 40.0 0.2 N/A 1.10 2.50 2.80 5.00 10.00 $110.00 N/A 12.0 70.0 60.0 20.0 80.0 2.5 N/A $ 1.00 $ 2.25 $ 2.00 $ 4.50 $ 6.50 $65.00 Three power supplies 2 . Five volt only supply Two-chip hybrids and 64K RAM partials 4 N/A - Product not available Source: DATAQUEST, Inc. June 1979 Total Percent Change From Previous Year Units (Millions) IK ( IK ( IK ( 4K ( 4K ( 8K ( 8K ( 16K ( 16K ( 32K 64K iKxl) 256x4) Fast) Slow) Fast) Slow) Fast) Slow) Fast) Average Sailing Pirice IK ( IK ( IK ( 4K ( 4K { 8K ( 8K ( 16K { 16K [ 32K e4K IKxl) 256x4) Fast) Slow) Fast) Slow) Fast) Slow) Fast) Table 3 ESTIMATED WORLDWIDE STATIC MOS RAM CONSUMPTION 1977 1978 1979 1980 1981 $97 56% $170 75% $252 48% $342 36% $434 27% " ^ N / A - Product not available 1982 $560 29% 1983 Value ( $ in Millions) IK (IKxl) IK (256x4) IK (Fast) 4K (Slow) 4K (Fast) 8K (Slow) 8K (Fast) 16K (Slow) 16K (Fast) 32K 64K $22 19 6 39 11 0 0 0 0 0 0 $ 17 13 7 96 36 1 0 0 0 0 0 $ 11 10 13 137 66 11 1 2 1 0 0 $ 8 7 16 144 84 32 12 18 17 4 0 $ 6 3 9 90 120 48 30 50 45 32 1 $ 3 1 3 56 126 84 60 96 70 50 11 $ 0 0 1 27 120 108 96 144 135 80 28 $739 32% 17.0 10.0 2.0 4.3 0.4 N/A^ N/A N/A N/A N/A N/A $ 1.30 $ 1.85 $ 2.80 $ 9.00 $28.00 N/A N/A N/A N/A N/A N/A 15.0 8.0 3.0 18.3 1.8 0.04 N/A N/A N/A N/A N/A $ 1.10 $ 1.60 $ 2.40 $ 5.25 $20.00 $22.00 N/A N/A N / A • • N/A N/A 12.0 7.0 6.0 42.0 5.5 0.8 0.02 0.05 0.01 N/A N/A $ 0.95 $ 1.40 $ 2.15 $ 3.25 $12.00 $14.00 $35.00 $35.00 $75.00 N/A N/A 10.0 5.5 8.0 60.0 14.0 4.0 0.5 0.9 0.3 0.05 N/A $ 0.80 $ 1.20 $ 1.95 $ 2.40 $ 6.00 $ 8.00 $24.00 $20.00 $55.00 $70.00 N/A 8.0 3.0 5.0 45.0 32.0 12.0 2.5 5.0 1.5 0.7 0.01 $ 0.80 $ 1.10 $ 1.70 $ 2.00 $ 3.75 $ 4.00 $12.00 $10.00 $30.00 $45.00 $95.00 4.0 1.0 2.0 30.0 45.0 28.0 10.0 16.0 5.0 2.5 0.2 $ 0.80 $ 1.00 $ 1.50 $ 1.85 $ 2.80 $ 3.00 $ 6.00 $ 6.00 $14.00 $20.00 $55.00 N/A N/A 1.0 16.0 50.0 40.0 20.0 32.0 15.0 8.0 0.8 N/A N/A $ 1.40 $ 1.70 $ 2.40 $ 2.70 $ 4.80 $ 4.50 $ 9.00 $10.00 $35.00 Source: DATAQUEST, Inc, June 1979 o r-t la o o i-i 'T o) »» r > 4 ko CN in n w-dp P-o iH '» in o\ tN in 1-1 n i H O <N i H rH <A-O O m « • o M •a: in o o o o o Z o in 00 o C N ^ ^ CM < o o o o a o Z - H O " i n CN i H , H i-I CN i H < o in o o o o .i-( C N in in m o Z r-I i H CN n i n VO i-t « • « > « > • < / > t o - w < in o o m o o \ c N ^ 00 r~ in o Z r-I i-t M ^ 00 i n CN vt-w-i/i- w-</y o c t" w M P» fao\ D r - I a < <u f c < 3 z o H EH 0< § CO z O U § Pi vr m O (U X fi -O H 10 Q &H M g i J O S o 3 O H t« < S 1..) & < cn u 00 O l p.( o 00 9> . 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\ > • > z z z i n CM CM r H n </y</yvy i^ hii m fii iti tti CM 00 VO <N ^ 00 r H n VO CM r^ 10 J J o c 4J o 3 T J o u 04 I < \ Z r H o c e-<n w r-CdO« a - ^ o < 41 E- c ^ =» O f^ (U u u 3 O CA I M O I Table 6 ESTIMATED WORLDWIDE CCD CONSUMPTION 1977 1978 1979 1980 1981 1982 1983 Value {f 16K 64K 256K 1024K Total in Iti^Cionft} Percent Change From Previous Units (Millions) 16K 64K 256K 1024K • Average Selling Pr 16K 64K 256K 1024K N/A - P r o d u c t not Ylair ice : ava $2 0 0 0 S2 33% 0.25 0.001, N/A^ N/A $ 8.00 $50.00 N/A N/A ilable $2 1 0 _0 $3 50% 0.4 0.02 N/A N/A $ 4.80 $40.00 N/A N/A $ 1 7 0 0 $ 8 167% 0.2 0.2 N/A N/A $ 3.75 $35.00 N/A N/A $ 0 11 4 0 $15 88% 0.1 0.6 0.04 N/A $ 3.25 $18.00 $90.00 N/A $ 0 11 11 0 $22 47% N/A 1.0 0.2 N/A N/A $ 11.00 $ 55.00 N/A $ 0 2 25 0 $27 23% N/A 0.3 1.0 .001 N/A $ 8.00 $ 25.00 $125.00 Source: $ 0 0 32 1 $33 22% N/A N/A 2.0 .01 N/A N/A $16.00 $80.00 DATAQUEST, Inc. June 1979 Table 7 M I ESTIMATED WORLDWIDE MOS MEMORY CONStJMPTION (Bits in Billions) RAM Dynamic Static ROM EPROM EEPROM CCD Shift Register Total MOS Memory Percent Change Previous Year 1977 323.7 274.9 48.8 246.6 38.1 1.1 4.1 19.0 632.6 From 136% 1978 771.5 662.1 109.4 518.5 119.1 5.4 7.9 20.0 1,442.4 128% 1979 1,515 1,287 228 954 321 12 16 19 2,837 97% 1980 2,737 2,301 436 1,565 519 20 51 19 4,911 73% 1981 4,194 3,613 581 2,386 911 40 118 18 7,667 56% 1982 6,954 5,889 1,065 4,104 1,634 80 283 17 13,072 70% 1983 10,560 8,733 1,847 6,902 3,039 140 535 16 21,212 62% Compound Annual Growth Rate 1979-1983 63% 61% 69% 64% 75% 85% 140% (4%) 65% . Source: OATAOUBST, I no. June 1979 ^ . T.r' t t . ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ . ^ ^ ^ ^ ^ H ^ ^ ^^-r RESEARCH J ^ ^ \ ASubsldmrvot A.C.NIelseitCo. ? INCORPORATED I ^ I ^ S W V ^ S ^ B ^ M 1 1 E l F ^ SIS Code: Newsletters May 11, 1979 GENERAL INDUSTRY UPDATE Summary U.S. semiconductor, consumption for 1979 is expected to be about 21 percent higher than in 1978. This increase follows strong 1978 growth for semiconductor consumption, which was up about 21 percent over 1977. The extremely strong growth in semiconductor shipments in the fourth quarter of 1978 and strong expected growth in the first half of this year provide most of the momentum for 1979 growth. It seems increasingly likely that later this year the economy will enter a slowdown, but not a full recession. Even in a slowdown^ the Strong demand for semiconductor devices is expected to provide the industry with continued growth. We believe that factors outside the semiconductor industry's normal relationship to the economy will provide this strong semiconductor demand throughout 1979 and 1980. These factors include: the effects of inflation; new markets such as automotive electronics, telecommunications, and industrial products; a Strong military mari^et; the low price of the dollar; and outside purchases by captive manufacturers. Although demand has been excep-tionally heavy recently, we do not see a situation similar to that of 1974 developing, and we do not see the industry entering a period of significant negative growth in the foreseeable future. Recent Economic Trends , ' -U.S. economic growth slowed markedly in the first quarter of 1979, partly due to inclement weather, but is expected to increase in the second quarter. Nevertheless, economic growth is expected to slow later in 1979, and early indications that this is happening have appeared. Currently, there is less concern that a slowdown may turn into a major recession; however, the effects of inflation on economic indicators make forecasts highly questionable. Almost,unanimously, economic and econometric forecasters grossly miscalculated the Strength of the economy in the fourth quarter of 1978. The appearances of an imminent slowdown in the economy may give the readers a feeling of deja vu: similar indications have arisen several times during the current upturn of the economy. Current in-dications, however, are more prevalent and stronger. Copyright © 11 May 1979 by DATAQUEST - Reproduction Prohibited The Content of this report represents our interpretation and analysis of information generally available to the public or released by responsible Individuals in the subject companies, but Is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by oui clients Tliis information is not furnished in connection wuh a sale or offer to sell sccuntIes or in conIieciIon with the solicitation of an offer to buy securities. This firm and its parent and/or tlieir officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and iTiay sell or buy sucli securities 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO The following recent economic developments are noteworthy: • The Index of Leading Indicators declined in March for the third consecutive month. Normally, this pattern indicates a future economic downturn, but because of extremely strong growth in previous months, it is a less certain indication in this instance. • The gross national product (GNP) grew about 0.7 percent in real terms in the first quarter of 1979, following a growth of 6.9 percent in the fourth quarter of 1978. • Retail sales in recent months have not kept pace with in-flation. Housing starts and automobile sales have slowed. • Industrial production has continued to grow at a steady pace in the first quarter. Taken with declining retail sales, this situation indicates that inventories are in-creasing. • Money supply declined considerably throughout the first quarter of 1979, although most of that decline was reversed 'with a spurt in April. • Economic growth in Europe will apparently slow as a result of higher oil prices. Furthermore, the strengthening dollar increases the European inflation outlook. Measures to abate this inflation cloud the economic outlook. • Movements to spur consumption in Japan indicate that its economy should see excellent growth in 1979. The U.S. economy currently remains strong. Its resiliency, despite efforts to slow it down, indicates that the economy may grow more slowly in the next year but not suffer severe problems. Semiconductor Industry Trends U.S. semiconductor demand in the first quarter of 1979 was ex-tremely Strong. Book-to-bill ratios have been running in the range above 1.3 to 1. Early indications are that bookings for April showed little slackening in this trend. The extremely strong bookings result from a combination of heavy demand, an increase in long-term orders, and stable and/or increasing prices. In general, industry prices declined throughout 1978. Forward pricing in early 1978 reflected a consensus that demand would slow later in the year. Current heavy demand and large backlogs of semi-conductor manufacturers are changing that practice. Semiconductor users, in their quest to get priority treatment, have recently been more than willing to accept higher prices. Longer term orders are also an indication of users' attempts to obtain adequate allocation of parts from their suppliers. This is not an entirely healthy situation for the industry. If price stability or price increases - 2 -continue, they can set the semiconductor industry up for a painful reversal when demand slackens. At this point, we believe the situa-tion has not yet existed long enough to be critical, but it must be watched closely. Semiconductor manufacturers have had cost control problems related to their attempts to rapidly expand production. We believe that yields have not increased nearly as much as might be expected under normal circumstances. Ideally, this problem will work itself out gradually during reduced demand later this year. Heavy demand is reflected also in other industry problems: shortages of devices, equipment shortages, and some double ordering. None of these problems has reached the levels of 1974. Generally, although the situation is tight, people are receiving the devices and equipment needed. In many cases, the scarcity of labor is the pacing item in increasing capacity. Lead times, however, are excessive. We feel that management so far has been far more cautious than in 1973 and 1974. As a result, the double ordering of semiconductor devices and inventory accumulation has been fairly moderate. It is our perception that the very strong demand for semicon-ductors is based on real and expanded usage, and is not an illusion created by the economic situation. New applications, new companies using semiconductors, and the use of more semiconductors in old applications is the primary engine of the current strong semicon-ductor demand. This is a much more positive situation than in past cycles. The current situation differs from 1974 in several other respects, including the ability to use order entry data processing to police double ordering, greater management caution, less inventory accumulation, and more long-term ordering of semiconductors. It is increasingly evident that the cumulative effects of infla-tion are a major market stimulus to semiconductor demand. Basically, while Other prices have risen, the cost of electronic products for any given function has decreased. The electronics deflation has provided capital equipment using electronics with a strong market advantage. There is no reason to expect this trend to cease abruptly. The perception of continued inflation, as well as past history, should maintain this basic shift in the market pattern for many years. The growth in semiconductor production, especially in the fourth quarter of 1978, has increased the stress on semiconductor production capacity. It is clear that the industry is operating in excess of comfortable capacity both in terms of facilities and people. Although the capital expenditures of the industry have grown tre-mendously in recent years, new facilities coming on stream are estimated by DATAQUEST to be only barely adequate for reasonable future industry expansion. An overcapacity situation is definitely not expected. - 3 -Semiconductor Industry Forecast Table 1 gives our estimate for U.S. semiconductor consumption in dollars. We believe 1978 semiconductor consumption increased about 21 percent over 1977. For 1979, we expect semiconductor consumption to increase by about 21 percent over 1978. This increase from our previous forecast is primarily because the strong finish in 1978 provided the industry with a running rate entering 1979 significantly above the average for 1978. While we see integrated circuits accounting for the majority of the increase in semiconductor con-sumption, we also see considerable growth in the discrete device market. Our current estimates for 1979 U.S. semiconductor consumption by calendar quarter are shown in Table 2. It should be remembered that normally the first and third quarters of the year are seasonally slower in growth. We expect stronger growth in the first half of 1979 to be moderated late in the year and in the first quarter of 1980. The current general economic activity and the high rate of semi-conductor orders and backlogs indicate that strong shipments in the first half of the year and through most of the third quarter are assured. While we see some slowdown in demand developing, we do not at this time see a prolonged downturn occurring. A seasonal pause in the first quarter of 1980 should be followed by a resumption of Strong semiconductor demand growth. Our econometric model does not take into account factors that do not have historical precedence, nor does it take into account factors not relating to the economy. However, several of these non-economic and non-historical factors have increased actual semiconductor demand in 1978, and should continue to increase demand for semiconductors in 1979 and 1980. Thus, we expect greater possible variance from our forecast on the up side. Major factors are shown below: • The effects of inflation, as previously mentioned. It is also possible that the high rate of current inflation may add some industry growth in terms of current dollars. In a deflationary industry, we have no good way to account for this. • Large new markets: The automotive industry. This will see its greatest increment in semiconductor usage in model year 1981. This relates to semiconductor deliveries beginning in early 1980. The telecommunications market. This is an extremely large market with its growth phase spread over the next several years. - 4 -Industrial products. The microprocessor revolution is changing many products from a mechanical or an electromechanical base to electronics, which is creating heavy demand with a large new customer base for the industry. • The military and government markets are experiencing strong growth for the first time since the early 1960s. This is exactly the opposite of the situation in 1974. • We believe the captive semiconductor manufacturers will need to make major purchases of semiconductors beginning late 1979. We see no prospect that these companies—especially General Motors, IBM, and Western Electric—^will be able to meet their needs for several years. • The devalued dollar is making U.S. semiconductor companies more competitive in overseas markets. These factors are helping to spur semiconductor demand. The advent of VLSI is making semiconductor design and semiconductor manu-facturing an increasingly scarce resource. Unless a major recession occurs, the outlook for the industry appears quite positive. Frederick L. Zieber James F. Riley Mary Ellen Hrouda - 5 -Table 1 ESTIMATED U.S. CONSUMPTION OF SEMICONDUCTORS (Dollars in Millions) Percent Percent Increase Increase 1977 1978 1977-78 1979 1978-79 Discrete Devices $ 925 $1,017 9.9% $1,140 12.1% Integrated Circuits 1,787 2,264 26.7% 2,823 24.7% Total $2,712 $3,281 21.0% $3,963 20.8% Source: DATAQUEST, Inc. May 1979 - 6 -Table 2 ESTIMATED QUARTERLY U.S. SEMICONDUCTOR CONSUMPTION (Dollars in Millions) 1978 1st Qtr. $ 233 495 2nd Qtr. $255 559 3rd Qtr. $ 255 572 4 th Qtr. $ 274 638 Total Year $1,017 2,264 Discrete Devices Integrated Circuits Total $ 728 $814 $ 827 $ 912 $3,281 Percent Change From Previous Quarter or Year Discrete Devices Integrated Circuits Total Percent Change From Previous Quarter Percent Change From Previous Year Discrete Devices Integrated Circuits Total 0.6% 1st Qtr. $ 279 660 $ 939 3.0% 29.0% 1st Qtr. $ 295 740 $1,035 11.8% 2nd Qtr. $290 697 $987 5.1% 21.3% 1.6% 1979 3rd Qtr. $ 287 716 $1,003 1.6% 21.3% 1980 10.3% 4th Qtr. $ 298 736 $1,034 3.1% 13.4% 21.0% Total Year $1,140 2,823 $3,963 20.8% Percent Change From Previous Quarter 0.1% Source: DATAQUEST, Inc. May 1979 - 7 -w mm:r R E S E A R C H /^ ^ . A Subsidiary of A.C.NldscnCc. ^ IMCORPORATED I ^ I E S W ^ 3 ^ H ^ Z I 1 ^ M P 4 • -• SIS Code: Newsletters May 11, 1979 MOS MICROPROCESSOR SHIPMENTS Summary Worldwide shipments of MOS microprocessors in the first quarter of 1979 were an estimated 10.3 million units, up about 23 percent over estimated fourth quarter shipments. Shipments of 4-bit micro-processors were an estimated 6.7 million units, or 65 percent of the total; shipments of 8-bit microprocessors were an estimated 3.5 million units, or 34 percent of the total, and 16-bit products represented about 1 percent of total first quarter shipments with an estimated 121,000 units. Single-chip microcomputer shipments in the first quarter of 1979 were an estimated 7.6 million units representing about 73 percent of total first quarter microprocessor shipments. This percentage remains about the same as in the fourth quarter of 1978, but is up from 55 percent in the first quarter of 1978. Quarterly Microprocessor Shipments Table 1 presents DATAQUEST's estimates processor CPU shipments for the first quarter shipments refer to CPU chips only peripheral chips. and do of worldwide micro-of 1979. Estimated not include any I/O or Estimated shipments in the first quarter of 1979 were 10.3 million units, up about 23 percent over the fourth quarter of 1978. This quarter to quarter change in microprocessor shipments is up from the 13 percent increase registered in the fourth quarter of 1978 but is not as strong as the 34 percent increase of the first quarter 1978 over the fourth quarter 1977 registered one year ago. At that time, however, the total base was significantly lower. In fact, total shipments in the first quarter of 1979, at 10.3 million units, are more than double the estimated 4.5 million units shipped in the first quarter of 1978. Table 2 presents DATAQUEST's estimates of worldwide shipments of single-chip microcomputers. Estimated first quarter 1979 shipments of microcomputers were 7.6 million units, up about 24 percent over estimated fourth quarter 1978 shipments of 6.1 million microcom-puters. Copyright © 11 May 1979 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public oi relea,sed by responsible individuals in the sutaieci completeness. It does not contain material provided to us in confidence by our clients. This informal Ion is not lurnishcd in connection with a sale oi offer to sell securities buy securities This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the secur companies, but i or in connection Ties meniioned a not guaranteed as to accuiaey or A/ilh the sohcilation of an offer to i d inay sell or buy such securities 19055 P r u n e r i d g e Ave. / C u p e r t i n o , CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO The growing importance of single-chip microcomputers is demon-strated by the rapid growth in total units shipped as well as the growing number of product offerings. The 7.5 million units shipped in the first quarter of 1979 is up 203 percent over estimated first quarter 1978 shipments of 2.5 million units. Furthermore, in the first quarter of this year there were 11 distinct single-chip micro-computer families on the market, up from eight families one year ago. 4-Bit Microprocessors Table 3 presents DATAQUEST's estimates of worldwide micro-processor shipments by bit length. Shipments of 4-bit microcomputers in the first quarter of 1979 are estimated at 6.7 million units, up about 21 percent over estimated fourth quarter shipments. Shipments of 4-bit microprocessors continued to grow at a strong rate in the first quarter. This quarter-to-quarter change is sig-nificantly larger than the fourth quarter 1978 change over the third quarter of that year. The increase reflects the cost-effectiveness of these products. For example, note that shipments of the TMS 1000 and the COM-4 are up dramatically over the first quarter of 1978. Prices of 4-bit microprocessors for delivery in the second quarter are in the $1.25 to $3.00 range. These prices represent large-quantity shipments in excess of 100,000 units. The 4-bit market continues to grow because of its cost-effectiveness and the continued new product introductions that add to the flexibility and ease of use of these low-cost controllers. 8-Bit Microprocessors Worldwide shipments of 8-bit microprocessors in the first quarter of 1979 were an estimated 3.5 million units, up 29 percent over estimated fourth quarter shipments. This quarter-to-quarter growth in 8-bit microprocessor shipments continues the trend of the fourth quarter after a relatively flat quarter-to-quarter growth in 1978. Much of the gain for 8-bit microprocessors, however, comes from single-chip 8-bit microcomputers. In the first quarter 1979, 8-bit microcomputers represented 28 percent of the total 8-bit micro-processor shipments. This is up from 23 percent in the fourth quarter of 1978. Prices of 8-bit microprocessors remain in the $4 to $8 range for deliveries in the second and third quarters of 1979. Prices have been relatively stable since the last publication of this newsletter in March. Strong demand for some single-chip microcomputers such as the 8048 and the 3870 is keeping their prices in the $6 to $7 range. These prices, which are higher than fourth quarter 1978 prices, are expected to continue well into the second half of 1979. - 2 -16-Bit Microprocessors Worldwide shipments of 16-bit microprocessors in the first quarter of 1979 were an estimated 121,000 units, up about 14 percent over estimated fourth quarter shipments. Most of the increase was due to the increased shipments of TMS 9900 products. Continued Strong increases are expected in coming quarters as product designs incorporating 16-bit microprocessors move into production and as new 16-bit microprocessors become available. Prices for 16-bit microprocessors still vary widely as they are correlated with availability and quantities being shipped. The TMS 9980 is available for $10 to $15 in quantities of 1,000 units, whereas the 8086 still commands a price in the $75 to $100 range, depending upon the quantity purchased. Daniel L. Klesken James F. Riley Frederick L. Zieber - 3 -E i n i / i o o o c o o o i n o o i n c o o o r a m o o o o i n f n o m o o o o i n o w o o c D o o o o m o i n i n i / l o m o m o m m o o o i o o o ro.-Hrorn m ^ i n r i o . - 4 r o n r - i f n f N m i - H m r - i H r H v D v o o v o m v o i / i a 3 o r o . - i m o ( N O U ) f > l i r » o o . H O r ^ ^ . - t o o f O v D u i (_J I.J . . . U I .! l..; 1.., I_l U I 1' I t,J U I t_, I..J t..^ ^_, U I %^ UJ ...• I..) i—f U , .w. ..,. u I '—I u I u I u I V,. u I \^ " I . r o n r - i f n f N m i - H i n r - i H r H v D v o o v o f n v D i / i a 3 o r o . - i m o ( N O U ) f > l i r » o o . H O r ^ .-H . - ^ < N . - ^ . 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^ x; >, Ul J3 M "D 01 01 O l f H C "O o c r-( a £ o c » o u c ..-1 01 B "H 01 10 Ul O Ot U Ul Ul 01 01 . C U l ^ I N f n I I « a Table 2 Ul I ESTIMATED WORLDWIDE SHIPMENTS OF SINGLE-CHIP MICROCOMPUTERS (Units in Thousands) 1978 Company ' MPU Products AMI Fairchild General Instrument Hitachi Intel Mostek Motorola National NEC Rockwell Signetics Texas Instruments S2000 3870 PIC-1650 HMCS-40 8048/8021 8748 3870 141000 3870 COPS COM-4 8048 PPS-4 8048 TMS 1000 Total Microcomputers Percent change from previous quarter 2,498 3,439 5,353 6,087 17,377 1979 1st Qtr. 0 3 75 85 60 0 20 0 5 300 150 0 400 0 1,400 2nd Qtr. 9 5 95 95 100 0 50 0 10 500 225 0 550 0 1,800 3rd Qtr. 8 5 105 110 150 5 75 5 15 675 525 S 675 S 3,000 4 th Qtr. 12 10 175 120 170 25 205 15 40 850 600 15 650 S 3,200 Total 2 1. 2 9 29 23 450 410 480 30 350 20 70 ,325 ,500 15 ,275 S ,400 1st Qtr. 30 40 300 130 210 50 260 30 80 900 1,100 25 700 15 3,700 37.7% 55.7% 13.7% 7,570 24.4% Source: DATAQUEST, Inc. May 1979 Table 3 ESTIMATED WORLDWIDE SHIP.MENTS OF MICROPROCESSORS BY BIT LENGTH (Units in Thousands) 1978 Total Percent change from previous quarter 8-Bit Products AMD AMI EFCIS Fairchild General Instrument Hitachi Hughes Intel MOS Technology Mostek Motorola National NEC RCA Rockwell Sescosem Signetics Synertek Texas Instruments Zilog Total Percent change from previous quarter 12-Bit Products 8080A 8085 6800 6800 F8 3870 6800 6802 PIC-1650 6800 1802 8008 8080A 8048/8021 8748 8085 6500 F8 Z80 3870 6800 6802/6808 6809 3870 8080A SC/MP 8080A 8048 8085 Z80 1802 6500 6800 2650 8048 6500 TMS 8080A Z80 57.8% 90 0 35 0 . 110 3 55 0 75 10 5 28 165 60 0 50 50 50 70 20 120 5 0 5 85 65 70 0 0 0 75 260 5 20 0 325 30 90 35.0% 105 0 30 0 130 5 45 0 95 15 3 28 170 100 0 80 55 30 50 50 140 20 0 10 90 70 85 0 0 0 75 200 6 25 0 225 30 100 55.5% -il 30 0 190 5 80 0 105 20 10 25 180 150 5 95 60 35 60 75 150 65 0 15 100 100 90 S 5 5 85 75 7 35 S 60 40 150 8.6% 125 5 35 0 200 10 90 S 175 25 12 22 190 170 25 125 60 45 80 205 160 90 0 40 100 100 60 15 25 25 90 60 7 45 S 70 35 210 435 5 130 0 630 23 270 S 450 70 35 103 705 480 30 350 225 160 260 350 570 180 0 70 375 335 305 15 30 30 325 595 25 125 S 680 135 550 2,031 2,072 2,222 2,731 9,056 18.8% 2.0% 7.2% 22.9% Total Percent change from previous quarter 68 83 98 106 355 1979 4-Bit Products AMI Hitachi Intel Motorola National NEC Rockwell Texas Instruments MPU Products S2000 HMCS-40 4004 141000 COPS 4004 IMP COM-4 PPS-4 TMS 1000 1st Q t r . 0 85 42 0 300 30 20 150 400 1,400 2nd Qtr. 9 95 42 0 500 35 20 225 550 1,800 3rd Qtr. 8 110 40 5 675 35 20 525 675 3,000 4th Qtr. 12 120 35 15 850 30 20 600 650 3,200 Total 29 410 159 20 2,325 130 80 1,500 2,275 9,400 1st Qtr. 30 130 35 30 900 30 18 1,100 700 3,700 2,427 3,276 5,093 5,532 16,328 6,673 20.6% 135 15 38 8 150 40 155 20 300 30 12 20 190 210 50 175 65 60 100 260 165 150 S 80 150 100 65 25 55 80 115 75 0 45 15 100 32 250 3,535 29.4% Harris Intersil Total Percent change from previous quarter 1 6 - B i t Products General Instrument Intel National Texas Instruments 6100 6100 CP-1600 8086 PACE TMS 9900 5 8 13 30.0% 10 0 18 40 5 10 15 15.4% 20 1 18 44 5 10 15 0% 15 10 25 48 7 10 17 13.3% 15 13 25 53 22 38 60 60 24 86 185 8 10 18 5.9! 15 13 25 68 13.3% 22.1% 18.1% 8.2% 121 14.2% S = Sampling - 6 -Source: DATAQUEST, Inc. May 1979 SIS Code: Newsletters May 4, 1979 DYNAMIC AND STATIC MOS RAM AND EPROM SHIPMENTS Summary Worldwide shipments of 16K dynamic MOS RAMs increased to 10.2 million units in the first quarter of 1979, up about 27 percent over an estimated 8.0 million units in the fourth quarter of 1978. Prices are remaining relatively stable in the $5.50 t i o $6.50 range, as demand far outstrips available supply and lead times remain in the 20 to 25 week range. Worldwide shipments of 4K dynamic MOS RAMs in the first quarter of 1979 were an estimated 18.9 million units, down about 3 percent from an estimated 19.5 million units shipped in the fourth quarter of 1978. Shipments continued to decline, as some suppliers are dropping their commitment to this product. An estimated 8.3 million units of 4K static MOS RAMs were shipped in the first quarter of 1979, up about 30 percent over the fourth quarter. Of this number, about 340,000 units were 4R static CMOS RAMs. - • First quarter shipments of 8K EPROMs were an estimated 4.2 million units, up about 23 percent over the fourth quarter. Ship-ments of 16K EPROMs were an estimated 1.4 million units, up about 57 percent over estimated fourth quarter shipments. Dynamic MOS RAMs 16K RAMS DATAQUEST estimates of worldwide 16K dynamic WpS RAM shipments are presented in Table 1. We estimate that worldwide shipments in the first quarter of 1979 were 10.2 million units, an increase of 27 percent over estimated fourth quarter shipments of..8.0 million units. DATAQUEST estimates include the total shipments by,each company, in-cluding any shipments to other divisions of the same company. Note that our estimates of Intel's 16K RAM shipments for 1978 have been revised. Long lead times associated with i6K dynamic RAMs that developed suddenly in the first quarter of 1 9 7 1 9 continue in the second quarter. Extremely strong demand has resulted in lead times that are still in the 20 to 25 week range. We expect the long lead times to continue Copyright © 4 May 1979 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public • conipletcni^ss it does not contain material provided to us in confidence by our clients This inforrnatIon is nol furnished in co buy securities This firm and its parent and/or their officers, stockholders, or inembers of their families may, from time to I leased by responsibl lection with a sain or offe e. have a long or 'iiorl po iduals in the subject companic! ;ei to sell sncuritit n the sec ; not guaranteed as lo accuracy oi connection with ihe solicitation of an offer to mentioned and may sell or buy such securities 19055 Pruneridge Ave./Cupertino, CA 95014/ (408) 725-1200/TWX (910) 338-7695/ DATAQUEST CPTO into the third quarter when some shortening is likely. By that time, added capacity and improved yield, coupled with slightly lower demand, should ease lead time problems somewhat. Prices of 16K dynamic RAMs for current delivery remain in the $5.50 to $6.50 range for plastic package types and in the $6.50 to $7.00 range for ceramic and cerdip packages. At this time, we are expecting prices of 16K dynamic RAMs to remain relatively firm throughout the year with price declines of only 10 to 15 percent. 4K RAMs DATAQUEST estimates of worldwide 4K dynamic MOS RAM shipments in the first quarter of 1979 are presented in Table 2. We estimate that about 18.9 million units were shipped in the first quarter of 1979, down about 3 percent from estimated fourth quarter shipments. Unit shipments of 4K dynamic RAMs have now declined for two consecutive quarters and will probably continue to decline, because new product designs are using 16K RAMs and older designs are being upgraded to the 16K RAM. However, there will certainly be several more years of important usage of the 4K dynamic RAM for some long-running product designs. Lead times for 4K dynamic RAMs remain in the 15 week range and are likely to remain there throughout the second quarter. Prices for current deliveries have increased from the $1.40 to $1.60 range for plastic packages up to the $1.80 to $2.00 range. This recent price increase reflects a strong demand for the part as well as a price that was previously too low to yield reasonable margins. 32K RAMs In 1978, Mostek introduced a hybrid 32K dynamic RAM consisting of two chip carriers each containing a 16K chip and mounted side-by-side on an 18-pin ceramic substrate. Currently, Mostek is the only supplier of this hybrid part and shipped an estimated 30,000 units in the first quarter of 1979. Prices of this unit are in the $17.00 to $20.00 range. It is not known how many suppliers will follow suit with a similar hybrid package, but it appears that Mostek is vigor-ously pursuing this market. It appears that a significant market may develop for 32K RAMs which are 64K RAM partials. The initial low yields on 64K RAMs result in a large number of chips which have a defect in half of the memory but can still function as a 32K dynamic RAM. For many memory system applications the partials with error correction function meet all the system specifications. 64K RAMs Currently, Fujitsu, Motorola, and Texas Instruments are sampling 64K dynamic RAMs. Motorola and TI are following the same practice of Shipping samples to their customer at no cost but retaining ownership and requiring that the parts be returned at some future time. Sample quantities shipped in the first quarter were in the range of 100 to - 2 -300 units for each company and will likely continue in that range during the second quarter. We expect additional suppliers to announce 64K RAMs in 1979, but we currently foresee no more than 25,000-50,000 units being shipped in the year. IK RP^s Intel is the only remaining supplier of IK dynamic RAMs, as ITT dropped out in late 1978. Intel has publicly stated that 1979 will be its last year to supply this product. In light of this situation, we expect the remaining users of the device to redesign their products to use 4K and 16K RAMs. Static MOS RAMs 4K RAMs Table 3 presents DATAQUEST estimates of 4K static MOS RAM ship-ments in the first quarter of 1979. An estimated 8.3 million units were shipped in the first quarter, up about 30 percent over estimated shipments in the fourth quarter of 1978. Included in this total are an estimated 340,000 units of 4K static CMOS RAMs. The current suppliers include Harris, Hitachi, NEC, and RCA. Others are expected to enter the market in the next few quarters.. Lead times for most 4K static RAMs are in the 10 to 15 week range with prices for the 2114 type in plastic being in the $3.75 to $4.75 range. Packages in cerdip or ceramic command a $.50 to $1.00 premium above this. 4K static CMOS RAMS are currently commanding prices in the $16 to $20 range in the smaller quantities being shipped; however, CMOS RAM prices are expected to fall to the $9 to $12 range when suppliers are able to ship larger volumes later in 1979. Intel is Still the only producer of the 2147 fast 4K static. A number of suppliers are beginning to sample the product, but have not begun production shipments. We estimate that Intel shipped 800,000 2147's in the first quarter or one-half of its estimated first quarter 4K static RAM shipments. 8K RAMS The 8K Static MOS RAM market is just beginning to develop. Mostek shipped an estimated 30,000 lKx8 static RAMs in the first quarter of 1979, and EMM sampled its lKx8 RAM. Several suppliers are developing products for this market while others have decided to bypass it and focus attention on the 16K static RAM market. IK RAMs IK Static RAMs are available from suppliers. Lead times are in the range of 8 to 10 weeks and prices are in the $1.00 range. EPROMs 8K EPROMs Table 4 presents DATAQUEST's estimates of worldwide shipments of 8K EPROMs. We estimate that worldwide shipments in the first quarter - 3 -of 1979 were about 4.2 million units, up about 23 percent from fourth quarter shipments. Prices are currently in the $4.00 to $6.00 range. Prices actually increased slightly in the first and second quarters of 1979, as the demand for EPROMs has been far greater than available supply. 16K EPROMs Table 5 presents our estimate of worldwide shipments of 16K EPROMs. It shows that an estimated 1.4 million units were shipped in the first quarter of 1979, up about 57 percent over estimated fourth quarter shipments. Currently prices are in the $16.00 to $22.00 range, depending upon quantity and speed of the device. Lead times remain greater than 20 weeks and are likely to remain firm throughout the second quarter and into the second half of the year. 32K and 64K EPROMs Intel and Texas Instruments are both shipping limited quantities of 32K EPROMs. We estimated that Intel shipped about 5,000 units in the first quarter while TI shipped an estimated 10,000 units. Prices range from $50.00 to $80.00 depending upon quantity and speed. We understand that some vendors plan to bypass the 32K EPROM; they are working on 64K EPROMs, which might be introduced in late 1979 or early 1980. Daniel L. Klesken James F. Riley Frederick L. Zieber - 4 -Table 1 ESTIMATED WORLDWIDE SHIPMENTS OF 16K DYNAMIC MOS RAMS-"-(Units in Thousands) 1978 1979 'Indicates sampling Company AMD Fairchild Fuj itsu Hitachi Intel Intersil ITT Mostek Motorola National NEC Siemens Signetics Texas Instruments Toshiba Zilog 1st Qtr. 0 25 250 120 400 0 3 700 200 12 650 5 S 300 20 10 2nd Qtr. 0 40 350 240 500 0 25 1,000 500 50 800 15 30 500 35 15 3rd Qtr. 0 200 500 350 600 0 75 1,400 550 75 1,100 25 30 950 80 15 4 th Qtr. s2 200 900 500 900 S 100 1,800 500 150 1,300 40 80 1,400 150 20 Total S 465 2,000 1,210 2,400 S 203 4,900 1,750 287 3,850 85 140 3,150 285 60 1st Qtr. S 300 1,100 800 600 S 200 2,400 700 250 1,700 65 75 1,800 225 20 Total 2,695 4,100 5,950 8,040 20,785 10,235 Percent Change From Previous Quarter 146.2% 52.1% 45.1% 35.1% 27.3% Includes Merchant Market and Internal Shipments 2. Source: DATAQUEST, Inc. May 1979 - 5 -Table 2 ESTIMATED WORLDWIDE SHIPMENTS OF 4K DYNAMIC MOS RAMS' (Units in Thousands) 1978 Total Percent Change From Previous Quarter 2.3% 7.6% 1.0% (1.0%) 1979 AMD Fairchild Fuj itsu Hitachi Intel Intersil ITT Mostek Motorola National NEC Signetics Texas Instruments 1st Qtr. 1,100 500 600 330 3,000 150 200 4,000 1,000 1,200 1,600 250 4,200 2nd Qtr. 1,500 400 600 500 3,000 100 300 4,000 1,300 1,200 1,600 300 4,700 3rd Qtr. 1,800 200 400 500 2,700 100 300 4,800 1,500 1,500 1,600 300 4,000 4th Qtr. 2,200 100 300 450 2,300 100 800 4,200 1,900 1,700 1,350 300 3,800 Total 6,600 1,200 1,900 1,780 11,000 450 1,600 17,000 5,700 5,600 6,150 1,150 16,700 1st Qtr. 2,600 0 200 350 2,000 100 1,100 3,800 1,500 2,000 1,350 300 3,600 18,130 19,500 19,700 19,500 76,830 18,900 (3.1%) Includes Merchant Market and Internal Shipments Source: DATAQUEST, Inc. May 1979 - 6 -Table 3 ESTIMATED WORLDWIDE SHIPMENTS OF 4K STATIC MOS RAMS^ (Units in Thousands) 1978 1st 2nd 3rd 4th Qtr. Qtr. Qtr. Qtr. Total ^ D 200 250 300 230 980 ^^I 0 0 0 15 15 v/EMM 900 1,150 1,000 1,1002 4,150 N/Fairchild 0 0 0 S S K.^ujitsu 50 75 100 100 325 v^arris 0 0 S 15 15 Uiitachi 90 130 200 300 720 v^ntel 800 1,050 800 1,400 4,050 U'ntersil 70 50 140 200 460 v^ostek 120 250 200 230 800 v^otorola 50 200 250 250 750 \/^ational 0 100 250 400 750 v^EC 500 600 650 800 2,550 ^^^CA 0 0 0 0 0 " ^ S i g n e t i c s 0 0 0 0 0 x/Synertek 160 280 350 450 1,240 y t e x a s I n s t r u m e n t s 700 800 700 800 3,000 v-^Zilog 6^ 90 40^ 90 280 Total Percent Change From Previous Quarter 80.0% 1979 1st Qtr. 180 115 1,100 50 80, 40-600' 1,600 300 450 300 650, 1,100: 50-S 560 1,000 110 3,700 5,025 4,980 6,380 20,085 8,285 35.8% (0.9%) 28.1% 29.9% "Includes Merchant Market and Internal Shipments 'Indicates Sampling U K CMOS RAMs only includes 150,000 4K CMOS RAMs in 1st Qtr. 'includes 100,000 4K CMOS RAMs in 1st Qtr. Source: DATAQUEST, Inc. May 1979 - 7 -Table 4 ESTIMATED WORLDWIDE SHIPMENTS OF 8K EPROMS' (Units in Thousands) 1978 1979 Company AMD Electronic Fairchild Fujitsu Intel Motorola National Signetics Arrays Texas Instruments Toshiba 1st Qtr. 15 30 40 50 700 100 150 75 350 0 2nd Qtr. 50 50 60 90 900 220 300 75 550 0 3rd Qtr. 80 60 60 70 800 300 300 80 400 10 4 th Qtr. 340 60 120 70 1,000 400 500 50 800 30 Total 485 200 280 280 3,400 1,020 1,250 280 2,100 40 1st Qtr. 600 75 160 70 1,100 700 600 0 800 50 Total 1,510 2,295 2,160 3,370 9,335 4,155 "Includes Merchant Market and Internal Shipments Source: DATAQUEST, May 1979 Inc. Table 5 ESTIMATED WORLDWIDE SHIPMENTS OF 16K EPROMS' (Units in Thousands) 1978 Total 350 650 465 905 1979 Company Fairchild Fujitsu Hitachi Intel Mostek Motorola National Texas Instruments Toshiba 1st Qtr. 0 0 0 250, S 0 0 100 0 2nd Qtr. 0 0 0 400 S S 0 250 0 3rd Qtr. 0 0 5 250 S 10 S 200 S 4 th Qtr. 0 5 30 450 25 90 S 300 5 Total 0 5 35 1,350 25 100 S 850 5 1st Qtr. S' 70 125 550 90 160 5 400 25 2,370 1,425 'Includes Merchant Market and Internal Shipments 'Indicates Sampling - 8 -Source: DATAQUEST, Inc. May 1979 I H L - ' T : _ ^ ^ =.=^=^ -rt.= = ^s-3- R E S E A R C H A Subsidiary of AC. Nielssn Co. ' ? INCORPORATED I ^ I ^ S W ^ 3 ^ H ^ H 1 1 ^ S F ^ SIS Code: Newsletters A p r i l 4 , 1979 UPDATE O N BIPOLAR MEMORIES Stjmmary DATAQUEST estimates that worldwide consumption of bipolar memory will grow at a compound annual rate of 15 percent, from an estimated $249 million in 1978 to $435 million in 1982. Consumption of bipolar ROMs and PROMs was an estimated $143 million in 1978 or about 57 per-cent Of the total. We expect ROMs and PROMs to represent about 58 percent of the total in 1982, or $254 million. Signetics had a 20 percent share of the 1978 bipolar memory market, followed by Fairchild with 19 percent. Monolithic Memories with 12 percent, and Harris with 10 percent. Other suppliers in 1978 included AMD, Intel, Intersil, Motorola, National, and Texas Instruments. Overview Table 1 presents DATAQUEST's estimates of worldwide consumption Of bipolar memory. Consumption is expected to grow about 15 percent per year through 1982 to a total of $435 million. The split between ROMs/PROMs and RAMs is expected to remain relatively stable at about 57 percent and 43 percent, respectively. Consumption of bipolar memory by major regions of the world is also presented in Table 1. We estimate that North American consumption was about 76 percent of the total in 1978, but expect it will decline to about 68 percent of the total in 1982. Consumption in Japan is expected to increase from about 12 percent of the total in 1978 to about 16 percent of the total in 1982 while consumption in Western Europe is expected to increase from 12 percent to 14 percent during this time frame. Table 2 presents DATAQUEST's estimates of bipolar memory market shares for the years 1976 through 1978. These shares are believed accurate, but not all RAM production has been identified, especially for older products. Table 3 presents the market shares expressed as a percent of the total. Signetics has gained a number one position in bipolar memory in 1978, and had an estimated 20 percent of the market in 1978. Fairchild is a close second, with about 19 percent market share in 1978. Copyright © 4 April 1979 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpietation and analysis o! infoi mation generally available to the pulalic or relRased by responsible individuals in the subjccL coni[)anies, but is not quaranteed as to accuracy or completeness It does not contain material provided to us in confidence by oui clients This information is not furnished in connection with a sale or offer to sell seem ities or in connection wuh the solicitation oi an offer to buy securities This firm and its parent and/or their officers stockholders, or members of Uneir families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such sccunnes 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO Table 4 presents DATAQUEST's estimates of 1978 North American bipolar memory consumption by technology, i.e., TTL or ECL. The TTL technology accounts for 97 percent of the total 1978 bipolar ROMs/PROMs devices, but only 58 percent of the 1978 bipolar RAM devices. Bipolar ROMs/PROMs The PROM represents the major portion of the bipolar memory market although only a few manufacturers participate in this market segment. PROM sales are closely tied to minicomputer and high-performance microcomputer applications for control store memory. The automotive industry is expected to use large quantities of PROMs to adjust engine control computers for specific "strategies" that are functions of the transmission, axle ratios, etc, used with the engine. Masked ROMs are an insignificant part of the bipolar memory market. Most of the requirement for the ROM function is filled with factory—or distributor—programmed PROMs. We estimate that 10 percent of PROM shipments are programmed by the manufacturers and that another 15-20 percent are prograiraned by distributors. Thus, approximately one-third of the PROM shipments are for "ROM" applications. The economics of mask charges, inventory, and lead times appear to have been resolved in favor of the PROM. Semiconductor manufacturers use four different technologies to fabricate the programming feature of bipolar PROMs. These technologies include nichrome links, titanium tungsten links, polysilicon links, and avalanche-induced migration (AIM). The links technologies open the circuit; the AIM technology completes the circuit. The choice of technology for the link method is held to be primarily a function of the process the manufacturer has available and understands. Nichrome links are said to be the most expensive technology since more process steps are required. Titanium tungsten metallurgy is used for making Schottky diodes and is an integral part Of the process flow for TTL memories. Intersil has chosen not to enter the Schottky-TTL marketplace; therefore, its memories are lower performance since they rely on older gold-doped processing. NEC is the only other manufacturer known to be using the AIM technology. The industry position on relative reliability is that AIM holds a slight positive edge and that the others are essentially equal to each Other. The 16K PROM represents state-of-the-art PROM density. Signetics has been actively shipping its 16K PROM since mid-1978 when its competitors began shipping the 8K PROM, and is reported to have shipped nearly as many 16Ks as its competitors have shipped 8Ks. Signetics reports that it has its 32K PROM ready and is now developing a 64K PROM. Intel is known to be sampling its 16K PROM now. The status of the other suppliers is shown in Table 5. - 2 -'.i Bipolar RAMs The market for bipolar RAMs is currently defined as those appli-cations requiring speeds faster than 50 nanoseconds. However, this speed is continually decreasing as faster MOS RAMs become available. Access times for TTL RAMs are 10-20 nanoseconds for IK devices and 20 nanoseconds for 4K devices . ECL RAMs are now being offered at speeds below 10 nanoseconds and are projected to reach speeds below 2 nano-seconds. The State-of-the-art for bipolar RAMs is illustrated by the following projected product introduction schedule for Fairchild: Time 2Q79 2Q79 3Q79 1Q80 Archi-tecture 1024x4 4096x1 4096x1 16Kxl Tech- Access nology Time (ns> TTL TTL ECL TTL 25 35-45 25-35 35-45 Current (mA) 180 100 120 100-135 Part Number 10475/100475 93471 F10470/100470 Undecided Conclusions Bipolar devices have long been characterized as requiring larger die and consuming more power than MOS devices to achieve their higher Speeds. According to a WESCON paper by Jasper, Shields, and Campbell, these generalizations are not always true. For example, they cite a comparison of the 82S400 and the 2147-3: Maximum Power Access Time Die Size 82S400 (Bipolar) 130mA 2147-3 (MOS) 180mA 45ns 55ns 17K sq. mils 25K sq. mils However, bipolar processes are generally more complex. The com-petition between fast static MOS ROMs and bipolar RAMs is expected to intensify in coming years. Recent MOS devices described by Intel at trade conferences have access times as low as 15 nanoseconds. Willard T. Booth Daniel L. Klesken Mary Ellen Hrouda - 3 ->.^ Table 1 ESTIMATED WORLDWIDE BIPOLAR MEMORY CONSUMPTION''' (Dollars in Millions) 1976 1977 1978 1979 1980 1981 1982 rldwide Total ROMs/PROMs RAMS North America Europe Japan Rest of World $162 $100 $ 62 $128 $ 21 $ 13 $ 0 $205 $115 $ 90 $159 $ 25 $ 21 $ 0 $249 $143 $106 $189 $ 30 $ 30 $ 0 $280 $160 $120 $207 $ 36 $ 37 $ 0 $325 $188 $137 $235 $ 42 $ 45 $ 3 $375 $217 $158 $263 $ 52 $ 56 $ 4 $435 $254 $181 $297 $ 61 $ 69 $ 8 Captive consumption is not included. Source: DATAQUEST, Inc. April 1979 - 4 -J-, Table 2 ESTIMATED BIPOLAR MEMORY MARKET SHARES (Dollars in Millions) AMD 1 Fairchild yj\ Harris 1 Intel Intersil Monolithic Memories Motorola National Semiconductor Signetics Texas Instruments Others Total RAMS $ 0 25 0 1 4 1 3 2 12 6 1 $55 1976 ROMS/ PROMs $ 0 9 15 8 6 18 0 3 10 10 1 $80 Total $ 0 34 15 9 10 19 3 5 22 16 2 $135 RAMs $ 0 31 0 1 0 1 7 2 10 2 36 $90 1977 ROMs/ PROMS $ 2 9 21 10 6 23 2 5 30 6 1 $115 Total $ 2 40 21 11 6 24 9 7 40 8 37 $205 RAMs $ 0 38 0 1 0 1 11 4 12 2 37 $106 Source: 1978 ROMs/ PROMs $ 4 10 25 13 7 27 2 8 38 8 1 $143 Total $ 4 48 25 14 7 31 13 12 50 10 35 $249 DATAQUEST, April 1979 Inc Table 3 ESTIMATED BIPOLAR MEMORY MARKET S H A J f f i S (Percer^t: of Total) I a\ I AMD Fairchild Harris Intel Intersil Monolithic Memories Motorola National Seiniconductor Signetics Texas Instruments Others RAM 0% 45 0 2 7 2 5 4 22 11 2 1976 ROM/ PROM 0% 11 19 10 8 23 0 4 12 12 1 Total 0% 25 11 7 7 14 2 4 16 12 2 RAM 0% 35 0 1 0 1 8 2 11 2 40 1977 ROM/ PROM 2% 8 18 9 5 20 2 4 26 5 1 Total 1% 20 10 5 3 12 4 3 20 4 18 RAM 0% 36 0 1 0 1 10 4 11 2 35 1978 ROM/ PROM 3% 7 17 9 5 18 1 6 27 6 1 Total 2% 19 10 6 3 12 5 5 20 4 14 Total 100% 100% 100% 100% 100% 100% 100% 100% 100% Source: DATAQUEST, Inc, April 1979 ^^ Table 4 ESTIMATED NORTH AMERICAN BIPOLAR MEMORY CONSUMPTION - 1978 (Dollars in Millions) ROMs/PROMS RAMs Total TTL $111 43 $154 Source: ECL $ 4 31 $35 DATAQUEST, April 1979 Total $115 74 $189 Inc. 1 - 7 -Company Fairchild Harris Intel Intersil Monolithic Memories Motorola National Raytheon Signetics Texas Instruments Table 5 PROM TECHNOLOGY AND STATUS Programming Technology Nichrome links Nichrome links Polysilicon links Avalanche-Induced Migration (AIM) Nichrome links; new product to use Titanium Tungsten links Nichrome links Titanium Tungsten links Nichrome links Nichrome links Titanium Tungsten links Status Densities to 4K in production 256x4 in ECL IK family Densities to 8K in production 32K and 64K not expected until 1980 16K now being sampled Densities to 2K in gold-doped TTL 16K scheduled for current introduction; with production late 1979 Densities to 8K TTL; IK ECL 8K in production Densities to 8K; expects to sample the 16K in Q2 1979 16K in volume production 32K believed to be ready for introduction 6 4K in development 8K sampled Q3 1978; 16K expected to be available in 1979 Source: DATAQUEST, Inc, April 1979 - 8 --^ r-M > E ^ S S = S S B ^ ^ S ^ g^j- RESEARCH ASubsJdIarvof A.C.Nielsen Co. ^ INCORPORATED I ^ I I ^ Z W ^ 3 ^ ^ Z 1 1 ^ Z ^ F ^ 1 SIS Code: Newsletters April 4, 1979 CAPTIVE SEMICONDUCTOR MANUFACTURING Introduction Semiconductor manufacturing facilities owned b ' y electronic equipment manufacturers are called "captive facilities." During the last four years, the number of captive facilities has increased from 19 to 43, while the number of merchant suppliers has dropped from 93 to 81. DATAQUEST has maintained an ongoing dialogue with a number of these captive suppliers; this newsletter summarizes their per-spective. The driving force behind captive manufacturing is the continuing increase in complexity of LSI and VLSI circuits. As a result, more and more system functions are being performed within the LSI circuit, forcing electronic equipment manufacturers to seek control of LSI circuit architecture in order to control the architecture of their equipment. The LSI circuits they require have high design costs and low production volumes—a combination that may be unattractive to the merchant semiconductor supplier. The resultant lack of responsive-ness from the semiconductor industry, combined with strong strategic implications for competition, control, and security have led many electronic equipment manufacturers to develop captive semiconductor capability. Captive suppliers represent a significant market for design software and for semiconductor manufacturing equipment; it is esti-mated that they consume betwen 30 and 40 percent of the manufacturing equipment in the United States. The last section of this newsletter deals with the way in which their needs differ from those of the merchant semiconductor firms. The chip is the System LSI chip complexities have now reached the point where a single device may encompass a significant portion of the circuitry in a system. As a result, the performance of the system is more and more determined by the way the circuitry inside the LSI device is inter-connected; therefore, electronic equipment manufacturers desiring to differentiate their products from those of competitors must control the design of LSI devices. Copyright © 4 April 1979 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy Or completeness, It does not contain material provided to us in confidence by our clients This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO As device geometries shrink, LSI computing speeds improve. Eventually, the performance of an LSI device cannot be duplicated with conventional MSI and SSI logic; the physical volume of equipment constructed from these conventional circuits is so large that the logic delays in the wiring are greater than they are inside an LSI chip. Since most mainframes and large minicomputers are sold on a "computations-per-second-per-dollar" basis, competition tends to force computer makers to seek high-speed LSI circuits. This helps explain why Hewlett-Packard has developed its own SOS process and also why many computer manufacturers have become captive suppliers of their own custom designed ECL devices. The high cost of assembling MSI and SSI circuits is another factor that pushes electronic equipment manufacturers toward LSI. A typical system using these devices may have a manufacturing cost for items like printed circuit boards, power supplies, cabinetry, and labor that is many times the cost of the circuits themselves. Table 1 indicates the way these costs change as more complex LSI devices are introduced into the system. Table 1 IMPACT OF LSI ON SYSTEM MANUFACTURING COSTS Component Price Manufacturing Cost per Component Component Price MSI/SSI Design 10 Gates $0.40 $3.14 LSI 100 Gates $ 4.00 $12.00 Gate Arrays 500 Gates 2,000 Gates $20.00 $140.00 $18.00 $ 23.00 per Gate Manufacturing Cost per Gate Total Manufacturing Cost per Gate Component Cost (Percent Of Total) $0.04 0.314 $ .354 11% $0.04 0.12 $ .16 25% $ 0.04 0.036 $ .076 53% $ $ 0.07 0.0115 .0815 86% Source: DATAQUEST, Inc. April 1979 In Table 1, the device price per gate remains relatively constant as the number of gates in the array increases. This reflects current pricing practices in the industry for gate arrays. - 2 -Gate arrays are used in the example because they are more cost-effective than custom LSI devices for the production quantities typical of most computer manufacturers. In the example in Table 1, it is interesting to note that as LSI devices increase in complexity, the component cost constitutes an in-creasing percentage of the total manufacturing cost. This implies that the computer factory of the future may have more capital invest-ment associated with the manufacture of LSI devices than with their assembly. IBM's commitment to gate arrays is well known; there are 10 electron-beam machines at IBM dedicated exclusively to the direct wafer exposure of gate arrays. Currently, IBM has two gate arrays in production, one of 704 gates and one of 1,500 gates. Judging from Table 1, these arrays would seem to be of about the right complexity to minimize total manufacturing cost per gate. Make What You Cannot Buy The semiconductor industry has always felt that captive suppliers cannot be competitive. In one sense DATAQUEST agrees, for there are many examples where head-on competition with the semicon-ductor industry by captives has failed. However, electronic equip-ment manufacturers have many needs that are not filled by the semi-conductor industry. The captive semiconductor manufacturers that focus on satisfying these unfilled needs are usually successful and make a positive contribution to their company's profits. However, "vertical integration" by itself has not proven to be a profitable Strategy; it does not appear viable to build a captive semiconductor facility with the sole objective of capturing the profits that merchant semiconductor suppliers make on standard components. However, the current strategy of focusing on those applications and technologies that the semiconductor industry is unwilling or unable to address appears eminently workable. Semiconductor companies and electronic equipment manufacturers have markedly different perspectives regarding what it takes to be successful in business. These different perspectives cause them to operate their semiconductor organizations in dissimilar manners. Semiconductor manufacturers operate in an almost perfectly com-petitive environment. Indeed, many of them have difficulty convinc-ing equipment manufacturers to buy their product unless a completely equivalent second source is available. They have little or no control over the prices that can be charged and, as a result, tend to focus on cost reduction rather than achieving higher prices through product differentiation. Two factors are of supreme importance in reducing costs: achieving full utilization of plant capacity and obtaining market leadership so that costs can progress down the learning curve more rapidly than those of competitors. Semiconductor manufacturers believe their markets are elastic. If they cut selling prices, they expect that the increase in unit sales will be great enough to cause - 3 -the market to be larger than it was before. By being the price leader one can thereby hope to dominate what is ultimately a larger market. By contrast, electronic equipment manufacturers operate in a market that most economists would characterize as imperfectly com-petitive. Usually, their products are not identical to those produced by others, and the product features are often as important as the price in making a sale. Accordingly, they tend to concentrate more on improving product features than on reducing costs. Equipment manufacturers believe their market is relatively in-elastic compared to the components market. Indeed, most equipment products are segmented into recognizable classes (e.g., small, medium, and large computers) that fit into a definite hierarchy of selling prices, and most manufacturers strive to preserve this hierarchy and avoid pricing that causes products in one class to compete with those in another class. While costs are important, most equipment manufacturers do not attach as much significance to achiev-ing full utilization of plant capacity and to learning curve effects as do the semiconductor manufacturers. Table 2 illustrates how these different perspectives lead to sharply different goals for competitive (merchant) and captive semi-conductor manufacturers. COMPETITIVE AND Competitive (Merchant) Manufacturer Goals Keep factory full. Cut prices to expand market. Improve yields. Sacrifice design time for manufacturing efficiency. Seek second sources for products. Lower components cost. Table 2 CAPTIVE MANUFACTURER GOALS Captive Manufacturer Goals Save capacity for emergencies. Increase component complexity to expand product per f ormance. Seek new uses for excess capacity. Ensure quick turn-around. Strive for unique product features. Expand component complexity to reduce assembly costs. Source: DATAQUEST, Inc. April 1979 - 4 -Semiconductor companies have limited research and engineering capabilities. Typically, these budgets may be 6 percent to 20 percent of sales. In turn, semiconductor component costs may be only 10 percent of the ultimate system selling price. If an electronic equipment manufacturer budgets 10 percent of systems sales for research and engineering, the funds available are equal to 100 percent of component purchases—10 times larger than those available to the component maker. The electronic equipment maker can therefore afford to develop processes and LSI circuits that enhance his products only and do not necessarily have a broad market. Hewlett-Packard's commitment to SOS technology falls in this category. It is a technology that makes HP's products more competitive yet represents a market sufficiently limited that it is unlikely to interest semiconductor firms. Competition, Control, and Security Competition, control, and security represent important strategic factors that motivate the equipment companies to set up their own captive facilities. Some companies are concerned about competition from semiconductor manufacturers integrating upwards into their markets, or about their competitors' use of captive semi-conductor technology. Others seek to incorporate custom LSI devices into their equipment to make it difficult for other equipment makers to copy. Finally, many hope to become more competitive through the cost savings generated by LSI. Some companies build captive semiconductor facilities to gain control of their own future. They seek to control the design of LSI SO that they can control system performance, and look to the captive facility as a means of shortening design times and educating their engineers. Security is the final motivator. The captive facility is seen as providing assured delivery or a second source to merchant suppliers. The existence of a captive facility is also a help in pur-chasing: it can improve a company's negotiating position, assist in vendor qualification, help vendors with delivery problems, and provide support in reliability analysis. Software and Equipment Needs of Captive Suppliers The captive supplier environment is typically characterized by a greater emphasis on circuit development than is typical of the merchant semiconductor companies, by relatively low production volumes, and by a relatively large variation in month-to-month pro-duction rates. These differences lead to software and equipment demands that differ from those of merchant suppliers. Captive manufacturers need software aids to help reduce their relatively high design costs. These software aids include automatic chip layout, automatic wire routing in gate arrays, and automatic - 5 -generation of LSI chip test sequences. Since each design or design variation of an LSI chip is produced in relatively low volume, most captive manufacturers (unlike the merchant suppliers) are willing to sacrifice LSI chip area in order to reduce design time and cost. Even IBM, the largest of the captives, has stated that 4 percent to 20 percent of the area of its 704 gate array chip is associated with extra logic that serves only to make test program generation simpler, Many captive suppliers use their semiconductor fabrication areas as engineering pilot lines for prototyping purposes. Typical pro-duction volumes may be on the order of 100 to 5,000 wafers a month— approximately 5 percent to 30 percent of the volume produced in the typical module of a merchant supplier. Thus, a captive supplier may be satisfied with relatively low throughput capital equipment if it satisfies other requirements. We believe that direct slice writing with electron-beam equip-ment will be particularly appealing to captive suppliers. The relatively low throughput of this equipment will be more than com-pensated for by its ability to handle fine lines and compensate for wafer distortion on a die-by-die basis. Another advantage to captive manufacturers is the fact that this equipment shortens design time by completely eliminating the maskmaking step. Captive suppliers try to maintain a relatively large variety of processes at relatively low production rates—rates that may vary markedly if merchant suppliers are unable to meet current demand for a part. These factors lead captive suppliers to favor flexible, automatic equipment. It is flexible so that it can handle many different processes, and automatic so that the process is programmed into the equipment rather than being in the operator's head. Automatic equipment also has the advantage of reducing the number of operators required, which tends to make line management simpler because the number of operators need not vary widely as production rates change. Howard Z. Bogert - 6 -SIS: Newsletters March 23, 1979 INTEL ANALYSTS' MEETING Introduction DATAQUEST attended the Intel Analysts' Meeting on March 2, 1979. Dr. Robert Noyce made the opening remarl<:s, commenting briefly on the recent change of titles among the top three executives. Dr. Noyce is now Vice Chairman, and Dr. Gordon Moore is Chairman of the Board. Dr. Andrew Grove, formerly Executive Vice President, becomes President of Intel. Dr. Noyce mentioned that the new titles more accurately re-flect the roles that these three executives have already been playing at Intel. The meeting consisted primarily of presentations by Leslie Vadasz and David House on microprocessors, and then a lengthy question and answer session. Intel officers and managers in attendance included: Robert Noyce, Gordon Moore, Andrew Grove, Larry Hootnick, Leslie Vadasz, David House, and Roger Borovoy. # Intel's Microprocessor Strategy Leslie Vadasz, Vice President and General Manager of the Micro-computer Components Division, made the presentation on Intel's micro-computer businesses. He made an interesting comparison between the new MCS-86 family and the older MCS-80 family of microprocessors. He noted that the MCS-86 family had a total of 19 products at the time of its introduction, including components, system hardware, and soft-ware, versus nine products in the MCS-80 family. One year after its introduction, the total MCS-86 family contains 36 total products, whereas the MCS-80 family contained 12 products. He pointed at this situation as an example of the dedication and level of investment by Intel in its MCS-86 family. The product introductions history for these two microprocessor families is shown in Table 1. He showed a chart that compared the complexity of memory devices and microprocessor devices versus time. He then described how a memory device or technology led naturally to a corresponding microprocessor product or family. Table 2 shows the lead memory products and the microprocessor products that evolved from that memory lead product. Mr. Vadasz closed his presentation with the very emphatic state-ment that the Microcomputer Components Division of Intel is the fastest growing division in the Company. Copyright © 23 March 1979 by DATAQUEST - Reproduction Prohibited The content of this report represents our inti^rpIetation and analysIs of information generally available to the public or reiea^eci by lesiionsibU; n i::oi"npleteness. It does not contain material proviided to us in confidence by oui clIents This information is no! fui nistiud in connection wilh a siile o buy secut ities This firm and its parent and/or their officers, stockholders, or members of then families may, from time to Lime, have a lor-ij or sht divirjuals in the ^ubsec; co;r:->c ction with ined and ii lai anieoti as to accuracy ot ] solicitation of an olfcr lo sell oi bLi bLiy such secui it ics | 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO Table 1 Intel Corporation COMPARISON OF MCS-80 AND MCS-86 PRODUCT FAMILIES MCS-80 (1974) Products at Introduction Number of Components System Hardware Software Total Total Products One Year Later Number of Components System Hardware Software Total Total Products Two Years Later Number of Components System Hardware Software T o t a l 3 5 1 MCS-86 iTTrw 7 4 8 19 5 5 2 10 15 11 12 36 9 10 7 26 S o u r c e : I n t e l C o r p o r a t i o n Marcbi 1979 # - 2 -Table 2 Intel Corporation MOS MEMORY LEAD PRODUCTS AND FOLLOWING MICROPROCESSOR PRODUCTS Memory Lead Products Microprocessor Products 1103 (IK Dynamic) 4004, 4040, 8008 2107 (4K Dynamic) 8080 2102 (IK Static) 8021, 8022, 8048, 8049 2716 (16K Dynamic) 8748, 8755, 8741 2147 (4K Fast Static) 8086 Source: Intel Corporation March 1979 - 3 -David House, General Manager of the Microprocessor and Peri-pherals Operation, discussed Intel's microprocessor product lines and their positions in the product life cycle. He noted that the 8086 is Still in the early introduction and distributor stocking portion of its life cycle, while the 8048 mask-programmed microcomputer is in a great many initial design-ins. The 8085 has been in a number of de-sign-ins and is now moving into some fairly good-sized production orders. The 8080 product line has been in existence for several years and is now supported by a good number of second sources. The 4040 is now a commodity product and has passed the peak of its product life cycle. Mr. House indicated that in the first quarter of 1979, Intel expects its quarterly unit shipments of 8085s to exceed its quarterly unit shipments of 8080 microprocessors. He also noted that the 8048 microcomputer had a very substantial step function increase in unit shipments in 1978. It is now Intel's highest volume microprocessor product. The year 1979 will be an important design-in year for the 8086, and Intel expects that 1980 will be the year when the 8086 moves into a number of production programs. Question and Answer Session A lengthy question and answer session followed. 1. Q. How is Intel supporting the service required for its micro-computer systems products? A. About two years ago, Intel made a commitment through its IBM add on memory systems business to set up the sales and service centers required to support a systems business. 2. Q. What is the drag factor associated with Intel's micro-processor products? A. The CPU is becoming a smaller percentage of the total mi-croprocessor revenues. About one or two years ago the CPU represented about 40 percent of the revenues. It is now less than 25 percent and is expected to become less than 10 percent in the future. The major impact has been the large amount of memory being used in microprocessor systems. The average memory size for an 8086 micro-processor system is about 128K bytes of memory. 3. Q. How much do you sell in kits? A. Kit sales of microprocessors are not the majority but still represent an important part of our business. - 4 -4. Q. How many 8086 design-ins displaced minicomputers? A. This was not a significant number. The microprocessor and the minicomputer business do not have an extensive overlap. We note that Intel stated that it shipped more 8080s in 1978 than Digital Equipment Corporation has shipped mini-computers in its total corporate lifetime. 5. Q. Discuss the 8022 microprocessor and the new analog micro-computer recently announced. A. The 8022 microcomputer fits a broad number of applications very well including consumer, energy management systems, and industrial processing. The marketplace is much broader than was originally expected with industrial processing turning out to be significantly larger than originally ex-pected. The analog microcomputer is designed to handle signal processing and filtering applications. Intel is not totally sure about the breadth of the applications or the total unit volumes. The answer must evolve over time. 6. Q. Compare the Z8000 and the 8086 microprocessors. A. The basic difference between the 8086 and Z8000 is archi-tecture. The State of the art in computer architecture in the late 1960s and the early 1970s was very much oriented toward assembly level languages and this spawned the PDP-11 and ECLIPSE series of minicomputers. However, in the late 1970s, there was a need to focus on compiler-generated code with a more regular and organized software system. This is the philosophy behind the 8086 architecture. The compiler group that developed P/LM-1 for Intel was instrumental in the basic architecture design of the 8086. The Z8000 is a generalized architecture and uses more memory than the 8086 to do the same function. 7. Q. Are there any patents on the 8086 family? A. Several patents have been applied for on the bus structure Of the 8086. 8. Q. Comment on the LSI-11 versus the 8086. A. The overlap between these products is minimal. Some users need the maturity of the PDP-11 product line and quickly choose the LSI-11. However, the 8086 is finding many applications where the LSI-11 is not a factor in the market. 9. Q. In light of limited resources, what might be expected from Intel in terms of memory products? - 5 -A. Intel must support its sole source products even at the ex-pense of multiple sourced products such as the 16K dynamic RAM. 10. Q. Discuss the product life cycle of Intel's memory products. A. Intel will cease producing the 1103 IK dynamic RAM in 1979. There are only two major users now. The 4K dynamic RAM is in the mature part of its product life cycle while the 16K dynamic RAM is still building. We don't expect any significant quantity for the 64K dynamic RAM until 1981. The IK Static RAM is a mature product, the 4K static is Still growing. 11. Q. When will Intel's capacity catch up with its demand? A. Not until the economy slows a little. We can't accelerate the rate of our capacity additions any more than we are currently doing. Our Fab V facility in Portland, Oregon, is now processing its first silicon, and in February Intel broke ground in Phoenix, Arizona, for its largest plant ever. 12. Q. What are the lead times on some of your major products? A. Lead times for EPROMs are about 48 weeks; the 2147 4K Static, about two weeks; and the 8086 is available from Stock. The EPROM microprocessor products (8748/8755/8751) are running some 30-40 weeks. The 8085 has about a 20-week lead time. Note that the real demand on EPROMs is nowhere as high as the 48-week lead time would suggest. This is one area where significant double ordering exists. The overall average lead time for Intel products is about 20 to 26 weeks. 13. Q. What level of capital spending do you project for 1979? A. Capital spending is projected at $120 million in 1979. 14. Q. How will Intel handle its short-term debt? A. We are looking at alternatives to roll it over into longer-term debt, but will have to look at the economy over the next six months. 15. Q. Comment on the Intel add-on memory business since the IBM announcements. A. Intel's add-on memory business serves two purposes for Intel. First, it provides flexibility on the upside when memory component output is excessive. Second, it puts Intel into direct contact with the commercial end users of data processing products and exposes it to the marketing - 6 -and servicing problems of its customer base. Previously, Intel did not l i a v e any good contact in that area. The ex-perience helps Intel to understand how complex silicon systems are moving toward the data processing users. 16. Q. Discuss the magnetic bubble memory efforts at Intel. A. The technology of magnetic bubbles is reasonably compatible with that of silicon. Intel had the opportunity to acquire a good group of people and did so. The program is pro-gressing well. 17. Q. Is the Intel lead time on unique or leadership products in-creasing or decreasing? A. In the microprocessor area, it is definitely increasing since one must consider total system capability. It is also increasing in HMOS. Intel is somewhat surprised at the length of time it is taking our competitors to catch up in EPROMs. However, it isn't totally unexpected, as it takes a good understanding of oxides to succeed in EPROMs. 18. Q. What will keep Intel ahead of the competition in the next 10 years? A. We expect fewer new entries because of the high capital cost of entry. Intel is about to become the largest semi-conductor research institution in the world. 19. Q. C o i t m i e n t on the raultichip substrate approach with IBM. A. Intel Started in business with three major goals: Schottky TTL, silicon gate MOS, and multichip substrates. It has achieved the first two, but not the last as priorities and goals have changed. IBM, however, has become the world leader in multichip substrates. Intel focuses its efforts on more complex integrated structures. We believe this approach better serves the merchant market needs. 20. Q. Why did IBM go to the multichip approach? A. IBM gets a density advantage with more bits per board or system. However, we still find the cost of bumps on the chips too high. It is possible you may get a cost advantage if you can put the entire mainframe memory on a single board. 21. Q. Comment on your start-up costs and the possible effect on margins. A. Start-up costs are a continuing aspect of our doing business. It is not a one-time thing for Intel. We hope this doesn't have a major impact on margins. - 7 -22. Q. Comment on the total microcomputer market in 1978 and the outlook for the future. A. In the past five years, the microcomputer market grew slowly but Steadily and continued unabated through the 1974-75 recession. Now microcomputer unit shipments are growing at large rates, especially in the last six months. The present growth rate is probably greater than 50 percent per year. 23. Q. How is the codec being accepted by telecommunication com-panies? A. Much Slower than originally expected. However, this might have been anticipated when one analyzes the telecommunica-tions industry. We expect that there will be different designs including per-line codecs and shared-line codecs. Telephone networks are going toward a more distributed network which favors the per-line codec Intel now has design activities with all major telecommunication customers in the free world except NTT. 24. Q. Can Intel maintain its pretax margins of about 22 percent? A. Our interest expense is up this year and next, but we need to keep margins high to fund future growth. 25. Q. What growth can we expect in the first quarter of 1979 versus the fourth quarter of 1978? A. The dollar growth will probably be about the same as the fourth quarter of 1978 versus the third quarter of 1978, but this represents a declining percentage growth. 26. Q. Will the availability of capital equipment from the suppliers be a problem? A. No. We don't expect it to be. We've been able to order and plan for equipment and materials well in advance of our needs. 27. Q. Will Intel move into Japan? A. We need to have a scenario by which we can move a plant there successfully, but we do not presently have one. However, our business in Japan is quite strong. The Japanese are buying more in foreign markets, so this helps Intel. 28. Q. Comment on the size of your 64K dynamic RAM effort. A. It is a major effort at Intel. Intel has a sizable dedicated effort on dynamic RAMs. - 8 -29. Q. Discuss the Mostek and Intel agreements on 64K dynamic RAMS. A. We are trying to get a common pin-out agreement, but have not yet reached that point. 30. Q. Is automotive electronics a good business with good margins? A. There are two parts to this market: engine control, and comfort and convenience. Intel's effort is with the engine control. The semiconductor industry must learn to meet the Strict delivery requirements and the reliability require-ments of the auto industry. Daniel L. Klesken - 9 -SIS Code: Newsletters March 23, 1979 UPDATE ON DISCRETE SEMICONDUCTORS Summary This newsletter is the first of a regular series dealing with discrete semiconductors. DATAQUEST estimates of worldwide consumption of discrete devices are presented in Table 1. Total consumption of discrete devices is expected to grow at a compound annual rate of 7.2 percent between 1978 and 1982. In this period power transistors, power diodes (rectifiers) , and thyristors are expected to have strong compound annual growth rates of 8.7 percent, 9.2 percent, and 10.4 percent, respectively. Small signal transistors and small signal diodes are likely to grow more slowly, at compound annual growth rates of 3.1 percent and 3.8 percent, respectively. DATAQUEST estimates of North American consumption of discrete devices are presented in Table 2. Total North American discrete con-sumption is expected to grow at an annual compound growth rate of 6.0 percent, with power transistors growing at 7.3 percent, power diodes (rectifiers) at 7.2 percent, and thyristors at 8.6 percent. Overview The microprocessor's pervasive growth into areas not previously served by electronics provides a major impetus for the growth of dis-crete devices. These new applications, including automobiles, appliances, and telecommunications, require discrete devices for power supply rectification and regulation, power handling, and actua-tion. The market for small signal transistors and diodes has been adversely affected by the integration of discrete devices onto inte-grated circuit (IC) chips. Improved technology and expanded applications for integrated circuits have been the driving forces behind the gradual shrinking of the small signal discrete markets. The major technological events impacting the discrete device world recently have been associated with the packaging. In power transistors, plastic packages capable of handling up to 200 watts are now appearing. Other packaging activities include the use of a steel TO-3 package for better seal integrity and cosmetics. General Instrument's "Super Rectifier," utilizes lead braze under glass with a plastic overmold and is reported to be a very successful approach to achieve high quality and low cost. Copyright© 23 March 1979 by DATAQUEST - Reproduction Prohibited The c a m biiv conten pletene securIt t c ss. es f thi s report represents o It does not contain mater Thi firm and its parent ur a ^ interpretation provided to us Td/or their off an in ce d analysis of in confidence by c s, stockholders, o o mation clients qen Th members c erally s info f thei aval m a t fan-able on i ilies to the pu not f may, u r n rorr jlic or shed ir released by c o n time to tin Taction Te, hav respon with a " a long ibie i sale o or sh -idividL r offet-3rt pos als in to se tion the s 1 secu n the jbject compan rities or ir securities c o n m e n es. but lectio loned is not with and m f)L t h ay aianteed as to ace = solicitation of an jracy offe sell or buy such securit o r t o es. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 TWX (910) 338-7695 / DATAQUEST CPTO Unitrode's "Chip Strate" package places a thyristor chip on a suitable ceramic substrate; it can be used as a stand-alone package in some applications, or it can be incorporated in an enclosure. For industrial control applications, some manufacturers are making a hybrid assembly with diodes, Silicon Controlled Rectifier (SCR)/Triac, and possibly an IC, to facilitate use in controllers. This packaging concept is known by several names including "Power Mod" (FMC), "Power Cube" (GE), and "Paceback" (International Rectifier). However, packaging is not the only area benefiting from tech-nological innovation. Schottky rectifiers are being developed and introduced to satisfy the demands of the switching power supply manu-facturers for rectifiers with low forward voltages for increased efficiency. The switching power supply is rapidly becoming the most popular power supply design, and the switching power supply market is expected to grow nearly 30 percent per year. Ballasts for fluorescent lamps are now being implemented with small switching power supplies. Virtually every rectifier manufacturer (FMC, Inter-national Rectifier, ITT, Motorola, TRW, Unitrode, Varo) is starting production of Schottky rectifiers. The VMOS transistor represents a major process innovation in the power transistor segment. The fast switching speeds and low "ON" voltage provide the VMOS device with the potential to replace the traditional bipolar transistor in many applications and to open many new ones. For example, the major deterrent to using semiconductors to control automotive lighting has been the voltage loss across the power transistor; VMOS technology promises to remove that restric-tion. The market for VMOS is only beginning: the present market is about $2 million; Fairchild, Siliconix, and Supertex are the leading suppliers. Nearly all power transistor manufacturers are installing or developing VMOS processing. Selenium rectifiers are still being produced by a few manu-facturers as replacement items for older TV and other entertainment products. Triacs are the fastest growing part of the thyristor segment due to the demands for AC control in appliances; the microwave oven is a very large consumer of triacs in current ratings up to 40 amperes. Hair dryers are large consumers of small SCRs. In the European market. Philips is estimated to be the largest supplier followed by Siemens, Motorola, Texas Instruments, ITT, AEG Telefunken, Sescosem, and RCA. The total discrete market in Europe is reported to be flat, with power transistors enjoying an increasing market. The epitaxial-base general purpose power transistor is built Offshore by nearly all of the major suppliers; for example. Inter-national Rectifier builds its transistors in Mexico and India. - 2 -The discrete market is dominated by Motorola in all categories except thyristors, where it is an important competitor, and small signal diodes, where it does not participate. Texas Instruments, General Electric, ITT, RCA, and Fairchild follow for U.S.-based manu-facturers. The remainder of the U.S. market consists largely of com-panies serving special interest markets with narrow product lines. The major Japanese manufacturers, Hitachi, Matsushita, Nippon Electric, and Toshiba are each roughly one-half the size of Motorola in worldwide discrete sales. Mitsubishi's sales are approximately one-half of the other Japanese suppliers. The RF power transistor, which primarily serves the communica-tions industry, is enjoying stable growth fed by mobile radio and pocket pagers. Approval of 900 MHz pocket paging systems is expected to cause significant new growth. Touch-Tone telephone systems are also viewed as a growth opportunity for this device. The market for the small signal diode is less vulnerable to integration than is the small signal transistor market, because very large numbers of small signal diodes are used as transient suppressors in systems using MOS. Metal-can small signal transistors are becoming rare except in high reliability applications. The cost of metal has increased, and acceptance of the plastic package by most computer manufacturers has removed most of the demand. U.S.-Based Suppliers A listing of the major U.S.-based suppliers in each of the dis-crete devices categories follows: Small Signal Diodes Fairchild, General Electric, General Instrument, ITT, Texas Instruments, and Unitrode. Small Signal Transistors Amperex, Communication Transistor Corp. (CTC), Fairchild, General Electric, Intersil, ITT, Motorola, National Semiconductor, RCA, Raytheon, Signetics (DMOS), Siliconix (principally FET), Sprague, Texas Instruments, and TRW. Zener Diodes Fairchild, ITT (to 5 watts only), MicroSemiconductor, Motorola, Semtech, Texas Instruments, and unitrode (primarily military). Teledyne is withdrawing from the zener market. Rectifiers (Power Diodes) Fairchild, FMC, General Electric, General Instrument, Inter-national Rectifier, ITT, Motorola, National Electronics, Semtech, Sensitron, Texas Instruments, TRW, Unitrode, Varo, and Westinghouse. - 3 -Power Transistors Amperex, CTC, Fairchild, General Electric, Germanium Power Tran-sistors, Motorola, National Semiconductor, Power Tech, RCA, Siliconix (VMOS), Solid State Scientific, Solitron, Supertex (VMOS), Texas Instruments, TRW, and Unitrode. Thyristors FMC, General Electric, Hutson, International Rectifier, Motorola, National Electronics, RCA, Teccor, Texas Instruments, Unitrode, and Westinghouse. Willard T. Booth Daniel L. Klesken - 4 -Table 1 ESTIMATED WORLDWIDE DISCRETE SEMICONDUCTOR CONSUMPTION (Dollars in Millions) 1978 1979 1980 1981 1982 Compound Annual Growth Rate 1978-1982 Total Discrete $2,825 $2,987 $3,207 $3,460 $3,730 7.2% Transistor Small Signal Power Diode Small Signal Power Zener Thyristor Other $1 $1 $ $ ,387 744 643 ,008 278 595 135 298 132 $2 $1 $ $ ,451 754 697 ,068 285 639 144 326 142 $2 $1 $ $ ,540 777 763 ,161 302 700 159 353 153 $1 $1 $ $ ,641 811 830 ,254 312 769 173 393 172 $1. $1 $ $ ,739 840 899 ,354 323 846 185 442 195 Source: 5.8% 3.1% 8.7% 7.7% 3.8% 9.2% 8.2% 10.4% 10.2% DATAQUEST, Inc March 1979 Table 2 ESTIMATED NORTH AMERICAN DISCRETE SEMICONDUCTOR CONSUMPTION (Dollars in Millions) Total Discrete Transistor Small Signal Power Diode Small Signal Power Zener Thyristor Other 1978 $897 $430 207 223 $310 69 178 63 $115 $ 42 1979 $943 $450 210 240 $324 72 187 65 $125 $ 44 1980 $996 $474 216 258 $343 74 200 69 $132 $ 47 1981 $1,064 $ $ $ $ 504 227 277 366 75 218 73 143 51 1982 $1,133 $ $ $ $ 528 232 296 388 78 235 75 160 57 Compound Annual Growth Rate 1978-1982 6.0% 5.3% 2.9% 7.3% 5.8% 3.1% 7.2% 4.5% 8.6% 7.9% Source: DATAQUEST, Inc March 1979 - 5 -1 .' ^ E ' s s ^ S =^= ^ = = ^^g RESEARCH ^SubsJdlaryofA.C. Nielsen Co. 7 INCORPORATED I ^ I ^ M W & B ^ H ^ H 1 1 ^ H F 4 ip SIS Code: Newsletters March 19, 1979 MOS MICROPROCESSOR SHIPMENTS Summary Worldwide shipments of MOS microprocessors in the fourth quarter Of 1978 were an estimated 8.4 million units up about 13 percent over estimated third quarter shipments of 7.4 million units. For the year 1978, total microprocessor shipments were an estimated 25.8 million units up 206 percent from an estimated 8.4 million units shipped in 1977. Single-chip microcomputer shipments in the fourth quarter were an estimated 6.1 million units and represented about 72 percent of total fourth quarter microprocessor shipments. In 1978, an estimated 17.4 million single-chip microcomputers were shipped representing about 67 percent of all microprocessor shipments in 1978. During 1978, shipments of 4-bit microprocessors were an esti-mated 16.3 million units representing about 63 percent of the total. Total shipments of 8-bit microprocessors were about 9.1 million units, or 35 percent of the total microprocessor shipments. Sixteen-bit products represented about 1 percent of the total shipments with an estimated 355,000 units. # Quarterly Microprocessor Shipments Table 1 presents DATAQUEST estimates of worldwide microprocessor CPU Shipments for the fourth quarter of 1978. The estimated ship-ments refer to CPU chips only and do not include any I/O or peripheral chips. Estimated shipments in the fourth quarter were about 8.4 million units, up about 13 percent over the previous quarter. This was the smallest quarter-to-quarter change in 1978, but is not totally unex-pected in light of the seasonality of the toy, game, and appliance markets that use these microprocessors. By comparing previous DATAQUEST newsletters on MOS micro-processor shipments, one notes that total annual shipments have risen dramatically in the past three years. In 1976, total estimated worldwide shipments were 2.4 million units, 1977 total shipments were 8.4 million units, and 1978 shipments were up dramatically to 25.8 Copyright © 19 March 1979 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of informaiion generally available to the public or released by responsible individua completeness It does not contain material provided to us in confidence by our clients. This information is not furnished in connection with a sale or offer t buy securities This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short posit s in the subiect companies, but is not guaranteed as to accuracy or ) sell securities or in connection with the solicitation of an offer to on in the securities mentioned and may sell or buy such securities 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 TWX (910) 338-7695 / DATAQUEST CPTO million units. Part of the large growth is due to high volume usage of 4-bit microcomputers in game and appliance applications. We ex-pect this rapid growth to continue for the low-cost microcontrollers as well as many other microprocessor families. Table 2 presents DATAQUEST's estimates of worldwide shipments of single-chip microcomputers. Estimated fourth-quarter shipments of microcomputers were 6.1 million units, up about 13 percent over esti-mated third-quarter shipments of 5.4 million units. In the fourth quarter, shipments of single-chip microcomputers represented about 72 percent of total shipments, up sharply from 55 percent of the total in the first quarter of 1978. 4-Bit Microprocessors Table 3 presents our estimates of worldwide microprocessor ship-ments by bit length. Shipments of 4-bit microprocessors in the fourth quarter of 1978 are estimated at 5.5 million units, up about 9 percent over estimated third quarter shipments. For the entire year 1978, worldwide shipments of 4-bit microprocessors reached 16.3 million units, up very dramatically from an estimated 4.1 million units in 1977. In the fourth quarter of 1978, the shipments of 4-bit micro-processors continued to grow, but at a slower rate than in previous quarters. This slowing in shipment growth is primarily attributable to the seasonality of the end-user markets which these devices serve. The toys, games, and appliance markets are very large users of 4-bit microprocessors. Prices for 4-bit microprocessors are in the $1.50 to $2.50 range for deliveries in the first and second quarters of 1979. These prices represent shipments of quantities in excess of 100,000 units. We expect to see continued significant growth in this 4-bit micro-processor market because of their utility as low cost controllers for consumer applications. 8-Bit Microprocessors Worldwide shipments of 8-bit microprocessors in the fourth quarter of 1978 were an estimated 2.7 million units, up 22 percent over estimated third—quarter shipments. This is the first strong quarter-to-quarter gain for 8-bit microprocessors since the first quarter of 1978. Total 1978 shipments of 8-bit microprocessors were an estimated 9.1 million units, more than double the estimated 4.1 million units shipped in 1977. Prices of 8-bit microprocessors still remain in the $4.00 to $8.00 range for deliveries in the first and second quarters of 1979. Prices have been relatively stable during the last quarter and, in some cases, have actually increased. Because of the large demand for 8-bit single-chip microcomputers, such as the 3870 and the 8048, the - 2 -# prices for these devices have actually increased during the first quarter of this year. In late fourth quarter 1978, large quantity orders were being shipped for $5.00 to $5.50. In mid-first quarter 1979, increased demand and limited supply actually forced prices up to the $6.50 to $7.00 range. We expect these higher prices to con-tinue well into the second half of 1979 until additional capacity becomes available. Quarterly shipments of several major 8-bit microprocessor families are presented in Table 4. The quarter-to-quarter increase in shipments is generally declining because of the maturity of several of these products. The greatest emphasis now appears to be in the single-chip, 8-bit microcomputers. During the fourth quarter, 8-bit microcomputers comprised 23 percent of the total 8-bit micro-processor Shipments, up from 13 percent in the second quarter of 1978 and 16 percent in the third quarter. 16-Bit Microprocessors .Worldwide shipments of 16-bit microprocessors in the fourth quarter of 1978 were an estimated 106,000 units, up about 8 percent over estimated third quarter shipments. We do not expect the 16-bit microprocessor shipping rates to increase dramatically for several more quarters until more participants have entered the market and these devices have passed the design-in stage. Later in 1979, as some products move toward first production stages, unit volumes should begin to grow dramatically. Announced prices on some 16-bit microprocessor products fell in the first quarter of 1979. However, since most of these products are not available in large production quantities yet, their higher unit prices for quantities under 100 are not totally representative. We understand that the TMS-9980 is available for $10.00 to $15.00 in 1,000-unit quantities, while the 8086 is still priced above $50.00 in quantities under 1,000. The drag factor for peripherals, I/O, and memories is an important factor for 16-bit devices. Many of the new 16-bit product designs are using about 128K bytes of memory as compared with 16K to 32K bytes of memory for typical 8-bit microprocessor applications. This heavy usage of memory, together with peripherals and I/O, leads to drag factors in the range of 7 to 12 and increasing as high as 15 to 20 in some cases. It is dangerous, however, to generalize about drag factors because they vary so dramatically depending upon application. Daniel L. Klesken James F. Riley - 3 -Table 1 ESTIMATED WORLDWIDE SHIPMENTS OF MOS MICROPROCESSORS (Units in Thousands) 1978 Company AMD AMI Fairchild General Instruments Harris Hitachi Hughes Intel Intersil MOS Technology Mostek Motorola National NEC RCA RocKwell Sescosem Signetics Synertek Texas Instruments Zilog MPU Products 8080A 8085 6800 S2000 F8 3870 6800 CP-1600 PlC-1650 6100 HMCS-40 6800 1802 4004 8008 8080A 8048/8021 8748 8085 8086 6100 6500 F8 Z80 3870 141000 6800 6802 3870 COPS 4004 IMP 8080A SC/MP PACE COM-4 8080A 8085 Z80 1802 PPS-4 6500 6800 2650 8048 6500 TMS 1000 TMS 8080A THS 9900 Z80 Bits 8 8 8 4 8 8 8 16 8 12 4 8 8 4 8 8 8 8 8 16 12 8 8 8 8 4 8 8 8 4 4 4 8 8 16 4 8 8 8 8 4 8 8 8 8 8 4 8 16 8 MOS Process N N N N N N N N N C p&c N C P P N N N N M C N N N N C N N N N&C P P N P P N N N N C P N N N N N P&C N N N 1977 Total 165 0 89 0 655 0 15 31 0 13 140 25 10 215 124 510 95 0 55 0 16 280 90 85 20 0 435 0 O2 S/A^ 110 55 145 189 47 225 162 0 0 222 575 225 20 39 0 250 2,825 100 95 95 1st Qtr. 90 0 35 0 110 3 55 10 75 5 85 10 5 42 28 165 60 0 50 0 8 50 50 70 20 0 120 5 5 300 30 20 85 65 18 150 70 0 0 75 400 260 5 20 0 325 1,400 30 40 90 2nd Qtr. 105 0 30 9 130 5 45 20 95 5 95 15 8 42 28 170 100 0 80 1 10 55 30 50 50 0 140 20 10 500 35 20 90 70 18 225 85 0 0 75 550 200 6 25 0 225 1,800 30 44 100 3rd Qtr. 115 s -^ 50 8 190 5 80 15 105 5 110 20 10 40 25 180 150 5 95 10 10 60 35 60 75 5 150 65 15 675 35 20 100 100 25 525 90 5 5 85 675 75 7 35 s 60 3,000 40 48 150 4 th qtr. 125 5 55 12 200 10 90 15 175 7 120 25 12 35 22 190 170 25 125 13 10 60 45 80 205 15 160 90 40 850 30 20 100 100 25 600 60 25 25 90 650 60 7 45 S 70 3,200 35 53 210 Total 435 5 170 29 630 23 270 60 450 22 410 70 35 159 103 705 480 30 350 24 38 225 160 260 350 20 570 180 70 2,325 130 80 375 335 86 1,500 305 30 30 325 2,275 595 25 125 S 680 9,400 135 185 550 Total Microprocessors Percent change from previous quarter S = Sampling ^N/A = Not Available 8,447 4,539 5,446 7,445 8,381 25,811 34.1% 20.0% 36.7% 12.6% Source: DATAQOEST, Inc. March 1979 - 4 -Table 2 ESTIMATED WORLDWIDE SHIPMENTS OP SINGLE-CHIP MICROCCMPUTERS (Units in Thousands) 1978 Company AMI Fairchild GI Hitachi Intel Mostek Motorola National NEC Rockwell Texas Instruments MPU Products S2000 3870 PIC-1650 HMCS-40 8048/8021 8748 3870 3870 141000 COPS CCM-4 PPS-4 IMS 1000 1977 Total 0 0 0 140 95 0 20 0 N/A-^ 225 575 2,825 1st Qtr. 0 3 75 85 60 0 20 5 0 300 150 400 1,400 2nd Qtr. 9 5 95 95 100 0 50 10 0 500 225 550 1,800 3rd Qtr. 8 5 105 110 150 5 75 15 5 675 525 675 3,000 4 th Qtr. 12 10 175 120 170 25 205 40 15 850 600 650 3,200 Total 2, 1. 2 -i. 29 23 450 410 480 30 350 70 20 ,325 ,500 ,275 ^400 Total 3,880 2,498 3,439 5,353 6,072 17,362 N/A = Not Available Source: DATAQUEST, Inc. March 1979 - 5 -Table 3 ESTIMATED WORLDWIDE SHIPMENTS OF MICROPROCESSORS BY BIT LENGTH (Units in Thousands) 1978 Total Percent change from previous quarter 8-Bit Products 57.8% 35.0 55.5% 8.6% General Instruments CP-1600 Intel 8086 National PACE Texas Instruments TMS 9900 Total Percent change from previous quarter 173 68 13.3% 83 98 22.1% 28.1% Source: 106 8.2% 4-Bit Products AMI Hitachi Intel Motorola National NEC Rockwell Texas Instruments MPU Products S2000 HMCS-40 4004 141000 COPS 4004 IMP COM-4 PPS-4 TMS 1000 1977 Total 0 140 215 ° 1 N/A-^ 110 55 225 575 2,825 1st Qtr. 0 85 42 0 300 30 20 150 400 1,400 2nd Qtr. 9 95 42 0 500 35 20 225 550 1,800 3rd Qtr. 8 110 40 5 675 35 20 525 675 3,000 4 th qtr. 12 120 35 15 850 30 20 600 650 3,200 Total 29 410 159 20 2,325 130 80 1,500 2,275 9,400 4,145 2,427 3,276 5,093 5,532 16,328 AMD AMI Fairchild General Instruments Hitachi Hughes Intel MOS Technology Mostek Motorola National NEC RCA Rockwell Sescosem Signetics Synertek Texas Instruments Zilog Total Percent change from previous quarter 12-Bit Products Harris Intersil Total -Percent change from previous quarter 16-Bit Products 8080A 8085 6800 F8 3870 6800 PIC-1650 6800 1802 8008 8080A 8048/8021 8748 8085 6500 F8 Z80 3870 6800 6802 3870 8080A SC/MP 8080A 8085 Z80 1802 6500 6800 2650 8048 6500 TMS 8080A Z80 6100 6100 165 0 89 655 0 15 0 25 10 124 510 95 0 55 280 90 85 20 435 0 0 145 189 162 0 0 222 225 20 39 0 250 100 95 4,100 13 16 29 90 0 35 110 3 55 75 10 5 28 165 60 0 50 50 50 70 20 120 5 5 85 65 70 0 0 75 260 5 20 0 325 30 90 2,031 18.8% 5 _8 13 30.0% 105 0 30 130 5 45 95 15 8 28 170 100 0 80 55 30 50 50 140 20 10 90 70 85 0 0 75 200 6 25 0 225 30 100 2,072 2.0% 5 10 15 15.4% 115 s -^ 50 190 5 80 105 20 10 25 180 150 5 95 60 35 60 75 150 65 15 100 100 90 2 5 85 75 7 35 S 60 40 ISO 2,239 8.1% 5 10 15 0% 125 5 55 200 10 90 175 25 12 22 190 170 25 125 60 45 80 205 160 90 40 100 100 60 15 25 90 60 7 45 S 70 35 210 2,726 21.8% 7 10 17 13.3% 435 5 170 630 23 270 450 70 35 103 705 480 30 350 225 160 260 350 570 180 70 375 335 305 17 30 325 595 25 125 S 680 135 550 9,068 22 38 60 31 0 47 95 10 0 18 40 20 1 18 44 15 10 25 48 15 13 25 53 60 24 86 185 355 DATAQUEST, Inc. March 1979 - s -Table 4 ESTIMATED 8-BIT MICROPROCESSOR SHIIMENTS BY TYPE (Units in Thousands) 1978 Microprocessors 8080A F8 6800 6500 Total Numbers in this table include all manufacturers of these types. 1977 Total 1,082 745 584 755 1st Qtr. 440 160 225 635 2nd Qtr. 480 160 236 480 3rd ^tr. 525 225 307 195 4 th Qtr. 510 245 337 230 Total 1,955 790 1,105 1,540 3,166 1,460 1,356 1,252 1,322 5,390 Source: DATAQUEST, Inc. March 1978 - 7 -xi. ^ mmjw- R E S E A R C H Ldiaryof A.C. NioUenCo. ^ li)CORPORATED i N I ^ S V l f ^ S L M ^ Z ^ I I S H SIS Code: Newsletters March 16, 1979 SILICON ON SAPPHIRE S"">"^ary ^, ]/\^ ^ In the four years .
.
e d T n c e DATAQUEST published its "Silicon on Sapphire" (SOS) note^oc^ section, SOS technology has been established as a ^ai5le~ technology^ Substantial commitments by several major manufacT^3re1^^-havo advgriced the technology, thus removing much of the uncertainty that it faced in earlier years. While major technical problems remain, the recent announcements of the HP-3000 Series 33 and HP 300 (AMIGO) computers have demonstrated that an SOS-based system can now compete in a major commercial systems market. However, a significant commercial market at the component level still does not exist. H-P's vertically integrated operation and its corporate commitment to SOS are felt to be important keys to bringing SOS to market. Overall market penetration has been much slower to achieve than had been forecast in 1973-74. On the other hand, many major tech-nical problems have been overcome, and SOS has found a place in several diverse applications. The 1978 component-level SOS market is estimated to have been $15 million in 1978, and is expected to double to approximately $30 million in 1979. SOS activity at a dozen companies lends credence to the belief that the industry continues to look upon SOS as a potentially com-petitive technology. In 1978, each of the high-volume MOS manuf-acturers, Intel and Motorola, increased its corporate commitment to the SOS technology, joining long-standing SOS programs at Hewlett-Packard, RCA, and Rockwell. There continue to be a number of lower-level programs at companies that wish to stay abreast of developments but that lack resources or commitment to forcefully develop the tech-nology. SOS Technological Evolution In the semiconductor industry, many technologies and process concepts have continued to be proposed and researched, but frequently they are not developed. SOS fits this pattern to a large degree. In the early 1970s, every major semiconductor firm worldwide experimented with a small number of SOS wafers (the sales of which Copyright © 16 March 1979 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy oi completeness It does not contain material provided to us in confidence by our clients. This information is not furnished in connection with a sale or offer to sell secuiities or in connection with the solicitation of an offer to buy securities This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 TWX (910) 338-7695 / DATAQUEST CPTO sustained the life of Inselek in this time period). During this time frame, relatively major technological advances were being made in both silicon PMOS and NMOS. Profits could be made by simply improving device yields, reducing critical dimensions (from 10 micrometers to 7 micrometers, then to 5, and finally to 3-4 micrometers), and increasing manufacturing volume. From the beginning, SOS has promised an exceptionally low speed-power product unattainable in bulk silicon technology; but all the test data indicated that it could not be achieved profitably in volume manufacturing. SOS devices also feature higher noise immunity, operate over a wider temperature range, and have much-increased radiation hardness over devices built on silicon substrates. These qualities have provided the basis for a steadily growing space and military market since the early 1970s. Finally, SOS is particularly well suited for use in VLSI applications because: (1) the insulating substrate is inherently free of defects between transistors; and (2) the payoff for lower power will become increas-ingly advantageous as geometries become smaller. Current Technical Status Two major technical limitations have slowed the rate of develop-ment of commercially available SOS products. First, sapphire wafers of adequate quality remain very expensive and in short supply. From a user's point of view, only Union Carbide (UCC) sapphire is of adequate quality for widespread SOS production use today. RCA's Edge defined. Film fed. Growth Process (EFG) wafers can match the ~UCC wafers in"surface quality, and RCA is now moving its EFG process from its research facility to its production facility in Mountain Top, New Jersey, for wafer production. Allied Chemical and Kyoto Ceramics currently manufacture EFG sapphire wafers. High quality EFG wafers should become available in 1979. UCC is also expanding its sapphire wafer production near the lower-cost Columbia River hydroelectric power. Prices to date have shown little tendency to decline quickly, but price declines may speed up, possibly as increased demand for sapphire substrates makes market entry more lucrative. Second, despite a number of technical advances, the poor quality of the silicon-sapphire interface continues to limit device per-formance. The silicon epitaxy layer on the sapphire is of very poor crystal quality. Recently, it was reported that the crystal Structure of the silicon epitaxy layer could be destroyed by heavy silicon implants into silicon at liquid nitrogen temperature. The implant process was done in a manner that left the epitaxy surface silicon undamaged. This surface layer acts as the seed crystal for the recrystalization or regrowth process performed at 550 C. The resultant silicon crystal is almost free of crystal defects. It may now be possible to manufacture dynamic RAM and bipolar devices via SOS, if the carrier mobility and lifetime are shown to be near their values in bulk silicon. - 2 -Major Corporate Teclinical Efforts and Results Bell Telephone Labs (BTL) Scientists at BTL are actively looking at SOS for its future low-power, high-speed communications, memory, and logic circuits. Bell's effort currently is research only. Digital Equipment Corporation Standard MOS device designs have been built in SOS to evaluate the SOS processing techniques. Devices using the special features of SOS are not yet being manufactured. Hewlett-Pacltard (H-P) H-P initially field tested the CMOS SOS ROMs in its 2640, 2644, and 2645 general purpose display terminals beginning in late 1976. However, in these cases, the systems were not designed around the Special SOS features, but the components merely replaced NMOS ROMs piece for piece. The present SOS utilization in the HP-3000 System 33 and HP 300 has gone further, with unique SOS designs incorporated at the chip level and complete systems built around these unique features. H-P is continuing its major effort in SOS. Two new genera-tions of devices and processes incorporating reduced dimensions will soon be used in their systems. Hughes Aircraft An R&D group has expanded its SOS manpower in recent years. All developments and devices have been for internal system applications and Other military programs. Hughes could become a second source to RCA. Intel The intentions of Intel in cross-licensing its microprocessor line to RCA in exchange for SOS technology have yet to be fully revealed. Intel's stated purpose was to broaden its 8085 applica-tions base, but the cross-licensing agreement also clearly provides it access to SOS developments. Motorola EFCIS, the joint-venture company of Thompson-CSF and the French Government, is reported to have begun its SOS/CMOS design of Motorola's 6802 microprocessor in June 1978 and expects to sample SOS/CMOS 6802 devices in mid-1979. While SOS technology is not an explicit part of Motorola's agreement with EFCIS and the French Government, it is possible that Motorola will transfer SOS/CMOS tech-nology to the United States in late 1979. Nippon Electric Company (NEC) NEC^s effort is concerned with short channel devices of 1 to 2 micrometers, where it believes SOS is superior to bulk silicon MOS devices. - 3 -RCA T^HK has designed and produced working 16K static RAMs with access times of 75 nanoseconds at 10 volts and 130 nanoseconds at 5 volts and with quiescent power dissipation of 0.01 milliwatts. Customers have been sampled, with production scheduled in 1979. Currently, RCA is selling its SOS/CMOS 4K static RAM at a competitive price of $7.00 each, but a second source is needed. Raytheon (Bedford) This Raytheon group has designed the AMD 2901 and 2909 in SOS/CMOS, initially for internal system application. However, if SOS acceptance expands rapidly, these 2900 series 4-bit microprocessors could become available commercially. Rockwell Both the Microelectronics Division and the Aerospace Systems Division are actively producing SOS/CMOS LSI devices. The highest volume product is an SOS/CMOS frequency synthesizer for military portable radios. Rockwell is a strong contender for the U.S. Department of Defense's Very High Speed Integration (VHSI) program money, as it is working on 100 megahertz logic. Rockwell has not as yet returned to the commercial market in SOS/CMOS, and continues to use all its SOS production internally in systems applications. Sperry Univac Univac has an internal effort to manufacture SOS devices for its military and commercial systems. Its first group of circuit designs is nearly complete. After manufacturing is proved, the process tech-nology will probably be moved from the research level to the manu-facturing facility in Minneapolis, Minnesota. Texas Instruments (TI) Ti, naving twice reauced its SOS activities, is believed to be building up its program again. Toshiba Tosnioa produced an SOS/CMOS microprocessor in 1977, mostly for its own internal applications. Its SOS activity is less visible at the present time. U.S. Government VHSI Program The U.S. DOD-funded VHSI program will allocate $200 million over the next six years, with the goals of producing large chips populated with fast and very dense circuits. It is expected that SOS tech-nologies will receive as much as 15 percent of these development funds. VLSI Labs A small group of engineers is looking for major development leaps to yield better quality silicon crystal on sapphire. It will be interesting to see what success they have beyond the recent advances reported above. - 4 -SOS Markets There are two noteworthy features of the SOS market, which have developed over the last several years. First, the major successes of SOS to date have been in military and space markets, which can afford a higher price premium for higher performance than can the strictly commercial markets. Second, an SOS-based systems market exists to a greater degree than an SOS-based components market. It is not surprising that the available major systems level products making use of SOS technology are from vertically integrated firms such as H-P. Vertical integration enables designers to take full advantage of component-level features in systems level applica-tions through total systems design. Manufacturers for military markets (Hughes, RCA, Rockwell) use a large portion of their produc-tion in their own systems. Furthermore,' the higher SOS component cost can often be effectively buried in the system price, which may be why the first SOS applications are coming from systems manu-facturers having their own design and wafer fabrication capability. Conclusion and Prospects While SOS technology has not in the last four years developed as fully as had been thought possible, it has secured a foothold in the market, but more at the systems level than at the component level. Military and space applications continue to contribute to overall demand for the process technology. Technical progress has been steady, although slower than hoped for. The potential of the technology remains great, although its reputation is somewhat diminished by its failure to pay off more quickly. At present, there appears to be ample support in U.S. Government-funded programs and in private firms to carry the commercial and technical development of SOS into at least the mid-1980s. Future growth of the market may, in the short term, be limited by the availability of quality sapphire wafers. However, recently increased industry commitment to the SOS technology should eventually be reflected in the sapphire supply market with an attendant reduc-tion in substrate costs. O. D. Trapp Lane Mason - 5 -A Subsidiary of A.C. Nielsen Company INCORPORATED SIS Code; Table of Contents March 9 , 1979 LIST OF RESEARCH NEWSLETTERS 1 9 7 7 - 1 9 7 9 SEMICONDUCTOR INDUSTRY SERVICE 1979 T i t l e Update on Fairchild (8.02) Preliminary Market Share Estimates of Leading , Domestic Merchant Semiconductor Suppliers (Appendix B) Update on National Semiconductor (8.08) General Industry Forecast (2.0) 1978 Government Issues Affecting the Semiconductor Industry (2.2) Automotive Semiconductor Market Expected to Reach $1 Billion by 1985 (2.8.7) Update on Intel (8.04) Update on Texas Instruments (8.12) MOS Microprocessor Shipments (2.8.1) Producing LSI Without a Factory (3.2) MOS Memory—Static and Dynamic RAM and EPROM Shipments (2.8.6) General Industry Forecast (2.0) Government Issues Affecting the Semiconductor Industry (2.2) Date 2/20/79 1/24/79 1/24/79 1/19/79 12/29/78 12/28/78 12/20/78 12/18/78 11/27/78 11/16/78 11/10/78 11/10/78 10/31/78 Copyright © 9 March 1979 by DATAQUEST - Reproduction Prohibited 19055 Pruneridge Avenue / Cupertino, California 95014 / (408)725-1200 TWX (910) 338-7695 / DATAQUEST CPTO Title Date Semiconductor Industry Capacity Expansion (1.6) Laser Annealing (4.17) National Semiconductor Analysts' Meeting (8.08) Estimated Worldwide MOS Memory Consumption (2.8.6) Advanced Micro Devices Annual Meeting (8.20) Update on Motorola (8.06) Bipolar Microprogrammable Microprocessors (2.8.1) A 64K RAM from Texas Instruments (2.8.6 or 4.13) Potential Stimulants for 1979 U.S. Semiconductor Consumption (2.0) General Industry Forecast (2.0) The Domestic ECL Market (4.12) Government Issues Affecting the Semiconductor Industry ((2.2) MOS Memory—Static and Dynamic RAM and EPROM Shipments (2.8.6) IBM Enters the Commercial Memory Marketplace as a Customer (2.5) Electron-Beam Lithography (4.17) MOS Microprocessor Shipments (2.8.1) MOS Memory—Static and Dynamic RAM and EPROM Shipments (2.8.6) Update on National Semiconductor (8.08) Geographic Distribution of Integrated Circuit Sales (7.0) General Industry Forecast (2.0) Government Issues Affecting the Semiconductor Industry (2.2) Update on Fairchild (8.02) 10/11/78 10/11/78 10/6/78 10/6/78 10/6/78 9/29/78 9/29/78 9/20/78 8/17/78 8/11/78 8/3/78 7/19/78 7/14/78 7/14/78 7/6/78 6/21/78 6/9/78 4/20/78 4/18/78 4/14/78 4/13/78 3/20/78 - 2 -Title Date Update on Texas Instruments (8.12) Update on Intel (8.04) MOS Microprocessor Shipments (2.8.1) Update on Motorola (8.06) Government Issues Affecting the Semiconductor Industry (2.2) MOS Memory—4K and 16K Shipments (2.8.6) Proposed 1978 Semiconductor Industry Service Publications (Table of Contents) Japanese Semiconductor Industry (1.3) 3/15/78 3/7/78 3/2/78 2/23/78 2/21/78 2/3/78 1/20/78 1/13/78 1977 General Industry Forecast (2.0) MOS Microprocessor Shipments (2.8.1) Government Issues Affecting the Semiconductor Industry (2.2) MOS Memory—4K and 16K Shipments (2.8.6) Semiconductor Memory Consumption and Market Shares (2.8.6) MOS Memory—4K and 16K Shipments (2.8.6) European Semiconductor Consumption (1.3) Microprocessor Development Systems ((2.8.5) Government Issues Affecting the Semiconductor Industry (2.2) General Industry Forecast (2.0) Update on Intel Corporation (8.04) Update on Texas Instruments (8.12) MOS Microprocessor Shipments (2.8.1) 12/28/77 11/23/77 11/18/77 11/11/77 10/7/77 9/30/77 9/16/77 8/26/77 8/16/77 7/29/77 7/14/77 7/7/77 7/6/77 - 3 -Title Update on Motorola (8.06) Update on National Semiconductor (8.08) Government Issues Affecting the Semiconductor Industry (2.2) General Industry Forecast (2.0) MOS Memory—4K Shipments (2.8.1) MOS Microprocessor Shipments (2.8.1) Optoelectronics Market (4.14) General Semiconductor Industry Outlook (2.0) Date 6/14/77 6/6/77 5/6/77 4/20/77 3/25/77 3/18/77 1/28/77 1/21/77 Out Of Print - 4 -> ^^mM ^ ^ f e ^ = = s = s a S s S s ^^s^ E3^QP ADd-l ^^^^S ^^I^^J^^^I i •! 1 jsidiarv of A.C. [Mielssn Co. " INCORPORATED SIS Code: Newsletters March 9, 1979 MOSTEK ANALYSTS' MEETING February 26, 1979 DATAQUEST attended an Analysts' Meeting given by Mostek on February 26. Our observation of the meeting was that it was a forthright, upbeat meeting. Among those present were Vin Pothro, President; Berry Cash, Vice President of Marketing; Robert Palmer, Vice President of Wafer Fabrication/R&D Jim Peoples, Vice President, Manufacturing; and Chuck Barker, Vice President of Finance. The beginning of the meeting was devoted to a discussion of 1978 results and the impact of the Fab IV start-up problems on 1978 results. Looking into 1979, some interesting data were presented. 1. Financial Mostek's long-term goal is to achieve a 14 percent net profit before taxes. In light of the Company's 11.8 percent NPBT in 1978, DATAQUEST is assuming that Mostek's NPBT will improve slightly this year. DATAQUEST expects that the first quarter will continue to show to some extent the financial effect of the Fab IV yield problem which was resolved in late 1978-early 1979. 1977 Sales per employee increased to $29,000 in 1978 from $26,000 in 2. Capital and Capacity Mostek expects capital expenditures to reach $32 million in 1979 of which $7 million will be for new facilities. DATAQUEST anticipates that a significant portion of this capital will be expended on its new facilities in Colorado Springs. We understand that the initial facility will be about 150,000 square feet. It will contain one wafer fabrication module which will be roughly equivalent in capacity and technology to Fab IV, which began processing silicon in mid-1978. Copyright © 9 March 1979 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to tfie public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. IT does not contain material provided to us in confidence by our clients. This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and mEiy sell or buy such securities, 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 TWX (910) 338-7695 / DATAQUEST CPTO 3. 1977-1978 Comparisons Mostek displayed several charts showing the shift of business mix between 1977 and 1978 and also data relative to unit shipments on various key products. Table 1 represents DATAQUEST's estimates of dollar shipments by major business segment. This table was constructed by using the slide presented by Mostek showing major segments and DATAQUEST's estimates within the Miscellaneous category. Table 2 was presented at the meeting. Table 1 MOSTEK CORPORATION ESTIMATED REVENUES BY MAJOR CATEGORY ( $ in Millions) 1978 1979 Memory Memory Systems Microprocessors & Systems Telecommunications Miscellaneous Total Revenues $105 5 5 8 11 $134 $119 12 20 12 12 $175 Source: Mostek Corporation DATAQUEST, Inc., Estimates March 1979 Table 2 MOSTEK CORPORATION KEY PRODUCT SALES COMPARISONS (Units in Millions) Product Type 1978 1979 16K Dynamic RAM 4K Dynamic RAM 4K Static RAM Microprocessors Telecommunications 5, 16, 0, 1, 13, 10, 3, 3, 3.0 4.4 Source: Mostek Corporation March 1979 - 2 -4. Corporate Focus/New Products l^ostek then commented on its areas of concentration: Memory In 1978, the Company introduced four new products. In 1979, the plan is for eleven new memory products—four dynamic, five static, one EPROM, and one ROM. The 64K dynamic MOS RAM is scheduled for sampling in the second quarter. Telecommunications In 1978, the Company introduced four new products. In 1979, Mostel^ expects to introduce seven new products including a filter utilizing CCD technology. The part number is MK5200. It will be a rather small chip, 88x201 mils. Microcomputers In 1979, Mostek expects to introduce eight new products. Miscellaneous Mostek's backlog of orders for dynamic and static RAMs is scheduled into the third quarter. Distributor shipments in 1978 were about 15 percent of total sales. The outlook for Mostek in 1979 appears quite good. If DATAQUEST's sales estimate of $175 million is achieved, along with a retention of the 40 percent tax rate, Mostek should earn between $2.55 and $2.65 per share in 1979 (based on 12 percent NPBT). James F. Riley - 3 -•, ? ^ kj SS S.S. S S S . b^ijdi^ry Pf A^C. Nielsen Co. • ^ . . ! r^^^ ^^^^^^ t ^ ^ -^^^^^ ^S '^^S ^K ^ INCORPORATED RE I^IE I^E :SE r\A# i W •A ^ 1 al RCI-C^" MB I -1 rL|_j 1 Bn SIS Code: Newsletters March 6, 1979 U.S GOVERNMENT ISSUES AFFECTING THE SEMICONDUCTOR INDUSTRY: INTERNATIONAL TRADE NEGOTIATIONS AND EXPORT CONTROL LEGISLATION Summary Federal Government activities that could impact the U.S. semi-conductor industry continued on two fronts in recent months. First, the Executive branch is presently lobbying to secure eventual Con-gressional support for a trade bill containing the key provisions of agreements reached recently at the Multilateral Trade Negotiations in Geneva. These agreements address several nontariff issues that are felt to restrain free and open trade among participating countries, i.e., subsidies and countervailing duties, technical barriers to trade, government procurement policies, import-licensing procedures, and customs valuation policies. Second, the proposed Technology Transfer Ban Act of 1978 (see DATAQUEST Research Newsletter, October 31, 1978) has been revised, and a new, less restrictive bill is ex-pected to be introduced soon in the House of Representatives. Provisions of the Multilateral Trade Negotiations - Geneva Selected representatives from various industry groups, includ-ing the U.S. semiconductor industry, have been meeting in Washington, to review those key provisions of an international trade agreement that have already been agreed to in the Multilateral Trade Negotia-tions in Geneva. The purpose of these initial meetings is to assess the results of the international negotiations on tariff and nontariff barriers to trade, and to begin to prepare an analysis of the outcome of these negotiations and their likely impact on U.S. industry. These provisions will likely form a significant part of a trade bill which the Carter Administration will submit to Congress in April 1979. The President's Special Trade Advisor, Robert Strauss, is heading an intensive lobbying program aimed at securing congressional approval for this bill. Of particular interest to the U.S. semiconductor industry are the agreements reached in the following nontariff areas: 1. Subsidies and countervailing duties 2. Technical barriers to trade (standards) Copyright © 6 March 1979 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 TWX (910) 338-7695 / DATAQUEST CPTO 3. Government procurement 4. Import licensing procedures 5. Customs valuation DATAQUEST has Obtained a copy of the working documents covering these and other issues on which agreement has been reached during the Multilateral Trade Negotiations. These documents will form the basis for drafting the final legal agreement that should be signed in Geneva shortly. Below is a summary of those agreements of particular interest to the semiconductor industry. Subsidies and Countervailing Duties Stronger controls have been sought over use of foreign govern-ment subsidies that confer what are felt to be unfair competitive ad-vantages upon the products of the subsidizing country. A draft Arrangement on Subsidies and Countervailing Duties was developed in Geneva and provides the following items that address this issue. 1. A flat prohibition of export subsidies on nonprimary products as well as on primary mineral products 2. A definition of export subsidy that abolishes the existing dual-pricing requirement and provides an updated list 3. Recognition that while domestic subsidies are often used to promote important objectives of national policy, they can also have harmful trade effects. Relief, including countermeasures, is made available where such subsidies either: (a) Injure producers in the importing country (b) Nullify or impair benefits of earlier concessions reached under the General Agreements on Trade and Tariffs (GATT) (c) Cause serious prejudice to the interests of other GATT signatories 4. Recognition that where domestic subsidies are granted on noncommercial terms, trade distortions are likely to arise. Commitment by the signatories to "take into account" con-ditions of world trade and production (e.g. prices, capacity, e t c ) in drafting of their subsidy practices 5. Provision for special and differential treatment under which Less Developed Countries (LDCs) could not use export subsidies where such subsidies adversely affect the trade or production interests of other countries. Provision for negotiated phase-outs of export subsidies by LDCs 6. Adoption of tight dispute settlement process to enforce the Code which would require that panel findings regarding rights and obligations within 120 days of a complaint - 2 -7. Provision for the design of an injury and causation test to afford relief in cases where subsidized goods have impacted producers in the importing country either through a volume or price effect. This provision mal<es no distinction between export or domestic subsidies, but is concerned only with whether the goods have been subsidized. These countervailing duty action requests must include sufficient evidence of the existence of: (a) A subsidy and, if possible, the amount of that subsidy (b) Injury, which is talcen to mean material injury or threat of injury to an industry in the importing country, or material retardation of the establishment of such an industry (c) A causal link between the subsidized products and the alleged injury No countervailing duties may be levied on any exported product in excess of the amount of the subsidy, calculated in terms of subsidization per unit of the subsidized ex-ported product. In instances where a finding of a threat of injury or material retardation is made (but no injury has yet occurred), countervailing duties may be imposed only from the date of the finding of the threat of injury or material retardation. Techiiical Barriers to Trade (Standards) The Code of Conduct for Preventing Technical Barriers to Trade (Standards Code) is designed to reduce trade obstacles that result from the preparation, adoption, and application of product standards and certification systems. The code contains specific obligations and procedures to ensure that standards and certification systems are not used as barriers to trade. Standards (both voluntary and mandatory) and certification systems promulgated by central govern-ments. State and local governments, and private sector organizations are all subject to the Code's provisions, although only central governments are bound by the Code. A fundamental obligation of the Code is that signatories not allow Standards and certification systems to be prepared, adopted, or applied so as to create unnecessary obstacles to international trade. The Code also obliges national and regional certification systems to grant access (i.e., permit goods to be certified under the rules of the system) to foreign or nonmember suppliers on the same basis that access is granted to a domestic or member supplier. All Standards and rules of certification systems must be published. Upon a specific request. Code signatories are to provide tech-nical assistance in the standards field to developing countries. - 3 -Government Procurement The keystone of this Code is the elimination of discrimination against foreign suppliers when governments purchase articles for their own use. The most obvious form of such discrimination against foreign suppliers is the clearly stated preference maintained by some countries for domestic suppliers. A much more difficult t a s l « addressed by the Code is the elimin-ation of discrimination caused by the absence of procurement rules, or the invisible use of existing practices and procedures to bring about discrimination. The first obligation of the Code signatories is that they publish their procurement laws and regulations and that those laws and regulations reflect the rules of the Code. Purchasing entities are obligated to publish all bid oppor-tunities. Under this procedure, all interested suppliers may bid, but the Code does provide for a "selective" procedure under which the government may invite bids from selected suppliers. Use of "single tender" procedures, or going to a single supplier is permitted only under strictly defined conditions, e.g., when a national disaster demands immediate procurement from the first available source. Code rules are designed to discourage discrimination against foreign suppliers and supplies at all stages of the procurement process. Specific rules are prescribed on the drafting of specifica-tions for goods to be purchased, advertising of prospective purchases (including the details for inclusion in the notice and the tender document), and time allotted for the preparation and submission of bids. Governments will be prohibited from requiring that a supplier license his technology as a condition for an award of a procurement contract. While the Code would not prohibit the granting of an off-set as a condition of award, signatories might recognize that offsets should be limited and used in a non-discriminatory way. Import Licensing The draft Code deals with the administration of import licensing procedures, rather than with the existence or extent of quantitative import restrictions. Its purpose is to simplify and harmonize to the greatest extent possible the procedures that importers must follow in obtaining an import license. To accomplish this simplification, the draft Code stipulates that the rules governing procedures for sub-mitting applications to import licensing systems must be available in published form. The Code also specifies that importers will have to go to only one administrative body to apply for a license. A "reasonable" time period is to be allowed for applying for a license, and no application is to be refused for minor documentation errors. A section on automatic import licensing (defined as instances under which licenses are granted freely) specifies that automatic import licensing systems should be maintained for as long as the cir-cumstances that gave rise to their introduction prevail, or as long - 4 -as their underlying administrative purposes cannot be achieved in another way. The Code states that licenses required under this type Of system are to be made available to anyone fulfilling the prescribed criteria, and that they are to be granted immediately. A section on nonautomatic import licensing systems (those under which licenses are not granted automatically, including licenses re-quired for the administration of quotas and other import restrictions) specifies that governments are to provide information concerning the number and value of licenses granted, and to permit any person, firm, or institution to apply for a license. Customs Valuation The Customs Valuation Agreement sets out five methods for de-termining customs value. These five methods are arranged in a hier-archical fashion; that is, the order of precedence governs the application of each of the methods. The first, or primary, method is to be used in all cases unless a valid customs value cannot be found. In such cases, the second method is to be used. If a valid customs value cannot be found using the second method, the third method is to be used and so on. The first or primary method specifies that a customs value shall be determined based on the transaction value of the imported goods. The transaction value is the price actually paid or payable for the goods with additions of certain charges, costs, and expenses incurred with respect to the imported goods that are not actually paid for or payable (i.e., selling commissions, brokerage fees, and container costs) . The Code specifies four conditions for which the transaction value of the imported goods may be rejected as the customs value. These are: 1. Where the seller places restrictions on the buyer as to the use or disposition of the goods 2. Where the sale or price of the goods is contingent on some factor for which a value cannot be determined 3. Where the seller, in partial payment for his goods, receives some percentage of the proceeds from the resale of the goods by the importer, and the transaction value cannot be adjusted to reflect this amount 4. Where the buyer and the seller are related and their rela-tionship influences the price of the imported goods The second method of calculating customs value uses the trans-action value of identical goods for export to the same country of im-portation at about the same time as the sale of the imported goods. - 5 -The third method of determining customs value, to be used if the first and second cannot, uses the transaction value of similar goods for the export to the same country at, or about, the same time as the sale of the imported goods. The fourth method bases customs value on the unit price at which the imported (or identical or similar) goods are resold in the greatest aggregate quantity, at or about the time of the importation of the goods being valued, in the country of importation, and in the same condition as imported to unrelated buyers. The fifth method bases customs value on a computed value, which consists of material and manufacturing costs, profit, and general ex-penses. This method is similar to the constructed value method in U.S. customs law. Export Controls—Technology Transfer Ban Act A new, less restrictive version of the Technology Transfer Ban Act of 1978 will be introduced into the U.S. House of Representatives soon. Last year's version of this legislation, which was endorsed by 77 members of the House of Representatives, would have prohibited the sale of any technology or product which had a potential military or crime control and detection application to any Communist country or to any other country which failed to impose similar restrictions on the sale of such equipment to non-market countries. U.S. high tech-nology companies were strongly opposed to this legislation last year because of its lil<ely adverse impact on the sale of many products to destinations throughout the world. The new version of the Technology Transfer Ban Act, expected to be introduced later this month by Rep. Clarence Miller (R.-Ohio), will shift the responsibility of determining what technologies and products should be banned or otherwise controlled for sale to Communist countries from the Coimnerce Department to the Department of Defense (DOD). Under the draft provisions of the new legislation, the Secretary of Defense would have 180 days to develop a list of "critical" and "significant" goods and technologies whose export would be either banned or subject to additional controls. Under the proposed legislation, the export of "critical" goods and technologies would be prohibited to Communist countries, while the sale of "significant" technologies or products would be permitted only after review by the U.S. government on a case-by-case basis. Even significant technologies or goods could not be sold to non-Communist countries unless that country provided "adequate assurances" that the exported item will not be re-exported to a Communist country. Under the provision of the draft proposal, "critical goods" are defined to be any product which: - 6 -1. May contribute significantly to the transfer of a critical technology because it: (a) Embodies extractable critical technology (b) Fills a gap in the recipient nation's knowledge and so would enable it to utilize fully a critical technology which it had partially developed or otherwise obtained 2. If analyzed, would reveal all or part of the nature of a U.S. military system and thus facilitate the development of countermeasures to such a system "Significant" technologies and goods are defined to be: 1. A U.S. technology or good (other than a critical technology or good) which would make a significant contribution to the military potential of a controlled (i.e.. Communist) country 2. A technology which is obsolete by U.S. standards, but which nevertheless is superior to a controlled nation's technology or goods While the proposed legislation does not specifically outline which criteria should be used by the DOD to develop the lists of "critical" and "significant" technologies and goods, U.S. firms have some idea of what the DOD might consider to be critical in nature from the Department's own efforts to develop a "critical technologies" list. Late last year, the DOD identified nine technologies which it viewed as being critical to U.S. national security. These were: Array Processor Technology Acoustic Array Technology Computer Network Technology High Energy Laser Technology Diffusion Bonding Technology Large Scale Integrated Circuit Production Technology Jet Engine Technology Infrared Detection Technology Wide-Bodied Aircraft Technology Just last month, however, a DOD representative told a group of industry officials that the DOD's critical technologies list would consist of "about 18 items" or twice the number originally identified. The list of 18 critical technologies has been distilled from an initial list of over 130 items originally compiled by the DOD about two years ago. In fact, however, many of the original 130 categories not now listed as "critical" could well find themselves on the list of "significant" technologies should the revised Technology Transfer Ban Act be enacted into law. - 7 -Should this bill be enacted into law, U.S. high technology ex-porters could be faced with a whole new set of unilaterally imposed controls on the shipment of goods and the exchange of technologies to most countries in the world. Even if U.S. companies are allowed to sell their products, many such sales will have to be reviewed on a case-by-case basis, whicli will add delay, uncertainty, and possibly result in a competitive disadvantage in world markets. James F. Riley Daniel L. Klesl^en Frederick L. Zieber - 8 ^ " J ^^1 RESEARCH osidiaryotA.C. Nielsen Co. 7 INCORPORATED V \ l ^ ^ W V ^ 3 ^ B ^ Z 1 1 E 1 ^ 4 1 SIS Code: Newsletters March 1, 1979 PROPOSED 1979 SEMICONDUCTOR INDUSTRY SERVICE PUBLICATIONS This newsletter contains the proposed research schedule of DATAQUEST's Semiconductor Industry Service for 1979. We are planning approximately 53 newsletters, 14 notebook sections, and 29 company financial updates. Among the notebook sections are major research efforts on telecommunications, semiconductor markets by end-user, distribution, and semiconductor equipment markets. DATAQUEST's annual Semiconductor Industry Conference is sched-uled for October 17 to 19 in Scottsdale, Arizona. Newsletters Newsletters are published on timely industry events and issues. Quarterly newsletters are published on MOS memory shipments, MOS microprocessor shipments, the general industry forecast, and U.S. Government issues affecting the semiconductor industry. Beginning in the second quarter of 1979, we plan an important series of newsletters on the European semiconductor industry and markets, which we propose to update semiannually. We also plan a newsletter on the Japanese semiconductor industry and updates on the five major U.S. semiconductor companies. We plan to publish a number of other short newsletters through-out the year on subjects of interest to our clients, including semi-conductor procurement outlook, captive suppliers, silicon forecast, capital expenditures, facilities, and packaging. Major notebook sec-tions dealing with semiconductor markets by end-user, telecommunica-tions, and distribution trends will be accompanied by a condensed version in newsletter form. Notebook Sections In 1979, we plan to publish an expanded edition of Appendix A in which the problem created by fluctuating exchange rates will be dealt with more completely. We have already published a preliminary version of Appendix B: Market Share Estimates, in February 1979; the final version will be available in the second quarter. Copyright © 7 March 1979 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation anid analysis of information generally available to the public or released by responsible individuals in completeness. It does not contain material provided to us in confidence by our clients This information is not furnished m connection with o sale or offer to sel buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or shott position the subject companies, but is not guaranteed as to accuracy or securities or in connection with the solicitation of an offer to n the securities mentioned and may sell or buy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 TWX (910) 338-7695 / DATAQUEST CPTO Several major market reports are proposed for the notebook in-cluding semiconductor equipment markets, the telecommunications market, trends in distribution, and semiconductor markets by end-users. As in past years, financial updates for major semiconductor manufacturers and distributors will be provided. As always, the Semiconductor Industry Service attempts to be re-sponsive to the needs of our clients and to report on timely issues in a timely manner. Therefore, items may be added to or deleted from this list SO that we may be flexible enough to respond to changing needs. Your recommendations and requests are always welcome. Conference The annual DATAQUEST Semiconductor Industry Service Conference is scheduled for Scottsdale, Arizona, on October 17 through 19. The Conference will focus on several important aspects of VLSI and the electronics world trade issue. James F. Riley Frederick L. Zieber Daniel L. Klesken - 2 -1979 PROPOSED SIS NEWSLETTERS General Industry Forecast •European Semiconductor Industry and Markets Major European Semiconductor Manufacturer Updates Japanese Semiconductor Industry Fairchild Update National Update Intel Update Motorola Update Texas Instruments Update Signetics Update MOS Memory Quarterly Sliipments MOS MPU Quarterly Shipments •Bipolar Memory Market Share Estimates MOS Memory Market Share Estimates •Estimated MOS Microprocessor Consumption Estimated MOS Memory Consumption •Discrete Device Market •Magnetic Bubble Market •CCD Market U.S. Government Issues Affecting the Semiconductor Industry •Optoelectronics Market •Telecommunications Market •Manufacturing Model Update •Semiconductor Procurement Outlook •Captive Supplier Analysis •Silicon Forecast and Trends •Semiconductor Markets by End User •Silicon-on-Sapphire Update Capital Expenditures •Facilities Census •Packaging Trends Preliminary Market Share Estimates-Appendix B •Semiconductor Equipment Trends Totals 1 s t Qtr. 1 2nd Qtr. 1 1 3rd Qtr. 1 4th Qtr. 1 1 Total 1 1 1 1 1 1 13 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 . 1 1 1 1 1 I 1 1 1 TI 1 T5 T2 1 2 2 1 1 1 1 4 4 1 1 1 2 2 1 1 4 1 1 1 2 2 1 1 1 2 1 1 1 1 53 •Indicates new subjects for 1979 - 3 -1979 PROPOSED SIS NOTEBOOK SECTIONS Chapter/ Section 2 2 2 3 3 3 4 6 7 App. App. App. App. App. .
A .
B .
B , B , C 1st Title Qtr. Semiconductor Equipment Trends Telecommunications Market Microprocessor Update Manufacturing Model Update Facilities Census Packaging Trends Silicon Forecast Techonology/Trends International Subjects (to be determined) Quo Vadis Distribution? Market Estimate WorksJieets Preliminary Market Share Estimate Worksheets 1 Final Market Share Estimate Worksheets Captive Semiconductor Production Semiconductor Markets by End-User Totals ~T 2nd Qtr. 1 1 1 1 1 1 T 3rd Qtr. 1 1 1 X 1 1 -T 4th Qtr. 1 T Company Financial Updates U.S. Companies 8.02 8.04 8.06 8.08 8.10 8.12 8.20 8.24 8.25 8.26 8.30 8.34 8.40 8.41 8.56 8.86 Fairchild Intel Motorola National Signetics Texas Instruments AMD AMI Analog Devices Electronic Arrays International Rectifier Intersil Mostek Siliconix Unitrode Varo 1 1 1 1 1 1 1 1 i Indicates new subjects for 1979 Total 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X . 1 1 1 1 1 i 1 1 1 1 1 1 1 1 1 - 4 -1979 PROPOSED SIS NOTEBOOK SECTIONS (Continued) Cliapter/ Section Japa; 10.02 10.04 10.06 10.08 10.10 10.12 Title nese Manufacturers Hitachi Matsushita Electric Mitsubishi Nippon Electric Co. Toshiba Fujitsu Distributors 12.00 12.01 12.02 12.03 12.04 12.05 12.15 Totals Arrow Avnet Cramer Pioneer Standard Sterling Wyle Kierulff 1st Qtr. X 1 7 2nd Qtr. 1 1 1 1 1 1 10 3rd Qtr. 6 4th Qtr. 1 1 1 1 1 -6 Total 1 1 1 1 1 1 1 1 1 1 1 1 1 29 •Indicates new subjects for 1979 - 5 -IJ 4 1 ^^^^ H ^ • 1 tjdiarv of A.C. Nielsen Co, ^ INCORPORATED i RE NE :SE IMS/ •A S I RCI--ET" -1 r E R SIS Code: Newsletters March 6, 1979 INTERNATIONAL SOLID STATE CIRCUITS CONFERENCE 1979 Introduction The International Solid State Circuits Conference (ISSCC) is probably the most important annual technical conference in the semi-conductor industry; it is at this forum that many new technological trends become apparent. The conference was held in Philadelphia from 1953 to 1977. The 1978 meeting in San Francisco marked the first time the conference was held elsewhere. The 1979 conference was held in Philadelphia on February 14 to 16. In the future, it will alternate between the two cities. Large Scale Integration The tenor of this year's conference was set in the keynote speech by Dr. Gordon Moore of Intel. Dr. Moore indicated his belief that we are entering a new era in large scale integration—one in which it is difficult to define complex functions that totally util-ize all the components that can be placed on an LSI chip. Dr. Moore showed a slide that plotted the complexity of various Intel products by calendar year. Interestingly, memory products have increased in complexity, according to "Moore's Law," but other products such as microprocessors and microprocessor peripherals have not. ("Moore's Law," as formulated by Dr. Moore, predicts a doubling in complexity every year, declining somewhat in the 1980s.) Dr. Moore believes that the lower complexity of non-memory products stems from an in-ability to create functions that totally use the power of today's LSI circuits. A manufacturer of complex LSI circuits must have a span of capability that ranges from silicon processing to systems. That span Of talent is being assembled by components manufacturers, by systems manufacturers with captive manufacturing capability, and by various cooperative arrangements between systems and semiconductor manu-facturers. Dr. Moore commented that systems manufacturers with captive semiconductor facilities now have a greater opportunity for success because they can make unique systems functions that preserve their investment in architecture and software; generally the necessary LSI circuits are made in such small quantities that the semiconductor industry cannot handle these requirements Copyright © 6 March 1979 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subicct companies, but is not guaranteed as to accuracy or completeness It does not contain material provided to us in confidence bv our clients. This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy secui ities This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a lonq or short position in the securities mentioned and may sell or buy such securities 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 TWX (910) 338-7695 / DATAQUEST CPTO economically. Dr. Moore supported this thesis by citing DATAQUEST information that indicates that the number of captive suppliers in-creased by 226 percent (from 19 to 43) between 1975 and 1979, while the number of merchant suppliers fell by 13 percent (from 93 to 81). Dr. Moore also commented that the cost of designing a circuit is in-creasing, roughly in proportion to its complexity. Since manufactur-ing cost does not increase in proportion to complexity, each new design will need to be amortized over a larger production quantity if the design cost is to remain a constant percentage of the manufactur-ing cost. This trend may favor increased captive production of LSI. Papers Presented at Technical Sessions Interestingly, a number of papers, presented mainly by systems organizations, tended to support Dr. Moore's thesis. These papers all described LSI devices that tolerated inefficient use of LSI tech-nology to obtain other objectives: •m. Random access memories (RAMs) that incorporate extra bits to replace those rendered inoperative by yield defects were described by Bell Labs (Session 12.6), IBM (Session 12.8), and in Session 1.4 by Nippon Telephone and Telegraph (NTT). Bell Labs' 64K RAM stores the bad locations on-chip through the use of laser-fusible links. IBM's 64K RAM stores bad locations in fusible links that are blown by a high current pulse. Significantly, it appears that IBM has the only 64K RAM now in production, although Bell Labs may also be pro-ducing the device. In NTT's circuit, a one megabit full-wafer RAM is achieved, and the "bad location" storage is off-chip. • LSI arrays were described in four papers given in Session 6. These arrays reduce design cost because only the metal mask or masks need be changed to produce a custom circuit. These arrays use silicon inefficiently because most designs do not require all the logic available on the chip. These papers were given by IBM (2 papers), NTT-Hitachi, and Siemens. • A method of designing a chip that reduces both the en-gineering cost of developing a test program and the manu-facturing cost Of performing the test was described by Philips (Session 18.4) and IBM (Session 18.5 and 18.6) . Philips estimates that the method adds 3 percent to chip area and IBM estimates the added area is between 4 percent and 20 percent. IBM estimates that only 10,000 test patterns are required with the new method whereas at least 10 to 100 times more test patterns are required with older methods, and implied that the savings in test time more than makes up for the cost of the added silicon. This year, 97 papers (exclusive of panel discussions) were pre-sented at ISSCC. This is an increase of five papers over last year - 2 -and an increase from 49 papers in 1964. However, if anything, the quality of papers has improved with the increasing quantities, thus indicating that the technological capability of the semiconductor in-dustry is Still Strong. Of the 97 papers presented, 65 percent were of U.S. origin, 21 percent of Japanese origin, and 14 percent of European origin. In-terestingly, these percentages roughly reflect the share of merchant semiconductor sales shipped by U.S., Japanese, and European companies—63 percent, 23 percent, and 14 percent, respectively. All but two of the European papers were given by either Philips, Siemens, or Thompson-CSF. Other Highlights The topic of combined digital and linear circuitry accounted for the largest number of papers (25). Sessions 2 and 7 were devoted to telecommunications circuit techniques and analog signal processing. Of the 11 papers presented at these sessions, five described filters mechanized with the switched capacitor technique, while only two de-scribed COD filters; it appears that the switched capacitor filter represents an important new technique. The other four papers did not discuss filtering. Sessions 11 and 14 were devoted to data acquisi-tion and mostly discussed various analog-to-digital converter imple-mentations. Notable among these was AMD's circuit (Session 14.2) that managed to achieve 12-bit accuracies using only untrimmed diffused resistors. Intel (Session 16.3) described a novel micro-processor with analog inputs and outputs. This device can be pro-grammed to achieve up to 40 poles of filtering and can also perform functions usually done by mixers, detectors, and automatic gain con-trol circuits. Semiconductor memory, with three sessions and 21 papers devoted to it, represented the second most popular topic It appears that it will someday be possible to eliminate capacitor storage from dynamic RAMs. Instead, charge will be stored under the gate of an MOS transistor, where it effectively acts to modify the threshold of the device. This technique has three advantages: • The Storage cell is smaller because no capacitor is re-quired. • Sensing is much simpler; the impedance of the MOS device is sensed instead of the charge being stored on a capacitor. • Storage times are longer at high temperature because certain types of leakage current are rendered ineffective. Texas Instruments described a "taper isolated cell" (Session 1.6) and Intel described a "vertical CCD" (Session 12.7). Both approaches promise to achieve the three objectives listed above. - 3 -Also notable in the memory sessions were descriptions of NTT's 128K-bit ROM (Session 1.1), a device fabricated with direct electron-beam data writing and boasting 2-micron geometries. Intel described a self-refreshing n-channel 4K RAM (Session 1.3) that achieves Standby power similar to that of CMOS RAMs. Intel also described a 4K Static RAM (Session 9.2) with access time of 25 nanoseconds and a 16K Static RAM (Session 9.5) with access time of 40 nanoseconds. Both devices employ channel lengths of 2 to 3 microns. Bipolar memories still maintained a speed advantage, with two RAMs by Hitachi achieving a 5.5 nanosecond access time for a IK-bit chip (Session 9.1) and a 6 nanosecond access time for a 4K-bit chip (Session 9.6). The 4K-bit chip employed 2-micron geometries. Dynamic RAMs showed few unexpected technical innovations, but both Mostek's 2Kx8 RAM (Session 12.3) and Zilog's 4Kx8 RAM (Session 12.9) provided on-chip circuitry that manages refreshing for the user. These RAMs offer 8-bit outputs and are intended for use in micro-processor applications. Digital circuits (18 papers) and microwave applications (13 papers) were the third and fourth most popular areas. Howard Z. Sogert - 4 -^ 1 .
^ ^ B j ^ ^ ^ ^ ^ ^ 1 ^ ^ ^Hi i H ^ ^ ^^-^^ ^m. ^—-=- D^S^iVDCI-l ^ ^ ^ ^ 5 p ^ ^ H i ^ ^ H ^ ^ r ^ ^ ^ r r 1^, Jlsubsidlaiv of A.C. Nielsen Co. " 5 tIMCORPORATED IMbWa^BS 1 1 Bl-I SIS Code: 8.02 Fairchild Camera & Instrument February 20, 1979 UPDATE ON FAIRCHILD Summary Fairchild has reported total 1978 sales of $534 million plus royalties and other income of $16 million for total revenues of $550 million. This is an increase of 17 percent over 1977's $470 million. Net income in 1978 was $24.8 million ($4.48 per share) up sharply from $11.2 million ($2.06 per share) in 1977. This increase comes despite continued difficulties in consumer electronics. Fairchild faces intense competition, especially in semiconductors, but has benefited from a strong market. The following major factors shape the Coiripany's current outlook: • Inadequate capacity expansion in 1977 caused Fairchild's 1978 semiconductor growth to lag the semiconductor industry, resulting in a loss of market share. This loss was exacerbated by product positioning problems in some of the Company's key product lines. • Fairchild's major LSI strength—bipolar memories—con-tinues to expand with extremely strong market demand, but faces increased competition from other companies. DATAQUEST expects that Fairchild will make MOS corporate priority in 1979. a major • Fairchild has had successful market entry with its new high-speed Schottky circuits, but market size and acceptance remain in doubt. • Fairchild is expected to become an important second source of 6800 microprocessors to General Motors, and is also ex-pected to participate in other significant automotive opportunities. • Fairchild's Government and Industrial Products Group is profitable and should grow about 17 percent this year, while its Test Systems Group is quite profitable and should grow about 56 percent in 1979. • DATAQUEST expects that Fairchild may withdraw totally from the consumer electronics business in 1979 as this group had losses and write-offs estimated at $18 million in 1978. Copyright © 20 February 1979 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in thI^ subject companies, but is not guaranteed as to accuracy or completeness It does not contain material provided to us in confidence by our clients This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 TWX (910) 338-7695 / DATAQUEST CPTO • Capital expenditures for 1979 are expected to increase to more than $80 million, up more than 150 percent from $32 million in 1978. • Part ownership of Magnuson (35 percent) and a joint venture with GEC in England appear to be progressing satisfactor-ily. Estimated Revenues DATAQUEST's revenue estimates for 1976 through 1979 for each of Fairchild's operating groups are presented in Table 1. Total rev-enues in 1978 were $550 million, up 17 percent from $470 million in 1977. We expect Fairchild's 1979 revenues to grow about 12 percent to $615 million. This growth is reasonable in view of declining rev-enues from its consumer operations. Estimated consumer revenues were $59 million in 1977, $36 million in 1978, and are expected to be about $5 million in 1979. Fairchild's growth in 1979 should come from systems, which is expected to grow about 56 percent to $125 million, and semiconductors, which is expected to grow about 14 percent to $434 million. DATAQUEST expects Fairchild's first quarter 1979 revenues to decline about $15 million from the fourth quarter of 1978 because of lower consumer product revenues and fewer shipments of test systems. The latter group experienced a shipping bulge in the fourth quarter and is now adding three new systems service centers. Fairchild is allocating some of its first quarter test system production for the equipping of these service centers. This will result in higher manufacturing costs with no commensurate increase in first quarter shipments and revenues. Royalties and other income provided Fairchild revenue of about $16 million in 1978. We believe that about $6 million came from interest income, sale of Cray Research stock, and special one-time technology licensing. About $10 million, therefore, represents a recurring but decreasing base of patent royalty income. Semiconductors are the largest product group in Fairchild. DATAQUEST estimates of Fairchild's revenues from semiconductors are shown in Table 2. Fairchild divides its Semiconductor Group into two areas, components and LSI (large scale integration). Generally, small chips are included in the Components Group and larger chips in the LSI Group. Because of changes in reporting from year to year, comparisons for these groups over time are hazardous. During 1978, some product groups were moved from LSI to Components. Thus, year-to-year growth in the digital IC area is not as high as the numbers imply and the LSI numbers do not reflect all growth in the bipolar memory area as some of the products are in the Components Group. - 2 -Table 1 Fairchild Camera and Instrument Corporation ESTIMATED REVENUES 1976-1979 (Dollars in Millions) 1976 1977 1978 1979 Semiconductor Government and Industrial Government Industrial Test Systems Consumer Games Watciies , Components Intracompany ^ Royalties & Licensing Total Revenues $450 $470 $550 $615 Net Profit After Tax (Percent) 2.77% 2.37% 4.50% 5.00% Net Income $12.46 $11.16 $24.76 $30.75 Earnings Per Share (In IJcllars) $ 2.41 $ 2.06 $ 4.48 $ 5.55 This figure, primarily Optoelectronics, is included in Semiconductor after 1976. 2 $307 42 — — 23 104 10 69 25 (33) 7 $323 49 -— 43 59 29 30 -(14) 10 $380 57 36 21 80 36 18 18 -(19) 16 $434 67 43 24 125 5 ---(25) 9 In 1978, approximately $10 million of the total was royalty income. Source: DATAQUEST, Inc. February 1979 - 3 -Table 2 Faircliild Camera and Instrument Corporation ESTIMATED SEMICONDUCTOR REVENUES 1976-1979"^ (Dollars in Millions) Components Digital ICs Linear Discrete Hybrids Optoelectronics Total Components 1976 $236 1977 $225 1978 $278 1979 $ 70 63 78 -25 $ 78 52 79 -16 $ 92 61 87 20 18 $102 68 95 25 20 $310 LSI Bipolar MOS Total LSI Total Semiconductor $ 36 35 $ 71 $307 $ 40 58 $ 98 $323 $ 51 51 $102 $380 $ 63 61 $124 $434 During 1978, some product groups were moved from LSI to Components. Thus, year-to-year numbers are not comparable. Source: DATAQUEST, Inc. February 1979 - 4 -Margin Analysis In 1978, Fairchild earned $24.8 million after taxes ($4.48 per share) for an after-tax margin of 4.5 percent. Its pretax earnings were $40.6 million, which includes an estimated $18 million of operating losses and write-offs in its consumer operations. Partially offsetting the consumer losses were some one-time income items from the sale of Cray Research stocl<, patent settlements with Thompson CSF, and possibly other items. Discounting the heavy losses in consumer operations, Fairchild's operating margins for the other operations are estimated by DATAQUEST to be: Semiconductors about 8 percent. Government about 10 percent. Industrial Products about 15 percent, and Test Systems about 20 percent. On a normalized basis, excluding nonrecurring items such as losses from consumer operations, the sale of Cray Research stock, and individual patent settlements, DATAQUEST estimates that Fairchild could have earned about $52 million net profit before taxes in 1978, or $31.2 million net profit after taxes ($5.65 per share). True earnings computations are never as simplistic as the above, but the analysis indicates Fairchild's ability to be reasonably profitable in its basic businesses of semiconductors, systems, government, and industrial. We believe, that these basic and continuing operations earned about $1.40 per share in the fourth quarter of 1978, after excluding year-end adjustments as discussed above, versus the $1.09 per share reported. Realizing that in 1979 Fairchild must invest substantially in its basic semiconductor business, and assuming a 13 percent growth in U.S semiconductor consumption, DATAQUEST estimates that Fairchild can earn at least 5 percent net profit after taxes on revenues of about $615 million for a net after-tax profit of at least $30.75 million ($5.55 per share). We believe the above numbers can be achieved, despite a substantial investment in MOS and Test Systems in 1979. Semiconductor Groups In 1978, the Semiconductor Groups at Fairchild grew by about $57 million or 17.6 percent. This performance is somewhat less than U.S. semiconductor consumption, which grew about 20 percent; therefore, the Company lost market share in 1978. In integrated circuits (ICs), it slipped from' third to fifth in dollar volume among U.S. suppliers, taking a place behind Texas Instruments, Motorola, National, and Intel. Fairchild's growth in 1978 was limited by a lack of wafer fabrication capacity at the start of the year. This problem has been remedied by new capacity coming on stream, and 1979 revenue growth for the Semiconductor Groups is expected to be about $54 million or 14.2 percent, which is slightly above the expected growth in U.S. semiconductor consumption of 13.1 percent. Achieving this growth is closely related to Fairchild's ability to improve its position in MOS. - 5 -Both Fairchild's competitive position in semiconductors and its long-term growth are constrained by its current product mix. This product positioning problem can be expected to remain for some time. Although over two-thirds of the semiconductor revenues are ICs, a number of major revenue segments are in product areas that are currently experiencing slow growth, or are expected to slow in the near future. Specifically, these include small signal transistors and diodes, digital bipolar integrated circuits (SSI - small scale integration), some linear circuits, and some MOS products. The Com-pany's position in MOS (eleventh among U.S. producers) was a weakness in 1978 and is the major corporate challenge in 1979. To support both future growth and profits, Fairchild needs to find growth areas in which it can gain a significant market share and then use these growth areas to strengthen its competitive position. Because of its general weakness in MOS, it must invest heavily in this area and find those market niches where it can excel. Fairchild does have several areas of promise, including bipolar memory, COD devices, low-power Schottky, CMOS, ECL, hybrids, and others. Digital ICs The digital bipolar market grew rapidly in 1978, but it is ex-pected to have much slower growth rates in the future as its markets are eroded by incursions from MOS LSI. Thus, we believe Fairchild's position in TTL SSI has only a limited future. However, Fairchild is well positioned within that segment to take advantage of the growing low-power Schottky TTL market. While this market is still dominated by Texas Instruments, Fairchild has a significant market share. Recently, Fairchild introduced a new line of fast Schottky TTL devices. These devices, with the acronym FAST (Fairchild Advanced Schottky TTL), are designed to compete in the market niche between TTL and very fast ECL devices. They have improved performance over the older Schottky TTL. Because of Fairchild's product announcements, a similar line due to be introduced by Texas Instruments was delayed. These circuits were designed at Fairchild's facility in England, with initial production at its facility in Portland, Maine. Initial market acceptance has been enthusiastic, but Fairchild will have to fill-out the line with a full range of products. It is Still too early to estimate total market size and acceptance. How-ever, the movement of minicomputer manufacturers to faster logic may open some large potential markets. Fairchild has become increasingly competitive in ECL (see DATAQUEST's newsletter dated August 3, 1978, "The Domestic ECL Market"). Overall in ECL, Fairchild is second in production only to Motorola. There are no other major merchant competitors at this time, although ECL is produced by Signetics and will probably be introduced in 1979 by National Semiconductor. Fairchild has the - 6 -largest market share of ECL memory. Its lOOK series devices, with subnanosecond gate delays, is providing competition to Motorola. Fairchild's ECL gate array, being the only one currently in production, is proving popular with computer manufacturers. Although Other companies have more complex devices in the process of being designed, the availability of the Fairchild part has given it a significant market advantage. Linear and Discrete Fairchild's linear product line suffers from a number of older products. As a result, the Company has been losing market share in this product area for the past several years. Fairchild suffers in the discrete semiconductor market from a lack of strong product focus and the generally slow (or negative) market growth for small signal devices. By generally holding margins in discrete, Fairchild can use it as a "cash cow" to finance invest-ment in newer high-growth areas. As a result of this strategy, the Company has been gradually losing market share in discretes. Hybrids The Automotive/Hybrid Division makes devices for the automotive, consumer, industrial, and telecommunications industries. The majority of its production is automotive ignition systems; Fairchild recently shipped its ten millionth ignition module to General Motors. Because of the increase in automotive electronics and the general growth of hybrid devices in other areas, this division is expected to grow rapidly. The introduction of solid state engine control systems in automobiles in 1980 should allow rapid expansion. Sales in 1978 were about $20 million for this division and are expected to exceed $25 million in 1979. DATAQUEST believes Fairchild has been selected by General Motors to second source the 6800 type microprocessor for GM's engine control system. Other substantial automotive revenues could result for 8K PROMs, as automobile manufacturers are planning to use PROMs in odo-meters and engine control systems. In the odometer application, a PROM fuse could be blown every 10 miles, thereby yielding a tamperproof odometer. Fairchild has licensed Bosch in West Germany and Femsa in Spain to produce hybrids for automobiles. The Company gets royalties as well as device sales, and in this way has penetrated Ford Europe, Opel, and Volkswagen. Optoelectronics Fairchild's Optoelectronic Division is prospering despite the loss of significant captive business as its consumer operations decline. The Company has become a major producer of liquid crystal displays (LCDs), especially for the large digits used in industrial displays. LCD revenues were about $5 million in 1978 and are expected to double in 1979. - 7 -Bipolar Fairchild is the leading producer of bipolar RAMs and has dominated this market for several years, but it now has competition from Signetics and Motorola. In addition. National Semiconductor is believed to be poised to enter the market in 1979, and MOS fast static RAMS available from Intel affect the market for bipolar RAMs. In 1978, Motorola and Signetics provided price competition in the bipolar RAM market in their bids to increase market share. Prices for IK RAMS fell to about $3.00, resulting in decreased margins for Fairchild in this area. However, we note recent activity by Signetics appears to emphasize bipolar PROMs over bipolar RAMs. Demand for bipolar RAMs has exceeded available supply, a con-dition that should last through part of 1979. We perceive that Fair-child has a cost advantage in bipolar RAMs and that competitive pressures have eased in recent months. Fairchild's 4K bipolar RAMs Should be available in production volumes in 1979. In bipolar PROMs, Fairchild shipped an estimated $15 million in 1978. This is an area where Signetics has a clear market advantage by virtue of being the only company shipping 16K bipolar PROMs—an advantage that it has used as a lever to increase its penetration in bipolar memory. Fairchild must meet this competition in 1979 to maintain its market leadership. Fairchild is still the only major producer of devices with isoplanar technology—a technology that enables it to design extremely small die sizes. We understand that its IK bipolar RAM is 6,000 square mils, the smallest on the market. As the market moves to 4K and 16K bipolar RAMs, this ability should be of increasing importance to Fairchild. We estimate that this process will account for 50 percent of its bipolar digital revenues by 1980. The 9440 16-bit I L microprocessor has been sampled to more than 100 accounts. While this microprocessor may miss the mainstream 16-bit market, it should nonetheless provide good business for Fairchild. The microprocessor can compete effectively at the board or system level in specific applications and should prove popular with the military market. Fairchild's board and system products incorporating the 9440 are referred to as its Microflame products. MOS In MOS, Fairchild suffers from a lack of scale and a limited in-vestment in design personnel. The inability to become a major MOS producer has been a significant problem with the Company for several years. However, rapid market growth in 1979 and industry undercapacity for MOS could provide the Company with time to improve its product and market position and attain improved economies of scale. We believe the Company will make a significant effort with substantial investment in MOS in 1979. Fairchild and TI are the only major producers of charge coupled devices (CCDs). While market acceptance of this technology has been - 8 -slower than previously anticipated, it is accelerating; the use of these devices for digital and optical applications can provide good future growth. Storage Technology and Memorex, among others, have designed CCDs into new memory systems that buffer large amounts of data between disc memory and main memory. The Company's 64K CCD has a $15 million bacl<log and production is capacity limited. Fairchild must get its CCD production down the learning curve quicl -J r. SCT RESE ARCI ASubsidiarvofA.C. Nielsen Co. ^ INCORPORATED I ^ I ^ ^ W ^ S I H ^ Z I SIS Code: Vol. I, 2.0 GENERAL INDUSTRY UPDATE SUMMARY m DATAQUEST continues to expect a resumption of growth for U.S. semiconductor consumption in the first half of 1981. However, because present concerns about the future of the U. S. economy are causing extreme caution in the business community, weakness in semiconductor shipments is expected to continue through the first quarter. The current contraction in U.S. semiconductor consumption, forecast by DATAQUEST at the beginning of this year, is continuing along a very moderate course. We believe that shipments in the third quarter have been only about 3.1 percent lower than in the second quarter of 1980. We expect a similar contraction in the fourth quarter of this year, with a leveling of shipments continuing through the first quarter of 1981. DATAQUEST estimates that U.S. semiconductor consumption for all of 1980 will be 26.2 percent higher than in 1979, reflecting very strong momentum at the beginning of 1980. Although we expect strength to return to U.S. semiconductor consumption in early 1981 and to accelerate throughout the year, we forecast the total for 1981 to be only about 8.1 percent more than in 1980. The U.S. economy, which fell abruptly in the second quarter of this year, has been recovering at a slow to moderate pace for the last four or five months. But the currently high (approximately 21 percent) prime rate precludes a strong economic recovery. For this forecast we assume a benign economy with very gradual improvement. Nevertheless, in planning for the future, the probability of a second major downturn in the U.S. economy cannot be excluded. That occurence could have major negative consequences in the semiconductor industry. So far, we remain optimistic. The electronics industry, and specifically the semiconductor industry, continues to outperform significantly the U.S. and world economies. The current situation bears no resemblance to the debacles of 1970 and 1975. RECENT ECONOMIC TRENDS The Good News The economic recession that arrived abruptly during the second quarter of this year has bottomed out, and conditions have been on the road to slow improvement: • Retail sales have been improving for the last six months (in current dollars). • The Index of Leading Indicators has been up for the last five months. Copyright © 22 December 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients This information Is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer TO buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position m the securities mentioned and may sell or buy such securities 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO • Housing Starts have been up for the last five months. • Industrial production has been up for the, last four months. / This news is both consistent and encouraging. Declines in unemployment, and other indications that the business cycle is on an upturn, confirm this good news. The Bad News Efforts to curb inflation contributed greatly to the recession just experienced. Those efforts were a dismal failure, and the downturn was perhaps too brief to prime the economy for a major upward cycle. Efforts to control inflation have led to some definite bad news: • Inflation continues at double-digit rates. • The prime rate is approximately 20 percent. • Although at this writing no major economic measures have turned down, their delayed reporting may conceal the fact that the recovery has been halted abruptly. • Efforts to contain the money supply (worldwide) have met with little success. • The economies of Japan and Europe are presently in a downturn, having trailed the U.S. economy by several months. The Outlook Obviously, the high prime rate has engendered considerable caution in the business community. We cannot predict whether this high prime rate will cause a renewed contraction of the U.S. economy. But clearly, the probability of a W-type (double dip) economic cycle has increased (we will know within a few weeks whether that probability becomes a reality). Just as clearly, a new administration in the government would prefer to incur economic pain now rather than two or four years hence. However, the high interest rates are also a reflection of the economic recovery. If the recovery were less strong, inflation and interest rates would be lower. In other words, the very high cost of money may be as much a result of renewed economic strength increasing the demand for money as it may be an indicator of future problems. It is not fore-ordained that the economy will turn down. It is more probable that the economy will experience much slower growth, with a very gradual recovery. This benign economy is the basis for our forecast of semiconductor consumption. Part of the current economic problems results from a major restructuring of the U.S. and world economies. Those industries that are sensitive either to inflation or to the higher cost of energy—directly or indirectly—are continuing to suffer severe problems. These industries include such areas as housing, forest products. - 2 -automotive, steel, airlines, tourism, and so forth. On the other hand, some industries benefit from this restructuring including the electronics and semiconductor industries. SEMICONDUCTOR INDUSTRY TRENDS The U. S. semiconductor industry presently is experiencing a contraction in Shipments. As expected and forecast by DATAQUEST, this contraction has been relatively mild. We can expect lower shipment levels due to recent order weakness. Shipments in the third quarter of 1980 were approximately 3.1 percent less than in the second quarter. A further contraction of about 2.9 percent is expected in fourth quarter of 1980 and 0.2 percent in the first quarter of 1981. Semiconductor orders have increased consistently since bottoming in July. The book-to-bill ratio for the industry in November appears to have been close to unity. This is encouraging, although DATAQUEST has noted considerable inconsistency among individual companies. Major semiconductor manufacturers appear to have book-to-bill ratios in November varying from 0.7 to 1.2—a highly unusual degree of variation. Early this summer major order problems were in MOS devices, especially memory. This situation appears to have spread generally throughout the industry with less severity recently in MOS, and some present order weakness occurring in bipolar digital, linear, discrete devices, and optoelectronics. Distribution currently is a very weak segment for suppliers. The price weakness in MOS memory of the past several months appears to have Stabilized. Interestingly, the rapid price declines in MOS memory occurred despite a continued growth in unit consumption throughout 1980. However, the unit consumption did not keep pace early in the year with the rapid growth in capacity. Recently, order strength in MOS has been encouraging. In addition, low prices have slowed expansion of capacity. Although DATAQUEST has noted price weakness in bipolar devices, we do not expect a major decline in prices similar to that which has occurred in MOS memory. DATAQUEST believes that additional new capacity coming onstream in bipolar devices will be somewhat limited for the next nine months; this fact may help maintain a balance between supply and demand. Some discrete device areas have been especially weak, particularly those associated with consumer products. In optoelectronics, LED displays are experiencing significant weakness in orders. Oddly enough, lack of new capacity in Japan (possibly due to excessive attention to MOS LSI) has caused a temporary shortage in small-signal devices. It is DATAQUEST's perception that actual usage of semiconductor devices remains relatively strong and is increasing. There are some other positive aspects: • Virtually all double orders now have been purged from backlogs. • Inventory levels of semiconductors at the user level are believed to be quite low (with a few exceptions). Generally the high cost of money has caused significant attention to inventories, and further reductions are not likely. - 3 • DATAQUEST does not foresee further major reductions in semiconductor prices. • Order changes for either a stretch-out of delivery or for price reductions caused a major problem in the second and third quarter. We do not expect a continuation of this trend. It is likely that the factors mentioned above preclude any problems of the magnitude experienced in previous recessions. Those problems, such as double ordering, excessive inventory, and excessive prices, have now been worked through, which places the order book in a fairly healthy condition. However, backlogs of most semiconductor manufacturers have been declining during the last several months. Further order weakness could cause significant problems in maintaining shipments at present levels. Suppliers of material to the semiconductor industry recently have been experiencing a fairly stable shipment and order situation. Most shipments and orders are at levels moderately below the peak of early 1980. Equipment suppliers, especially those with long lead time products, have experienced continued strong demand throughout the third quarter. It is our belief that that demand may be slackening, but major weakness is not expected. Manufacturers of smaller, lower cost equipment, the purchase of which is more easily postponed, have experienced most of the softness in this area. Semiconductor manufacturers have not significantly reduced capital expenditure plans. Such spending is further augmented by major capital expenditures for semiconductor facilities and equipment by captive manufacturers and foreign governments. The expected conversion to VLSI production capability in wafer fabrication (sub 5 micron dimensional tolerances) is an additional positive factor for the equipment market. That portion is independent of the strength in semiconductor orders. As a result, DATAQUEST expects no future weakness of equipment orders. The current situation is significantly different from previous slowdowns in semiconductor demand. Manufacturers of semiconductors do not wish to be caught Short of capacity when significant growth resumes in demand. Those manufacturers that did not expand in capacity in 1975 paid a significant price in lost growth potential after the market resumed strength in 1976 through 1979. Most major companies in the industry will have work stoppages (layoffs) during the Christmas holidays ranging from 5 to 10 days (including the holidays). These stoppages are as much a result of the timing of Christmas and New Years on Thursdays as it is a reflection of demand weakness. Even in times of strong growth, many Silicon Valley companies have closed for a week during this season. It is highly significant that the semiconductor industry has yet to have or to need major layoffs. Hiring freezes were begun early this year, and employment reductions through attrition have been adequate to match any ciianges in shipment rates. Employment advertisements in Silicon Valley have remained at high levels throughout the fourth quarter. We believe this is significant, a rapid increase in the demand for components in 1981 could find the industry short of personnel—both hourly - 4 workers and professionals. In previous recessions, reductions of employment in the industry have exceeded 30 percent. These reductions represented excess available capacity—both in people and in facilities. That excess capacity is not currently available, and could engender a supply/demand imbalance sooner in the economic cycle. Semiconductor Industry Forecast Table 1 presents DATAQUEST's estimate for U.S. semiconductor consumption in dollars. We believe that U.S. semiconductor consumption in 1980 will show an increase of about 26.2 percent over 1979. In 1979, U.S. semiconductor consumption increased approximately 37.6 percent over that of 1978. It should be noted that these figures also include exports to the United States from Japan and Europe, and these exports increased significantly over the last two years through the first half of 1980. However, the falling prices in MOS memory have recently caused a decline in the rate of semiconductor imports into the United States. DATAQUEST expects further growth in U.S. semiconductor consumption in 1981, to an estimated level of 8.1 percent over this year. Table 1 ESTIIVIATED U.S. SEMICONDUCTOR CONSUMPTION (Millions of Dollars) Discrete Devices Integrated Circuits Total 1979 $1,322 $3,375 $4,697 Percent Increase 1979-80 4.5% 34.7% 26.2% 1980 $1,382 $4,545 $5,927 Source Percent Increase 1980-81 (0.7)% 10.8% 8.1% 1981 $1,373 $5,035 $6,408 : DATAQUEST, Inc. December 1980 Table 2 presents our current estimates for U.S. semiconductor consumption by calendar quarter. (See Figure 1.) We expect the moderate decline in semiconductor consumption experienced in the third quarter of this year to continue through the fourth quarter, with a leveling in the first quarter of 1981. Specifically, we forecast that fourth-quarter semiconductor consumption will be about three percent below that of the third quarter of 1980. DATAQUEST forecasts a healthy resumption of growth in semiconductor consumption in 1981, beginning by the second quarter. (However, we should reiterate that if the economy does move strongly negative, a resumption of growth in semiconductor consumption would be delayed further.) - 5 -Table 2 ESTIMATED QUARTERLY U;S. SEMICONDUCTOR CONSUMPTION (Millions of Dollars) 1979 Discrete Devices Integrated Circuits Total Percent Change From Previous Quarter 1st Qtr. $ 301 700 $1,001 4.4% 2nd Qtr. $ 340 805 $1,145 14.4% 3rd qtr. $ 344 868 $1,202 5.0% 4th Qtr. $ 347 1,002 $1,349 12.2% Total Year $1,322 3,375 $4,697 Percent Change From Previous Year Discrete Devices Integrated Circuits Total Percent Change From Previous Quarter Percent Change From Previous Year Discrete Devices Integrated Circuits Total Percent Change From Previous Quarter 33.6% 1st Qtr. $ 354 1,066 $1,420 5.3% 41.9% 1st Qtr. $ 329 1,125 $1,454 (0.2%) 36.0% 2nd Qtr. $ 364 1,185 $1,549 9.1% 35.3% 2nd Qtr. $ 340 1,216 $1,556 7.0% 39.1% 1980 3rd Qtr. $ 334 1,167 $1,501 (3.1%) 24.9% 1981 3rd Qtr. $ 343 1,278 $1,621 4.2% 40.7% 4th Qtr. $ 330 1,127 $1,457 (2.9%) 8.0% 4th Qtr. $ 361 1,416 $1,777 9.6% 37.6^ Total Year $1,382 4,545 $5,927 26.29 Total Year $1,373 5,035 $6,408 Percent Change From Previous Year 2.4% 0.5% 8.0% 22.0% 8.1% Source: DATAQUEST, Inc. December 1980 - 6 -Figure 1 ESTIMATED QUARTERLY U.S. SEMICONDUCTOR CONSUMPTION $2,000-^ »1,500--& I SI ,000--$500--V 01 02 Q3 I 1 1 1 1 i 1 1 1 • m rf> m n j ' n i ni m nA ' 04 • 01 02 03 04 • 01 02 03 04 A A / 1979 i9ao 1981 # Source: DATAOUEST, Inc. December 1980 - 7 -The decline in semiconductor consumption in the second half of 1980 is of course tied to the very rapid decline in the U.S. economy during the second quarter of this year. But this decline has been caused essentially by an adjustment in semiconductor prices. It is important to point out that unit demand for large chips has remained strong. In other words, actual usage has not collapsed. The resumption of price stability coupled with this growth in unit demand can provide market growth. Long-Term Outlook Over the last two years, the semiconductor industry has clearly outperformed the economy. Any econometric model, including ours, no longer can be used to predict semiconductor demand. While we feel our model remains reasonably accurate for timing or inflections, it no longer holds for accurate assessments of the magnitude of industry growth. Thus, the past is no longer useful to predict accurately the future of the industry. In the eight quarters ending with the second quarter of 1980, U.S. semiconductor consumption grew 79.3 percent. During the same period of time, industrial production, after a long period of stagnation, fell more than nine percent. Automobile sales were down more than 30 percent, and housing starts were down more than 40 percent from their peak. Obviously, demand for electronics is not linked strictly to economic strength. Changes in the structure of the U.S. economy are providing a background for significant sales of electronics. We believe that 1979 and early 1980 presage a period of several years in which the semiconductor industry will experience only moderate problems in recessions and extremely rapid growth in periods of economic strength. There are very strong engines of demand driving semiconductor consumption: • The increasing price performance of semiconductor devices and the electronic systems made from them compared with inflating prices of almost everything else. • Sales of electronics to combat higher material and energy costs. • Sales of electronics to combat higher inventory costs. • Sales of electronics to combat higher expected future labor costs. The high costs of inventory, energy, labor, and materials have had a major effect on the economics of the purchasing decision for equipment. The payback on many types of electronic equipment has been significantly increased. We discussed these engines of demand in our "Outlook for 1981" presented at the DATAQUEST annual conference in October. DATAQUEST believes the long-term outlook for the industry is highly positive. Frederick L. Zieber # 8 -SIS Code: Vol I, 1.3 JAPANESE EQUIPMENT MANUFACTURERS INCREASE PRESENCE AT SEMICON/JAPAN '80 OVERVIEW The Semiconductor Equipment and Materials Institute, Inc., (SEMI) of Mountain View, California, presented the fourth annual SEMICON/Japan '80 show at the Tokyo Harumi Fairground, November 19-21. SEMICON/Japan is clearly the second most important of five technical/trade shows held for semiconductor equipment manufacturers by SEML The three-elieve that their engineers have special requirements that only domestic manufacturers can meet. Others have the feeling that the United States neglects the Japanese market. These beliefs, combined with the perceived high quality of some Japanese semiconductor equipment, will put increased pressure on U.S. equipment manufacturers to establish a strong presence in Japan, and to develop a worldwide market outlook. Ted Rafalovich Susan A. Thomas Howard Z. Bogert - 4 -^.f ^ ± ^ S ^S^^ ^S ^ ? ^ = ^ = ^ £ ^ = ^= =—=—=~ L J ^ ^ 4 ^ ^V E3^^t4 ' ^ ^ • H . • ^ H B m M^m.m • M M ASubsidiary of A.C.Nielsen Co. " ^ INCORPORATED SIS Code: Vol. I, 1.6 1980 CAPITAL SPENDING HOLDS STEADY - CAUTIOUS PLANS FOR 1981 -SUMMARY Recent estimates of U.S. merchant semiconductor manufacturers' capital spending plans for facilities and equipment are holding firm, seven months after the first signs of a business flattening appeared. Small reductions from some companies' early-year spending plans appear to have been made up by increases from other companies, and total 1980 industry outlays are, in fact, up about five percent from earlier expectations. Furthermore, preliminary 1981 plans by these manufacturers indicate that the business slack is expected to be shallow and short-lived. Tentative 1981 plans show an increase of about 12 percent over 1980 levels. Table 1 shows DATAQUEST's estimates of merchant manufacturers' capital spending. In the first column are DATAQUEST's 1980 estimates from an earlier newsletter (see DATAQUEST Research Newsletter dated 1 April 1980 entitled "U.S. Semiconductor Manufacturers'Capital Spending 1979-1980"). The second column has current estimates of what 1980 will finally see. Third are estimates of 1981 spending plans based on public statements by company spokesmen and industry sources. Based on a preliminary estimate of 1981 U.S. semiconductor manufacturers' factory shipments as shown in Table 2, it appears that capital spending will rise at about the same rate as revenues next year. MANUFACTURERS' RESPONSE TO 1980 RECESSION The mild recession now evident has done little to shake the merchants' solid commitment to build additional capacity for the future. Total capital spending by all manufacturers has remained firm, although there has been more commitment to put in brick and mortar than to place firm orders for equipment. There have been stretch outs on equipment orders—which we view as an adjustment for the short term—and reductions in backlogs among equipment suppliers. However, forfeitable down-payments and extremely long lead times on the highest ticket items have forced semiconductor manufacturers to plan carefully and hold to their contractual delivery agreements. Copyright © 12 December 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness It does not contain material provided to us in confidence by our clients. This information is not furnished in connection vwith a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities This firm and its parent and/or their officers, stockholders, or members of Their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO Table 1 ESTIMATED U.S. MERCHANT MANUFACTURERS' CAPITAL SPENDING (SEMICONDUCTORS ONLY) (Millions of Dollars) Advanced Micro Devices Fairchild Intel Mostek Motorola National Semiconductor Signetics Texas Instruments Other U.S. Companies Total Spending Earlier 1980 Estimate $ 65 70 125 85 200 90 80 190 415 $1,320 Current Estimate For 1980 $ 65 95 125 85 175 120 80 220 415 $1,380 Planned 1981 $ 80 120 140 85 175 145 110 250 450 $1,555 DATAQUEST Researcli Newsletter dated 1 April 1980 entitled "U.S. Semiconductor Manufacturers' Capital Spending 1979-1980" Source: DATAQUEST, Inc. December 1980 Table 2 U.S. MERCHANT SEMICONDUCTOR CAPITAL SPENDING AS PERCENT OF REVENUES (Millions of Dollars) Year 1973 1974 1975 1976 1977 1978 1979 1980 1981 Industry Capital Revenues $2,830 $3,366 $2,796 $3,519 $4,079 $5,123 $6,880 $8,650 $9,650 Expenditures $ 341 $ 421 $ 195 $ 356 $ 431 $ 680 $1,065 $1,380 $1,555 Percent 12.0% 12.5% 7.0% 10.1% 10.6% 13.3% 15.5% 16.0% 16.1% 1980 and 1981 data are preliminary estimates Sourcer DATAQUEST, Inc. December 1980 - 2 1980 RECESSION DIFFERS FROM 1974-75 RECESSION...SO FAR In the 1974-75 recession, total capital spending by merchant manufacturers was cut in half compared to pre-recession levels. In our opinion, the present situation differs in many ways: • The business weakness to date has been much more modest than during the previous recession period with no massive long-term layoffs, no manufacturers reporting unprofitable quarters, and no large return of products from users. • Users' inventories have been better controlled, and market declines have been less precipitous. • Semiconductor manufacturers had expected the recession for 18 months and planned accordingly. • The general industry consensus is that hesitancy to build during or after 1974-75 resulted in lost opportunities in 1978-79. • Two Strong years of industry growth have left long lead times for much equipment. These lead times have kept equipment shipments playing catch-up in a flat components market. The situation has been exacerbated by significant increases in the time required to build high-complexity manufacturing equipment. • Supply excesses are confined to just a few markets, and, we believe, the failure of revenues to grow in the last half of 1980 has resulted more from component price attrition than from relaxation of demand for units. RISING INTEREST RATES PROLONG UNCERTAINTY Recent weeks have seen a continual rise in interest rates, and many economists are expressing concern that the overall economy will turn down again. If this occurs, it would essentially nullify the scenario that had the semiconductor industry experiencing a continuing slow rebound in the first and second quarters of next year. It might force merchant semiconductor manufacturers to reconsider their spending plans for next year, as profits are squeezed and borrowing becomes increasingly expensive. In an extreme situation, it may be difficult for manufacturers to keep focused on the post-reeession recovery when the present makes investment so difficult. Concern over interest rates seems to have dampened earlier positive signs within the semiconductor industry when bookings improved and prices firmed up. It seems apparent that the longer interest rates remain at their present level, the more probable it will be that the economy will turn down and that capital spending plans for 1981 will need to be adjusted downward. Lane Mason Susan A. Thomas Jean Page - 3 -SIS Code: Vol III, 8.04 INNOVATION This newsletter is a condensation of remarks delivered by Robert N. Noyce, vice chairman of Intel Corporation of Santa Clara, California, on September 8, 1980 to the Affiliates Program of the Graduate School of Business at Stanford University. INNOVATION Innovation is declining in America, despite its importance to our economy and society. The evidence is substantial. The number of patents issued to Americans by the U.S. Patent Office, the number of new companies issuing stock to the public, the productivity of American industry, and U.S. expenditures on research and development are all declining. Innovation benefits our society. It has accounted for about half of our economic growth, outranking capital and the increase in our labor force in its contribution. The present administration recognized the importance of innovation and initiated a Domestic Policy Review of Industrial Innovation. The findings were submitted to the president nearly a year ago, but little action has been taken. Innovation cannot be mandated, but it can be encouraged by creating an environment conducive to innovation. Nearly every government action affects innovation in some way, either positively or negatively. Necessity is not the only mother of invention. • Motivation. The innovator must see some personal advantage. Rewards may include recognition, personal satisfaction, and money. • Optimism. The innovator must believe that problems can be solved with available resources. Without optimism, the individual is risk-averse. • Opportunity. A growing economy presents the potential innovator with more problems to attack. In a static world, there is little opportunity for the success of innovations. Knowledge. This is the basic tool kit for the innovator and must be replenished through basic research. Money. The innovator must have private, corporate, or public risk capital to explore new ideas. Copyright © 12 December 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally availabIe to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness It does not contain material provided to us in confidence by our clients This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securitieSf This firm and its parent andfor their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO Unfortunately, conditions that would encourage innovation have eroded over the last 10 to 20 years in the United States. • Increasing regulation bars the introduction of new ideas and reflects the risk aversion of our society. • Inflation has made a mockery of the ethic of saving, and has promoted immediate consumption. Consequently, the availability of capital has suffered. • Poor investment performance also has limited the availability of risk capital. • Anti-technology sentiment has caused many of our brightest young people to choose careers in which innovation is unlikely. • Zero growth sentiment, espoused by the Club of Rome, has convinced many that economic growth is undesirable. Even the most optimistic innovator is discouraged. • Conflict in our society discourages both the innovator and the cooperative effort that is necessary to make innovation effective. Policy Options Any actions that restore vitality to the American economy will promote innovation. Such actions include the elimination of inflation, control of government spending, elimination of counter-productive regulations, increases in savings and investment rates, and increasing rewards for success. There are other options, however, that are necessary today for the health of emerging industries and that will benefit our industry tomorrow. One option is to set an industrial policy. The United States has not deliberately set an industrial policy that favors a particular industrial group, and that in itself is an industrial policy. This informal policy tends to maintain established industries at the expense of the emerging industries. Mature industries gain favor because emerging companies based on new technology and innovation have not yet established relationships with the government. They are typically small companies, and the expense of lobbying is beyond them. Consequently, they are not adequately represented in government decision making. And, although only 25 percent of the labor force in the U.S. belongs to unions, unions represent labor in government decisions. Again, emerging industries are not adequately represented in Washington because their labor forces do not, typically, belong to unions. - 2 -An industrial policy based on shifting requirements for industrial output and the relative competitiveness of American industry would back our strengths and not our weaknesses. The Chrysler loan, for example, would create many more jobs if used to promote new ventures instead of to preserve life support systems for a corporate geriatric. Research and Development As a nation, we are not investing enough in research and development, which lies at the heart of innovation. R&D expenditures have dropped by about one-third in the last decade. Any policy that promotes innovation should include increasing our national expenditures on research and development, preferably by private industry and in areas in which the results can be used by the private sector. Public support of research, except in the areas of public health or national defense, tends to drive out corporate funding. The best methods available to increase corporate R&D expenditures are tax incentives. Such incentives could include investment tax credit for research and development or greater than 100 percent deductibility for research and development. University Research Our universities have become increasingly more dependent on government funding since World War II. As a result, they are becoming less responsive to the needs of the private sector. University research has two important characteristics in particular: it produces trained manpower, and research results are spread rapidly, through publication and departing students. However, students are too often trained in fields in which the government is nearly the only employer or in which there are few job opportunities. There is little university researcli directed toward the needs of industry, yet such direction is common practice in countries that have an articulated industrial policy. Industrial sponsorship of university research is limited today because its benefits are also available to the sponsor's competition. Sponsorship benefits the entire society, and its cost should be borne in part by that society. The most effective way to promote industrial sponsorship of university programs is to give tax credits rather than deductions to sponsors. Such credits could be limited to a fraction of internal research and development to ensure that programs are approved by those active in managing research and development and that jobs await graduates. New Companies, Growth Companies Innovation is the most successful strategy for a new company. Therefore, any policies that support new companies will have a favorable effect on innovation. Sucli policies could include more favorable treatment of capital gains on new issues, easing of SEC regulations for issuing new stock, or more favorable treatment of loss carry forward for start-up companies. - 3 -Furthermore, successful innovative companies become growth companies and usually continue to innovate. Policymakers have another opportunity to support innovation through increased tax credits for the creation of jobs and deferred taxation on increased earnings, both of which help solve a major problem for a growth company — financing that growth. The re-establishment of the restricted stock option also favors the growth company and at the same time increases federal revenues. Social Philosophy If we as a nation are to excel, we must reward excellence. It is a simple tenet, but one that is not accepted by large segments of our society. All men are created equal, but some contribute more than others. If we wish to encourage such contribution, we cannot insist that all men finish the contest together because they were equal at the beginning. Countries that outperform us, most notably Japan, have an operating meritocracy as a practical philisophy. We should insist upon equality of opportunity because that will promote innovation. But we must let each seek the rewards that must be, both corporate and individual, or we will complete the job of killing America's golden goose. Robert N. Noyce - 4 -SIS Code: Vol. II, 3.1 DRY ETCH PROCESSING SUMMARY The semiconductor industry is fast approaching two, one, and even submicron lines in its quest for small-geometry, high-speed devices. Fine-line geometries demand changes in many wafer fabrication processes and the etch process is no exception. In response to the demand, the industry is developing dry etch processes, including plasma etching, reactive ion etching (RIE), and ion mill etching. DATAQUEST believes that worldwide dry etch wafer processing equipment consumption was $50 million in 1979, up from $29 million in 1978. We believe that worldwide consumption should reach $90 million in 1980, and $335 million in 1984. The most important advantage of dry etch processing is that some methods can perform an anisotropic, or vertical, etch. It will be necessary to etch vertically as device lines become finer. So far, the most successful application of dry etch processing is to nitride and polysilicon layers but dry etch processing applied to other materials is some months away from production use. The opportunities in the dry etch market have created a proliferation of suppliers that shows no sign of slowing at this time. Consequently, DATAQUEST believes that it may be some time before a dominant supplier emerges. THE PROCESS Wet Chemical Etching Traditionally, the most common method of etching a wafer patterned with photoresist is to submerge the wafer in a wet chemical etch solution that attacks the exposed surface at a slower rate than the rate at which it attacks the photoresist. DATAQUEST estimates that 70 to 90 percent of mask layers are etched in wet chemical solutions. Wet chemical etching has some very positive characteristics. The equipment used in the process is relatively inexpensive, and it produces relatively high selectivity. Selectivity is the difference in etch rates between the material in the layer that is being etched and the underlying layer. Copyright © 5 December 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally availabIe to the public or released by responsible individuals in the subiect companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients This Information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO Wet chemical etching has some negative characteristics, however. It may be •hazardous to personnel because of the potentially dangerous chemicals used in the solution. The use of wet chemicals also creates a waste disposal problem. Another production problem may occur as the acids and bases in the solution are used up, which may cause the etch to change during the processing of a batch of wafers. In addition, wet chemical etching has some serious technological limitations. It produces an isotropic etch—an etch that proceeds horizontally as well as vertically—that may lead to resist undercutting. It is also difficult to control the Slope of the walls produced by the etch. These problems will become more critical as the industry approaches submicron lithography. Faithful reproduction of fine-line geometries may require vertical walls; isotropic etching broadens the lines by undercutting. Dry Etching Dry etch processing has both production and technological advantages over wet chemical etcliing. Dry etching is safer because it requires fewer potentially dangerous chemicals in less volume, and because human operators are not directly exposed to the chemicals in the process. Furthermore, dry etching partially eliminates the waste disposal problem, and reduces the problem of inconsistent etching associated with processing a batch of wafers in wet chemicals. Among its technological advantages, dry etching produces clean lines, and may allow control of the slopes of the waUs. Some types of dry etching produce an anisotropic etch, which is a single-direction (vertical) etch that creates 90 degree w£dls, and some types eliminate undercutting. Of the three types of dry etch processes currently in use or in development, plasma etching is the most common. This process employs gases to remove the material that is being etched in a chemical reaction. Reactive ion etching (RIB) is partly a chemical process and partly a mechanical process. It combines chemical activity and directed, charged particles to remove the material that is being etched. Ion mill etching is entirely a mechanical process. It employs accelerated gas ions to t»ombard the wafer in a collimated beam. Another process, reactive ion beam etching (KIBE), is actually a combination of RIE and ion mill etching. The plasma etching process uses two different types of equipment—barrel reactors and planar (or parallel plate) reactors. Barrel reactors are currently the most common and inexpensive type of equipment and are used for etching and photoresist stripping. Wafers are positioned vertically inside the barrel reactor chamber, which is then evacuated and the gas mixture admitted. The ionized gas forms around the wafers and the etching process is performed by the ions, which are chemically activated. Barrel reactors generally perform an isotropic etch. They have greater wafer throughput than planar reactors, however, and are relatively inexpensive, at about $30,000. - 2 -Mr V Planar reactors etch wafers as they lie flat between parallel electrodes. Planar reactors can perform anistropic etches and they have good selectivity. However, the equipment is more expensive than barrel reactors ($125,000 and up) and cannot process as many wafers per hour. RIE equipment is similar to planar reactors; in fact, there is some controversy in the industry over the similarities/differences between planar reactors and RIB equipment. DATAQUEST has not attempted to settle the issue, but we do combine planar reactors and RIE equipment under the same heading in our estimates of consumption of dry etch processing equipment. Some industry observers believe that RIE equipment produces a better anisotropic etch than plasma planar equipment. RIE equipment tends to be expensive, in the same range as planar reactors. The ion mill etching process performs the best anisotropic etch of all the dry etch processes, but the process is slow because it is entirely mechanical. Selectivity is also very low. Ion mill equipment costs are in the range of $150,000 to $200,000. MARKET GROWTH DATAQUEST estimates that worldwide dry etch wafer processing equipment consumption was $50 miUion in 1979, an increase of 72 percent over the $29 million of consumption in 1978 (see Table 1). Worldwide consumption should reach $90 miUion in 1980, and $335 million in 1984, representing a 39 percent compound annual growth rate (CAGR) between 1980 and 1984. Table 1 ESTIMATED WORLDWIDE DRY ETCH WAFER PROCESSING EQUIPMENT CONSUMPTION, BY GEOGRAPHICAL AREA (Millions of Dollars) 1978 1979 1980 1984 North America Japan Western Europe Total $15 12 _2 $29 $28 19 _3 $50 Source: $60 $253 25 52 5 30 $90 $335 DATAQUEST, Inc. December 1980 By geographical area, North American consumption of dry etch processing equipment should increase at 43 percent CAGR between 1980 and 1984. Japanese consumption should increase at a 20 percent CAGR during that same period. Western European consumption should increase at a 57 percent CAGR. - 3 -/ » North American equipment consumption estimates by product reveal that the fastest growth is in consumption of planar/RIE equipment (see Table 2). North American consumption of planar/RIE equipment was an estimated $3 million in 1978, rose to $10 million in 1979, and should reach $32 million in 1980, representing a 227 percent CAGR. North American consumption of barrel reactors should increase at a 35 percent CAGR and consumption of ion mill equipment should increase at a 183 percent CAGR between 1978 and 1980. Table 2 ESTIMATED NORTH AMERICAN DRY ETCH WAFER PROCESSING EQUIPMENT CONSUMPTION, BY PRODUCT (Millions of Dollars) 1978 1979 1980 Barrels/Strip & Planar/RIE Ion Mill Total Etch $11 3 _1 $15 Source: $15 $20 10 32 3 _8 $28 $60 DATAQUEST, Inc December 1980 Japanese consumption of planar/RIE equipment should increase at a 41 percent CAGR between 1978 and 1980, while consumption of barrel reactors should increase at a 51 percent CAGR during the same period (see Table 3). Japanese consumption of ion mill equipment is negligible at this time. Table 3 ESTIMATED JAPANESE DRY ETCH WAFER PROCESSING EQUIPMENT CONSUMPTION, BY PRODUCT (Millions of Dollars) 1978 1979 1980 Barrels/Strip Planar/RIE Ion Mill Total & Etch $3.5 8.5 -$12.0 Source: - 4 -$ 5.5 13.5 — $ 19.0 $ 8.0 17.0 — $ 25.0 DATAQUEST, Inc. December 1980 Production of planar/RIE equipment in North America and Japan has increased more than two times over the last three years. In addition, the production ratio between North America and Japan has changed from Japan producing slightly more to North America producing more (about 2:1). DATAQUEST believes that this change reflects a greater commitment to dry etch processing in proportion to wafer Starts in North America than in Japan. The advent of dry etch processing may affect other wafer fabrication process markets. For example, as more manufacturers shift to dry processing, they should require fewer wet chemicals in less volume. There are more than two dozen wet chemicals used in the wafer fabrication process and it is likely that dry processing wiU affect each chemical usage separately. However, the increase in wafer starts and the number of layers per device creates growth potential for both dry etching and wet etching, and DATAQUEST believes that the wet chemical market should continue growing at least through 1985. The photoresist market may also change as a result of dry etch processing. One property of photoresist is that it erodes faster at higher temperatures. One way to increase etch rates is to use a photoresist that erodes more slowly at high temperatures. High etch rates are particularly important in the single-wafer dry etch machines. Currently, single-chamber machines do not have etch rates comparable to typical line throughputs in most wafer processing factories. Thus, high throughput machines require more than one chamber and, as a result, are more expensive than single-chamber machines. Consequently, suppliers of photoresist may be under some pressure to develop photoresist that can withstand higher temperatures. A high-temperature photoresist could also improve the sales of single-chamber etch machines. One new growth market that should emerge because of dry etch processing is the specialty gas market. The gas usage per wafer is not particularly large, but the overall market should grow significantly between 1980 and 1984. Excluding dopant and deposition gases, the specialty gas market is an estimated $6 million to $10 miUion in 1980 and should reach $30 million to $50 million in 1984. Specialty gases currently constitute only 10 percent of the total gas market. There is a lot of experimentation with specialty gases, and the gases used currently may not necessarily be the gases used in the future. At present, manufacturers use oxygen in dry photoresist stripping, and use mixtures of fluorocarbons and geises such as argon in dry etching. TRENDS The ideal etch is controlled, selective, and uniform throughout the wafer and the run. No one etch process can perform the ideal etch, so there are some trade-offs in the use of dry etch over wet etch and vice versa. The most important advantage of dry etch processing over wet chemical etching is that some methods can perform an anisotropic etch; it will become necessary to etch vertically as device lines become finer. DATAQUEST believes that 5 -ultimately all etching will be performed with dry etch processes, but that it could take a long time to complete the transition. So far, dry etch processing has been applied most successfully to silicon nitride and polycrystalline silicon layers. Nitride etching is the most popular application and polysilicon etching is becoming more popular. DATAQUEST believes that there is some difference in perception between customers and suppliers over the current capabilities of dry etch processes for other materials such as aluminum or silicon oxide. Effective processes for use with aluminum and oxide may be further away than suppliers think. It appears that offering the equipment is sometimes not enough—many customers need to be told what gases to use and how to use them. Suppliers often do not have the resources to do that kind of research, or they do not have the qualified process personnel to work with customers. Some of the larger customers are purchasing equipment and developing their own processes, but that information does not get baci< to the supplier to pass along to other customers. Nevertheless, opportunities in the dry etch market have created a proliferation of suppliers and a large number of suppliers who are considering the market. There are currently about 20 suppliers with products to offer, and perhaps as many as 12 additional suppliers plan to enter the market in the next year or two (see Table 4). One reason for the proliferation of suppliers is that suppliers must invent lots of technology before device manufacturers can perform the previously described ideal etch. There are many possible solutions to the problems and no one company can provide all of them. Companies tend to concentrate on just one or two solutions, which means that the field is crowded, and it may be some time before a dominant supplier emerges. Howard Z. Bogert Susan A. Thomas Table 4 DRY PROCESSING EQUIPMENT SUPPLIERS Anelva (NEC) Japan Applied Materials Santa Clara, CA CHA Menlo Park, CA Commonwealth Scientific Alexandria, VA CVC Rochester, NY D&W (Eaton) Santa Clara, CA ET Equipment (Electrotech) Hauppauge, NY GCA Bedford, MA IPC/Dionics Hayward, CA LFE Waltham, MA MRC Orangeburg, NY Perkin-Elmer Norwalk, CT Plasma-Therm Kresson, NJ Technics Alexandria, VA Barrel Reactors Planar/ RIE Ion Mill X X X X X X - 7 -Table 4 (continued) DRY PROCESSING EQUIPMENT SUPPLIERS Tegal Richmond, CA Tokuda (Toshiba) Japan Tokyo-Oka Japan Varian Palo Alto, CA Veeco Sunnyvale, CA Barrel Reactors Planar/ RIE X Ion Mill X Source: DATAQUEST, Inc. December 1980 - 8 -^^1 MUH 1 HULIU f ^ SECURITIES, IW^ ^ H ^ H 1 1 ^ H R ^ C Vol. II- No. 10 December 2, 1980 This letter is a condensation of recent Research Newsletters and internal thinking from the industry research groups at DATAQUEST, Inc. Requests for amplification of our thoughts or for specific Newsletters should be directed to the author. A list of recent DATAQUEST Newsletters appears at the end of this letter. SMALL COMPUTERS/OFFICE AUTOMATION The recent introduction of Datapoint's high-end processor, the 8800, was important not only because of the product itself, but also because of some information that was made available in conjunction with the announcement, indicating that Datapoint is making very encouraging progress in penetrating the office automation market. One of the potential weak spots at Datapoint was the relatively small main memory capacity of the 6600 processor, which was its largest processor prior to the 8800 announcement. The 6600 has only 256 Kbytes of main memory, which could have potentially limited its ability to process large programs. Each 8800 can support up to one megabyte of main memory, four times the size of the 6600, eliminating any problem with main memory capacity. While the 8800 uses a different operating system, its compatibility with the operating system used on the existing ARC system is relatively good, which was another strong point of the announcement. Delivery of the 8800 with software that will allow it to be integrated into ARC systems will not begin until the summer of 1981, but it could have some impact on orders for this fiscal year. Potential customers who were concerned about the processing power of individual units of the ARC system may now see a clear upgrade path, and this could encourage them to order ARC systems now, with the knowledge that they can add 8800 processors in the future as needed. During the announcement, it was indicated that there were over 1,000 ARC systems installed and that 300 of these installations are already using Datapoint's integrated electronic office. The company's definition of an integrated electronic office user is a customer who is utilizing at least two of the four functions that Datapoint offers (data processing, word processing, electronic mail, communications management), but the nature of Datapoint's product line makes it very hard to determine accurately how intensively each function is being used. Copyright © 2 December 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients. This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. Member, New York Stock Exchange 19055 Pruneridge Avenue / Cupertino, California 95014 / (408) 725-1200 For example, a data processing user has only to invest about $1,000 to be able to use word processing on an ARC system. The incremental cost for electronic message switching is equally minimal for a user who has spare processing capacity. This difficulty in accurately determining the functional use of an ARC system makes the company's statement regarding 300 integrated office users a little loose, but it also speaks to one of Datapoint's major advantages—the low incremental cost of adding features onto an ARC system once it is installed. Based on the present installed base, Datapoint would have to be placed among the leaders in office automation. Furthermore, when the company's widely expected digital PBX announcement is made, Datapoint will have a feature that not even Wang Laboratories can offer. Order trends at Datapoint appear to be improving somewhat domestically and weakening in Western Europe. We ascribe the softness in Western Europe more to the deceleration in economic growth in that part of the world than to any difficulties with the TRW distributors in light of the anticipated sale of this distribution network to IDatapoint at the end of this fiscal year. Obviously, however, the progress in Western European orders and sales must be monitored very closely over the next nine months because of economic and internal reasons. We believe that overall order growth at Datapoint during this fiscal year will be sufficient to sustain a 30 percent increase in revenues in fiscal 1981 to a level of $415 million. Margin trends in the first quarter of fiscal 1981 were encouraging. Operating margins turned up after having declined during the last half of fiscal 1980. Flex, Incorporated, the subsidiary that owns Inforex, made a positive contribution to Datapoint's earnings in the first quarter. This contribution is a small plus in itself, but somewhat enhances our confidence in Datapoint's ability to make the difficult integration of TRW's distributors next year without any major problems. We believe that earnings gains in excess of 30 percent to around $5.00 per share are likely in fiscal 1981. If Datapoint can successfully integrate the TRW European dealers into its sales network, we believe that earnings in the $7.00 per share range are not unreasonable in fiscal 1982. INSTRUMENTS The last year or so at Perkin-Elmer has been a period during which all five of its divisions have been enjoying strong growth in orders, sales, and earnings. It is not reasonable to expect that five divisions that are affected by very different economic variables would continue to aU fare extremely well at the same time, and indeed there were several comments at the recent Perkin-Elmer analysts' meeting to indicate otherwise. Specifically, analytical instrument orders were flat year-to-year in the first quarter of fiscal 1981 and, after a number of years of above average growth, it appears that fiscal 1981 may be one of average- to below-average results in instruments, with our target being 10 percent revenue growth and flat margins. Second, after experiencing revenue growth of over 20 percent in fiscal 1980, it is likely that U.S. government revenues will be flat this year. Third, the peripherals - 2 -year-to-year basis and growth this year is being deemphasized at the expense of higher profit margins. Finally, first quarter earnings in fiscal 1981 were generally below expectations ($0.77 vs. $0.74). In our opinion, the negatives noted above were offset by a number of other factors. The company clearly expects that operating profit margins will improve in fiscal 1981 versus 1980, with the principal swing occurring in the semiconductor equipment division because of the absence of startup costs on the Micralign 200. First quarter operating profit margins were down somewhat year-to-year, but the company noted that first quarter results are usually not indicative of full-year trends. There are a lot of companies where a similar explanation for lower margins would be viewed with skepticism, but our long experience with Perkin-Elmer makes us very comfortable in taking management at its word. We were very impressed with the company's very frank discussion of its position in the minicomputer industry. In our view, its assessment of Perkin-Elmer Data System's strengths (very high performance hardware for the price) and weaknesses (relatively poor application software support and lack of experience in making anything but an engineer-to-engineer sell) was very accurate. The company appears to have a very good concept of its opportunities and limitations in the minicomputer industry and we believe that this will allow Perkin-Elmer to obtain reasonably good growth in this division without major downside risks. In our estimation, the most important discussion was the progress cited by the company in its development of the next generation of projection alignment equipment for the semiconductor industry, the Micralign 500. Perkin-Elmer has completed its preproduction run of the Micralign 500 and has met or exceeded all of its specifications in terms of speed, resolution, and distortion. It has not shipped any products to customers yet but is presently ordering equipment to begin its first production run. If Perkin-Elmer can achieve the same results with Micralign 500 on a full production basis that it has experienced in its preproduction run, then there is little question that this wiU be a major contributor to the company's growth over the next three to five years. Perkin-Elmer expects to begin shipments of Micralign 500 during the first half of calendar 1981 and hopes to achieve volume production during the first part of calendar 1982. It is not unreasonable to expect a $100 to $200 million increment to revenues during calendar 1982 at very high profit margins. The revenue gains should be largely incremental because the revolutionary nature of the Micralign 500 should have very little initial impact on shipments of the Micralign 200, which we believe has a present backlog in excess of $200 million. The net result of the meeting in our view was, first, to centralize earnings expectations for fiscal 1981 at around $4.00 per share (up 23 percent from fiscal 1980) and, second, to increase one's confidence that Perkin-Elmer can achieve earnings gains in excess of 20 percent in fiscal 1982 and 1983. SEMICONDUCTORS After being consistently bullish about the prospects of the semiconductor industry in 1981, we would like to temper our enthusiasm. The forecast that we made at our annual Semiconductor Conference for a 10 to 11 percent growth in domestic semiconductor consumption in 1981 was based on a moderate upturn in the economy beginning early next year. We are not changing either our forecast or our economic outlook; however, because of the increase in interest rates that heis occurred in the past month, we now believe that the chances of the economy taking another downward dip may approximate 40 percent versus perhaps a 10 percent probability one month ago. If the recovery is postponed until later in 1981, this will definitely impact semiconductor demand. If the downturn affects the consumer, auto, and industrial markets, but capital-equipment related areas (computers, telecommunications) remaiijfrelatively strong, then we believe that the linear and bipolar digital markets will weaken more relative to MOS, which has taken the brunt of price weakness (collapse) to date. In this scenario, Intel may do relatively better than the norm among the major participants, and Texas Instruments and National Semiconductor may do worse. In a more general economic slowdown, all sectors of the industry (and therefore all companies) will be affected. We want to emphasize that we are not changing our economic forecast at this point. However, we want to point out that the risks of our forecast being too optimistic have increased, as have the stock prices. Just as the domestic market seems to be picking up somewhat, there is clear evidence that the Western European market is turning down. One major difference between that market and the United States is that there is evidence of excessive inventories on both the user and distributor levels in Western Europe, a situation that has not prevailed in the United States this year. We understand, for example, that one major user hasn't taken delivery on a 16K RAM in six months. We expect a turnup in semiconductor demand in the second half of 1981 in Western Europe, but, because of the inventory overhang and the heavier mix of consumer and lower mix of computer business, we believe that semiconductor consumption wiU grow only five to eight percent in Western Europe in 1981. Of the major semiconductor suppliers. Advanced Micro Devices (AMD) seems to have a good degree of protection against a downturn in the market. AMD has been very successful in picking good market niches, where overall unit growth may not be as high as in other sectors, but where price competition is generally less severe and where AMD can effectively gain market share. This strategy is less risky in an economic downturn than competing in the more commodity-type items. Of the $310 million in revenues that we expect in the March 1981 fiscal year, something over 50 percent should come from bipolar operations. Within bipolar, about half of revenues come from what could legitimately be called proprietary products — its bipolar microprocessor line and the related memory chips that are "dragged" along by microprocessor demand. The remainder of bipolar revenues come from the bipolar logic and the linear area, where AMD has somewhat less of a competitive advantage. AMD's MOS Strategy is to emphasize its microprocessor product line and the peripherals and other support devices that can be sold with it. To date, AMD has not had a large part of its revenues in the most highly competitive MOS memory markets. The present weakness in MOS has hurt AMD by slowing its ability to move into these high-growth markets, which may defer the company's intention of gaining market share in MOS memory. 4 -If we get another downturn in the economy that affects the automotive, consumer, and industrial markets, AMD should fare better than the typical semiconductor manufacturer, as it does no business at all in the automotive or consumer sectors. Only in a severe downturn that affects all areas of semiconductor demand do we think that AMD would be markedly impacted. We expect a 19 percent increase in earnings per share in fiscal 1981 to $1.75 per share and, assuming our still positive industry outlook for 1981 does not have to be revised, we believe that growth may accelerate to a 26 percent rate in fiscal 1982, with earnings reaching $2.20 per share. COPYING AND DUPLICATING Our long-term positive stance on Xerox has been based on two premises. First, that the company was getting its house in order in terms of internal cost controls, and that profit margins would begin stabilizing, allowing profits from copying and duplicating to begin rising as fast as revenues. Second, that Xerox had a reasonably good chance of being successful in office automation and that, given the Stabilization of margins in its copier business, the market was not paying anything for this opportunity in office automation. We have not changed on viewpoint on Xerox, but we are getting a bit more concerned about the first of our two premises — profit margin stabilization. The company is leading one to expect that pretax profit margins in 1980 will drop to about 16.3 percent compared with 18.3 percent in 1979. This number would imply a drop in fourth quarter profit margins to 13.2 percent versus 15.5 percent last year. Last year's fourth quarter was depressed by operating losses and a large one-time write-off in word processing, but we believe that word processing is operating close to break even in the fourth quarter of this year. The question is whether the drop in fourth quarter margins is a function of earnings "management" against a weak quarter in 1979, whether it relates to write-offs on the 3300 copier (see below), or whether there are more deep-seated problems. The 3300 Copier program has been a source of disappointment to Xerox. This machine was developed under the "new culture" at Xerox, when products were supposed to be introduced without glitches—in the Xerox vernacular, "do it once - do it right." Yet, Xerox had to suffer the embarrassment of pulling the 3300 off of the market shortly after initial customer installations were made, because of machine malfunctions. The problem has not been fixed yet and the machine has not been re-introduced. We know that there were relatively large write-offs relating to the 3300 in the third quarter and wonder if there are more write-offs coming in the present quarter. The key to Xerox's margins remains the middle and especially the high end of the copier market. Despite recent rumors and announcements by IBM, Canon, and Others, there is nothing occurring to shake our belief that Xerox will remain dominant at the high end. This dominance should translate to a stabilization of copier profit margins, but we frankly need a bit of encouragement from management that our positive premise is correct. - 5 -PAPER AND FOREST PRODUCTS We are somewhat more optimistic than some on the housing picture over the next two years, expecting 1.5 million starts in 1981 and 1.8 million starts in 1982. We are also very optimistic on the outlook for lumber and plywood pricing over the next two years. Because of cost-push factors in 1981 and demand-pull factors in 1982, we believe that plywood and lumber prices can increase 15 to 30 percent annually in each of the next two years. The major beneficiaries of this trend should be the large integrated forest products producers, which have a relatively fixed stumpage cost structure. Champion International should benefit from the rapidly rising plywood and lumber prices that we project, and it is also in a favorable position relative to the industry in its paper operations. The recently completed 50-percent expansion in Champion's linerboard capacity is the key element in Champion's strategy to change its Hoerner Waldorf subsidiary into a competitor in the larger tonnage sector of the market. We believe that Hoerner Waldorf's very capable sales organization can effectively place this new capacity, and we believe that linerboard will be one of the most attractive profit sectors in the paper market over the next few years, due to low rates on industry expansion and the optimistic outlook for linerboard exports. Readers of the Paper and Forest Products section of the Portfolio Letter should note that we have been positive on the long-term outlook for linerboard for over a year, and it appears that the rest of Wall Street is starting to agree with us. Operating income at Champion's Paper Packaging Division (which is primarily linerboard), should be 50 percent higher in 1982 than in the previous peak achieved in 1979. In its paper and milk carton division, Champion should benefit from a new pulp mill that will ensure pulp self-sufficiency over the next few years and a longer-term Strategy of enhancing its appeal to paper distributors by combining a mix of lower-cost commodity paper with highly desirable premium grades and ensuring continual increases in capacity to the distributors. We believe that operating income in paper and milk cartons will increase by 9.5 percent next year and by 15 percent in 1982. In the aggregate, we project a strong rebound in earnings at Champion during 1981, up to $3.80 per share fully diluted, and we believe that record earnings of $5.80 per share fully diluted can be attained in 1982. The major driving force in both years should be a turn-around in its building products division. We readily concede that our outlook for the company and for the forest products industry is more optimistic than many, but the stocks seem to be discounting a much more conservative outlook and we believe that our argument for higher lumber and plywood prices because of cost-push factors is a very compelling case for the group. We should also note that some paper companies with high linerboard exposure (Union Camp, for example) have done well in the stock market recently. Linerboard operating rates will be good in 1981 only if there is an economic recovery and it is hard to justify a recovery without better housing markets. CAPITAL EQUIPMENT The Japanese competitors in the capital equipment business have been relatively quiet for the past few years, but we believe that they may be readying a much more aggressive assault on the U.S. market. Most of the Japanese technology has been developed by licensing agreements with various U.S.-based competitors. Some of the licensing agreements are joint ventures in which both the U.S. and Japanese company contribute funds to construct a facility for development of products in Japan and tlien share in the profits in such a facility. One example is International Harvester-Komatsu (KIMCO), and Caterpillar Tractor-Mitsubishi. These joint arrangements are relatively firm ones and it would be very difficult for the Japanese partner to break an agreement in order to begin shipments into the United States. A more common type of license agreement, however, is one in which neither company contributes capital and a paper corporation is set up to hold the licenses and to funnel royalties back to the parent organizations. This type of arrangement is relatively easy to dissolve by one of the partners. For example, Bucyrus Erie and Komatsu had such a "paper" agreement allowing Komatsu to build hydraulic excavators in Japan. Tlie agreement terminated on July 25, 1980, and was not renewed. On July 27, 1980, Komatsu introduced a new line of hydraulic excavators. While there is no intention at present to ship this new excavator line into the U.S. market, Komatsu is in the process of negotiating a new agreement for mining machinery with Bucyrus that could influence its marketing decision. Clark Equipment and Toyo Umpaki have a license agreement for the production of wheel loaders in Japan that expires in April 1981. It is our belief that this agreement will not be renewed by the Japanese partner. Harnischfeger and Kobe Steel have a similar arrangement for cranes and mining machinery that is being renegotiated at this time. The rapid rise in the value of the yen during 1978 and 1979, and the very poor U.S. construction equipment market have delayed the efforts of the Japanese, but we believe they will soon make a major assault on the U.S. market. We are starting to see hydraulic excavators from Hitachi and Mitsubishi, expect Kawasaki to introduce a line of rubber-tired loaders, and expect Komatsu and Kobe Steel to introduce a number of different product lines. If our analysis is correct, the strength will lie in the hands of the U.S. distributors. There will be more products available to sell than there will be distributors and, therefore, there will be tremendous pressure to carry multiple product lines, including Japanese products. Only companies that have the power to force dealers to carry the company's products exclusively would prosper in this competitive environment. Caterpillar and Deere are the only U.S. manufacturers that have this power. TELECOMMUNICATIONS Although data communications equipment is a small piece of the total U.S. telecommunications market (estimated revenues of $2.0 billion in 1980 versus industry revenues of $66.5 billion), it is the fastest growing sector of the marketplace, with an estimated five-year growth rate of 20 percent. - 7 -The data communications equipment market is composed of four elements: communications terminals ($800 to $900 million), communications processors ($300 to $350 million), modems ($700 million), and data multiplexers ($80 million). We believe that the modem market will grow at a 21 percent compound rate between 1980 and 1985. The low-speed sector (including acoustic couplers) accounts for about one-third of the total modem market and should grow at an 11 percent compound rate. The high-speed sector (2400 bits per second and up) should grow at 25 percent. Western Electric is the leading supplier in the low end, followed by General DataComm Industries, Inc., the UDS subsidiary of Motorola, and a Racal subsidiary. Racal/Milgo has the largest market share at the high end, followed by Western Electric, the Codex subsidiary of Motorola, and Paradyne. While Paradyne is only number four in the overall high end, it is widely regarded as an innovator and a technology leader in this area. Paradyne is also a major factor in the very high end of the market, which is also the fastest growing. The data multiplexer market is a relatively small one but it is growing at an estimated 27 percent rate overall, and at a 30 percent to 35 percent rate at the high end (statistical multiplexers and intelligent statistical multiplexers). The major participants in the high end of the market are the Codex subsidiary of Motorola, Micom, Timeplex, Infotron, DCA, and Halcyon division of Torotel. Micom, Infotron, and DCA are privately held companies. The DCC subsidiary of M/A-COM is also a participant in this market. DATAQUEST defines communications terminals as terminals that are connected to computers via common carrier circuits. This market is highly competitive with over 150 participants. Major suppliers to the market are the mainframe and minicomputer manufacturers as well as plug-compatible manufacturers such as Telex and Memorex. Suppliers to this market do not normally segment their market by telecommmunications applications, so this segment of the terminal market is not separately identifiable for investment purposes. Communications processors provide such functions as off-loading the communications functions from mainframes. This area is a relatively slow-growing part of the whole data communications market (about 11 percent per year), and is dominated by the computer and minicomputer manufacturers—especially since NCR's acquisition of Comten. However, Paradyne is trying to attack this market by selling IBM-compatible systems that combine the communication processor, modem, and display terminal capabilities. Michael R. Weisberg - 8 RECENT NEWSLETTERS OF NOTE SMALL COMPUTERS Main and Disk Memory Purchases on New Computer Systems 10/10/80 SEMICONDUCTOR Estimated U.S. Quarterly Semiconductor Consumption Intel Corporation - Financial Analysts' Meeting Advanced Micro Devices, Inc. - Financial Analysts' Meeting National Semiconductor Corporation - Financial Analysts' Meeting 11/21/80 11/10/80 11/10/80 11/10/80 COPYING < 5 c DUPLICATING 3M Announces Six New Copiers Visit to Minolta's New "MIZUHO" Copier Plant Canon Introduces Three New Copiers Based on Its "Jumping" Toner Technology Rumors Reach Fever Pitch That IBM Will Begin Marketing The Minolta EP310 and EP520 on an OEM Basis 11/13/80 11/13/80 10/24/80 10/24/80 CAPITAL EQUIPMENT U.S. Farm Tractor Sales Outlook - 1981 10/31/80 TELECOMMUNICATIONS Worldwide Market for Central Office Switching Equipment Forecasted to Exceed $16 Billion in 1985 10/15/80 WORD PROCESSING Digital Reduces Price of its WS78 Stand-Alone Word Processor IBM Reduces Prices on Memory Typewriters Xerox Office Products Division Announces the 8000 Network System for Ethernet 11/21/80 11/21/80 11/21/80 - 9 -h :-_. _ f - V ^ ^ ^ K . ^ ^ ^ B M k ^ ^ ^ V ^ H ^ ^ ^ ^ ^ ^ ^ H s — = — = ~ t^t^rl^ ^K F^^^l ^ = ' ^ S ' " •" A Subsidiary ot A.C. Nielsen Co. ~ INCORPORATED SIS Code; Vol. I, 2.0 ESTMATED U.S. QUARTERLY SEMICONDUCTOR CONSUMPTION This newsletter presents DATAQUEST's quarterly estimates for U.S. semiconductor consumption. These estimates have been compiled from several different sources, including trade association data, U.S. Government statistics, foreign government statistics, and estimates supplied by major manufacturers. The information is useful to clients wishing to study the historical growth of semiconductor consumption in the United States. Several items should be noted: I • The volatility of the semiconductor industry, and its sensitivity to declines in the economy, are shown in Table 1. Semiconductor consumption has become consistently less sensitive to declines in industrial production during the last four recessions. • The seasonal variation of shipments is clearly visible in Table 2, especially in years such as 1978 and 1979. The second and fourth quarters of the year are normally significantly stronger, and the first and third quarters of each year are weaker. • Table 2 shows the time lag of semiconductor consumption from the general economy, although the lag is somewhat ot>scured by seasonal factors. For example, shipments fell in the first quarter of 1967, two quarters after a decline in industrial production. Similarly, consumption increased in the fourth quarter of 1975, two quarters after a similar resumption of growth in the U.S. Gross National Product. • Quarterly information, especially percentage growth, is somewhat less exact than annual data. Shipment information may be shifted to a preceding or following quarter. This is true particularly during periods of especially rapid growth. For example, between the third quarter of 1972 and the third quarter of 1973 (four quarters), industry shipments increased 54 percent. Between the fourth quarter of 1978 and the fourth quarter of 1979, U.S. consumption of semiconductors rose 41 percent. The four quarters in 1972 and 1973 represent the fastest growth achieved by the industry. • The data presented here include imports. U. S. imports have grown significantly in recent years, and this has added incremental annual growth of 1-3 percent, in addition to the increase in domestic shipments. Copyright © 21 November 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generaIly available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or rnmpIfitPnfi';'! It rine"; not contain material provided to us in confidence bv our clients. This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy sucn securities 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO Between 1973 and 1975, no trade association collected data in the United States. (This void occurred prior to the existence of DATAQUEST's Semiconductor Industry Service.) Therefore, these data are potentially less accurate than data for other years. Data for the third and fourth quarters of 1980 are still not available. Table 1 includes DATAQUEST's forecasts for U.S. consumption for those quarters. The data have been adjusted to provide a basis consistent with that normally used by DATAQUEST. Captive manufacturing of semiconductors and the consumption of captive production—primarily that of IBM and Western Electric—are not included in these data. Data include only merchant semiconductor consumption and the captive production of those companies that also marlcet semiconductors. Fredericl< L. Zieber Jean Page Table 1 FOUR RECESSIONS - PEAK TO TROUGH (Percent of Decline) Years 1966-1967 1970-1971 1974-1975 1980-1981 Industrial Production (1.7%) (6.8%) (14.6%) (9.5%) Semiconductor Consumption (9.6%) (27.4%) (28.6%) n.a. Multiple 5.7 4.0 2.0 Source: DATAQUEST, Inc. November 1980 - 2 -# Table 2 ESTIMATED U.S. QUARTERLY SEMICONDUCTOR CONSUMPTION (Millions of Dollars) Year and 1966 Total 1967 Total 1968 Total 1969 Total 1970 Total 1971 Total 1972 Total 1973 Quarter 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 Discrete 1 $ $ $ $ $ $ $ $ $ Device n.a. n.a. n.a. 1 n. a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. 183 199 190 201 773 177 169 153 133 632 131 139 142 151 563 156 167 174 199 696 223 245 249 258 Integrated Circuit n.a. ••.:• $ $ $ $ $ $ $ $ $ n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. 96 117 113 124 450 130 127 107 110 474 105 112 119 131 467 140 158 163 178 639 205 248 269 297 Total Semi-conductor $ 250 270 262 267 $1,049 $ 250 250 244 261 $1,005 $ 263 268 251 270 $1,052 $ 279 316 303 325 $1,223 $ 307 296 260 243 $1,106 $ 236 248 261 285 $1,030 $ 296 325 337 377 $1,335 $ 428 493 518 555 Percent Change From Previous Quarter ^ • B . 8.0% (3.0)% 1.9% (6.4)% 0.0% (2.4)% 7.0% 0.6% 1.9% (6.3)% 7.6% 3.3% 13.3% (4.1)% 7.3% (5.5)% (3.6)% (12.2)% (6.5)% (2.9)% 5.1% 5.2% 9.0% 3.9% 9.8% 3.7% 11.9% 13.5% 15.2% 5.1% 7.1% Total $ 975 $1,019 $1,994 - 3 -Table 2 (Continued) ESTIMATED U.S. QUARTERLY SEMICONDUCTOR CONSUMPTION (Millions of Dollars) m Year and 1974 Total 1975 Total 1976 Total 1977 Total 1978 Total 1979 Total 1980 Total Quarter 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 est. 4 est. Discrete $ 260 $1 $ $ $ $ $ $ $ $1 $ $1 $ $1 261 255 229 ,005 199 197 187 209 792 235 241 229 230 935 228 239 233 236 936 239 264 268 289 ,060 301 340 334 347 ,322 354 364 357 347 ,422 Integrated Circuit $ 316 340 314 289 $1,259 $ 251 244 242 281 $1,018 $ 316 351 370 381 $1,418 $ 404 432 447 501 $1,784 $ 510 578 596 670 $2,354 $ 700 805 868 1,002 $3,375 $1,066 1,185 1,135 1.099 $4,485 Total Semi-conductor $ 576 601 569 518 $2,264 $ 450 441 429 490 $1,810 $ 551 592 599 611 $2,353 $ 632 671 680 737 $2,720 $ 749 842 864 959 $3,414 $1,001 1,145 1,202 1.349 $4,697 $1,420 1,549 1,492 1.446 $5,907 Source: Percent Change From Previous Quarter 3.8% 4.3% (5.3)% (9.0)% (13.1)% (2.0)% (2.7)% 14.2% 12.4% 7.4% 1.2% 2.0% 3.4% 6.2% 1.3% 8.4% 1.6% 12.4% 2.6% 11.0% 4.4% 14.5% 5.0% 12.3% 5.3% 9.1% (3.7)% 1 (3.1)% ( DATAQUEST, Inc. November 1980 !^A .^^ - 4 -X r<-^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ k ^ H ^ B = = £ % = # % = » = = =—=""=" D P ^ Q ^ A ^^^gfe^ 5 r ^ i ^ 11 #•% ^ A Sufanidiarv al A.C. Nielsen Co. ^ I N C O R P O R A T E D IR^ .^^t^^r SIS Code: Vol. HI, 8.04 INTEL CORPORATION FINANQAL ANALYSTS' IVIEETING Intel Corporation held a meeting for financial analysts on October 29, 1980 in Palo Alto, California. Gordon E. Moore, chairman and chief executive officer, gave an overview of the outlook for the Company. Edward L. Gelbach, senior vice president and general manager, Components Group, commented on the worldwide business outlook, Intel's capacity expansion program, and the progress of the 64K RAM. Jack C. Carsten, vice president and general manager. Microcomputer Components Division, reported on MOS markets, new products, and new technologies. William H. Davidow, vice president and general manager. Microcomputer Systems Division, gave an update on Intel's 16-bit microprocessor marketing program. Vaemond Crane, vice president and general manager. Commercial Systems Division, reported on storage deviceHsased products, systems level hardware products, and the Database Systems Division. OVERALL OUTLOOK Mr. Moore said that Intel will probably not show sequential growth in revenues in the fourth quarter of 1980 because of significant price erosion in MOS memory markets, particularly the I6K RAM and 16K EPROM. Consequently, any bias on profit margins in the fourth quarter should be down rather than up. Significant price pressure will continue in 1981, limiting revenue gairts and putting continued pressure on profit margins. There are signs that the worst is over in price erosion, however, and there is some indication that orders have improved, as welL Intel's overall book-to-bill ratio in October was greater than 1, according to Mr. Gelbach. The book-to-bill ratio in the fourth quarter should be about 1. COMPONENTS GROUP Mr. Gelbach said that Intel had expected bookings to decrease during the summer, but that the company had also expected bookings to improve in September and October. Bookings picked up in September, but did not meet forecasts and the book-to-bill ratio was less than 1. Unit number forecasts were met, but the Company did not neet its dollar volume forecasts because of a decline in average selling prices (ASP). Intel now expects a fourth quarter book-to-bill ratio of about 1 in the Components Group. The U.S. economy has been flat in at least the last three quarters but began to pick up in September. Nevertheless, orders from Intel's major accounts have slowed. There have been no problems with excess inventory, but there has been Copyright © 10 November 1S80 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally avaiIable to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy Or completeness. It does not contain material provided to us in confidence by our clients. This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent andfor their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO significant price pressure, according to Mr. Gelbach. The Company's mid-sized accounts ($100,000 to $500,000) have been very strong and distribution seems to be -firming, especially in the United States where distributors seem willing to make long-term commitments. In Europe, the signals are confusing but there is a definite wealttomed out and bookings and billings are up. Bookings did not turn around at the end of the summer as much as the company predicted, however. By product area, Intel has experienced some weakening in the 8-bit single chip microcomputer market and is projecting a two- to three-month slowdown. The Company also sees a flattening in the 8-bit microprocessor market and a Strengthening in the 16-bit microprocessor market, said Mr. Gelbach. The 16K RAM market is strong, but the 4K RAM market, both static and dynamic, is slow. The EPROM market remains strong. In particular, the 16K EPROM unit demand remains strong, but once again declining prices are a problem. The price of 16K EPROMs declined 20 percent in the first quarter, 30 percent in the second quarter and another 40 percent in the third quarter (from $21.70 to $17.40 to $12.45 to $7.45). Intel has priced its 16K EEPROM at $100.00, compared to Hitachi's price of $57.00. However, the Intel product has 50 percent better performance, according to Mr. Gelbach. The Components Group's emphasis for 1980 and 1981 is to introduce between 50 and 75 new products—the largest introduction of new products in Intel's history. New products include the 64K dynamic RAM, 64K EPROM, 16K E2pROM, 16K Static RAM and the 8051/8751 8-bit microcontroller. All of these products are being sampled; at least half will be in production by early 1981. Intel plans to increase wafer fabrication capacity overall by 85 percent between September 1980 and the fourth quarter of next year, with $100 million in capital investments. The expansion will take place in Santa Qara; Livermore; Aloha, Oregon; Phoenix; and Albuquerque. Activity in the assembly area should increase about 40 percent in the same time period, with expansion slated for Malaysia, the Philippines, and Barbados, with a concentration on Barbados. Overall, Intel plans $150 million in capital expenditures in 1980, according to Mr. Moore. With the exception of recent college graduates, Intel has been very selective about hiring, however, especially in administrative functions. There have been no cuts in technical or long-term programs, however. In response to a question from the audience, Mr. Gelbach commented that the price pressure Intel has experienced comes t>oth from oversupply and raw competition. For example, Intel has 12 competitors in the EPROM product markets. He also feels that pricing has bottomed out in the 16K EPROM market, but that price erosion win continue in other areas. - 2 -In response to another question, Mr. Gelbach commented that he did not thinl< that the advent of the 64K RAlVl will have any effect on the availability of the 16K RAlVl, at least not at Intel and probably not in the industry overall. IVlr. IVloore said that it is unlikely that any competitor in the 64K RAM marlcet will have a marlcet share greater than 20 percent because too many suppliers are starting at the same time. At least eight producers are lil<ely to have 10 to 20 percent marl<et shares, however. NEW PRODUCTS AND TECHNOLOGY The 16-bit microprocessor is Intel's fastest growing business, according to Mr. Carsten. The marlit microprdcessors was $25 million in 1979, was $100 million in 1980, and should reach $175 million in 1981. Still, it is not a big business compared to the total components marJ<et, which is $500 million now and should reach $1.5 billion by 1982. And, the 8-bit microprocessor is still nearly 60 percent of Intel's business. The number of products offered by Intel continues to increase, said Mr. Carsten. The company now has 85 different sets of tooling, with each set reflecting R&D and tooling costs of between $100,000 and $1 million. Many of the tooling sets for Intel's new products will exceed $1 million. Technology—not volume-related effects—is the key to cost reduction, performance, and reliability, said Mr. Carsten. In particular, costs can be reduced by making die smaller on new products; long-term cost reduction demands a strategic program at the time of original design. Finally, quality and reliability must be designed into the technology. For example, the 8049 8-bit microcontroller is a large volume device introduced in 1977. At the time, Intel was using NMOS technology and the die size was 223 mils on a side and the price was $15.00. In 1980, when Intel is using HMOS, the 8049 is 182 mils on a side and the price is $6.00 to $7.00. The area was cut by one-third and the price was cut by 55 percent. Intel plans to move to advanced HMOS technology in 1982, thereby decreasing die size to 145 mils on a side with an expected price of $4.00 to $6.00. The product should also be three times more reliable, said Mr. Carsten. " • o • There are tremendous tooling costs of up to $500,000 associated with that kind of technology improvement, however. Intel is using computer-aided design (CAD) to cut costs and reduce design times. All changes are now done via software and not optically. The process now takes only four to six months and costs only 10 percent of what it would otherwise. Mr. Gelbach commented that Intel's use of CAD is not unique but the company's ability to use it practically is, and this provides Intel with its ijest weapon against second sourcing. In response to a question about the current status of bubble memory at Intel, Mr. Moore said that the Company is making a major push but it lost momentum because of problems with the controller. The Company has been trying to regain the lost momentum, but with little response thus far. - 3 -MICROCOMPUTER SYSTEMS Mr. Davidow told analysts that the microcomputer business has been mostly flat, but that business is beginning to pick up because of design wins of the 8086 and the introduction of Intel's 16H3it microprocessor development system. Mr. Davidow also updated Intel's progress on the Q-ush Program for Intel's 16-bit microprocessor, which was started in late 1979 when competitors to the Intel product emerged. The objectives were to produce 100,000 inquiries, generate 10,000 qualified leads and win 2,000 designs. The program began by identifying the strengths of the iAPX 86, Intel's 16-bit integrated central processor. The top five selling Strengths identified by Intel were that the product is a "complete solution;" Intel is viewed as a leader; product performance; ease of use; and the system bus architecture. Intel launched a blitz in the first quarter of FY1979 to address 59 customer locations. The company held 38 seminars with 7,000 attendees worldwide, conducted three press tours and placed 12 major articles, hired recruits from college campuses and developed a sales campaign with an arsenal of 35 pitches. From the 59 accounts, Intel won 37 designs, lost 7 and registered 15 as undecided. The system is logging 500 design wins a quarter, according to Mr. Carsten, and Intel should reach its goal of 2,000 design wins in early FY1981. Mr. Davidow outlined potential revenues from the program as follows: « 1981—2,000 designs 150 systems each ASP=$320 $ 96 million revenue • 1982—2,000 designs 500 systems each ASP=$250 $250 million revenue COMMERQAL SYSTEMS Mr. Cfane reported that Intel continues to market IBM memory add-on units, but primarily to loyal customers. The company does not plan to expand its actitivies in that area. In the systems level hardware business, Mr. Qane highlighted two products—the 3805 semiconductor disk, which is 16-bit microprocessor based and uses high quality "partial" memory parts, and the 3805 block memory, which has a wide range of high performance applications. Shipments of the 3805 started in June 1980. Intel acquired MRI of Austin, Texas two years ago to provide database software systems. MRI operated as a separate company in the first year following the acquisition and revenues were up 40 percent. This year has been flat and somewhat disappointing, but it has also been a year of integration. Intel has doubled MRI's sales force, but Mr. Moore commented that it takes time for a new salesperson to sell a software product. Intel expects that MRI will announce new products within 12 to 15 months. Susan A. Thomas Michael R. Weisberg - 4 -ll R ^ . ^^ \ B ^S S K = % s . ^ S E B "'S = A Subsidiary of A.C. NieisRri Co. ^ INCORPORATED 1 ?T3u^f^TT3Wi^z SIS Code: Vol. Ill, 8.20 ADVANCED MICRO DEVICES, INC. FINANQAL ANALYSTS' MEETING Advanced Micro Devices, Inc. (AMD) held a meeting for financial analysts on October 30, 1980 in Sunnyvale, California. W.J. Sanders, III, chairman, president and chief executive officer, expressed confidence that AMD's sales will continue "monotonic growth in sequential quarters." In addition to Mr. Sanders' report on the Corporation, Frank Zurcher, president of Advanced Micro Computers (AMC), reported on the activities of that subsidiary; James Downey, vice president and division manager for MOB operations, reported the progress of the MOS Division; and Anthony B. Holbrook, vice president and division manager of bipolar operations, delivered an update on the company's bipolar activities. CORPORATE Mr. Sanders' projection forecasted monotonic growth in sales for AMD. He said that current market conditions are cyclical and will improve, but cited major new forces in the form of increased foreign competition in the marketplace. AMD's Strategy in dealing with increased foreign competition has two parts. First, AMD has embarked on a program to improve the quality of outgoing products above the company's recent average quality level (AQL) of 0.65 percent. The progam is called "secundus nuUi"—second to none—and establishes the "tightest quality level in the history of the industry". Specifically, the goal for outgoing AQL of MOS RAM and ROM products will be 0.1 percent; 0.2 percent in bipolar commodity products; and 0.3 percent in LSI logic and other memory. The new Standard of quality, which AMD has pledged to achieve by the end of the current fiscal year, will enable AMD to achieve parity with the Japanese, said Mr. Sanders. Once AMD has achieved parity with the Japanese in quality levels, the second part of the Strategy is to compete with a broad product line. Mr. Sanders predicted sales of more than $300 million in FY1981, ending in March 1980, up from $225 million in FY1980. If the industry grows 14 to 17 percent in 1981, AMD should achieve sales of $400 million in FY1982. He also forecast $80 million in sales in the next quarter and an overall book-to-biU ratio of 1. Copyright© 10 November 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but Is not guaranteed as to accuracy or completeness, It does not contain material provided to us in confidence by our clients This information Is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to lime, have a long or short position in the securities mentioned and may sell or buy such securities 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO Mr. Sanders said that AMD's capital spending plans will proceed unabated. Capital spending in FY1981 should exceed capital spending in FY1980 by 20 percent, yet, the total figure is $15 million to $20 million less than planned. Mr. Sanders attributed this difference to a rescheduling of construction at the Gilroy site and at the site of an assembly plant in Malaysia because of a laclc of demand, and to slow delivery of some fab and test equipment for other facilities. AMD will continue to spend in excess of 10 percent of sales on research and development. In response to a question on pre tax margins, Mr. Sanders reminded the analysts that AMD has been saying for a year that margins in FY1981 would not be as good as those in FY1980. He attributed that to extensive start-up costs for both the Sunnyvale Technology Development Center and the wafer fab facility in Austin, Texas. Mr. Sanders predicted that margins will decline for one more quarter but will improve when more fab plants are up to full capacity and overhead is spread out. Another question addressed the possibility that AMD will develop CMOS technology; the Company currently does not have any CMOS products on the marl<et. "We will.not tell you that we have a secret plan; but if we did we'd announce it soon," said Mr. Sanders. He added that any company that plans to be competitive must be in the CMOS business. A final question about financing elicited a response from Mr. Sanders that AMD had $17 million cash equivalents at the end of the last quarter, and that the Company plans no additional financing beyond its banl< lines for the next 18 to 24 months. AMC Mr. Zurcher reported on AMD's two-year-old subsidiary, AMC He noted that Mr. Sanders has set "modest financial goals by Silicon Valley standards" for AMG 100-plus percent annual growth, $10 million in sales in FY1981, and $100 million in sales in FY 1984. The future thrust of AMC will be on the AmZSOOO 16-bit microprocessor, develbped by Zilog and second sourced by AMD. AMCs focus will be on development and board systems for the AmZSOOO, said Mr. Zurcher. AMCs sales in FY 1980 were $6.6 million and are expected to reach $10 million in FY1981. In response to a question that followed his prepared remarks, Mr. Sanders noted that AMCs book-to-bill ratio is about 1. MOS AMD had earlier forecast FY1981 sales of between $150 million and $170 million for the MOS division, reported Mr. Sanders. The Company still expects to be in that range, but probably at the low end. This compares with sales of $113 million in FY 1980. FY 1980 unit volume was 30 million, according to Division Manager Mr. Downey. The forecast for FY1981 is about 35 million units. This implies an increase in the average selling price (ASP) for MOS products, despite severe price erosion in MOS memory markets. In fact, FY1980 ASP was $3.67 and increased to $4.40 thus far in FY1981. The higher ASP was achieved through improving product mix, however, and not through raising prices, noted Mr. Sanders. - 2 -The MOS division began producing the AmZSOOO nine months ago and is ramping up production each quarter, noted Mr. Downey. Originally, AMD was using masks made from designs obtained from Zilog but now is using AMD masks. This has improved yields despite the relatively large chip size of the AmZSOOO, which is 250 mils on a side. Production of the AmZSOOO was transferred to AMD's wafer fabrication plant in Austin in September 19S0. The product is winning "its fair share of designs," added Mr. Downey. In an update on the progress of AMD's present and planned wafer fab plants, Mr. Downey noted that the Austin plant, which includes Fab V and Fab X, consists of 100,000 square feet. Fab V is currently producing 16K RAMs and the AmZSOOO. Fab X should be producing advanced RAM by the end of the summer of 19S1. The Sunnyvale Technology Development Center houses Fab VI, Fab VII, and Fab vni. Fab VI went into production in August 19S0. It consists of 7,200 square feet and is AMD's VLSI center, in which AMD is using its polyplanar technology to produce the 64K RAM. FAB vn is operational in three shifts and is producing non-volatile memory such as MOS EPROMs. The focus is on producing 16K EPROMs and developing 32K EPROMs. As AMD's non-volatile memory center, it is also developing EEPROMs. Mr. Sanders noted that the near-term sales outlook for the MOS division is "modest," and that sales should accelerate, depending on market conditions. The book-to-bill ratio in the MOS division is "less than 1." AMD suffers along with the rest of the industry from overcapacity in some MOS memory markets. AMD recently repriced its backlog in MOS to market prices. The book-to-bill ratio in September was 0.85:1, and AMD considers September to be the trough for the Company during the 1980 recession. Mr. Sanders expects the MOS division to grow 30 percent in the next fiscal year. In response to a question from the audience on market shares of the AmZSOOO microprocessor family between AMD and Zilog, Mr. Sanders said that market share wiU depend on price and delivery. He is confident, however, that AMD will achieve "at least 50 percent." AMD's telecommunications products fall into the MOS division. The Company plans to introduce new subscriber-line audio processor circuits (SLACs, which convert voice signals to digital signals); and subscriber-line interface circuits (SLICs, which condition voice signals so that SLACs can handle them); and modulator/demodulators (modems, which allow digital transmissions over analog lines). Mr. Sanders predicted that telecommunications will be AMD's largest market by 1990. Consequently, the proliferation of captive semiconductor manufacturing among computer manufacturers does not worry him. BIPOLAR AMD had earlier forecast sales in the bipolar division in the $150 million to $170 million range. The company still expects to be in the upper end of that range and also expects that bipolar sales will exceed sales of MOS products. Sales in the bipolar division were $110 million in FY 1980. - 3 -Mr. Holbrook provided the update for the bipolar division, which includes microprocessor, logic, and interface (MLI); bipolar memory; and linear. Mr. Holbrook also has responsibility for AMD's lOO-acre Gilroy bipolar facility, which should break ground in November or December of 1980 and should be in production by the end of FY1982. The bipolar division has achieved a tripling of sales from FY 1978 to FY 1981 (a compound annual growth rate of about 50 percent). The greatest sales growth occurred in memory products, which grew seven times over the last three years; microprocessors and interface products have grown five times in that same period. Mr. Holbrook noted that the division is limited only by its manufacturing capacity; AMD's goal is to be the leader in bipolar LSI products. In an update on bipolar wafer fab facilities, Mr. Holbrook said that Fab I is producing linear products and is currently near capacity; Fab II produces logic and interface and is at capacity; and Fab IV, which started out evenly split between bipolar and MOS products, will be converted completely to bipolar by March 1981. The conversion is currently 70 percent complete. Fab Vin, which is part of the Sunnyvale Technology Development Ctenter, is currently under construction and should be producing IMOX process devices by the first quarter of 1981. Fab VIII initially wiU produce bipolar digital products and then shift to linear. Fab XI, to be located in Gilroy, will be primarily a production facility but will eventually house some technology and product development. The sales outlook for the bipolar division should moderate somewhat from its recent 12 percent quarter-to-quarter growth because of AMD's inability to increase capacity. Bipolar memory bookings in the last quarter were the highest in Company history. The current book-to-bill ratio in the bipolar division is greater than 1. In response to questions from the audience, Mr. Sanders said that AMD has seen some price attrition in bipolar products as well as in MOS products. Lead times have dropped from 26 weeks to 8 weeks for 8K PROMs, for example, and the Company expects prices to come down in new orders. The softening business outlook in Europe may also affect bipolat products because it could cause some delay in the inventory liquidation of U.S. computer manufacturers. AMD's proprietary oxide-isolated process, called IMOX (implanted micro oxide), allows smaller geometries, increased speed and improved yields. IMOX n is playing an important role in AMD's development of bipolar PROM and RAM markets. Susan A. Thomas Lane Mason - 4 -SIS Code: Vol m, 8.08 NATIONAL SEMICONDUCTOR CORPORATION FINANQAL ANALYSTS' MEETING National Semiconductor Corporation held a meeting for financial analysts on October 30, 1980, in Sunnyvale, California. Oiarles E. Sporck, president, expressed guarded optimism about the future sales and profits of the Company. John R. Finch, vice president and member of the general manager's office of the Semiconductor Division, presented the outlook for the data acquisition segment of National's business. Pierre Lamond, vice president, technical director, and member of the general manager's office of the Semiconductor Division, discussed upcoming technology and new product improvements. E. Joseph WiUits, vice president, Finance, and secretary, summarized the Company's financial performance in recent years. BUSINESS OUTLOOK Mr. Sporck characterized National as a company primarily in the semiconductor component business, which represents about 70 percent of the Company's sales. That percentage should stay about the same, he said. Mr. Sporck cited National's broad-based and balanced approach to the semiconductor business as particular strengths of the Company. Net sales have Shown a compound annual growth rate (CAGR) of 44 percent since the present management took over in 1967, and profits have been good in all years except FY1977, which ended May 31, 1977. Sales in FY1980 were $960.4 million, up from $719.7 million in FY1979. Components National saw a decline in order strength in the semiconductor area beginning in June 1980 when the Company's overall components book-to-bill ratio dropped below 1. The book-to-biU ratio dropped even further during the summer, then improved in September and October, but is still below 1. The figures cover all markets except the military markets. Mr. Sporck noted that the book-to-biU ratio is worse in the MOS product families than in the bipolar families. MOS has suffered from severe overcapacity, inadequate unit volume and a significant decline in prices, particularly in the 16K RAM market. The overcapacity is particularly severe in the 16K RAM market. Mr. Sporck said that he does not know how long it will last, but noted that the Copyright © 10 November 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released h\ responsible individuals in the subject coInpanies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO decline in 16K RAM prices may delay the production of the next-generation 64KRAM by customer decision, because the comparative economics have now shifted Strongly in favor of 16K parts. The price erdsion may have the same effect on the development of bubble memory. Prices of some bipolar products, on the other hand, are higher this year than they were last year. Bipolar memory prices are especially strong, bipolar logic is strong, and pricing is firm in both digital eind linear products. The book-to-bill ratio in the bipolar area is in excess of 1: bipolar memory is greater than 1, linear is close to 1, digital is "relatively close" to 1, and I W O S memory, in both units and prices, is considerably lower. The book-to-bill ratio for MOS LSI products, however, is greater than 1. Mr. Sporck said that he does not know how long the softness in some of National's components business will last, noting that it depends on the recession. He does not expect that the book-to-bill ratio will reach 1 in the current quarter. National will suffer if the book-to-bill ratio does not return to 1 before the current backlog runs out. That probably will not happen in the first or second quarters of 1981, but could happen in the second half of the year. A major shakeout in the MOS RAM market is expected over the next two years, during which a number of present participants should drop out. Nevertheless, management at National "is as confident as ever." Some forecasts estimate that the semiconductor industry will be a $50 billion or $60 billion industry by 1990. "We expect to participate in that growth in the same manner as we have in the past," said Mr. Sporck. Systems Mr. Sporck reported that National's point of sales (POS) business seems to follow interest rates in an inverse relationship. Now that interest rates are Climbing, the POS business is again softening. National still expects to meet its business plan in POS in the current fiscal year. National's plug-compatible mainframe (PCM) business is relatively strong and should meet the Company's forecast for the current fiscal year and should be profitable in FY 1981. The Company lost $20 million in the PCM business last fiscal year when Itel, National's sole outlet, disappeared from the marketplace. National originally entered the P C M business to address the largest single end-user market for its components and it is a major contributor to the Company's profits and cash flow. LINEAR AND BIPOLAR Mr. Finch highlighted National's activity in the data acquisition/conversion market, which he characterized as a $260 million business in 1980 that should reach $780 million by 1985. The Company plans three new A/D converters leading from the Naked-8 product line and he focused on one, the COP-330 8-lead mini-dip serial I/O. - 2 -& 1 the area of programmable array logic (PAL), National has 15 device types and is the only direct second source for Monolithic Memories. PALs are a natural lead-in to gate arrays, noted Mr. Finch. The fiber optics marl<et is forecast to be a $1 billion marl<et by about 1990 and offers a rapid growth opportunity for fiber optics interface products. The Company has complete transmitters and receivers in development and is addressing the data communications segment of the marl<et with the introduction of its universal receiver/amplifier, the LH0082. TECHNOLOGY Mr. Lamond discussed National's activities in low power technology, the COPS (Controller Oriented Processor Systems) 4-bit microprocessor, and speech synthesis. He reviewed the advantages to designing with high performance, low power CMOS. These advantages include the capability of portable operation, improved noise immunity, lower system cost and improved reliability. National has pioneered use of its oxide-isolated p2 CMOS applications in the military, automotive, telecommunications, and portable instrumentation markets. In a comparison of instruction capability features of the NSC800 and competitive products, Mr. Lamond made the following distinctions, among others: the NSC800 is capable of 158 instructions, while the 8085 is capable of 80; the Z80, of 158; the 6800, of 72; and the 1800, of 91. National implements COPs microcontrollers in two technologies, NMOS and CMOS. A key feature of the COP400 family is its fully upward-compatible software. National wins more designs than its major competitors in the 4-bit marl<ets, according to Mr. Lamond. National is addressing the speech recognition and speech synthesis markets because the two features are part of greater efforts toward higher productivity through the use of electronics. National's present focus in the development of speech synthesis is on the telecommunications and automotive markets. Mr. Lamond also reviewed the Company's progress with the 16000 16-bit microprocessor and the 64K RAM. The design of the 16000 began two years ago. The Company will see silicon on the 16032 by the end of November and plans to introduce one peripheral every two months for a total of 6 in 12 months. The 16000 compares very favorably with the 68000, 8086, and Z8000, and it has some upward expansion capabilities tliat are absent in some of the competitive products. National heis implemented the 64K RAM using a triple poly silicon process and will Start sampling in December 1980 or January 1981. National chose this approach, even though it offers a significant technical challenge, because it will give the Company a competitive advantage in the move to the 256K RAM, said Mr. Lamond. . f,3r - 3 -CAPITAL SPENDING Capital spending in FY1981 should exceed that of FY1980 by at least 50 percent. Capital spending in FY1980 was $116.2 million, up from $72.1 million in FY1979. A portion of the planned capital spending is for short-term growth and that may in fact be slowed, but the long-term plans for wafer fab capacity increases are not expected to change. Specifically, capacity in the West Jordan, Utah wafer fabrication facility will increase and will have large amounts of MOS and advanced process capability. The Arlington, Texas plant should break ground in November or December of 1980 and will process entirely 5-inch wafers. Eventual capacity will be 100,000 wafers every four weel<s. The Greenoch, Scotland plant is undergoing expansion into MOS and bipolar in addition to linear. The plant will also process 5-inch wafers. The expansion represents a tripling of European wafer fab capacity. No new physical expansion is planned for the Santa Qara facility, but the plant is being refurbished with heavy investment in conversion of older processes to new processes and increased wafer size. Two bipolar modules will be converted from 3-inch and 4-inch wafers respectively to 5-inch wafers. FINANaAL HIGHLIGHTS Mr. Willits presented the 1 Percent Increase in Sales Percent Return on Beginning Equity Capital Expenditure ($ Million) Percent Total Debt to Equity (May 31) 'ollowing financial information for National: FY 1977 19.1 10.9 $42.4 25.3 FY 1978 27.6 21.0 $43.1 19.0 FY 1979 45.6 26.1 $72.1 37.1 FY 1980 36.2 31.2 $116.2 46.7 The Company's debt-to-equity ratio reached 50 percent at the end of the first quarter of FY 1981 and it will be maintained at that level in the near future. National's recent offering of $1.5 million shares raised nearly $63 million. The offering was designed to reduce debt and to provide a base for future financing. ME. Willits showed how the offering combined with a 50 percent debt-to-equity ratio enabled the Company to produce signficant additional capital. - 4 -Reborrow Amount Received 50 Percent Debt/Equity Total Additional Capital $62.8 million 31.4 million $92.2 million Mr. Willits also said that if National can maintain its historical 20 percent petum on average capital employed after tax it can achieve per share earnings of $11.27 from the $94.2 million additional capital. 20% After Tax Return on Additional Capital .20 x 94.2 = $18.8 million Interest Expense on Additional Debt at 6% After Tax Net Earnings Added Per Share Issued .06 X 31.4 = (1.9) million $16.9 million $11.27 National's net sales in the first quarter of FY1981, which ended September 21, 1980, were $346.2 million, up from $242.1 million in FY1980, representing an increase of 43 percent. Net earnings in the first quarter of FY1981 were $18.9 million, up from $12.6 million in FY1980, representing an increase of 50.8 percent. Earnings per share were 91 cents, up from 62 cents, representing an increase of 46.8 percent. Susan A. TTiomas Lane Mason - 5 -0 .,A-. A Subsidiarv of A-C. Nielsen Co. ~ I ^^-f- RESEARCH N c o R P O R A T E D I M E N A / S L E T T E R SIS Code: VoL 11, 3.1 MASKMAKING INTRODUCTION AND SUMMARY Maskmaking is important to the semiconductor industry because masks create the patterns that make it possible to place more and more functions on a single integrated circuit. The production of an integra:ted circuit includes between 6 and 11 masking steps. Each step requires a unique mask, which consists of patterns reproduced hundreds of times in emulsion, chrome, or iron oxide on a coated blank. These patterns must remain intact during the maskmaking process, and the mask is ruined if it is scratched, smudged, or contaminated. In a very real sense, then, progress in the semiconductor industry depends on progress in the technology of maskmaking. The U.S. coated blank market reached an estimated $78 million in 1979 and Should grow to an estimated $156 million in 1984. The total U.S. maskmaking market, which includes coated blanks, was an estimated $375 million in 1979 and we believe that it will reach $697 million in 1984. The most significant trends in the maskmaking industry are the developments of higher quality, longer lasting masks and of non-contaet aligner technology in the wafer manufacturing process. DATAQUEST believes that these trends will affect the maskmaking industry in two ways: first, the push for higher quality products and equipment should change the industry's orientation from one of commodity production to one of service, and, second, the push for higher quality may eventually put smaller maskmakers at a competitive disadvantage. PROCESS Maskmaking involves creating a set of masks from an engineering drawing of a VLSI circuit. The masks are used in the manufacturing process to expose photosensitive material on semiconductor wafers. The process of making a mask from an engineering drawing usually includes digitizing, pattern or reticle generation, step and repeat, and the making of tooling and working plates (see Figure 1). Digitizing converts VLSI circuit drawings, which are usually 400 times the final part size, into a form that can be read by a computer. Points on the drawings are converted into x,y digital coordinates. In the next step, a set of photographic images or reticles are created from data generated during the digitizing process. Each Copyright © 31 October 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients This information is not furnished in connection vuith a sale or offer to seII securities or in connection with the solicitation ot an offer to buy securities This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO Figure 1 THE IWASKIVIAKING PROCESS Artworl< 1 1 Optical Reticle Generation « 10X ' ' ' Digitizing 400X ' E-Beam Reticle Generation 10X r Step and Repeat IX 1 ' Contact Print Submasters & Working Plates ^ ^ IX 1 ' • r " 1 1 1 1 • • i • ' 1 ' E-Beam Masks 1X _ -J ^ • -^ ' Emulsion Priotoplates Chrome on Soda-Lime Photoplates Chrome on Low Expansion Glass Photoplates Chrome on Quartz Photoplates Wafer Steipper Reticles 'Indicates scale in relation to actual size of mask Source: DATAQUEST, Inc. October 1980 - 2 -reticle contains the desired mask pattern for a single layer of a device, enlarged 10 times. The step and repeat process reduces the oversized image to final part size and exposes copies of the image to create the final master mask image. In some cases, the process continues with the creation of submasters from the meister masks, which are in turn used to make working plates. The term "tooling plate" is used to identify any photoplate that is not a working plate; for example, reticles, masters, and submasters are all tooling plates. A working plate is the plate that will l>e used in factory production of integrated circuits. Figure 2 presents the relationships between suppliers and customers in the maskmaking industry. Note that photoplates are made from three types of glass: soda-lime, low-expansion, and ultraviolet transmissive. Low-expansion glass is favored for VLSI circuits with smaller critical dimensions because it does not change size with temperature changes as much as do other types of glass. Ultraviolet transmissive glass is used in applications in which the photosensitive material on the semiconductor wafer is exposed in ultraviolet light. The short wavelength of ultraviolet light makes it useful for applications with extremely small criticed dimensions. Hoya and Corning are the major suppliers of glass to the maskmaking industry. Hoya supplies soda-lime glass, low-expansion glass (quartz and fused silicia), and uncoated glass to the U.S. market. Emulsion coaters include major suppliers of materials to the photographic industry, such as Kodak, Konishiroku, and Agfa Gevert. Since the semiconductor industry consumes only a small portion of the photographic materials produced by these companies, some of the companies do not cater to the industry. Emulsion conversion companies, on the other hand, serve the industry directly. They generally purchase large sheets of emulsion-covered glass and convert them into smaller working plates. At the same time, emulsion conversion companies perform an important quality control function. Hard-surface coaters purchase new glass and coat it with an opaque material and with a photosensitive material, usually chrome and photoresist. MARKET GROWTH Coated Blanks A coated blank is a mask in its raw state, that is coated with a photosensitive material but without an image. The U.S. coated blank market in 1979 was an estimated $78 million. The market should grow to an estimated $156 miUion in 1984, representing a compound annual growth rate (CAGR) of 15 percent (see Table 1). These estimates were developed from an analysis of wafer starts and the installed aligner base. They are based on no increase in the average selling prices (ASP) of coated blanks. "Q^ui-vvu/y^ UJM y^i/CjUt it> U M ( U ^ ^^ ^ -fZ/Cs^ -^ U^^-Aftj( y^H/^ -\t> I A M J U ^ ^ ^ ^ -i-L^c^ - 3 -Figure 2 MASKMAKING SUPPLY FLOWCHART Substrate Glass Soda-Llme Low-Expansion Emulsion Coaters Conversion Houses Ultraviolet Transmissive Hard-Surface Coaters Maskmakers Semiconductor Companies Source: DATAQUEST, Inc. October 1980 - 4 -Table 1 ESTIMATED U.S. MERCHANT AND CAPTIVE COATED BLANK MARKET 1979-1984 (Millions of Dollars) Emulsion 1979 $ 18 1984 $ 16 CAGRI 1979 to 1984 (2%) Chrome Total 60 $ 78 140 $156 21% 15% ^Compound Annual Growth Rate Source: DATAQUEST, Inc. October 1980 The two most common materials used to coat blanks are emulsion and chrome. Maskmakers have shifted from emulsion coating to chrome coating in recent years, however, for several reasons. Emulsion is more susceptible than chrome to scratches and Other defects. Furthermore, emulsion is not made especially for the semiconductor industry; instead, it is made for the photographic market. Chrome coating for masks is made primarily by the semiconductor industry for use in the semiconductor industry, which ensures higher quality. Chrome coated blanks produce a better quality product and also garner a higher ASP in the marketplace. Customers seem willing to pay the higher prices for improved yields. The yield improvements achieved through using chrome masks are particularly significant for larger die sizes. Average yields for some VLSI circuits are running well under 50 percent, so there is obviously considerable opportunity for yield improvement. In addition, chrome coated masks do not wear out as easily as Other masks, even when they come in contact with wafers. Thus, chrome masks may actually offer a reduced mask cost per wafer, even though the mask is more expensive. Current typical selling prices for five-inch by five-inch coated blanks are $2.50 for emulsion, $12.00 for chrome on soda-lime glass, $120.00 for chrome on low-expansion glass, and $850.00 for chrome on ultraviolet transmissive glass. - 5 -Merchant coating companies comprise about 40 percent of the hard-surface (chrome) mask market. They sell to both merchant maskmaking companies and semiconductor companies. DATAQUEST believes that the merchant market will grow more rapidly than the captive market because it is unlikely that merchant semiconductor manufacturers will begin making their own coated blanks if they do not already make them. The companies that do not make their own coated blanks tend to be among the faster growing in the industry and they are generally conserving capital to build manufacturing plants, not maskmaking facilities. Furthermore, the trend in the industry is to buy products rather than make them in-house. The major merchant emulsion conversion and chrome coating facilities are listed in Table 2. Some merchant semiconductor companies with captive chrome coating facilities are Mostek, Motorola, and Texas Instruments. Maskmaking and Tooling The total U.S. merchant and captive maskmaking market was an estimated $375 million in 1979 and should grow to $697 million in 1984, representing a CAGE of 13 percent (see Table 3). Mask tooling accounted for 53 percent of the total market in 1979; in 1984, tooling should account for 61 percent. The increase in tooling reflects a shift to the use of tooling plates instead of working plates in the manufacturing process. Tooling includes digitizing, reticle generation, and pattern generation. DATAQUEST believes that a typical VLSI circuit has between 6 and 11 mask layers and passes through the maskmaking cycle 3 times: once for the initial design and twice to correct major or minor design errors. A typical 9-layer circuit of 200 mil by 200 mil might incur maskmaking charges of $4,500 in digitizing, $5,800 in pattern generation, and $8,000 in step and repeat. DATAQUEST estimates that approximately 290,000 reticles were generated in 1979 to support $6.9 billion in U.S. semiconductor industry sales. This corresponds to revenue of $24,000 per reticle, or $648,000 per circuit design. The cost of finished tooling and working plates depends on defect density. ASPs for five-inch by five-inch photoplates for four-inch wafers are: $5 to $8 for emulsion plates with approximately 12 defects per square inch; $50 to $70 for chrome plates with approximately 8 defects per square inch; and $600 to $1,000 for repaired masters with approximately 1 defect per square inch. Manufacturers generally want only 1 defect per square inch, however, and consequently should expect to pay about $1,000 per plate. Maskmakers may quote different prices if they include some tooling costs in plate costs. Plates are currently inspected for defects by humsm operators. However, some manufacturers have installed computerized inspection equipment and these systems tend to discover more defects than their human counterparts. DATAQUEST believes that semiconductor companies may eventually use similar systems to inspect wafers in the manufacturing process. 6 -Table 2 COATED BLANK SUPPLIERS Emulsion Conversion Suppliers Imtec Products, Inc. Oak Laboratories Precision Photoglass, Inc, R.O.K. Semi Mask Sempro, Inc. Others Sunnyvale, CA Los Angeles, CA Mountain View, CA Mountain View, CA Oak Park, IL Sunnyvale, CA Chrome Coating Suppliers (Merchant) Basic Microelectronics, Inc. EMC (Micro Mask, Inc.) IMR Optifilm Co. Precision Photoglass, Inc. (Supplier Only) Tau Labs Telic Corp. Towne Laboratories, Inc. Others Lake Park, FL Sunnyvale, CA Santa Clara, CA Gardena, CA Mountain View, CA Yorktown Heights, NY Santa Monica, CA Somerville, NJ Table 3 Source: DATAQUEST, Inc. October 1980 ESTIMATED U. S. MERCHANT AND CAPTIVE MASKMAKING MARKET 1979-1984 (Millions of Dollars) Photoplates Mask Tooling Total 1 Compound Annual Growth Rate 1979 $177 198 $375 k 1984 $270 427 $697 Source: CAGRI 1979 to 1984 9% 17% 13% DATAQUEST, Inc October 1980 -7 -Merchant maskmaking companies (see Table 4) supplied only 13 percent of the total maskmaking market in 1979; however, these companies should increase their market share 1 or 2 percent per year, primarily because the faster-growing semiconductor companies seem unwilling to commit resources to meiskmaking as long as they can buy masks. The trend is already evident among some of the industry leaders; neither Advanced Micro Devices nor Intel(^^^P their own maskmaking facilities. , has CURRENT TRENDS The trends toward higher quality, longer lasting masks and non-contact alignment in the manufacture of integrated circuits have significant implications for both maskmakers and semiconductor manufacturers. In particular, longer leisting masks and non-contact alignment reduces the number of masks requirqd in the manufacturing process. The most dramatic effect of the reduction in the number of masks required in manufacturing is that the unit count of plates sold by maskmakers is growing less rapidly than semiconductor component sales. The plates are of higher quality, however, and higher quality plates cost more. Consequently, maskmakers are concentrating on generating more revenue for higher quality products to compensate for the Slower growth in unit count. The shift from emulsion coating to chrome coating is one push for quality in the maskmaking industry that is already evident. Its implications have already been discussed: chrome produces a better quality, longer lasting mask that garners a higher ASP in the marketplace. DATAQUEST believes that the shift to chrome will continue as the maskmaking market grows. The size of the emulsion coating market may not necessarily decrease, but it certainly will not keep pace with growth in the chrome coating market. One benefit of making masks that last longer is that tooling plates can now be used in the manufacturing process. In the past, when emulsion was the standard coating, maskmakers made tooling masks first and then made working plates, which were used in factory production. These plates were brought into contact with wafers during the manufacturing process and, as a result, would wear out. Tooling plates made from chrome coated masks do not wear out as easily. In addition, they can be used in non-contact aligners, which almost eliminates wear. DATAQUEST believes that the shift to the use of tooling plates instead of working plates in manufacturing wiU continue and, consequently, that tooling will continue to command larger shares of the total maskmaking market. The shifts from emulsion coating to chrome coating and from working plates to tooling plates complement the new strategy in the maskmaking industry of generating more revenue for higher quality products. One result of the strategy is a change in the maskmaking industry from an orientation of commodity production to 8 -Table 4 MERCHANT MASKMAKING COMPANIES Company Align-Rite Corp. Electromask, Inc. Master Images Micro Arrays Microfab Systems Corp. Microlab Micro Mask, Inc. NBK Corp. Photronic Labs, Inc. Qualitron Corp. Tau Labs Telic Corp. Towne Laboratories, Inc. Transmask, Inc. Ultratech Others Burbank, CA Woodland Hills, CA San Jose, CA Newtown, PA Palo Alto, CA Livingston, NJ Sunnyvale, CA Santa Clara, CA Danbury, CT Danbury, CT Yorktown Heights, NY Santa Monica, CA Somervilie, NJ Newport Beach, CA Santa Clara, CA Source: DATAQUEST, Inc. October 1980 -9 -service. We expect that the semiconductor industry will generate more custom designs with longer design times, and that maskmaking companies will become more responsive to the needs of their customers in order to survive. It will become essential for maskmaking companies to give customers quick turnaround times and firm delivery commitments. The development of non-contact aligners for use in the wafer fabrication process parallels the development of higher quality masks. There are several non-contact technologies in use today. The most common is projection alignment, but by 1984, aligners that perform the step-and-repeat function during the process of exposing photoresist on the wafer will have gained a visible presence. Several manufacturers are developing Electron-beam (E-beam) equipment that writes directly on the wafer and totally eliminates the need for maskmaking. DATAQUEST expects that a number of products of this type will be introduced between 1981 and 1984 by companies such as ETEC, OCA, Varian, and Veeco. These products should have little effect on the maskmaking industry during this time period, however, because so few systems will be sold. The effect may be more significant by 1990, when more equipment is installed. Nevertheless, it is likely that the production of wafers will in most cases require masks. In particular, DATAQUEST believes that many semiconductor manufacturers will use X-ray aligners, which require masks. Electron-beam equipment is already used in maskmaking to generate reticles. This equipment can produce both low defect densities and quick turnaround. Turnaround is particularly improved when E-beam equipment is used for complex designs. However, E-beam equipment creates roughly four times more capacity for a typical mix of die sizes than optomechanical equipment; therefore its use makes more sense for maskmakers who can use the additional capacity. The use of E-beam equipment in the maskmaking process may eventually put smaller maskmakers at a competitive disadvantage. E-beam equipment has been commercially available for several years and it is estimated that about 25 systems are in use in the United States. However, most maskmaking companies still use optomechanical reticle generators because E-beam equipment is not cost effective unless used for larger chips, and because E-beam reticle generators cost about $1.5 million. Howard Z. Bogert Susan A. Thomas 10 i.^1 MUH 1 HUI-IU ( ^ SECURITIES, INC. ^ H ^ ^ • • ^ ^ • • Vol. II - No. 9 October 27, 1980 This letter is a condensation of recent Research Newsletters and internal thinking from the industry research groups at DATAQUEST, Inc. Requests for amplification of our thoughts or for specific Newsletters should be directed to the author. A list of recent DATAQUEST Newsletters appears at the end of this letter. SEMICONDUCTORS Turning points in industry fundamentals are usually a time of controversy and indecision and we believe that we are presently in that situation in the semiconductor industry. DATAQUEST has long forecasted that the semiconductor industry will ride through a recession relatively well and that order trends should start improving in September of this year. It is our belief that this is exactly what is happening. We know of at least three major broadbased suppliers who had order months in September that exceeded expectations; and it is our perception that the overall domestic book-to-bill ratio in September was close to 0.9. We also perceive that MOS memory pricing, which has been one of the hardest hit areas in 1980, has Started to stabilize. These events justify what we consider to be a very optimistic outlook for 1980 and 1981: a 25 percent increase in revenues this year and a 10-11 percent increase in revenues in 1981. At our just completed Semiconductor Conference in Scottsdale, Arizona, the general feedback from most of manufacturers and distributors was somewhat less optimistic than the DATAQUEST forecast outlined above. They tied the improvement in September more to seasonal factors than any real evidence of a recovery, and concern about MOS pricing in particular was very widespread. In justifying these two divergent sets of opinions, we should make one thing clear. We are not forecasting a period of strong industry conditions over the next three to five months. Rather, we are saying that business will still be relatively lackluster, but that the valley has been passed and that fundamentals will gradually start to improve from present levels, first in orders and then in sales and profits. It is sometimes difficult for people within the industry to sense a change in conditions, particularly when the change is not a dramatic one. We believe that industry participants will confirm a better order climate later this year, after a few more montlis of data is received. It is likely that MOS may lag the rebound because of the heavier competitive pressures existent in this market, but we believe that the rebound will be widespread across all sectors of the industry. Copyright © 27 October 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients. This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. Member, New York Stock Exchange 19055 Pruneridge Avenue / Cupertino, California 95014 / (408) 725-1200 The major risk in our forecast is the chance that the overall economy could fall back into a significant recession. This would obviously moderate the optimistic tone of our forecast. If this relapse does not occur, however, then it appears that the semiconductor industry has come through a recession better than it ever has before and that industry growth will begin accelerating markedly by the second quarter of 1981. COPYING AND DUPLICATING Several points of controversy regarding Xerox have arisen recently that need to be addressed. Canon has announced a new product at the higher end of the copier market. Named the SUPER NPX, this copier is the fastest on the market, with a speed of 135 copies-per-minute versus 120 copies-per-minute for the Xerox 9000 Family. No price has been announced for the SUPER NPX, but we would expect it to be very aggressive. On the surface, this appears to be a problem for Xerox — the initial sign of Japanese competition at the high end of the copier market. It is DATAQUEST's opinion, however, that the long-term fundamental impact of this announcement will not be significant. The major roadblock for the Japanese in penetrating the high end of a copier market has always been distribution, and things have not changed in this regard. Canon has a limited direct sales force in Europe and almost none at all in the United States, and this type of product must be marketed on a direct seiles basis. Down the road, we believe it is likely that Canon or other Japanese suppliers will sign distribution agreements with U.S. and European companies that have the requisite direct distribution and financial resources. Even then, however, there are very few companies that can successfully market and support a product such as the SUPER NPX. Another very important feature on a high-end copier is its input and output features: the development of a good, reliable, high-speed document handler and sorter is not a trivial task and the Canon product does not yet have these capabilities (nor do any other Japanese copiers). Nevertheless, we are not naive enough to disregard any new product announcement from the Japanese, particularly from a company with Canon's technical capability and this announcement may be a harbinger of increased competition. However, the fact remains that we do not believe this product can make any meaningful penetration of the high-end copier market in the foreseeable future. Even if Canon is very successful in initial development and production of the new machine, the Company would be unlikely to ship more than 100 machines in 1981; in comparison, Xerox's worldwide shipments at the high end in 1981 will range between 10,000 - 15,000 units. Xerox's third quarter earnings grew 10 percent compared to a 17 percent increase in revenues. The lower margins were attributable to a lower rate of gain in outright copier sales and to lower margins in Xerox's OEM computer-related businesses (Shugart Associates, for example). Both shortfalls are recession related. Xerox has already changed commission schedules to bolster outright sales, and has raised prices nine percent to try to bolster overall margins. We believe that the margin slide at Xerox will abate in 1981, allowing earnings growth to accelerate to a - 2 -14 percent rate from 10 percent this year. This would produce earnings of $8.40 per share in 1981 versus $7.35 for this year. The third quarter earnings report does not change our view in this regard. IBM finally announced an extension of its copier family, the Series III, Models 30 and 40. There was concern in some quarters several montlis ago that IBM would be making a very strong competitive entry into the high end of the copier market to compete directly with the Xerox 9000 Family. If the people expecting this new aggressive stance from IBM were banking on the Models 30 and 40, we think that they will be very disappointed. These products provide the expected improvements in IBM's existing position, but are not significant threats to the Xerox (Segment 6) 9000 Family. IBM badly needs replacements for its Copier I (Segment 1) and Copier II (Segment 2) and we expect this to occur within six months. To meet this deficiency, we think that IBM will do the unthinkable — we expect that the two low-end copiers to be announced and marketed by IBM will be manufactured for the Company by a major Japanese company, probably the Minolta 310 and 520. The most significant recent new product announcement at Xerox in the past month was the announcement of the 5700 Intelligent Copier. Because this product really relates to the word processing/office automation industry, we will discuss its ramifications in our section on Word Processing. PAPER AND FOREST PRODUCTS In an earlier Portfolio Letter (Vol. II - No. 6), we commented on the outlook for stumpage prices in the present recession. It was our thesis that the relative scarcity of woodlands would cause bid prices for stumpage to rebound much more rapidly than in the past two recessions, when prices did not move back above their cyclical peak for three years and two years, respectively. It appears that our thesis is being borne out. Bid prices for all species of wood peaked at $345 per thousand board feet (tbf) in the first quarter of 1980 and dropped to $295 in the second quarter. The average bid prices in July and August have already bounced back to $354 per tbf. Bid prices may come down again if the housing market weakens, but it appears clear that we are not getting the extended and Steep declines in bid prices that occurred during past recessions. Our previous Statement that we would see a new high in stumpage prices by early 1981 appears more likely than ever. The implications of these pricing trends are that there will be a tremendous cost push on plywood and lumber prices from the smaller producers in late 1982 and early 1983. This fits very well with our scenario for the forest products industry over the next four years, namely that end-product prices will escalate much more rapidly than inflation, allowing material profit increases for the companies who are well integrated, and have plentiful, low-cost fiber bases. All of the major forest products companies should benefit from these trends, but Weyerhaeuser may be the company most positively impacted. - 3 -INSTRUMENTATION Order softness has now spread to all aspects of the automated test equipment (ATE) market. Circuit board tester demand, which was reasonably strong in the first half, is now flattening out or declining from levels achieved earlier this year. Semiconductor testers remain soft, although some areas (LSI testers) have improved recently. Present revenue gains being achieved by companies are primarily a function of working off high backlogs. It is DATAQUEST's belief that order rates in the ATE industry will turn up early in calendar 1981. This would mean that the industry has come through the economic downturn better than it ever has before. We project sales gains in the semiconductor tester area of 19 percent in 1980 and 21 percent in 1981, and sales gains in circuit board testing of 31 percent this year and 29 percent in 1980. The pattern in both sectors of this industry should be the same: order gains trailing revenue gains this year and exceeding revenue gains in 1981. The two "pure plays" in the ATE business, GenRad and Teradyne, are both very well-positioned longer term, although each approaches the market somewhat differently. GenRad has been very aggressive in trying to attract a lot of the new customers in the ATE business. In semiconductor testing, the Company has done very well at the very low end of the market and will soon have its first products announced at the very high end — LSI and VLSI testing. In circuit board testing, GenRad has been trying to hold its dominant position in functional testers and is gaining share rapidly in the fast growing in-circuit sector of the circuit board testing market. DATAQUEST gives GenRad's management very high marks in terms of its product positioning and for its aggressiveness in pursuing many of the growth opportunities open to it. It gets somewhat lower marks in terms of its financial controls. GenRad was late in recognizing the likelihood that its orders would slow down and this has resulted in disappointing earnings results in 1980. Further, the company's inventories were allowed to grow disproportionately and have caused the company to be a heavy cash user. GenRad should earn $L35 to $1.40 per share in 1980 versus $1.25 last year. We expect the Company's order growth to accelerate early in 1981 and, therefore, believe that revenue growth may exceed 25 percent next year. At this juncture, we would expect earnings to approximately track the rate of revenue growth, with our full year estimate for next year being $1.70 per share. There is room for considerable variance on either side of this estimate, however, depending on how effectively the company improves profit margins and manages its cash needs. GenRad is extremely well-positioned longer term, but it needs to improve its ability to bring revenue gains down to the bottom line. Teradyne is taking a somewhat different tack, concentrating more heavily on servicing its existing client base. Its soon-to-be announced high-end functional board tester will probably improve its position in functional testers in general. However, the company may not grow as fast as the industry in in-circuit testers because of a lack of emphasis on the low end of this market. Teradyne is the number two participant in the semiconductor test area with very broadbased capabilities. We expect its entry into the LSI tester market to occur some time in 1981, and we believe that Teradyne should at least hold market share in semiconductor testers over time. - 4 -Teradyne experienced the worst of its order slowing during the summer and we expect a gradual improvement in orders from this point on. The company managed its backlog very well this year during the period of order slowing and, as a result, should be able to keep its earnings growth intact. We project $2.75 per share in earnings in 1980, up 17 percent from last year, with a 24 percent gain to $3.40 likely in 1981. Teradyne is not as aggressive a company as GenRad, but is well positioned to share in the growth in the ATE market. SMALL COMPUTERS The recent Prime Computer analysts' conference could hardly have been more upbeat. Order trends continue excellent and management forecasted a 50 percent increase in revenues in 1981. Based on comments by management on margins and tax rates, reasonable targets for earnings appear to be $1.55 per share in 1980 and $2.20 per Share in 1981. Apart from the numbers, a few interesting things came out of the meeting. First, one of the longer term results of the very heavy emphasis that Prime is putting on the office automation market may be to dramatically increase its average system sales. The Company claims to be looking at orders of very large magnitude (50-60 CPUs, 1500 terminals) versus its present $150,000 average selling price. DATAQUEST has not yet completed a full evaluation of Prime's word processing software or its overall office automation capabilities, but the company is moving very aggressively in this regard and the opportunities facing it are obvious. Second, Prime's development work in the CAD/CAM field appears to be unique. The company has developed an in-house CAD system that puts more processing power in each terminal and requires less transfer of data with the central computer. Prime is also the first company to use a 32-bit computer to drive its CAD system. These improvements allow the computer to be stationed up to 500 yards away from any of the terminals and dramatically increases the number of terminals that can be strung on a CPU. The pilot CAD system was shipped to Ford Motor, which is doing a lot of the development work on the system itself. It does not appear that CAD/CAM will be a major business for Prime in itself, but rather that it may create another functional area of customer needs that the company can satisfy with its computer systems. In general, Prime is doing all of the "right" things — its basic minicomputer business is booming and it is moving into hot areas such as office automation and CAD/CAM, which is just what analysts and portfolio managers want to hear. It is important to understand that Prime's efforts in both of these new areas are in the formative stage and one should not expect too much too soon. Nevertheless, the story is a good one. The only legitimate question may be the extent to which its near-term prospects are discounted in the stock. WORD PROCESSING We understand that some of IBM's salesmen may have been too aggressive in promising early 1981 delivery of the Displaywriter. Some major accounts who were promised January delivery when they ordered quantity early, have apparently been told to expect delivery in the fall. This slippage is not widespread, however and we do know of accounts expecting March 1981 deliveries. - 5 -The recent software enhancements for the Displaywriter fill out the product, making it more of a complete word processing machine. In order to take advantage of all of the new hardware and software features, however, the typical single unit price rises to $11,500 from the announced price in June of $7,895. Thus, as the features and capability of the Displaywriter improve, its price advantage is being reduced or eliminated. We believe that the Displaywriter is basically sold out for next year, and that IBM will Ship 30,000 to 35,000 units domestically in 1981, or about 17 percent of total industry shipments. In our opinion, the market is growing fast enough to easily absorb the impact of IBM in 1981 and beginning in 1982, IBM should become more of a competitive factor. Xerox's announcement of the 5700 Electronic Printing System is another important step in Xerox's attempt to penetrate the office information market. The 5700 is designed to work as a direct output medium from multiple word processing Stations and can operate as the hub of a combined word processing/data processing printing system. Xerox made the 5700 compatible with all Xerox word processors and the IBM 6670 printer. It is not compatible with any Wang products. The compatibility Strategy at Xerox becomes fairly clear: it wants to use the 5700 to stimulate demand for its word processing systems and does not want to strengthen Wang's position in the marketplace by allowing compatibility with Wang's products. If it had done SO, it would have generated increased sales for the 5700, but would have also justified the use of Wang word processors. The compatibility with IBM is guided by the fact that the 5700 is a direct replacement for the IBM 6670 and, assuming comparable reliability and copy quality, the 5700 appears to be clearly superior in price/performance. The 5700 may allow Xerox to knock numerous IBM 6670s out of users' offices and possibly allow Xerox to penetrate the offices with word processing systems as well. The 5700 fits.well with Xerox's strategy of eliminating the need for a central computer to control all aspects of an integrated office system. In order for this Strategy to work, there must be wid^pread acceptance of Xerox's Ethernet intra-office communication system, so that a user can mix products from different vendors. Otherwise, Xerox's lack of data processing capability may prove a major negative relative to offerings from Datapoint, IBM, Prime, W'ang, and others. Michael R. Weisberg - 6 -RECENT NEWSLETTERS OF NOTE SEMICONDUCTOR Semiconductor Industry Status Update Japanese Semiconductor Production and Trade Statistics 10/17/80 10/17/80 COPYING & DUPLICATING Nasliua Update Canon Announces Fastest PPC Copier in the World Ethernet Network Specs Completed and Basic Patent is Made Available Recent Industry Events IBM Realigns the General Business Group IBM Introduces the Series III, Models 30 and 40 Copier/Duplicators 10/17/80 10/17/80 10/15/80 10/10/80 10/03/80 10/03/80 PAPER A N D FOREST PRODUCTS Great Northern Nekoosa: Increased Earnings Projected for 1980-1981 INSTRUMENTS 10/17/80 Laboratory Power Supply Market Electronic Counter Market 09/30/80 09/30/80 CAPITAL EQUIPMENT IBH Holding Company Buys the Terex Division of General Motors Corporation 10/10/80 SMALL COMPUTERS Data General Unveils New MPT Family of Intelligent Terminals 10/16/80 WORD PROCESSING Exxon Enterprises, Inc., Forms New Office Systems Company IBM Displaywriter Survey Competitive Analysis of Olivetti Electronic Typewriters TELECOMMUNICATIONS IBM Realigns the General Business Group - 7 -10/13/80 10/06/80 10/06/80 10/03/80 WPIS Code: Newsletters UPDATE ON VOICE RECOGNITION AS we enter the 1980s, we expect automatic speech recognition to play an increasingly important role in man-machine communication due to three major factors: the inherent superiority of speech over other modes of human communication, technological breakthroughs, and the growing need for better control of complex machines. Even though recent technology has produced significant aids to human communication and information processing, nothing can replace or equal speech: it is the most familiar and convenient way for humans to communicate. Without speech recognition, man must interact with machines in machine languages. With speech recognition, a person can communicate with machines in natural-language human terminology. Furthermore, voice input allows the speaker to use hands and eyes to perform the primary task and to move about. The most significant advantages of effective voice control or voice data entry systems over other methoos of man-machine interaction are the dramatic reduction of operator training time and the reduction in operator errors, which result in reduced time utilization and operating costs. The first half of the decade should produce dramatic advances for voice recognition capability within word processing products. One of the earliest to be expected is the replacement of some or all function keys with voice input commands. Voice actuated electronic display typewriters are also a possibility in the early 80s but accuracy is only expected to be 90 to 95 percent. Continuous speech recognition products with almost perfect accuracy are not expected until after 1990. In August of this year, Interstate Electronics Corporation of Anaheim, California, presented a seminar on voice recognition in Santa Clara, California. At the seminar, Interstate demonstrated its automatic speech recognition system, the Voice Recognition Module (VRM). This seminar serves as an excellent update; and our notes are reprinted below. INTERSTATE ELECTRONICS SEMINAR Interstate is a subsidiary of ATO, Inc., a diversifiea manufacturer of industrial, consumer, and technical products, and markets a series of low-cost voice recognition modules that are priced from $1,650 to $2,255. These units recognize vocabularies of 40 to 100 words with as high as 99+ percent accuracy. Copyright © 20 October 1980 by DATAQUEST - Reproduction Prohibited The content of this reoort represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients. This information is not furnished in connection with a sale of offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO Interface Interstate's VRM is a single printed-circuit board that contains all analog-to-digital, processing, memory, and input-output interfaces necessary to convert the spoken word into digital code. It can be tied into a variety of users' systems by virtue of a full duplex 8-bit-wide parallel signal interface. The connection uses common TTL signal-level logic that may be connected to a host computer communications port or to the aigital control logic typical of modern control system panels. An optional asynchronous RS-232C or 20-mA serial port enables the display of host output on peripheral devices. Its other option replaces the parallel interface to the host with a second serial interface that permits full compatibility with standard computer communications ports and their associated software drivers. Accuracy Efficiency The VRM can achieve up to 99+ real-time accuracy under host computer control or by means of front-panel switches. An operator can select a particular threshold value for rejection of invalid words or background noise, thus ensuring word recognition accuracy independent of language, dialect, or accent. Three Vocabulary Sizes Voice recognition is a particularly valuable human-to-machine input technique because it allows the operator (speaker) to interact in his or her own language—a natural interaction that greatly reduces data capture errors and operator training time. Interstate considers a 40-word vocabulary the minimum possible size to permit basic entry of alphanumeric data along witli edit control words. To allow for increasingly complex requirements, the VRM is designed to accommodate 70- and 100-word vocabularies. A two-level syntax capability provides for automatic data-editing at the data capture source. Support Design Tools The VRM is supported by the VOTERM and VRM emulator. VOTERM, the chassis that houses the VRM, contains all the control switches, power supplies, and connectors required, and serves to speed up system integration. The VRM emulator is based upon Interstate's intelligent voice terminal, the Voice Data Entry System. By using the VRM emulator, the system designer can quickly detect confusing vocabulary words and build a data base for such features as automatic operator update training. The emulator also permits rapid testing of proposed system designs without requiring expensive modifications to host system computer software. - 2 -Training Interstate conducts a VRM Programming Workshop, a highly concentrated three-day training course for each user's system designer. Its purpose is to teach the system designer how to adapt the VRM product and its associated development support tools to handle desired applications. Language Compatibility The VRM is designed to be compatible with such high-level computer languages as FORTRAN, PASCAL, and BASIC by means of its special voice recognition communications protocol. Host system control programs for the VRM can be developed rapidly, debugged, and modified by the user, through the use of the software power inherent in these high-level languages. Voice Recognition Technology Interstate explains that two sets of criteria must be addressed in developing voice recognition technology: (1) speaker dependent or independent, and (2) discrete word or continuous speech. A speaker-dependent system recognizes the voice of the speaker for such applications as quality control inspection. This technology is much further advanced at the present time. While capable of handling many more users, the speaker-independent system is limited by its vocabulary size and universe of terms. Discrete-word systems separate words by stop gaps, while continuous-speech systems have no speech rate restrictions. The latter technology was stated to be several years away and will be preceded by "connected words" in specific patterns such as NEC's current products. Interstate's systems, which are an example of speaker-dependent/discrete word technology, emphasize the significance of the system designer's attention to human factors. A aigital pattern, called a "reference pattern," is created from multiple spoken samples: the speaker repeats discrete words several times to establish this individual's "pattern." These samples are stored in the interface processor, which correlates the speaker's input with the system's application features. Input speech is analyzed by a 16-filter spectrum analyzer and converted to a digital representation of the characteristics of the spoken input. This digital data is next converted to a fixed-size pattern that preserves the information content of the spoken inputs while discarding redundant features. These patterns are used during word training to derive a template for each utterance. These templates, which are stored in onboard random access memory (RAM), are then used during recognition for comparison with incoming spoken words. Processing algorithms are contained in real-only memory (ROM), operating in conjunction with a microprocessor. 3 -Device Training The VRM utilizes three basic training modes: (1) normal training in which the specified reference patterns are cleared and then trained during a selectable number of passes; (2) updating the word patterns in which the stored reference patterns for the specified vocabulary are augmented by additional training; and (3) single-word replacement mode in which to retrain a single word. In the latter mode, the single word is trained for the same number of passes as the other words in the vocabulary. Rejects During training, the VRM will automatically reject utterances that do not sufficiently agree with the same utterance from previous training samples of that word. This prevents significant alteration of a vocabulary reference pattern caused by spurious noise sources (such as bumping the microphone, coughing, speech inconsistencies, background noises, or simply failing to utter the specified vocabulary word). As a result, the user may need to repeat an utterance more than once before being prompted to the next sequential utterance. Operational Modes The VRM operates in either of two modes: under the control of a host processor, or in a stand-alone configuration with appropriate peripherals. In the host mode, vocabulary reference patterns can be transferred either from the host processor to the VRM or vice versa. This allows for permanent storage of reference patterns, much larger vocabularies, or separate files for different speakers. When in the host mode, the first and last word indices must be specified when placing the VRM in recognition, training, or update mode. Consequently, any contiguous sequence of vocabulary words can be selected for an operation. (This is particularly useful during a recognition operation in order to ensure that the VRM accepts only appropriate valid responses—a subset of the vocabulary—for input commands to a system.) A second syntax level (termed "common vocabulary") allows the user to select a second contiguous sequence of vocabulary words to be appended to the first set in the recognition mode. Therefore, command and edit words can be appended automatically to the specified set of valid input words without complex or redundant vocabulary structuring. 4 -Inputting The VRM's microphone preamplifier accommodates use of a light-weight microphone (Share Brothers SM-10), boom-mounted Telex CS-75, or equivalent microphone, for direct microphone input. Alternately, a preamplifier bypass switch on the board permits use of a remote microphone and preamplifier without any loss in audio signal integrity. Input is AC-coupIed and terminated by a resistance exceeding 10 kilohms. Typical remote preamplifier complex ^eech signal level should be 6.5V + 2V for average utterances. The VRM's useful audio bandwidth is from 200 to 7,000Hz. Excellent recognition can be maintained with the reduced telephone bandwidths. Performance Measurement Recognition accuracy is a function of training examples and optimum performance is usually achieved after seven to ten training examples of each word or phrase. Recognition accuracy of 99+ percent reflects the percentage of times the classification result will be correct on the first attempt when a valid utterance is spoken. This level was attained with properly trained speakers using typical application vocabularies of up to 100 words. Human Factors VRM performance is affected significantly by the manner in which the speaker uses the system. Recommended operator guidelines are: Microphone: Be consistent in how you hold or wear the microphone. • Significant changes alter the acoustical input, adversely affecting system performance. Speech: Speak normally while holding the microphone about a half inch from your lips and uttering the vocabulary words in a consistent manner. Update: If the VRM exhibits a high error rate in responding to your voice, update your reference patterns using the update command for the entire vocabulary. Single-Word: If the VRM exhibits a high error rate for a single word, execute a single-word training command. This will clear the reference pattern for the error word and generate a new template. Host Mode: When operating in the host mode, structure your vocabulary so that only those words that are valid responses at that point are checked for recognition with each spoken input. Selecting Vocabulary Words or Phrases: Avoid selecting words or phrases that are excessively long and that cause the VRM to decide to advance to the next item in the TRAIN mode before you have finished speaking. Similarly, avoid extremely short words that seem to be ignored consistently by the VRM. The ideal length of a word or phrase is between 200 milliseconds and 1.2 seconds. - 5 -Speech Recognition Applications Interstate's list of crit-eria that should exist when selecting automatic voice recognition applications includes: • Computerized reporting systems • Reasonable vocabulary (as natural as possible) • Data entry (repetitive steps) • Limited or defined number of operators (Chase Manhattan Bank is currently conducting a pilot application) • Importance of cost savings Other factors to look for include those in which operators must do one or more of the following: Capture data at the source Avoid mental encoding Use eyes and hands in transactions IVlove about from place to place Access a computer by telephone Data Entry Applications and Advantages Today's data entry systems are costly, error-prone, labor intensive, and result in Slow throughput. By using automatic voice recognition for these applications, one can: Reduce costs Improve data availability Increase productivity (capture and verify at the source) Improve data validity (0.1 percent error rate in Interstate's pilot text) Reduce manpower at the source point (supervisors, verifiers, etc.) Reduce training time and materials (learning to keypunch or enter key-to-disk, etc., takes much longer) Most of today's systems on the market are speaker-dependent applications. However, copiers will use speaker-independent systems since anyone is expected to use a copier. Examples of telephone input for speech recognition applications include: sales order entry, financial reports, PABX (digital), digital voice store and forward, and automatic dialing. Japan is currently making the most aggressive push and is several years ahead of the United States in product development and implementing internal company procedures utilizing speech recognition technology. - 6 -Cost Comparisons Using present methods of data entry, input represents 60-80 percent of the cost, while direct voice input results in two to three times cost reduction. A cost comparison study, in which speech recognition was used in place of other methods of input for quality control inspection, resulted in a one-year payback period in the worst situation. WHAT LIES AHEAD? Dave Culpiss, an attendee from Stanford Research Institute, stated that SRI predicts the future market size for speech recognition to be: 1980 1984 1987 Optimistic $15,000,000 $200,000,000 $1,400,000,000 Most Likely $10,000,000 $150,000,000 $1,000,000,000 Interstate predicts a dramatic increase in industrial applications, including movement into the professional area. Studies of data entry applications have shown excellent results. One of the many applications in wliich voice serves as supplemental input is in word processing where an operator enters voice commands. According to Interstate, it takes three months for a skilled word processing operator to learn the command structures for a new WP system, while it takes two days using automatic voice recognition. Another potentially significant application is that of access security. In this case, the major problem to be overcome is that of denying access to the correct person. In otlier words, the speech recognition unit is more apt to reject than accept the operator. Interstate predicts that two-chip technology should occur in the near future, while one-chip technology is further away. IBM's recent announcement of successful results with 1,000-word vocabularies, along with NEC's progress with connected-word installations, indicate significant technological breakthroughs. - 7 -COMPANIES OFFERING SPEECH RECOGNITION PRODUCTS IN THE EARLY 1980s Those firms marketing speech recognition products in the early 1980s include: Threshold Technology, Inc. (Delran, New Jersey): the first company to successfully market speech recognition equipment. Threshold has developed complete dedicated systems built around its voice entry terminals, Threshold's prices range from $10,500-$16,000 per terminal, and $26,000-$150,000 for a full system. Current installed terminals (estimated to be over 500 to date) serve applications ranging from inspection of motor vehicles to grading of meat. QUIKTALK, Threshold's latest market entry, an isolated speech system, offers a computer technique called dynamic programming allowing voice input at 180 words per minute with over 99 percent accuracy. The average person does not speak faster than 180 words per minute. QUIKTALK's peak rates range from 250 to 280 words per minute with 99 percent accuracy. Its dynamic programming technique allows pauses between words to be even shorter than pauses within words. Heuristics, Inc. (Sunnyvale, California): the current volume leader in terms of units sold to date has sold an estimated 11,000 units since 1977, mainly to owners of small personal computers. Heuristics' low-cost voice recognizer sells for $2,000 to $3,000 and recognizes a 32- or 64-word vocabulary with 85-95 percent accuracy. Its two most recent products, Model 5000 and Model 7000, interface a stand-alone voice terminal with lai^er computers and produce higher recognition accuracy. The 5000 is a 4-level 64-word vocabulary unit that sells for $2,220 and fits inside a Lear-Siegler 80M 3A terminal, while the 5000 stand-alone system has a 64-word vocabulary that produces better than 99 percent accuracy, is RS232 compatible, and sells for $3,330. Centigram Corporation (Sunnyvale, California): the company markets a speech recognition terminal called MIKE. Its main feature is recognizing 12 vocabularies, each containing 16 words. MIKE, a stand-alone unit, includes voice response (brief, nonsynthesized prerecorded messages), and sells for approximately $3500. Centigram is currently introducing OEM board versions for the PDP-11, an Intel multi-bus system. These units are priced under $1000. "Verbex" formerly known as Dialog Systems, a subsidiary of Exxon Enterprises (Bedford, Massachusetts): producer of the only American speaker-independent system on today's market. (Most speaker independence is accomplished by an assimilation of speech patterns by more than 1,000 different speakers over 1,000 different telephone lines. These patterns are then reduced to four composite patterns which are used for speech recognition.) Verbex utilizes a high-speed computer, and trains each system with hundreds of samples of each word as spoken by people with many regional accents. Verbex has recently delivered its first connected speech system to a large governmental agency. - 8 -NEC America, Inc. (Melville, New York, a subsidiary of Nippon Electric Company, Tokyo, Japan): NEC's ModelDP-lOO introduced in 1978 is the only connected Speech recognition system in the world. A DP-lOO user may speak without pausing after each word. A terminal without host computer, interactive software, or additional peripherals sells for about $48,000. A two-input channel version sells for about $56,000. NEC's terminal provides a 120-word vocabulary, and can handle up to five words per spoken utterance, provided the speaker's input is between .4 and 2.5 seconds per utterance. The terminal is trained by practicing each word and digit for consistency. Accuracy is lx)th vocabulary and user dependent. Scott Instruments, Inc. (Denton, Texas): has developed a speech recognition system designed to run on the Radio Shack TRS-80, Commodore Pet, and Apple computer. Auricle, Inc. (Cupertino, California): a wholly-owned subsidiary of Threshold Technology as of May 1980. Its charter is to serve the OEM markets and to incorporate the latest in micro-electronic technology to voice recognition. One product will be a semiconductor chip selling for an estimated price of less than $100, with introduction expected in the second half of 1981. Clifford M. Lindsey - 9 -^ 1 I K > ^ 1 Jfll fit If 1 ^ ^ 1 '' ••-y; ASubsidiarvof A.C.Nielsen Co. ^ I N C O R P O R A T E D Nl SIS Code: Vol. I, 2.0 JAPANESE SEMICONDUCTOR PRODUCTION AND TRADE STATISTICS SUMMARY This newsletter presents data derived from published Japanese import, export, and [M-oduction statistics. It summarizes a broader and more detailed data set. Current trends are presented graphically and numerically. The following comments are noteworthy: • Declining domestic consumption (in dollars) in 1979 and through the first quarter of 1980 was more than offset by increased exports; thus, Japanese semiconductor production increased and excess capacity was exported. Japan now enjoys substantial positive net balances semiconductors with all other regions of the world. of trade in • Japanese semiconductor consumption has grown more slowly tlmn that of the world as a whole since 1976. • Japanese production, consumption, and imports of semicontbictors turned up marl(edly in the second quarter of 1980. SOURCES The data presented in this newsletter are derived from the Ministry of International Trade and Industry's (MITI) published export, import, and production Statistics of Japan. The data include all production in Japan, including that by non-Japanese companies, notably Texas Instruments. Export of products by Japanese companies outside Japan is not included. The data are converted into dollars at the annual or quarterly exchange rates during each period. Note that consumption is derived from the published statistics by the following formula: Consumption equals production, less exports, plus imports. DATA Table 1 presents Japanese semiconductor production and trade statistics for 1970 through 1979 and gives a historical perspective on these trends that is graphically presented in Figure 1. Copyright © 17 October 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally availabIe to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients This information is not furnished in connection with a sale or offer to sell securities or in connection with The solicitation of an offer to buy securities, This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO These data are comparable to those found in Table A-8, Appendix A of the Semiconductor Industry Service notebooks. Data previously published in Appendix B-Mariased companies' production in Japan (e.g., TI Japan), while MITI includes them in Japanese production figures. However, Appendix B includes U.S.-based companies' production in Europe, Japan, and Rest of World in the U.S. totals. Conversion from yen to dollars can t>e misleading, and using either yen or dollars can distort data, depending on the situation. From early 1970 to 1979, the value of the dollar, expressed in terms of yen, declined from 360 yen to 221 yen. A low of around 170 yen per dollar was reached in late 1978. More recently, the value of the dollar increased about 20 percent from 205 yen in the first quarter of 1979 to 246 yen in the first quarter of 1980. In the second quarter of 1980, this trend reversed and the dollar declined about 8 percent to 221 yen. As a result of these currency fluctuations, the growth of Japanese production according to MITI data expressed in yen averaged 12.0 percent compound annual growth t)etween 1970 and 1979, while this same growth expressed in dollars averaged 17.9 percent. This is compared to growth in U.S. company production of 18.6 percent for the same time period. Table 2 gives quarterly data for 1979 and the first half of 1980. This is shown graphically in Figure 2. During this period, exports of integrated circuits—led by MOB RAMs—have increased more than 2-1/2 times. This has allowed increasing Japanese production despite declining consumption (in dollars) through the first quarter of this year. In terms of yen, however, consumption increased, albeit slowly. The future strength of exports in the current weak semiconductor market in the United States and Europe is questionable. In particular, falling prices of 16K dynamic RAMs should make growth of exports difficult for the remainder of 1980 and 1981. Table 3 presents 1979 Japanese semiconductor trade statistics segmented by product class. Table 4 s^ments Japanese trade by region. Noteworthy is the fact that Japan has eliminated its 1977 trade deficits in most regions of the world, and by 1980 has established itself £is a major net exporter of semiconductors. Most of the imports to Japan from the Rest of World are shipments from U.S. company assembly and test facilities in Asia. Becky Bogert Mary Ellen Hrouda Frederick L. Zieber - 2 -Table 1 JAPANESE SEMICONDUCTOR PRODUCTION AND TRADE 1970-1979 (Millions of Dollars) 1970 1971 1972 1973 1974 Production Integrated Circuit Discrete and Opto Total Export Integrated Circuit Discrete and Opto $148.9 502.3 $651.2 $ 0.0 27.1 $148.0 434.6 $582.6 $ 0.0 28.3 $239.4 579.1 $818.5 $ 0.0 42.1 $ 417.9 866.6 $1,284.5 $ 9.7 71.0 $ 430.1 759.4 $1,189.5 $ 23.0 98.0 Total $ 27.1 $ 28.3 $ 42.1 $ 80.7 $ 121.0 Import Integrated Circuit $ 57.5 $ 70.5 $ 54.3 $ 123.5 $ 175.2 Discrete and Opto 35.1 20.7 20.5 47.3 51.7 Total $ 92.6 $ 91.2 $ 74.8 $ 170.8 $ 226.9 Consumption! Integrated Circuit $206.4 $218.5 $293.7 $ 531.7 $ 582.3 Discrete and Opto 510.3 427.0 557.5 842.9 713.1 Total $716.7 $645.5 $851.2 $1,374.6 $1,295.4 Exchange Rate (Y/$) 357.8 343.3 302.0 268.7 291.8 ^By definition: Production, less export, plus import (Continued) - 3 -Table 1 (Continued) JAPANESE SEMICONDUCTOR PRODUCTION AND TRADE 1970-1979 (Millions of Dollars) 1975 Produc t ion Integrated Circuit Discrete and Opto Total $930.9 1976 1977 1978 1979 $396. 534. .1 ,8 $ 666. 868. .4 .6 $ 1 798. ,021. .4 .1 1 , 1, ,367, ,220, .2 .6 $1, 1; ,729. ,147. .9 .1 $1,535.0 $1,819.5 $2,587.8 $2,877.0 Export Integrated Circuit $ 45.5 $ 56.7 $ 100.8 $ 208.9 $ 397.1 Discrete and Opto 80.1 159.4 193.4 237.2 256.9 Total $125.6 $ 216.1 $ 294.2 $ 446.1 $ 654.0 Import Integrated Circuit $134.7 Discrete and Opto 36.4 Total $171.1 $ 199.5 $ 191.8 $ 262.8 $ 401.6 77.3 82.4 82.5 98.1 $ 276.8 $ 274.2 $ 345.3 $ 499.7 Consumption^ Integrated Circuit $485.3 $ 809.2 $ 889.4 Discrete and Opto 491.1 786.5 910.1 $1,421.1 $1,734.4 1.065.9 988.3 Total $976.4 $1,595.7 $1,799.5 $2,487.0 $2,722.7 Exchange Rate (Y/$) 296.9 296.2 265.9 205.9 221.3 ^By definition: Production, less export, plus import Source: DATAQUEST, Inc. MITI October 1980 - 4 -Figure 1 JAPANESE SEMICONDUCTOR PRODUCTION AND TRADE 1970-1979 (Billions of Dollars) Production Consumption 2 -1 -1970 1871 1872 1973 1974 1975 1876 1977 1978 1979 Source: DATAQUEST, Inc. - 5 -Table 2 JAPANESE SEMICONDUCTOR PRODUCTION AND TRADE 1978-1980 (Millions of Dollars) 1979 1980 1st 2nd 3rd 4th 1st 2nd 1978 Qtr. Qtr. Qtr. Qtr. Qtr. Qtr. Production Integrated Circuit $1,367.2 $415.8 $398.0 $443.1 $463.0 $489.7 $607.0 Discrete and Opto 1.220.6 305.3 278.5 291.6 270.6 267.9 317.4 Total $2,587.8 $721.1 $676.5 $734.7 $733.6 $757.6 $924.4 Export Integrated Circuit $ 208.9 $ 71.3 $_84.5 $105.4 $130.0 $147.5 $180.5 Discrete and Opto 237.2 64.4 58.9 62.5 69.3 61.6 60.2 Total $ 446.1 $135.7 $143.4 $167.9 $199.3 $209.1 $240.7 Import Integrated Circuit $ 262.8 $ 87.9 $108.7 $106.3 $ 96.6 $ 91.1 $103.5 Discrete and Opto 84.5 21.0 24.8 25.3 25.8 20.2 31.0 Total $ 347.3 $108.9 $133.5 $131.6 $122.4 $111.3 $134.5 Consumption! Integrated Circuit $1,421.1 $432.4 $422.2 $444.0 $429.6 $433.3 $530.0 Discrete and Opto 1.067.9 261.9 244.4 254.4 227.1 226.5 288.2 Total $2,489.0 $694.3 $666.6 $698.4 $656.7 $659.8 $818.2 Exchange Rate (Y/$) 205.9 205.4 220.1 221.2 241.7 246.7 226.8 I f i y definition: Production, less export, plus import Source: DATAQUEST, Inc. MITI October 1980 - 6 -Figure 2 JAPANESE SEMICONDUCTOR PRODUCTION AND TRADE 1978-1980 (Millions of Dollars) 800 -600 -200 -Production Consumption Exports Imports Source: DATAQUEST, Inc. - 7 -Table 3 JAPANESE SEMICONDUCTOR PRODUCTION AND TRADE BY PRODUCT 1979 (Millions of Dollars at 221.3 Yen = $1.00) Total Semiconductor Total Discrete and Opto Diode Transistor Thyristor and Otlier Optoelectronic Total Integrated Circuit Bipolar MOS Linear Hybrid Production $2,877.0 $1,147.1 153.2 471.7 373.6 148.6 $1,729.9 230.9 886.9 432.8 179.4 Export $654.0 $256.9 72.7 106.6 44.8 32.8 $397.1 N/A1 N/A N/A N/A Import $499.7 $ 98.1 18.8 52.4 10.4 16.5 $401.6 N/A N/A N/A N/A Consumption $2,722.7 $ 988.3 99.3 417.5 339.2 132.3 $1,734.4 N/A N/A N/A N/A ^N/A indicates not available Source: DATAQUEST, Inc. MITI October 1980 - 8 -Table 4 JAPANESE SEMICONDUCTOR TRADE BY REGION 1980-Six Months United States Europe Rest of World Total 1977-1980 (Millions of Dollars) Exports From Japan $194.2 71.7 197.5 Imports To Japan $143.6 19.0 82.4 Net of $ Balance Trade 50.6 52.7 115.1 Exchange Rate (Y/$) 236.8 $463.4 $245.0 $ 218.4 1979 United States Europe Rest of World Total $232.6 83.4 338.0 $333.9 28.0 137.8 $(101.3) 55.4 200.2 $654.0 $499.7 $ 154.3 221.3 1978 United States Europe Rest of World Total 1977 United States Europe Rest of World Total $118.5 44.5 276.5 $205.0 35.5 106.8 $ (86.5) 9.0 169.7 $446.1 $347.3 $294.2 $274.2 $ 92.2 $ 67.2 35.6 198.0 $141.4 43.3 89.5 $ (74.2) (7.7) 108.5 $ 26.6 205.9 265.9 Source: DATAQUEST, Inc. Mill October 1980 - 9 -^ ^ = ^ B = . . ^ S B E C T RESI A Subsidiary of A.C. Nielsen Ca. ^ INCORPORATED NEAA SIS Code: Vol. 1, 2.0 SEMICONDUCTOR INDUSTRY STATUS REPORT DATAQUEST perceives that positive indications signalling the end of order weakness in the semiconductor industry have occurred. Furthermore, the U.S. economy is now improving, which reinforces our belief that the effect on semiconductor demand of the current U.S. economic recession wiU be mild. Several factors are noteworthy: • Domestic semiconductor bookings exceeded expectations in September. At least three major broad-based suppliers had excellent bookings, and it is DATAQUEST's perception that the domestic book/bill ratio was close to 1.0. This is especially positive because DATAQUEST believes that September was a good shipping month. • The industry has successfully weathered the period of order weakness. DATAQUEST estimates that the value of shipments in the United States (including imports) declined only slightly in the third quarter, with only a moderate effect on margins. • Prices appear to have stabilized after falling rapidly for several months in some product areas, especially in MOS memory. However, some prices, such as those for bipolar logic gates, are expected to increase in 1981. • The semiconductor industry has had no major layoffs this year, in contrast to the 1970-71 and 1974-75 recessions when the industry reduced employment by 25 to 30 percent. This indicates the industry is operating close to capacity. • The U.S. economy appears to have bottomed out and is on a path of slow improvement. — Retail sales have been rising for the last four months. — The Index of Leading Indicators and housing starts have both improved during the last three months. — Industrial production increased in August, and early indications show a continued increase in September. Copyright © 17 October 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness It does not contain material provided to us in confidence by our clients This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO A stronger economy should give U.S. industry the confidence to maintain and increase capital expenditures for electronic equipment, although weaicness in the , ^ ^ European economy is expected to continue for two or three m(»>e quarters. Nearly ^ | B all inEHits Appear to be consistent. TTie inputs reinforce DATAQUEST^ beliefs that ^ ^ semiccmduetor booldngs will continue to improve, that shipments will t>e^n to show growth around year end, and that the industry growth rate will accelerate throughout 1981. ^ Frederick L. Zieber Daniel L. Kleslcen James F. Riley -2-r B=E-i- RESEARCH A Subsidisrv Ql A.C. Nielsen Co. ^ ' IMCORPORATED I ^ I ^ H W ^ 3 ^ B ^ H I 1 ^ S P K ) SIS Code: Vol. I, 2.8.1 MOS MICROPROCESSOR SHIPMENTS SUMMARY - ' Worldwide shipments of MOS microprocessors continued their strong growth in the second quarter of 1980. Unit shipments were up about 19 percent over the first quarter of 1980 to an estimated 37.4 million units. On a year-to-year comparison, worldwide shipments in the second quarter of 1980 were up about 137 percent over shipments in the same quarter of 1979. Microprocessor prices eased somewhat in the second quarter of 1980 as supply caught up with—and now generally exceeds—demand in most microprocessor families. In the second quarter of 1980, 4-bit microprocessors represented about 67 percent of the total worldwide unit shipments while 8-bit and 16-bit microprocessors represented about 32 percent and 1 percent, respectively, of the total unit shipments. Figure 1 depicts estimated quarterly microprocessor shipments, segmented by bit length. In the second quarter of 1980, worldwide shipments of 4-bit microcomputers grew an estimated 20 percent, while shipments of 8-bit microcomputers grew only 6 percent. As a result, microcomputers represented 82 percent of the total worldwide microprocessor shipments in the second quarter Of 1980, compared with 83 percent of the total in the first quarter. DATAQUEST's estimates for worldwide microprocessor Central Processor Unit (CPU) shipments for the second quarter of 1980 are presented in Table 1. Our estimates refer to microprocessor CPU units only and do not include I/O or peripheral chips. 4-Bit Products Table 2 presents DATAQUEST's estimates of worldwide shipments of 4-bit microcomputers. In the second quarter of 1980, estimated shipments of 4-bit microcomputers were 25.2 million units, up about 20 percent over estimatea first quarter 1980 shipments of 21.1 million units and about 146 percent over estimated second quarter 1979 shipments of 10.2 million units. Despite some softening of demand for microcomputers in the consumer segment, especially in the Far East, 4-bit microcomputers experienced good growth in the second quarter. Copyright © 10 October 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients. This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent andfor their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities^ 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO Table 3 presents DATAQUEST's estimates of worldwide shipments of 4-bit microprocessors. Note the change in format from earlier newsletters in which the 4-bit microprocessor table included all 4-bit microcomputers as well as microprocessors. These older products experienced no growth in the second quarter and are actually expected to decline in coming quarters as the current shipments are going only into older existing designs. No new designs are expected for these products. 8-Bit Products Table 4 presents DATAQUEST's estimates of worldwide shipments of 8-bit microcomputers. In the second quarter of 1980, an estimated 5.3 million units of the 8-bit microcomputers were shipped, up only 6 percent over an estimated 5.1 million units Shipped in the first quarter of 1980. The quarterly percentage gain in unit shipments of 8-bit microcomputers is notably less than the 20 percent gain in unit Shipments of 4-bit microcomputers. This anomaly in the data is not readily explainable other than to note that apparently there was a much stronger demand for the lower-priced 4-bit products than for the higher-priced 8-bit products. The majority of these microcomputers are masked ROM products whose lead times are governed by the turn-around time of the masking operation. In most cases these lead times are in the 15- to 20-week range. The only exception to these long lead times is the EPROM version used in limited quantities for product development. The EPROM versions generally are available off the shelf or within three to four weeks. Table 5 presents DATAQUEST's estimates of worldwide shipments of 8-bit microprocessors. Note the change in format from earlier newsletters in which the 8-bit microprocessor table included all 8-bit microcomputers as well as microprocessors. Second quarter 8-bit microprocessor shipments of 6.5 million units were up about 29 percent over first quarter 1980 shipments. Although these products generally are more mature than the 8-bit microcomputers, a few of them showed surprising strength in the second quarter. Some of this strength can be attributed to major contract shipments which distort the figures for one quarter. A similar large gain is not expected in the third quarter. 12-Bit Products There has not been a new product family or supplier in the 12-bit product arena for several years now, and none is expected. The quarterly shipments of 12-bit microprocessors, shown in Table 6, were an estimated 14,000 units in the second quarter, up slightly from an estimated 13,000 in the first quarter. 16-Bit Products • Worldwide shipments of 16-bit microprocessors during the second quarter of 1980, shown in Table 7, were an estimated 289,000 units, up about 25 percent over estimated first quarter 1980 shipments. Pricing on most 16-bit microprocessors declined during the second quarter as availability continued to improve. - 2 -The TMS 9900 and 8086 microprocessors have now been on the market long enough for some of their early designs to move into production. This is reflected in the substantial quarter-to-quarter unit gains for these products. The design cycle is typically about 18 to 24 months for most 16-bit applications. The newer 16-bit products have been available for only 4 or 5 quarters, hence the quarter-to-quarter unit growth for these products more closely follows a typical sampling and development cycle. Multi-Sourced Microprocessor Families Figure 2 compares the estimated total quarterly shipments of the major multi-sourced 8-bit microprocessors by all suppliers. The continued strong growth of the 8048, 6500, and Z-80 product families is evident from the graph. Some of the more mature 8-bit microprocessor families are experiencing lower quarter-to-quarter shipments growth. Additional Microprocessor Products DATAQUEST is aware of the fact that Fujitsu, Sharp, and Toshiba have been shipping microprocessors into the Japanese market for some time. Each of these suppliers is now beginning to ship microprocessor products into the United States. Estimates of the quantities shipped are not available, but as they become available they wiU be added to this newsletter. Products available from Fujitsu include the 8850, a 4-bit CMOS microcomputer; Sharp is offering the SM-4, SM-5, both 4-bit CMOS microcomputers, and the Z-80; and Toshiba is offering the TLCS-43, the TLCS-46 (4-bit NMOS and CMOS microcomputers, respectively), as weU as the 8048, 8049, and 8085. We understand that Oki also will soon be offering microprocessors in the U.S. market. Daniel L. Klesken Lane Mason - 3 -Figure 1 ESTIMATED WORLDWIDE MICROPROCESSOR AND MICROCOMPUTER SHIPMENTS I en I 10 M C o i 1st Qtr 2nd Qtr 3rd Qtr 4th Qtr 1st Qtr 2nd Qtr 3rd Qtr 4th Qtr 1st Qtr 2nd Qtr 1978 1979 1980 Source: DATAQUEST, Inc. % o g C o Q S S b p O > :s: £ 3 ^ § ^ S S « to '^g^Sfq g H t^ ft! ^a o > > s -qs s C o o a s H O s§ ^s ^§ g l Oj ?1 Co 1 i t-i H ss ^ :« 1 S ^ s § fcj 5 1 s CDOoasoocDooao-PooooaD o ^ o o o o o i - » ^ o O O l D U l l O M O O O O \ >^ O Oi I C n o O O O O O O t > O O O O . P O D a O O O O O 4 ? 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P c n M r o o j - k O o o o o t n O j o o c n o o o o c n t o o o o o c n o o o o o c n o i o M H » M i - f c i - f c r o i - c o i - ' ro cn H»>cjit-» lOH^ro OToro c n r o o c n o o i o c n o i - r o o r o o o c n c n c n c n c o o o t n o o o o o o o o c n O c n o o o O j o t n O O H^ CO ro ro M. h-kh-k i - k M C O I - ^ l - ^ M j r i - i . |-v.^l_kt-»4='IOCO 0 > O C 0 " C n t n O O O h O ' O l-» O H M O O C n o o o o c n c n o o c n O i C o O j O O O O O O O C n t n C o O j o O j c n c n o C O •sj ^ cn i-^co rou>4=' r o ^ i o ^ c o o o H ^ c n oo cn • P c o c n M - ^ c n o o C O O I D (7>ocnco ( } > o o < ^ i-^ cnC7>u>o c o o c n c n o o o o o o o o o O j C o C o o o o c n o o o o c n C o O j o O j c o h ^ o 1-^ - p r o r o r o o i M c o i - k t n -^ C I 1 I - » ^ I 0 - P r 0 4 r c n o c n 0 0 4 = ' O l - » C O O I O x J to O M M O o o c n o o o o o o c n o o i o c n C o o o o o o t n O i o c n C o t n c n C o - p r o o I- 4r K) C O I- -F-^Jco r O N > . p i - k r o j - k cn H o > i - t o i o r o c n i - u i o c o ro - J - ^ c n ^ - o o i - ^ •-'•-P O H O o o t n c n c n c n O c n o o o c n O O j c n c n o o C o O O o o c n c n O O t n ( O t D O ii Cq Co Co ^ i S Ik. 00 t-1 I JO I-' 13 ^ to "S I JO ro as 50 I C-1 I |JC> t-» 13 "Ji R3 "-a i tas 33 Cq Co a: 3:^ H S3 ^1 s l •! Co l-^ S S ^ S^S I^S^ '^ P KT wco < a N . ^ 3 I I Co t-a :t^ Co tn eg l§ So t i TABLE 2 ESTIMATED WORLDWIDE SHIPMENTS OF H-BIT MICROCOMPUTERS (THOUSANDS OF UNITS) COMPANY AMI HITACHI MATSUSHITA MOTOROLA NATIONAL NEC ROCKWELL (.PANASONIC) TEXAS INSTRUMENTS TOTAL MICROCOMPUTERS PERCENT CHANGE FROM PREVIOUS QUARTER PRODUCTS 52000 HMCS-^0 AW1400 141000 COPS UCOM-ti PP5-4 TMS 1000 1978 TOTAL 29 410 N/A 20 2325 1500 2275 9400 15959 152" QTR 50 130 500 30 900 1100 600 4200 7510 37.9 2ND QTR 300 150 800 75 1100 1300 1100 5400 10225 36.2 —1979-3RD QTR 675 175 1400 90 1500 2300 1100 7500 14740 44.2 >iTH grt? 400 200 1700 90 2100 3100 1100 9000 17690 20.0 1979 TOTAL 1425 655 4400 285 5600 7800 3900 26100 50165 — 1 9 8 0 - - -XST 2ND QTR 180 225 2200 70 2700 3300 1400 11000 21075 19.1 QTR 340 300 3000 50 3100 4200 1700 12500 25190 19.5 SOURCE: DATAQUEST. INC. OCTOBER. 1980 TABLE 3 ESTIMATED WORLDWIDE SHIPMENTS OF 4-BIT MICROPROCESSORS {THOUSANDS OF UNITS) COMPANY INTEL NATIONAL TOTAL MICROPROCESSORS PRODUCTS 4004 4004 IMP 1978 TOTAL 159 130 80 152" QTR 35 30 18 2ND QTR 32 26 15 —1979-ZRD QTR 28 20 15 HTH QTR 25 15 15 1979 TOTAL 120 91 63 — 1 9 8 0 — 157 2ND QTR QTR 20 25 12 9 14 12 369 83 73 63 55 274 46 46 PERCENT CHANGE FROM PREVIOUS QUARTER (2.4) (12.0) (13.7) (12.7) (16.4) 0.0 SOURCE: DATAQUEST. INC. OCTOBER. 1980 -8-TABLE h ESTIMATED WORLDWIDE SHIPMENTS OF 8-BIT MICROCOMPUTERS {THOUSANDS OF UNITS) COMPANY AMD FAIRCHILD GENERAL INSTRUMENT INTEL MOSTEK MOTOROLA NATIONAL NEC PHILIPS/MULLARD ROCKWELL SGS-ATES SIGNETICS ZILOG PRODUCTS 8048 3870 PIc-1650 8021/8022 8048 8049 8748 3870 6801/6803 6805 3870 8048 8049 8050 8070 8021 8048 8049 8048 6500/1 3870 8048 ZB 1978 TOTAL 0 23 450 5 480 10 30 350 0 0 70 0 0 0 0 0 15 0 0 0 5 S 0 1ST QTR 0 40 300 10 190 20 50 260 0 0 80 0 0 0 0 0 25 0 0 0 5 15 0 2ND QTR S 50 950 20 390 30 75 300 5 0 125 0 0 0 0 0 160 5 0 5 10 30 0 --1979-ZRD QTR 3 120 1250 50 570 60 75 425 3 S 125 0 S 0 0 0 250 100 0 3 15 60 0 42"^ QTR 20 300 1600 80 800 100 100 485 10 3 170 5 10 S 5 0 300 150 5 5 20 75 5 1979 TOTAL 23 510 4100 160 1950 210 300 1470 13 3 500 S 10 S S 0 735 250 S 8 50 180 S — 1 9 8 0 - — 1ST 2ND QTR 5 345 1700 110 1000 140 125 530 15 10 150 5 25 5 S 0 610 200 2 8 20 60 5 QTR 38 380 1700 200 1000 175 160 570 35 50 150 5 40 10 5 5 470 250 5 15 25 60 3 TOTAL MICROCOMPUTERS 1428 995 2140 3109 4228 10472 5060 5346 PERCENT CHANGE FROM PREVIOUS QUARTER 53.1 115.1 45.3 36.0 19.7 5.7 SOURCE: DATAQUEST. INC OCTOBER, 1980 -9-'tj si ^ § S"^ £5 S3 Oj te « ^ •= S a So S3 S a: • 9 i C-i ^ r> :« ^ to R § Co CJ N > -3 H pS t-< >< o 0] ^ ^ to a § ?; S Co Co Co ts '=>fc? ^ P ^ S ftl H ! W tlCq • ^ '•9 Dl C o H ^ C o &3 n Co Co :) to S !a F > S § 3 c q :i ^ : S cq Co p] t-Co t i r> S B 1» H t; J3 Co ^ 3: c: In t-1 I !a :t^ t^ I C-i S : I t-i : ^ fe 3: % ^Co a ta i t -< H as as ?! S " ^ i ta a 3 tq a: :^ M fti c^ Co as I a : t:: t l a I Co I I H to ^ C ^ ^ a > i ^ i o o o a o & a o > M t o ^ i o o o o C o o o ( 7 > a ) 0 > ^ a ^ ] a > o o a o o o o o M O ) 0 > o i ' > ] < 7 > ( n ( 7 ) C 7 ) O D a } o o % c n o o O ) O O O o c / i o o a > o o o o C > o o o a } O O C D O O c / i o o o o a o o o o o a o o o o o o o a > o o o o o C o o o c n m o o o o o u i o o o o o ' O ' v o o o o o o o o o o o o o o o o o o o o o o o o o o O M O O l O O I O O iji G St G iD to O O O O C n O O O N J O l O O t O O M O C / i O 00 ik a i ^ a k - ^ i k " ^ > s .
: ^ o CT> cn cn 00 00 00 00 o o o o :^ 00 00 00 I M O en a i c > 6 o i - k i o _ _ tD to c o c o o c o - j oo-«JO»cnK> c n o o o ) ^ M C O CO CO ~ ~ a i c ; i o i o o o o o t n o o a i o > a i o C o o o o o o o o i < / i O) -^ M en o o O) -o K) 0> ' C O u > c o o i - ^ . p cni-k o o c n o i o c j i c n o o t o o ^ t o r o M i n cocn COMCA) c n r o o o c n O c o c n o a i O O c n c n o o C o o c / i o o t n o c n o o r o o C / j t n o o o o C o c n t n t n O tn O i-k o 1 I <0 -P lO (-»• M t-k .p- -J lO N3 -O K> lO Ol O l-k H O c n r o i O M U ) i-ha»t- o o - J t o - P ^ . P - J I O M - O c n o i - k ^ w — w , ^ _ ^ . _ o o o i o o i O O c n O O o i r o o c n o t n o o o o o o ^ o O j c n o o o o o o c n h-i i-> a> -p to ro to . 4r •~] . C/l Cd G O U> l-» OS 1 C O • J 11" 1 1 -p 1 «1 1 o ro H^ I- > 00 H ^ h lo lo ot ro • o r o o c n u i o i o c n l - k M M K > l O r O M I - k 0>IOOCT>K) O M t O r O O O l O O c n O o o o c n c n a i c n O ' C O ro h -^ M OH^t-^h-^roM-FToo > o o < n o o c n c / i o o CO M h CO - J CO » K3 o o tn en Co o <5 to D cq S "3 ^ ^ o :^ CD«i B c; to Co • Co ^•a h • ID 00 H O S! «~1 hO o . • NJ ID t- h C O Ol Ul ^ in O C O at Ol o K) Oh i-k H k | _ k | _ k | o c > i O M i - k cot-k I- j-k ro O M h - k h - k ^ c o o c o . p ( 7 i O - ^ - l = ' i ^ ' 0 0 - ^ c o ( D c n o o t - k r o c n c o - p ^ M c o . p > j o o c n O o o o o c n O t n O i o o o c n o o c n c n o o o o o o i O N j o o o o o c n o o o c n to 00 C O to 4= h o - p c o c n ^ iD^cn^PCA) o ^ -p M O ) H ^ r o o ^ o o o . P c n i - ^ < - < J O o c o i D a > o a > o o o r O ( D C 7 ) t - ^ ^ o o o o o c i o > K > - P c n a i - f r e / i c o o o o O O O c o t n c n o o o o o C o O O O c / i c n O O O c n O c n O C n o c n o i c n c n O O O c n o c / i O O ' en en h ro en o i-fcro.p.po>en o o o o e n o o o e n o i l O M H ' i o cororo lo .pro to M o o . p c o ^ e n r o r o o M e n e n o o i - c o o e n c o ^ _ . _ . _ l O O t n e n O t n m o e n e n O i o o o o e n o P ^ o o r o o o o e n o c n h 4r ^ en C O -NJ o o o 0 » i - rco r o i - k » - i o - P r o ' c j - P K > co i-^ o i - r o r o e n e n a > f O ^ - > ] J ^ e n < > i D r o o . ^ o ^ o j r o i D C o e n # « n / « . - » / - » Q C ) y i ( j i o c n o e / i o e n o o o e n c n O ' » o e n o o o o o o en en en o to en o o 00 I o o o o en ••9 M O (O M ^ rt. G O t-i < 5 I-' ta ^ to '•a I? to to | «b w I- a & "> :fl to -J u > I I I I «^ .p I to a: I 9 '-' P ID M ~1 n : ^ ID C-i 1 1 ^ UD IO jto to i I I i s E? 'a t?a t^ §g Cq C« ^ tri Cq Co Ci 'J 00 t a i Co C M ! Co TABLE 6 ESTIMATED WORLDWIDE SHIPMENTS OF 12-BIT MICROPROCESSORS (THOUSANDS OF UNITS) CmPANY HARRIS ISTERSIL TOTAL MICROPROCESSORS PRODUCTS 6100 6100 1^78 TOTAL 22 15 1ST QTR 7 4 2Nb QTR 7 4 3RD QTR 7 5 4ra QTR 7 5 1979 TOTAL 28 18 — 1 9 8 0 - — 1ST 2m QTR QTR 8 9 5 5 37 11 11 12 12 46 13 14 PERCENT CHANGE FRCM PREVIOUS QUARTER 0.0 0.0 9.1 0.0 8.3 7.7 SOURCE: DATAQUEST. INC. OCTOBER. 1980 TABLE 7 ESTIMATED WORLDWIDE SHIPMENTS OF 16-BIT MICROPROCESSORS (THOUSANDS OF UNITS) - .
' COMPANl AMD AMI GENERAL INSTRUMENT INTEL MOTOROLA NATIONAL NEC TEXAS INSTRUMENTS ZILOG PRODUCTS Z8000 9900 cP-1600 8086 68000 PACE 768 TMS 9900/9980 TMS 9940 Z8000 1978 TOTAL 0 0 60 24 0 86 0 185 0 0 152" QTR 0 0 15 13 0 25 0 68 0 0 2ND QTR 0 0 20 15 0 25 0 80 0 1 3RD QTR 0 S 20 19 S 25 0 92 0 2 47 gTi? S 5 25 25 3 25 S 105 5 4 1979 TOTAL S 5 80 72 3 100 S 345 5 7 — 1 9 8 0 — 1ST 2ND QTR 1 5 30 32 4 22 5 120 10 7 QTR 1 5 40 60 5 18 S 140 15 5 TOTAL MICROPROCESSORS 355 121 141 158 197 617 231 289 PERCENT CHANGE FROM PREVIOUS QUARTER 14.2 16.5 12.1 24.7 17.3 25.1 SOURCE: DATAQUEST. INC. OCTOBER. 1980 -11-Figure 2 ESTIMATED WORLDWIDE SHIPMENTS OF MULTISOURCED MICROPROCESSORS I I I f 2.5-2.0-1.5-0 8048 ^ ^ - - ^ ^ ' ' ' Family / / >6500 6800,6802, eeoaX ^^Z-80 F.--—3870 Family 1st Qtr 1979 2nd Qtr 1979 3rd Qtr 1979 4th Qtr 1979 .^8085 •8080A F8 1st Qtr 2nd Qtr 1980 1980 Source: DATAQUEST, Inc. - 1 2 -^^^^^^^^^^m ^ ^ ^ ^ ^ ^ ^ ^ I i ^ ^ ? i ^ M ^ ^ i ^ ^ ^ — ^ ^ ^ ^ ^ » ^ ^ ^ — ^ ^ ^^S^S ^K ^S ^S ^K^^E ^S ^S ^E ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ K ^ ^ ^ H k i ^ ^ ^ ^ " ^ ^ K ^ ^ ^ ^ ^ ^ ^ v ^ ^ ^ ^ ^ ^ ^ ^ ^ v ^ ^ ^ ^ ^ ^ ^ r ^ ^ ^ ^ ^ ^ A Subsfcdiarv ot A.C. Nielsen Co, » ^ 1 s =^ s r4^£^3^£ A n k r^^rfii ^^—^'^^ ^^^^ s S ^^ ^^" ^^^^ I N C O R P O R A T E D I M E \ A / a L . E 1 1 B H SIS Code: Vol. I, 2.8.6 CORRECTIONS TO NEWSLETTER "DYNAMIC AND STATIC MOS RAM AND EPROM SHIPMENTS" SUMMARY This brief newsletter corrects two errors that appeared in the DATAQUEST Semiconductor Industry Service Newsletter dated September 19, 1980. Dynamic MPS RAMs 32K RAMs The newsletter indicated that Mostek shipped an estimated 200,000 units in the second quarter of 1980 at prices in the range of $8.00 to $10.00. The correct price was in excess of $15.00. MOS EPROMs 64K EPROMs The newsletter indicated that Texas Instruments was the sole supplier of 64K EPROMs in the second quarter. The correct statement is that Motorola and Texas Instruments were the only suppliers sampling the 64K EPROM in the second quarter of 1980. Motorola and Texas Instruments shipped an estimated 1,000 and 3,000 units respectively in the second quarter. Daniel L. Klesken Copyright © 10 October 1980 by DATAQUEST - Reproduction Prohibited The content of tliis report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness It does not contain material provided to us in confidence by our clients This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities, This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 /TWX (910) 338-7695 / DATAQUEST CPTO ^ ^ 1^^-.. ..J^^ = -— - — = = ECT RESEARCH A Subsidiary QtA.C. Nielsen Co."" ^ IMCORPORATED i \ I ^ Z W ^ D I V I S I 1 C S H h SIS Code: Vol. I, 2.1 APPENDIX B MARKET SHARE ESTIMATES DATAQUEST's Semiconductor Industry Service has recently completed the final version of Appendix B - Market Share Estimates, which can be found in Volume III of the SIS notebooks. This 32-page Appendix update analyzes semiconductor markets through estimation of market share by manufacturer. Please see the SIS notebook holder in your location for more details. Appendix B follows all semiconductor product segments chronologically and divides the merchant semiconductor market among 50 U.S. companies, 7 European companies, 8 Japanese companies, and Rest-of-World (ROW) companies. Worldwide Semiconductor Market Share Estimates Worldwide semiconductor market share estimates segmented by geographical region, are shown in Figure 1 for the years 1974 through 1979. The worldwide semiconductor market grew at a compound annual rate of 15.5 percent between 1974 and 1979. Semiconductor shipments by U.S.-based companies, which grew at 15.4 percent, were very close to the industry growth rate, while Japanese company Shipments grew faster (19.8 percent) and European company shipments grew more slowly (10.4 percent). The U.S. companies' percent of market has remained at approximately 62 percent of total factory shipments between 1974 and 1979 while the Japanese Shipments have grown from 21 percent in 1974 to 25 percent in 1979. European factory shipments have decreased from 16 percent of total factory shipments in 1974 to 13 percent in 1979. Estimates of total semiconductor revenues for over 65 merchant market semiconductor suppliers can be found in Appendix B for the years 1974 through 1979. Included are U.S companies, as well as European, Japanese, and Rest-of-World companies. The growth rates for specific companies can be calculated from the data presented and compared against one another, against industry averages, or against regional factory shipments' growth. The totals given for U.S. companies reflect worldwide production. For example, Texas Instruments manufactures semiconductors in many parts of the world; however, its entire production is included under the U.S. companies' market share section. In contrast, foreign-owned subsidiaries such as FMC, Litronix, and Signetics, are included in the U.S. total market, not in the total of the parent company location. This inconsistency occurs because most foreign-owned subsidiaries in the United States maintain their own identity and do not always carry the name of their parent company. Copyright © 3 October 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients. This information is not furnished in connection with a sate or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent andfor their officers, stockholders, or members of their families may, from time to time, have a long or short position m the securities mentioned and may sell or buy such securities 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO 12 H 10 H 8H I o 1 4H Figure 1 TOTAL SEMICONDUCTOR MARKET SHARE ESTIMATES w,. -T—t—r—? %t-:-:-:-European Japanese U.S. Companies Companies Companies ROW 2H + + •f + -^ I - + + + + + + + • + H • : • : • + + + -1 + + • + ^ " • + + + + ^ !• + + • + + + +1 1 ^ + + -+ + + + + + + ^ + + 4. • + + + + + + •• + + + H + + + + + J I + + J 1 i •:•] • + + + + + + V <i 1974 1975 1976 1977 1978 1979 Source: DATAQUEST, Inc. - 2 -Worldwide Integrated Qrcuit Market Share Estimates Figure 2 presents the DATAQUEST estimates of worldwide integrated circuit market shares segmented by geographical region for the years 1974 through 1979. The compound annual growth rate for total integrated circuit shipments between 1974 and 197 9 was 23 percent. During this period, U.S. factory shipments grew only 21 percent while European and Japanese shipments grew 24 percent and 34 percent respectively. IC shipments by U.S. companies represented 75 percent of the total integrated shipments in 1974, and 68 percent of the total in 197 9. IC shipments by European companies represented 8.5 percent of total IC shipments in both 1974 and 1979 while Japanese companies increased their percent of total IC factory shipments from 15 percent in 1974, to 23 percent of the total in 197 9. The Rest-of-World companies representing the remaining percent of total IC factory shipments decreased from just above one percent in 1 974 to just below one percent in 1 97 9. Appendix B presents the integrated circuit market share estimates for over 50 U.S., European, and Japanese companies, as well as breaking the IC market down into Bipolar Digital, MOS, and Linear market shares. Bipolar Digital is further segmented in TTL, DTL, E CL, and Other. Worldwide Discrete/Optoelectronic Market Share Estimates Figure 3 presents DATAQUEST's estimates of the worldwide discrete plus optoelectronics market share estimates for 1974 through 197 9 by geographical region. Unlike Appendix B which presents discrete devices and optoelectronic devices separately, Figure 3 includes optoelectronic revenues with discrete revenues. This combined product segment has experienced a compound annual growth of 6.6 percent between 1974 and 197 9. U.S. companies experienced similar growth with factory shipments growing at 6.4 percent. Between 1974 and 197 9, European discrete shipments only grew 4.7 percent per year, while Japanese Shipments' growth outperformed the industry at an 8.5 percent rate. The U.S. companies' discrete market share remained constant at 51 percent of total discrete factory shipments. European companies' market share during these years declined from 23 percent to 21 percent. The Japanese companies estimated market share increased from 26 percent of the total discrete-plus-opto shipments in 1 974, to 28 percent of the total in 1 979. The discrete market share tables of Appendix B provide market share estimates for over 30 U.S., European, and Japanese companies. The discrete market is segmented into Transistor, Diode, Thyristor, and Other. The diode market is further segmented into Small Signal, Power, and Zener Diodes, while transistors are segmented into Small Signal and Power Devices. The optoelectronics market is segmented into LED Lamps, LED Displays, Optical Cbuplers, and Other. Value of Appendix B Market Share Estimates Semiconductor Suppliers Appendix B is a valuable asset to semiconductor suppliers as it enables semiconductor manufacturers to assess their activity and potential in a particular - 3 -Figure 2 TOTAL INTEGRATED CIRCUIT MARKET SHARE ESTIMATES 1H 8H Is, » c o 4^ 2 H ^ + + -1 . . ^ ^ ^ ^ ^ ^ H European Japanese U.S. Companies Companies Companies .. '/////////l W///M + + + + + r nl + + + + + + 4 + + + + + + + n ^ -»- + + + + + 4 4 + + 4 + + 4 + 4 ^ + + + -^ 4- 4 + + + + 1 mw/ » • + + + 4 + + •» f + -K t- + •• + + + + + + (• + + + + f + -r- + + + + •• < • • • • + 4-1 y/}>}y//y 'wm, t + • + + + -^ 4- 'f P - + + + + 4' + h 4- + + t + + • » -K + 4 + 4 + - 1 - + + + + + + + t + + « ^ ^ .. •1' •1' + + 1 1 1 - + + t' + + • • + + + + + + + i • + + • + -t + + -• + • + + t' f + + + + + + + + + + + + + + f • f ^ '9/ + + + + + + + < + + + + + + + H + + + + + + H + + • + + + + 1 + + + + + + + + + + + + + + H -- + + + + + + 4 + + + + + 4 - 4 - 4 + 4- 4- 4-+ • 4- 4 + 4- 4- + + + 4- ^ + 4- 4- • 4- 4- 4- 4 4- 4 > 4-+ 4. 4- ^ + 4- 4. 4-+ + 4- + : • : • : • : • : - ; - : : : : : : ; > ^P MA •t -t + + 1 - + + 4-+ + 4 - + 1 - + 4- f - + 4- + 1 - 4- 4- 4- 4 ^ + + 4--4r -1- • + • 4- + 4-1- 4- + f 4. + . + + 1 - 4- 4- 4. + 4' 4 1- + 4- • 4- + 4- 1 - + 4- + + + + t' + + + + + 4 f- 4- 4- 4-+ + 4 • + 4- 4-+ +• + 4 + 4- + 4- 4 1. 4- 4- • 4' + + • < • • 4-4- + + 4 (• 4- 4- 4-1- + 4- H t + •• 4- 4- 4- 4 + + 4-+ + • • 4- 4- 4- 4-1 1974 1975 1976 1977 1978 1979 Source: DATAQUEST, Inc. Figure 3 TOTAL DISCRETEIOPTOELECTRONiC MARKET SHARE ESTIMATES 4 ^ -o a " S (ft s = 2 S 1 -European Japanese U.S. Companies Companies Companies 4. + + • t -4 . + + ^^^^T^^^m + H ( • 4 . + 4 + + 1974 1975 1976 W^^^^^^^ + + + • + + 4 + -k 1977 1978 1979 Source: DATAQUEST, Inc. - 5 -market segment by looking at their market share compared to that of their competitors; what other product areas their competitors are involved in; the scope of their competitors' activities; and the feasibility of entering foreign markets, based on the number and sizes of the competitors in those markets. Semiconductor Users Semiconductor users find Appendix B useful in identifying the suppliers wittiin a given product segment as well as in ranking their relative size, it is important for users to understand how their suppliers rank in the market, as well as against one another. Large users also can determine the fraction of their vendor's output they are consuming. Equipment Suppliers Equipment suppliers serving the semiconductor industry find Appendix B is a valuable reference. Since semiconductor markets are highly specific with respect to equipment, it is beneficial to know exactly to what degree their customers are involved in a particular market. It also provides a list of potential buyers for a given type of equipment associated with product segments. The growth of a given market indicates the need for new manufacturing equipment. In addition, the more rapidly growing companies tend to purchase more equipment in relation to sales than the more slowly growing companies. Material Suppliers Material suppliers find Appendix B useful for referencing semiconductor revenues of the semiconductor manufacturers in a particular market, applying the appropriate industry standard A/S ratio (sq. in. silleon/saies dollar), and determining the subsequent square inches of silicon consumed by a company. Many other materials suppliers develop similar ratios for materials such as chemicals, gases, photoresist, masks, and indirect materials. Since Appendix B shows historic semiconductor revenues by market, trends can then be observed. Appendix B also provides names of potential customers in new geographical markets. Electronic Distributors Electronic distributors use Appendix B to determine the relative market position of their principals in each market. By observing the overall growth of semiconductor shipments, the semiconductor distributors can also determine their potential market shares. Appendix B also provides insight into alternate vendors and potential geographical markets. Mary Ellen Hrouda I I . 1 ^ ^ i RESEARC - ' . A Subsidiary of A.C.r^icbetn Co. ^ INCORPORATED I ^ I ^ S w V ^ S ^ B ^ M SIS Code: Vol. 1, 2.1 MARKET ESTIMATES - APPENDIX A SUMMARY Estimates of semiconductor consumption for 1975 through 1984 and estimates of semiconductor factory shipments for 1970 through 1979, both worldwide and by major geographical segment, were published and mailed to all notebook holders by the DATAQUEST Semiconductor Industry Service on September 8, 1980, in Appendix A - Market Estimate Worksheets. The estimates are segmented into three major categories: integrated circuits, discrete devices, and optoelectronic devices; and each category is then further subdivided. CONSUMPTION Worldwide semiconductor consumption, as shown in Table 1 and Figure 1, was estimated at $11,116 miUion for 1979 and is forecast to reach $25,926 million by 1984; a compound annual growth rate of 18.4 percent. MOS integrated circuits are the fastest-growing segment of the industry. Worldwide consumption of MOS integrated circuits was estimated at $3,430 million in 1979 and is forecast to achieve a compound annual growth rate of 26.4 percent, reaching $11,084 niillion in 1984. Integrated circuits are estimated to have been 64.1 percent of total semiconductor consumption in 1971 and to be more than 75 percent of the total in 1984. Estimates for North America, Europe, and Rest of World are made directly in dollars, but estimates for Japan are first calculated in yen and then converted to dollars at the prevailing rate for each year. Because wide fluctuations in the yen/dollar exchange rate tend to distort the growth rate of the Japanese market, Japanese factory shipments and consumption estimates are expressed in dollars and also given in separate tables in Appendix A in yen. Historical estimates are given in current dollars for each year but forecasts are given in constant 1979 dollars using 1979 exchange rates. Copyright © 29 September 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients This information is not furnished in connection with a sale or offer to sell securities or in connection vuith the solicitation of an offer TO buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO Table 1 ESTIMATED WORLDWIDE SEMICONDUCTOR CONSUMPTION BY DEVICE TYPE (Millions of Dollars) Bipolar Digital MOS Linear Integrated Circuits Discrete Devices Optoelectronic Devices Total ^Compound Annual Growth 1979 $ 1,799 3,430 1,897 $ 7,126 3,395 595 $11,116 1984 $ 4,353 11,084 4.019 $19,456 4,923 1.547 $25,926 CAG^ 1979-1984 19.3% 26.4% 16.2% 22.3% 7.7% 21.1% 18.5% Source: DATAQUEST, Inc. August 1980 FACTORY SHIPMENTS Worldwide semiconductor factory shipments were estimated at $4,373 million in 1975, increasing to $11,116 million in 1979. The United States is the major producer of integrated circuits (ICs). In 1975 U.S. 10 production accounted for 48.0 percent of all ICs, and in 1979, the U.S. IC shipments total was estimated at $5,308 million, or 47.8 percent of worldwide factory shipments. Factory shipments segmented by geographical region are shown in Table 2. Figure 2 shows factory shipments by device type and major geographical segment for 1975 and 1979. -2-.«»^.. Table 2 ESTIMATED WORLDWIDE SEMICONDUCTOR FACTORY SHIPMENTS (Millions of Dollars) 1975 North America Japan Europe Rest of World World Total $2 1 ,119 925 ,209 120 $4,373 1979 $ 5,308 • 2,878 2,542 388 $11,116 CAG^ 1975-1979 20.2% 25.5% 16.0% 26.5% 20.5% ICompound Annual Growth Source: DATAQUEST, I n c . August 1980 USES OF APPENDIX A The data in Appendix A can be used in a variety of ways by those involved in different areas of the semiconductor industry. Equipment and materials manufacturers can use the forecasts in projecting the semiconductor industry's needs for materials and equipment over the next few years. Semiconductor manufacturers can use the information as a basis for production decisions, while users of semiconductors can use it to understand the expected growth rate of various product categories as well as ASP trends. Table A-11 gives a forecast of worldwide semiconductor consumption in units. Comparing the units estimate in Table A-11 with the worldwide revenues estimate in Table A-6 will show average selling price (ASP) trends. Jean Page Figure 1 ESTIMATED SEMICONDUCTOR CONSUMPTION BY DEVICE TYPE (Millions of Dollars) Optoelectronic 1,547 Optoelectronic 595 1979 Total $11,116 1984 Total $25,926 ESTIMATED SEMICONDUCTOR CONSUMPTION BY GEOGRAPHICAL REGION (Millions of Dollars) 1979 Total $11,116 1984 TotaI $25,926 Source: DATAQUEST. Inc. - 4 -Figure 2 ESTIMATED SEMICONDUCTOR FACTORY SHIPMENTS BY DEVICE TYPE (Millions of Dollars) 1975 Total $4,373 1979 Total $11,116 ESTIMATED SEMICONDUCTOR FACTORY SHIPMENTS BY GEOGRAPHICAL REGION (Millions of Dollars) 1975 Total $4,373 1979 ^°^' $11,116 Source: DATAQUEST, Inc. -5-s = ^^^ pr f \ y SECURITIES INC. ' ! • i^n^KFil I f f 1 Jr% 1 ^^Jkl^J ^E 1 1 EK VoL II - No. 8 September 22, 1980 This letter is a condensation of recent Research Newsletters and internal thinking from the industry research groups at DATAQUEST, Inc. Requests for amplification of our thoughts or for specific Newsletters should be directed to the author. A list of recent DATAQUEST Newsletters appears at the end of this letter. SMALL COMPUTERS Data General's recent announcement of a slowdown in orders that should cause sequential hardware shipments to be flat in the September and December quarters is the second disappointment in fundamentals in the last fifteen months and brings up several pertinent questions that need to be answered. Is the slowing in orders presently being experienced a company problem or the beginnings of an industry slowdown? Is the minicomputer market moving away from areas of Data General's strength? What are the near-term and long-term implications of the slowdown in growth being experienced? In general, we believe that Data General's difficulties are basically company — not industry — related, being heavily a function of relatively poor product positioning within areas of strength and weakness in the minicomputer industry. Two somewhat simplistic statements can be made about the minicomputer industry at present: first, companies with strong 32-bit product positions are doing better than companies that are heavily concentrated in 16-bit computers; second, companies with Strong end-user orientation are doing better than companies with strong OEM orientation. Data General has very high (at least 65 percent) exposure to the OEM market and has not yet shipped its first 32-bit computer; in our opinion, this explains to a great extent why the company is not growing as fast as the industry at present. AS we have previously stated, we believe that Data General's entry into the 32-bit marketplace, the MV-8000, is a very well-designed machine offering very easy software upgrades for existing Data General 16-bit users. Initial shipments of the 8000 will not be made until October and volume shipments are not expected before February or March. Data General has always been a fast delivery company, and its customers are not used to long lead times. In cur opinion, if Data General can meet its initial shipment schedules and experience no meaningful problems with initial installations (and these are two significant ifs), then we believe that MV-8000 orders will start to accelerate during the March quarter, when customers could reasonably order the machine in some quantity and receive delivery in three or four months. V V e also expect a general economic recovery in 1981 and believe that the OEM sector of Data General's business could start improving early next year. Copyright © 25 September 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or compteteness It does not contain material provided to us in confidence by our clients This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. Member, New York Stock Exchange 19055 Pruneridge Avenue / Cupertino, California 95014 / (408) 725-1200 Under the relatively positive scenario outlined above, total company orders could Start improving in the second quarter of fiscal 1981 and accelerate in the second half. Even in this case, earnings progress next year would be unexciting. We now project a 15 percent gain in earnings in fiscal 1981 (from $5.25 per share to $6.00 per share compared to our previous forecasts of $5.50 per share and $6.75 per share respectively), but almost all of the gain will come in the fourth quarter. If our scenario in terms of fundamental demand at Data General plays out, however, the groundwork would be laid for earnings gains well in excess of 30 percent in fiscal 1982, as year-to-year sales gains accelerate and margins improve. Awareness of this opportunity for earnings acceleration would certainly begin if orders started improving early in calendar 1981. A few cautionary notes. First, if we are wrong and the minicomputer industry is in the beginning stages of a general decline, then the recovery at Data General would be postponed. Second, as noted above, the company will be beginning shipments of a major new product very soon and the opportunities for problems in terms of initial product performance, software, or delivery are very real. These shortcomings would also serve to delay an acceleration in orders. Finally, and most importantly, is the question of long-term product positioning at Data General. The major growth opportunities in the small computer market are increasingly moving towards commercial applications, which carry with them the need for strong software and service support. Data General has recognized this trend and made some dramatic moves to improve the level of its support personnel, but in the last year, it has apparently retrenched on this effort somewhat in the effort to maintain margins. It is vitally important over the next year for Data General not to sacrifice the long term in exchange for short-term improvement in profit margins. In summary, then, in contrast to a year ago, the company was early in recognizing the extent of its problems and very forthright in discussing them. The near-term outlook is unexciting, but probably discounted in the stock. The intermediate term offers the opportunity of major increases in earnings if industry conditions hold and Data General's new product introductions proceed on schedule. The long-term challenge of diversifying into the more lucrative growth sectors of the small computer market remains. INSTRUMENTATION First quarter results at Tektronix were a bit of a shocker as incoming orders, revenues, and earnings per share were all well below expectations. A bit of analysis and a re-evaluation of the company's present positioning seems in order. The earnings shortfall was entirely a function of sales being about $10 million dollars below budget. The shortfall in sales was a real surprise to us at first, as the company's backlogs are swollen and would seemingly allow the company to meet its shipment forecasts irrespective of order trends. After a bit of checking, it appears that there were some internal problems in terms of metal parts fabrication that prevented the company from shipping everything it wanted to ship. The problem is not serious and should be corrected in the second quarter. However, one must note - 2 -that Tektronix has had a recurrence of seemingly unrelated production difficulties over the past 18 months, which is very surprising since this is a basically well managed company that is highly vertically integrated, and which has not uridertaken any major production changes that would explain its difficulties. Orders in the first quarter were down 11 percent (down 3.5 percent if one adjusts for the extra week in last year's first quarter) versus our expectation of about flat comparisons. The slowdown was fairly widespread throughout Tektronix, encompassing orders for graphic terminals from its Information Display Division (IDD) as well as test and measurement instrument demand. The drop-off in weekly order receipts was alarming, but we are somewhat encouraged by the fact that orders have apparently improved somewhat thus far in the second quarter. The slowing in instrumentation orders by Tektronix is indicative of trends that we believe are fairly widespread throughout the industry. It is our belief that industry and company instrument orders will remain soft through the end of this calendar year and then begin to improve early in calendar 1981. Graphic terminal-products, while experiencing somewhat stronger demand than that for instrumentation, need to be watched more closely. The softest part of IDD's business is its OEM sector and this in part reflects the evolution towards in-house production of raster scan displays by its CAD/CAM customers (an important component of total OEM business) instead of purchasing Tektronix storage tubes. This trend has long been expected, but Tektronix's difficulty in delivering tubes during fiscal 1980 has probably accelerated the trend somewhat. It has been our view that Tektronix can still sustain relatively good growth in its IDD business even allowing for reduced penetration of the CAD/CAM market. It is also true that its OEM sales have historically been somewhat cyclically sensitive. It will be vitally important for lektronix to demonstrate renewed growth in its Information Display Division as we move into 1981. We have dropped our earnings estimates for the May 1981 fiscal year to $4.85 per share from our most recent $5.60 per share estimate. If orders accelerate during the second half or if the company chooses to eat more heavily into its backlogs, our estimate may prove conservative. The funaamentals at Tektronix still look positive to us, but part of our positive thesis was strong earnings comparisons in fiscal 1981 and 1982 and there has clearly been some loss of momentum in this regard. In our opinion, the key investment development over the balance of this fiscal year will be the pace of new orders in its Information Display Division. WORD PROCESSING AS noted in previous Portfolio Letters, IBM's latest entry into the stand-alone word processing market, the Displaywriter, is not quite as inexpensive as it appears at first glance and is lacking in software support. It has already had the impact, however, of forcing competitive prices somewhat lower in the stand-alone market as well as offering a real long-term threat if the Displaywriter can be successfully integrated with a wide range of IBM computer systems. - 3 We believe that industry leader Wang Laboratories is readying a very effective response to the Displaywriter. We expect introduction of its newest stand-alone word processor, the WP 4 before the end of this calendar year, possibly as early as October. We would expect a retail price of $6,000-$?,800 compared with $7,800 for the IBM Displaywriter. Our information to date indicates that the Wang product will have two advantages over IBM: first, the Wang price will include software, while the IBM user must pay a separate license fee for all software; second, we expect the Wang daisy wheel printer to be 40 percent faster than the IBM printer. We do not expect the WP 4 to be a major revenue generator for Wang. The company derives only about five percent of its total revenues from the stand-alone word processor market and simply does not have enough sales and support people to market a stand-alone product widely to low volume customers. Rather, we expect the WP 4 to be sold in larger numbers to existing Wang customers and to other buyers who can use the product as an entry level means of upgrading into larger Wang systems. The real benefit to Wang will be that it should effectively keep IBM out of existing Wang accounts. We also expect this product to exert further downward pressure on stand-alone word processor prices generally, particularly if pricing comes in at the low end of our forecast. SEMICONDUCTORS While information in September is still very sketchy, there are some signs from a few of the major suppliers that business has improved from August levels. In part, this reflects normal seasonal patterns, but it is also a sign that inventory cutbacks and order deferrals by customers may have run their course. Industry bookings in August were relatively soft, but it is our understanding that all of the major companies made their booking goals for the month. We have been expecting an upturn to occur in the September-October period and these initial signs appear to be a confirmation of our forecast. Continuation of this trend would mean that the industry has weathered the recession extremely well and that it is poised for a resumption of substantial growth in 1981. The slowdown in hardware orders recently disclosed by Data General is a source of some concern, especially considering that Hewlett-Packard's computer orders are also relatively soft. It is very important for semiconductor demand from the computer industry to remain strong this fall. At this point, it is our view that the softening experienced by both of these companies is not an indication of industry trends, which we expect to remain reasonably strong. In MOS memory, a large number of returns are being experienced and there is also widely fluctuating month-to-month device requirements. Both are signs of market weakness. DATAQUEST projects consumption of 180 million 16K RAMS in 1980 versus 70 million parts last year. Our preliminary forecast for 1981 is for consumption of 260 million parts. This would leave an excess supply next year, so some pricing pressure on this product should continue into 1981. We should note, however, that we have detected some flattening in prices on 16K RAMS as the 1981 contract negotiations get underway. As prices come down, wafer allocations will increasingly shift toward the 64K RAM and other products. Bipolar prices have started to come down in some instances, but not nearly as dramatically as MOS prices. Prices have actually moved somewhat higher in the low end of the bipolar market, driven by higher packaging costs. Bipolar memory prices are still very strong and should stay that way for at least another nine months, driven by strong demand from General Motors. A clearer view of industry trends for the balance of 1980 may not be obtainable before early October, but initial signs are favorable. PAPER AND FOREST PRODUCTS We have previously noted that there was evidence of considerable cancellations and delays in new paper machines scheduled for the 1983-1985 time frame. We have now identified at least six machines, all with capacity of at least 150,000 tons per year, which have been either indefinitely delayed or cancelled. When the American Paper Institute capacity numbers for 1981-1983 are published in December of this year, we believe that they will show significantly less capacity additions during the last year of the survey than had been generally anticipated. We have always believed that brown paper (linerboard, etc.) was facing potential industry shortages beginning in the 1982 time span and recent cancellations could extend that period of tight industry supply. The postponements and cancellations have also allayed our fear of over capacity in white paper beginning in 1983. It still appears a bit early to get excited about the paper group in general, particularly with the degree of economic recovery in 1981 highly uncertain. However, a very favorable long-term supply demand picture is now in the process of being established. The forest products stocks have generally underperformed the market during the last six weeks or so. In good part, this is a function of the upturn in long-term interest rates. While acknowledging that the housing recovery next year may have been seriously impaired, we nevertheless think that the risk/reward for the forest products group looks very interesting here, particularly relative to the rest of the market. If indeed long-term interest rates maintain their upward trend, there will be a relatively unexciting housing picture next year. In this scenario, however, we would seriously question the degree of overall economic recovery next year. For example, there are sectors of the technology industry (OEM business, for example) that are very sensitive to prolonged levels of high interest rates. Conversely, as pointed out in our last letter, we believe that there are strong driving forces towards higher plywood and lumber prices even if housing starts reach only 1.5 million in 1981. In a 1.5 million start year, for example, we believe that the major integrated forest product companies could, as a group, have near record earnings in 1981 and major gains in earnings in 1982. There seems to be a lot of fundamental upside potential for these companies in a positive industry environment and the possibility of more adverse conditions is starting to be discounted by lackluster stock performance relative to the overall market. Michael R. Weisberg - 5 -RECENT NEWSLETTERS OF NOTE SMALL COMPUTERS A Review of 3270 Emulator Packages Tandy Announces Three New Personal Computers Burroughs Announces Long^Awaited B 900 Series 08/13/80 08/06/80 08/02/80 INSTRUMENTS Logic Analyzers Continue to be One of the Fastest-Growing Segments in the Test Instrument Market Oscilloscope Market 08/29/80 07/30/80 WORD PROCESSING Olivetti Update Xerox Lowers Price of 850 Display Typewriter Wang Laboratories Update Syntrex Announces Office Automation Products The European Market for Word Processing Workstations 08/27/80 08/22/80 08/22/80 07/25/80 07/11/80 SEMICONDUCTOR Manufacturing Model PAPER AND FOREST PRODUCTS Final Second Quarter Douglas-Fir Stumpage Bids Show Very Sharp Price Decline 08/28/80 08/11/80 CAPITAL EQUIPMENT Caterpillar Tractor Company Second-Quarter Results and Outlook for 1980 and 1981 08/12/80 COPYING & DUPLICATING AM Multigraphics to Consolidate United Kingdom/ United States Duplicator Manufacturing 08/15/80 TELECOMMUNICATIONS TV Services Forecast to Continue as Largest Factor in Worldwide Broadcast Markets World's Installed Telephones Estimated to be Nearly 600 Million in 1985 08/07/80 08/07/80 ELECTRONIC PRINTERS Overview of the North American Market for Electronic Printers 08/11/80 SIS Code: Vol. I, 2.8.6 DYNAMIC AN D STATIC MOS RAJVl AND EPROM SHIPMENTS SUMMARY In the second quarter of 1980 the worldwide supply of 16K dynamic RAMs caught up with and exceeded worldwide demand. Worldwide shipments of 16K dynamic RAMs in the second quarter of 1980 were an estimated 47.6 million units, an increase of about 28 percent over the estimated 37.3 million units shipped in the first quarter of 1980. The industrywide average selling price (ASP) for the second quarter was about $4.75, whereas in the third quarter the industrywide ASP is estimated at $4.00. These prices include both contract prices and spot market prices. Worldwide shipments of 64K dynamic RAMs are still growing slowly as the product is still in the sampling mode. We estimate that 68,000 units were shipped in the second quarter of 1980 with prices in the $60 to $100 range. The 4K dynamic RAM market continues to decline. An estimated 7.1 million units were shipped in the second quarter of 1980 a decrease of about 39 percent from the first quarter. Large quantity prices still remain about $2.00. The markets for the 2147 fast 4K NMOS static RAM softened in the second quarter of 1980, and shipments were up only 10 percent to an estimated 2.0 million units. The market for slow 4K static RAMs also softened in the second quarter and Shipments increased only three percent to an estimated 12.6 million units. Prices softened further to about $2.50 in the third quarter. Several companies sampled the 16K NMOS Static RAM in the second quarter. Shipments of 4K CMOS static RAMs continued to climb to an estimated 2.8 million units in the second quarter, up about 15 percent over estimated first quarter Shipments. Prices softened on this product with about a 25 percent decline in the second quarter. The first of the 16K CMOS static RAMs were sampled in the second quarter of 1980. Second quarter shipments of 8K EPROMs were an estimated 4.4 million units, down about four percent from estimated first quarter shipments. Worldwide shipments of the 16K EPROM increased about 22 percent to an estimated 6.5 million units in the second quarter of 1980. Prices on this device have plummeted drastically in the last two quarters, however, and are now being quoted as low as $6.00. Worldwide shipments of the 32K EPROM increased in the second quarter to an estimated 711,000 units, up about 122 percent. Limited samples of the 64K EPROM were also shipped in the second quarter of 1980. Copyright© 19 September 1980 by DATAQUEST- Reproduction Prohibited The content of this report represents our interpretation and analysis of informaiion generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness It does not contain material provided to us in confidence by our clients. This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to j buy securities^ This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO Dynamic MOS RAMs I6K RAMs Table 1 presents DATAQUEST's estimates of worldwide shipments of 16K dynamic MOS RAMs. In the second quarter of 1980 worldwide shipments were an estimated 47.6 million units, up about 28 percent over an estimated 37.3 million units shipped in the first quarter of 1980. These estimates include the two-chip hybrids shipped to IBM. IXiring the second quarter of 1980, the supply of 16K dynamic RAMs exceeded demand by a substantial amount. This is the first time that supply has exceeded demand since the product was introduced in 1977. As a result of the excess supply, prices dropped significantly in the second quarter and continued to fall in the third quarter of 1980. During the second quarter of 1980 the industrywide average selling price for 16K RAMs was close to $4.75 and in the third quarter, we estimate that it declined to about $4.00. This industrywide ASP reflects contract pricing as well as aggressive spot market pricing. For example, in the third quarter spot market prices for 16K RAMs were in the range of $2.25 to $3.00. Of course, these are not qualified parts and there is no guarantee of future availability. They do serve the need for some users, but the majority of EDP users must use fully qualified devices, and they were paying a third quarter price in the $3.80 to $4.20 range. The 16K RAM is available off-the-shelf from all suppliers as well as through distribution. IDespite the current excess supply, it appears that prices are beginning to Stabilize as major users are entering their 1981 contract negotiations with the suppliers. 32K RAMs Mostek continues to be the only merchant market producer of a 32K dynamic RAM hybrid device. It shipped an estimated 200,000 units in the second quarter of 1980 at prices in the range of $8.00 to $10.00. 64K RAMs Table 2 presents DATAQUEST's estimates of worldwide shipments of 64K dynamic MOS RAMs. As indicated in that table, seven companies are sampling or shipping limited quantities of the devices. In the second quarter of 1980, an estimated 68,000 units were shipped, up about 224 percent over estimated shipments in the first quarter. The 64K dynamic RAM market is essentially still in a sampling mode. Only Fujitsu, Hitachi, and Motorola are shipping significant quantities of the device at this time, but by year end, several additional suppliers are expected to enter the market. Prices of the 64K dynamic RAMs in the second quarter of 1980 were in the $60 to $100 range in the small quantities being shipped. However, these prices are expected to fall rapidly over tlie next two quarters as more suppliers enter the market. - 2 -4K RAMs Table 3 shows the 4K dynamic MOS RAM market continuing to decline in the second quarter of 1980. Demand for this device is definitely on the decline as most users are now using the 16K dynamic RAM and are beginning to design in the 64K dynamic RAM. Only the older existing product designs that are still in production are using the 4K dynamic RAM. Although 12 suppliers shipped this product in the second quarter of 1980, only five or six are still actively taking orders for new business. The rest are filling orders currently on the books but are not taking any new orders. Worldwide shipments in the second quarter were an estimated 7.1 million units, down about 39 percent from the first quarter. Average selling prices for this device are about $2.00, with ASPs for the plastic devices in the $1.80 to $2.00 range, and ASPs for the CERDIP devices in the $2.25 to $2.50 range. Lead times for this device are generally less than four weeks, but there is no excess inventory or capacity as this product is being phased out by most producers. NMOS Static RAMs 4K RAMs Table 4 presents DATAQUEST's estimates of worldwide shipments of the fast 4K NMOS Static RAMs. This market softened in the second quarter and worldwide shipments were up only 10 percent to an estimated 2.0 million units. Prices continued to decline and were about $8.00 during the second quarter; in the third quarter, prices were in the $5.50 to $6.00 range for plastic devices, and in the $6.25 to $6.75 range for CERDIP devices. About 80 percent of the devices are shipped in CERDIP packages because of hermeticity requirements on this high-speed product. Lead times are generally under six weeks. Some suppliers are offering 25 and 35 nanosecond versions. These faster parts command a $3.00 to $5.00 price premium over the prices quoted above for the 2147 standard device. Table 5 presents DATAQUEST's estimates of worldwide shipments of slow 4K NMOS Static RAMs. This market grew only slightly in the second quarter of 1980 with shipments up about three percent to an estimated 12.6 million units. The IK x 4 devices continued to be the more popular device with an estimated 8.9 million units, up about five percent over first quarter 1980 shipments. An estimated 3.7 million units of the 4K x 1 device was shipped which is down about one percent from the first quarter. Pricing on the IK x 4 device in the second quarter was in the range of $3.00 to $3.25 and fell to the $2.50 to $2.75 range for third quarter shipments. The 4K x 1 device usually commands about a $0.25 premium because it is not manufactured in such high quantities. Lead times on this device range from off-the-shelf to four or six weeks. Table 6 lists the five suppliers currently sampling 16K static NMOS RAMs. Now that several producers are sampling the device, we expect shipments to increase substantially over the next several quarters. Prices in the second quarter were in the $70 to $80 range and are expected to be under $50 by year end. 3 -It does not appear that the 8K static NMOS market will have many participants. At this time only GTE Microcircuits and Mostek are pursuing the market. GTE is still sampling and Mostek shipped an estimated 200,000 units in the second quarter. CMOS Static RAMs Harris, Hitachi, and Toshiba were sampling the 16K CMOS static RAM in the second quarter of 1980. Total shipments were an estimated 10,000 units as noted in Table 7. Additional participants are expected over the next few quarters. Table 8 presents DATAQUEST's estimates of worldwide shipments of 4K CMOS Static RAMs. Shipments of this product in the second quarter of 1980 were an estimated 2.8 million units, up about 15 percent over the first quarter of 1980. The IK X 4 architecture continued to be the more popular device as it represented 61 percent of the total units in the second quarter. Shipments of the IK x 4 device were up about four percent to an estimated 1.7 million units in the second quarter. Shipments of the 4K x 1 devices increased about 39 percent to 1.1 million units. Prices on these devices have dropped substantially over the last two quarters. In the second quarter, prices were still in the $12 to $14 range, but most shipments in the third quarter were in the $6.00 to $8.00 range. Lead times for these devices are still in the 6 to 12 week range from most suppliers. MPS EPROMs 8K EPROMs Worldwide shipments of 8K EPROMs continued a quarter-to-quarter decline that began in the fourth quarter of 1979. In the second quarter, worldwide shipments declined about four percent to an estimated 4.4 million units (Table 9). Prices for the 2708 EPROM in the third quarter of 1980 were in the $4.50 to $5.25 range. This device still represents about 90 percent of the total. Some suppliers are shipping the 2758, which is a partial 16K EPROM, selling at prices between $4.00 and $4.50 in the third quarter. We estimate that these devices represent about 10 percent of the total quarterly shipments. 16K EPROMs Worldwide shipments of 16K EPROMs increased about 22 percent in the second quarter of 1980 to an estimated 6.5 million units (Table 10). Prices for the device were in the $10.00 to $12.00 range in the second quarter of 1980 but fell substantially to the $6.00 to $8.00 range in the third quarter. Devices are available off-the-shelf from suppliers as well as distributors. 4 -32K EPROMs Worldwide shipments of the 32K EPROM were up about 122 percent to an estimated 711,000 units in the second quarter of 1980 (Table 11). At the end of the second quarter there were eight suppliers in this market. The second quarter prices were in the $35.00 to $40.00 range but average prices in the third quarter were in the $25.00 to $30.00 range and are expected to be close to $20.00 in the fourth quarter of 1980. 64K EPROMs Texas Instruments was the sole supplier of 64K EPROMs in the second quarter of 1980, shipping an estimated 3,000 units. Additional suppliers are expected to enter the market soon. Daniel L. Klesken Lane Mason 5 -TABLE 1 ESTIMATED WORLDWIDE SHIPMENTS OF 16K DYNAMIC MOS RAMS (THOUSANDS OF UNITS) COMPANY AMD FAIRCHILD FUJITSU HITACHI INTEL INTERSIL ITT MATSUSHITA MITSUBISHI MOSTEK MOTOROLA NATIONAL NEC SGS-ATES SIEMENS SIGNETICS TEXAS INSTRUMENTS TOSHIBA ZILOG 1ST QTR S 300 1,100 800 600 5 200 o 100 2,1+00 700 250 1,700 o 100 75 1 , 8 0 0 225 20 1 1 3 1 2 2 2ND QTR 5 i+OO , 3 0 0 ,1+00 700 5 300 0 200 . 6 0 0 , 2 0 0 1+50 , 2 0 0 o 150 1+0 , 2 0 0 550 50 - - - 1 9 7 9 - -ZRD QTR 10 500 1 , 6 0 0 2 , 2 0 0 950 5 500 o i+OO i+,800 1,000 i,ooo 3 , 2 0 0 o 250 50 1 , 8 0 0 900 50 i+ra QTR 50 700 2 , 5 0 0 2 , 7 0 0 i.ooo o 600 o 550 6 , 0 0 0 1,800 1,500 i+,200 3 375 10 3 , 2 0 0 1,800 70 YEAR 65 1,900 6 , 5 0 0 7 , 1 0 0 3 , 2 5 0 10 1,700 o 1,250 1 6 , 8 0 0 i+,700 3 , 2 0 0 1 1 , 3 0 0 3 875 175 9 , 0 0 0 3,1+75 190 1980 1ST QTR 300 800 3 . 0 0 0 3 , 2 0 0 1,150 o 750 5 7 0 0 7,1+00 3 , 0 0 0 3 , 5 0 0 6 , 1 0 0 10 600 o i+,200 2 , 5 0 0 50 2ND QTR 700 i,ooo i+,000 3 , 7 0 0 1,200 o 1,050 lOO 1,100 1 0 , 5 0 0 3 , 0 0 0 i+,800 7 , 5 0 0 30 750 o 5 , 2 0 0 3 , 0 0 0 o TOTAL 10,370 11+,750 19,315 27,058 71,1+93 37,265 1+7,630 PERCENT CHANGE FROM PREVIOUS QUARTER 2 8 . 2 "+2.2 30.9 i+O.l 37.7 27.8 SOURCE'. DATAQUEST, INC. TABLE 2 ESTIMATED WORLDWIDE SHIPMENTS OF 6^K DYNAMIC MOS RAMS (THOUSANDS OF UNITS) COMPANY FUJITSU HITACHI INTEL MITSUBISHI MOTOROLA TEXAS INSTRUMENTS TOSHIBA 1ST QTR 3 . 0 o.o o.o o.o S S o.o 2ND QTR 5 . 0 o.o o.o o.o i.o 0.1+ o.o —1979---3RD QTR 7 . 0 o.o o.o o.o 3 . 0 l . O o.o i+ra QTR 9 . 0 5 o.o S 6 . 0 l . O o.o YEAR 2 4 . 0 5 o.o 5 1 0 . 0 2.1+ o.o 1980 1ST QTR 1 0 . 0 S o.o 5 1 0 . 0 1.0 S 2ND QTR 2 5 . 0 1 0 . 0 S S 3 0 . 0 3 . 0 5 TOTAL PERCENT CHANGE FROM PREVIOUS QUARTER 3.0 6.1+ 11.0 113.3 71.9 THE LETTER S IN TABLE DENOTES SAMPLING. 16.0 36.4 21.0 68.0 1+5.5 31.3 223.8 SOURCE: DATAQUEST, INC. - 6 TABLE 3 ESTIMATED WORLDWIDE SHIPMENTS OF 4/? DYNAMIC MOS RAMS (THOUSANDS OF UNITS) COMPANY AMD FUJITSU HITACHI INTEL INTERSIL ITT MOSTEK MOTOROLA NATIONAL NEC SGS-ATES SIGNETICS TEXAS INSTRUMENTS 1ST QTR 2,600 200 350 1,700 100 1,100 3,800 1,500 2,000 1,350 150 300 3,600 2ND QTR 3,000 200 200 1,700 100 1,300 3,300 1,150 2,400 1,900 175 100 3,200 --1979--3RD QTR 3,000 200 200 1,500 300 1,300 3,400 1,800 2,000 1,300 200 50 2,700 HTH QTR 1,600 150 100 1,200 500 1,500 3.600 2,000 1,500 1,000 225 10 1,200 YEAR 10,200 750 850 6,100 1,000 5,200 14,100 6,450 7,900 5,550 750 460 10,700 1 1 2 1 1 1980' 1ST QTR ,300 100 100 900 600 ,400 ,500 ,700 ,500 400 300 0 700 2 1 1 2ND QTR 750 200 100 100 300 600 ,000 ,000 ,300 275 350 0 100 TOTAL PERCENT CHANGE FROM PREVIOUS QUARTER 18,750 18,725 17,950 14,585 70,010 11,500 7,075 (4.0) (0.1) (4.1) (18.7) (21.2) (38.5) SOURCE'. DATAQUEST, INC. TABLE 4 ESTIMATED WORLEWIDE SHIPMENTS OF FAST 4If NMOS STATIC RAMS (THOUSANDS OF UNITS) COMPANY AMD AMI FUJITSU INTEL INTERSIL MOSTEK MOTOROLA NATIONAL NEC TEXAS INSTRUMENTS TOSHIBA TOTAL 1ST QTR 0 5 0 800 0 0 0 0 25 0 0 830 2ND QTR 0 10 0 1,200 0 0 10 10 70 0 0 1,300 --1979--3i?Z7 QTR 0 5 15 650 3 0 20 25 250 0 0 968 4 r a QTR 0 5 60 900 20 0 50 65 250 5 15 1,370 YEAR 0 25 75 3,550 23 0 80 100 595 5 15 4.468 1980 152" QTR S 0 150 1,125 35 5 70 200 200 30 25 1,835 2ND QTR S 0 200 1,100 40 5 70 325 150 40 90 2.015 PERCENT CHANGE FROM PREVIOUS QUARTER 56.6 (25.5) 41.5 33.9 9.8 THE LETTER S IN TABLE DENOTES SAMPLING. SOURCE: DATAQUEST, INC. 1 -TABLE 5 ESTIMATED WORLDWIDE SHIPMENTS OF SLOW mf NMOS STATIC RAMS (THOUSAWS OF UNITS) 00 I COMPANT AMD AMI FAIRCHILD FUJITSU GTS MICRD(SE0m:TS HITACHI INTEL INTERSIL MATSUSHITA MITSUBISHI MOS TECHNOLOGY MOSTEK MOTOROLA NATIONAL NEC OKI SYNERTEK TEXAS iNs-mmBJif'S TOSHIBA ZILOG -—^TH QUARTER--lifxii 1^20 50 1+00 100 700 450 800 200 75 200 175 0 300 1.100 1,000 0 1.000 350 350 0 ^Kx^l 220 0 0 0 700 0 200 250 0 0 0 1,000 50 100 300 0 0 350 0 t+5 YEAR llfxii 1,175 250 850 580 1.400 1.800 2,650 880 145 800 305 0 1,340 3,430 2,800 0 3,060 1,900 1,010 0 4^x1 465 0 0 0 1,350 0 1,300 630 0 0 0 2,950 130 910 1,750 0 0 1,800 0 415 —1ST QUARTER--1A:X4 350 5 450 50 800 450 800 500 75 180 175 0 425 1,200 1,350 S 1,000 350 350 0 4A:X1 200 0 0 0 800 0 250 350 0 60 0 750 75 600 270 0 0 350 0 0 iO -—2ND QUARTER--IK^H " - ^ 400 0 450 0 800 450 800 250 75 270 175 0 425 1,500 1,800 50 750 350 350 0 41i:xl 250 0 0 0 800 0 250 130 0 125 o 600 75 750 330 0 0 350 0 0 TOTAL 7,670 3.515 24.375 11,700 8,510 3,705 8,895 3,660 PERCENT CHANGE FROM PREVIOUS QUARTER 2.6 10.9 11.0 5.4 4.5 (1.2) THE LETTER S IN TABLE DENOTES SAMPLING. SOURCE: DATAQUEST, INC. TABLE 6 ESTIMATED WORLWIDE SHIPMENTS OF 16X NMOS STATIC RAMS {THOUSANDS OF UNITS) COMPANY •1980-IST QTR 2ND QTR INTEL MITSUBISHI on TEXAS INSTRUMENTS TOSHIBA TOTAL S 0.0 3.0 S 0.0 S S 7.0 S S 3.0 7.0 PERCENT CHANGE FROM PREVIOUS QUARTER 0.0 133.3 SOURCE: DATAQUEST, INC. TABLE 7 ESTIMATED WORLIWIDE SHIPMENTS OF ISK CMOS STATIC RAMS (THOUSANDS OF UNITS) COMPANY -1980-IST QTR 2ND QTR HARRIS HITACHI TOSHIBA TOTAL 0.0 0.0 4.0 H.O S S 10.0 10.0 PERCENT CHANGE FROM PREVIOUS QUARTER 0.0 150.0 THE LETTER S IN TABLE DENOTES SAMPLING. SOURCE: DATAQUEST, INC. - 9 TABLE 8 ESTIMATED WORLWIDE SHIPMENTS OF i^K CMOS STATIC RAMS {THOUSANDS OF UNITS) COMPANY -kTH QUARTER--IK^k HK^l •1979--YEAR-IK^k i+^xi -1980-•--IST QUARTER--IKxH HK^l •—2ND QUARTER--lifxi^ 4-A:X1 o I FUJITSU HARRIS HITACHI MITSUBISHI NATIONAL NEC OKI RCA TOSHIBA TOTAL s 125 0 55 5 500 0 100 500 5 125 400 0 5 0 0 0 100 5 290 o 90 5 1.320 0 355 1,625 5 270 950 o 5 0 o o 275 30 150 50 60 15 600 o 150 soo 30 150 500 o 15 0 o o lOO lOO 200 lOO 60 30 425 5 150 650 150 200 600 o 30 o 5 o 120 1.285 630 3.685 1.500 1.655 795 1,720 1.105 PERCENT CHANGE FROM PREVIOUS QUARTER 6.2 20.0 28.8 26.2 3.9 39.0 " 2 5 f f f LETTER S IN TABLE DENOTES SAMPLING. SOURCE: DATAQUEST, INC. TABLE 9 ESTIMATED WORLDWIDE SHIPMENTS OF 3K EPROMS {THOUSANDS OF UNITS) COMPANY AMD ELECTRONIC ARRAYS FAIRCHILD FUJITSU INTEL MITSUBISHI MOTOROLA NATIONAL TEXAS INSTRUMENTS TOSHIBA 1ST QTR 600 75 160 70 1.100 190 700 600 800 50 2ND QTR 700 100 200 50 l.'+OO 240 750 800 800 100 • —1979--3RD QTR 700 125 350 50 l.itOO 240 1,000 800 800 100 ira QTR 500 35 600 50 1.100 270 1.000 900 800 50 YEAR 2.500 335 1.310 220 5.000 940 3.450 3.100 3.200 300 1980 1ST QTR 600 0 750 50 700 160 500 1.000 800 35 2ND QTR 700 0 1,000 50 500 60 500 1,000 600 0 TOTAL PERCENT CHANGE FROM PREVIOUS QUARTER 4.345 5.140 5,565 5,305 20.355 4.595 4.410 24.3 18.3 8.3 (4.7) (13.4) (4.0) SOURCE: DATAQUEST, INC. TABES 10 ESTIMATED WORLDWIDE SHIPMENTS OF 16K EPROMS {THOUSANDS OF UNITS) COMPANY AMD FAIRCHILD FUJITSU HITACHI INTEL MATSUSHITA MITSUBISHI MOSTEK MOTOROLA NATIONAL SYNERTEK TEXAS INSTRUMENTS TOSHIBA 1ST QTR 0 0 70 125 550 0 10 90 160 5 0 400 25 2ND QTR S 0 200 200 750 0 20 150 150 50 0 900 50 - - 1 9 7 9 - -ZRD QTR 5 0 300 350 800 0 50 250 160 80 0 1.100 90 4ra QTR 10 S 300 500 900 0 90 350 200 120 5 1,800 200 YEAR 15 S 870 1.175 3.000 0 170 840 670 255 5 4,200 365 1980 157 QTR 25 30 350 700 950 5 210 275 250 250 S 2,000 300 2ND QTR 50 300 750 700 1,200 50 260 250 350 250 25 2,000 330 TOTAL PERCENT CHANGE FROM PREVIOUS QUARTER 58.6 72.1 28.9 THE LETTER S IN TABLE DENOTES SAMPLING. 1,435 2,470 3,185 4,470 11,550 5,340 6,515 40.3 19.5 22.0 SOURCE: DATAQUEST, INC. - 11 TABLE 11 ESTIMATED WORLIMIDE SHIPMENTS OF 32K EPROMS (THOUSANDS OF UNITS) COMPANY FUJITSU HITACHI INTEL MITSUBISHI MOTOROLA NATIONAL TEXAS INSTRUMENTS TOSHIBA 1ST QTR 0 0 5 0 0 0 10 0 2ND OUR 0 0 30 0 0 0 35 0 --1979---ZRD QTR 0 0 50 0 0 0 60 0 • ^TH QTR S S 100 5 5 0 90 0 YEAR S S 185 5 S 0 195 0 1980 1ST QTR S S 165 5 5 5 150 0 2ND QTR 15 100 250 6 30 10 300 S TOTAL 15 65 110 190 380 320 711 PERCENT CHANGE FROM PREVIOUS QUARTER 333.3 69.2 72.7 68.4 122.2 THE LETTER S IN TABLE DENOTES SAMPLING. SOURCE: DATAQUEST, INC. 12 -SEMICONDUCTOR INDUSTRY SERVICE 3.0 MANUFACTURING (15 May 1980) ERRATA Page 3.0-1 Last paragraph, last sentence in parenthesis: see Appendix A, Volume in (not Volume H). Page 3.1-6 Last paragraph on Photomasking, fourth sentence beginning "On 4-inch wafers" should read "On 3-inch wafers." Page 3.2-8 Second item from bottom in parentheses - delete "and carbon." Page 3.2-20 Second series of bulleted items, second item beginning "Cumulative fab yields..." should read "...and 80%...," not "85%." Page 3.3-11 Dotted curve marked "C" should be marked "A." Dotted curve marked "A" should be marked "C." Page 3.4-2 Under heading "Production," item "d.," add "..., 13 accounting periods per year." Page 3.4-3 Under heading "Yields," item "a." should read "80%" not "75%." The content of this report represents our interpretation and analysis of information generaIIy available to the public or reIeased by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness It does not contain material Provided to us in confidence by our clients. This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securitIes mentioned and may sell or buy sucn securines. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO Page 3.4-5 Table 3.4-1: Under heading "Depreciation," change: "Equipment: $6,364,950; 60 months $106,083" to read: "Equipment: $5,144,460 (excluding test equipment); 60 months $85,741" The amounts ($195,407, $180,376, and $18.04) on the last part of this table should be deleted and this section should now read as follows: Total per calendar month $175,065 Total per period $161,598 For 10,000 yielded wafers out per period, the cost per wafer (Table 3.4-3, Item I) $16.16 Page 3.4-6 The values of the ordinates on the graph should be reduced by 1.0, i.e., 1 becomes 0, 2 becomes 1, etc.. Page 3.4-7 Table 3.4-2, the heading "Wafer Fab..." should read "...(80% Cumulative Yield)", not "75%." Under the "Materials" section, item four, replace the word "Indirect" with "Miscellaneous." Under the "Materials" section, item six, "DI Water," the amount should read $0.98, not $0.10. Change the amount on the line "Cost per wafer out (Table 3.4-3, Item n)" to read $21.81, not $20.93. Page 3.4-9 Table 3.4-3: Delete the following figures: $18.04, 29%, 20.93, 35%, 9.5%, 22.2%, 36%, $60.84, and 100%. This table should now read as follows: - 2 Fixed Monthly Costs Fab Materials Fab Labor: Direct Indirect Allocated Subtotal Total Cost Percent $ 5.75 2.59 13.53 $16.16 21.81 21.87 9.6% 4.3 22.7 27.0% 36.4 36.6 $59.84 100.0% Page 3.4-11 Table 3.4-4: Delete the following figures: $60.59, $0.1102, $0.1324 (a+b), 0.1324, $0.8275, $0.8275, $0.2300, $1.0575, 90%, $1.1750, $1.3786, 80%, and $1.7233. The relevant lines in this table should now read as foUows: E-Sort (Wafer Sort) • Wafer Fab cost per gross die = $59.84 ^550 = • Total cost per gross die • Cost per net die at E-Sort 0.131-: (16% E-Sort yield) Assembly • Cost of die from E-Sort = • Assembly cost per gross die = • Cost per gross die = (c) + (d) = Therefore, cost per net die = e-: 0.9 = Final Test • Total cost per gross die = (f) + (h) = Therefore, cost per net die = (i) r-0.8 = pack and Ship • Therefore, (j + k) = Total Cost per Net Die = $0.1088 (b) $0.1310 (a+b) $0.8188 (c) $0.8188 (c) $0.1800 (d) $0.9988 (e) $1,110 (f) $1.3133 (i) $1.6417 (j) $1.6616 Page 3.4-12 First sentence should read "The detailed equipment lists for the N-channel MOS are given in the Appendix." (Add "the" and delete "A".) • Page 3.4-13 Table 3.4-7: Delete all figure amounts. Table should now read as follows: Percent of Total 62% 38% 100% Darken the "Z"-shaped, cross-hatched section beneath the Word Line and adjacent to the Storage Line. Figure 3.4-2 16K DRAIVI CELL (Not to Scale) Equipment Facilities Grand Total Page 3.4-16 Figure 3.4-2 Capital Cost $ 6,364,950 3,832,300 $10,197,250 Storage Line P + lU£UMMMiikfek^^bb.^M ' ..Xo::::::::- x ": ;;-: --^^^ '•?.4- • " •!'!::^XHx:!fi:-. N-F t p+ Source: DATAQUEST, Inc. 4 -! ^ ^^1 RESEARCH ASubsidiafvot A.C. Nielsen Co. ^ INCORPORATED I ^ I ^ S W ^ S ^ H ^ B 1 1 E H P K SIS Code: Vol. H, 3.0 MANUFACTURING MODEL DATAQUEST's Semiconductor Industry Service has just published a comprehen-sive manufacturir^ model. This report of over one hundred pages is a complete revision of Section 3 of the Semiconductor Industry Service notebook and replaces earlier material publislied in 1975 and 1977. TECHNOLOGY AND EQUIPMENT Wafer fabrication technology continues to evolve, and the interplay of equipment technology, device technology, plant layout and design, site selection, cost, and personnel management becomes increasingly complex. The trend toward greater device complexity and larger die size has been spurred on by lowered defect densities. As device geometries approach the 2-micron level and below, processing, environ-mental and equipment technologies must be carefully coordinated. Of the many process technologies, photolithography has been one of the key factors in determining the pace of Very Large Scale Integration (VLSI) design and manufacture. The trend is away from contact printing toward proximity and projection printing. Dry etching techniques are being developed as a necessary concomitant of projection printing in order to etch fine patterns in a variety of materials. Deposition of materials is becoming more sophisticated with the addition of sputtering and plasma deposition to the tried-and-true electron beam and chemical vapor deposition technologies. Ion implantation techniques have kept pace to achieve, quickly and inex-pensively, control of impurity concentrations and junction depths. Although complex and expensive, with increasing delivery times, wafer fabrica-tion equipment is proving to be cost effective. The equipment is increasingly Copyright © 28 August 1980 (Rev.) by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO • controlled electronically (by the integrated circuits it is used to fabricate). The result is greater automation, control, and reproducibility of results, as well as lower defect levels due to lower operator/wafer interfacing. The clean room facilities in 1980 are geared toward Class 100 rating and better rather than toward the Class 1000 rating that was acceptable until 1978. Deionized (DI) water is being elaborately treated and tested to meet the new clean standards. The water is pretreated through activated carbon and diatomaceous earth filters before it goes through reverse osmosis and deionization stages. Four-inch diameter wafers are expected to be the standard during the mid-1980s: larger wafers may be used for many standard memory lines. Thus, for a facility processing 10,000 wafers out per four-week period with manufacturing costs of $40 to $80 per wafer and gross revenues of $300 to $600 per wafer, at least $3.0 miUion dollars per period can be realized. At the same time, equipment purchases for today's use must nevertheless be chosen for eventual upgrading to handle five-inch, and even six-inch diameter wafers, as long as the particular technology wiU not be obsolete by the time of the upgrading. It is also possible to adapt machines to suit other products. With the high capital cost of some equipment, care must be taken to obtain maximum utilization of such equipment while it is in service. PLANT LAYOUT AND DESIGN Several factors determine the way in which a particular plant is laid out. Cleanliness for VLSI production is influencing what portion of the equipment remains in the clean room. Only the loading end of diffusion furnaces are being allowed in the clean room. The heat and dust generating portions are being separated from the clean room by a fire waU. The same is true for ion implanters and the trend will be continued for other equipment where appropriate. Servicing of equipment and work stations in old facility designs meant frequent ingress of personnel into the clean room to deliver bottles of chemicals, replace furnace tubes, and repair plumbing. New layouts obviate the necessity for these entries by pumping chemicals (except photoresist) to other points of use. Plumbing can be done outside the clean room if a service corridor rings the fabrication area. Furnace tubes can be pulled and replaced behind the fire wall and outside the clean room. If gases are pumped overhead through a crawl space, gas lines can often be serviced in these crawl spaces without need for entry into the clean room. Philosophies of equipment design have shifted toward single wafer and in-line processing and wafer handling, away from the purely batch-type handling. Thus, there is greater interplay between different processing areas (as opposed to the almost strict quarantine that existed before) as long as cleanliness is maintained, material flow facilitated, and cross-contamination avoided. New demands for material account-ability have made production control supervision the heart of the entire operation and this fact has also affected the overall plant layout. Increased usage of computers and terminals wiU make this approach even more effective. AUTOMATION Perhaps the most persistent and pervasive trend is that towards automatic sequencing of events witliin a given piece of equipment. Also popular is the drive toward computer automation of the entire fabrication area for control, repro-ducibility, data collection, and analysis. The benefits to be reaped are legion and include: Less wafer handling Process monitoring and control Correct process sequencing Proper routing of material System self-diagnostics and self-correction Data collection for off-line processing Elimination of paper work Material accountability (especially useful since lot sizes vary for different operations in the manufacturing process) Equipment manufacturers are following the trend toward automated equipment, some with micro- and minicomputers. Some automation now exists in the areas of diffusion/oxidation, physical and chemical vapor deposition, ion implantation, masking, alignment, mask making, mask inspection, testing, plasma etching, DI water, and environment monitoring. Variables which constitute the particular process at the factory level are sensed and measured. The supervisory element compares the measured data against set values and adjusts the system to initiate or shut down the process. Communication and display terminals are at the floor or factory level and through them data are transmitted to the highest level, the management computer. Exciting as it is, the prospect of a fully computerized, semiconductor manu-facturing facility is not foreseen before the mid- to late-1980s, even thoi^h an experimental automated line has been constructed at Texas Instruments and auto-mated production lines are used by several captive manufacturers. The determining element is, of course, equipment development. Much of the equipment today is being "updated" by adding microprocessors for sequencing. However, very few pieces of equipment are designed around computer control with adequate supporting software. More £ind more companies have placed computer terminals in their manufacturing areas but these terminals are almost always to handle data rather than direct and control manufacturing processes. The development cycle for very sophisticated equipment can range from two to five years. Delivery times of equipment costing above $200,000 often range from nine to eighteen months. Development costs are often high too, as is the rate of obsolescence. Consequently, only the wealthiest semiconductor manufacturers can - 3 -undertake their own development programs toward fuU computerization of the factory. The rest must wait for market forces to react. Batch processing will probably never disappear in the foreseeable future. However, more and more equipment manufacturers are offering cassette-to-cassette wafer systems to eliminate tweezer handling. Tweezers are a well-known cause of damaged patterns, silicon particle generation, and wafer defects. In properly con-trolled equipment, each wafer is subject to almost the same set of process parameters. STAFFING The cumulative effects of the recessions of 1970 and 1974 are now evident in the acute Shortage of trained engineering staff. The trend of decreased enrollment in engineering colleges since these recessionary periods has not been reversed at rates compatible with industry growth. For those engineers who remained, it has become a sellers' market. In Santa Clara (Silicon) VaUey, California, unemployment at 4.7 percent in September 1979 was at a five-year low, unparalled anywhere in the country. At the lower end of the wage scale, turnover rates ranged from 50 to 100 percent among operators. Although mothers of young children have rejoined the work force, the industry stiU faces severe labor shortages while professional personnel are being wooed by "headhunters" and by print, skywriting, radio, and television ads. Incentives and bounties are offered to staff already in place to ensure successful recruiting. Housing costs, already prohibitive for engineering staff, are even more pro-hibitive for operators (see "Site Selection"). Commuting is only a partial solution to the problem of staffing expanding operations. The trend, therefore, has been to relocate new operations in more favorable labor markets, aU other things being equal. WAFER FABRICATION GUIDELINES Certain guidelines became apparent as U.S. merchant and captive semiconductor manufacturers were surveyed to develop the costs to be used in this model. A summary of these guidelines follows. Direct labor in most wafer fabrication areas correlates weU with the number of wafers out (assuming adequate wafer fabrication yields) and with the number of mask layers; the product of these two factors is approximately 250. In other v/ords, if an 8-layer device were being meinufactured, each worker should account for approxi-mately 31 wafers out per week. Supervision of direct labor typically runs 15 to 20 percent of direct labor hours and, because of higher pay rates, 36 to 48 percent of direct labor dollars. Allocated labor accounts for aU indirects in the wafer fabriction area. This category includes process sustaining engineers, product engineers, quality control and quality assurance, production control, and equipment maintenance. Allocated labor is the largest labor category and may run from 180 to 280 percent of direct labor cost. - 4 We found in our survey a few cases where older processes are in production and little technological change is taking place; in these cases, allocated labor costs were much lower. Typically, the wafer fabrication area floor space depends on the wafer start capacity required. Our model assumes approximately 12,500 wafer starts per period (there are 13 four-week periods per year) and has approximately 12,160 square feet of wafer fabrication area and 12,840 square feet of area for testing and office space. Thus, the wafer fabrication area required is approximately 1 square foot per wafer Start. The construction costs for these facilities are substantial, particularly in wafer fabrication areas. An analysis of company annual reports suggests that the semicon-ductor industry spends about 25 percent of its capital on facilities and 75 percent on equipment. Our model shows higher facilities expenditures on a percentage basis because aU construction is new; as the equipment ages, it is to be expected that new equipment wiU be purchased before the facilities become obsolete. This phenomenon accounts for the lower ratio in mature companies. In our N-channel RAM wafer fabrication model, total capital expenditures for facilities and equipment are: Percent Facilities: $ 3,832,300 38% Equipment 6,364,950 62 $10,197,250 100% The facilities expenditure includes both wafer fabrication and office space and is divided as follows: $ Cost 3,832, 6,364, 300 950 Cost $3,319,300 513,000 $3,832,300 Cost Per Sq.Ft. $273 $ 40 Fab Area (12,160 sq.ft.) Offices and Test (12,840 sq.ft.) In the table above, the costs per square foot are in addition to the cost of the basic building sheU. In our model, it is assumed that the land and building shell are leased at a cost of $1.00 per square foot per month. If land were purchased and a building constructed, additional costs of $40 to $85 per square foot would be incurred. The variation in these figures depends on the price of the land; it may vary from $40,000 to $400,000 per acre or more. - 5 -MODEL COSTS Our 1980 cost model is based on an MOS 16K DRAM, fabricated using a 6-layer process that does not employ silicon nitride. Other companies may use an 8-layer process. Basic assumptions are listed below: Technology • 16K DRAM, MOS N-channel • 6-layer double-poly process • 5-micron geometry • 140 mil X 140 mil chip size (= 20,000 mil^) • 16-pin DIP plastic package • 4-inch diameter silicon wafer • 1:1 projection aligners (UV) • Negative photoresist • Wet etching • Plasma ashing of photoresist Production • Two full shifts per day (skeleton graveyard shift mainly for maintenance) • Seven hours effective work per shift • Five day week = 20 days per period • 12.5 productive periods per year • 25 percent benefit package including shift premiums • Minimum throughput at any step = 60 wafers per hour • 10,000 wafers out per period • Productivity at approximately 42 wafers out per operator per week (6 layers) • An assembly operations offshore - 6 Yields • Cumulative Fab yield - 80% • E-Sort (16K DRAM) - 16% • Assembly yield - 90% • Final test yield - 80% Facilities • Building rented as shell at $1.00 per sq.ft. per calendar month • Space rented = 25,000 sq.ft. • Minimum of 15 percent inflation rate on construction, materials, and equipment • AU facilities and services supplied from scratch • AU design services contracted to outside engineering firms • AU chemicals (except photoresist) to be pumped into the fab area from Storage tanks to points of use • Masking can accommodate up to 10 projection aligners • Diffusion can accommodate 20 furnaces • Fab area = 12,160 sq. ft; E-Sort, Test, Offices = 12,840 sq.ft. total Equipment • Highly automated operation • Convertible for use on 5-inch diameter substrates • Equipment will be used eventually on 2- to 3-micron gates and shallow junctions (less than 1.0 micron) • Need fiUed for data coUection and information management to facilitate trend analysis Volume-sensitive wafer making costs appear in Table 1, a summary of wafer making costs appears in Table 2, and a summary of equipment costs in Table 3. The fixed monthly costs of Table 2 include building rent, sewage, electric power, gas, and depreciation of buildings and equipment. Howard Z. Bogert Table 1 VARIABLE (VOLUME-SENSITIVE) COSTS (Data Gathered From Company Surveys) Wafer Fab (80% Cumulative Yield) Materials: Cost per Wafer Out - Silicon - Masks - Chemicals - Indirect Materials - Gases - DI Water Cost per Wafer Out Labor: - Direct (Adjusted for - Indirect - Allocated 6-layer Process) $13.33 0.25 3.00 2.25 2.00 0.98 $ 5.75 2.59 13.53 $21.81 $21.87 Source: DATAQUEST, Inc. June 1980 Table 2 COST PER WAFER OUT Cost Total $59.84 Percent Fixed Monthly Costs Fab Materials Fab Labor: Direct Indirect Allocated Subtotal $ 5.75 2.59 13.53 $16.16 21.81 21.87 9.6% 4.3 22.6 27% 36 37 100% Source: DATAQUEST, Inc. June 1980 Table 3 EQUIPMENT COSTS: N-CHANNEL MODEL Diffusion Area Masking Area Deposition Area Fab Support and Test Areas Backside Processing Grand Total (6^% Tax Included) Capital Cost $1,339,450 2,283,300 1,039,700 1,287,900 414,600 $6,364,950 Source: Percent of Total 21.0% 35.9 16.3 20.3 6.5 100.0% DATAQUEST, Inc August 1980 9 -SIS Code: Vol. I, 2.0 GENERAL INDUSTRY UPDATE SUMMARY DATAQUEST expects a moderate downturn in U.S. semiconductor consumption during the second half of 1980, primarily caused by weakening demand and falling prices. This downturn in consumption results from the surprising strength of semiconductor consumption in the first half of 1980 and recent effects on semiconductor usage due to the current economic recession. U.S. semiconductor consumption grew an estimated 5.3 percent in the first quarter of 1980 compared to the fourth quarter of 1979, and grew another 9.1 percent in the second quarter of 1980. DATAQUEST forecasts U.S. semiconductor consumption in both the third and fourth quarters will decline by 3 to 4 percent on a quarter-to-quarter basis. U.S. semiconductor consumption for all of 1980 is expected to be 25.8 percent higher than 1979, reflecting a strong momentum entering this year. An upturn in U.S. semiconductor consumption is expected to begin in 1981, increasing in strength throughout the year, with the total for 1981 up about 10 percent over 1980. The U.S. economy, which was flat in 1979 and fell abruptly in the second quarter this year, appears to have bottomed out. A gradual recovery appears likely, but not certain. In this recession, the electronics industry has been relatively much less affected than other economic segments. This fact and the lack of serious excess components inventory leads us to cautious optimism. As we have stated in previous Research Newsletters, the current situation bears no resemblance to the 1974 debacle. RECENT ECONOMIC TRENDS The U.S. economy is in a moderate-to-severe recession. Some segments of the economy reacted strongly to the very high interest rates earlier this year. From the second quarter, several major segments of the economy have been severely hit: automotive sales are down approximately 30 percent; housing starts are down approximately 40 percent; steel, forest products, air transportation, agriculture, and tourism are strongly affected. Additionally, small business in general has felt the effects of the slowdown. Although the immediate cause of the recession has been the tightening of credit by the Federal Reserve Board, the longer term causes include the long period of industrial expansion beginning in 1975, problems with persistent and pernicious inflation, energy costs, and the lack of productivity improvements in industry. Copyright©22 August 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generallv available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness It does not contain material provided to us in confidence by our clients. This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy sucn securities 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO The GNP fell at a 9.1 percent annual rate in the second quarter of 1980. Momentum will cause it to fall further in the third quarter. Inflation remains high as wholesale prices surged 1.7 percent in July, an annual rate of more than 20 percent. Except for the week ending August 6, the money supply appears to have shown very modest growth, indicating continued restraint by the Federal Reserve Board despite the political pressures of an election year. The Index of Leading Indicators declined in April and May, but showed a significant 2.5 percent increase in June, presaging potential improvement in the economy. Capital expenditures for business equipment have weakened in recent months, reflecting their normal lag behind the general economy. The economic outlook in both Europe and Japan appears to be worsening. Unlike 1974, but similar to 1970, economies in the rest of the world appear to be lagging developments in the United States. Consumers have been reducing their overall level of indebtedness quite rapidly, even though disposable incomes have been falling. The prime rate has fallen rapidly from its high of approximately 20 percent to about 11 percent now. Further declines of interest rates, if any, are expected to come slowly. Evidence is mounting that the rapid deterioration of the economy during the second quarter is over. Both housing starts and automotive sales have shown very modest increases recently; retail sales are again rising; and the Index of Leading Indicators is improving. Temporarily, the rise in the unemployment rate has halted. Falling interest rates have reduced problems and pressures throughout the economy. A salient aspect of this recession is that it is affecting various segments of the economy quite differently. We believe the U.S. economy is undergoing some major structural changes, partly causing this recession. Up to now, the general structure of the U.S. economy has remained relatively unchanged since the end of World War II. This structure, we believe, is now being altered more significantly than in any period during the last 35 years. Segments of the economy which are highly affected by inflation or energy, or industries which have recently matured are bearing the brunt of the downturn. Changes in buying habits and foreign competition are having a major effect. Some of these industries, such as the automotive industry, may experience slower future growth and a declining role in the economy. DATAQUEST believes that electronics, and the semiconductor industry, will play an increasingly more important role in the worldwide economy. -2-The outlook for the U.S. economy is not particularly bright in the short term. The general problems causing this recession have not yet been resolved. In particular, it is very likely the United States will have significant inflation for some time. This may cause potential problems as the Federal Reserve Board attempts to fine-tune an economic recovery. If interest rates fall rapidly and money supply increases, consumer spending and inflation will rebound rapidly, leading to major future problems. Conversely, if the money supply remains too tight, rising interest rates could cause severe problems for those segments of the economy already experiencing difficulties, and the current recession could worsen markedly. Thus, it is generally expected that the Fed will try to hold middle ground, with little change in availability of money or interest rates and the probability of only a slowly improving economy. SEMICONDUCTOR INDUSTRY TRENDS The U.S. semiconductor industry is experiencing a decline in orders. The "imminent slowdown" forecast in our Update Newsletter of April 11 has arrived. DATAQUEST estimates that the ratio of book-to-bill remained significantly above 1.1:1 throughout the first four months of 1980. But in June, that ratio was an estimated 0.85 and fell further to about 0.6 in July. Bookings are expected to remain weak in August. However, because of strong bookings in the first part of the year, most backlogs remain adequate. The recent poor bookings have several causes: • Semiconductor shipments and consumption in the United States grew 12.2 percent in the fourth quarter of 1979, over the previous quarter; another 5.3 percent in the first quarter of 1980; and 9.1 percent in the second quarter. Qearly, these increases do not fully reflect additional capacity—they are partly the result of price stability and price increases. With supply now exceeding demand in many product areas, price reductions are having a major effect. Indeed, DATAQUEST believes that price corrections will be the primary cause of negative growth in the value of semiconductors consumed in the United States. • The extremely heavy demand in 1979 and early 1980 has resulted in some chaos among bookings that is now being cleaned up—including double-ordering, incorrect product mixes, overpricing, etc. Significantly, the bookings decline in July affected ICs more than discretes, a clear sign that order correction is more responsible than end usage. • With supplies more readily available, most users have reduced inventories from an estimated average of about 12 weeks to 4 weeks. • July and August are traditionally weak months for semiconductor bookings. -3-• Order changes, reflecting delivery stretchouts and price reductions, appear to be having an effect on recent bookings. • Obviously, although unit demand remains strong, some weakness in general semiconductor usage exists. It is DATAQUEST's perception that usage of semiconductors remains relatively Strong. Most major areas of semiconductor demand remain strong, with the exception of consumer products. We do not expect unit demand to show significant weakness. However, with slower industry growth, improvements in yield and other costs will result in a reduction in prices. This is expected to have an effect on dollar volumes, as is already being experienced in memory products. (See DATAQUEST's Semiconductor Industry Status Report, July 25, 1980.) The effects of the demand slowdown have not fallen evenly on the industry. Bipolar LSI remains strong in total units and revenue. MOB memory, especially the overpriced devices, is experiencing major price adjustments. Linear products have seen only moderate effects while discretes see little change from the weakness that began some quarters ago. Suppliers of material to the industry (except silicon) felt a swift contraction of orders about May as semiconductor manufacturers adjusted order rates and inventory levels. Orders have rebounded and stabilized about 10 to 15 percent below peak levels. Fears of wafer shortages moderated effects on the silicon suppliers. Conversely, equipment suppliers, especially long lead time products, have seen demand remain strong. Semiconductor manufacturers have not significantly reduced capital expenditure plans. Most major semiconductor companies reacted swiftly to the economic decline in the second quarter, instituting many of the following: Hiring freezes, except in critical areas Inventory reduction and control Acceleration of new product development Cost controls and other spending limits Yield and cost improvement programs Increased scrutiny of the order book These measures were not as universally applied early in 1974. Significantly, the industry has yet to have, or need, major layoffs, although employment reductions in some companies (especially suppliers) have occurred. The Sunday employment ads of the San Jose Mercury-News are at 40 pages—hardly a recession, but down from 55 pages in February and 60 pages in December. -4-SEMICONDUCTOR INDUSTRY FORECAST Table 1 presents DATAQUEST's estimate for U.S. semiconductor consumption in dollars. We believe that U.S. semiconductor consumption in 1980 will show an increase of about 25.8 percent over 1979. In 1979, U.S. semiconductor consumption increased approximately 37.6 percent over 1978. It should be noted that these figures not only include shipments by U.S. manufacturers within the United States, but also exports to the United States from Japan and Europe. These exports to the United States have increased significantly over the last two years. DATAQUEST expects further growth in U.S. semiconductor consumption in 1981, to an estimated level of 10.4 percent over this year. However, given the high degree of economic uncertainty, long-term forecasts are currently not well-founded. Our current estimates for U.S. semiconductor consumption by calendar quarter are shown in Table 2. We expect a moderate decline in semiconductor consumption for the second half of 1980, with average quarterly consumption declining by 3 to 4 percent for each quarter. A healthy resumption of growth in semiconductor consumption is expected for 1981, beginning early in the year. The decline in consumption forecast for the second half of the year is somewhat less optimistic than our previous forecast. This results from two primary factors: significantly greater than expected growth in the second quarter, primarily due to price stability; and a very rapid decline in the U.S. economy during the second quarter. Essentially, unit demand is expected to remain strong, but price weakness and a correction of other imbalances resulting from the market strength of the last two years will cause a market contraction in terms of dollars. Given the level of the current recession in the economy, our forecast for semiconductor consumption is optimistic. We believe the semiconductor industry will continue to outperform other segments of the U.S. economy. The long-term demand factors of the industry remain extremely positive. Although currently the supply/demand imbalance of 1979 has moderated, we expect tight semiconductor supply to resume sometime after the world economy improves. This viewpoint is apparently shared by many semiconductor manufacturers; expenditures for increased capacity remain at high levels. It is important to point out some major differences between the current situation in the semiconductor industry and that of 1974. In particular, we are impressed by the very strong consumption of semiconductors over the last few years. Past relationships of semiconductor consumption and the economy no longer hold. For example, industrial production leveled in November 1973 and remained level through the first three quarters of 1974. This was reflected rapidly in semiconductor demand with orders falling in the first quarter of 1974 and shipments peaking in the second quarter. Similarly, industrial production leveled in November 1978 and remained essentially extremely flat through March 1980. However, during this period, semiconductor demand and shipments grew extremely rapidly. Semiconductor consumptionduring the second quarter of 1980 was more than 50 percent higher than the first quarter of 1979. Semiconductor demand was affected only after the economy began a rapid downturn in April 1980. Thus, semiconductor consumption is outperforming the U.S. economy. DATAQUEST believes this has several causes, including structural changes in the economy and the indirect effects of inflation, which have made nearly all electronics far better bargains. This altered relationship with the economy is expected to continue. Frederick L. Zieber -6-Table 1 ESTIMATED U.S. SEMICONDUCTOR CONSUMPTION (Millions of Dollars) Discrete Devices Integrated Circuits Total 1979 $1,322 $3,375 $4,697 Percent Increase 1979-80 7.6% 32.9% 25.8% 1980 $1,422 $4,485 $5,907 Percent Increase 1980-81 1.8% 13.2% 10.4% 1981 $1,447 $5,076 $6,523 Source: DATAQUEST, Inc. August 1980 Table 2 ESTIMATED QUARTERLY U.S. SEMICONDUCTOR CONSUMPTION (Millions of Dollars) 1979 Discrete Devices Integrated Circuits Total 1st Qtr. $ 301 700 $1,001 2nd Qtr. $ 340 805 $1,145 3rd Qtr. $ 334 868 $1,202 4 th Qtr. $ 347 1,002 $1,349 Total Year $1,322 3,375 $4,697 Percent Change From Previous Quarter Percent Change From Previous Year 4.4% 33.6% 14.4% 36.0% 5.0% 39.1% 12.2% 40.7% 37.6% - 7 -Table 2 (Continued) ESTIMATED QUARTERLY U.S. SEMICONDUCTOR CONSUMPTION (Millions of Dollars) 1980 Discrete Devices Integrated Circuits Total Percent Change From Previous Quarter 1st Qtr. $ 354 1,066 $1,420 5.3% 2nd Qtr. $ 364 1,185 $1,549 9.1% 3rd Qtr. $ 357 1,135 $1,492 (3.7%) 4 th Qtr. $ 347 1,099 $1,446 (3.1%) Total Year $1,422 4,485 $5,907 Percent Change From Previous Year 41.9% 35.3% 24.1% 7.2% 25.8% 1981 Discrete Devices Integrated Circuits Total Percent Change From Previous Quarter 1st Qtr. $ 349 1,123 $1,472 1.8% 2nd Qtr. $ 360 1,233 $1,593 8.2% 3rd Qtr. $ 361 1,289 $1,650 3.6% 4th Qtr. $ 377 1,431 $1,808 9.6% Total Year $1,447 5,076 $6,523 Percent Change From Previous Year 3.7% 2.8% 10.6% 25.0% 10.4% Source: DATAQUEST, Inc. August 1980 -8-1 ^ a s l =%= ^ 1 1 h^i MUH 1 l-ULIU ^^ B SECURITIES. INC. LETTER VoL II - No. 7 August 21, 1981 This letter is a condensation of recent Research Newsletters and internal thinking from the industry research groups at DATAQUEST, Inc. Requests for amplification of our thoughts or for specific Newsletters should be directed to the author. A list of recent DATAQUEST Newsletters appears at the end of this letter. WORD PROCESSING The momentum at Wang Laboratories in terms of new orders and mgirket penetration is so strong at present that one must ask two basic questions: can competition seriously impair the company's progress and can an internal organization that is Stretched very thin hold together and manage the company's phenomenal growth? To the first question, we would answer a reasonably comfortable no. The recent IBM Displaywriter affects about 5 percent of Wang's present market and we believe that Wang will have a new product in the stand-alone word processing market during the current fiscal year. IBM's other recent move of adding word processing software to its 8100 line would have been very effective if there were thousands of 8100s in the field that could make an inexpensive upgrade and incorporate word processing. However, the new version of the 8100 has just begun to be shipped during 1980. Effective shared resource word processing that could easily tie into the 4300 line of IBM might be more of a problem for Wang, but no such product is available. The successful implementation of Xerox's ETHERNET network might pose a longer term problem for Wang, but this product is at least a year away from full implementation. By announcing the product early, Xerox definitely aided its own ability to sell word processing machines; it also afforded Wang a long time to study the Xerox proposal and effect a defense. Datapoint and Prime Computer have both announced intriguing integrated office systems, but both companies are well behind Wang in implementation and the market is certainly large enough to allow all three companies to prosper and not get in each other's way. The question of Wang's ability to handle its growth internally is a much harder one to answer. The most visible problem is the difficulty the company has had in the numbers and quality of its field service organization. We have been aware of considerable dissatisfaction among many Wang word processing users about service. It is difficult to determine whether any large customers who would have otherwise purchased Wang equipment were dissuaded by the reputation for bad service. We know of no customers who have actually replaced Wang equipment because of this problem, though we know of one large university who took Wang off their acceptable vendor list. Copyright © 21 August 1980 by DATAQUEST- Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients. This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities, Member, New Ydrk Stock Exchange 19055 Prgneridge Avenue / Cupertino, California 95014 / (408)725-1200 Wang management is acutely aware of the difficulty and has been working very hard to solve it. In our opinion, the critical point was probably passed sometime during fiscal 1980. With the rate of revenue growth likely to slow to more reasonable rates (40 to 50 percent) this year, the company has a good opportunity to truly get a handle on this problem. The company is chewing up cash at about a $10 million per month rate and its balance sheet looks more like that of a public utility than a technology company (debt is approximately 63 percent of total capitalization). However, 60 percent of its debt is in the form of convertibles, half of which can be called and converted into common stock at the company's convenience and the recent convertible offering should cover the company's cash needs for at least nine months and possibly longer. The company's relatively lower rate of growth in its European business has also been a problem in the past, but extensive management changes have apparently improved the European situation markedly. The risks are certainly there at Wang, but in our view, they are outweighed by two clear and overwhelming positives: excellent products, and brilliant product positioning and integration. Our earnings estimate is $2.80 per share fully diluted in the June 1981 fiscal year on a 45 percent revenue gain to $780 million. PAPER AND FOREST PRODUCTS One of the concerns voiced about the forest products companies is that an upturn in long-term interest rates could abort any major housing recovery in 1981, which in turn would exert downward pressure on lumber and plywood pricing. The concerns about housing starts next year is a valid one, but in our view, there are forces at work that can push plywood and lumber prices higher next year even with only a moderate rebound in housing starts. In most years, prices are demand driven; in relatively weak years, prices are cost driven in this industry. In our opinion, the major determinant of lumber and plywood prices at present is the marginal cost of the small producer. Statistical work that we have done indicates that the correlation between marginal producer costs and end market prices during soft economic periods is very high. Because the small producer has been paying substantially higher prices every year for stumpage, his costs are escalating at a very rapid rate. This in some measure explains the very rapid rebound in Western plywood pricing from $189 per thousand board feet in the second quarter to $224 at present. In our view, even if housing starts move from an estimated 1.2 million level this year to only 1.5 million in 1981, the escalation in small producer costs will push plywood prices up 15 percent next year from present levels and lumber prices up 25 percent. We should caution that our model works in moderate housing start years, but not in very poor years. For example, if starts rebounded to only 1.3 million next year, we do not believe that our price expectations would be met. - 2 -If, however, starts reach 1.5 million next year and then move closer to 2 million by 1982, we believe that the outlook for the forest products producers would be extremely positive. In this environment, for example, we envision Western plywood averaging $265 per thousand board feet next year and reaching $400 per thousand board feet in the mid-1980s. Because of the relatively low stumpage costs of the large integrated producers, we believe that this scenario would produce very high rates of earnings gains for them. We are in the process of working up earnings forecasts over the next two years for the major forest products companies, given differing housing scenarios. In a 1.5 million housing start year in 1981, for example, we believe that Weyerhaeuser could earn $3.75 per share and that Champion International could earn $4.15 per share, fully diluted. SMALL COMPUTERS In our view, there are currently two important developments at Digital Equipment. First, it is clearly gaining market share at the expense of its major rivals in the minicomputer business. Second, it is making a major bet on continued strong growth in demand for its products over the next two years. Digital Equipment's fourth-quarter earnings were close to forecast. Hardware Shipments in the fourth quarter at Digital grew 32 percent and total revenues grew 33 percent. It is our belief that incoming orders are presently running 30 percent or more higher than last year's. In comparison, we estimate that Data General's order growth at present is running at a 15 to 20 percent rate and that Hewlett-Packard's computer orders (excluding its Corvallis operation) are running 10 to 15 percent ahead on a year-to-year basis. In part, the high order rate at Digital can be explained by differences in product cycle timing. Digital's major new product, the VAX 11/780, is now in a relatively full order and shipment phase. In comparison, volume deliveries of Data General's new 32-bit machine will not begin until early 1981 and upgrades to HP's 3000 line have not yet been announced (more on HP in our Instruments section). Capital expenditures at DEC are expected to increase to $350 to 400 million in the June 1981 fiscal year compared with $210 million in fiscal 1980. Most of the capacity will not be added until the end of fiscal 1981 or the beginning of fiscal 1982. While strong orders and long lead times at Digital ensure good revenue and operating income gains in fiscal 1981, the key is the level of demand about one year from now, when the new capacity comes on-stream. DEC is restricting new OEM customers because of long backlogs and we have some concern that this restriction, plus possible double ordering by existing OEiVl's, could cause a softening in demand in mid-1981 similar to that in 1978. While there are obvious economic risks, particularly because the minicomputer industry tends to lag the overall economy, it seems a good bet that the demand will be there when DEC needs it. For example, the much-rumored scaled-down version of its VAX 11/780 could be introduced to coincide with the increase in capacity. We are projecting a 34 percent increase in operating earnings this year at DEC, but the earnings per share gain will be held down to about 15 percent, or $6.25 per - 3 -share, by the heavy use of cash anticipated over the next twelve montlis, and by dilution caused by the recent convertible offering. Price increases instituted in the last six months will not impact shipments until the third fisced quarter. We are anticipating only a modest improvement in operating margins in the second half when these products are shipped and more favorable margin comparisons would make our $6.25 per share estimate conservative. More importantly, if demand maintains itself in the following year, the rate of gain in earnings per share in fiscal 1982 should accelerate considerably. INSTRUMENTS Year-to-year gains in Test and Measurement (T&M) orders, by our estimates, are now running at or below 10 percent for the industry. leaders (Hewlett-Packard, Tektronix) and at lower rates for some of the smaller competitors. The slowdown, first evidenced in the United States earlier this year, is now spreading overseas. More than half the gains are probably coming from price increases instituted in the last year. To date, the deceleration is no greater than we had forecasted; as noted in our last Portfolio Letter we expect orders to begin turning up in the first quarter of 1981. Hewlett-Packard's third fiscal quarter sales were in line with our expectations but at the low end of our expected ranges in both incoming orders and earnings per share. Our biggest concern at Hewlett-Packard in terms of orders lies in its Computer Division. Total EDP Group orders for the third quarter were up 20 percent, but if one excludes the Corvallis, Oregon Division, which makes the highly successful hand-held calculators and personal computers, orders for the rest of the group were up an estimated 13 percent in the last quarter. As noted above in our Small Computer section, this order rate gain is markedly below that of Digital Equipment and somewhat below that of Data General, and it indicates particular softening in HP's major product line, the 3000. The slowing in 3000- orders may be attributable to several different factors. First, IBM has begun shipping its System/38, which is a direct competitor to the HP 3000. Second, Hewlett-Packard has made very good penetration in the manufacturing market in the Mid-West, which has been particularly hard hit in the present recession. Third, customers may have heard about possible new products by Hewlett-Packard and may be holding back on orders. There is no question but that Hewlett-Packard needs some upgrades of its 3000 line. We expect two introductions by Hewlett-Packard before the end of calendar 1980; one of them should be a higli-end extension of the 3000. At present, Hewlett-Packard appears to be committed to 16-bit architecture in its 3000 line, despite the fact that all of its competitors have now introduced 32-bit products. In the commercial and manufacturing end markets that the HP 3000 serves, we do not believe that 32-bit capabilities are particularly important, and well designed 16-bit offerings can meet its customers' needs very effectively. However, the 3000 is reaching the end of its product life cycle. It is likely that the next generation product will incorporate 32-bit architecture. 4 -Our estimates for Hewlett-Packard's earnings for fiscal 1980 and 1981 are now $4.40 to $4.45 per share and $5.10 per share respectively, down slightly from our previous forecasts. To maintain a positive attitude on Hewlett-Packard at this juncture necessitates a belief that management can make the right moves to accelerate the relative growth of its computer operation. Considering management's previous record, this does not appear to be a dangerous bet. In fact, it is the first time in several years that fundamental questions of any consequence about Hewlett-Packard have arisen. SEMICONDUCTORS The recent Motorola Analysts' Meeting contained almost no good news. Communications orders are soft and communications earnings will likely be down for all of 1980. Motorola's Semiconductor Group seems to be doing less well at present than its major competitors; as expected, the outlook for the automotive related divisions is uninspiring, and Codex profits will be down for the year. Looking over the next 18 months, however, the positives and negatives are a bit more balanced. On the negative side are the following items: o The major reason for DATAQUEST's historic enthusiasm for Motorola was the dramatic turnaround that we saw in the company's Semiconductor Group. In essence, that turnaround has already been effected. There appears little further room for margin expansion in semiconductors. o The opportunities for management to improve profit margins in the Communications Group have silways been present, but this has not happened to date and there is little reason to project any meaningful change in this scenario. In fact, if anything. Communication's margins seem to be declining somewhat on secular basis. o The highly promising Codex Division is also suffering margin declines and the rate of revenue growth is decelerating. o Its automotive business is skewed heavily towards domestic manufacturers. On the positive side, however, we note the following: o A good way of making money in Motorola historically has been to buy the Stock when fundamentals look dull and sell the stock when consensus seems to be warming up to the opportunities for earnings acceleration. It appears that we are much closer to the former situation than the latter right now. 6 iVlotorola is taking a much more conservative stance on the outlook for the semiconductor business over the next twelve months than are many of its competitors. In part, this is due to the fact that the company's large discrete business makes it the first to feel an economic downturn. The conservatism is also a sign of management's desire to avoid the bloodbath that occurred in 1975. If the semiconductor industry does get hit fairly hard in the next six months, Motorola will probably be better prepared than its competition. - 5 -The company has sold two components of its Automotive Group this year, both of which were money losers. While the company will of course deny any intentions of further de-emphasis on the automotive market, any further retrenchments in the future would certainly be viewed very positively from an investment standpoint. We are presently estimating earnings of $5.35 per share for Motorola in 1980, versus $5.21 per share last year, which implies slightly lower earnings in the second half. Next year, however, earnings comparisons appear relatively easy in the communications group, government electronics, automotive, and Codex. It is not hard for us to make a case for $6.10 per share in 1981, although at this time we would view that as the top of a $5.70-6.10 range. The company's management has laid out such a conservative scenario for 1980, that it appears to us that any surprises that occur during the balance of 1980 may be on the upside, which would positively affect expectations for next year. CAPITAL EQUIPMENT We continue to believe that the outlook for Caterpillar Tractor over the next 12 to 18 months is unexciting, but that the ground work is being laid for a strong rebound in earnings beginning in 1982. Caterpillar has filled up its dealer pipeline much more rapidly than we had anticipated in the first half of this year and this fact, coupled with the recession-related decline in retail sales of construction equipment, causes us to project only a 4 percent increase in total revenues this year, which adjusted for price increases would indicate a 6 percent decline in real unit sales. Fully diluted earnings should approximate the strike-depressed results in 1979, or about $5-50 per share fully diluted. We believe that domestic revenues should start to improve by the second half of 1981 and foreign revenues should start accelerating in the fourth quarter of next year, but the turnaround will not come soon enough to result in good full-year comparisons. In total, we expect flat real domestic shipments in 1981, a 5 percent decline in real foreign shipments, and (assuming 10 percent price increases) a 7 percent increase in overall sales. Earnings may improve slightly next year to a $5.50 to $6.00 per share range fully diluted. As noted above, the groundwork is being laid for a strong resurgence in growth beginning in 1982. Caterpillar is about to announce officially its first hydrostatic drive crawler loader, which we mentioned in our last Portfolio Letter. We expect hydrostatic drive to be expanded to cover almost all of Caterpillar's crawler loader and crawler tractor line within the next two years and we believe this could allow Caterpillar to make definite inroads into the market share of its competition, with the probable exception of Deere. In addition, we believe that demand for surface - 6 -coal mining equipment will start to rebound in the second half of 1981 and that 1982 will be a very strong demand year for such products. Caterpillar has one of the largest exposures to the coal mining market, with about 25 percent of its domestic sales potentially affected. Therefore, it appears that many positive factors could Start to affect the company simultaneously. Michael R. Weisberg RECENT NEWSLETTERS OF NOTE WORD PROCESSING Syntfex Announces Office Automation Products The European Market for Word Processing Workstations 07/25/80 07/11/80 PAPER AND FOREST PRODUCTS Final Second Quarter Douglas-Fir Stumpage Bids Show Very Sharp Price Decline 08/11/80 SMALL COMPUTERS A Review of 3270 Emulator Packages Tandy Announces Three New Personal Computers 08/13/80 08/06/80 INSTRUMENTS 1979 ATE Market for Interconnect Verification Analysis 1979 ATE Market for Circuit Board Testing 1979 ATE Market for Semiconductor Testing Oscilloscope Market 08/15/80 08/15/80 08/15/80 07/30/80 (continued on next page) - 7 -RECENT NEWSLETTERS OF NOTE (continued) SEMICONDUCTOR Semiconductor Industry Status Report MOS Microprocessor Shipments 07/25/80 07/08/80 CAPITAL EQUIPMENT Caterpillar Tractor Company Second-Quarter Results and Outlook for 1980 and 1981 08/12/80 TELECOMMUNICATIONS TV Services Forecast to Continue as Largest Factor in Worldwide Broadcast Markets World's Installed Telephones Estimated to be Nearly 600 Million in 1985 08/07/80 08/07/80 COPYING 5 c DUPLICATING AM Multigraphics to Consolidate United Kingdom/ United States Duplicator Manufacturing Xerox Goes Retail Environmental Concerns Regarding Xerox Toners and Cadmium Products • 08/15/80 07/29/80 07/28/80 ELECTRONIC PRINTERS Overview of the North American Market for Electronic Printers 08/11/80 - 8 -'v7 = ^%^i MUH 1 HULIU ECURiTIES, INC. ^ H ^ H I 1 ^ M P ^ Vol. II- No. 6 July 28, 1980 This letter is a condensation of recent Research Newsletters and internal thinking from the industry research groups at DATAQUEST, Inc. Requests for amplification of our thoughts or for specific Newsletters should be directed to the author. A list of recent DATAQUEST Newsletters appears at the end of this letter. COPYING AND DUPLICATING A lot of rumors seem to be in the air regarding Xerox. Speculation seems to center on possible new competitive product introductions at the high end by IBM and Kodak and the increasingly competitive stance of the Japanese manufacturers. Xerox has the only products in the very high end of the copier market (DATAQUEST's Segment 6). The key to the long-term growth of Xerox in the copier business lies in Segment 6, which we expect to grow at a compound rate of between 25 and 30 percent worldwide over the next four years. Some of our competitors are talking about a direct competitive product announcement from IBM, and while this is possible, our sources indicate otherwise. We do expect an enhanced version of the IBM Copier III to be introduced within the next three months. However, this enhanced version should compete in Segment 4 and the lower portion of Segment 5 rather than Segment 6 and should not have any material impact on Xerox. In fact, our placement forecasts for Xerox assume just such an announcement by IBM. A Strong competitive product by IBM at the high end of the market would definitely cause us to reduce our placement numbers for Xerox in Segment 6, but we frankly do not believe that such a product is likely. By 1984 DATAQUEST expects Xerox to still have 90 to 95 percent of the Segment 6 market revenues. Ultimately, we do expect Kodak to introduce a direct competitive product to Xerox in Segment 6, but we do not expect this to happen soon. We believe that the next move for Kodak is down the product line (Segments 3 and 4) not up. If Kodak did introduce a product, the impact on Xerox would be much less significant than an IBM introduction, since Kodak lacks the extensive sales and service organization to make really strong penetration with such a product. Copyright© 28 July 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients. This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. Member, New York Stock Exchange 19055 Prgneridge Avenue / Cupertino, California 95014 / (408) 725-1200 To restate our often expressed opinion about the Japanese, we believe that they presently dominate the entire low end of the market, but that the lack of a sales and service organization will be an important impediment to their moving up the product line into some of Xerox's more lucrative markets. The recent introduction of the Canon NP Color Copier into the middle-range segment of the marketplace should have no reed impact on Xerox. This product has been available in Japan for 7 years and has not been a strong competitive offering. Our stance on Xerox continues to be that in a copier market growing at a long-term rate of about 18 percent, Xerox will grow at a 12-13 percent rate, maintaining share at the high end and losing it at the low end. Our earnings estimates remain at $7.25 per share for this year and $8.45 for 1981. SEMICONDUCTORS Industry conditions are clearly deteriorating, but the situation is not as bad as some would have us believe. The industry book-to-bill ratio, by DATAQUEST estimates, declined to a .83 to .87 range in June, not the .6 to .65 range reported by some. Inventories and back orders are getting cleaned out and only real business is presently being booked. Overpriced devices, principally memory, have seen prices •fall more in line with oosts. These are he«dthy industry developments at this stage in the economy. It is our expectation that book-to-bill ratios in the industry should remain below 1.0 in July and August. By the fall, conditions should stabilize and then begin to improve, with book-to-bill ratios climbing back above 1.0 by year end. In terms of shipments, we presently project a 4 percent sequential decline in third-quarter shipments followed by a 2 percent decline in the fourth quarter of this year, bringing the full year gain in shipments to about 26 percent. Beginning in the first quarter of 1981, some upturn in sequential shipments should occur. We expect U.S. consumption of semiconductors to increase by about 10 percent in 1981, but such an increase is as misleading towards understatement as this year's 26 percent growth is towards overstatement. The important factor is the rate of acceleration and deceleration in orders, and it is presently our posture that industry orders should begin accelerating early next year and gain momentum through 1981. In terms of year-to-year shipment and earnings comparisons, the three most difficult periods should be the fourth quarter of 1980 and the first two quarters of 1981. While the possibility of lower earnings comparisons in some of these quarters is very real, our stance is basically a very positive one: there will be ample evidence of improving order trends in these quarters even though earnings comparisons may be disappointing. At its quarterly analyst's meeting, Intel was understandably cautious about near-term business trends. They made one comment that was very relevant to our positive thesis, namely that unit demand is very strong and does not show signs of softening. As we have stated in the past, unit demand is the key to the industry outlook. If it holds, further price deterioration can be contained. 2 -National Semiconductor is a company we have spoken favorably of in the past and we maintain our positive stance. National has two strong points going for it during a slowdown in industry activity: it is a low- cost producer in general who can fare relatively well when industry conditions tighten up and also it has a relatively large amount of linear and related industrial business where there are fewer competitors and where price competition during slacl< periods is usually somewhat less than for other market areas. The biggest risk area for National in our view remains the computer business. We Should point out two things in this regard however. First, National presently makes several times as much money in its semiconductor operation as it did five years ago. The relative impact of any writeoffs in computers would therefore not be nearly as significant in the total scheme of things at National as the problems in the consumer business were several years ago. Second, the company ran the consumer business very aggressively, trying to become a major factor in the market; it is not adopting the same strategy with computers. Because its aggressiveness is greatly diminished, the risk of downside surprises is diminished as well. We are presently forecasting $3.10 per share for National in its 1981 fiscal year versus $2.58 per share in fiscal 1980. Our estimate conservatively assumes a $10 million operating loss in computers, despite the fact that this business is reportedly running at breakeven now. Our estimate implies little or no earnings growth in the second half of fiscal 1981, with a resumption in earnings growth beginning early in fiscal 1982. INSTRUMENTS It is clear that the rate of order growth in test and measurement (T&M) instruments is slowing, but thus far the deceleration has been very gradual. We are presently forecasting 15 percent growth in T&M industry shipments in 1980, somewhat higher than our 13 percent growth forecast made at the beginning of this year. This shift reflects the fact that the slowing in orders is coming somewhat later than we had anticipated. We would expect total industry order rates to slow in the second half of 1980 and then begin improving early in 1981. Our preliminary projection for 1981 industry revenue growth is 16 percent, buoyed by continued strong growth from military and defense markets and a rebound in demand from communications end markets, which have been relatively lackluster S O far this year. Normally, backlogs are worked down to below average levels after a period of order slowing, but because backlogs were very high entering the present Slowdown, they should be at average levels entering 1981. This better than normal situation will edso aid shipment growth next year. In short, then, we do not presently believe that the T&M market has much economic exposure over the next 12 months. This situation will benefit companies such as Hewlett-Packard, Tektronix, and luke. - 3 Tektronix reported surprisingly good fiscal fourth-quarter results, with incoming orders up 23 percent and some improvement in gross margfins. We believe that new product introductions at Tel IV. Z' M i ^^'-f^ 06/22/80 06/09/80 yn-'Yf'i^ INSTRUMENTS DATAQUEST's Coverage of the ATE Market 07/15/80 SMALL COMPUTERS DATAQUEST Looks at the First-Time Minicomputer User Four-Phase Systems Inc.: Company in Transition Prime Computer Enters Office Information Systems Market Summary of the 1980 DATAQUEST/Mini-Micro Systems Survey 07/17/80 07/02/80 07/01/80 06/18/80 PAPER AND FOREST PRODUCTS Stumpage Bid Prices Decline in Second Quarter Long-range Forecasts of Wood Products and Stumpage Prices and Costs Stumpage Bid Prices Continue to Increase in Pacific Northwest National Forests 07/24/80 06/27/80 06/16/80 WORD PROCESSING Rapid Growth & Change are Forecast for Word Processing in New DATAQUEST Market Statistics XOPD Announces Half-Page Version of the 860 Information Processing System Prime Computer Enters Office Information System Market 06/27/80 06/10/80 06/10/80 -7 -RECENT NEWSLETTERS OF NOTE (continued) CAPITAL EQUIPMENT Outlook for Surface Coal Mining Machinery Notes and Comments on the 1980 Coal Show Farmer Profitability and Farm Equipment Sales Expected to Decline in 1980 1980 First-Quarter Census 06/16/80 06/15/80 06/15/80 06/12/80 ELECTRONIC PRINTERS National Computer Conference 1980 Hannover Fair Report 06/20/80 06/09/80 TELECOMMUNICATIONS Worldwide Market for Telephones Forecast to be 86.5 Million Units in 1985 07/25/80 U.S. PBX Market Forecasted to be $3.64 Billion at End-User Level in 1985 07/18/80 Worldwide Revenues for Telecommunications Services Forecasted to Exceed $200 Billion in 1985 07/16/80 Worldwide Data Communications Service Revenues Forecast to Grow 16% Annually through 1985 07/07/80 8 -- i MM%=. M\^ J l 1 n 1 A Sutjsidiary o5 A.C. Nielsen Co, r 1 ^^1 RESEARCH N C O R P O R A T E D l \ I E \ A ^ S L E T T E •JlfcJ v ^ V U C i V \Ji. F £iU SEMICONDUCTOR INDUSTRY STATUS REPORT SUMMARY Semiconductor demand is reflecting the rapid worsening of the economy in the second quarter. Bookings have softened in the last three months with the June book-to-bill ratio for the U.S. semiconductor market declining to an estimated 0.85. Further weakness is expected in July, August, and September. Second-quarter U.S. consumption of semiconductors was up about 11 percent over the first calendar quarter, but quarter-to-quarter declines are expected in the third and fourth quarter. Despite this expected weakness, U.S. semiconductor consumption in 1980 is expected to be up 26% over 1979. DATAQUEST presently estimates that 1981 will be up about 10% over 1980, reflecting the lack of momentum entering the year. Hiring in the semiconductor industry has become much more selective. There have been a few layoffs by both semiconductor manufacturers and distributors, but most companies appear to be reluctant to reduce employment. U.S. SEMICONDUCTOR MANUFACTURERS In our Industry Update in April, we noted that a demand slowdown was imminent. That order weakness has now occurred. DATAQUEST has recently polled many of the U.S. semiconductor manufacturers and users regarding the current and future outlook. The integrated circuit manufacturers still see relatively strong business. Unit demand is still increasing, although at a slower rate. In most areas, excluding some memory, prices are not falling precipitously. MOS memory and microprocessor revenues in the third and fourth quarters are now projected lower than we expected six months ago. MOS memory is experiencing price softness, but still relatively good unit volume. In 1980 DATAQUEST expects worldwide consumption of 16K dynamic RAMs to be an estimated 185 million units, up from 70 million units in 1979. Additionally, worldwide consumption of microprocessors is expected to exceed 150 million units, up from 75 million units in 1979. This strong unit growth should keep the quarter-to-quarter MOS revenue growth positive despite the price weakness. The bipolar PROM and RAM business has been extremely strong with lead times still greater than 15 weeks. Demand is especially strong for some of the smaller volume, older components, due to discontinuation by some suppliers. We see strong demand and firm pricing holding in bipolar PROMs throughout 1980, with no near-term shortening of lead times. Copyright © 25 July 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released bv responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided lo us in confidence by our clients This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities This firm and its parent andfor their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO Low-power Schottky (LS) has become more available as Texas Instruments and others have increased their output. TI has taken LS off allocation, but this move has not been followed by all suppliers. Standard TTL has become more difficult to procure as fewer suppliers now remain and TI still has standard TTL on allocation. Discretes consumption has been soft for several quarters, since it is more Strongly tied to the consumer business. The first softening in discretes started over a year ago when the appliance industry and consumer electronics turned soft in the second quarter of 1979. DATAQUEST estimates that most discrete manufacturers are experiencing book-toHaill ratios below 0.8 at this time. During June a few U.S. semiconductor companies began to experience more product returns than in previous months. It is too early to determine if this phenomenon will spread, but it is something that will be monitored carefully in the coming weeks. INDUSTRY CAPACITY There is no doubt that some suppliers have excess capacity in some product areas. This is especially true in MOB memory as wafer starts have increased, yields have improved, and IBM has temporarily pulled out of the merchant market for 16K RAMs. AS a result of the excess of supply over demand, some suppliers have begun to de-emphasize this product as they shift their focus to the 64K dynamic RAM. DATAQUEST has noted only minor reductions in capital spending plans by the merchant market semiconductor manufacturers. However, Motorola has reduced its semiconductor capital spending from $200 million to about $160 million this year, representing a 20 percent reduction. The cancellation of the planned Vancouver, Washington, facility by National is expected to delay some purchases. Elsewhere we have seen capital spending cuts ranging from 5 to 15 percent. Companies are continuing the acquisition of land and construction of buildings because these are long lead items whose impact is more than two years out. The erratic behavior of the capital equipment business is evidenced by the fact that requisitions have been put on hold by certain manufacturers. In some cases this hold has been released once management has had time to reevaluate plans. Generally, captive manufacturers and merchant manufacturers acquired by larger corporations (e.g., Fairchild, Mostek) have retained their capital spending programs. SUPPLIERS TO THE SEMICONDUCTOR INDUSTRY DATAQUEST has learned that the suppliers of CERDIP and side-brazed ceramic packages have recently experienced a significant reduction in their business. In the first quarter of 1980, chemical suppliers for the industry experienced a decline in orders but they are now back to December's rate. Various other materials, such as mask blanks have seen order reductions. DATAQUEST believes this slowdown in business is partially due to a paring of incoming materials inventory by the semiconductor manufacturers. Reductions are more significant in the Eastern United States because the companies located in that area manufacture a higher proportion of discrete semiconductors. Silicon orders have not been impacted, and we believe industry wafer starts have not declined. - 2 The suppliers of capital equipment have seen business continuing strong, but somewhat uneven. Large ticket items ranging upwards from $200,000 are experiencing strong business. Orders for DSW and projection aligners continue at a very strong pace, but the contact aligner msirket has softened. Orders for small ticket items, such as $10,000 to $20,000 testers, have declined somewhat. Delivery of major items continues at earlier projected rates because of the long lead times. It appears that the delivery of less expensive items with shorter lead times is being postponed one or two quarters by semiconductor manufacturers to avoid spending the money in 1980 and to allow more time to watch developments in the second half of the year. Orders for test equipment being shipped into the integrated circuit manufacturers have remained quite strong, but demand for testers going into the discrete device manufacturers has softened. DISTRIBUTION DATAQUEST has polled several of the major distributors of semiconductors and has found that book-to-bill ratios in April, May, and June have been quite soft with book-to-bills as low as 0.85. Shipments have been affected by customers purging their backlog and reducing incoming inventory. For example, DATAQUEST has learned that many mainframe and minicomputer companies have cut their incoming inventory from about twelve weeks down to less than four weeks as products have become much rhore readily available. Distributors have found that the computer segment is still strong with peripherals becoming a little soft. Telecommunications and military have been good, but the consumer sector has been very soft. Daniel L. Klesken Frederick L. Zieber TCIS Code: Newsletters WORLDWIDE REVENUES FOR TELECOIMMUNICATIONS SERVICES FORECASTED TO EXCEED $200 BILLION IN 1985 SUMIMARY This Newsletter provides a brief overview of the material presented in Telecommunication Industry Service, Section 1.2.1 on worldwide telecommunication service revenues. DATAQUEST's fwecasts for total WOTldwide revenues are $138.6 billion in 1980, rising to $217.6 billion in 1985 at a compoimd annual growth rate of 9.4 percent. Our estimates for the three major regions covered are as foUows: • North American revenues should go from $58.9 billion in 1980 to $94.6 bUlion in 1985, at a compound annual growth rate of 9.9 percent. • Western European growth should go from $50.1 billion in 1980 to $73.7 billion in 1985, at a compound annual growth rate of 8.0 percent. • Growth toe the Rest of the World should go from $29.6 billion in 1980 to $49.3 bUlion in 1985 at a compound annual growth rate of 10.7 percent. WORLDWIDE REVENUES AND GROWTH FACTORS DATAQUEST's estimates for worldwide revenues f c M telecommunications services fw the years 1980 and 1985 are shown in Figure 1. These figures are basically fa voice communication and do not include revenues f O T data communication (covered in Telecommimication Industry Service, Section 1.2.2), telex, telegraph, or facsimile transmission services. Also excluded from our estimates are non-communications revenues, such as those for directory advertising which in North America, for example, we expect to exceed $3 billion in 1980. However, the figures do include revenues for image transmission —television and video telephone — where these transmissions are by common carrier service. Such revenues amount to only about 1 percent of the total. • Copyright © 16 July 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO Figure 1 ESTIMATED WORLDWIDE REVENUES FOR TELECOMMUNICATIONS SERVICES (Billions of Dollars) 1980 Total: $138.6 Billion 1985 Total: S217.6 Billion Worldwide Average Annual Growth Rate: 9.4% Source: DATAQUEST, Inc. • - 2 -The estimated total worldwide revenues of $138.6 billion in 1980 and $217.6 billion in 1985 mal. 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^ ^ ^ H H U > K) t> U tn a > i o p K } M a i < £ > i-»h-»t-i O I O M a s - J c n l r ) o ^ o - p ' • j M r o o lo 4^ ^ - J O l o ^ ^ - ^ P i - c n ^ 4 = o o » - a » M O u > K3m c u t n o t- J - ^ O J O ^ ^ M i - ^ o o o o o c n p o i - o o C 4 o o e n 0 3 0 0 t n o o o p ( j i o o o L n o o o o o u t c n ( n p O L n N 3 0 0 C ; i u i u i P o v i c > o ^ £ = c n o u i o P o a c t i o < p p P - - J o o C o c n P P O o o o o o o C o o c n ii s a ^ ? s : > > t o g C O •fl to gl I t) ^ 1 3.^ oj tnro I- i-i-» i - t j i - » a i t - w u i t - » r o » o r H i - » . | r u or>io i-t-» K) - » I O a> to - J t D h ^ O O O H ^ C P t - ^ ( 0 » - K 3 d O t O O l r O t n O O r O O ) K 3 l - I O P M - J l - ^ l D r O I O I O O D O l - ^ O - i - J P l - ^ ^ - ^ - - ) t O U I t - ^ - P t O - ^ t- t - A t i J - J ^ C A > I O ( / 1 0 0 C O ^ O ( n O O I O O O t / 1 t / 1 t n < J 1 C ^ O P t 7 ) O O P o O O L ^ O t n O O O C Q O O t n O O O ^ ( J t C » C o t n t U t n O l / 1 t / l ( n O O t i 1 i O P U 1 0 0 0 V I G D O D l J 1 t n - - J O O U t O O t / l O l O C o O O U 1 0 ( } t ^ t ^ ID 1- ( J M h h - 4r M O U t- t-^t- • - ' ^ • H ' H ' I - ' lO | - t _ » u r o ^ ^ t - ^ t - ^ ' x l 0 > t - ' t - 0 l - t - » r O a» > W .p- to 01 O O O H - > l l - l - » ^ K > W O t O O ^ t n o i O O i O - J i-k j r t - » M O - . J h r O I - > - p i D o a ^ < « > i O O M O i O O O 0 0 i - f O » O t n O t O O t i > - P O C n M t d ^ ' O N J - J O D . p o C o o t n t n t / ) O O O c n 0 0 o o i n i / ) 0 0 t / i O ) C q 0 3 o o o o o v i a i C o < ^ o O ] O t n t n o t i > o o C i > ( n o u i O c n o O P O t n t n o o o o o i O t J i i o o P > ^ t n O O O O O C Q u i t n o o o O ) O O t n to t-^ tn UJ ^ tn t -» ^ » - r o 4^ » - » » - » ro c > » - » o o » - c j lOiD-P io4^XJcjcDi-»ui - j m t n u > - . j i o . F t n . p a J . p p u i i s ) r o - > 3 t ^ - P O ) > . » i - » ( 7 i c o »-»? » o o -«i . p O D o o - P m t n t - ^ ~ ~ ] t n a ) c i i o u > o i o c » c n o o - ~ j )- a>(T>u>p o i o i D i - a t < » . ^ H > - o o o t - ^ a > o c i O a > < n » 0 ( T > t O L n t o o o 0 . p ( n » ' C D -P t n u i K 3 I O O O D • > - i o & 3 0 v i ( ^ o P o u o L n t n o D O o a > o o o C o C o C o o o t n o o o L / i 0 3 t > i o C o u i C A J M O u o o u p i i > o u i o u T P t n O c » r o ( n o p o o i n P c n t n t n a > o o u i o o c n C o tn i - » O t n h 4^ro l O o D i - ' a J t - lo ^ H u t o t n f o i o i o . F t - ' i - ^ o j i o ^-^^ - j I»H t- to tn Hro o o o ^ i - i t o . p K > . p - - J O a i o o - p M t o o r o ^ to t n t - ^ t - o t / i r o M K > t - ^ o ~ - 3 c < J i - ^ t n t n o o > o ^ O t n o o t - ' ^ s ^ t > > < a ^ o b > o t n b i - P O ) t- J = . P a ) ou 152" QTR 180 225 2200 70 2700 3300 1400 11000 21075 19.1 SOURCE: DATAQUEST. INC. JUNE 1980 TABLE 3 ESTIMATED WORLDWIDE SHIPMENTS OF B-BIT MICROCOMPUTERS (THOUSANDS OF UNITS) COMPANY AMD FAIRCHILD GENERAL INSTRUMENT INTEL MOSTEK MOTOROLA NACTIONAL NEC PHILIPS/MJLLARD ROCKWELL SGS ATES SIGNETICS ZILOG TOTAL MICWPROCESSORS PERCENT CHANGE FROM PRWIOUS QUARTER PRQmTS 8048 3870 PIC-1650 8048/8021 8049/8022 8748 3870 6801/6803 6805 3870 8048 8049 8050 8070 8048/8049 8048 6500/1 3870 8048 Z8 1978 TOTAL 0 23 450 480 10 30 350 0 0 70 0 0 0 0 15 0 0 S s 0 1428 1ST QTR 0 40 300 200 20 SO 260 0 0 80 0 0 0 0 25 0 0 5 15 0 995 53.1 2ND QTR S 50 950 400 40 75 300 S 0 125 0 0 0 0 160 0 S 10 30 0 2140 115.1 — 1979-3RD sm 3 120 1250 600 70 75 425 3 S 125 0 S 0 0 350 0 3 15 60 0 3099 44.8 4ra QTR 20 300 1600 1000 100 100 485 10 3 170 5 10 S 5 450 S 5 20 75 S 4348 40.3 1979 TOTAL 23 510 4100 2200 230 300 1470 13 3 500 S 10 S S 985 S 8 50 180 5 10582 1980 1ST QTR 5 345 1700 1300 150 125 530 15 10 150 5 25 5 5 810 2 8 20 60 S S260 21.0 SOURCE: DATAQUEST. INC. JUNE 1980 - 6 TABLE 4 ESTIMATED WORLEWIDE SHIPMENTS OF i^-BIT MICROPROCESSORS {THOUSANDS OF UNITS) CQ^IPANY AMI HITACHI INTEL MATSUSHITA MOTOROLA NATIONAL NEC ROCKWELL TEXAS INSTl TOTAL MIC {PANASONIC) iUMENTS :ROPROCESSORS PERCENT CHANGE FROM PREVIOUS QUARTER PRODUCTS 52000 HMCS-W 4004 MNIWO 141000 COPS 4004 IMP COM-4 PPS-4 TMS 1000 1978 roT^Ij 29 410 159 N/A 20 2325 130 80 1500 2275 9400 16328 1ST om 50 130 35 500 30 900 30 18 1100 600 4200 7593 37.3 2ND om 300 150 32 800 75 1100 26 15 1300 1100 5400 10298 35.6 3RD om 675 175 28 1400 90 1500 20 •15 2300 1100 7500 14803 43.7 42'ff om 400 200 25 1700 90 2100 15 15 3100 1100 9000 17745 19.9 1979 •JIOTAL 1425 655 120 4400 285 5600 91 63 7800 3900 26100 50439 laou 1ST QTR 180 225 20 2200 70 2700 12 14 3300 1400 11000 21121 19.0 SOURCE: DATAQUEST, INC. JUNE 1980 -7 IS) »-3 ai '•^ tntQ a :s " = > >« as c-i a cq H toE^a j-j ra Co ? ^ ta Co :t. 1.3 i.a 1 S i to to 3 Co Co ^a 82 i t) E; e^ E I f: 5§ coco m ••a !»! B i trt H ss) aj Ci ^Si:iS •q 0} ru cq C-i M 2 Sl to at a> H t i I •^ eg I ^ pl I oi ^ Q C ^ c 7 t S 0 1 M o o ^ J O o o o c l J ^ 4 0 l O l l - k o o ^ J ^ a o o a > a l 0 3 C D C c a D a ) a > o > o l ( n o > o > o > b > ^ 4 ^ a > a > a a o D C D O o c D H » a n • ^ a > a t c ^ C D O D o i 3 2 C L n o o o a > o o o o a Q u i i n O D o a i c D o o o c ^ o o o o o o o a > a > O D a > a > c D O c > o D i n O ' ^ o o o o a D O o > - i c D a o a i a ) 0 9 a D o s a > o o o O o C 0 O O 4 r t 7 i 0 0 0 0 - 3 O O O O - P t / » O 0 D . P 0 ) " ^ - J c n - P ^ a > - J O O O O O O O O 0 0 ' f ? . P 4 ? 0 D O O O ^ O O - > 4 O O O O - P O O O D o o r o o o o c n o o o o ^ o o o o u i C D o ^ o O i D o o o o m t / i r o H ^ o o o c / i o o < D a » o c D f o o i i o o o l o o t o o a o c n o f « a ^ -. • ^ : ^ ' g : ^ • ^ ' ^ • > . - ^ : ^ i - » ^ ^ -.^ >» t-^ 00 o>0) t s o D o i a i O) Co K3 I 00 I (ji t-^Ol •- t n W W W OJ ( - » W 1 W I O t - K > W . p - J I - • F l O O l t-» .p (j\ K 3 u a ) K > N> K 9 u i w i - k a D O o w - . j u i t - ^ i o w w w O O c n c n O N i < J 3 ( / > O O C o C o O c n u i O O O O ( / > t n t n O O O O u i O O O O O O O O O U i O O O O C n w a i O O C i 3 0 U O O O O O O L n a ) H » i -' •- t-^ l - » - M r O I -» l - K 3 » - W t -» »- ID u o t - ^ i - - P cni-« o o m i o o i o tnoo ui ^ o i o i D c n < ^ u i t a o a > ^ J i - ^ c n o w - t ^ t n w H W ( j i o o r o o o v i u i o c j > > c n v i o o u i o o o u t L n c n o o o o o o o C o o o o c f i o o o c n c n o o o o o i o o o O i c n o o o o o c q u i O u i t j ) N3 (-^ h l - M Ht- K 3 t - W t - H I O ^ M t-(D tn r o K > t - w a j -!-»»- a>i-» ao-^cni£>.p: -^jro ^ - 4 o r o r o ^ o > - J 4 ? o o i - ^ M o u i o o o ( j i o - o o C o o o u » O i o w o o o u » o o o O o o o t n m i o o o c o t n o o u » ' ^ ' ^ ' " ' ^ ' ^ ' - ' ' ' ' - ' ^ — lO U ^ 0 > - J J = ^ O O I - ^ I - O U 1 W t / ) 0 H^h-kU - P K ) O O m O O O C D - P O O C O U i O O O O O O C o O C n cj w - H M W - ^ t - » lOH f o i o ^ i - t - » w cnro i-»ro h»o w -^ i-a>t-»o>t- iot-K> o»io a > M O » o o » M I O - J H » i o r o » o o o o » - J O - H » t - ' K > t n H » . p i o - a t-»t-»aj - j w ( j i O O o a o i o o O c n i / i c n u i W O u i O O O O O u i O O O C Q O o c n O o O j c n w u i t / t L n i / t o O i n o O O i n o o c n o m o O i n O i o o o w t / i c n eg i S S Dg m ^n cs en O i - » - J t - » - ' - P l O W 0> O C o O U i O O d O O O O U i C n O H I- l_k l ^ . p l - k t . A K 3 l - k W f 0 . p l - k | - k W M t - ^ O h t - ^ O ) O l i o o> . p u t m o ^ •-> £ ^ M t o t - k O a o - J u u > c n o o o o D M N } m o u . p o o > u i C o O i o o o o u i C o C o o C o O o o u m o t / i u i o o o o o o o o i o r o o o o o o o O ) H^ W . p K» . ^ m Ut O O O O U i K> 4? lO OJ U) ^ o fD qt ^ H» |_» ^ j • . < J . P U i . P W O W r O K 3 < - J M o t - ' ^ i - ^ ^ o o a o w o a o i ^ l-» r- w. > o> ro o 4? ui t-k I r- ro o ^ tn u lo o 00 -J o o O ' P b o u i t - ^ ' ^ v i o o w i b c n o f D O t - J - O D O I O i O M a t ' ^ i - ^ ^ o o i > o c > ' o a > o > o > i o o . P u i H ' ( D • p t n u K ^ O o o o 0 3 0 o o w O L n u i o o o o < P o o C o C a o o ( n o c n C Q C o o C Q u > o o w o w o o c n o c j i u i o o o o i n o ) u i o a i o o i n C o u i o c n w o o t-» i- tri t n h lO r O 0 D t - » l - k M - W W t / i l O I O J ? l - » - w M l - ' - J W H M c/i o m i - ^ i o - P t o - p -Jcjt a o 4 r i - w - 4 fo ( / l U i r o H ^ r o t - ^ o w i - ' u i u t o i o u i o o M w ^ o u t u . p t n »-k.p4r o i w o C / : ] O o o o o L n o o o o o o o o r o m o o o i / > u i C o i / < m C Q O O i n o u i u i o o L n u i O o c n o o o o t n i / ( O . P O L n ( D i o o o O c j i u i o c n a ^ TABLE 5 ESTIMATED WORLDWIDE SHIPMENTS OF 12-BIT MICROPROCESSORS ..-•.. - {THOUSANDS OF UNITS) ^.' . COMPANY HARRIS INTERSIL TOTAL MICROPROCESSORS PRODUCTS 6100 6100 1978 TOTA^ 22 15 152 om 7 1 + 2ND O.TR 1 4 —1979--ZRD Q.TR 7 5 i^TH om 7 5 1979 XOTAL 28 18 1980 152" QU 8 5 37 11 11 12 12 45 13 PERCENT CHANGE FROM PREVIOUS QUARTER 0.0 0.0 9.1 0.0 8.3 SOURCE'. DATAQUEST, INC. JUNE 1980 TABLE 7 ESTIMATED WORLDWIDE SHIPMENTS OF 16-BIT MICROPROCESSORS {THOUSANDS OF UNHS) COMPANY AMD AMI GENERAL INSTRUMENT INTEL MOTOROLA NATIONAL NEC TEXAS INSTRUMENTS ZILOG PRODUCTS Z8000 9900 CP-1600 8086 68000 PACE 768 TMS 9900 TMS 9940 Z8000 1978 TOTAL 0 0 60 24 0 86 0 185 0 0 1ST QTR 0 0 15 13 0 25 0 68 0 0 2ND QTR 0 0 20 15 0 25 0 80 0 1 --1979--ZRD QTR 0 S 20 19 S 25 0 . 92 S 2 ^TH QTR S 5 25 25 3 25 S 105 5 4 1979 TOTAL S 5 80 72 3 100 S 345 5 7 1980 1ST QTR 1 5 30 32 4 22 5 120 10 7 TOTAL MICROPROCESSORS 355 121 141 158 197 617 231 PERCENT CHANGE FROM PREVIOUS QUARTER 14.2 16.5 12.1 24.7 17.3 SOURCE: DATAQUEST, INC. JUNE 1980 - 9 -•#- '.'k^ Figure 2 ESTIMATED WORLDWIDE SHIPMENTS OF MULTISOURCED MICROPROCESSORS I (0 •o e IB (0 3 O <0 ^M c « E o. !
c (0 I 2,400 2,200 2,000 1,800 -1 , 2 0 0 1 , 0 0 0 800 600-400 200 8048 3870 ,Z80 ' 6500 and 6500n .
. 8085 6800 —•• 6802 and 6808 '•F8 j _ 1st Qtr 2nd Qtr 3rd Qtr 4th Qtr 1st Qtr 1979 1979 1979 1979 1980 Source: DATAQUEST, Inc. 10-- ' .^ SS "^S S ^ S S^ ^F TBtS S ^^^ RESEARCH ;;;>...i ASubsidiarvofA.C. Nielsen Co. ^ IIMCOR PC RATED I ^ I ^ H W ^ S ^ B ^ M I 1 ^ H F 4 SIS Code: Vol. HI, 9 THE WESTERN EUROPEAN SEMICONDUCTOR MARKET SUMMARY The Western European market for semiconductors was an estimated $2.9 billion in 1979, up about 26 percent from $2.3 billion in 1978. In 1980 the market is forecast to grow about 15 percent to an estimated $3.4 biUion. European consumption of integrated circuits should grow about 22 percent from $1.6 billion in 1979 to $1.9 biUion, and total consumption of discrete devices should grow about 6 percent from $1.3 billion in 1979 to $1.4 billion in 1980. The European semiconductor market is expected to experience a strong demand from the computer and industrial segments, but a weak demand from the consumer segment. Excess inventory of color television sets as well as a softening of the European economy are leading to reduced consumer electronics consumption. The 1980 semiconductor consumption in France is expected to grow about 26 percent to $646 million, up from an estimated $510 million in 1979. In West Germany 1980 semiconductor consumption is estimated up 20 percent to about $1,237 miUion compared with $1,031 million in 1979. The United Kingdom's 1980 semiconductor consumption is estimated up 18 percent to about $572 million. WESTERN EUROPEAN SEMICONDUCTOR CONSUMPTION H Table 1 presents DATAQUEST's estimates of semiconductor consumption in Western Europe. Total European semiconductor consumption in 1980 is estimated at $3.4 billion, up about 15 percent from 1979 levels. Total IC consumption is estimated at $1.93 biUion, up about 22 percent, whereas discretes are up about 7 percent to $1.29 billion, and optoelectronic components are is up about 26 percent to $195 million. The year-to-year growth of semiconductor consumption in various countries depends greatly upon the currency valuation used to express the growth. Table 2 compares the years 1978 and 1979 for the United States, France, Germany, Japan, and the United Kingdom. First the year-to-year growth is expressed as a percent change in local currency, and then it is expressed as a percent change in U.S. dollars where the local currency was converted to U.S. doUars at the exchange rate of the given year. Copyright © 22 June 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation aniJ analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO Table 1 ESTIMATED WESTERN EUROPEAN SEMICONDUCTOR CONSUMPTION (Millions of Dollars) 1977 1978 1979 1980 Total Semiconductor Total IC Bipolar Digital MOS Linear Total Discrete Transistor Diode Thyristor Other $1,819 $ 830 $ 259 $ 278 $ 293 $ 907 $ 453 $ 327 $ 99 $ 28 $2,340 $1,166 $ 371 $ 428 $ 367 $1,059 $ 485 $ 422 $ 113 $ 39 $2,940 $1,578 $ 496 $ 612 $ 470 $1,207 $ 532 $ 510 $ 121 $ 44 $3,414 $1,930 $ 587 $ 763 $ 580 $1,289 $ 570 $ 543 $ 130 $ 46 Optoelectronic 62 $ 115 $ 155 $ 195 Source: DATAQUEST, Inc. June 1980 # - 2 -Table 2 EFFECT OF CURRENCY VALUATION ON SEMICONDUCTOR CONSUMPTION GROWTH RATES Country United States France Germany Japan United Kingdom Country United States France Germany Japan United Kingdom Currency (in Millions) U.S. Dollars French Francs Deutsche Marks Yen Pounds Currency (in Millions) U.S. Dollars U.S. Dollars U.S. Dollars U.S. Dollars U.S. Dollars Exchange Rate (Foreign currency units France (Francs) Germany (Deutsche Marks) Japan (Yen) United Kingdom (Pounds) 1978 3,323 1,683 1,663 512,048 195 1978 3,323 379 840 2,487 375 per U.S. Dollar) 1978 4.44 1.98 205.89 0.52 1979 4,625 2,162 1,876 592,305 228 1979 4,625 510 1,031 2,676 485 1979 4.24 1.82 221.34 0.47 Source: Percent Increase in Local Currency 39. 28. 12. 15, 16. ,2% ,4% .8% .7% .9% Percent Increase in U.S. Dollars 39, 34, 22, 7, 29, .2% .6% .7% .6% . 3 % DATAQUEST, Inc. June 1980 Between 1978 and 1979, the currencies of France, Germany, and the United Kingdom strengthened against the dollar (i.e., it took fewer local currency units to buy $1.00) and, hence, the percent change in 1979 expressed in the local currency is lower than the percent change expressed in doUars. In West Germany and the United Kingdom, the growth rate of semiconductor consumption expressed in the local currency was a little more than half the growth rate expressed in doUars. Tlierefore, to a company conducting business in dollars, the market in West Germany or the United Kingdom appeared to be much better than to a company conducting business in the local currency. In Japan, tlie yen weakened against the dollar, hence the percent change expressed in yen was higlier than the percent change expressed in dollars. In generating Table 1, every attempt was made to look first at the consumption expressed in local currency and then to convert it to U.S. dollars. All percentage changes expressed in this Newsletter were calculated using values in U.S. dollars unless otherwise stated. ESTIMATED EUROPEAN SEMICONDUCTOR CONSUMPTION BY COUNTRY Western Europe cannot easily be treated as a single economic entity. The different nations, differing nationalities, customs, and political leanings affect each country differently. In the following paragraphs, we present estimates of European semiconductor consumption by country (Table 3) as well as a discussion of GNP growth for the individual Western European countries (Table 4). Table 3 ESTIMATED EUROPEAN SEMICONDUCTOR CONSUMPTION BY COUNTRY (Millions of Dollars) 1978 1979 Country West Germany France United Kingdom Italy Sweden Netherlands Switzerland Spain Belgium Austria Denmark Finland Norway Portugal Ireland Semiconductor Consumption $ 840 379 375 220 98 84 77 56 54 37 35 28 27 18 12 Percent of Total 35.8% 16.2 16.0 9.4 4.2 3.6 3.3 2.4 2.3 1.6 1.5 1.2 1.2 0.8 0.5 Semiconductor Consumption $1 ,031 510 485 295 115 98 85 61 62 50 42 35 34 22 15 Percent of Total 35.0% 17.4 16.5 10.0 3.8 3.3 2.9 2.2 2.1 1.7 1.4 1.2 1.2 0.8 0.5% Total $2,340 100.0% $2,940 100.0% Source: DATAQUEST, Inc. June 1980 - 4 -Table 4 includes a composite number for GNP growth in Western Europe. It Shows annualized GNP growth for 1980 estimated to be 2.7 percent, down slightly from estimated growth of 2.9 percent in 1979. This compares favorably with estimated decline in the U.S. GNP of 1 percent in 1980 and increase of 2.3 percent in 1979. Table 4 ESTIMATED GROSS NATIONAL PRODUCT GROWTH (Percent Increase Over Preceding Year) European Countries Austria Belgium Denmark France Italy Netherlands Norway Portugal Spain Sweden Switzerland United Kingdom West Germany All of Western Europe United States Japan Estimated Growth 1978 1.5% 2.2% 2.0% 4.7% 2.5% 2.0% 3.0% 3.3% 2.0% 2.2% 1.0% 3.2% 3.3% 2.8% 5.0% 8.6% Estimated Growth 1979 5.0% 3.2% 2.0% 3.2% 3.7% 3.1% 3.0% 3.0% 1.0% 4.2% 1.5% 1.0% 4.7% 2.9% 2.3% 6.1% Source: Estimated Growth 1980 2.2% 2.0% (1.0%) 1.5% 0.5% 2.5% 3.8% 3.7% 0.5% 3.0% 3.0% (1.5%) 2.5% 2.7% (1.0%) 3.2% DATAQUEST, Inc June 1980 - 5 West Germany After growing almost 23 percent in 1979 to $1,031 million, West German consumption of semiconductors is expected to grow about 20 percent to an estimated $1,237 million in 1980. Computers and telecommunications are the major elements of this semiconductor consumption growth as the consumer segment is expected to be weak in 1980. GNP growth in West Germany in 1980 is estimated to be 2.5 percent, down markedly from 1979 growth of 4.7 percent. The balance of payments surplus decreased sharply in the first quarter of 1980 and the Bundesbank's efforts to control the growth in the money supply could result in increased unemployment. Consumer prices are expected to increase by 6.3 percent in 1980 after very slow growth of 3.7 percent in 1979. France Semiconductor consumption in France during 1980 is expected to grow about 26 percent to an estimated $646 million, up from $510 million in 1979. Just as in West Germany, the fastest growing markets in France are expected to be the computer and communications segments. The French GNP grew by 3.2 percent in 1979, but in 1980 the increase is expected to be only about 1.5 percent. The inflation rate in 1980 is expected to be about 15 percent, up from an estimated 11.5 percent inflation rate in 1979. United Kingdom Total semiconductor consumption in the United Kingdom in 1979 was an estimated $485 million, up from an estimated $375 million in 1978. In 1980 this total is expected to increase about 18 percent to an estimated $572 million. The outlook for semiconductor consumption in the United Kindom is still reasonably good in spite of the fact that the United Kingdom is facing a period of sharp recession. Mrs. Thatcher's monetary policies do not appear to be working and potentially high wage inflation is still a serious problem. The consumer price index is expected to increase by 16.5 percent in 1980, which is up from an increase of 13.4 percent in 1979. The GNP is expected to decline by at least 1.5 percent in 1980 compared with 1979. Benelux Semiconductor consumption in Belgium and the Netherlands, is somewhat moderate compared with France and West Germany. In 1979 Belgium consumed an estimated $62 million in semiconductors while the Netherlands consumed an estimated $98 miUion. Belgium and the Netherlands are expected to achieve moderate economic growth in 1980 of 2.0 percent and 2.5 percent, respectively. Belgium depends to a large degree on its exports of steel for its income, so a downturn in the world economy is likely to affect Belgium adversely. - 6 Scandinavia Sweden was the largest user of semiconductors in Scandinavia, consuming $115 miUion in 1979. Denmarl< and Norway consumed $42 million and $34 miUion respectively in 1979. The economies in the Scandinavian countries are generally expected to grow more slowly this year than in 1979. Sweden's GNP is expected to grow only by 3 percent compared with 4.2 percent in 1979. A decline of 1 percent is predicted for the Danish economy since Denmark as well as Sweden is adversely affected by the need to import oil. North Sea oil makes Norway a net exporter of oil and this, combined with the relaxation of the austerity measures in effect in 1979, should produce a growth in GNP Of 3.8 percent in 1980. Central and Southern Europe The countries of Austria, Italy, Portugal, Spain, and Switzerland are included in this region. Among these, Italy has the largest semiconductor consumption estimated at $295 million in 1979. Each of the other countries consumed less than $100 million during 1979. Austria's GNP grew by 5 percent in 1979 making it one of the fastest growing countries in Europe in that year, but a more modest growtli of 2.2 percent is forecast for 1980. Switzerland's GNP grew by only 1.5 percent in 1979, but a liigher growth rate of 3.0 percent is expected for 1980. Italy achieved an increase of 3.7 percent growth in 1979. However, the worsening economic situation will probably result in growth of less than 1 percent in 1980. Spain, witli its serious problems of unemployment and inflation, is expecting a 1980 GNP growth of less than 1 percent, whereas Portugal's GNP is expected to increase an estimated 3.7 percent, up from 3 percent growth in 1979. THE SEMICONDUCTOR INDUSTRY IN WESTERN EUROPE Joint Ventures and Government Participation In tJie last three years, the governments of the major Western European countries have come to realize the importance of the semiconductor industry to their economies. Additionally, European industry has recognized the importance of becom-ing more self-sufficient in integrated circuits. As a result of this awareness, a number of joint ventures and government-funded development programs have been establislied. Some of these are described briefly in the following paragraphs. - 7 United Kingdom Britain's major entry into the integrated circuits arena is INMOS. Partly funded by the National Enterprise Board (NEB), it has a design facility in Bristol, England, and a production facility in Colorado Springs, CO. The initial products of INMOS will be a 16K static MOS RAM and a 64K dynamic MOS RAM which are to be followed by microprocessor products. Since the founding of INMOS in 1978, tliere has been a change of government in Britain and with it a change in the political climate. The Conservative Government of Margaret Thatcher has been selectively disposing of NEB holdings since it took office. Although the rationale for funding INMOS was the establishment of a British presence in the integrated circuits field, the suitability of government involvement in an entrepreneurial role in such a fast-moving, unpredictable industry has been questioned. The possibility of a link between General Electric Company (GEC) (Britain) and INMOS was discussed but GEC has now decided against this. Other private investors are apparently considering INMOS at present. The Government has stiU not given INMOS the second $50 miUion grant that was expected. GEC is also involved in a joint venture with Fairchild to build a semiconductor plant in Neston, Chesliire. Since the agreement was made, Fairchild has been acquired by Schlumberger of France, but the plant is going ahead on schedule according to GEC. The British Government has also made substantial investments in microprocessor applications funding, specifically with the Microprocessor Applications Project (MAP). Under this project, companies can obtain financial support from the Government for the investigation and application of microprocessors to their products. West Germany The West German government gives matching funds to a number of semicon-ductor projects tlirough the Ministry for Research and Technology. It is giving major support to VLSI research; AEG-Telefunken, Siemens, and Valvo are the major companies involved in this area. Several German companies have established connections with American semicon-ductor companies. Siemens purchased Litronix as well as Microwave Semiconductor and Sitronix (formerly FMC); it also has a minority holding in Advanced Micro Devices (AMD). Siemens second-sources the Intel 8080 and 8085 microprocessors. Robert Bosch has an interest in American Microsystems. France In 1977 the French government acted to establish a French semiconductor industry. The plans included $200 million of government subsidies and the encourage-ment of links between French and American semiconductor companies. In April 1979 National Semiconductor and Saint-Gobain-Pont-a-Mousson agreed to establish a joint MOS manufacturing subsidiary known as Eurotechnique. National Semiconductor has a 49 percent holding in the company and is mainly contributing technological information. Funding for the venture is coming from Saint-Gobain and from the French government's IC program. - 8 -The Matra Group is building a $40 miUion fabrication facility in Nantes, France, in cooperation with Harris Semiconductor of Melbourne, Florida. The facility will manufacture CMOS circuits and plans to start shipping products in 1981. EFCIS, a joint venture between Thomson-CSF and the French atomic energy authority, currently produces mainly custom MOS circuits but is planning to expand its line of Standard NMOS circuits and hopes to double its sales and place more emphasis on standard products by 1982. Thomson-CSF and EFCIS also made a technology transfer and seeond-souree agreement with Motorola in November 1978. Italy Italy has developed an overall electronics plan which includes support for the semiconductor industry. SGS-ATES is the major recipient of this support. They manufacture linear and MOS integrated circuits as well as discrete components. They have agreements with Zilog to second source the Z-80 and Z-8000 microprocessors. Government Incentives for the Location of Industry Apart from involvement in joint ventures, many countries in Europe, realizing the need to establish local microelectronics fabrication facilities, are offering substantial incentives to companies that build facilities in their areas. Some examples are given below. United Kingdom The United Kingdom offers a variety of incentives for different locations. These include tax breaks, grants for factory building, and financial assistance for retraining employees. In England, the main areas to receive such support are in the industrial North. Scotland - Depending on the location chosen, the Scottish Development Agency wiU offer substantial financial assistance and concessions for plants located in Scotland. The Wolfson Microelectronics Institute at Edinburgh University (recently nominated as one of the two U.K. centers for the development of microelectronics technology) offers a source of appropriately trained graduates. Both Motorola and National Semiconductor have established facilities in Scotland. Wales - Wales offers a wide range of grants and tax incentives to companies locating there. Several Welsh universities, including Bangor and Swansea, have major electronics departments. Bangor includes an Industrial Development Unit to make the facilities and expertise of the University available to industry. Siliconix has an assembly plant near Swansea and is considering a wafer fabrication facility. Several Japanese companies, including Sony and Matsushita, are also established in Wales. Ulster - In Northern Ireland the Industrial Development Organization is offering cash grants for plant construction, equipment, and training costs to encourage new industry. International Rectifiers has had a subsidiary in Newry since 1969. Republic of Ireland The Industrial Development Authority of the Republic of Ireland is endeavoring to attract high-technology industry to the country by offering grants of up to 55 percent of the cost of fixed assets as well as tax exemptions for profits on exports until 1990. A new plan, which will eventually replace the existing one, reduces the current tax rate of 45 percent on corporate profits to 10 percent. Analog Devices built a design and fabrication facility near Limerick in 1978 and Unitrode is building a plant near Shannon which wiU be completed this year. Mostek has committed to a major expansion in Dublin. It will begin with testing of components but will eventually do wafer fab there as well. France There are a number of areas in France that are currently endeavoring to attract high-technology industry. The West Atlantic area, which includes Brittany and the Loire Valley, is offering an incentive package which includes $5,000 per job created, local tax exemptions, and vocational training aid. They are particularly interested in establishing the area as a center for electronics, and several major electronics facilities including Thomson-CSF and SGS-ATES are already in operation. Tax incentives and low-cost sites are being offered to attract the electronics industry to the Valbonne area close to the IVlediterranean coast between Nice and Cannes. Texas Instruments and IBM both have plants in the area. Public Perceptions of the Microelectronics Industry Despite the incentives offered by European governments for the establishment of semiconductor facilities in their countries, public opinion on the subject is more ambivalent. In an environment where unemployment is increasing, the most immediate worry is that with more automaticki unemployment will increase further. Recent forecasts published for the United Kingq&RT predict total unemployment by the end of 1980 will be 1.7 million compared with 1.2 million in October of 1979. The microelectronic revolution is viewed by many as comparable to the Industrial Revolution of the last century. In Europe major technological change is seen as causing short-term upheaval followed by long-term benefits. It is the magnitude of the possible short-term upheaval that worries many people. European Trade Union concern is that the introduction of microelectronic technology will cause high structural unemployment. The European Trade Union Institute (ETUI) in Brussels published a report in November 1979 expressing these concerns. Specifically they feel that unions should have early access to information on the proposed introduction of new technology in order "to ensure that the technology is introduced at a pace at which its social impact can be spread fairly over societies, and to ensure that the benefits of new technology accrue to working people." The general opinion seems to be that, while the technological advances are welcome, care must be taken so that no one sector of the population bears an unreasonable burden because of the changes. 10-END-USER MARKETS IN WESTERN EUROPE Table 5 presents DATAQUEST's estimate of end-user consumption in Western Europe compared with that of the United States. The consumer segment plays an important role in semiconductor consumption in Western Europe using about 33 percent of the total as compared with only 16 percent of the total in the United States. In tlie industrial segment, Europe consumes about 35 percent of the total whereas the United States consumes an estimated 32 percent. The United States consumes far more semiconductors in the computer segment witli an estimated 40 percent compared with only 23 percent computer consumption in Europe. The government and military consumption is nearly equal, with Europe consuming 9 percent and the U.S. consuming 12 percent. Table 5 ESTIMATED END-USER MARKETS - 1979 (Percent) Computer Industrial Consumer Automobile Television All Other Consumer Government < k Military Discrete 14% 44% 35% 3% 18% 14% 7% Western Europe Total Total IC Semiconductor 29% 28% 32% 5% 14% 13% 11% 23% 35% 33% 4% 17% 12% 9% Source: United States Total Semiconductor 40% 32% 16% 4% 4% 8% 12% DATAQUEST, Inc. June 1980 EUROPEAN MARKET SHARES Table 6 presents DATAQUEST estimates of the worldwide revenues of European semiconductor manufaturers for the years 1977, 1978, and 1979. Worldwide semi-conductor revenues of the European producers in 1979 were an estimated $1.8 billion, up about $300 miUion from an estimated $1.5 billion in 1978. This growth rate of 21 - 11 percent is less than the 27 percent growth rate of worldwide semiconductor con-sumption in 1979. The worldwide revenues of Philips and Signetics are presented in Table 6; however, the European revenues of Philips without Signetics and of Signetics alone are presented in Tables 7 and 8 respectively. Table 7 presents DATAQUEST's estimates of the European revenues of European semiconductor companies. In 1979 the European producers shipped an estimated $1.3 billion of semiconductors into the Western European market, up 18 percent from an estimated $1.1 billion shipped into Europe in 1978. Table 8 presents estimated European revenues of American semiconductor manufacturers. For 1979, total shipments into Europe by American producers were an estimated $1,542 million, up about 31 percent from an estimated $1,179 million in 1978. IC shipments by American companies in 1979 were an estimated $1,037 million, up about 36 percent from $760 million whereas discretes grew an estimated 21 percent from $419 million in 1978 to $505 million in 1979. Table 9 presents the estimated European revenues to the Japanese companies. In 1978 they shipped an estimated $55 million into Europe whereas in 1979 they shipped an estimated $95 million, up alx)ut 75 percent. Table 10 summarizes the data in Tables 7, 8, and 9 showing the percentage of European semiconductor consumption supplied by the European, American, and Japanese companies. Although Japanese sales in Europe represent a small percentage of total sales, they are growing rapidly, from 2 percent in 1977 to 4 percent in 1979. Daniel L. Klesken Jean C. Page 12-# Table 6 ESTIMATED WORLDWIDE REVENUES OF EUROPEAN SEMICONDUCTOR MANUFACTURERS (Millions of Dollars) 03 I 1977 1978 1979 Company AEG Telefunlcen AEI (Subs GEO ASEA Brown-Boveri Cogie EFCIS EMI Eurosil Ferranti GEO , Philips (with Signetics) Piher Plessey RIFA Semikron SGS-AT|S Siemens TAG Thomson-C&j? Others IC $ 16 12 1 0 0 0 0 9 13 0 286 0 17 7 0 49 83 0 20 2 Discrete $ 71 0 1 19 9 0 9 0 10 4 244 7 0 0 15 35 167 18 73 10 Total $ 87 12 2 19 9 0 9 9 23 4 530 7 17 7 15 84 250 18 93 12 IC $ 23 14 1 0 0 0 0 10 16 0 379 0 25 8 0 59 106 0 30 3 Discrete $ 88 0 1 20 10 0 10 0 11 4 266 8 0 0 20 41 186 20 100 11 Total $ 111 14 2 20 10 0 10 10 27 4 645 8 25 8 20 100 292 20 130 14 IC $ 28 17 2 0 0 7 0 11 19 0 480 0 27 10 0 74 150 0 40 4 Discrete $ 107 0 1 22 12 0 12 0 12 5 290 9 0 0 25 46 206 21 120 13 Total $ 135 17 3 22 12 7 12 11 31 5 770 9 27 10 25 120 356 21 160 17 Total $515 $692 $1,207 $674 $796 $1,470 $869 $ 901 $1,770 Philips (w/o Signetics) $111 Signetics $175 2 Includes Litronix, excludes MSC and FMC for 1979. $244 $ 0 $ 355 $ 175 $165 $214 $266 $ 0 $ 431 $ 214 $215 $265 $ 290 $ 0 $ 505 $ 265 Source: DATAQUEST, Inc. June 1980 Table 7 ESTIMATED EUROPEAN REVENUES OF EUROPEAN SEMICONDUCTOR MANUFACTURERS (Millions of Dollars) 1977 1978 1979 Company AEG Telefunlcen AEl (Subs. GEO) ASEA Brown-Boveri Cogie EFCIS EMI Eurosil Ferranti ^ GEC ti^ Philips (w/o Signetics) ' Piher Plessey RIFA Semikron SGS-ATES Siemens TAG T[iomson~CSF Others IC $ 13 12 1 0 0 0 0 9 11 0 90 0 15 7 0 20 65 0 18 1 Discrete $ 66 0 1 17 9 0 9 0 9 4 220 7 0 0 14 31 151 18 68 9 Total $ 79 12 2 17 9 0 9 9 20 4 310 7 15 7 14 51 216 18 86 10 IC $ 20 14 1 0 0 0 0 10 12 0 134 0 18 8 0 43 85 0 26 2 Discrete $ 82 0 1 18 10 0 10 0 10 4 244 8 0 0 18 37 170 20 91 10 Total $ 102 14 2 18 10 0 10 10 22 4 378 8 18 8 18 80 255 20 117 12 IC $ 21 17 2 0 0 7 0 11 13 0 168 0 20 10 0 57 117 0 30 3 Discrete $ 97 0 1 20 12 0 12 0 11 5 262 9 0 0 23 42 187 20 111 15 Total $ 118 17 3 20 12 7 12 11 24 5 430 9 20 10 23 99 304 20 141 18 Total $262 $633 $895 $373 $$733 $1,106 $476 $827 $1,303 Source: DATAQUEST, Inc. June 1980 # # Table 8 ESTIMATED EUROPEAN REVENUES OF AMERICAN SEMICONDUCTOR MANUFACTURERS (Millions of Dollars) 1977 1978 1979 Company AMD AMI Fairchild General Electric General Inst. Harris Hewlett-Packard Intel ' International Rectifier tn Intersil 1 ixT Most elf Monolithic Memories Motorola National RCA Signetics Texas Instruments TRW Westingliouse Zilog O tilers IC $ 12 10 48 0 16 15 0 52 0 10 39 20 7 70 46 18 42 120 2 0 0 18 Discrete $ 0 0 15 15 12 0 19 0 20 0 65 0 0 82 10 26 0 55 0 8 0 13 Total $ 12 10 63 15 28 15 19 52 20 10 104 20 7 152 56 44 42 175 2 8 0 31 IC $ 18 15 60 0 24 21 0 82 0 13 50 33 9 90 65 23 56 165 5 0 3 28 Discrete $ 0 0 18 17 14 0 22 0 25 0 78 0 0 96 13 29 0 73 0 9 0 25 Total $ 18 15 78 17 38 21 22 82 25 13 128 33 9 186 78 52 56 238 5 9 3 53 IC $ 28 27 72 0 35 29 0 116 0 18 65 58 11 122 102 27 68 215 7 0 5 32 Discrete $ 0 0 23 19 22 0 25 0 30 0 92 0 0 125 18 32 0 90 0 11 0 18 Total $ 28 27 95 19 57 29 25 116 30 18 157 58 11 247 120 59 68 305 7 11 5 50 Total $545 $340 $885 $760 $419 $1,179 $1,037 $505 $1,542 Source: DATAQUEST, Inc. June 1980 Table 9 Total ESTIMATED EUROPEAN REVENUES OF JAPANESE SEMICONDUCTOR MANUFACTURERS (Millions of Dollars) 1977 1978 1979 Company Fujitsu Hitachi Matsushita NEC Toshiba IC N/A^ N/A N/A N/A N/A Discrete N/A N/A N/A N/A N/A Total 4 9 1 18 7 IC N/A N/A N/A N/A N/A Discrete N/A N/A N/A N/A N/A Total 6 13 3 24 9 IC N/A N/A N/A N/A N/A Discrete N/A N/A N/A N/A N/A Total 12 22 6 40 15 $23 $16 $39 $33 $22 $55 $65 $30 $95 N/A = Not available Oi I Source: DATAQUEST, Inc. June 1980 Table 10 SEMICONDUCTOR SUPPLIERS TO WESTERN EUROPE (Percent of Total) 1977 1978 1979 Company American companies European companies Japanese companies Total IC 66% 31 3 100% -Discrete 34% 64 2 100% Total 49% 49 2 100% IC 65% 32 3 100% Discrete 34% 64 2 100% Total 50% 47 3 100% IC 65% 30 5 100% Discrete Source: 37% 61 2 100% Total 52% 44 4 100% DATAQUEST, Inc. June 1980 1 J # Vohn-No. 5 June 12, 1980 This letter is a condensation of recent newsletters and internal thinking from the industry research groups at DATAQUEST, Inc. Requests for amplification of our thoughts or for specific newsletters should be directed to the author. A list of recent DATAQUEST Research Newsletters appears at the end of this letter. SEMICONDUCTORS Price declines in semiconductors have begun to accelerate in the last eight weeks and book-to-biU ratios are coming down as well. W e expect book-to-bill ratios to be below 1.0 for certain products in the second quarter and we would expect book-to-bill ratios for many of the semiconductor companies to be around 1.0 for the next four months, resulting in a pronounced slowing of industry growth. None of these developments should be any news to DATAQUEST clients as these developments were within our earlier forecasts of 20 percent revenue growth in domestic semiconductor consumption this year £ind 18 percent growth in European consumption. As we have stated in the past, our positive scenario for the semiconductor industry is based on our belief that unit demand will remain relatively strong. The key question is the extent to which the slowing in capital expenditures affects the growth rate of the computer-related industries. If computer industry growth continues at a relatively healthy rate, which is our present expectation, then we believe that semiconductor industry fundamentals wiU remain intact as well. If computer industry growth rates fall by 50 percent or more, then the downside variance from our semiconductor growth expectations wiU increase accordingly. As you know, the Japanese threat in this industry is a very real one. In our view, the ball is squarely back in the court of the U.S. manufacturers. Domestic manufacturers have spent the last year concentrating on maximizing unit production to take advantage of extremely attractive price/cost ratios and have increased market share in all segments of the semiconductor business as a result. The major Japanese companies, by comparison, have sacrificed market share and have concentrated more on increasing product reliability, improving manufacturing processes, and allocating wafers to new devices, such as 64K dynamic RAMs and 16K Static RAMs. Copyright © 12 June 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients. This information Is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities Member, New York Stock Exchange 19055 Pruneridge Avenue / Cupertino, California 95014 / (408) 725-1200 vath industry conditions softening, we believe that the Japanese will put more emphasis on pricing and market share, but we feel that the Japanese are too sensitive about the political cross-currents to be extremely aggressive on the pricing front, with the exception of Europe where they are seeking to establish inroads into new markets. Actually, one could look at the present industry slow-down as being of some long-term benefit to U.S. manufacturers, as it will allow them time to focus on areas such as reliability and process improvements where the biggest threat from the Japanese will ultimately eome. One company that does not have to worry about keeping up with the Japanese is Intel; it remains far ahead of its competition in terms of technology, product positioning, processing, and systems expertise. There is always the risk that the competition will catch up with Intel in key product areas and eliminate its sole source pricing advantage faster than Intel can generate new proprietary product positions. The present risk in this regard centers on 4K static RA]\ls and 16K EPROMs. By our estimates, these two products accotmted for 21 percent of revenues last year with extremely high profit margins. W e estimate that average pricing on these two components may drop 40-50 percent in 1980 and that Intel will have to find other lucrative products in new areas in order to maintain margins. Finding such products should not be a problem: opportunities exist for Intel in memory over the next year in 32K and 64K EPROiVls, 16K static RAMs, and 16K EEPROlVIs. In addition, its very profitable microprocessor divisions are more price protected and continue to grow more rapidly than the company as a whole. Obviously, risk of a shortfall by Intel in a difficult economic period always exists, but Intel has a lot of alternatives that the other manufacturers do not. For example, Intel is puttit^ very little silicon into the 64K R A I V I development effort at present, yet we believe that they could be the number one producer in fairly short order should they choose to be. As a second alternative, Intel could push 16K EEPROIVI prices, where they have a sole source position, down more rapidly to force conversion of 16K EPROM users, where Intel is facing some competititMi. If there is a margin glitch at Intel, it is most likely to come in the third quarter of this year, since that is the period when the company may have difficulty in increasing volume on new products fast enough to offset declining prices on formerly proprietary products that are becoming more competitive. For the year, we expect only a slight decline in pretax margins at Intel, with earnings increasing by 30 percent to $4.65 per Share on a 34 percent gain in revenues. Probably the most significant activity right now at Intel is the company's attempt to develop a standardized operating system that will be available on a chip as a key part of its microcomputer product line. If Intel is successftil in executing this program, the potential end markets will be huge and the company will have made the transition to a true microcomputer systems company. If the software that Intel develops on a chip is patentable (and we believe there to be some legal question), then Intel should not only have created a broader market for its products, but may protect itself from second sourcing as well, which has very positive implications for longer term profit margins. - 2 -SMALL COMPUTERS W e are searching for evidence that the recession has affected demand in any sector of the small computer industry, but there is little indication to date. At this juncture, we are forecasting growth of at least 20 percent in revenues for every sector of the smaU computer marlcet in both 1980 and 1981. The strength in orders at Digital Equipment may be attributable to double ordering to compensate for long lead times, but Data General, where deliveries are generally under three months, is also experiencing relatively strong demand. It is now our feeling that the economy will have more of a negative impact on the general purpose minicomputer (GPMC) sector of the small computer marlcet in 1981 than 1980. W e now expect 29 percent growth in revenues in the GPMC marl<et in 1980 versus our previous 25 percent forecast. W e are tentatively forecastir^ a decline in growth to 20 percent in 1981, but have little current evidence to justify this deceleration. W e continue to believe that the most dynamic growth in this industry will come in very small business computers (VSBC), which we define as computers selling for $5,000-15,000. DATAQUEST expects revenues to grow 60-70 percent this year and 40-45 percent in 1981, even allowing for a fairly severe recession. One of the reasons for the forecast is that we expect new product introductions in VSBC from Apple Computer and Tandy, as both companies expand their offerings beyond the personal computer market. The public company on the fastest growth tracl< in this industry right now is Tandem Computer. Tandem has developed a unique architecture that allows for virtually 100 percent reliability without loss of data should any single element in the system fail. Tliis h i ^ reliability is offered at very little incremental cost to the user. There are some disadvantages to tlie Tandem approach, chiefly relatir^ to difficulty in writing applications software and the additional system overhead required to provide non-stop operation. However, the benefits to the user are obvious. Tandem's marlcet to date has been primarily transaction processing in tlie commercial sector, but we see opportunities for the company in other areas as well, including the office automation market. Very simply, we believe that Tandem has achieved something relatively unique in the computer industry and that the demand by users for continuous processing is something that will grow, forcing other manufacturers to offer similar capabilities. The problem that we foresee for other manufacturers is the ability to offer continuous processing at a reasonable cost while maintaining compatibility witli existing software. W e believe that Tandem can probably generate revenue growth greater than 50 percent through fiscal 1981 and probably through fiscal 1982 as well. Earnings per share growth will lil<ely traU revenue growth somewhat because of equity dilution. W e are projecting earnings of $2.05 per share in the September 1980 fiscal year on revenues of $110 million and are tentatively projecting $2.85 per share in fiscal 1981 ( X I revenues of $180 million, assuming that another equity financing is needed next year. - 3 -PAPER AND FOREST PRODUCTS Vfithin the next two months, the U.S. Forest Service plans to publish its preliminary draft of "The Outlook for Timber in the United States." The most recent published edition was in 1973. Having seen some of the preliminary data used in the report, we believe that it will point out that the growing shortage of mature softwood sawtimber in the Pacific Northwest will be only partially compensated for by increased cutting in the South. As a result, the Forest Service expects stumpage prices in the South to appreciate more rapidly than prices in the Northwest, so that by 1990 prices from the two regions should be almost equal. W e expect that the Forest Service will project aimual real price increases for stumpage of 3.2 percent in the Northwest and 4.6 percent in the South during the next 10 years. Having talked to several of the people who put together the data, we believe that the Forest Service could be using a somewhat optimistic forecast of housing starts over the next ten years (2.2 million starts per year). However, using our own assumptions of 1.8 million starts per year, DATAQUEST projects minimum real price increases in the two regions of 2.6 percent and 3.6 percent per year respectively, which would still be considerable. The implications of this data are that stumpage, lumber, and plywood should continue to rise in prices at rates considerably above the overall inflation rate in the future. By the mid-1980s, we expect increased substitution of plywood by waferboard and composite board, which could weU result in plywood prices increasing less rapidly than stumpage and lumber prices. The clear beneficiaries of these trends would be, first, those companies who are most self-sufficient in their forest products production and, second, those companies who have extensive mature Southern woodland holdings. On the first score, only Weyerhaeuser is even close to being fiber self-sufficient in its forest products manufacturing. Weyerhaeuser also has extensive holdings of mature Southern timberlands. International Paper, after the purchase of Bodcaw last year, has the largest absolute acreage in the South, but we are not sure how much of IP's holdings are of the more mature woodlands that should enjoy the most rapid price appreciation. Potlatch Corporation is another interesting beneficiary, as over one-third of its woodlands are in the South and it also has two waferboard plants under construction. The forest products stocks have appreciated 15-20 percent since our favorable comments about the group in our last Portfolio Letter. The new Forest Service report could stimulate additional interest in companies with strong Southern woodland holdings. COPYING AND DUPLICATING Despite booming conditions in the European copying and duplicating market in general. Rank Xerox continues to have margin problems. Rank has been slower than Xerox USA in adjusting its prices downward to meet the competitive threats of European and Japanese companies. Xerox USA took the steps in 1976-78 while Rank Xerox did most of its price adjusting in 1979, so comparisons for Rank wUl be - 4 -difficult this year, as it has many machines on rentals that are generating less revenue than they were a year ago. In addition, they have not yet received the benefit of all of the new product introducticms at the medium and high end (5600, 8200, 9500) that the domestic subsidiary has. W e had expected that Ranlc Xerox's operating earnings could increase about 10 percent this year on a 14 percent gain in revenues, but it now looks as if operating earnings (ex-currency effects) will be up only about 3 percent, which has caused us to bring our full year estimate for Xerox down to $7.25 per share from $7.40 per share. However, we do believe that most of the problems facing Rank Xerox will have sufficiently abated by the end of this year to allow margins to remain almost flat in 1981 and earnings growth to therefore accelerate. For one thing, the comparisons with this year should be easier in terms of average pricing on machines. Secondly, new products such as the 3450, 5600, 8200, and 9500 should all be introduced in Europe this year, with the benefits starting to accrue in 1981. Third, we believe that a totally new low-end copier could be coming from Fuji Xerox late in 1980 and that this product wiU be introduced in both Europe and the United States. Finally, we think that the impact of the recession should begin hitting Europe by the second half of 1980 and that the depth or length of the recession will be less than in the United States, allowir^ Europe as a whole to show about 2 percent real growth in 1981. Thus, while we are somewhat more pessimistic about Rank Xerox this year, we do believe that earnings gains from the subsidiary can exceed 13 percent in 1981. Coupled witli a swing to at least break-even operaticms in word processing, the result should be an acceleration of earnings growth at Xerox next year to about $8.45 (excluding currency fluctuati(»is) which would represent a gain of over 16 percent from our present 1980 estimate. More on Xerox's ETHERNET network in our word processing section. WORD PROCESSING The recent joint announcement of development efforts on ETHERNET by Xerox, Digital Equipment, and Intel has interesting implications not only for these companies, txit for other participants in the office of the future. Xerox is trying to establish ETHERNET as the industry standard for intra-office communications. Conceptually, it is a relatively simple system designed to allow various peripherals to attach to a coaxial cable running through an office with fuU communication between each peripheral. Theoretically, the products of any manufacturer standardizing on ETHERNET will be able to commimicate with products of other standardized manufacturers. If ETHERNET can be implemented successfully (and we should note that we believe this to be at least one year away) the clearest beneficiaries would seem to be DEC and Xerox, since both lack the full product line necessary for implementing an integrated office, yet are relatively strong in certain segments of the office environment. Having DEC assist on the design of the system will certainly increase the likelihood that it will operate effectively in a data processing mode. - 5 -The degree to which ETHERNET is adapted as a standard is open to considerable question. If it is successful, however, it may pose some threat to companies who have already announced office communications systems encompassing only their own products, such as Datapoint and Wang Laboratories. Much would depend on their ability and desire to adapt to this standard. The impact of ETHERNET, of course, is purely hypothetical. In the real world, Wang and others are selling products today into a marl<et that is growing at a tremendous rate and which shows no sign of falling prey to recessionary influences. While deliveries of ETHERNET are still well in the future, it is having the impact of generating word processing orders for Xerox now. Xerox can effectively use ETHERNET as a marl<eting tool in selling its word processing worltstations by claiming that its products will be compatible with the intra-office commiuiication standard, while other products may prove to be incompatible with this standard in the future. This marl non-residential construction spending for some time, and together these areas account for about 60 percent of demand for mobile construction equipment. The dragline and power shovel manufacturers (Bucyrus-Erie and, to a lesser extent, Harnischf^er) are heavily concentrated in coal-related markets and would therefore benefit more dramatically from an upturn in coal-related business. Michael R. Weisberg - 6 -RECENT NEWSLETTERS OF NOTE Semiconductors 1. Update on Intel 2. Gate Arrays and Other Semicustom Logic 05/31/80 04/21/80 Small Computers 1. Record Crowds at National Computer Conference Reflect Continuing Boom in the Industry 06/02/80 2. Four-Phase User Survey Results 05/29/80 3. Price Comparisons: 32-Bit General Purpose Minicomputers 05/13/80 4. Very SmaU Business Computers 05/02/80 5. The Ultra High-PerfOTmance General Purpose Minicomputer Marlcet 04/29/80 6. The Eagle Has Landed, Data General Announces 32-Bit Eclipse MV/8000 04/29/80 7. Highlights of Datapoint's Security Analysts' Meeting 04/18/80 Paper & Forest Products 1. Van Gelder Problem Could be Solved in Near Term 2. The Recession Reaches the Paper Industry Copying & Duplicating 1. 1980 Hannover Fair Report 2. Recent Industry Events 3. Minolta Introduces a Di-electric Intelligent Copier 05/30/80 05/30/80 05/31/80 05/09/80 04/16/80 Word Processing 1. IBM Introduces the Selectric ni Typewriter and Raises Purchase and Service Prices for Selectric n 2. Datapoint Adds Word Processing and Electronic Message Software to Product Line 3. New Product Introductions at the Hannover Fair 4. NBI Raises Lease Rates and Introduces Forms Application 06/05/80 05/29/80 05/15/80 05/08/80 Capital Equipment 1. Survey Results of Mobile Construction, Forestry and Mining Equipment End Users 2. Report of Caterpillar Tractor Company's Annual Meeting (continued on p£^e 8) - 7 -04/25/80 04/17/80 RECENT NEWSLETTERS OF NOTE (continued) Instrumentation 1. Update on Telctronix 05/30/80 2. XY Recorder IWarJcet 05/30/80 3. Growth of In-Circuit Testers 05/07/80 Electronic Printers 1. Hewlett-Pacl<ard 7310A Graphics Printer 05/15/80 2. Documation Announces Fiscal 1980 Loss and Further iVIanagement Re-alignments 04/18/80 Telecommunications 1. The FCC IVIalces a Landmarl< Deregulation Decision 04/18/80 - 8 -bCii HbbtAHUH ^ ^'^^^Subsibia^vo1A.C. Nielsen Co. 7 INCORPORATED I ^ I ^ Z W W ^ 3 ^ ^ M 1 1 ^ Z I F K SIS Code: Vol. m, 7.8 SEMICONDUCTOR SALES THROUGH DISTRIBUTION SUMMARY "Tiglit" is the Icey word when considering U.S. semiconductor distribution in 1980. Although the situation is not as extreme as in 1974, tliere is still tight money for growth, and a resulting tight monitoring of inventory levels and accounts receivable. Distribution depends heavily upon the availability of money. The high prime rate has affected distributors' short-term borrowing capability and has also caused accounts receivable periods to lengthen. Semiconductor supply is presently catching up with demand. The long lead times for specific parts in 1979 have shortened in the first half of 1980, and supply is not as tight as it was in 1974. Formerly hard-to-get components are more readily available from both U.S. and Japanese vendors. For example, low-power Schottky devices which had one year lead times through distribution three months ago are now available off-the-shelf or in a few weelcs. The 16K dynamic RAMs are available off distributor shelves as are most static MOS RAMs and most EPROMs. In spite of a tight component supply in 1979, semiconductor distribution resales were up 33.5 percent, and are expected to increase 24 percent in 1980. The estimated semiconductor distributor resales are shown in Table 1. Table 1 ESTIMATED U.S. DISTRIBUTOR SEMICONDUCTOR AND SYSTEMSl RESALES (Millions of Dollars) 1978 1979 1980 Distributor Semiconductor Resales Percentage growth from previous year $1,075 $1,435 $1,780 33.5% 24.0% Systems include board-level computers and development systems. Source: DATAQUEST, Inc. June 1980 Copyright © 9 June 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsibIe individuals in the subject companies, but is not guaranteed as to accuracy or cornpleteness It does not contain material provided to us in confidence by our clients. This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buv securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO Tlie geographical breakdown of the semiconductor distribution resales sliows all geographical segments to have 1979 marl B ^ S B = S B f ' ^ S S ^ ^ ^ S ^ ^ ^ B A Subsidiary of A.C. Nielsen Co. ^ INCORPORATED RE NE •SE EW/ • A SI RCh -ET" -1 rER SIS Code Vol. I, 2.8.6 DYNAMIC AND STATIC MOS RAM AND EPROM SHIPMENTS SUMMARY Worldwide shipments of 16K dynamic RAMS in the first quarter of 1980 were an estimated 37.3 million units, up about 38 percent over an estimated 27.1 million units Shipped in the fourth quarter of 1979. Prices for first-quarter shipments were in the $5.00 to $5.25 range. However, recent price quotes for 16K RAMS have fallen into the $4.00 to $4.75 range. 64K dynamic RAMS are still in a sampling mode with first-quarter shipments in the range of 21,000 units, and prices generally in the $100 to $125 range. Worldwide shipments of 4K dynamic MOS RAMS continued to decline in the first quarter of 1980, dropping about 21 percent to an estimated 11.5 million units. Volume prices are about $2.00. 4K Static NMOS RAM shipments increased in the first quarter of 1980 to an estimated 14.1 million units. Lead times for most of the slow 4K statics are now less than 10 weeks and prices have declined to about $3.25. Worldwide shipments of the 2147 fast 4K static RAM increased by about 34 percent to an estimated 1.8 million units in the first quarter of 1980 and lead times are generally well under 10 weeks. Prices in the first quarter for the fast statics were about $10. Worldwide Shipments of 4K CMOS static RAMS increased about 30 percent to 2.5 million units in the first quarter of 1980. First-quarter shipments of 8K EPROMS were an estimated 4.5 million units, down about 11 percent from an estimated 5.1 million units in the fourth quarter of 1979. Shipments of the 16K EPROM increased by about 20 percent to an estimated 5.3 million units. Prices have continued to soften and are currently about $15. The 32K EPROM is available in limited quantities; an estimated 320 thousand units were Shipped in the first quarter of 1980 at prices in the range of $45 to $60. This product is receiving increased attention with 7 suppliers either sampling or shipping products. DYNAMIC MOS RAMS 16K RAMS Table 1 presents DATAQUEST estimates of worldwide shipments of 16K dynamic MOS RAMS in the first quarter of 1980. Worldwide shipments were an estimated 37.3 million units, up about 37.7 percent over the 27.1 million units shipped in the fourth quarter of 1979. These estimates include the 2-chip hybrids shipped to IBM on the Caribou program. Copyright © 6 June 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our InterpreTation and analysis of information generaIly available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness It does "Ot contain material provided to us in confidence bv our clients. This information is not furnished in connection vwith a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities This firm and its parent andfor their officers, stockholders, or members of their families may, from time to time, have a long or short position m the securities mentioned and may sen or ouy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO During the first quarter of 1980 demand was still quite strong and prices remained relatively stable in the $5.00 to $5.25 range. However, starting in March the supply and demand outlook for 16K dynamic RAMS began to change markedly. A greater supply of 16K RAMS is now available as the result of more wafer starts by some suppliers as well as better yields at most suppliers. Concurrently, there has been a slightly diminished demand as the result of some cancellations and Stretch-outs—primarily from IBM. AS a result of this increased supply and diminished demand, the 16K RAM was removed from most suppliers' allocation lists, and lead times are now less than 12 weeks. Some suppliers have 50,000 units available in as little as 4 weeks. Consequently, prices of slow (250 nanosecond) plastic devices are now being quoted at about $4.00. However, the majority of the second-quarter shipments will still go out at prices closer to $5 since most of the large commitments liave been made on long-term purchase agreements. It is the only incremental or newly booked business for the second and third quarters that will go out at these lower prices. Furthermore, there is still about a $1.00 spread between the slower parts (250 ns) and the fast parts (under 125 ns). If a user requires a side-brazed ceramic package, the premium over a pltistic package is $3.50 to $5.00 because of the high gold content. 32K RAMS Of all suppliers of 16K RAMS, Mostek is still the only one in the merchant market with a 32K dynamic RAM hybrid device. This 2-chip device is gaining some popularity, and Mostek shipped an estimated 220,000 devices in the first quarter of 1980 at prices around $14.00. 64K RAMS Table 2 presents DATAQUEST estimates of worldwide shipments of 64K dynamic MOS RAMS. Worldwide shipments in the first quarter of 1980 were an estimated 21 thousand units, up about 31.3 percent over shipments in the fourth quarter of 1979. This market is still in a sampling mode with six suppliers sampling or shipping prototype quantities during the first quarter. Others are expected to enter the market over the coming quarters. Up until now most MOS memory suppliers have been extremely limited in new wafer starts that could be dedicated to the 64K RAM. With the increased supply and weakening demand in the 16K dynamic MOS market, more suppliers should be able to devote more wafer starts to the 64K dynamic RAM. Please note that our estimate for shipments by Fujitsu for 1979 have been revised upward. Although these parts were the two power supply parts (+7v, -2.5v), Fujitsu has recently begun sampling a 5-volt only device. Prices on 64K RAMS in relatively low quantities are still in the $100 to $125 range. These prices should fall about $70 range by the fourth quarter of 1980. 4K RAMS Worldwide shipments of 4K dynamic MOS RAMS continued to decline in the first quarter of 1980 (Table 3). Worldwide shipments were down an estimated 21.2 percent to about 11.5 million units. Some suppliers have stopped taking orders for this product and are only shipping against the existing backlog. This phenomenon 2 -# is normal as suppliers are de-emphasizing the product and begirming to put emphasis into the 64K RAMS. Lead times for tliis product still remain in the 12-to-18 week time frame as a result of this diminished supply. Prices in the first quarter were at}out $2.00 and are continuing at that level in the second quarter. STATIC MPS RAMS 4K RAMS Table 4 presents DATAQUEST estimates of worldwide shipments of slow 4K NMOS Static RAMS. Total shipments in the first calendar quarter were up about 9 percent over the fourth calendar quarter of 1979. Ttie IK x 4 device shipped an estimated 8.5 million units, up about 1 1 percent over the fourth quarter. The 4K x 1 device shipped an estimated 3.6 million units, which is up 2.6 percent over the fourth quarter. Lead times for most of the 4K slow statics are under 10 weeks and prices for Slow plastic p£urts are down in the $3.00 to $3.50 range. The faster devices in CEEOIP package command prices in the $4.00 to $4.50 range. Shipments of fast 4K NMOS static RAMS in the first quarter were up about 34 percent to an estimated 1.8 million units (Table 5). This total includes an estimated 125,000 units shipped by Intel of the 2148 (IK x 4) fast static RAM. As a result of the increased number of suppliers, lead tim^ iiave shrunk to less than 10 weeks and prices for second and third quarter deliveri^ are now under $10. Shipments of 4K CMOS static RAMS in the first quarter of 1980 were an estimated 2.5 million units, up about 30.5 percent over the 4th quarter of 1979 (Table 6). The IK x 4 devices were up about 32.7 percent to 1.7 million units, whereas the 4K x 1 devices were up about 26.2 percent to 800 thousand units. Lead times for these devices are still generally longer than 20 weeks, and prices for second and third quarter delivery remain relatively strong in the $12 to $14 range. MOS EPROMS 8K MPS EPROMS Worldwide shipments of 8K EPROMS continue to decline in the first quarter of 1980 (Table 7). They were down an estimated 11.4 percent to 4.5 million units. Most prices for this device for second-quarter delivery are in the $5.00 to $5.50 range. Some suppliers, including Intel, National Semiconductor, and Texas Instruments, are Shipping a partial 16K EPROM as an 8K 5-volt only EPROM labeled as a 2758. These Shipments are still a relatively small percentage of total shipments and are not included in the above table. 16K EPROMS Shipments of 16K EPROMS continue to increase in the first quarter of 1980 to an estimated 5.3 million units, which is up atsout 19.5 percent over the fourth quarter of 1979 (Table 8). Prices are generally in the $14 to $16 range in the second quarter of 1980, with lead times in the 12-to 18-week range. There is some price pressure in tliis market as more suppliers come into the market. - 3 -32K EPROMS Worldwide shipments of the 32K EPROIVI were up at>out 68.4 percent to an estimated 320 thousand units in the first quarter of 1980 (Table 9). At present there are 7 suppliers in this market and prices in the second quarter are generally in the $45 to $60 range. 64K EPROlVi Texas b^truments is the only supplier sampling the 64K EPROiVI and it shipped fewer than 1,000 units during the first quarter of 1980. Daniel L. Kl^ken Lane Mason - 4 TABLE 1 ESTIMATED mRUMIDE miPMESTS OP lU. DINMIC MOS RAMS iTHOUSAHDS OP UfflTSy COMPASI AMD PAIRCHILD PUJITSU aXTAGMI IHTEL INTERSIL ITT MATSUSHITA MITSUBISHI MOSTSK MOTOROLA NATIONAL NBC SSS ATES SWIB9S SIGNEnCS TEXAS INSTRUmSTS TOSHIBA ZILOG TOTAL PERCENT CHAUGE PROM PREVIOUS QUARTER 1978 lEAR S 465 2.000 1,210 2,i»00 5 203 0 100 «.900 1,750 287 3.850 0 85 IW 3,150 285 60 20.885 lOT GTR S 300 1.100 800 600 5 200 0 100 2.«»00 700 2S0 1.700 0 100 75 1,800 225 20 10,370 28.2 WD QTR MAMMB 5 1+00 1.300 l.WO 700 5 300 0 200 3.600 1,200 %50 2,200 0 ISO 1^0 2.200 550 50 l'+.750 42.2 ZRD QTR 10 500 1.600 2,200 950 5 600 0 400 4,800 l.OQO 1.000 3,200 0 250 50 1,800 900 50 19,315 30.9 4ra QTR 50 700 2,500 2,700 1,000 0 600 0 550 6.000 1,800 1.500 4.200 3 375 10 3,200 1.800 70 27,058 40.1 lEAR 65 1.900 6.500 7.100 3,250 10 1,700 0 1,250 16,800 4,700 3.200 11,300 3 875 175 9,000 3,475 190 71.493 1980 1ST QTR 300 800 3.000 3,200 1,150 0 750 5 700 7,400 3,000 3,500 6,100 10 600 0 4,200 2,500 50 37.265 37.7 SOURCE: DATAQUEST, INC. - 5 TABLE 2 ESTIMATED WORLDWIDE SHIPMENTS OF Qi^K DYNAMIC MOS RAMS {THOUSANDS OF UNITS) COMPANY FUJITSU HITACHI MITSUBISHI MOTOROLA TEXAS INSTRUMENTS TOSHIBA TOTAL PERCENT CHANGE FROM PREVIOUS QUARTER 1ST QTS 3.0 0.0 0.0 S S 0.0 3.0 2ND QTR 5.0 0.0 0.0 1.0 o.«» 0.0 6.4 113.3 ZRD QTR 7.0 0.0 0.0 3.0 1.0 0.0 11.0 71.9 ira QTR 9.0 S s 6.0 1.0 0.0 16.0 45.5 YEAR 24.0 5 5 10.0 2.4 0.0 36.4 1980 1ST QTR 10.0 5 5 10.0 1.0 5 21.0 31.3 SOURCE; DATAQUSST, INC. TABLE 3 ESTIMATED HORLDVIDE SHIPMENTS OF 4iiC DYNMilC MOS RAMS {THOUSANDS OF UNITS) QQHfm mo FAIRCUILD FUJITSU HITACHI INTEL INTERSIL ITT MOSTEK MOTOROLA NATIONAL NEC SGS ATES SIGNETICS TEXAS INSTRUMENTS 1978 YEAR 6,600 900 1,900 1.780 11.000 450 1,600 17.000 5,700 5.600 6,150 360 1.150 16.700 1ST QTR 2.600 0 200 350 1.700 100 1.100 3.800 1.500 2.000 1.350 150 300 3,600 2ND QTR 3,000 0 200 200 1.700 100 1.300 3,300 1,150 2.400 1,900 175 100 3,200 —1979— 3RD QTR 3.000 0 200 200 1,500 300 1,300 3,400 1,800 2,000 1,300 200 50 2,700 42'tf QTR 1.500 0 150 100 1.200 500 1.500 3,600 2,000 1,500 1,000 225 10 1,200 YEAR 10.200 0 750 850 5,100 1,000 5,200 14,100 6.450 7,900 5,550 750 460 10.700 1980 1ST QU 1.300 0 100 100 900 600 1,400 2,500 1.700 1.500 400 300 0 700 TOTAL 76,890 18,750 18,725 17,950 14,585 70,010 11.500 PERCENT CHANGE FROM PREVIOUS QUARTER (4.0) (0.1) (4.1) (18.7) (21.2) - 6 -SOURCEi DATAQUEST, INC. o» i X I as Ml b i i I ^1 i 05 XI 1-1 fti I «^i I I I ^ 1 I X I 1 ^ i I »t I I ^ g 1 1 I «-ll J X I S« ^ 1 60 3 i I § ?ai I »-»i I X I 1 § l l I »1l t I o o o c« o o O O O O O O O i A O O O O O O voi/) (O u)c>>orv ui C M C M t- «> C M m a to o o o lA o wi m ill In O lA O en Co <A O O _ ^ _ C M a to O id lA ;;^ d C9 o c^ C O g o o i o o o o o a o o o o a o o o o a a o « o « a i o o<o m o s f ^ i o o ^ » O' (0(0 o t « - » a » r « a a . ^ • « • • • C4 vM CM «-i 'T.t to O <A « SO to o o C M t o o o o o o o o i o a i o o o o a o o a o • m o i o o u i S o i o a B t f a a ^ m o « e o ^ ir«-«HCM<o«eioiS(OaDi-as<q m d r o s o m o i m • m • a !
< H C M «HOM «ii>l03CMmi-«<-l i i O I C M I o CM CM O O O r» o o gs° CM CM O O O O O O to O O O < > > O O O to to m C M 1 0 o a a S o C» JT •-• CO o o gS^'SS § ¥> O «« O ^ O ^ C M C M O O Q o to to C O ^ O O C O <} o o o o o o o o o o o o o o o o o o to O V O O O l O O t O t O %0 T- C M . : r . : ^ r . < O i O O O O O O O O O O O n o i o o i o i o i o i o i o a o e » » C.c«9CM0PCM CM »-• o> g o o o o _ _ o o O O to O 00 9) lO <0 10 fi lO rt I O I r I to I a I CO I O Co to p» d-( J J 13 I i at o to CM CM a m 00 CM ^ g »-I 1 & 2»-»Ci 3.^ »-aN^S ^'J k H : 3 ^ - , ) - , ^ w . , r , t j ^ G5ic3<i?:5?s6-.6tjasci QSH^cidaQCoco ^ O H 1 J g H 3 s '^ la » BQ 1^ re « ^ N< C O oj >H aa Q 1-I wi s-t SH eg I I Go Ci a : I S ^5 £ « S ^S -7-TABLE 5 ESTIMATED WORLWIDE SHItMSNTS OF FAST >K NWS STATIC RAMS {THOUSANDS OF UNITS) COMPANY A14D Mil FUJITSU HTUCHI INTEL INTERSIL MOSTEK MOTOROLA NATIONAL NEC TEXAS INSTRUtdENTS TOSHIBA TOTAL PERCENT CHANGE FROM PREVIOUS QUARTER 1ST QTR 0 5 0 0 800 0 0 0 0 25 0 0 S30 2ND QIR 0 10 0 0 1.200 0 0 10 10 70 0 0 1,300 55.6 3i?i? QIS. 0 5 15 0 650 3 0 20 25 250 0 0 968 (25.5) urff QTR 0 5 60 0 900 20 0 SO 65 250 5 15 1,370 m.5 YEAR 0 25 75 0 3,550 23 0 80 100 595 5 15 4,468 1980 1ST QTR S 0 150 0 1.125 35 S 70 200 200 30 25 1,835 33.9 SOURCE'. DATAQUEST, INC. - 8 -2 5 25 1 1 t i l 1 1 X 1 1 Q ; ^ 1 1 B 3 i i ^ O 5 es :% at cy «4 1 Es d-l 1 C O X 1 I •-• i e i 1 1 '•.^i t 1 1 1 1 I t - i i 1 ) X I 1 1 ^ i 1 i -a-i 1 1 ! 51 1 i!«a 1 >^ 1 1 » i 1 1 X 1 ! 1 ^ j 1 1 1 1 «-ii 1 1 X 1 1 03 i o o o o o CO lA U) <0 «-• < o o o o o r in C4 en C O O O Q 05 Ci« C O m O o o CM O 1-t # m o o 1-t tf) O O i-« vn m (O 1H lo a o U} O t o C M m <o c j • ••• m o o 3 1-t o o w o l A r CM vn CM • T H O O 1-1 i I I J i 1 t 1 1 1 1 1 1 t 1 1 1 i r -1 1 1 1 I I 1 t 1 1 1 1 1 m at P" irt o c^ m r^ O O xn m i H m ca (O • CO O CO (O CM • iO CM c» « CM (O O • O IN • ^ s H • & s i QP 2 & i 5 1 3 s § s C O at i &1 M ( Mi I V<4t t I »-»l X I » n o p a i vo C M us o o o I « B il Ul It lA I CM I • I t -« o o m o o o O CM 1 -1 CO O O O o O Q o lO O c^ O O U) O lA CM O .
d 1 -4 lA lA CM lA O It CM CM (O 0» lA O ^ ^ i § a H i -i < -a ^ -^ C O U 3 % m S) % < Q ^ Q § S 6 - I § S S J - ^ ^ = a ^ H H 2 - ^ g ^ Q > -3 ii as eg ^§ EH H Sfe S § 2 -9-TABLE 7 ESTIMATED i/ORLDUIDE SHIPMENTS OF iK EPROMS {THOUSANDS OF UNITS) QQftmi AMD ELECTRONIC FAIRCHILD FUJITSU INTEL MITSUBISHI MOTOROLA NATIONAL SIGNETICS ARRAYS TEXAS INSTRUMENTS TOSHIBA 1978 UM <485 200 280 280 3.400 S 1.020 1,250 280 2.100 40 1ST QTR 600 75 160 70 1,100 10 700 600 0 800 50 2ND m. 700 100 200 50 1,400 15 750 800 0 800 100 ZRD QTR 700 125 350 50 1.400 25 1.000 800 0 800 100 HTH SCR 500 35 600 50 1.100 40 1.000 900 0 800 50 YEAR 2.500 335 1,310 220 5.000 90 3.450 3.100 0 3.200 300 1980 1ST QXR 600 0 750 50 700 60 500 1.000 0 800 35 TOTAL PERCENT CHANGE FROM PREVIOUS QUARTER 9.335 4.165 4.915 5,350 5,075 19,505 4^,495 23.5 18.0 8.9 (5.1) (11.4) SOURCEX DATAQUEST^ INC. QQHVmX Al-W FAIRCHILD FUJITSU anACtil INTEL MITSUBISHI MOSTEK MOTOROLA NATIONAL SYNERTEK SSTriATSD VORLWIDE SHIPMENTS OF 16K {THOUSANDS OF UNITS) l 7 /O YEAR 0 0 5 35 1.350 S 25 100 5 0 TEXAS INSTRUMENTS 8 5 0 TOSHIBA 5 \ST QTR 0 0 70 125 550 10 90 160 5 0 400 25 2ND QTR S 0 200 200 750 20 150 150 S O 0 900 50 ZRD QXR 5 0 300 350 800 50 250 160 80 0 1.100 90 EPROMS >TH SIR 10 s 300 500 900 90 350 200 120 5 1.800 200 YEAR 15 S 870 1.175 3.000 170 840 670 255 S 4.200 365 1980 1ST QXR 25 30 350 700 950 210 275 250 250 S 2.000 300 TOTAL PERCENT CHANGE FROM PREVIOUS QUARTER 2,370 1.435 2,470 3,185 4,470 11,560 5,340 58.5 72.1 28,9 40.3 19.5 SOURCE: DATAQUEST, INC. - 1 0 -TABLE 9 ESTmATSD WORLDUIDE SHIPMENTS OP Z2K EBROHS {THOUSANDS OP UNITS) COMPANY FUJITSU aiTAOUI INTEL MITSUBISHI MOTOROLA NATIONAL TEXAS INSTRUMENTS TOTAL PBSCBNT CHANGE PROM PRWIOUS QUARTER 1ST QTR 0 0 5 0 0 0 10 15 2ND axR 0 0 30 0 0 0 35 65 333.3 ZRD QTR 0 0 50 0 0 0 60 110 69.2 iTH QTR S S 100 s s 0 90 190 72.7 YEAR S S 185 S S 0 195 380 1980 1ST QXR S S 165 5 5 S 150 320 68.1^ SOUSCE'. DATAQUEST, INC. - 11 -^ ' r, "' >.^s RESE> , ^ ^ ^ A Subsidiary of A.C. Nieiien Co. ^ I N C O R P O R A T E D NE\A/S SIS Code: Vol. II, 3.0 MANUFACTURING MODEL DATAQUEST's Semiconductor Industry Service has just published a comprehen-sive manufacturing model. This report of over one hundred pages is a complete revision of Section 3 of the Semiconductor Industry Service notebook and replaces earlier material published in 1975 and 1977. TECHNOLOGY AND EQUIPMENT Wafer fabrication technology continues to evolve, and the interplay of equipment technology, device technology, plant layout and design, site selection, cost, and personnel management becomes increasingly complex. The trend toward greater device complexity and larger die size has been spurred on by lowered defect densities. As device geometries approach the 2-micron level and below, processing, environ-mental and equipment technologies must be carefully coordinated. Of the many process technologies, photolithography has been one of the key factors in determining the pace of Very Large Scale Integration (VLSI) design and manufacture. The trend is away from contact printing toward proximity and projection printing. Dry etching techniques are being developed as a necessary concomitant of projection printing in order to etch fine patterns in a variety of materials. Deposition of materials is becoming more sophisticated with the addition of sputtering and plasma deposition to the tried-and-true electron beam and chemical vapor deposition technologies. Ion implantation techniques have kept pace to achieve, quickly and inex-pensively, control of impurity concentrations and junction depths. Although complex and expensive, with increasing delivery times, wafer fabrica-tion equipment is proving to be cost effective. The equipment is increasingly Copyright © ^ June 1980 by DATAQUEST - Reproduction Prohibited The Content of this report represents our interpretation and anaIysis of information generaIly available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not cental" material provided to us in cnnfidence by our clients, This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO controlled electronically (by the integrated circuits it is used to fabricate). The result is greater automation, control, and reproducibility of results, as well as lower defect levels due to lower operator/wafer interfacing. The clean room facilities in 1980 are geared toward Class 100 rating and better rather than toward the Class 1000 rating that was acceptable until 1978. Deionized (DI) water is being elaborately treated and tested to meet the new Clean standards. The water is pretreated through activated carbon and diatomaceous earth filters before it goes through reverse osmesis and deionization stages. Four-inch diameter wafers are expected to be the standard during the mid-1980s; larger wafers may be used for many standard memory lines. Thus, for a facility processing 10,000 wafers out per four-week period with manufacturing costs of $tfO to $80 per wafer aid ^oss rev«iues of $300 to $600 per wafer, at least $3.0 million dollars per period cstfi be realized. At the same time, equipment purchases for today's use must nevertheless be chosen for eventual upgrading to handle five-inch, and even six-inch diameter wafers, as long as the particular technology will not be obsolete by the time of the upgrading. It is also possible to adapt machines to suit other products. With the high capital cost of some equipment, care must be taken to obtain maximum utilization of such equipment while it is in service. PLANT LAYOUT AND DESIGN Several factors determine the way in which a particular plant is laid out. Cleanliness for VLSI production is influencing what portion of the equipment remains in the clean room. Only the loading end of diffusion furnaces are being allowed in the clean room. The heat and dust generating portions are being separated from the clean room by a fire wall. The same is true for ion implanters and the trend will be continued for other equipment where appropriate. Servicing of equipment and work stations in old facility designs meant frequent ingress of personnel into the clean room to deliver bottles of chemicals, replace furnace tubes, and repair plumbing. New layouts obviate the necessity for these entries by pumping chemicals (except photoresist) to other points of use. Plumbing can be done outside the dean room if a service corridor rings the fabrication area. Furnace tubes can be pulled and replaced behind the fire wall and outside the clean room. If gases are pumped overhead through a crawl space, gas Unes can often be serviced in these crawl spaces without need for entry into the clean room. Philosophies of equipment design have shifted toward single wafer and in-line processing and wafer handling, away from the purely batch-type handling. Thus, there is greater interplay between different processing areas (as opposed to the almost strict quarantine that existed before) as long as cleanliness is maintained, material flow facilitated, and cross-contamination avoided. New demands for material account-ability have made production control supervision the heart of the entire operation and this fact has also affected the overall plant layout. Increased usage of computers and terminals will make this approach even more effective. - 2 AUTOMATION Perhaps the most persistent eind pervasive trend is that towards automatic sequencing of events within a given piece of equipment. Also popular is the drive toward computer automation of the entire fabrication area for control, repro-ducibility, data collection, and analysis. The benefits to be reaped are legion and include: Less wafer handling Process monitoring and control Correct process sequencing Proper routing of material System self-diagnostics and self-correction Data collection for off-line processing Elimination of paper work Material accountability (especially useful since lot sizes vary for different operations in the manufacturing process) Equipment manufacturers are following the trend toward automated equipment, some with micro- and minicomputers. Some automation now exists in the areas of diffusion/oxidation, physical and chemical vapor deposition, ion implantation, masking, alignment, mask making, mask inspection, testing, plasma etching, DI water, and environment monitoring. Variables which constitute the particular process at the factory level are sensed and measured. The supervisory element compares the measured data against set values and adjusts the system to initiate or shut down the process. Communication and display terminals are at the floor or factory level and through them data are transmitted to the highest level, the management computer. Exciting as it is, the prospect of a fully computerized, semiconductor manu-facturing facility is not foreseen before the mid- to late-1980s, even though an experimental automated line has been constructed at Texas Instruments and auto-mated production lines are used by several captive manufacturers. The determining element is, of course, equipment development. Much of the equipment today is being "updated" by adding microprocessors for sequencing. However, very few pieces of equipment are designed around computer control with adequate supporting software. More cind more companies have placed computer terminals in their manufacturing areas but these terminals are edmost cdways to handle data rather than direct and control manufacturing processes. The development cycle for very sophisticated equipment can range from two to five years. Delivery times of equipment costing above $200,000 often range from nine to eighteen montlrs. Development costs are often high too, as is the rate of obsolescence. Consequently, only the wealthiest semiconductor manufacturers can - 3 undertake their own development programs toward full computerization of the factory. The rest must wait for market forces to react. Batch processing will probably never disappear in the foreseeable future. However, more and more equipment manufacturers are offering cassette-to-cassette wafer systems to eliminate tweezer handling. Tweezers are a well-known cause of damaged patterns, silicon particle generation, and wafer defects. In properly con-trolled equipment, each wafer is subject to almost the same set of process parameters. STAFFING The cumulative effects of the recessions of 1970 and 197^^ are now evident in the acute shortage of trained engineering staff. The trend of decreased enrollment in engineering colleges since these recessionary periods has not been reversed at rates compatible with industry growth. For those engineers who remained, it has become a sellers' market. In Santa Clara (Silicon) Valley, California, unemployment at ^.7 percent in September 1979 was at a five-year low, unparalled anywhere in the country. At the lower end of the wage scale, turnover rates ranged from 50 to 100 percent among operators. Although mothers of young children have rejoined the work force, the industry still faces severe labor shortages while professional personnel are being wooed by "headhunters" and by print, skywriting, radio, and television ads. Incentives and bounties are offered to staff already in place to ensure successful recruiting. Housing costs, already prohibitive for engineering staff, are even more pro-hibitive for operators (see "Site Selection"). Commuting is only a partial solution to the problem of staffing expanding operations. The trend, therefore, has been to relocate new operations in more favorable labor markets, all other things being equal. WAFER FABRICATION GUIDELINES Certain guidelines became apparent as U.S. merchant and captive semiconductor mzinufacturers were surveyed to develop the costs to be used in this model. A summary of tliese guidelines follows. Direct labor in most wafer fabrication areas correlates well with the number of wafers out (assuming adequate wafer fabrication yields) and with the number of mask layers; the product of these two factors is approximately 250. In other words, if an 8-layer device were being manufactured, each worker should account for approxi-mately 31 wafers out per week. Supervision of direct labor typically runs 15 to 20 percent of direct labor hours and, because of higher pay rates, 36 to 'tS percent of direct labor dollars. Allocated labor accounts for all indirects in the wafer fabriction area. This category includes process sustaining engineers, product engineers, quality control and quality assurance, production control, and equipment maintenance. Allocated labor is the largest labor category and may run from 180 to 280 percent of direct labor cost. We found in our survey a few cases where older processes are in production and little technological change is taking place; in these cases, allocated labor costs were much lower. Typically, the weifer fabrication area floor space depends on the wafer start capacity required. Our model assumes approximately 12,000 wafer starts per period (tliere are 13 four-week periods per year) and has approximately 12,000 square feet of wafer fabrication ^ e a and 12,000 square feet of area for testing and office space. Thus, the wafer fabrication area required is approximately 1 square foot per wafer Start. The constrtiction costs for tiiese facilities are substantial, particularly in wafer fabrication areas. An analysis of company annual reports suggests that the semicon-ductor industry spends about 25 percent of its capital on facilities and 75 percent on equipment. Our model shows higher facilities expenditures on a percentage basis because all construction is new; as the equipment ages, it is to be expected that new equipment will be purchased before the facilities become oteolete. This phenomenon accounts for the lower ratio in mature companies. In our N-channei RAM wafer fabrication model, total capital expenditures for facilities and equipment are; Cost Percent Facilities: $ 3,832,300 38% Equipm«it 6,36^,950 62 $10,197,250 100% The facilities expenditure includes both wafer fabrication and office space and is divided as follows: Cost $3,319,300 513,000 $3,832,300 Cost Per Sq.Ft. $273 $ 40 Fab Area (12,160 sq.ft.) Offices and Test (12,840 sq.ft.) In the table above, the costs per square foot are in addition to the cost of the basic building shell. In our model, it is assumed that the land ^id building shell are leased at a cost of $1.00 per square foot per month. If land were purchased and a building constructed, additional costs of $40 to $85 per square foot would be incurred. The variation in these figures depends on the price of the land; it may vary from $40,000 to $400,000 per acre or more. MODEL COSTS Our 1980 cost model is based on an MOS 16K DRAM, fabricated using a 6-layer process that does not employ silicon nitride. Other companies may use an 8-layer process. Basic assumptions are listed below: Technology • 16K DRAM, MOS N-channel • 6-layer doubie-poly process • 5-micron geometry 2 • 1^0 mil X 1^0 mil chip size (= 20,000 mil ) • 16-pin DIP plastic package • 'A-inch diameter silicon wafer • 1:1 projection aligners (UV) • Negative photoresist • Wet etching • Plasma ashing of photoresist Production • Two full shifts per day (skeleton graveyard shift mainly for maintenance) • Seven hours effective work per shift • Five day week = 20 days per period • 12.5 productive periods per year • 25 percent benefit package including shift premiums • Minimum throughput at any step = 60 wafers per hour • 10,000 wafers out per period • Productivity at approximately kl wafers out per operator per week (6 layers) • All assembly operations offshore - 6 -^ Yields • • • • Facilities Cumulative Fab yield E-Sort (16K DRAM) Assembly yield Final test yield - 85% - 16% - 90% - 80% • Building rented as shell at $1.00 per sq.ft. per calendar month • Space rented = 25,000 sqJt. • Minimum of 15 percent inflation rate on construction, materials, and equipment • All facilities and services supplied from scratch • All design s«-vices contracted to outside engineering firms • All chemicals (except photoresist) to be pumped into the fab area from Storage tanks to points of use • Maying can accommodate up to 10 projection aligners • Diffusion can accommodate 20 furnaces • Fab area = 12,160 sq. ft; E-Sort, Test, Offices = 12,8W sq.ft. total Equipment • Highly automated operation • Convertible for use C M I 5-inch diameter substrates • Eqiiipment will be used eventually on 2- to 3-micron gates and shallow junctions (less than 1.0 micron) • Need filled for data collection and information management to facilitate trend analysis Volume-sensitive wafer making costs appear in Table 1, a summary of Wcifer making costs appears in Table 2, and a summary of equipment costs in Table 3. The fixed monthly costs of Table 2 include building rent, sewage, electric power, gas, and depreciation of buildings and equipment. Howcird Z. Bogert Table 1 VARIABLE (VOLUME-SENSITIVE) COSTS (Data Gathered From Company Surveys) # -Wafer Fab (75% Cumulative Yield) Materials: Cost per Wafer Out - Silicon - Masi 20.93 21.87 $60.8'^ Source; 9.5% 1^.3 22.2 Percent 29% 35 36 100% DATAQUEST, Inc. June 1980 Table 3 EQUIPMENT COSTS: N-CHANNEL MODEL Diffusion Area Masking Area Deposition Area Fab Support and Test Areas Backside Processing Grand Total (6^2% Tax Included) Capital Cost $1,339,^50 2,283,300 1,039,700 1,287,900 t^ltt,600 $6,36^,950 Source; Percent of Total 21.0% 35.9 16.3 20.3 6.5 100.0% DATAQUEST, Inc. June 1980 IS r s± ^=.^= ^£ ^ ^ ^= ^= ^= ^ f ^= ^= = — — — = ~ k r f ^ ? ^ ^ XA k^L.P^ ^ ^ ^ ^ ^ -^^B ^ 5 ASubsidiarv of A.C, Nielsen Co, ^ INCORPORATED J SIS CODE: VoLIII, S.Cf UPDATE ON INTEL SUMMARY Intel is in the pM-ocess of making a majw shift in tlie value-added component of its product base, away from semiconductor memufacturing and into design, software, and systems integration. This strategy will make Intel more of a true microcomputer company and less of a commodity semiconductor supplier. The basic core of its strategy is to make a standardized operating system available on a chip. The investment required to accomplish this goal is huge—DATAQUEST estimates the development costs to be in the order of $100 million, a portion of which has already been expended by the Company. The key to this program is its execution—if the Company is successful in bringing these products to market, then the investment should prove higlily successful. If the integration is not successful, demand will not be as great and Intel will have lost some momentum over its competition. DATAQUEST projects a ^k percent gain in revenues at Intel in 1980 to $880 million. Despite tlie potential margin pressure of a weakening in semiconductor demand in the second half, we believe that margins will closely approximate last year's and that earnings will increase by 30 percent to $^.65 per share. MARGIN ANALYSIS During 1979, Intel not only maintained, but increased its historically high profit margins, as forecasted by DATAQUEST in its newsletter of December 20, 1978. Intel's ability to maintciin its margins was aided by the price stability brought on by a very Strong demand for semiconductors. In 1980, DATAQUEST perceives some weakening of the rate of growth of semiconductor dememd in the general industry. Intel will also face increcised competition in certain of their high-margin product areas, such as the 2\kl fast ^K Static RAM, the 2732 EPROM, and the SCfS microprocessor. This competition will Copyright © 31 May 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and anaIysis of information generally availabIe to the public or released by responsible individuals in the subject companies, but rsjiot^guaranteed-aitaaccuraGyer completeness, It does not contain material provided to us in confidence by our clientsrTMs" iriTormaTTonis not turnished iri connection with a sale or offer to sell secuTiTies or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO cause some pressure on margins, but DATAQUEST believes that meu-gins can remeun at alx)ut the present level through 1980. Intel has developed several product areas which should provide excellent margins and afford some protection from the competitive environment: • The new high-speed, HMOS II static RAMs. The new high-speed EPROMs The new EEPROMs The 8086 microprocessor family Five-volt dynamic RAMs Microcomputer board products The new high performance microprocessor products Microprocessor and microcomputer support products—peripherals, soft-ware, and development systems The microprocessor products are inherently less competitive than some of the high-volume commodity products such as standard memory products. We believe these product areas and their increasing percentage of revenues at Intel will offset the decline in margins from specific memory products. The 8086 and 8085 microprocessor families still are essentially free of intense price competition. Additionally, the support products in the total package pricing of microprocessor and microcomputer related products promise excellent meirgins. Msmy of these products can be priced on a value-added basis rather than a cost basis. Intel still has processing advantages over most of its competitors. The new HMOS II memory devices are coming into production even as the original HMOS devices are just beginning to see effective competition. It is our belief that Intel still is a low-cost producer for standard products. If the current heavy demand slackens, we believe that Intel can significantly increase yields and reduce costs. Additionally, the exceedingly strong market in 1979 has allowed Intel to spend very large amounts for research and development and other costs in developing a rapidly growing corporation. Since some of those costs are discretionary, they can be somewhat reduced if necessary. Secondly, those costs should begin to bear fruit in revenue and profit in 1980 and beyond. These factors give Intel a measure of protection from an uncertain market environment. First quarter sales increased 52 percent to $205 million and pretax margins rose slightly to 22.5 percent. We expect sequential sales growth of at least 5 percent in the second quarter and a 3it percent increase in full year revenues to $880 million, as shown in Table 1. DATAQUEST estimates that so far in the second quarter the component book-to-bill ratio is in the range of 1.2. Of the major divisions, the two fastest growing are Microcomputer Components (50 percent) and Microcomputer Systems (35 percent). Table 1 Intel Corporation ESTIMATED REVENUES 1977-79 (Millions of Dollars) Memory Components Division Components IBM Contract OEM - Memory Systems Operation Special Products Division Total Memory Components Group Microcomputer Components Division Microcomputer Systems Division Commercial Systems Division Service End User CSD-Austin (MRI) Solid-State Disk Microma Division Intel Magnetics Intracompany Total Company Revenues Percent change from previous year 1977 $ 8^ 69 15 93 $177 $ 38 52 22 -17 0 (23) $283 25.2% 1978 $132 97 5 30 123 $255 $75 75 20 20 0 0 (2^) $^01 41.7% 1979 $203 l'f3 20 0 170 $373 $15i^ 148 30 20 10 0 1 '-(43) $663 65.3% 1980 Estimate $235 195 40 $210 $445 $230 200 55 15 12 18 10 5 (55) $880 32.7% ^Service revenues were estimated at $8 million for 1979 but these revenues were not credited to CSD in that year. Source: DATAQUEST, Inc. May 1980 Assuming only a slight decline in profit margins this year, we believe that earnings can increase by 30 percent to $^.65 per share. MICROCOMPUTER COMPONENTS DIVISION AND MICROCOMPUTER SYSTEMS DIVISION Since the activities of these divisions cire so closely related, we are electing to deal with them together in our discussion of microcomputers and microprocessors. However, separate estimates of their revenues are given in Table 1. The Micro-computer Divisions are probably in the fastest growing area currently in Intel. Thus area is the focal point for some major changes in corporate direction. Strategy Reflecting its new slogan, "Intel Sells Solutions," Intel is putting major emphasis on its future in microprocessors and microcomputers. The basic points of this strategy are: • Move from commodity components to high-margin quasi proprietary micro-processor systems • Be a "Full Service" microcomputer company, offering processors, peri-pheral devices, software products, development systems, board products, e t c • Sell solutions in addition to hardware • Capture revenue at the system, rather than the chip level, with increased non-semiconductor product, including design, software, e t c • Utilize current and future high margins to support extensive R&D to out-distance competition Intel's current strategy is both a corporate strategy and an attempt to meet competition in the microprocessor area. Centred to this strategy is a multi-faceted development program in Intel which arose from concern with some basic problems in the microprocessor area. These problems are: • Increased competition from the new 16-bit microprocessors—the 68000 and Z8000, for example, the loss of the Olivetti business to the Z8000 • The tremendous costs being incurred in software and systems development by people applying the new, powerful 16-bit microprocessors • The need to recoup development costs for these very complex devices • The long lead time, often exceeding two years, from product inception to final design and software application of a microprocessor-based system - If' Meeting these problems has resulted in a coherent future microprocessor Strategy for Intel, which includes: • Going to higher level building blocks for semiconductor systems • Expanding th« value added from basic semiconductor manufacture into systems design and software • Moving toward bringing some of that software back to the chip level The 68000 microprocessor made by Motorola and the Z8000 microprocessor made by AMD and Zilog are regarded as competitive to the 8086 16-bit microprocessor, especially if only the CPU chip is considered. Such comparisons are somewhat unfair: the 8086 has been in production for a considerable time and, therefore, it is natural that newer devices should have some technical edge. More importantly, these complex microprocessors are not stand-alone devices. Their performance in any given application is aided by other peripheral chips, the applications software, e t c For many applications, the speed or cost of system design is as important as final cost. This is essentially true of applications where quantity production is limited. Thus, for many applications, these products do not compete as individual chips, but within the environment of a set of chips and support material. Intel's approach to this situation is to invest heavily in the development of these complex systems, including all phases of support products as well as the new microprocessors themselves. This approach has been well publicized by the Company as a pre-emptive strike against the 68000 and the Z8000. By pre-product announcement, they hope to delay and stop the movement of the potential customers to these competing products. The addition of "coprocessors" to a basic microprocessor greatly enhances the power of the system in some applications. Peripheral devices, such as the 8089 I/O processor, the 8087 math chip, and others, such as the DMA memory controllers, peripheral device controllers, amd SDLCs, are highly complex chips, and, in some cases, significantly more complex than the 8086. They are microprocessors optimized to do special functions quickly and efficiently. Telecommunications and Automotive Operations This newly formed operation reports to the Microcomputer Components Division. Sales volume in 1979 was small but has tremendous growth potential. In telecommunications, Intel has introduced the 2910 Codec, the 2912 filter, and the 2920 analog microprocessor. DATAQUEST estimates that Intel has invested $1..5 to $2 million in advanced test equipment to help get this business started. In automotive, Intel is working on a large 16-bit microprocessor program for Ford, and DATAQUEST believes that Intel is very active in this field overseas. It is DATAQUEST's perception that Intel has changed its attitude to the automotive market after opting not to pursue General Motors' business and having General Motors accept the decision and award substcintial amounts of business to Intel's competitors. 5 -Table 2 Intel Corporation ANTICIPATED 1980 MICROPROCESSOR PRODUCT INTRODUCTION I. 3 Microprocessor Systems • 16-bit Microprocessor (iAPX 186) Enhanced 8086, with support chips integrated Enhanced instruction set • 16/32-bit Microprocessor (iAPX 286) 32-bit internal Some operating system integration (into hardware) Memory meinagement High performance duster controller • 32-bit Microprocessor (iAPX ^^32) "Micromainframe" High-level on chip language integration (on chip!) Object oriented Will support transparent multiprocessing Multilingual New architecture (memory-driven processing) II. Peripheral Processors • 8087 - Numeric Processor 6'f-bit floating point math processor Compatible with all languages, hardware and software transparency 68 Numeric Processor • 8089 - I/O processor • Support Chips SDLC, UART Memory Controller Error Correction Chip Floppy Disk Controller Timer/Counter Table 2 (Continued) Intel Corporation 1980 MICROPROCESSOR PRODUCT INTRODUCTION ni. Software • Intel Standard Languages: Systems Programming Languages ASM/86 PL/M/86 PASCAL/86 Applications Oriented Languages PASCAL/86 BASIC (to be introduced in 1981) FORTRAN/86 COBOL (to be introduced in 1981) • Operating System Software (iRMX 86) "R^eal Time Multi-Tasking Executive" Executive (23K bytes) I/O Control (t^OK bytes) IV. Development Aids • Disk file sharing system • Multi-Station microprocessor development systems • Mainframe link for distributed development Source: Intel Corporation and DATAQUEST, Inc. May 1980 7 -The range of products planned by Intel to meet its strategy goals is outlined in Table 2. Their overall impact is impressive. They could significantly increase the computing power possible with microprocessors. Some basic comments cire in order: • The investment required is extremely large. DATAQUEST estimates that ultimate costs will be in the order of $100 million. • The concept of a ststndardized product is implied, i.e., moving the component mentsdity into the computer systems area. This is a question-able Strategy, but one which DATAQUEST believes appropriate to many applications. The movement to standardized operating systems is reminiscent of the move to standardized logic designs in the early 1960s. At that time the movement was highly resisted by the computer companies; however, the benefits in economy, convenience, and design time ultimately became overwhelming. Intel has the opportunity of being the first to set the initial standards, and, if successful, the Company could realize a powerful, long-term competitive advantage. • The overall Intel strategy is highly application dependent. DATAQUEST believes that this strategy could be successful for a large percentage of applications, but that it will not exclude other microprocessors from gaining marl<et acceptance in certain other applications. • Intel is clearly moving the value-added component of its product base away from semiconductor mainufacturing and into design, software, and systems integration. Essentially, in this area they will be more and more a microcomputer company and less a commodity semiconductor company. Insofar as this trend deviates from past strengths, it is potentially hazardous. • The general architectural approach taken by Intel generates neither high praise nor scorn from computer manufacturers. The inference is that the approach is one of several acceptable possibilities. What is important is that Intel executes this product development. If the Company is successful in bringing these products to the market, then the investment should prove highly successful. If there are significant product problems and the integration of these products is less successful than desired, then this will affect market demand. Detailed estimates of the revenues of the Microcomputer Com-ponents Division are given in Table 3. Table 3 Intel Corporation ESTIMATED MICROCOMPUTER COMPONENTS DIVISION REVENUES - 1979 Estimated Product itOOk 8008 8080A 80'f8/8021/8035 80^^9/8022 S7t^& 8085 8086 Other Units (Thousands) 120 65 780 1700 230 300 1085 75 -Average Price $ It.50 $ 5.50 $ 5.00 $ 6.95 $12.00 $75.00 $ 8.00 $80.00 . -Drag Factor 2 3 5 0 0 0 5 3 -Revenues (Millions of $) $ 1.6 1. 23.^ 11.8 2.8 22.5 52.1 21^.0 l^f.^f Total The drag factor is used to maleen dealt with by the FCC Computer Inquiry of 1966/67 in which two major ongoing concerns were addressed: —That a regulated common carrier (particularly AT\elieve that the FCC can relinquish its authority or that it desires to do so. Type approval of terminal equipment, for example, will still be required. We also do not expect any near-term action by the Congress or the Courts to take away the FCC's authority over these areas. • Are the terms "basic services" and "enhanced services," which are used by the FCC, clearly defined in the technical or trade literature of the communications and/or computer industry? The FCC states that all network services are either basic or enhanced and deregulates those which are enhanced. We t)elieve that in due course the FCC will provide more complete definitions and/or guidelines than it has so far. However, we - 4 -do not find these to be definitive terms in the usage of either the communications or computer industries. • Do the service offerings of carriers which operate value added networks (VANs) become deregulated? TV^^net, ITT, and Graphnet are providing enhanced ("value-added") services of this kind, but their operations are not large enough to constitute dominant market forces. DATAQUEST believes that these services will now qualify for deregulation. • Will the Bell System's Advanced Communications System (ACS) (if and when it is re-introduced) be a regulated common carrier service? Or will it be an enhanced data communications/processing service offered by AT&T's unregulated subsidiary? We believe that the answer to this question will depend to a large extent on the features of ACS when it is re-introduced, but that it will most likely qualify for deregulation. • Will GTE be required to operate its Telenet public data network subsidiary - also a VAN - as a deregulated "arm's-length" subsidiary? GTE acquired Telenet for two million shares (approximately $58 million) in 1979. We expect that Telenet and probably other planned services of GTE's new Communications Network Sytems Group (e.g., "GTE Viewdata") will become offerings of the deregulated subsidiary. • Will non-communications companies such as IBM, Xerox, or Exxon be allowed to enter the enhanced data communications services market and operate non-regulated public data networks similar to, or more advanced than, Telenet for example? DATAQUEST believes that the Order will allow them to enter this unregulated market as long as they offer sufficient "enhancement" beyond the transportation (common carrier) function. We anticipate that Xerox's XTEN, for example, would qualify. • Will Western Electric be allowed to manufacture equipment for sale to the public through an unregulated arm's-length Bell System marketing entity? The 1956 Consent Decree appears to restrict Western Electric to the manufacture of equipment for sale to the Bell System only (other than D.O.D. work). Western Electric's manufacturing capacity is approximately ten times the size of any other telecommunications equipment manufacturer's U.S. plant. The resultant economies of scale provide Western with the potential for major competitive advantages. We anticipate that Western will, therefore, be "handicapped" in some still undetermined way in its sales outside the Bell System. • Will those operations of AT&T and GTE which manufacture terminal equipment be required to become parts of the arm's-length subsidiaries of those companies? Their manufacturing competitors will presumably contend that the potential for subsidy from these companies' monopoly common carrier services exists if full - 5 - . separation is not effected. We believe that this issue will be a difficult one to resolve, particularly for AT&T, but that, in the long run, those manufacturing operations will become separated. • Does this Order change the regulatory status of the specialized common carriers (SCCs), eg., MCI, SPCC? We interpret this Order as having no serious impact on the SCCs. Their services will remain regulated. They could previously offer data processing services through unregulated subsidiaries. Apparently they can now offer such services directly without a separate subsidiary. However, in order to avoid potential conflicts with state regulators, they would probably use separate subsidiaries if and when they do offer enhanced services. • Does this Order deregulate the services of the SBS partnership (IBM, COMSAT-General and Aetna)? The Services to be offered are technologically innovative. Nevertheless, we believe that they are predominantly services "offering transmission capacity for the movement of information" which the FCC regards as subject to basic common carrier regulation. LEGAL ROADBLOCKS: The courts have played a major and increasing role in the resolution of issues arising from FCC decisions on deregulation and the introduction of competition. Those who oppose this latest FCC Order can attack it through the courts in some of the several ways listed below: • The FCC decision'appears to be inconsistent with AT&T's 1956 Consent Decree in at least two areas: —AT&T will be allowed to offer non-common-carrier services. —Western Electric will be allowed to sell equipment outside the Bell System. • The unregulated sales and/or manufacturing subsidiaries of AT&T (and perhaps GTE) would become sufficiently large that they could be construed to dominate the markets in which they operate. • Arm's-length separation of major portions of Western Electric and possibly Bell Telephone LatX)ratories means the fragmentation of a major national resource (the integrated Bell System) and is not in the public interest. • Adequate studies of the economic impacts of this Order have not been made, and it should not be implemented until satisfactory studies have been completed. • The March 1982 deadline is too short for an orderly transition of this magnitude; several more years should t>e allotted. - 6 -• The 1934 Communications Act gives the FCC jurisdiction to regulate, but not to deregulate. The potential litigants in such challenges cover a wide spectrum including: • The Justice Department • State Public Service Commissions • Industry associations, e.g., Computer and Communications Industry Association (CCIA), U.S. Independent Telephone Association, North American Telephone Association (NATA), representing Interconnect companies • Companies offering telecommunications and data communications services and equipment THE OUTLOOK To a large extent, the question of whether the FCC's decision will be sustained and implemented depends upon the support and actions of other government organizations, including the Justice Department, NTIA, as well as the White House and the House and Senate: Questions relating to the 1956 Consent Decree are undoubtedly of most immediate concern to the Justice Department which was a party to tliat decree. Although the Justice Department has not announced its position, in view of its present antitrust suit against AT&T, the department is expected to take a posture that may range from caution to outright opposition and legal challenges. In recent correspondence to the House Committee on Interstate and Foreign Commerce, the Department of Justice objected to vacating the 1956 Consent Decree. The letter also advocated divestiture of Western Electric and Bell Laboratories and represented arm's-length subsidiaries of AT&T to be imperfect substitutes that would not be effective in restraining anti-competitive behavior. •We believe that the Justice Department wiU show some independence of other organizations within the executive branch, most of which we consider to be favorably inclined toward the FCC decision. The NTIA is judged to be in favor of the FCC's Order and its director, Henry Geller, is reported to have been acting in a liaison role between Congress, the FCC, and the administration. Based upon its attitude toward regulation in general and its recent support of pending congressional telecommunications deregulation measures in particular, we t>elieve that the White House will support the FCC action. Congress has not been successful in its efforts to rewrite the 1934 Communications Act. Both the Senate and the House version of the proposed bills stress, to varying degrees, deregulation and broader participation in the computer/communications industry. Representative Lionel Van Deerlin, the - 7 -chairman of the House Communications Subcommittee, has been frustrated in his attempts over the last four years in securing passage of a Communications Act rewrite bill. The latest version to reach the floor has once again run into opposition to certain details and has virtually no chance of passage during the current year. The bill's proposed measures largely follow those contained in the FCC Order. Thus, we expect that Congressman Van Deerlin would support the FCC's action as a means to accomplish similar ends. Senator Howard Gannon, chairman of the Senate Commerce Committee, and Senator Ernest Hollings, chairman of the Communications Subcommittee, have been somewhat non-committal, and DATAQUEST anticipates that they will not oppose the FCC's Order. In the past, challenges to FCC decisions on the basis of insufficient evidentiary information or unresolved economic impact have not been successful. Similarly, the Justice Department's recent suit contesting the FCC's approval of Satellite Business Systems on antitrust grounds has not been effective. In view of these and other precedents set in the recent history of the Interconnect and SCC activities and the anticipated largely supportive attitudes of other cognizant government organizations, DATAQUEST expects that the FCC's Order will be carried out without undue delay. IMPACTS AND IMPLICATIONS Because the FCC Order is so broad in scope, it is expected to have impact upon a wide range of markets and their participants. Voice Terminal Equipment Deregulation of these products which include telephones, PBXs, and other voice station equipment, implies major restructuring of the market and present tariffs. Telephone companies are allowed to earn a return on their investments, which is under the control of the FCC and state public utility commissions. The companies derive further income from a pool of toll revenues, which are allocated in part on the basis of investments in customers' station equipment. For the telephone industry in total, these revenues amount to about $5 billion annually, or approximately $4.80 per month per subscriber. Removing customer premises equipment from the telphone companies' rate base would have a significant impact upon their revenues, and will undoubtedly require some readjustments in the tariff Structure if local rates are to remain unaffected. We would expect that all present and future equipment market participants, including the AT&T and GTE unregulated subsidiaries, would act quickly to establish a posture in the newly created markets. At stake is a market that DATAQUEST estimates will be over $6 billion at the retail level in 1982 when the FCC Order is intended to t)eeome effective. Whereas the business segment of the market has been served to a growing extent for a number of years by the foterconnect suppliers, the residential market for telephones has been dominated by the telephone companies which provided the instrument as part of the wrvice and at bundled tariff rates. The FCC - 8 -Order requires the outright sale of telephone instruments, so that a large retail market would be created with opportunities for new market entrants. The Interconnect market which serves the business community with PBXs and key telephone systems would also be affected immediately. The unregulated sutjsidiaries of AT<5cT and GTE will compete in direct sales of PBSs and KIS systems with Interconnect vendors who previously were the only non-tariff sources for purchase of this equipment. The fact that all equipment will now t>e supplied on a non-tariff basis will tend to put all vendors on an equal footing. Besides the present AT&T and GTE manufacturing subsidiaries (Western Electric and GTE-Automatic Electric), a large number of other companies are involved in this market, and include: • Northern Telecom • Stromberg-Carlson (General Dynamics) • Rolm « NEC « ITT • OKI Data Communications Equipment The market for data network interface equipment, which in 1982 is estimated to reach at>out $600 million, has been much less dominated by the telephone industry than the voice terminal markets, and deregulation would have a lesser immediate impact. In the long term, as Bell and GTE assert their presence through the unregulated subsidiaries, we should expect a very competitive climate to develop, particularly in the much larger and broader market for data communications equipment, including terminals. A very large number of data communications equipment suppliers jmrticipate in this market, including: IBM DEC Motorola/Codex General Datacom Anderson-Jacobsen - 9 -Data Communications Services The distinction between regulated and unregulated data communications services will undoubtedly require clarification and will probably also be subject to further controversy. We would expect to see the marlcet participants, especially potential new ones, take a cautious posture until a clearer understanding is reached of what constitutes service enhancement. Present and future participants in this market include: GTE-Telenet lymnet SPCC SBS ITT Xerox (XTEN) Data Processing Services The FCC decision permits the smaller telephone companies and the AT&T and GTE subsidiaries to offer unregulated data processing services. This is an area in which no precedents exist in this country. In Europe and Japan, the PTTs are moving or are poised to move in the direction of becoming full-fledged "information utilities" that in time will offer a range of data bank and data processing services. The FCC Order appears to have prepared the grounds for similar activities in the U.S.A. Current market participants include computer teleprocessing and data base service companies, such as: • CDC/SBC • General Electric • ADP • Computer Services Corporation - 1 0 -Semiconductor Industry The semiconductor industry is now selling more than $500 million in components annually to the U.S. telecommunications manufacturers. Participants in the industry have S O far elected not to pursue vertical integration into the telecommunications equipment market as they have in the computer market. With a market approaching 20 million units a year in 1982 for new and replacement telephones, and with increasing semiconductor content, we anticipate that one or more major semiconductor manufacturers will have decided to pursue vertical integration into this market by the March 1982 deadline. Courtesy of DATAQUEST's Telecommunication Industry Service Martin W. Fletcher Victor Krueger -11 -Vol. II - No. 4 April 18, 1980 This letter is a condensation of recent newsletters and internal thinking from the industry research groups at DATAQUEST, Inc. Requests for amplification of our thoughts or for specific newsletters should be directed to the author. A list of recent DATAQUEST Research Newsletters appears at the end of this letter. SEiMICONDUCTORS The turn has come. There is now enough corroborating evidence from users, distributors, and manufacturers to confirm the fact that the balancing of supply and demand, which we had been anticipating for some time, is finally occurring. Parts that were previously very hard to get are now becoming more readily available, lead times are coming down, selective instances of price weakness have occurred (such as 16K RAMS in Europe), and backlogs are shifting more towards longer term contracts than short-term delivery items. All of these are clear signs of softening. We would expect to see some reductions in user inventories over the next few months because of high interest rates and greater uncertainty about end demand. We Should emphasize, however, that we do not believe inventory levels are at excessive rates and any liquidation that does occur should be brief in duration and moderate in extent. In fact, a recent cheek of mainframe companies indicates that production schedules will meet or slightly exceed the projections made three months ago. We are not painting a negative scenario. Rather, supply and demand are acting much as we forecasted they would in projecting a 20 percent increase in industry shipments in 1980. A number of compensating factors will start to assert themselves once the softness continues for a short time: • There is a tremendous opportunity for the semiconductor manufacturers to reduce costs and get more efficient once industry conditions moderate sufficiently for the frantic pace of activity that has been present for the last year or more to subside somewhat. For example, removing some third shifts will actually reduce unit component costs. • AS more silicon is freed up, producers wiU shift more towards making 64K RAMs and other parts that consume large amounts of silicon. • It is very possible that, for a variety of reasons, the Japanese may lose market share when supply becomes more generally available. Copyright © 18 April 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness It does not contain material provided to us in confidence by our clients. This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. Member, New York Stock Exchange 19055 Pruneridge Avenue / Cupertino, California 95014 / (408) 725-1200 The single most important factor in our forecast for this year is unit demand. In our forecast of a moderate recession, we assume that unit demand will continue to increase at very strong rates, acting as a buffer against any sharp deterioration in price. In this scenario, reductions in costs will almost match those of price, and as a result, industry profit margins should decline only modestly in 1980. Only if we have a severe enough recession to markedly affect unit semiconductor demand, which is presently not the DATAQUEST forecast, will the industry be badly hit. SMALL COMPUTERS A recently completed survey of Four-Phase System customers yielded two pieces of data that we think are worth expanding on: first, that the users were very satisfied with the Four-Phase equipment; second, that the great bulk of them are utilizing the equipment almost exclusively for shared processor data entry. The case that the company makes is that its products are multifunction in use (word processing, data input, COBOL processing, file management). Our survey indicates that Four-Phase has a ways to go before completely achieving that goal. The difference is important: the growth rate for data entry devices is, by our estimates, 15-20 percent per year; the growth in true multifunction office products probably twice that. Four-Phase is a company in transition. It needs to make improvements in its word processing software and possibly in operating system compatibility before truly being able to expand the applications and use of its products into the office automation area. Unfortunately, it picked a difficult economic year to make the transition. Earnings this year are hard to predict (and probably not that meaningful anyway). Our guess is $2.00 per share versus $3.25 per share last year. The news from last week's Datapoint meeting was very favorable. Orders are Still very strong, the lease/sales mix is not shifting, lead times that were stretching out a bit on the low end are now back to where the company wants them (8-12 weeks, for the most part) and the stable of new products already introduced seems very full. In retrospect, Datapoint has gone through a major transition in the past 15 months that has been masked by continued strong earnings growth. The company's sales force had to learn to sell the new ARC systems, which were larger than prior product offerings and had a longer selling cycle. As a result, DATAQUEST would estimate that unit shipments of Datapoint's high-end products grew by no more than 20 percent in calendar 1979. Offsetting this relatively modest increase, however, was extremely rapid growth in sales of low-end terminals into the very small computer market. The direct sales force now seems well up the learning curve and can probably start accelerating their productivity, which positions Datapoint very well as we head into unchartered economic waters. Two potential weak spots should be noted: the company's contract with its foreign distributor, TRW, will not be renewed after its expiration in 1983. Management expects a lower relative rate of growth in its foreign business because of the less than optimal marketing arrangement and this area is one that should be watched closely. The recently announced letters of intent to acquire Inforex and its foreign sales and service organization may be the start of a solution to the 2 -overseas marketing problem. Second, the low end of the market, which has been very important to Datapoint, could be susceptible in a downturn. In the aggregate, however, we remain positive on the company's fundamentals. We project earnings of $3.90 per share in the July 1980 fiscal year, up 33 percent and a 22 percent rate of growth to $4.75 in fiscal 1981, even allowing for a recession. Data General is expected to announce its long awaited 32-bit computer before the National Computer Conference (May 19-23). The introduction of this product should be very positive for the company's order and shipment position in 1981, although start-up expenses might cause a slight drain on fourth-quarter earnings. We project 1980 earnings at $5.50 and believe 1981 could reach or exceed $6.80 with volume shipments of the new machine. A 32-bit machine wiU provide upward growth to DGN's current customers as well as allow the company to compete in a new market segment from which they have previously been blocked by DEC, Perkin-Elmer, Prime, and SEL. INSTRUMENTATION Instrument business generally remains good, but the first signs of the inevitable slowing in orders appear to be sporadically cropping up. We sense that the rate of order growth at Hewlett-Packard will not be nearly as great in the second quarter as it was in the first. We do not detect any order softening at Tektronix, but it is probably only a matter of time; the company has been expecting its order rate to start dropping for two years now. The decline in third-quarter earnings at Tektronix was the first such drop in eight years. Managements' indication that two of the major problems that have been restricting the company's shipments (poor yields on storage tubes and general manufacturing inefficiencies) have been solved suggests that the worst is behind the company. However, don't expect any big rebound in the fourth quarter. For one thing, last year's 31 percent tax rate in the last period makes comparisons difficult. For another, one major factor is still depressing margins: the company's LIFO inventory policies are continuing to squeeze margins, and relief in terms of higher prices will not be felt until the first quarter of fiscal 1981. Given these factors, we would not be surprised to see a flat fourth quarter, which would put full year earnings in the $4.50-$4.55 range. The good news, however, is that the factors working against Tektronix in this fiscal year could well work for them next. The company will enter fiscal 1981 with very high backlogs and if we experience only a modest recession, we believe that incoming order growth could easily justify sales growth of over 20 percent. Conversely, if (as appears more likely) we experience a more severe recession and Tektronix and other companies' order rates are more severely affected, the company still has a high backlog to partly offset any softening. More importantly, in these conditions, it is likely that both inflation and short-term interest rates would moderate significantly. Both of these occurrances would benefit Tektronix. We would estimate that the use of LIFO accounting will negatively affect earnings comparisons in fiscal 1980 by more than 25^ per share and this same negative impact may not be present next year. By our estimates, every one percent change in Short-term interest rates means about Zi a share to Tektronix. A decline in interest rates would therefore have a meaningfully positive impact on comparisons in fiscal 1981. 3 -The net of things is that we are reasonably confident that Tektronix can have very strong earnings comparisons in fiscal 1981. Our estimated earnings range is $5.30-5.50 per share. If the economy only weakens modestly, the company will generate the growth through a large increase in shipments. In a deeper recession, the financial factors noted above will aid comparisons. PAPER AND FOREST PRODUCTS Demand remains surprisingly good for most paper products, but everyone expects deterioration to start in the very near future. The 11 percent price increase in linerboard that was instituted in February by some companies has been followed by almost every major producer, but since most manufacturers are integrated, the key determinant is the ability to raise box prices. At this juncture, we would anticipate that only about half of the linerboard price increase will be passed along in the second quarter. Production remains at high rates in linerboard, but the momentum now appears to be heading downward. We would forecast a $275 linerboard price realization by the end of the year vs. $285 at the end of the second quarter and believe that it could bottom at $250-260 per ton sometime in mid-1981. This pricing scenario would indicate no great catastrophe on the brown paper side of things over the next two years. However, as previously noted, we believe that operating rates could deteriorate dramatically in white paper. In any event, we do not anticipate any improvement in the paper industry fundamentals until late 1981, which means to us that it is too early to get interested in the group, particularly since things haven't really started to deteriorate fundamentally as yet. The one positive thing that could be said about the forest products industry is that at least one does not have to wait for fundamentals to collapse. By our calculations, southern plywood prices in April were 21 percent below their 1979 average, western plywood prices were 25 percent below last year, and Douglas fir prices were a whopping 39 percent lower than 1979. Approximately 25 percent of the softwood plywood industry is presently shut down and the plants that are operating were running at 79 percent utilization rates in early April, which in total means that the industry is operating at only 59 percent of total capacity. This would indicate that more closedowns are likely in the near future. Everyone is now losing money on converting, the housing outlook for the remainder of this year is bleak, and there are almost no positive signs on the horizon. All of which is somewhat encouraging to us, since that is usually the time that stocks bottom out. CAPITAL EQUIPMENT As might be expected, the current high level of interest rates is having a very negative impact on demand for both construction and farm machinery. Retail farm tractor sales declined by 29 percent in March and are down 19 percent thus far this year. It now appears that sales for the full year may decline by 10-15 percent, versus our last published forecast (Feb. 1, 1980) of a 2 percent decline. Sales next year are very difficult to project at this time, but our best guess would be for flat to slightly higher levels of retail demand in 1981 from the low levels expected this year. - 4 -The present industry slump has positive longer term implications for the stronger competitors in the farm machinery field. There is significantly higher dependence on the manufacturers to finance end-user leeising and purchases as well as dealer inventories. One could reasonably make the case that the current industry downturn is an important longer term plus for Deere in that International Harvester has been severely injured by the combination of lower retail sales, its lengthy strike, and the disadvantages of a weakened financial condition. Nearer term, however, the ability of Deere to exceed the $4.90 per share fully diluted that it earned in 1979 seems open to considerable question. We remain fairly optimistic about the earnings outlook at Caterpillar this year, as we still believe that primary earnings can exceed $7.00 per share. We expect to see a very good second quarter at Caterpillar, reflecting increases in physical volume to fill up its dealer pipelines that were depleted by the strike last year. However, we expect 1981 to be a difficult comparison year for Caterpillar. In terms of new products from Caterpillar, we expect to see a new hydrostatic-driver crawler loader introduced to its dealers by June, an upgrade to its rubber-tired loader line introduced in September, and important improvements on its high-end crawler tractors to be made in October. It remains our belief that some time in 1981, Caterpillar will enter the high end of the four-wheel drive farm tractor market. COPYING AND DUPLICATING The Xerox Retail Markets Division expansion that we speculated about in our last Portfolio letter has now been publicly confirmed by the company. As we indicated, the first six stores will be in Dallas and Denver, and if the trial stores go well and are profitable, the pace of new store openings will be very rapid. We believe Xerox is still testing different store layouts, methods of merchandising, e t c and has not yet decided upon the final configuration to be used in all stores. The one addition to the product offerings in the stores that we did not anticipate was a new, very low-priced ($1,195) Xerox copier, the 550. The 550 is a modified 660, so it uses old technology, but should be replaced by a new low-end machine (more expensive, but much more reliable) within 12 months. The major potential negative for Xerox in this venture is its lack of experience in the retail environment. Tandy, for example, has been successful by hiring young aggressive store managers and offering them highly incentivized pay packages. Xerox has not traditionally had to attract this type of employee and the transition in terms of staffing the stores will not be inconsequential. The major positive is service. Xerox has a highly trainea service organization in place. If it can integrate a level of service on products sold by the retail stores without upsetting its service cost structure, it will have an important competitive advantage. Additionally, this approach will hopefully be a very cost-effective way of selling low-end copiers. Win or lose on this venture (and we still lean towards win), it shows a new level of aggressiveness at Xerox that was not present before Dave Kearns took over as president. This change, in itself, is an important plus for the company. Michael R. Weisberg - 5 -RECENT NEWSLETTERS OF NOTE Semiconductors 1. General Industry Update 2. U.S. Semiconductor Manufacturers Capital Spending 1979-80 3. Update on Motorola 4. International Solid State Circuits Conference 1980 04/11/80 04/01/80 03/18/80 03/17/80 Small Computers 1. Personal Computer iMarket Update 2. 1979 World iMarket Estimates Class II, HI & IV General Purpose iVIinicomputers 3. Small Computer Suppliers' Terms and Conditions Update 4. General Purpose Minicomputer Market Still Strong in 1979 04/10/80 03/26/80 03/11/80 03/11/80 Instrumentation 1. Electronic Counter Product Review 2. Digital Voltmeter/Multimeter Market 3. ATE 1979 Market Overview 4. Hewlett-Packard Company Annual Meeting-Feb. 26, 1980 5. Circuit Board Tester Product Review Paper and Forest Products 1. Uncoated Free Sheet: through 1985 Profit Decline Possible from Mid-1980 03/25/80 03/21/80 03/21/80 03/06/80 03/03/80 03/25/80 Capital Equipment 1. Caterpillar Tractor Company Update 04/02/80 2. Potential Impact of Changes in Housing Patterns on Machinery Demand 03/15/80 Copying < S c Duplicating 1. Xerox Cuts Quantity Purchase Prices on Low-end Copiers, Announces Additional Price Plans for 8200 and 9500, and Raises Supply Prices 04/03/80 2. Xerox's New Retail Markets Division Offers Model 550 Through the Mail 04/01/80 3. Konishiroku Introduces New Copiers and Expands Marketing 03/31/80 4. Notes on Xerox 03/20/80 5. SCM Out of Copier Business 03/13/80 6. Pitney Bowes Reports 1979 Results 03/13/80 Word Processing 1. Analysis of the Xerox 860 Information Processing System 2. Wang Announces Large Lease and Maintenance Increases 03/24/80 03/24/80 - 6 -... & SS ' ^ B S S = S ^ S ' ^ S = ^^= RESEARCH ^-^'^ _ A Subsidiary of A.C.tMielsen Co. ^ INCORPORATED I ^ I S S W ^ 3 ^ ^ M 1 1 C i F ^ SB Code: Vol. I, 2.0 GENERAL WDCSTRY UPDATE SUMMARY Imminent Slowdown Expected DATAQUEST expects a marlced slowing in U.S. semiconductop consumption growth during the balance of 1980. While booldngs in the semiconductor industry have remained strong through March, many of the early signs are visible that indicate supply is catching up with demand. Boolc-to-bill ratios should be affected imminoitly, reflecting both the ino'easing rates of shipments and a leveling out of demand. We forecast U.S. semiconductor coiBumption for 1980 to show a growth of 19.8 percent over 1979. This percentage is somewhat misleading because the semiconductor industry entered 1980 significantly above average shipment l e v ^ for 1979. U.S. semiconductor consumption in 1979 grew approximately 37 percent over 1978. The future outloolc is fcarmed by several strong opposing forces, including: • A flat U.S. economy, with a pessimistic future outloolt • Tremendous unit demand for semiconductors • Recent caution by manufacturers of equipment using semiconductors • Hi^ semiconductor jyices and other marl = government to solve this problem have not yet Iiad the anticipnt«»'^ .^-.cct on the economy. No solution will come easily. Tliroughout 1979 :^,K2 the first few months of 1980, the general U.S. economy has been relatively stagnant. While there has been sli^t growth in the GNP, industrial production has remained essentially flat. How-ever, either a prolonged downturn or a short, sharp downturn in the economy is currently considered liltely by economists. The possibilities of deep recession are becoming increasingly prot>able. Furthermore, forecasting is unreliable: there is no recent historic jwecedent for today's situation. Obviously, energy, inflation, and foreign affairs {^oblems malce the world situation very tentative. Outside the United States, higher energy prices have already impacted the economic outloolc for Europe and Japan, resulting in increased inflation and slower economic growth. The following recent economic developments are noteworthy: • Hyperinflation is now a reality. Currently, the f^ime banic interest rate in the United States is at the banana republic level of 20 percent. • Hi0i rat^ of inflation have appeared in Europe and Japan during the first quarter of 1980. In the past, tliis has led to strong economic measures by most of these countries to comt>at inflation, faulting in slower economic growth. • The United States has experienced severe problems with foreign affairs, compounded by military wealcness. Th^e [ffoblems are not new, but the increased perception of them is a significant development. • Government leadership has been inactive, indecisive, and impotent. • The gross national product grew at an annual rate of about 2.1 percent in the fourth quarter of 1979, following a growth of about 3.1 percent in the tliird quarter. This growth was imexpected. IVIost forecasters expect real GNP to be level or down in the first half of 1980. fiicreasingly, the second half of 1980 loolmance. SEMICONDUCTOR INDUSTRY TRENDS U.S. semiconductor consumption lias continued to rise at remarlcable rates despite the laclduster U.S. economy. UJS. semiconductor demand for the fourth quarter of 1979 rcrae an estimated 12.3 percent over the third quarter. Ttis strong semiconductOT demand reflects general strength in all areas of electi>onics to date, and relatively statde pricing for s^niconductor devices. Throi^h the first cpiarter of 1980 boolc-to-bin ratios have remained in the range significantly above 1.1 to 1. Nevertheless, DATAQUEST believes supply is catching up with demand. Some of the very early sigm appear to be emerging: • Fewer devices a^^ar to be on the critical shopping list of major corporations. • Smaller companies are now receiving parts with greater ease than in late 1979. • Lead times for product shipment appear to be dropping. • A larger percentage of the backlog of semiconductor manufacturers now liave extended delivery times. • Prices appear to be wea[eginning outside the United States and spreading internally; LSTTL devices appear to be increasingly availatde, with new supply coming from several areas, including Japan, and capacity inoreases among U.S. manufacturers. U.S. semiconductor consimiption is significantly outperforming its historical relationship to the economy. If past relaticMiships had remained true, a significant softening of semiconductor demand would have occurred in mid-1979, but it did not occur. This continuing demand is due to several special factors which DATAQUEST has «iundated many tim^ before: • The indirect effects of inflation. The declining [Mrices of electronics malce them increasingly popular in industrial and consumer marlcets. General industry capital expenditures have not been particularly strong, but 3 -expenditures for electronics liave far outpaced other areas. The cumula-tive effects of inflation are a very positive aspect of semiconductor demand and are without historical decedent. New markets—such as automotive and telecommunicatiOTis. Increased purchases of semiconductors from U.S. manufacturers for over-seas delivery. A movement to electronic use by electromechanical and mechanical equipment manufacturers. Elastic demand in some markets such as EDP. Increasing purchases of electronics for military applications. InCTeased purchases of semiconductors from the merchant market by captive manufacturers, especially IBIVI, General MotOTS, and Western Electric. In surveying market applications for semiconductors, DATA QUEST is struck by the extremely strong future unit demand for semiconductors, particularly for LSI and VLSI devices. It is awesome: massive amounts of wafer fab capacity will be needed. For examfde: 1) The demand in 1980 for 16K dynamic RAlVls—one part—is expected to be three times that of 1979—^the production equivalent of over 10 new wafer fabrication modules, 2) The automotive industry is making a major change to microprocessor controlled engines and digital radios. Worldwide, this development will increase semiconductor consumption up to a billion doUars in the future. A major increment will come in 1980. These new applications are a change in product and are, therefore, independent of the economy, 3) The mia-oprocessor revolution has finally occurred: major areas of indiBtry are converting mechanical and electromechanical equipment to electronic control. On a more sotiering side, semiconductor prices have remained relatively stable over the past 15 months. While cost/price imbalances are not at 1974 levels, many products have not seen normal price attrition. Furthermore, it is DATAQUEST's perception that semiconductor manufacturing cost did not fall at normal rates in 1979. Other imbalances have begun to appear, including out-of-mix production, a slowing of new product introductions, and some increases in inventory. General caution in the electronics industry is at a very hi^ level. The tuibridled optimism of 1973 and 1969 are not in evidence. Thus business practices have not been excessive. It is oiff perception that althoi^h inventory levels are rising, they are not at severe levels. The current cost of money is encouraging management at all industry levels to keep inventwy under reasonable control. A f urtho check on market deterioration is the pr^ent lack of excess capacity in the semiconductor industry, which provides a cushion to a demand softening. Many, if not most, companies are operating above comfortable capacity, using third slufts, foregoing product and process development wafer starts, reducing relative production of engineering or wafer intensive products, etc. The ability of the U.S. semiconductor industry to expand capacity is inffeasing^y constrained by lack of engineering personnel both for captive and merchant manufacturers alike. The majOT business Structure of the industry has been undergoing change. The number of very large users - 4 -of semiconductors is rapidly inoreasing wliile the number of merchant suppliers is declining. In addition, major multinational corporations are acquiring more and more merchant suppliers, including Fairchild and Mostei< wliich were purchased in 1979. What effect this trend may liave on their willingness to actively supply the merchant market is speculative, although no sJiort-term changes are foreseen. SEBflCONDUCrOR INDUSTRY FORECAST Table 1 gives our estimate for U.S. semiconductor consumption in doUars. We believe that semiconductor consumption in 1980 will show an increase of about 19.8 percent over 1979. to 1979, U.S. semiconductor consumption increased ap^oximately 37.1 percent over 1978. This figure not only includes shipments by U.S. manufacturers to the United States, but a major net increase in experts to the U.S. from Japan. DATA QUEST expects continued growth in semiconductor demand in 1981, althovgh given the very high degree of economic uncertainty a useful forecast is not possible. Our current estimates for U.S. semiconductor consumption by calendar quarter are shown in Table 2, We expect significantly slower growth this year than in 1979, with average quarterly growth dropping to the level of 2 to 3 perc«it. This forecast reflects the consequences of several powerful forc^—poor U.S. economic performance, those special factors causing strong unit demand, and a rebound from the excesses and imbalances of two very strong years. Essentially, price weakness and a correction of other imbalances resulting from the strength over the last two years will cause slower revenue growth even thoi^h unit demand will be Strong. Semiconductor demand will always have a close tie to the economy, but currently other factors are allowing the industry to outperform its Iiistorical relation-ships to the economy. Even so, as the performance of the economy weakens, so will the rate of demand growth. We do not expect semiconductor industry demand to show a Sharp downtirn, as in 1975, but instead to show relatively slow growth for a period of time. The effects of inflation on semiconductor revenues are difficult to determine. In the past, there has been no measurable effect of inflation on semiconductor costs, prices, or revenues. That should be modified in 1980. Those device areas that have a major material content, such as SSI integrated circuits and discrete devices, wiU show some pass-tlirough of material cost. In particular, the soaring price of gold should impact semiconductor revenue. Hyperinflation is now affecting all areas to some extent. While engineering salaries have increased tremendoiely, it is DATAQUEST's perception that they have not been matched by the pay of hourly workers, fiicoming pay for workers in the semiconductor industry has not kept pace with other areas, and with Other industries or jobs, especially in Silicon Valley. Thus we expect cost for direct labor to increase rapidly over the next few years. The long-term secular demand factors in the industry remain extremely positive. DATAQUEST expects the current supply/demand imbalance to moderate temporarily, but to become even more pronounced when the world economy improves. Increases in capacity are limited by the high cost of wafer fabrication facilities, the high technical content of VLSI products and the increasing difficulties aicoimtered in their manu-facture, Shortages of labor, and other factors. These considerations would argue for moderate capacity increases over time. - 5 -Three things eoiild blunt this optimistic scenario: untoidled capacity increases; irresponsible (i.e., not cost-based) pricing and restricted marl<et access by companies, industries, or nations. The participation in the semiconductor industry by national interests and mifltinational corporations poses a concern: they have unlimited financial resources. Diligence must be maintained to ensure that they act legally, fairly, responsibly, and with reserve. Fredericlc L. Zieber - 6 -Table 1 ESTIMATED 0.S. SEMICONDUCTOR CONSUMPTION (Millions of Dollars) Dista'ete Devices Integrated Circuits Total ' 1978 $1,019 2,304 $3,323 1979 $1,246 3,310 $4,556 Percent Increase 1978-79 22.3% 43.7% 37.1% 1980 $1,368 4,088 $5,456 Percent Inra'ease 1979-80 9.8% 23.5% 19.8% Source: DATAQUEST, Mc April 1980 - 7 -Table 2 ESTIMATED QUARTERLY U.S. SEMICONDUCTOR CONSUMPTION (Millions of Dollars) 1979 Discrete Devices Integrated Circuits Total Percent Change From Previous Quarter Percent Change From Previous Year 1st £tr^ $ 285 685 $ 970 4.4% 32.0% 2nd gtr^ $ 321 789 $1,110 14.4% 35.0% 3rd Qtr. $ 314 852 $1,166 5.0% 39.3% 4th Qtr. $ 326 984 $1,310 12.3% 41.0% Total Year $1,246 3,310 $4,556 37.1< 1980 Discrete Devices Integrated Circuits Total Percent Change From PrevioiB Quarter 1st 9tr. $ 331 987 $1,318 0.6% 2nd 9tr. $ 345 1,026 $1,371 4.0% 3rd Qtr. $ 343 1,019 $1,362 (0.7%) 4th Qtr. $ 349 1,056 $1,405 3.2% Total Year $1,368 4,088 $5,456 Percent Change From Previous Year 35.9% 23.5% 16.8% 7.3% 19.8% Source: DATAQUEST, Inc. April 1980 - 8 -n L Subsidiary of A.C.NiGl^en Co. ^ INCORPORATED r N I ^ Z W ^ S ^ E S 1 1 ^ Z F ^ SIS Code; Vol. I, 1.6 UJS. SEMICONDUCTOR MANUFACTORERS CAPITAL SPENDING 1979—1980 Capital spending plans for 1980 by merchant semiconductor manufactttrers show that manufacturers plan to ccwntinue spending at a liigh level—mope than 20 percent over 1979 levels. They regret that they were not ready for the record-brealcing 1979 season and they looic with confidence beyond any soft^iing in 1980 to a strong marlcet in the future. Occasional component shortages from the merchant marlcet, or concerns about possible shortages, have motivated several captive manufacturers to buy outright, build from the ground up, or expand existing semiconductor manufacturing capacity as a means of protecting their critical component supplies. These captive manufacturers are expected to spend heavily in the coming year, accoimting for an estimated 30 percent of total equipment purchases in 1980. Major semiconductor manufacturing equipment continues to be increasingly expensive and, to qiwte one industry source, "lead times now exceed any conceivable downturn." Several companies would have spent more in 1979 if they could have obtained equipment and those purchase wiE now have to wait until 1980 or later. Long equipment lead tim^ would probably have a moderating effect on any tendency of the industry to bring too much capacity on line t soon. Estimated capital spending for facility (which includes land, building, facility improvements, and hook-ups) and equipment for 1979 and 1980 is summarized in Tables 1 and 2. It should be kept in mind that "proposed spending," often made public at the beginning of the fiscal year, is not necessarily committed nfioney: Intel underspent by 20 percent their early-year pronouncements. Nor, as recent history tells us, is actual spending limited to proposed spending: in 1979 alone, Mostek overspent early-year plans by 40 percent and Motorola by 33 percent. Manufacturers have means available of reducing capital commitmaits, should economic events take a drastic turn for the worse—witness the events of 1974-1975 when industry capital spending was halved because of excess capacity. Similarly, as the last two years indicate, additional investment money is readily available should market prospects appear to be better than previously expected. WHAT HAPPENED IN 1979— U.S. manufacturers were unprepared for a banner year in 1979. Virtually all had been slow to add capacity after the 1975 recession and found themselves capacity-limited tliroi^hout the entire year. Equipment and facilities costs have continued to rise, as a result of general price increases of purchased materials and labor as well as Cnpyright g) 1 April 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and anaIysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness It does not contain material provided to us in confidence by our clients. This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO Table 1 KTIMATED U.S. SEMICONDUCTOR MANUFACTURERS 1979 CAPITAL SPENDING (Millions of Dollars) Facility Equipment Total Merchants $ 355 710 $1,065 Captives $150 295 $445 Total $ 505 1,005 $1,510 Source: DATAQUEST, Inc March 1980 Table 2 ESTIMATED U.S. SEMICONDUCTOR MANUFACTURERS 1980 CAPITAL SPENDING PLANS (Millions of Dollars) Facility Equipment Total Merchants $ 440 880 $1,320 Captives $185 370 $555 Total $ 625 1,250 $1,875 Source: DATAQUEST, Inc March 1980 - 2 -the increasing technical content of the equipment. Coupled with this rise has been the ongoing trend to larger, more fab-intensive chips, requiring more equipment dollars per unit of output. Lead times to bring new capacity on line have lengthened to the point that a new facility's cOTitributlon to billings is now often more than two years after the decision to build. These factors Imve all contributed to the capacity-demand difficulty, and reduced the industry's ability to respond to heavy demand. Spending forecasts early in 1979 also had implicit in them the specter of economic recession late in that year, and were cautious so as to avoid a repeat performance of 1974-1975's capacity excess and attendant [ffice competition to hold maricets. That dire view has gradually given way to one expecting only a period of slt^gish economic activity (and welcome relief) coupled with long-term optimism. PROSPECTS FOR 1980 AND BEYOND— As semiconductor boolcings have shown continuing strength, so capital spending plans for 1980 continue to build for a growing marlcet. Year-long short supplies and uncommonly firm prices have compelled component manufacturers to expand as rapidly as possible, and component users to commit to manufacturing their own key components or to investigate the possibility of doing so. Ttiere is also a p-owing consensus of those inside and outside the industry that semiconductor devices will play a critical role in the economics of the 80s and beyond. This view has tentatively convinced corporate planners that the right place to focus is the remainder of the decade, beyond any possible economic difficulties in 1980. U ^ MERCHANT MANUFACTDREBS Virtually every U.S.-based merchant manufacturer expanded or announced sig-ruficant capacity expai^ion plans in 1979, most of which will run into 1980 and beyond. Table 3 summarizes DATAQUEST's estimated company capital expenditures for semiconductor facility and equipment for 1978, 1979, and planned for 1980. If these capital expenditure amounts are compared with U.S. semiconductor factory shipments, it is apparent that the 1979 ratios, at greater than 15 percent of sales, are well above the liistorical average of about 11 percent of sales, and far above the low for the 1970s of about 7 percent of sales in 1975. If merchant capital expenditiffes for 1980 reach planned levels, they will be nearly 16 percent of 1980's forecast U.S. companies' factory shipments. Th^e ratios indicate not only increasing capital intensity in the industry, but also a timing problem. Today's catch-up capacity expansion hss been teought on by a slow post-recession recovery and phenomenal 1979 industry growth. FUrthermOTe, lengthening lead times to get the facility up and running have stretched out the building cycle. Manufacturers need a longer head start than formerly and can't wait until 1982 to add 1983's capacity. Texas Instruments Texas Instruments reported 1979 capital expenditures for the entire Components Group of $230 million. Of this, an estimated $190 million was spent on the semiconductor portions of that group's PP&E additions. TI has filed with the SEC for $200 million worth of debentures, some of which will be used for capital expenditures as well as retirement of short-term debt and increase of their working capital. 3 -Table 3 ESTIMATED U.S. MERCHANT MANUFACTURERS CAPITAL SPENDING (SEMICONDUCTORS ONLY) (Millions of Dollars) 1978 1979 1980 Texas Instruments Motorola National Intel AMD Fairchild Mostek Signetics Other U.S. Compsuiies Total Merchant $115 72 49 85 22 23 19 40 255 $680 $ 190 159 70 82 42 58 42 50 372 $1,065 Source: $ $1 DATAQUEST March 1980 190 200 90 125 65 70 85 80 415 ,320 ', Inc - 4 -Motorola Motorola corporate raised their 1979 estimate in mid-year and reported $265 million for the year. Of this, $159 million went to the Semiconductor Group, primarily in Austin, TX, and Mesa and Tempe, AZ. For 1980, the corporate capital budget is ejected to be about $325 million and the Semiconductor Group should account for about $200 million. National Semiconductor National continues to expand its wafer fab capacity in Salt Lake City, UT, and Greenoch, Scotland. In October 1979, it also annmmced plans to build in Vancouver, WA. This plant is expected to be in production in late 1981, and to expand to full capacity in 1984. Intel The final tally for Intel's 1979 capital expenditures was $97 million, with about $82 million ^ent for semiconductor operations. After corporate spending of $104 million in 1978, Intel was exceptional in tiiat its capital expenditures in 1979 declined both in dollars and as a percentf^e of its sales. Total corporate expenditures for 1980 are planned for the $150 million range, with its Phoenix, AZ, facilities getting the largest share, followed by the Livermore, CA, and Aloha, OR, facilities. Some capital is also budgeted for a^embly facilities offshore. AMD AMD recently placed $24 million in long-term notes with four msurance companies, and plans to spend at>out $80 million in fiscal year 1981 (ending March 31) with a variety of expansion plans in Santa Clara, CA, and their newest operating facility in Austin, TX. Fairehild Since a principle motivation of Schlumberger in purchasing Fairehild last year was to gain a foothold to a h^h-technology industry, we expect a change in corporate philosophy with respect to capital spending. Fairehild underestimated the growth potential of the market in 1978-1979, and this fact likely contributed to their loss of market shares during that period. Now under Schlumberger, corporate capital expenditures in 1979 were reported at $73 million, with an estimated $58 million for the semiconductor group. Fairehild will likely have access to adequate capital in the 1980s to grow the business as fast as the market will aUow. Mostek Mostek's capital expenditures for 1979 are estimated to have been about $42 million, after its spending plans were raised twice in mid-year. Now, having a $200 million line of credit at 10 percent available from United Technologies, Mostek will likely accelerate its building plans for CarroUton, TX, (Fab 5), Colorado Springs, CO, (Fabs 6 and 7), and Dublin, Ireland, (Fabs 8 and 9). - 5 -Signetics In 1979, Signetics ^ent about $50 minion on capital equipment and facilities and plans to spend about $80 million in 1980. This will include new bipolar facilities in Santa Clara, CA; significant expansion of facilities in Orem, UT; and its R&D Center now in the initial building stages in Simnyvale, CA. Other companies that have announced new wafer fab locations are: International Rectifier IR has broken ground for a new fab facility in El Segundo, CA, to manufacture its new Hexfet power transistors. This facility is expected to be producing in the first quarter of 1981. Zilog Zilog has begun producing wafers at their new fab module in Nampa, ID, near Boise. Construction is scheduled to begin in 1981 on a second module at the same location. Total capital expendittire for the modules is expected to be in the ne^hborhood of $40 million by the end of 1982. Synertek Synertek will break ground this spring for its new fab facility in Santa Cruz, CA, with the expectation that it will contribute to billings in the second half of 1981. It has also announced a $7 million assembly plant to be built this year in Thailand. Harris Harris Semiconductor announced a $25 miUion expansion of its Palm Bay, FL, manufacturing facility, and expansion of its assembly facilities in Kuala Lumpur, Malaysia. U.S. CAPTIVE MANUFACTURERS In the past, DATAQUEST has foctissed its attention primarily on merchant semiconductor suppliers. However, from the viewpoint of a materials or equipment supplier to the industry, merchant manufacturers are indistinguishable from captive manufacturers: both captives and merchants constitute a part of the market for fab, assembly, and test equipment. Secondly, the development of the captive semiconductor manufacturing market has begun to have significant impact on the size and characteristics of the merchant market. IBM's need for $120 miUion in 16K RAMs from the merchant market cannot be ignored, and neither can IBM's decision to enlarge its own in-house manufacturing capacity and maintaui its relative independence from the merchant market. Of 23 major semi<K)nductor users listed in DATAQUEST Research Newsletter Major Semiconductor Users (19 December 1979), only OUvetti is known to have no semiconductor manufacturing c£^ability whatsoever. Of 17 firms expected to purchase at least $100 million of semiconductor components in 1981, 12 are known or thought to be adding significant semiconductor manufacturing capacity themselves. - 6 -Captive semiconductor manufacturing could result in a significant erosion of the growth potential of the merchant market by the mid-eighties. Historically, captives have made what was not available from a merchant supplier, and only IBM and Western Electric have attempted to produce all their internal needs—standard plus custom parts. From 1979 to 1982, dramatic increases in purchases by major users (e.g., GM, IBM) have added and will probably continue to add a s^if icant adjunct to a broad base of semiconductor users. IVteke-or-buy decisions by these major users in succeeding years wiU determine to what extent ttiese "new markets" will remain the province of merchant suppliers, or whether they win be cbrawn inside the user firm. The capability of these large purchasers to supply their own needs should be monitored carefully in any strat^c assessment of long-term merchant market potential. With l^ese developm^its in mind, we have decided to incorporate a brief discusssion of capital spending plans by major captive manufacturers side-by-side with those of merchant manufacturers. The capital spending by captive manufacturers for semiconductor capacity is difficult to ascertain. It is estimated that about 30 percent of semiconductor manufacturii^, assembly Eutd test equipment sales go to captive manufacturers. Their facility and equipment purchases are probably growii^ as fast as those by merchant manufacturers. Spending by captive merchants therefore adds about $555 million for 1980 to the total market for semiconductor facilities and equipment. Below are listed several of the major building commitments by cs^tive manu-facturers made during 1979 which will contribute to the heavy demand for semicon-ductor manufacturing and test equipment for 1980 and 1981. Northern Telecom In August 1979, Northern Telecom, Ltd. announced plans to begin btiilding a $33 million dollar LSI fab facility in Rancho Bernardo, CA, which is expected to be producing components early in 1981. Burroughs Burroughs Corporation broke ground in November 1979 for their second MOS facility, also located in Ranclio Bernardo with their existing bipolar and MOS lines. The expected cost is between $15 and $20 miUion. General Motors Expansion of Delco's manufacturing capacity is now taking place, and will more than double their semiconductor production capacity by 1983, but merchant market purchases of semiconductors will increase more than three times over the same period. Further significant increases of their in-house capability over the following three to five years would be entirely consistent with GM's make-it-yourself philosophy. IBM IBM has committed immense amounts of money for capital equipment in 1978 and 1979 and expects to do so in 1980 as well. They set up a $1.5 billion line of credit with 37 banks in July 1979, sold a $1 billion bond offering in September 1979, and borrowed $300 miUion in December 1979 from the Saudi Arabian Monetary Agency. - 7 -Their semiconductor component purchases from the merchant market rose to an estimated $175 million in 1979, and will probably be between $250 and $300 million in 1980. IBM has made, and will continue to make, very large investments in semi-conductor plant and equipment in the next few years. Principal expansions are a large fab line in Austin, TX; expansion of their Burlington, VT, facility where the 64K RAM is made; and continuii^ capacity increases in East Fishkill, NY, for MOS and bipolar products. NCR NCR, whose earnings were impacted in 1979 by both external and in-4iouse chip shortages, continues to expand both its Colorado Sprii^ and Ft. CoUins, CO, operations, with still further capacity planned for San Diego, CA. Digital Equipment Corp. DEC has recently added capacity in Hudson, MA, to supply some of their internal MOS needs. Mainframe manufacturers CDC, Honeywell, and Sperry-Univac, as well as Storage Technology Corp., have all announced semiconductor manufacturing additions or expansions for 1980-1981. CONCLUSIONS Two very clear trends are apparent in these industry capital spending plans. Semiconductor companies are optimistic about the lot^-term future of their industry, and captive manufacturers are continuing to match, if not exceed, merchants brick for brick, aligner for aligner, wafer for wafer in their own expansion plans. Cs^itives see that semiconductors will play an i"'reasingly crucial role in their products, and they want to reduce their dependence on merchant suppliers for these critical components. Lane Mason Frederick L. Zieber - 8 -T' 1 =111 s%^ 11 i ^ ^ 1 Hb&3b^\Hi^n |^..^....„ . ........NEWSLETTER SIS Code: Volume HI, 8.06 Motorola UPDATE ON MOTOROLA SUMBAARY DATAQUEST projects an 18 percent revenue increase in 1980 for Motorola to $3.21 billion and a 16 percent gain in earnings to $6.05 per share. Motorola's ability to achieve this forecasted earnings gain in the light of current economic cwiditiOTis should have a positive effect on investor perception of this company. The Semiccmductor Group faces a particularly challenging year. It has made very strong progress with its 68000 16-bit microprocessor, but must meet its schedules on peripheral and support chips if it is to establish a strong position in this market. At the same time, MotOTola must maintain impetus in its memory business; the 64K RAM is a keystone product in this effort. The group must also provide for a ramp up in shipments to General Motors. Meeting these challenges wiU sweep Motorola into the billion dollar class as a semiconductor producer and firmly establish this group as one of the major semiconductor forces in tlie world. DATAQUEST forecasts a somewhat below average year in revenues and growth for the Communications Group. The Communications Group continues to maintain its dominant marlcet position in both pagers and two-way communicaticffis systems. The Start up problems experienced in late 1978 and early 1979 at its Fossil Greelc, Texas plant have been largely resolved. DATAQUEST feels that the historic margins of the Communications Group have not been consistent with the margins generated by other technologically dominant electronic firms. Automotive Products continues to be the troubled division at Motorola. This group lost over $16 million in 1979. The group continues to suffer from both product mix and margin problems. DATAQUEST does not forecast a rapid profit turn around in 1980. Government Electronics Divisirai (GED) had an excellent booking and revenues year in 1979 and is poised to become the fastest growing Motorola entity in 1980, both in sales and earnings growth. Codex, which includes Universal Data Systems (UDS), grew in excess of 40 percent in 1979 achieving margins well above corporate average, despite making sutjstantial teclmical investments in products of the future. Motorola had a productive international year. Among its accomplishments overseas were the setting up of a semiconductor joint venture with a French Government entity (EFCIS); the establishment of an automotive lab in Japan; negotiating an agreement to sell advanced pagers to NTT in Japan (Motorola has previously had minimal market penetration in Japan in this product line). Copyright © 18 March 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generaIIv availabIe to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients. This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent andfor their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities meniiom^d and may sell or buy such securities, 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO While preparing this update DATAQUEST was impressed by the pervasive use of solid state technology tliroiighout the Company. REVENUE AND PROFIT ANALYSE Our estimate of revenues and operating profits for each of Motorola's major groups are shown in Tables 1 and 2. These estimates assume a 1.5 percent decline in real gross national product this year. Specific comments regarding our estimates are as follows: • , We believe that the Semiconductor Group can continue, to gain market share in both discrete and integrated circuits this year. We believe that both areas improved margins in 1979 and that additional increases in profitability can accrue in the future. Our estimate of flat operating margins from this group in 1980 is, therefore, conservative and makes some allowance for economic uncertainties. • One could reasonably make the case for a good tum-around in Automotive Products profitability. Given the uncertain automobile environment, however, and the likelihood of losses from this operati). Includes Government Electronics, Codex, Autovox, Display Sy^ems, and miscellaneous units. 'Before special charge. Source: DATAQUEST, Inc. March 1980 Table 2 is a DATAQUEST estimate of revenues for which Motorola does not provide a breakdown. Table 2 ESTIIWATED OTHER PRODUCTS (MiUicxis of DoUars) Government Electronics Codex Auto VOX Display Systems Watch Modules, LCD Miscellaneous Total 1978 $140 75 50 55 20 36 $376 Source 1979 $180 110 55 60 17 30 $452 1980 $250 150 60 60 0 30 $550 s DATAQUEST, Inc. March 1980 - 4 -CAPITAL EXPENDITtJRE DATAQUESTs estimates of Motorola's capital expenditure are as foUows: Table 3 MOTOROLA CAPITAL EXPENDITURES BY GROUP (Milliofis of Dollars) SemiccHiductor Commimications Automotive Other Total 1977 $ 53.1 55.4 9.7 10.2 $128.4 1978 $ 72.1 45.6 13.0 15.7 $146.4 1979 $160 60 10 35 $265 Estimated 1980 $200 70 15 40 $325 Source; Motorola Annual Reports DATAQUEST Estimates SEMiCONDnCTOR GROUP Operating profits increased 60 percent in 1979 to $172 miUion from $107 million on a revenue increase of 38 percent. DATAQUEST estimates that the Inte^ated Circuits Division grew 50 percent to $500 miUion in 1979 and that MOS shipments gained over 80 percent. Motorola was the second fastest growing MOS supplier last year following Natiaial Semiconductor and is now the number three supplier after Intel and Texas Instruments. Other higlilights of the group last year include: • Introductitxi and marlit microprocessor manufacturers in 1980. Motorola's lack of peripherals has not gone unnoticed by InteL - 7 -Memory Motorola has broadened its lines of memories and talcen a leadership position in development and production of the 64K dynamic MOS RAM. DATAQUEST estimates total memory component shipments exceeded $95 million for MOS and $18 million for bipolar. CMOS Motorola introduced its 14406 and 14407 Codex-decoder coders and 14414 filter in 1979. A second source agreem«it, made in December 1979 with RCA, will greatly enhance acceptance of these products. In development are a subscriber loop interface circuit, a time slot assignment circuit, another filter, and an 8x1 time slot interchange circuit. These parts are CMOS logic compatible. DATAQUEST estimates that Motorola's CMOS sales increased 50 percent to $115-$125 million in 1979, giving Motorola the leading market position in this technology. Memory Systems This business had experienced difficulty in its initial phase. The minicomputer add-in memory business has not grown as expected; however, custom memories have booi<ed well. There is a lag between booiclng and shipment. DATAQUEST expects this group to ship $10 million in 1980. Microsystems A new marketing organization, reporting directly to the World Marketing Director has been set up to market microcomputer development systems, computers on a board, subsystems, and memory systems. DATAQUEST anticipates shipments from this group to be approximately $85 million in 1980. In 1979, the $40 miUi<»i of microsystems sales was divided roughly evenly between Europe and the United States. Further, approximately two-thirds of this $40 miUi(»i was for microcomputer development systems and the balance was for boards. The subsystem area consists of a product mix of input/output modules, solid state switches, and switching power supplies which has been developed by the Discrete Products Division, but is being market by the Integrated Circuits Division and will be covered in this part of the newsletter. We understand that Motorola has a joint venture with Tandy and Western Union to develop a data communication system for farmers. From his home, the farmer can tie into the county agricultural agency computer to get data on such subjects as weather, fertilizing, and crop rotation. The EXORmaes will be introduced within the next 60 days. This is the Microprocessor Development System (MDS) that will t>e used with the 68000. The average selling price will be aH>roximately $30,000. It is DATAQUESTs feeling that $7 to $10 minion of these can be shipped in the calendar year 1980, if they can be manufactured. The EXORcis^, Motorola's original MDS system, is being updated from EXORciser n to EXORciser III. We understand the change simply means the inclusion of a faster clock and some other refinements. - 8 -The Microsystems Group is also selling the EXORterm in conjunction with Codex. The EXORterm is a smart terminal and can be used with the EXORciser, and wiien it is, it is called EXORciser 50. When the EXORterm is used with the EXORciser in a terminal complete with CRT, it has applications for software development. Another product that was developed in Europe is the EXORset 30, wluch is a 6809 based development system and is an excellent cost effective MDS vehicle for the low end of the market. We also anticipate a large effort in computers on the board with the 68000, these products are known as K D I V I modules. t: Discrete Products Division This divisiOTi grei^l8 percent in 1979 versus a world market growth of 9 percent. The growth in dBscr^el?y the major suppliers is increasingly beii^ conc®it:ated in the hands of Motorola suRi the Japanese. DATAQUEST believes tliat Motorola's continued ag^essiveness in the discrete area win benefit the Company since there is a continuous drag business of discrete with ICs in all applications. In brief conversations with a number of customers of Motorola, DATAQUEST has the impressiOT that the quality program instituted well over a year ago by the General Manager of the Division is having substantial payoffs with Motorola's discrete customers. DATAQUEST believes that this attrition to quality, which includes having the Reliability Motjager report to the Division Manager, will enable Motorola to compete effectively with the Japanese for tMs market as the years go on. DATAQUEST understands further that in some cases capital equipment which has a good useful life, but which has had to be replaced for teclmological E»irposes, has been transferred from the IC Division to the Discrete Division. This type of equipment utilization has substantial positive Earofit ramifications. The details of product developm^t are somewhat difficult to procure, but it is DATAQUESTs opinion that Motorola continues to emphasize automation on its TO 92 line (the division is the largest supplier for auto and consumer tuning diodes, and has essentially become an industry sole source for rectifiers and rectifier buttons; it is emphasizing RF power especially in the module area). DATAQUEST estimates that Motorola's RF transistor business is growing rapidly and could reach $50 to $60 million in 1980. btematicnal One of the notable achievements last year in this third operating (fivisiwi was the joint venture between EFCIS and Motorola to manufacture NMOS in France. It is our opinion that Motorola will become a dominant supplier to both the French commercial and military market as a result of this, and that there will be a substantial fall out to Other parts of Motorola's business such as pagers and two-way data communications. International has plants in East Kilbride, Scotland and Toulouse, France; both plants have undergone substantial expansion. Between exports and direct shipments, • International accounts for about 40 percent of the division's sales doUars. The International Division has made very successful and extensive use of European distributors. DATAQUEST estimates that the sales through European distribution are approximately 40 percent. - 9 -Capacity The Semiconductor Group is headquartered in Phoenix, Arizona with facilities in Phoenix, Mesa, and Tempe, Arizona; Austin, Texas; France; Germany; Scotland; Hong Kong; Japan; Korea; Malaysia; and Mexico. There are two MOS modules in Austin, Texas, one for CMOS and one for NMOS. Each module is capable of 10,000 wafer starts per week. The module in Tempe, Arizona produces HMOS wafers for the 64K dynamic RAM. There are also two MOS modules in Tempe, Arizona. Motorola wafer fabrication facilities outside the United States include 270,000 square feet in East Kilbride, Scotland for the manufacture of CMOS and NMOS wafers, and power discrete and linear IC lines in Toulouse, France. The facilities in Hong Kong, Korea, and Malaysia are used for assembly and the facility in Munich, Germany is for bipolar test. Motorola lias now converted most of its wafer fab lines to four-inch wafers and plans considerable expansion of its wafer fab facilities in 1980-81. Capital expenditure in the Semiconductor Products Group in 1980 is expected to be approximatdy $200 million. A new bipolar line is planned to begin operatioi in Mesa in mid-1980 and an MOS facility for later in the year. Two more wafer fabrication modules are being built in Austin, Texas. Expansion is also planned for Phoenix, Arizona in 1981. The Company, which already has a design facility in Japan, is seeking a manufacturing site in Japan, intended to produce circuits for the Japanese automotive industry. COMMUNICATIONS GROUP Communications Group operating profits increased 33 percent in 1979 on a 17 percent gain in sales, as a recovery was made from the margin difficulties experimced in 1979. The manufacturing problems at Fossil Creek and Fort Lauderdale appear to be behind the Company. DATAQUEST believes that the CommunicatiOTS Group derives substantial product benefits because of the corporate semiconductor capability as represented by MICARL and the Semiconductor Group. DATAQUEST also estimates that Motorola has 800 independent service stations and 50 Company service facilities in place; we believe this capability to be a very powerful marketing tool. This group is acgaidzed into the following entities: • POTtable Products Divisile Products Divisiim This division was formed in 1979 as part of the split from Communications Products Division. The Division Manager is Mort Topfer. DATAQUEST estimates that this division has well over 50 percent maricet share in its available market. DATAQUEST understands that, as discussed at the Motorola stockholder meeting last summa:, the Portable Products Divisicm has a signed agreement to supply pagers to NTT in Japan. TTi^e E»gers incorporate many advanced technological features such as a CMOS microprocessor; we understand that future design changes can be made by replacing the ROM. This capabilty will have a substantial effect on this product's market share in both Japan and the United States. The initial order is for 150 pagers. DATAQUEST estimates that the Portable Products Division sales were about $250 million in 1979. Motnle PrtKhicts Division This division is a sec<md spin out from the former Communications Product Division. Mobile basically covers applications that are non-marine between a station area and moving aitity or between two moving aitities. We estimate the volume in this groi^ was about $250 million in 1979. Substantial product activity has been imderway in this group—some of the activity that DATAQUEST perceives is as follows: • For many years the standard two-way set was MICOR. It is our understanding that MotOTola is replacing MICOR, which operates at a lower frequency, with an 800 MHz set of radios, the SYNTOR and the SYNTOR X. These units make extensive use of microprocessors, frequency synthesizers, and ROMs for feature customization. These two uruts bracket the costs and the features that used to be supplied by MICOR. We understand that MICOR will continue to be offered as a product for some period of time. DATAQUEST believes that having these two sets in the hi^er frequency can expand Motorola's customs base. • Maxar—It is DATAQUESPs feeling that the Maxar is as much a philosophy as a product. Basically, it is defined as a low-cost radio for under-dash instaUatioi. It is our feeling that Maxar is the area where the most cost effective technical and manufacturing breakthroughs are applied. The next versi(»i of Maxar known as Maxar II will be operating at 800 MHz and will again use such advances as microprocessor frequency synthesizers. • The Hi^ Capacity Mobile Telephone System (HCMTS), which is a product in the 900 MHz spectrum, is still under test at the FCC. - 1 1 -• The Motorola cellular system which has been in test in the Washington-Baltimore area is expected to commaice fufl service in 1981-82. The FCC, in beginning the regulatory process leading to final rules for cellular systems, is addressing a number of major questions. • We also understand that an Electronic Mobile Exchange (£MX) is being (teveloped by this group. It is designed to get the user to the first available transmissi(xi channel as quickly as possible. This application is another example of Motorola's use of advanced solid state technology. Motorola has obtained two large orders for this sytem, one from Austria and one from Pacific Telephone and Telegraph. Commuiiications Fi3»d Prodacts Divisloo This division is the progenitor of the two previous divisions. The product line residue is basically the Hxed apparatus and the equipment at base stations consisting of the base static itself, consoles, and other point-to-point communications equipment. We estimate the volume for this group last year to be approximately $175 million. Once again, the pervasiveness of semiconductors is shown in that the equipment currently offered by this group has a smaller conHguration accompanied by higher wattage. Communications Systems Diviaon A U the previous product divisions focused on voice communications, an area in which Motorola has a dominant position. We understand that the charter of the Communications Systems Divisicm is to achieve that dominance in data communications. Data communications represents a substantial potential for Motorola. We estimate Communicaticm Systems Divisitm volume at approximately $150 million. We understand that they are worldng on programs such as vehicular tracicing, which is a mcmitoring system for commercial transportation systems. We also understand that they are working with utility companies looking at such concerns as load management. This system would control power input to houses, using such features as selective cut-off to water-heaters, refrigerators, and air-conditioners, and the ability to charge varying rates for power according to the time of vse. We understand that this group is also working with some of the telephone companies in custom work in the digital synthesizing area. Common carrier mobile radios are also the responsibility of this division. Commimicatiaffi Distribution Division This division is the marketing area for the group. In addition to the hardware sales realized by the other divisions, this division billed an estimated $125 million in service revenues in 1979. This business is typically low-margin and high return on net assets (RON A). Ihtematicnal Division This division has its own product development group to design and market equipment to foreign standards. The division has facilities in Germany, South Africa, - 1 2 -Israel, Canada, Scotland, and Mexico. DATAQUEST estimates that the international activity wiU have revenues of about $200 million in 1980. Manufacturing As indicated in past Motorola releases and our previous newsletters, the Communication Group suffered from start up cost and manufacturing problems at its Fossil Creek facility. It is DATAQUESTs opinion that the Fossil Creelc facility is fully operational, and liighly automated in both manufacturing and warehousing. We understand that there is a four-story Kenway automated warehouse wMch picks work in process as needed by lot and brings it to the line. We also understand that the Fort Lauderdale facility has had all of its functions combined and now reports as a total manufacturing facility to Mort Topf^. As publicly released. Motorola has acquired a property in Boynton Beach, Florida for future expansion of communications. ADTOlMOTIVE AND DISPLAY SYSTEMS Last year was another <fifficult one for the Automotive and Display Systems Group. This Group ran at a los in excess of $16 million in 1979. At the annual Shareholders meeting last summOT, the Company predicted a loss for the Group. At this meeting, Carl Lindholm, General Manager of Automotive and Display Systems, dealt with responsiblities for the following groups: • Automotive Products Divisicai a) Electronic Systems b) Entertainment c) Industrial Controls d) International • Angers Operatims • Display Systems • Autovox Automotive and Display Systems Group includes the Angers operation in France but does not include Autovox. Autovox does, however, report to Carl Lindholm of Automotive and Display Systems Group. The Automotive and Display Systems Group has been working with a combination of problems some of which DATAQUEST perceives are the following: • The automotive market was generally soft in 1979. • Entertainment business especially car radio, classically an area of strength for Motorola, has been very weak the last several years. Motorola still has a business in this area which DATAQUEST estimates to be about $25 minion; howevw Ford's move to inhouse manufacture ra<£<» has resulted in lost business of about $25 millicxi compared with reveni^s several years ago. • Display systems appears to have both margin and market sliare problems. - 1 3 -This group is the E^ofit trouble spot in Motorola Corporate. We believe that the problems have been identified and that a substantial amount of corporate energy is being focused on this group. Automotive Products Division APD has penetrated Ford very heavily. It is DATAQUEST's estimate that in 1979 about 40 percent of APD sales were to F c H d in these areas: pressure sensors, engine control modules, ignitim systems, EEC ni module, radios, and remote CBs. Electronic Systems DATAQUEST estimates that Motorola shipped between 150,000 and 250,000 EEC m units at $125 each in 1979. These units were used for the high end cars. Motorola has also shipped a motor control unit using an Intel 8048 which we believe markets for about $40 a unit. It is our estimate that APD supplied about 500,000 MCUs to Ford. APD has opened an automotive lab in Japan and is, DATAQUEST believes, working very hard on an engine control unit for a major Japanese car manufacturer. Substantial marketing and applicati<Hi effort is being devoted to heavy equipment manufacturers such as Deere; focusing on instrument panels, two-way communication systems, and microprocessor controls. Industrial Controls The industrial systems program, wliich consists mainly of two microwave oven control programs, generated an estimated $5 to $10 million in 1979; this revenue could grow in 1980. International We believe that Motorola is making good progress in Europe. We perceive increasing penetration in Volkswagen with alternators; extensive development work with Weber in electronic control mochiles; and very dose development work with Peugeot and Fiat. Automotive Prochicts Europe has recently hired Mr. Gerhardt Schulmyer as General Manager. He comes from Sony, Europe, and is weE regarded. In addition, the new General Manager of the Automotive Parts Division, Mr. Levy Katzir, is also well reg^ded. The Angers operation has been a dra^ on Motorola's profits since the operation was acqidred in 1974. It is DATAQCESTs understanding that pricing on alternators tor tt» European market was very aggressive initially in order to get market share and the Angers operation is just now catciiing up to its costs with its princing. We look for Angers to make a cwitributiai next year after breaking even in 1979, This group continue to have problems with product mix (entertainment), slow automobile sales, and Ford market share problems. Nevertheless, DATAQUEST has seen indications that the future for this group might be brighter than it appears. - 1 4 -The Automotive Products Group represents a substantial profit improvement program for the corporation. It is DATAQUEST's opinion that it wiU take longer than this one year, 1980, to complete the transition from a heavy commitment to entertainment to the business of the future—under the hood. Given an uncertain automotive climate, we do not expect much improvement in losses this year. GOVERNMENT ELECTRONICS DIYISON The Government Electronics Divisioi participates in four markets; Commimications,—approximately 40 percent of sales; Radar—35 percent of sales; Tactical and Electronics MissUes combined, 25 percent of sales. It is DATAQUEST's perception that this division which in the past has operated under constraints related to percent of sales per contract aivi percent sales to a given agency has had these restraints lifted. The bookings activity in 1979 was extremely good. The major accomplisliment was obtaining the contract for the Stand Out Target Acquisition System (SOTAS). SOTAS mounts a surveillance radar system on a United Technology Sikorsky Blackhawk helicopter and relays target data in real time to command post groimd Stations. Motorola won this award in fierce competition with General Dynamics Electronics. This contract is for $56 milliMi initially. DATAQUEST believes that this is the largest single contract the group has ever received. Production potential is extremdy high—between $500 milli<»i and $1 billion. Other awards this year include DAMA (Demand Assignment Multiple Access System) which works in conjunction with the Galileo SateEite. Motorola has continued its excellent penetration with the National Security Agency (NSA). Motorola is now one of the preferred suppliers to NSA. DATAQUEST estimates that this division grew from $140 million to $180 million in 1979. Our estimate for 1980 sales is $250 million, a growth of approximately 39 percent. The strains of accelerated growth depressed margins in 1979 undo? 10 percent pretax, but we expect a recovery in margins this year. As maitioned in a previous DATAQUEST newsletter, this divisicai has set up a production group called the Specialized Production Center, designed to bid on military contracts in which the technological content is minimal and has been reduced to routine production practice. The production line concept will receive its test under fire this year with the FMU 110 Fuse and an Army Fuse contract running on this line. DATAQUEST estimates that as much as 10 perc«it of division sales will run through this line this year. The division is adding 300,000 square feet of space in Tempe, Arizona, when completed, the facility wiE total 1.25 million square feet. Radar and Tactical groups will go to Tempe. It is our understanding that this group is looking for still another site for future expansion. The encrypticMi device originally designed by MICARL and marketed by GED, is now being marketed by Codex. This is another example of the synergy that exists with the use of MICARL to provide technical uniqueness in limited quantities and hi^ ASP type black box business. - 1 5 -CODEX This subsidiary consists of Codex, UDS, (both recent acquisitions), and a smaU intelligent terminal operation in Phoenix and reports directly to the President of the Company. This group made a heavy investment in technical development in 1979 and still achieved margins 10 percent NPAT. The charter of this group is total data communciations systems from computer to man-computer interface—(sgecificaUj excluding thIe computer). Sales in 1979 are estimated at $108 million, with Codex responsible for approximately $90 miUitxi and UDS for approximately $18 million. UDS worI<s in the low speed end of the modem product spectrum. Codex margins declined somewhat in 1979, reflecting heavy Research and Development investment. We would anticipate flat margins in 1980. Codex works <xi high speed modems (4,000 to 9,000 baud range) and a variety of specialty data communications equipm^t such as data concentrators, pre-processors, and channel sdectors. Codex has established Codex/West to market the Motorola SPG developed EXORterm terminal and to interface with MotOTola iitegrated Circuit Advanced Research Laboratory (MICARL). MICARL developed chips are begiiming to appear in Codex equipment. mCABL Throughout this newsletter we have repeatedly mentioned Motorola Integrated Circuit Advanced Research Laboratory (MICARL). We believe that MICARL processes in excess of 200 custom chips per year. It has been an effective solution to the problem that affects most equipment manufacturers: the timely design and fabrication of solid-state chips that have a Iiigh value-added and technological content in a finished system, but require an extremely limited production run, in some cases as small as coie hundred wafers. James F. Riley Jean C. Page Michael Weisberg Frederick L. Zieber Daniel L. Klesken - 1 6 -B "^2 ^ ^ E S S S ^ P '^KaS S ( A Subsidiary of A.C. Nielsen Go. ^ 1 ^^1 RESEARCH N C O R P O R A T E D | \ | ^ Z V V O l L a ^ Z 1 T ^ S l ^ SIS Code: Vol. I, 4.0 INTERNATIONAL SCUD STATE CIRCDITS CONFERENCE 1980 SUMBiARY The International Solid State Circuits Conference (ISSCC) is the premier high technology conference of the year for the semiconductor industry. This year, the conference was held in San Francisco from February 13 to 15. Next year, it will go to the East Coast, but will be in New York City rather than in the traditional East Coast site of Philadelphia. This site change is necessitated by the burgeoning conference attendance; there were 3,000 attendees this year, up from 2,000 the previous year. ELECTRONICS IN THE 80s Once again, the tenor of the conference was set in the keynote speech delivered this year by Mr. J. Fred Buey, President of Texas Instruments. He discussed the increasing growth rate of the industry and the challenges for U.S. companies to maintain their share of the world market. Mr. Buey estimated that by 1990 worldwide semiconductor markets would grow from the 1979 total of $11 billion to the range of $60 to $80 billion; he projected that 40 percent of that total would be MOS memory. In order to grow to that level, the worldwide industry will have to add between $50 and $70 billion of additional manufacturing capacity. U.S. companies alone will have to add at least 60 percent of this capacity to maintain their share of world markets—$30 to $40 billion of new capacity. This increased capital spending in the 1980 decade is up significantly from the $5 to $6 billion of capital spending by U.S. based companies in the 1970s. This productive capacity will be difficult to add not only because it is larger in absolute magnitude but also because more capital investment is required to generate an additional dollar of revenue. Mr. Bucy emphasized that the U.S. economic system encourages Jiigh debt and low capital formation; therefore, it is not presently structured to encourage this level of investment. He mentioned that, as a result, 49 company acquisitions have been made in the U.S. semiconductor industry, 18 of these by foreign firms. Mr. Bucy also discussed two other challenges to U.S. industry: its ability to develop the managerial capabilities to handle this growth and the electronic industry's capability to use the potential of semiconductor technology. Copyright © 17 March 1980 by DATAQUEST- Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accLjracv or completeness It does not contain material provided to us in confidence by our clients. This information is not furnished in connection with a sale or offer to sell securrties or in connection with the solicitation of an offer to I buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. I 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO OVERVIEW OF THE TECHNICAL PAPERS The country of origin for technical papers at ISSCC shows an interesting trend inasmuch as it indicates the level of R « 5 c D within that country. Table 1 shows this data for the teclmical papers, exclusive of the panel discussions. U.S. presence has declined from 76 percent in 1978 to 68 percent in 1980, whereas the Japanese presence increased from 14 to 25 percent over tlie three years. Table 1 COUNTRY OF ORIGIN FOR TECHNICAL PAPERS AT ISSCC Country United States Japan Europe Total Technical Papers (Exclusive of Panel Sessions) 94 97 90 Source: DATAQUEST, Inc. March 1980 Amc»ig U.S. papers, Intel's paper on a 16K bit electrically erasable nonvolatile read only memory was well received (sessicm 12.6). Intel erases tliis memory with a 20 volt pulse across 200 angstroms of oxide, surely an exceUait oxide. TPs 64K RAM paper generated interest (session 17.6) and IBM's paper on an automated wafer production area (session 16.1) described their direct E-beam personalization of gate arrays. This facility handles one hundred more bipolar chip part numbers per year than comparable facilities did five years ago. Many of the technical papers from Japan were indicative of the long-range research going on in Japan. They tended to lool< two to five years into the future whereas many of the U.S. papers were looking at the next one to three year time frame. The Japanese papers (session 2) covering imaging sensoi^ for color TV cameras were particularly good as were the papers on 256K RAMs by NEC-Toshiba Information Systems and NTT Musashino Electrical Communication Laboratory (session 17). 1978 76% 14 10 100% 1979 65% 21 14 100% 1980 68% 25 7 100% # - 2 -It should be noted that the two Japanese papers on 256K dynamic MOS RAMs indicated a Jiigh level of R&D activity in Japan as well as the increasing pressure to "publish or perish." However, in light of the fact that the worldwide semiconductor industry shipped less than 20,000 64K dynamic RAMs in 1979 it is clear that tlie 256K RAM is Still a couple of years away from serious sampling. Nevertheless, the two papers from Japan did indicate that tliey have a very good technical ability in advanced state-of-the-art products. Table 2 indicates the number of papers within various categories which have been presented over the last three years. Howard Z. Bogert Daniel L. Klesl<en Table 2 PAPER COUNT BY APPUCATION AREA AT ISSCC Topical Area Analog Circuits and Applicaticais Digital Circuits and Applications Semiconductor Memory Combined Digital and Analog Design Aids, Processing, and Manufacturing CCDs and Imaging Telecommunications Gate Arrays Total 1978 28 19 15 12 7 7 6 __ 94 1979 24 11 21 13 11 7 6 _4 97 1980 15 24 16 10 11 6 8 - _ 90 Source: DATAQUEST, Inc. March 1980 - 3 -VoL II - No. 3 IVIarch 14, 1980 This letter is a condensation of recent newsletters and internal thinking from the industry research groups at DATAQUEST, Inc. Requests for amplification of our thoughts or for specific newsletters should be directed to the author. A list of recent DATAQUEST Research Newsletters appears at the end of this letter. COPYING AND DUPLICATING Xerox's recent announcement of its intention to establish a Retail Markets Division was made in a relatively low-key fashion, but we believe that this move may be very significant for the company longer term. Within the next two months, DATAQUEST expects Xerox to establish three to six company-owned retail stores in Dallas, Denver, and Minneapolis. These stores would begin selling a line of office equipment including low-end Xerox copiers along with non-Xerox manufactured typewriters and dictation equipment. Ultimately, we believe that the product line will be expanded to include supplies for a wider range of Xerox and other manufacturers' copiers, an electronic typewriter directly competitive with the IBM 70 and 75 that Xerox could announce mid-year, a new low-end copier likely to be introduced within the next twelve months, and standalone word processing systems. The product line might also include small business computers and home computers If the initial three city test market proves successful, we believe that Xerox will move very aggressively to expand this retail store network nationwide, with as many as 100 stores possible within twelve months and 600 stores by the end of 1982. Robert Rieser, formerly Vice President of Marketing and a leading candidate for more senior management positions, was put in charge of the operation. This indicates to us that the company has big plans for the retail enterprise. Considering the costs of leases, leasehold improvements, inventories, staffing, training, and advertising, the financial commitment required for starting this operation will be enormous. If the pilot stores prove successful and a rapid expansion is started, we estimate that pretax losses from this division will run between $10 and $20 million in both 1980 and 1981. As a result, we are shaving our 1980 earnings estimates from $7.50 to $7.40 per share. The division could turn profitable by 1982 and potentially generate significant profits by 1983. Conversely, an unsuccessful effort would mean stores closings, more red ink, and more red faces. DATAQUEST believes that the concept of retail stores makes a lot of sense. We envision Xerox becoming a one-stop office equipment supermarket that can fulfill almost edl needs of a small business. In addition, by selling the low-end copiers on a retail basis, Xerox frees its direct sales force to concentrate on the more lucrative mid- and high-range products, where the marketing cost are better absorbed by a higher average selling price. Copyright © 14 March 1980 by DATAQUEST ~ Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients. This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. Member, New York Stock Exchange 19055 Pruneridge Avenue / Cupertino, California 95014 / (408) 725-1200 Although the risks of this venture are certainly significant, we think they are far outweighed by the potential rewards. More good news on Xerox in the Word Processing section. WORD PROCESSING It looks to us as if 1980 may be the year in which the big players finally get serious about the word processing business. Under the direction of Don Massaro, we sense that Xerox's office products division (OPD), which encompasses word processing, has started to generate more momentum. Most of the initial software problems that have plagued the 850 word processors are now resolved and we believe that a very aggressive marketing effort on the 850 and the new 860 product is paying off in a marked pickup in new orders. Xerox's word processing revenues could jump as much as 70 percent in 1980 to almost $200 million and although the division will lose money this year, we believe that the losses will be down considerably from the levels of 1979. The long-term key for Xerox in the word processing market is the success of ETHERNET, its intra-office communications network. We do not believe that all of the pieces of ETHERNET are ready as of yet, but the pieces that we have become aware of look extremely well thought out and promising. It remains our belief that Xerox can finally obtain profitability in word processing in 1981. That success would dramatically change investor's attitudes about top management's capability and direction. At the same time, it appears that IBM is readying a noteworthy product for the word processing business as well. Likely to be introduced in the third quarter of 1980, the product should be IBM's first real entrance into the CRT standalone sector of the market. We expect that the new machines will have very good communications capabilities with other IBM office and computer products. The real key to the success of this machine wiU be pricing and software support. We will not be sure of those details until after the equipment's introduction. Initial indications however are that pricing may be very aggressive and that user interface will be emphasized. Do we think that these stronger efforts by Xerox and IBM will have a significant negative impact on the well entrenched companies in the word processing business? - NO. Do we think that they very well could impact some of the less well-positioned companies? - YES. SEMICONDUCTORS As we have been predicting, we are starting to see clear signs that supply is catching up with demand for certain semicionductor parts. We should note however, that conditions are still very tight in 16K RAMs, bipolar PROMs, low power Schottky, and microcomputers and are likely to remain so for almost all of 1980. In short, business is still very good. In fact, we are raising our forecast of U.S. semiconductor consumption growth for 1980 from 14 percent to 20 percent. This altered forecast does not reflect any change in our economic outlook, but rather the fact that sales in the fourth quarter of last year significantly exceeded our preliminary estimates. This means that the run rate entering 1980 is at a higher level and therefore year-to-year growth should be higher. In addition, overall orders during the first two months of 1980 remained strong. - 2 -Our present thinking is that the rate of gain in year-to-year sales will approximate 35 percent in the first quarter of this year and then decelerate down to a 7 percent rate of year-to-year growth in the fourth quarter, before starting to gradually improve during 1981. As we have stated before, the major question mark is pricing; we remain convinced that unit demand will remain fairly strong this year. A few comments about the Japanese seem in order since there appears to be increasing concern about their penetration into various sectors of the semiconductor industry. First, in 1979, the Japanese semiconductor manufacturers lost market share in every single product category (bipolar, MOS, linear, discrete), primarily as a result of losing their dominance of the Asian consumer products markets. Second, a good portion of the business the Japanese have received in the United States in the last year has been overflow business that the U.S. suppliers could not meet, which is a healthy development. We do not want to minimize the potential impact of the Japanese, particularly with their ability to spend large amounts of money in development and product reliability assurance without commensurate economic return, as well as the support that the companies get from the Japanese government. We do not want to over-emphasize the risk either. The turnaround in Motorola's semiconductor operation has been predicted and documented by our staff for the last three years, but unfortunately the rest of the company has not been able to support the turnaround that the semiconductor group affected. We understand that our $6.05 per share earnings estimate for Motorola this year is high by Wall Street standards. Frankly, we were somewhat hard pressed to keep the numbers down that low and have factored a reasonable degree of conservatism into our forecast (i.e., no improvement in the large losses incurred last year by automotive products). Motorola's 16-bit microprocessor, the 68000, is an extremely strong product offering. The company faces a tremendous challenge this year to introduce the necessary support chips to take advantage of the product's potential. If Motorola can accomplish this goal and also show good earning gains in what is likely to be a tough economic year, we think investors' perceptions of the company can change radically. PAPER AND FOREST PRODUCTS The surprising strength of the U.S. economy thus far in 1980 has translated into generally strong levels of demand for almost all paper products. In addition, the companies in general have been able to raise prices at a more rapid rate than cost. All of which means that industry profitability should be very strong in the first quarter of 1980 and probably in the second quarter as welL Despite these glad tidings, however, we have become somewhat more pessimistic about the intermediate term outlook since our last writing. We are more and more convinced that while the recession this year may not be a very steep one, the recovery is likely to be very moderate as well. Our official DATAQUEST forecast is for a 1.5 percent decline in real GNP in 1980 followed by a 1.5 percent increase in 1981. In this scenario, paper industry pretax profits would likely decline by about 10 percent in the third quarter of this year and tjy 20 percent or more in the fourth quarter of 1980 and first half of 1981, before recovering - 3 somewhat late next year. A further unsettling note is that we now feel that there is clear evidence of overbuilding in wholesale inventories of white paper in particular, and probably of almost all paper grades. This overload will obviously work to the industry's disadvantage late this year. The one saving grace for the paper industry in 1980 may be the possibility of Strikes in eastern Canada. Labor contracts for the entire eastern Canadian paper industry wiU expire in the fall and the initial reports are that the gap between management and labor is fairly wide. A prolonged strike in Canada this year could bail out the U.S. producers much the same as it did in 1975. As noted in previous Portfolio Letters, we have particular concern about the white paper sector of the industry. We foresee relative imbedances between supply and demand continuing off and on through 1985 and believe that the peak year of profitability in this sector of the industry until 1985 may be achieved in the first half of 1980. Conversely, while 1980 and 1981 will not be banner years in brown paper, we remain convinced that over the ensuing years, brown paper supply and demand will be relatively tight and will work to the benefit of the producers. Our attitude about the relative weightings of the different sectors of this industry remains the same: a de-emphasis on companies with high white paper exposure (Boise Cascade, HammermiU Paper) and an emphasis on companies with high brown paper exposure (Union Camp). Our overall view of the industry over the next 18 months, however, is somewhat more pessimistic because of the likelihood of a slower recovery next year. We think it is reasonable to expect the forest products companies to lead the recovery. With this in mind, we would particularly point to one forest products concern, Champion International, that is particularly interesting because it has a relatively good exposure to brown paper. INSTRUMENTATION Several instrument companies have recently cited the problems brought on by the present high rate of inflation, namely that with relatively long backlogs, these companies have found it difficult to raise prices fast enough to offset rising costs, particularly since most companies use LIFO accounting. We have few words of wisdom to add on this subject other than to project when these problems should abate for each of the companies involved. Hewlett-Packard was hurt by high component costs as early as the fall of 1979 and has been steadily raising prices throughout fiscal 1980. Prices are already up an average of more than 3.5 percent this year; we would anticipate that another 1.0-1.5 percent price increase scheduled for May 1 will be moved up by a month. In general, we believe that cost pressures are actually becoming somewhat less of a problem at Hewlett Packard because of the relatively early steps it took to raise prices. We would anticipate that sequential profit margin would improve in the second fiscal quarter and continue to move higher during the balance of fiscal 1980. The problem is somewhat more significant for Tektronix because of manufacturing problems that are holding up shipments. This slowdown could cost the company $10-15 million in revenues in the present quarter. This problem has the additional negative effect of stretching out backlogs, which means that - 4 -price increases take longer to be reflected in revenues. We do not expect any improvement in margins at Tektronix until the first quarter of fiscal 1981 (August) and our $4.70-$4.80 per share estimate for fiscal 1980 implies only slight improvement in earnings during the final two quarters of this year. Teradyne's backlogs in certain semiconductor tester products are stretched out over six months and the lag before the company can raise prices on products that flow into sales will definitely constrain margins during most of 1980. This consideration is factored into our $3.30 per share earning estimate for this year. GenRad, which is working off of backlog that generally do not exceed three months, is experiencing fewer problems in this regard. SMALL COMPUTERS Our final estimates indicate that the U.S. based general purpose minicomputer (GPMC) market grew by 29.8 percent to $5.0 billion in 1979. The increase in unit shipments was only 16 percent, a clear indication that sales of peripherals amd add-ons as well as service revenues greatly exceeded the growth in new system Sales. Two small companies. Tandem Computer and Prime Computer, were standout performers with revenue gains of 133 percent and 51 percent respectively. Among the larger participants, IBM, Honeywell, and Hewlett-Packard also gained market share. Data General held about constant and Digital Equipment lost about one percentage point in share. Despite the increasing economic uncertainties, we are inclined to increase our growth forecast for the GPMC market from 25 percent to a 25-30 percent range in 1980. This alteration does not reflect a change in fundamentals, but rather one in pricing. IBM recently raised prices by an average 7 percent across most of its product line. Digital Equipment has announced price increases ranging from 5-15 percent, and Datapoint has just raised prices (for the first time in its 11-yeeir fiistory) an average of 4 percent on purchases and 8 percent on leases. We would expect selective price increases from Data General and Hewlett-Packard in the near future, as the industry adapts to a more inflationary environment. We hesitate to become more optimistic about increases in growth rates that are purely a function of pricing, but we are encouraged by the recent moves in that they increase the likelihood that the industry can maintain profit margins this year. Michael R. Weisberg 5 -RECENT NEWSLETTERS OF NOTE Copying &. Duplicating 1. Eastman Kodak Raises Sale and Rental Prices 2. Xerox Forms a Retail Markets Division 3. Xerox Shows Strong Gains in 1979 4. SEROMDA 1980 03/06/80 02/21/80 02/12/80 02/01/80 Word Processing 1. Lanier Announces Three New Options 2. Wang Raises Rental Prices 3. IBM Reduces Word Processing Purchase Prices 4. Vydec Announces Model 1800 and Price Changes 5. Qyx Raises Price and Maintenance Charges 6. IBM Announces Price Increases 02/21/80 02/21/80 02/21/80 02/21/80 02/13/80 02/13/80 Semiconductors 1. An Update: Automotive Semiconductor Market 2. MOS Microprocessor Shipments 3. Dynamic and Static MOS RAM and EPROM Shipments 02/29/80 02/29/80 02/22/80 Paper Sc Forest Products 1. The Outlook for Coated Paper: 1980-82 02/06/80 Instrumentation 1. Digital Test Program Generation Systems 2. Hewlett-Packard Company Financial Analysts Meeting 02/26/80 01/29/80 Small Computers 1. Key Issues Facing Small Computer Suppliers in 1980/81 02/26/80 2. IBM Announces 5120 Computing System 02/12/80 3. Summary of 1980 DATAQUEST Small Computer Industry Conference 02/12/80 - 6 -1 p^ i Ifll fit 1 1 1 ^wi RESEARCH A Subsidiary of A.C. Nielsen Co. ' 5 INCORPORATED i \ I ^ Z V V ^ S l ^ l S 1 1 ^ S i ^ SIS Code: VoL I, 2.8.7 AN UPDATE: AUTOMOTIVE SEIVIICONDUCTOR MARKET In December 1978, DATAQUEST's Semiconductor Industry Service published a Service Section and a Researcli Newsletter on the market opportunities for semicon-ductor devices in automobiles. This newsletter updates subscribers on this important market segment. Government-mandated systems for fuel economy, exhaust emissi<»is, and safety are expected to remain the major incentive for production of electronic systems for several years. However, feature items are being incorporated more quickly tJian DATAQUEST anticipated; for example, Ford is offering electronic door locks on several of its 1980 models. Our revised forecast of semiconductor consumption (Table 1) for U.S. and Canadian cars is 40 percent higher than our forecast of a year ago. There are 3 major reasons for the increase: • General Motors is equipping nearly all of its 1980 models with electronic engine controls; in 1978, we estimated that incorporation on this scale would not obcur until model year 1981. • Semiconductor content in the systems is higher tlian expected because the systems are more complex than expected and unit prices did not faU as projected. • More feature systems are being offered than were expected. Note that we are revising our forecast for model year 1980 only; the assumptions and predictions for future years stiU appear to be valid. In Table 2, we show some representative equipment installed in 1979 model cars as reported by Ward's Automotive Reports. In general, DATAQUEST's forecasts of December 1978 compare very favorably with these reported actuals. Use of the V-8 engine has declined dramatically as we expected; the rapidly rising price of fuel is expected to cause the decline to continue even more rapidly. Buick has already cast its last V-8 engine. The 4-cylinder engine is gaining popularity faster than we expected and sales of this engine appear to be limited only by production capacity. Waiting times for some 4-cylinder models is reported to be 13-14 mc«ths. Dealers report that the typical car buyer's perception is that 8 cylinders are required for performance and 4 cyjlinders are required for economy; surprisingly, the 6-cylinder engine, which really offers both, has little inherent demand. Copyright © 29 February 1980 by DATAQUEST - Reproducticxi Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities This firm and its parent andfor their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO Diesel engine sales are limited somewhat by availability. Even without the planned 260 cubic inch diesel, General Motors' diesel sales now surpass the sales volume of all of the imported diesel automobiles. CM is now offering the diesel engine in other divisions, so sales are expected to continue growing; however, its engine has not yet gained certification for sale in California for 1980 models. Since the popularity was highest in California, this is expected to have significant negative impact on diesel market penetraticai. Cruise Control is stiU largely non-electronic; in 1979, only Ford (all lines) and Cadillac used electronic solutions. Delayed windshiield wipers and digital clocks are not electronic in all cases, but we expect that they will soon be converted. The higher than originally expected use of electronic catalytic-converter controls in 1979 was primarily due to GM's acceleration of electronic programs. The electronic dashboard promises to be the major area for feature distinction. Trip Computer emd Message Center functions are expected to be integrated further with the traditional instrument cluster functions. Diagnostic functions and warning devices are expected to take advantage of animation capabilities of LCD displays. Audible warnings and messages are expected to abandon buzzer and chimes in favor of speech synthesizer-generated messages. Table 3 presents DATAQUEST's estimates of the 1980 model year procurements by the domestic automobile manufacturers and the market shares of the semicon-ductor suppliers. By winning major supply contracts at General Motors, Texas Instruments is now estimated to be the number two supplier to the domestic automobile industry. The impact of the impending recession on the accuracy of the auto industry's forecasts for automobile production is viewed as the most significant factor affecting the accuracy of our forecasts. We expect that any further loss of market share by Chrysler wiU tend to decrease the total market for semiconductors as Chrysler's implementations tend to be higher in integrated circuit content than those of GM and Ford and, further, to shift some of the North American automobile market to Japan and Western Europe. We expect that in the future Delco Electronics will build a smaller percent share of GM's semiconductor requirements. Toshiba, a significant microprocessor supplier for model year 1979, is estimated to be participating at a considerably smaller market share in 1980. American Microsystems, Inc. (AMI) is moving into a position of significance as an automotive supplier. Although several AMI programs were curtailed when the company's VMOS process was withdrawn, AMI is expected to become a significant supplier to the European market throi^h its affiliaticai with Robert Bosch GmbH. In addition to their semiconductor sales, Motorola and Fairchild are significant suppliers of electronic assemblies. We estimate that Motorola's 1979 sales of automotive electronic modules were about $100 milliOTi and Fairchild's 1979 sales, principally electronic ignition modules were about $25 million. Motorola's sales of automobile radios are not included in the at)ove estimates. 2 -Table 4 presents DATAQUEST's estimate of the component unit volumes required for U.S. domestic ear production in model year 1980. This estimate includes the components supplied by module manufacturers. Willard T. Booth Daniel L. Klesken Table 1 ESTIMATED SEMICONDUCTOR COMPONENT VALUE IN FACTORY INSTALLATIONS BY MODEL YEAR IN FREE WORLD VEHICLES Model Year Total Free World United States & Canada United States Canada Japan Western Europe (Millions of DoUars) 1978 $243 $126 $111 $ 15 $ 41 $ 76 1979 $270 $143 $126 $ 17 $ 46 $ 81 1980 $450 $280 $255 $ 25 $ 70 $100 1981 $640 $450 $410 $ 40 $ 80 $110 1982 $820 $610 $540 $ 70 $ 90 $120 • ^ 1985 $980 $700 $620 $ 80 $110 $170 Source: DATAQUEST, Inc. February 1980 - 3 -Table 2 SELECTED 1979 EQUIPMENT INSTALLATION RATES U.S. DOMESTIC CARS (Percent of Total Production) 8-Cylinder Engines Gasoline 56.4% Diesel 2.2% 6-Cylinder Engines 23.8% 4-Cylinder Engines 17.6% Cruise Control Electronic 6.0% Other 31.1% Digital Clocks 20.5% Delayed Windshield Wipers 25.7% Tachometer 9.2% Burgler Alarm , 1.0% Headlamp Timing 4.5% Trip Computer 0.1% An-Electronie Radio 1.3% Electronic Engine Controls Fuel Injection 2.5% Spark Advance 14.9% Catalytic Converter Control 3.7% Climate Control 9.8% Source: Ward's Automotive Reports January 28, 1980 4 -Table 3 ESTIMATED SEMICONDUCTOR COMPONENT PROCUREMENTS FOR MODEL YEAR 1980 (Millions of Dollars) Motorola Texas Instruments Delco Electronics National Semiconductor RCA Signetics Intel Fairchild AMI Toshiba GM $ 90 30 40 20 5 10 -5 --Ford $12 14 -1 -2 10 2 4 2 Clirysler $ 8 6 -^ $ 12 i -• • -1 -Total $110 50 40 26 17 13 10 7 5 2 Total $200 $47 $33 $280 Source: DATAQUEST, Inc. February 1980 Table 4 ESTIMATED COMPONENT REQUIREMENTS OF U.S. DOMESTIC CARS FOR MODEL YEAR 1980 BY TECHNOLOGY (MiUions of Units) Integrated Circuits Bipolar NMOS PMOS CMOS Discrete Devices Transistors Diodes Passive Devices Resistors Capacitors 190 85 15 10 80 360 175 185 3,100 1,700 1,400 Source: DATAQUEST, Inc. February 1980 5lo y/ 3'^0 % I ' 'ho ii - lo y]<- ito yff,7S=^V /^dO - 6 •f! •^> i^#%l flS Si 1 ^^1 RESEARCH ASubsicjiPi'YOf A.C.Ni^lsenCo. ^ INCORPORATED l ^ l E S W ^ d ^ ^ S I 1 1 E H P ^ SIS Code: VoL L, 2.8.1 MOS MICROPROCESSOR SHIPMENTS SUMMARY In the fourth quarter of 1979, worldwide shipments of IVlOS microprocessors were an estimated 26.3 million units, up alDOUt 20 percent over estimated third quarter 1979 Shipments, and up about 216 percent over the fourth quarter of 1978. Worldwide Shipments for the year 1979 were an estimated 75.1 million units, up a dramatic 193 percent over an estimated 25.6 million units shipped in 1978. In the fourth quarter, 4-bit microprocessors represented about 67 percent of the total shipmaits with estimated shipments of 17.7 miUiOTi units, up about 20 percent over the tJiird quarter of 1979. Ei^ht-bit microprocessors had estimated shipments of 8.4 miUicai units, representing about 32 percent of the total. Sixteen-bit products, with estimated shipments of 203,000 units, represented about 1 percent of the fourth quarter 1979 totals. Figure 1 demwistrates the continued dramatic growth in quarterly microprocessor shipments. Quarter-to-quarter growth of total microprocessor Shipments has exceeded 20 percent for each of the four quarters in 1979. The rapid growth of the 4-bit and 8-bit single-chip microcomputers is also easily seen in this figure; microcomputer shipments represaited about 82 percent of the fourth quarter shipments, compared to 81 percent in the third quarter. Demand for single-chip microcomputers remains strong in this first quarter of 1980. Lead times for these ROM-based devices are generally in excess of twenty weeks, and prices have remained firm. Lead times on some microprocessors have Shortened to under five weeks, and prices have declined slightly. QUARTERLY MICROPROCESSOR SHIPMENTS DATAQUEST estimates of worldwide microprocessor CPU shipments for the fourth quarter of 1979 are presented in Table 1. Our estimated shipments refer to microprocessor CPU chips wily and do not include I/O or peripheral chips. Total microprocessor shipments in the fourth quarter of 1979 were an estimated 26.3 million units, up about 20 percent over the third quarter of 1979 and up about 216 percent over the fourth quarter of 1978. Total shipments of IWOS microprocessors for 1979 were an estimated 75.1 millitxi units, up about 193 percent over an estimated 25.6 million units shipped in 1978 and up dramatically over the estimated 8.4 million imits shipped in 1977. Copyright © 29 February 1979 by DATAQUEST - Reproductiai Prohibited The content of ttiis report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness, It does not contain material provided to us in confidence by our clients This information is not furnished in connection vuiih a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities This firm and its parent andfor their officers, stockholders, or members of their families may, from time to time, have a long or short position in the securities mentionsd and may sell or buy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO DATAQUEST has been tracking MOS microprocessor shipments since our first newsletter on the subject in September 1976, and Figure 2 is a plot of estimated worldwide shipments of MOS microprocessors for the years 1975 throi^h 1979. These shipments have increased dramatically from an estimated 1.1 million units in 1975 to an estimated 75.1 miUion units in 1979. The compound annual growth rate between 1975 and 1979 has been a remarlcable 188 percent. This figure indicates almost a tripling of shipments every year. Sueii a growth rate cannot continue forever, but we do expect to see a doubling of total unit shipments in 1980. Table 2 presents DATAQUEST's estimate of worldwide shipments of 4-bit, single-Chip microcomputers. In the fourth quarter of 1979, estimated shipments of 4-bit bit microcomputers were 17.7 million units, up about 20 percent over estimated third quarter shipments of 14.7 million units. In 1979 an estimated 50.2 million 4-bit microcomputers were shipped, up dramatically over an estimated 16.0 millioi imits in 1978. Table 3 presents DATAQUEST's estimates of worldwide shipments of 8-bit microcomputers. In the fourth quarter of 1979, an estimated 3.9 million units of the 8-bit microcomputers were shipped, up 32 percent over an estimated 2.9 million units in the third quarter of 1979. For the year 1979, 8-bit microcomputers totalled 9.8 million units, up sharply from an estimated 1.4 milliOTi units in 1978. In this first quarter of 1980, the demand for single-chip microcomputers continues to be very Strong. It appears that all the major users of microcomputers, including the toy and games, automobile, instrument, and terminal manufacturers, have expanded their requirements for single-ehip microcomputers in 1980. Lead times are still generally beyond twenty weeks for these ROM-based products and prices remain relatively firm in this first quarter of 1980. The 8-bit microcomputers are generally in the $7.00 to $9.00 range for first and second quarter deliveries. However, some very high volumes (200,000 units) have been quoted as low as $5.00. 4-BIT BflCROPROCESSORS Table 4 presents DATAQUEST's estimates of worldwide shipments of 4-bit microprocessors. In the fourth quarter of 1979, shipments of these products were for an estimated 17.7 million units, up at>out 20 percent over third quarter of 1979. For the year 1979, total 4-bit microprocessor shipments were an estimated 50.4 million units, up from 16.3 millicwi units in 1978. In this first quarter of 1980, pricing on the 4-bit microcomputers generally remains firm in the $1.50 to $3.50 range for large volume purchases. However, some of the newer devices on the marlcet are not quite as low priced: for example, the S2000 family is generally priced in the $4.00 to $6.00 range for 10,000 unit quantities, whereas the 141000, a CMOS product, is priced in the $7.00 to $9.00 range. Several of the 4-bit microcomputer families contain 10 to 20 distinct products differing in memcffy size, package size, and technology. Prices for devices at the high end of the family are often two or three times the prices of devices at the low end of the line. - 2 -8-BIT MICROPROCESSORS Worldwide shipments of 8-bit microprocessors in the fourth quarter of 1979 were an estimated 8.4 million units, up about 20 percent, over estimated third quarter shipments and up about 211 percent over estimated fourth quarter 1978 shipments (see Table 5). Eight-bit single-chip microcomputers are playing an increasingly important role in the overall 8-bit market. Over the four quarters of 1979, 8-bit microcomputers increased their share of the total 8-bit products from 30 percent in the first quarter, to 39 percent in the second quarter, 42 percent in the third quarter, and 46 percent in the fourth quarter. IVIature 8-bit microprocessors scheduled for delivery in the first half of 1980 are currently priced in the $3.75 to $6.50 range. These prices have fallen slightly from those of late 1979 and reflect some softness in the microprocessor market. Lead times in the various 8-bit microprocessor families are generally less than five weeks. 12- AND 16-BIT MICROPROCESSORS Table 6 presents estimates of worldwide shipments of 12- and 16-bit micro-processors. Shipments of 12-bit microprocessors were an estimated 12,000 units in the fourth quarter, the same as the third quarter total. This market still has not moved significantly and is not expected to ever be a majca' microprocessor market. Worldwide shipments of 16-bit microprocessors in the fourth quarter of 1979 were an estimated 203,000 units, up about 27 percent over estimated third quarter 1979 Shipments of 160,000 units and up 92 percent over estimated fourth quarter 1978 shipments. For 1979, total 16-bit microprocessor shipments were an estimated 625,000 units. Current pricing on most 16-bit microprocessors has remained relatively stable since fourth quarter of 1979. The TMS-9980 is currently available for about $12.00 in large volumes, whereas the TMS-9900 is priced in the range of $20.00 to $25.00. The newer 16-bit products, such as the 8086, are priced in the $60.00 to $90.00 range whereas the Z8000 and 68000 are currently priced in the $150.00 to $250.00 range. These prices are expected to decline over the coming quarters as shipments incresise. Daniel L. Klesken Lane Mason - 3 -I »(^ I t (0 3 O a > a •o 0) a a 'JE (/) tn "c D " o CO c o 28 26 24 22 20 18 16 14 12 10 8 6 4 2 0 Figure 1 ESTIMATED WORLDWIDE MICROPROCESSOR SHIPMENTS •4-Bit Multichip and. 16-BltMultichip ^.««?^5s?ssKK:Wi^ assess g^SSssss s:-:;:f;:ffff 'SS^iiafiliiiiiliiii;; |4-Bjt Single Chip^ :fe:-:;:::::::W::::::: •:-f;-i:-:-:-i-;:-^gsMi^sssgiSi iilKi^g^gil^^! vx-^'XiX'::::';'::::::!:; , - . ^ ' i ' . " . " . ' . " . \ ' . ' . j . ^ ; . " . " . " H ^mm ^^mmfi^^m^^m^^mm^^m^mmmm^^^m^^^m tmiMiiliiiiiiimmmiii m^0^Mivm[ {{piimaai ;>>.;;;.;.;.;.;.;.;.;.;.;.;.;.;.;. .....;.;.;...;.J.^%;.;.;.>:.:.;J.>>;;;.;.".;.';;^.;^.;;;^;;;;;.;^^ :.:.:.:.:....-:.:.:.:.:.:.:.:.:...^.:.:.:.:.; aai^-...-..-.v.....:--.....:.:..:...:.:.:.x.:.:. Q1 V-Q2 Q3 Q4 Q1 -1978-yv. Q2 0 3 1979' Q4 Source: DATAQUEST, Inc i Table 1 ESTIMATED WORLDWIDE SHIPMENTS OF MOS MICROPROCESSORS (Thousands of Units) 1978 1979 Company AMD AMI EFCIS Fairehild General Instrument Harris Hitachi Hughes Intel Intersil Matsushita MOS Technology Mostek .Motorola National .SEC-RCA Rockwell Siemens Signetics Solid State Scientific Synertek Texas Instruments Thomson - CSF Zilog Microprocessor 8080A 8085 8048 Z8000 S2000 6800 6802/6808 9900 6800 F8 3870 6800 6802/6808 PIC-1650 CP-1600 6100 HMCS-40 6800 1802 4004 8008 8080A 8048/8021 8049/8022 8748 8085 8086 6100 MN1400 6500 F8 Z80 3870 141000 6800 6801/6803 6802/6808 6805 6809 3870 68000 COPS 4004 IMP 8080A 8048 8049 8050 8070 SC/MP PACE COM-4 8080A 8048/8049 8085 Z80 768 1802 PPS-4 6500 6500/1 8080A 8085 2650 8048 1802 6500 TMS 1000 TMS8080A TMS 9900 TMS 9940 6800 Z8 Z80 Z8000 Bits 8 8 8 16 4 8 8 16 8 8 8 8 8 8 16 12 4 8 8 4 8 8 8 8 8 8 16 12 4 8 8 8 8 4 8 8 8 8 8 8 16 4 4 4 8 8 8 8 8 8 16 4 8 8 8 8 16 8 4 8 8 8 8 8 8 8 8 4 8 16 16 8 8 8 16 MOS Process N N N N N N N N N N N N H N N C P&C N C P P N N N N N N C N,P&C N N N N C N N N N N N N N i C P P N N N N N N N N.P&C N N N N N C P N N N N N N C N PitC N N N N N N N 4th Qtr. 125 5 0 0 12 35 0 0 0 200 10 30 S 175 15 7 120 25 12 35 22 190 170 10 25 125 13 ^ 2 N/A^ 60 4S 80 205 15 160 0 90 0 0 40 0 850 30 20 100 0 0 0 0 100 25 600 60 15 25 25 0 90 650 60 0 0 0 45 S 10 70 3,200 35 53 0 7 0 210 0 1978 Total 435 5 0 0 29 130 0 0 0 630 23 90 S 450 60 22 410 70 35 159 103 705 480 10 30 350 24 15 N/A 225 160 260 350 20 570 0 180 0 0 70 0 2,325 130 80 375 0 0 0 0 335 86 1,500 305 15 30 30 0 325 2,275 595 0 0 0 125 S 22 680 9,400 135 185 0 25 0 550 0 1st Qtr. 135 S^ 0 50 35 s 0 8 150 40 35 S 300 15 7 130 50 12 35 20 190 210 20 50 175 13 4 500 65 90 100 260 30 165 0 150 0 s 80 0 900 30 18 150 0 0 0 0 100 25 1,100 65 25 55 80 S 115 600 50 0 3 0 45 15 10 100 4,200 32 68 0 0 0 195 0 2nd qtr. 325 40 S S 300 30 10 0 10 200 50 35 s 950 20 7 150 100 14 32 18 200 300 40 75 260 15 4 800 70 125 120 300 75 175 s 240 0 2 125 0 1,100 26 15 175 0 0 0 0 140 25 1,300 90 160 75 80 S 115 1,100 60 s 10 S 90 30 11 120 5,400 25 80 S 0 s 250 1 3rd Qtr. 335 75 3 S 675 30 10 S 12 275 120 40 15 1,250 20 7 175 125 18 28 15 210 450 70 75 300 19 5 1,400 80 125 125 425 90 215 3 275 S 8 125 S 1,500 20 15 220 0 S 0 0 160 25 2,300 105 350 120 60 s 125 1,100 60 3 25 5 110 60 12 280 7,500 18 92 S 0 S 425 4 4th Qtr. 285 70 20 S 400 40 30 5 15 260 300 40 30 1,600 25 7 200 150 22 25 12 180 550 100 100 350 25 5 1,700 90 130 170 485 90 205 10 325 3 10 170 3 2,100 15 15 240 S 10 S S 175 25 3,100 100 450 150 40 S 135 1,100 60 5 40 10 110 75 10 300 9,000 5 105 5 0 s 700 10 1979 Total 1,080 200 23 S 1,425 135 50 5 45 885 510 150 45 4,100 80 28 655 425 66 120 65 780 1,510 230 300 1,085 72 18 4,400 305 470 515 1,470 285 760 13 990 3 20 500 3 5,600 91 63 785 S 10 s s 57 5 100 7,800 360 985 400 260 s 490 3,900 230 8 78 15 355 180 43 800 26,100 80 345 5 0 S 1,570 15 Total Microprocessors Percent change from previous quarter S = Sampling ^N/A = Not Available 8,340 25,628 11,120 15,695 21,922 26,327 75,064 33% 41% 40% 20% - 5 -Source: DATAQUEST, Inc. February 1980 CO 0) >• h . 0> OL •o a Q. • MM £ I W r 1 80 70 fe 60 50 .r 40 o < o 30 c o 2 20 10 1975 Figure 2 ESTIMATED WORLDWIDE MICROPROCESSOR SHIPMENTS 1976 1977 1978 1979 Source: DATAQUEST, Inc. Table 2 ESTIMATED WORLDWIDE SHIPMENTS OF 4-BIT SINGLE-CHIP MICROCOMPUTERS (Thousands of Units) 1978 1979 Company AMI Hitachi Matsushita Motorola National NEC Rockwell Texas Instruments Total Change from Microcomputer S2000 HMCS-40 MN1400 141000 COPS COM-4 PPS-4 TMSIOOO previous quarter ^N/A = Not Available 4th Qtr. 12 120 N/A^ 15 850 600 650 3,200 5,447 1978 Total 29 410 N/A 20 2,325 1,500 2,275 9,400 15,959 1st Str^ 50 130 500 30 900 1,100 600 4,200 7,510 38% 2nd Qtr^ 300 150 800 75 1,100 1,300 1,100 5,400 10,225 36% 3rd 9^ 675 175 1,400 90 1,500 2,300 1,100 7,500 14,740 44% Source: 4th Str^ 400 200 1,700 90 2,100 3,100 1,100 9,000 17,690 20% 1979 Total 1,425 655 4,400 285 5,600 7,800 3,900 26,100 50,165 ; DATAQUEST, Inc. February 1980 Table 3 ESTIMATED WORLDWIDE SHIPMENTS OF 8-BIT SINGLE-CHIP MICROCOMPUTERS (Thousands of Units) 1978 1979 Company AMD Fairchild General Instrument Intel Mostek Motorola National NEC Rockwell Signetics Zilog Total Microcomputer 8048 3870 PIC-1650 8048/8021 8049/8022 8748 3870 6801 6805 3870 8048 8049 8050 8070 8048/8049 6500/1 8048 Z8 Change from previous quarter S = Sampling 4th Str, 0 10 175 170 10 25 205 0 0 40 0 0 0 0 15 0 S 0 650 1978 Total 0 23 450 480 10 30 350 0 0 70 0 0 0 0 15 0 S 0 1,428 1st Qtr. s' 40 300 210 20 50 260 0 0 80 0 0 0 0 25 S 15 0 1,000 54% 2nd Qtr. S 50 950 300 40 75 300 S 0 125 0 0 0 0 160 S 30 S 2,030 103% 3rd Qtr. 3 120 1,250 450 70 75 425 3 S 125 0 S 0 0 350 3 60 S 2,934 46% Source: 4th Qtr. 20 300 1,600 550 100 100 485 10 3 170 S 10 S S 450 5 75 S 3,878 32% 1979 Total 23 510 4,100 1,510 230 300 1,470 13 3 500 S 10 S S 985 8 180 S 9,842 DATAQUEST, Inc. February 1980 - 7 -Table 4 ESTIMATED WORLDWIDE SHIPMENTS OF 4-BIT MICROPROCESSORS (Thousands of Units) 1978 1979 Company AMI Hitachi Intel Matsushita Motorola National NEC Rockwell Texas Instruments Total Percent change from previous quarter Microprocessor S2000 HMCS-40 4004 MN1400 141000 COPS 4004 IMP COM-4 PPS-4 TMS 1000 4th qtr. 12 120 35^ N/A 15 850 30 20 600 650 3,200 5,532 1978 Total 29 410 159 N/A 20 2,325 130 80 1,500 2,275 9,400 16,328 1st Qtr. 50 130 35 500 30 900 30 18 1,100 600 4,200 7,593 37% 2nd Qtr. 300 150 32 800 75 1,100 26 15 1,300 1,100 5,400 10,298 36% 3rd Qtr. 675 175 28 1,400 90 1,500 20 15 2,300 1,100 7,500 14,803 44% 4th Qtr. 400 200 25 1,700 90 2,100 15 15 3,100 1,100 9,000 17,745 20% 1979 Total 1,425 655 120 4,400 285 5,600 91 63 7,800 3,900 26,100 50,439 1 N/A = Not Available Source: DATAQUEST, Inc. February 1980 - 8 Table 5 ESTIMATED WORLDWIDE SHIPMENTS OF 8-BIT MICROPROCESSORS (Thousands of Units) Company M AMD AMI EFCIS Fairchild General Instrument Hitachi Hughes Intel MOS Technology Mostek Motorola National NEC RCA Rockwell Siemens Signetics Solid State Scientific Synertek Texas Instruments Thomson - CSF Zilog Total Percent change from previoiis quarter icroprocessor 8080A 8085 8048 6800 6802/6808 6800 F8 3870 6800 6802/6808 PIC-1650 6800 1802 8008 8080A 8048/8021 8049/8022 8748 8085 6500 F8 Z80 3870 6800 6801/6803 6802/6808 6805 6809 3870 8080A 8048 8049 8050 8070 SC/MP 8080A 8048/8049 8085 Z80 1802 6500 6500/1 8080A 8085 2650 8048 1802 6500 TMS 8080A 6800 Z8 Z80 J , 1978 4th Qtr. 125 5 0 35 0 0 200 10 30 s • 175 25 12 22 190 170 10 25 125 60 45 80 205 160 0 90 0 0 40 100 0 0 0 0 100 60 15 25 25 90 60 0 0 0 45 S 10 70 35 7 0 210 2,691 1978 Total 435 5 0 130 0 0 630 23 90 S 450 70 35 103 705 480 10 30 350 225 160 260 350 570 0 180 0 0 70 375 0 0 0 0 335 305 15 30 30 325 595 0 0 0 125 S 22 680 135 25 0 550 8,908 1st Qtr. 135 15 S 35 S 8 150 40 35 0 300 50 12 20 190 210 20 50 175 65 90 100 260 165 0 150 0 S 80 150 0 0 0 0 100 65 25 55 80 115 50 0 3 0 45 15 10 100 32 0 0 195 3,395 26% 2nd Qtr. 325 40 S 30 10 10 200 50 35 S 950 100 14 18 200 300 40 75 260 70 125 120 300 175 S 240 0 2 125 175 0 0 0 0 140 90 160 75 80 115 60 S 10 S 90 30 11 120 25 0 S 250 5,245 54% 1979 3rd Qtr. 335 75 3 30 10 12 275 120 40 15 1,250 125 18 15 210 450 70 75 300 80 125 125 425 215 3 275 S 8 125 220 0 S 0 0 160 105 350 120 60 125 60 3 25 5 110 60 12 280 18 0 S 425 6,947 32% 4th Qtr. 285 70 20 40 30 15 260 300 40 30 1,600 150 22 12 180 550 100 100 350 90 130 170 485 205 10 325 3 10 170 240 S 10 S S 175 100 450 150 40 135 60 5 40 10 110 75 10 300 5 0 S 700 8,367 20% 1979 Total 1,080 200 23 135 50 45 885 510 150 45 4,100 425 66 65 780 1,510 230 300 1,085 305 470 515 1,470 760 13 990 3 20 500 785 S 10 S S 575 360 985 400 260 490 230 8 78 15 355 180 43 800 80 0 S 1,570 23,954 S = Sampling Source: DATAQUEST, Inc. February 1980 - 9 -Table 6 ESTIMATED WORLDWIDE SHIPMENTS OF 12-BIT AND 16-BIT MICROPROCESSORS (Thousands of Units) 12-Bit Products 1978 1979 Company Microprocessor Harris Intersil Total Percent change from previous quarter 16-Bit Products Company M AMD AMI General Instrument Intel Motorola National NEC Texas Instruments Zilog Total Percent change from previous quarter 6100 6100 icroprocessor Z8000 9900 CP-1600 8086 68000 PACE 768 TMS 9900 TMS 9940 Z8000 4th Qtr. 7 4 11 1978 Total 22 15 37 1978 4th 91L^ 0 0 15 13 0 25 0 53 0 0 106 1978 Total 0 0 60 24 0 86 0 185 0 0 355 1st Qtr. 7 4 11 0% 1st Qtr, 0 0 15 13 0 25 S 68 0 0 121 14% 2nd Qtr. 7 4 11 0% 2nd Qtr. s' 0 20 15 0 25 S 80 S 1 141 17% 3rd gtr. 7 5 12 9% 1979 3rd 2t£i S S 20 19 S 25 S 92 S 4 160 13% 4th Qtr. 7 5 12 0% 4th St!^ S 5 25 25 3 25 S 105 5 10 203 27% 1979 Total 28 18 46 1979 Total S 5 80 72 3 100 S 345 5 15 625 1 S = Sampling Source: DATAQUEST, Inc. February 1980 - 1 0 -A 3ubsidiorV of A.C. Nielsen Co. INCORPORATED SIS Code: Vol. I - 2.8.6 DYNAMIC AND STATIC MOS RAM AND EPROM SHIPMENTS SUMMARY • In the fourth quarter of 1979, worldwide shipments of 16K dynamic MOS RAMs increased to an estimated 26 million units, up about 38 percent over an estimated 18.9 million units slTiK>ed in the third quarter of 1979. The total for the year 1979 was an estimated 69.7 million units, up about 236 percent over the 20.8 million units shipped in 1978. Demand for these devices still exceeds available supply with prices currently in the $5.25 to $5.75 range for plastic packages. CERDIP packages command a $0.25 to $0.50 price premium over plastic. The availability of 64K dynamic MOS RAMs is still quite limited; in the fourth quarter, five suppliers shipped an estimated 9,500 units. Total shipments for the year 1979 were an estimated 16,300 units. Prices for these small quantity shipments are in the range of $100 to $150. Worldwide shipments of 4K dynamic MOS RAMs declined sharply to an estimated 14.4 million units, down about 19 percent from an estimated 17.8 million units in the third quarter of 1979. Total shipments for the year 1979 were an estimated 69.3 million units, just slightly less than the 69.7 million 16K dynamic MOS RAMs shipped in 1979. Prices remained firm in the $2.00 range with some quotes as high as $2.50. Fourth quarter shipments of slow 4K NMOS static RAMs reached an estimated 11.0 million units up about 5 percent over estimated third quarter 1979 shipments. Shipments of fast 4K NMOS static RAMs were an estimated 1.4 million units, up from an estimated 968,000 units in the third quarter, but just slightly above second quarter Shipments of 1.3 million units. Shipments of 4K CMOS static RAMs increased to an estimated 2.0 million units in the fourth quarter of 1979, up about 15 percent from an estimated 1.7 miUion units shipped in the tliird quarter of 1979. Availability of slow and fast NMOS as well as CMOS static 4K RAMs has improved since our last DATAQUEST Research Newsletter dated 16 November 1979. Lead times for most of these products are under eight weeks. Fourth quarter shipments of 8K EPROMs declined to an estimated 5.0 million units, down about 5 percent from an estimated 5.3 miUion units in the tliird quarter. Prices are in the $5.25 to $5.50 range with lead times imder 4 weeks. Worldwide Shipments of 16K EPROMS were up sharply to an estimated 4.9 million units, which is up about 46 percent over an estimated 3.3 million units shipped in the third quarter of 1979. Prices for the 2716 devices have softened as more supply has become available. Prices currently range from $16.00 to $20.00 for plastic parts. These devices are now available on most distributor shelves. Fourth quarter shipments of 32K EPROMs from five different suppliers were estimated to be 190,000 units. Copyright © 22 February 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and anaIysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients This information is not furnished in connection with a sale or offer to sell securities or in connection with ttie solicitation of an offer to buy securities. This firm and its parent andfor their officers, stockholders, or members of their families may, from time to lime, have a long or short position in the securities mentionRd and may sell or buy such securities. 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO DYNAMIC MOS RAMS 16K RAMs DATAQUEST estimates of worldwide 16K dynamic MOS RAM shipments are presented in Table 1. We estimate that the merchant market suppliers of this device shipped an estimated 26.0 million units in the fourth quarter of 1979. This is up about 38 percent over an estimated 18.7 million units in the third quarter of 1979 and up a dramatic 223 percent over an estimated 8.0 million units shipped in the fourth quarter of 1978. These estimates also include 16K chips which were shipped in two-chip hybrid packages as 32K dynamic RAMs to IBM and other users. Two types of hybrid packages currently exist. One is the so-called piggy-back versicxi with one dual-in-line package riding on top of another. The other is the so-called camel-back version with two smaU chip carriers, each containing a 16K chip on top of an 18-pin ceramic side-brazed package. Currently, demand for 16K dynamic RAMs is extremely strong. DATAQUEST has conducted an informal survey of 16K RAM demand for 1980 and has found the demand to be approximately 205 million units, whereas currently projected supply is about 175 million units. This disparity explains why most suppliers of 16K RAMs are essentially fuUy committed for 1980. Current prices of 16K RAMs are in the $5.25 to $5.75 range for plastic packages and $0.25 to $.50 higher for CERDIP packages. The recent dramatic increase in the price of gold has resulted in a gold adder for ceramic side-brazed packages of $1.00 to $2.00 on top of the $1.00 to $3.00 premium that this package already had over the plastic package. The European market for 16K RAMs has softened since the third quarter of 1979 as several Japanese suppliers have been very aggressively marketing large quantities of 16K RAMs at very competitive prices. Key customers in Europe are able to receive 50,000 devices in 4 to 6 weeks. In Europe, liigh volume pricing on plastic parts is in the $5.50 range, whereas the overall average selling price for plastic is closer to $6.00. The rapid growth of unit shipments of 16K dynamic RAMs is graphically illustrated in Figure 1. Also shown in that figure is the market share of the U.S., Japanese, and European companies. 32K RAMS Mostek remains the only supplier shipping 32K dynamic RAMs into the merchant market. The company shipped an estimated 100,000 units in the fourth quarter with prices in the $16.00 to $18.00 range. Intel, Motorola, and Texas Instruments are not actively marketing their 32K piggy-back hybrids into the market. Instead, they are shipping them directly to IBM. These shipments are included in the overall estimates for the companies in Table 1. 64K RAMS At year end 1979, there were five suppliers sampling 64K RAMs: Fujitsu, Hitachi, Mitsubishi, Motorola, and Texas Instruments. Estimated shipments of these suppliers are presented in Table 2. In the fourth quarter, they shipped an estimated - 2 # % 9,500 units, up from 5,000 units in the third quarter. For the year 1979, an estimated 16,300 units were shipped. The current suppliers are finding the 64K RAM an extremely difficult device to manufacture; hence, the limited shipments and the absence of additional suppliers. 4KRAMS DATAQUEST estimates of 4K dynamic MOS RAMs shipments are presetted in Table 3. In the fourth quarter of 1979, worldwide shipments declined sharply to an estimated 14.4 miUiat units, down about 19 percent from an estimated 17.8 millicMi units shipped in the third quarter. This was the first dramatic decline in quarterly shipments after relatively small declines (less tJian 4 percent) in each of the previois four quarters. Most suppliers have de-emphasised this product because they are limited in wafer-start capacity aiKl are shifting tliat capacity to the 16K dynamic RAMs, 64K dynamic RAMs, and other memory products. Prices remain firm in the $2.00 range, with some as h i ^ as $2.50. Lead times have shortened somewhat to range between 12 and 16 weei C C O 3 o k. » a. •b » a. a. Ic OT c 3 .,2 o (0 c o H -4 -Flgure 1 ESTIMATED WORLDWIDE QUARTERLY SHIPMENTS OF 16K DYNAMIC MOS RAMS European Companies-U.S. Companies Q1 Q2 "T" Q3 "T" Q4 T " Q1 T " Q2 T 03 T Q4 Q1 02 03 T Q4 TV 1977 1978 1979 Source: DATAQUEST, Inc. Table 2 ESTIMATED WORLDWIDE SHIPMENTS OF 64K DYNAMIC MOS RAMS (TJiousands of Units) Total 1979 Company Fujitsu Hitachi Mitsubishi Motorola Texas Instruments 1st Qtr. S2 0 0 s s 2nd Qtr. 0.4 0 0 1.0 0.4 3rd Qtr. 1.0 S 0 3.0 1.0 4th Qtr. 2.5 S . S 6.0 1.0 Year 3.9 S S 10.0 2.4 1.8 5.0 9.5 16.3 Shipping devices using +7 and -2 Volt power supply. Other suppliers shipping 5-volt only devices I Indicates sampling Source: DATAQUEST, Inc. February 1980 Table 3 ESTIMATED WORLDWIDE SHIPMENTS OF 4K DYNAMIC MOS RAMS^ (Thousands of Units) 1978 1979 Company AMD Fairchlld Fujitsu Hitachi Intel Intersil ITT Mostek Motorola National NEC Signetics Texas Instruments Total Percent Change From Previous Quarter 4th Qtr. 2,200 0 300 450 2,300 100 800 4,200 1,900 1,700 1,350 300 3,800 19,400 (0.5%) Year 6,600 900 1,900 1,780 11,000 450 1,600 17,000 5,700 5,600 6,150 1,150 16,700 76,530 1st Qtr. 2,600 0 200 350 1,700 100 1,100 3,800 1,500 2,000 1,350 300 3,600 18,600 (4.1%) 2nd Qtr. 3,000 0 200 200 1,700 100 1,300 3,300 1,150 2,400 1,900 100 3,200 18,550 (0.3%) 3rd Qtr. 3,000 0 200 200 1,500 300 1,300 3,400 1,800 2,000 1,300 50 2,700 17,750 (4.3%) 4th Qtr. 1,600 0 150 100 1,200 500 1,500 3,600 2,000 1,500 1,000 10 1,200 14,360 (19.1%) Year 10,200 0 750 850 6,100 1,000 5,200 14,100 6,450 7,900 5,550 460 10,700 69,260 Includes merchant market and internal shipments Source: DATAQUEST, Inc. February 1980 - 7 -Table 4 ESTIMATED 1979 WORLDWIDE SHIPMENTS OF SLOW 4K NMOS STATIC RAMS (Thousands of Units) 1 00 • Company AMD AMI EMM Fairchild Fujitsu Hitachi Intel Intersil Matsushita MOS Technolt^ Mostek Motorola National NEC Synertelc Texas Instruirneiitii Toshiba Zilog Total Percent GbiEmge Ffom Pre vi Q M S Quartet Isti lKx4 150 50 600 50 80 450 400 200 0 5 0 270 530 400 560 500 150 0 4,395 Ej^rter 4Kxl 30 0 500 0 0 0 400 100 0 0 450 30 120 600 0 500 0 110 2,840 2nd Quarter lKx4 4Kxl 275 55 600 100 150 450 600 230 20 25 0 320 900 600 600 500 210 0 5,635 28.2% 75 0 600 0 0 0 600 130 0 0 600 20 190 450 0 500 0 110 3,275 15.3% 3rd 9uas lKx4 330 95 700 300 250 450 850 250 50 100 0 450 900 800 900 550 300 0 7,275 29.1% rter 4Kxl 140 0 650 0 0 0 100 150 0 0 900 30 200 400 0 450 0 150 3,170 (3.2%) 4th Quarter lKx4 4Kxl 420 50 700 400 100 450 800 200 75 175 0 300 1,100 1,000 1,000 350 350 0 7,470 2.7% 220 0 700 0 0 0 200 250 0 0 1,000 50 400 300 0 350 0 45 3 , 5 1 5 10.9% YeiEU' lKx4 1,175 250 2,600 850 580 1,800 2,650 880 145 305 0 1,340 3,430 2,800 3,060 1,900 1,010 0 24,775 4Kxl 465 0 2,450 0 0 0 1,300 630 0 0 2,950 130 910 1,750 0 1,800 0 415 12,800 Source: DATAQUEST, Inc. February 1980 Table 5 ESTIMATED 1979 WORLDWIDE SHIPMENTS OF FAST 4K NMOS STATIC RAMS (Thousands of Units) 1979 Company AMI Fujitsu Hitaahi Inter Intersil Mostek Motorola National NEC Texas Instruments Tosliiba Total Percent Cliange From Previous Quarter 1st Qtr. 5 0 0 800 0 0 S 0 25 0 0 830 2nd m^ S^ 0 1,200 0 0 10 10 70 0 0 1,300 56.6% 3rd Qtr, 5 15 S 650 3 0 20 •25 250 0 S 968 (25.5%) 4tli mi 5 60 S 900 20 S 50 65 250 5 15 1,370 41.5% Year 25 75 S 3,550 23 S 80 100 595 5 15 4,468 Indicates Sampling ^Includes an estimated 25,000 2148 (lKx4) devices in 3rd quarter and 60,000 2148 devices in 4th quarter Source: DATAQUEST, Inc. February 1980 - 9 -Table 6 ESTIMATED 1979 WORLDWIDE SHIPMENTS OF 4K CMOS STATIC RAMS (Thousands of Units) 1 I-" o 1 Harris -Hitachi Motorola National NEC RCA Toshiba 1st Quarter lKx4 4Kxl 25 0 0 0 100 50 175 Total Percent Change From Previous Quarter 15 50 0 0 0 0 25 350 2nd Quarter lKx4 4Kxl 40 0 0 0 270 80 450 90 140% 30 175 0 0 0 0 50 840 183% 3rd Quarter lKx4 4Kxl 100 °2 S " ^ S 450 125 500 255 40% 100 325 0 S 0 0 100 1,175 106% 4th Quarter lKx4 4Kxl 125 0 S 5 500 100 500 525 5% 125 500 0 5 0 0 100 1,230 39% Y lKx4 290 0 s 5 1,320 355 1,625 730 ear 4Kxl 270 1,050 0 5 0 0 275 3,595 Includes 25,000 6147 Fast CMOS Static RAMs in 2nd quarter, 100,000 in 3rd quarter, and 225,000 in 4th quarter ItKlicates sampling Source; DATAQUEST, Inc. February 1980 Table 7 ESTIMATED WORLDWIDE SHIPMENTS OF 8K EPROMS (Thousands of Units) 1 1978 1979 Company AMD Electronic Arrays Faircliild Fujitsu Intel Motorola National Signetics Texas Instruments Toshiba Total Percent Change From Previous Quarter 4th Qtr. 340 60 120 70 1,000 400 500 50 800 30 3,370 56.0% Year 485 200 280 280 3,400 1,020 1,250 280 2,100 40 9,335 1st Qtr. 600 75 160 70 1,100 700 600 0 800 50 4,155 23.3% 2nd Str, 700 100 200 50 1,400 750 800 0 800 100 4,900 17.9% 3rd 9tr. 700 125 350 50 1,400 1,000 800 0 800 100 5,325 8.7% 4th Qtr. 500 35 600 50 1,100 1,000 900 0 800 50 5,035 (5.4%) Year 2,500 335 1,310 220 5,000 3,450 3,100 0 3,200 300 19,415 Includes merchant market and internal shipments Source: DATAQUEST, Inc. February 1980 - 1 1 -Table 8 ESTIMATED WORLDWIDE SHIPMENTS OF 16K EPROMS^ (Thousands of Units) 1978 1979 Total Percent Change From Previous Quarter 94.6% 57.5% 71.9% 36.1% 46.3% Includes merchant market and internal shipments 2 Indicates sampling 3 Includes some parts having a 5-volt only power supply: 3rd quarter 1979: 10 percent 4th quarter 1979: 33 percent 4 Includes some parts having a 5-volt only power supply: 1st quarter 1979: 40 percent 2nd quarter 1979: 50 percent 3rd quarter 1979: 60 percent 4th quarter 1979: 60 percent Table 9 Company AMD Fairchild Fujitsu Hitachi Intel MosteJ< 2 Motorola National Synertek , TexEis Instruments Toshiba 4th Qtr. 0 0 5 30 450 25 90 S 0 300 5 Year 0 0 5 35 1,350 25 100 S 0 850 5 1st Qtr. ^2 70 125 550 90 160 5 0 400 25 2nd Qtr. 0 S 200 200 750 150 150 50 0 900 50 3rd Qtr. 5 S 300 350 1,000 250 160 80 0 1,100 90 4th Qtr. 10 S 300 500 1,400 350 200 120 0 1,800 200 Year 15 S 870 1,175 3,700 840 670 255 S 4,200 365 905 2,370 1,425 2,450 3,335 4,880 12,090 Source: DATAQUEST, Inc. February 1980 ESTIMATED WORLDWIDE SHIPMENTS OF 32K EPROMS (Thousands of Units) 1979 Company Fujitsu Hitachi Intel Motorola Texas Instruments Total Indicates Sampling 1st Qtr. 0 0 5 0 10 2nd Qtr. 0 0 30 0 35 3rd Qtr. 0 S 50 0 60 4th Qtr. si S 100 s 90 Year S S 185 S 195 15 65 - 1 2 -110 190 380 Source: DATAQUEST, Inc. February 1980 ^^T RESEARCH -•^—ASubsidiaiyof A.C.Nielsen Co. ^ IMCORPORATED V \ I ^ S W ^ 3 ^ ^ M 1 1 ^ M H I SIS Code: Vol HI, Appendix E THE CURRENT RECESSION IHPUCATIONS AND PROSPECTS m On January 15, 1980, DATAQUEST was honored to present Dr. Ezra Solomon, Dean Witter Professor of Finance at the StanfOTd Gradiate School of Business, as a speaker at its Small Computer Industry Service Conference. Dr. Solomoth affecting the consumer. These changes have l<ept U.S. activity at a high plateau. "Die first was a change in the ground rules by which the housing marlcet gets its finance mortage power. In the past whenever interest rates rose s^nificantly above the fixed levels of 5 OT 5 1/2 percent that the thrift institutions could pay to bwrow money from individuals, people disintermediated. That is, some smart people withdrew their funds for 5 1/2 percent deposit and put it in the money maricet. This disintemedation would cause a drying up of mortgs^e money, and the housii^ marlcet would collapse. This process has happened in every single downturn since W c M l d War IL However, just as it was about to happen in June 1978 the rules changed. TTirift instituticMis could now compete in the open market for funds with treasury biU plus certificates and so on. This extended the housir^ boom deep into 1979 by at least a full year. I wiU explain in a moment why I don't think it can continue. The second major change was in the attitude and behavior of the American consumer. We have been surveying the consumer fairly carefully since about 1950 and r^ht up to '74 his response to these questions was always what I like to refer to as the Protestant ethic or Protestant rationality. Until 1974, whenever it was believed that inflation was going to accelerate a little—2 to 4 percent or 3 to 5 percent— the consumer thought it was a bad time to splurge. In other words, if inflation was going to get worse, the consumer also believed it was a bad time to buy cars, homes, and Other big ticket items. The logic was that staples were going to cost a lot more, so it was no time to splurge on things that could be deferred. Starting in 1974 a smaU fraction of the respondents began to adopt what I caU the Brazilian attitude towards inflation - if you think prices are going to rise, this a good time to buy before the rise gets worse. By 1979 we were aU behaving like this. So consumer borrowing broke all records. Consumers borrowed $50 billion net on just short-term consumer credit. In addition to this record borrowing there was another record amount of borrowing in the mortgage market, where people were refinancing their homes in order to splurge. As a result, what we call the net saving rate, the ratio of net savii^ of aU savers and b<»>rowers combined to total disposable income, has broken aU records on the low side. In the last quarts in 1979 it was running 3 percent per annum. We have heard in the past that American saving is low relative to other national saving. The Japanese save about 22 percent of their disposable income, the Germans about 10 - 15 percent, even the British 10 - 15 percent, and the Americans' 6 percent was regarded as low; now it is running 3 percent. Why this behavior? Because inflation is not neutral with respect to the relationship between the rewards of saving and the pains of borrowing. It could be neutral in a world with no taxes, but progressive income taxes make all the difference. - 2 -We thinl< interest rates are high, when in fact they reaUy are the lowest they have ever beai in history. In terms of aftertax, and after-inflation interest rate, they have been running negative all through 1979. It is beginning to look positive now. We are aU in very high tax brackets partly because of inflation, partly because of affluence, and partly because of double incomes. Nevertheless, for someone in the 40 - 50 percent marginal tax braclcet, borrowing at 12 percent only costs 6 to 7 percent. On the Other hand, saving and earning 12 percent doesn't give them 12 at aU, it giv^ them 6 or 7 percent after inflation, that is, about minus 6 or 7 percent, because inflation has been rumiing 13 percent. In short as a society we have developed a set of ideas, regulations, and tax^ which fit the WOTW of the 1930s, not the world of the 1970s and 1980s. By that I mean in the 1930s for the first time eccmomists developed the idea that saving may not be a virtue. Pri(M to that it was obvious to the old orthodoxy that saving was a virtue and borrowing a bit of a vice, and a big vice for the federal govemmoit, meaning government deficits were bad things. However, in a world of unemployment and deflation the ecwiomist Keynes suggested that the ojM>osite might be true. The saver is not doins anybody a favor, he js merely <iisewplpyb^ his nei^bor; borrowing mig^t be a virtue, and it is oicay for the govemmtait in sueh times to itself be a borrower arid rtm a deficit. These ideas, which were the oM heresies, became the new or^odoxies of the 1960s, and we have so diai^ed our tax system that you might say that we are literaEy punishing the saver every time he saves and rewardii^ the borrower every time he bwrows and a rational people is responding to an irrational government. Simple as that! THE CURRENT SCENARK) While these two changes in the mcH'tgage markets and the consumer markets maintained the strei^th of total demand deep into 1979, even the fundamentals were b^inning to weaken. We never have an economy movii^ smoothly upwards without interruption—^imbalances develop. One imbalance that has developed is that the rate of inflation itself is chewing into real incomes so that real per-employee income has not been rising after taxes for the last 12 months. It is lower now than it was then. Gradually this must affect the consumer. Secondly, the attempt to aUow the thrift institutions to compete in the money market ran into other irrationalities like usury ceilings on the rate at which they could lend. In about 20 states they can't lend at more than a certain 10 or 9 percent, or whatever it is. They have been changing the usury ceilings, Ixit they still exist, so that this competition became increasingly joyless. The mutual savings banks, in the east particularly, began to see their profit margins squeezed as they were b^inning to pay 12 and 13 percent to borrow money and lending at 10. You and I know they can't make it up in the volume. Very quickly in the last few months we have seen high interest rates begin to grab so that housing Starts have fallen off sharply and the expectation is that housing will go into a recession in 1980 without a doubt. It wiU not be as severe as the 1973-75 housing recession. POT one thing the excess of building in 1972-73 was enormous compared to this period. Conventional houses were being built then at the rate of 2.4 million per year, and this time around at the peak it was 2.1 million. Mobile homes then were being sold at the rate of 600,000 a year, and this time around it was 300,000 a year. The same excesses did not build up this time. Nonetheless we wiU see a dip from 2.1 million housing starts in 1978, starting in 1979 we'll be down to 1.75, and I am expecting in 1980 to be down to about 1.4 million. At the worst quarter, it could be as low as 1.2 million. Last time housing starts feU below one million for several months. Housing is now a big sector of the economy. Secondly, the sharp rise in the price of - 3 -ltomes, especially in California, will continue, but it is not going to be as slmrp and dramatic as it has been in the last two or three years. Twenty or 21 percent per annum steadily adds a lot to the equity people own in homes and therefwe to their willingness and their ability to borrow. This steady increase is no loiter guaranteed, and therefore I don't see that same source of bullishness for the average house owner. The intermediaries, the banks and finance companies that lend to consumers, are finding that these consumer credit loans are no longer as lucrative as they used to be. The standard rate (xi consumer loans runs about 18 percent per annum; when the cost of money is 8 or 9 percent, 18 percent looks good even though there might to be a 5 or 6 percent default of some kind. With the prime rate at 15 percent, and the effective cost of money at around 15 percent, 18 percent no longer looks so good. So the willingness of the intermediary who puts money at the consumer's disposal has diminshed greatly. "Rie automobile market, which is the primary debt finance consumer item, has begun to decline. Car sales last year totaled 10.6 million; the most optimistic forecast, made early in the year by GM, predicted 11.6 million. We are off quite a bit. This year the figure is going to be about 9.6 million, including imports. This is a sharp fall in cars; production has been cut severely by all domestic manufacturers. So we are likely to see pains in that market. Cars and houses are the very typical items that cause a recession. I think other items are going to hold up rather weU, so there is not going to be a sharp recession of the kind we had in 1973-75. In that recession from peak to the trough, real gross national product fell about 6 percent. This time around the decline should be about only 3 percent from the peak, which was probably the third quarter of 1979 in terms of gross national product, to the trough, which will be about next summer. It wiU probably be about as severe as the 1957-58 recession, a middlesized one. Unemploy-ment will unquestionably rise; by the end of this year around election time, the unemployment rate wiU probably be pushing 8 percent. However I don't think it is goii^ to create the same kind of excitement it created in the '50s and '6Gs, because the Other problem in society wiU remain, and that is the more important one in my opinion—^inflation. Inflation from December to December both on the producer price index, previously the old wholesale price index, and the consumer price index, has been running about 12.6 percent over a 12 - month span. It has been considerably higher over a shorter span—about 13.5 in the consumer price index. This rate of inflation is worse than we suffered in 1974 in terms of consumer price index but not as bad in terms of the wholesale price index, which in 1974 jumped 20 percent in this country and much more elsewhere. Will that come down? How will govemmait react to this joint problem of recessirai with inflation? Nevertheless, more important than the recession itself, is the recovery from the recession on the other side. In a nutshell I expect it is going to be a slow recovery. We will remain in fairly recessed conditions without the major bounce-back that we typically get, partly spcmsored by government action in the interests of getting inflation rates down Mid, hence, getting interest rates down a little. This is a dangerous guess to make in an election year. Just as soon as things begin to look bad there will be a drumbeat for some stimulus from government and business as usuaL But I think the world has changed, and what 1 want to surest is that somewhere in 1973 the post war period ended. The only people who didn't realize it were those in Washington. By the end of a period I mean that you go through a sort of sluggish watershed for a while until a whole new set of ideas and objectives begin to become national policy. World War n - 4 -was a major watershed that ended the pre-WWn policies, and attitudes; we got a much more pro-growth, big government, let's-step-on-the-accelerator attitude wliich worlced beautifully in the 50s, worked beautifully in the 60s, and gave us tlie best growtli we liave ever had in our history. However, we overdid it and we got into trouble, so that about 1973 three things converged which ended the period. One was the onset of very liigh rates of peace time inflation. The second was the quantum jump in the price of oil—a fourfold jump then and a subsequent doubling, and oil is a major input in an industrial society. The third item was the collapse of the system of fixed exchai^e rates and the move to a so-called free floating rate, which the Swiss accuse us of using as a euphemism for fr^ sinkir^ rates. The dollar has been taking a bad beating. PRODUCTIVITY Why do these ttffee factors make such a difference? Most powerfully because they interact. But let's sort it out, and let me be an economist for a minute and ss^y s!t:0ly O R d demipd—yw have to say supply and demand once a month to retain your union card as an economist. I^ook at the supp^ side. Very simple, and straight-fcffward. The Industrial Revoluticm, and especially the postwar manifestation of the loKluslPial Revoiution, with its enOTmous increase in productivity per ©mflJayee has been Aie essiaitiiJly to ttoe saibstitottcm of M far sweat. We mms dl^wstwoittisllfg © n mm laclOT of prodW5ticffl-Njli, embodied ia the form of matatoes l!m^m$& % wm '-mmm and iflamtiful and gettii^ chea,per in real terms. We were ttierefare ctaiservlrij ifflfe ^tmmm fact of productioi^ humm swmt, and g e t t ^ twDPseives laffe ihwpeswss m productivity for a unit of sweat; that is the way 11ke to look i^ it. ^»ffit % iWwst f^ Industrial Revoluticai is all about, but mm afl of a swMem ©a is no lmig& ftoft»«ft, ®r cheap, and it is certainly not goii^ to get cheaper. It is getting more and more es^ensivehy the year and getting scarcer by the year. We cant do very much, and for the last three or four years U.S. productivity has not really been rising at all, it has been static. The consequences of this are a little frightening, because the only source of a rise in average standards of life mtist be average product per person; there is no Other s<Hirce for a rising standard of life in the material sense. So fi^m the supply side, the world has a difficult problem. As a result, growth has slowed significantly all over the world, especially industrial growth since 1973. From 1948 to 1973 Japan was the growth leader. Their irniustrial production grew at 13 1/2 percent per annum compound. These are fantastic growth rates that lias made Japan a giant economy. However, since 1973, Japanese industrial production has been growing at 1 percent per annum. That is quite a drop. The e^ht largest economies outside of Japan—^I am not talking of the U.S. now but of Europe—grew in the post war period at 5.7 percent per annum compound. This figure is far higher than their history of growth rates. Since 1973 it has been less than 1 percent per annum on industrial production, hi the U.S. we also had a slowdown, but much le^ than elsewhere. We had been growing at about 4 1/2 percent per annum. Which is a fuU 50 percent higher than our historic growth rate, and since 1973 we have slowed down to just under 3 percent per armum. In terms of industrial production we were among the slowest growers in the postwar period; since 1973 we have been the fastest growir^ nation in terms of industrial production. This leads me to the demand side of the equation. THE DOLLAR How did we achieve this production growth? We achieved it because we disregarded the new reality. We bravely barged ahead with expansive policies when - 5 -the rest of the world was cow-towii^ to these realities and pursuing much less expansive policies. The reason that this trilogy of economic iUs caused the slowdown or change in policy attitudes is simple. For most countries in a free-floating world with high inflation rates and a very high cost of oil, allowing their currencies to slip or fall is a very dangerous thing. The minute the currency slips on the foreign excliange market, the price of oil goes up because it is priced in doUars. Then begins a downward slope because there is an interaction there—^the exchange rate slips, the price of oil goes up, inflation gets worse at home, the exchange rate slips further, the price of oil goes up further—^it's a ratchet. NOTmally expansive countries like Brazil and the UK had to adopt relatively go-slow policy. They and other countries did so in 1977. The Germans did it automatically—^they were so scared of inflation that they adopted a relatively go-slow policy. So all of us together bounced out of the '75 recession; by the end of 76 the recovery b^an to peter out. When the recovery petered out elsewhere they let it; they were content with zero growth in 77, in some cases mini-recessions in '77 and '78, but not the U.S. We decided we were different; we had a new administration, the Carter administration, and we stepped on the gas. So 1977 and 1978 were a super years fw the U.S., at least for the U.S. economy and for U.S. employees, but it was a terrible year for the U.S. financial markets and the U.S. dollar. The dollar began to slip. We were immune from the usual restraints, discipline as it is called, normally imposed on a normal country because in a sense we were not a normal country in 1977; we now are. The reason we were not normal is that oil is denominated in our currency, S O when the U.S. dollar falls against the Swiss Franc it makes no difference in the price of oil. We pay no price for this-^we think. The second difference, and probably more important, is that another country that suffers a large deficit in its balances with the world has to go to the credit market to borrow money. You have to go hat in hand, the bankers tell you to behave, and you darn well better behave. Behave means slow down, cut out your fiscal stimulus. Stop expanding your money supplies, etc. Well the U.S. is again different from the rest of the world. We don't have to go and get credit when we run a deficit; it's automatic, we write ( H i the cuff. We are the only naticm that could be running a trade deficit of $45 billion a year, a tremendous sum, in early '78 and lai^h about it. The Secretary of the Treasury said, well, next year is going to be even worse. It is a policy of benign neglect. Fundamentally we come to yet another difference which existed, and no longer exists: the W O T l d financial community could not discipline the U.S. Not for political or military reasons, although that matters, but simply f O T economic reasons. The ultimate sanction against a country like the UK, Brazil, Japan, or Peru, which refuses to cow-tow to international banks is that they get no mwe credit and no mwe imports. Without imports they die, because they are either dependent on food or dependent on parts; they are not self-sufficient economies. The U.S. except toe oil, is essentially self-sufficient. As badly as we have behaved, can you imagine the Japanese saying to US, behave yourselves, you Americans, or no more Toyotas. Three day holiday and rejoicing in Detroit! Fun(ta.mentally we were different and we behaved differently. In other words, we said we are the locomotive we are going to charge ahead, we are going to lead the world back into full employment and fast growth and never mind anyone else. WeU we couldn't do it for long, because we suddenly woke up and realized that the falling dollar does have consequences for us. The price of other imports if not of oil goes up very rapidly. TTiere is a threat that oil might get repriced in some other currency and it is a very real threat. There is one group of nations that can say to us now, you pay in real money or else no imports, and that would hurt. - 6 -# So these changes began to dawn in Washington and we liad two major actions over the last four quarters or so. First was HaEoween day 1978, when we abandoned the policy of benign neglect. We said mia culpa, we too are going to behave like a sensible nation, and we are going to worry about the exchai^e value of tlie doUar. This m^nt raising interest rates, being competitive, etc. It didn't work too well. It worked f O T a while-—tlie dollar gained significantly, especially against the Yen, but it didn't work for long. The money supply again got out of hand. On October 6, when we had the so-called Saturday night special, Mr. Volper, then the new chairman of the Fed said "I am really going to tighten money, Fm not goir^ to fiddle around." The essential difference between the way policy had been conducted prior to October 6th and since then is that prioc to October 6th the govemmait always worried more atjout what was happaiing to the interest rate and how to control the rate at which that would rise. When there was tightening, it wasn't sufficient for the pressures that existed. The reason we are trying to ccMitrol the interest rate again is a populist reason, high interest rates are "bad". We have always believed so in this country. Presidents have always hated high interest rates and a populist Southern president really hated them very badly. That is why he tlirew Arthur Bums out, because Bums was worried about inflation and tried to tighten money early in the game, and that is why every time Bums' successor did anything to tighten money there was an adverse reaction from the White House. Since October 6th however, that has changed and it is with the support of the President completely. Will it work? Yes, I think it will. Tight money is one reason some of the exuberance on the demand side is disappearing. I think it is one reason Congress is at least talking about doing somethii^ to reduce the amount of fiscal Stimulus, which is very strong. We have been running deficits every year in boom period which was never what deficit financing was meant to do. For a recession, yes, but for a boom, no. It just inflames the situation. I think inflation has been given the highest priority amoi^ our various objectives. The questicMi is, how long will this last? Last time around we brought inflation down from 13 percent. In the last 12 montlis of the Ford administration it was down to 4.8 percent, and then it rose again. I don't think Mr. Carter will make the same mistake. It is politically unpolular today to say," I am going to inflate". Everybody is against it. BEYOND 1980 Do we have the staying power? If we do, the picture I see beyond 1980 is for much Slower total economic growth, down to below 3 percent per annum on the long range track as compared to 4 1/2 percent. The same is true for Europe and for Japan. The whole western world is going to have to grow more slowly. & i the process it will adapt to the energy shortage by curbing the growth of demand for energy and making some sort of transition to non-energy intensive forms of production. If we do that, the rate of inflation should come down gradually. I think it will be down to 9 or 10 percent by December from 13 percent and it can continue in 1981. I expect it wiU come down dramatically, because it is the year after the recession that you get the great results. If we get it down to the 4 to 5 percent range by the middle 80s, the problem is over in some sense. If we are impatient and we listen to the voices that say go foe the accelerator, I think this country is going to be in deep trouble. The only way you can go ioc the accelerator and preserve a modicum of sensible economic results is to slap on the whole paraphernalia of controls. The only person I can tell who might lead us in that direction is Mr. Kennedy. He would have the inclination and guts to try that; it is terribly wrong, but you don't have to be smart to be gutsy. More than wage and price control, we would have to have foreign exchange controls, credit controls, and many - 7 -others. I hope we don't go down the road of trying to reconcile very fast growth in a non-inflationary world. It can't be done. I hope we taJ<e the more judicious path of slowing down. I tliinlc the majority opinion is to foUow the latter path. THE ROLE OF INFORMATION TECHNOLOGY I have sounded fairly pessimistic but let me end with an optimistic note, which lias very much to do with your industry. Energy remains the pressing problem of the 80s. We are still heavily dependent on imported oil, more than ever before. The ratio of imported oil to total energy is the highest it has ever been in spite of the big jump in price. Everybody thinks that the solution of how to get rid of this dependence on foreign oil is to find a literal substitute such as coal and uranium. They are the two obvious ones, and theref(»e the ones we have tiumed our baclcs on in this society-—and looking to crazy things like solar, which may do something by 1995 but cant do very much now. Conservation, yes, but that means slow growth. I think some of this solution will come with Hnding a literal substitute for oil. It is more likely to come more from a shift in aggregate demand by the American people toward new products that don't require energy, and there is a new process and a new product right in our midst which is big enoi^h, in my opinion—^the microprocessor. It is big enough, plentiful enough, and versatile enough to be thoi^ht of as a factor of production. Let me restate what I was saying here. We have sweat, we have oil, and a third factor which used to be something called brains. However, brains were even scarcer and more expensive than oil so we had to conserve on them too. Now there is this extension of the brain which is very cheap and getting cheaper and very plentiful and gettii^ more plentiful and getting small. It can do a whole lot of things. If we can grow to love the products of this new electronic revolution as much as we grew to love the products of the industrial revolution, the future is very bright. We have this factor of production, we have this ability to generate goods and services, communications and applications we don't dream of yet. I say we wiU grow to love these things like we grew to love the car and the machine. The transitioi in the '80s is goii^ to be in this directiai. This is a major way of curing the energy shortage problem, in addition to doing all the things the government says it is going to do. But on this energy questi(Mi, nothing the govemmoit has done so far gives me any heart. They have made all the possible mistakes they could make and they continue to make them, and the only thing that gives me any comfort at all is what Winston Churchill once said about the United States: "You can count on the U.S. to do the right thing after it has tried every wrong thii^ possible." # - 8 -^ ^ ^ H ^ ^ k ^ ^ ^ ^ " ^ ^ ^ ^ ^ ^ ^ r ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ 1 J f l l #mt 11 i ^ ^ i MLJI-ITI-LJI.iU ^ ; ^ SECURlTiES, INC. Vol. n - No. 2 February 1, 1980 This letter is a condensation of recent newsletters and internal thinking from the industry research groups at DATAQUEST, Inc. Requests for amplification of our thoughts or for specific newletters should be directed to the author. A list of recent DATAQUEST Research Newletters appears at the end of this letter. CAPITAL EQUIPIVIENT In our most recent Portfolio Letter, we outlined a fairly optimistic scenario for farm equipment purchsises over the next yesir. However, a major assumption in our forecast was that the United States would export large amounts of grains; the recent embargo by President Carter has obviously changed this situation. Our concerns relate less to 1980 than they do to the 2-3 year impact of the embargo. During 1980, we believe that the Federal Government will be able to sustain reasonably high levels of grain prices through support programs. Longer term, however, we doubt whether these programs can have the same positive impact. If other grain growing nations are able to boost output enough to attract the Soviets as customers and maintain total worldwide demand for grains, then the longer term impact on farm prices and therefore machinery sales may not be significant. However, if due to lack of grain the Soviets have to slaughter their livestock herds, then we could be looking at a longer term reduction in Soviet grain needs. Were this to occur, we believe it would result in a secular decline in the demand for farm machinery. DATAQUEST estimates that every 1 percent of change in farm cash receipts precipitates a 1-1/2 percent change in farm machinery sales. That effect should be magnified somewhat in 1980 because of emotion surrounding the embargo issue. If the embargo continues, DATAQUEST foresees the possibility that retail tractor sales could decline 2 percent in 1980 and drop another 8-11 percent in 1981 to a level of about 125,000 units. Because grain farmers tend to buy larger tractors, the impact on revenues would be magnified somewhat. We have been forecasting $5.50 a share in earnings for Deere in fiscal 1980, and we are not changing our forecast. The company should benefit from low dealer inventories and the continuation of the stril<e at Harvester. However, given a decline in retail sales in 1981 as well as in 1980, it would appear very possible to us that Deere could have lower earnings in fiscal 1981. Once the strike at International Harvester ends, the company should be able to ramp shipments up fairly rapidly to restock dealer inventories. Longer term, however, a weak market for farm machinery would be even more a problem at IH than at Deere, since IH needs a strong farm market in order to accomplish its corporate goals of permanently higher levels of profitability. Copyright © 1 February 1980 by DATAQUEST- Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible individuals in the subject companies, but is not guaranteed as to accuracy or completeness. It does not contain material provided to us in confidence by our clients, This information is not furnished in connection with a sale or offer to sell securities or in connection with the solicitation of an offer to buy securities. This firm and its parent and/or their officers, stockholders, or members of their families may. from time to time, have a long or short position in the securities mentioned and may sell or buy such securities. Member, New York Stock Exchange 19D55 Pruneridge Avenue / Cupertino, California 95014 / (408)725-1200 r INSTRUMENTS Instrument demand in general remains very strong. The forecasts that we have made for the Test and Measurement (T&M) and Automated Test Equipment (ATE) markets assumed a moderate recession in 1980 and softening in demand. In the T&M area (which includes ATE) we have been forecasting 13 percent industry growth. Although orders have definitely slowed from last year's rates, we would estimate present order growth to still be close to 20 percent. In ATE, orders are now running over 30 percent ahead of 1979 orders, far higher than our 16 percent growth forecast for the full year. We are not changing our estimates at present, but we want to point out that backlogs are high, and unless order growth decelerates by the end of the first quarter, our growth forecasts will have to be raised. We commented last year that very strong product development efforts at Hewlett-Packard should allow the company to gain T&M market share in 1980 and probably 1981. Apparently that is exactly what is taking place. It appears that instrument order growth at H-P is presently running over 20 percent, and we believe that the company will exceed the industry order growth rate in 1980 by 5-6 percentage points. Our overall 1980 forecast for Hewlett-Packard is for order growth of 27 percent, sales growth of 31 percent, and earnings of $4.60 per share versus $3.43 per share in 1979. If these seem like abnormally high numbers in a "recession" year, we should point out that it is likely that first quarter orders at Hewlett-Packard will exceed $800 million and our 27 percent order growth forecast for the full year implies no sequential growth from the first quarter level. Even more importantly, our forecast implies a further expansion of backlogs at Hewlett-Packard this year, which would allow the company to enter fiscal 1981 with a very high backlog position, increasing the likelihood that fiscal 1981 would be another year where sales and earnings gains exceed 20 percent at the company. One further point regarding all of the instrument companies should be made. Almost all of the companies have complained about high component costs and the negative impact these costs are having on profit margins. If and when instrument demand does slow down somewhat, it is likely that demand for other high technology products may moderate as well. To the extent that this slowdown results in a lesser rate of demand growth for semiconductors and some errosion in semiconductor pricing, this situation could have a very beneficial effect on the profit margins of users, particularly since almost all companies have begun raising prices in anticipation of continued tightness in semiconductor pricing. The same argument could also be made for the computer industry. SEMICONDUCTORS If any of you were surprised when Intel indicated that a certain amount of price cutting was going on in Europe, you shouldn't have been. We indicated back in October of last year (Vol. I, No. 6) that selected price cutting was taking place in the European market by the Japanese in an attempt to gain market share. For the most part, the Japanese are focusing on 16K dynamic RAMs, but price cutting tends to spread from one device to others. For example, it is possible for a large European user to get 50,000 or more 16K RAMs in 4-6 weeks from various Japanese suppliers. The equivalent delivery time in the United States would be well in excess of six months. # - 2 Do not make the mistake, however, of thinking that the European situation is that bad or that it is a harbinger of what will happen in the United States. For one thing, basic demand in Europe is not as strong right now as it is domestically. More importantly, the Japanese are buying their way into the European market where they do not have a significant market share. By and large, the Japanese have, in our opinion, about as high a market share in key product areas in the United States as they are likely to get without major changes in buying habits by large U.S. customers. We do believe that sometime in the first quarter of calendar 1980, supply and demand will come somewhat into balance and that it will stay that way throughout most of 1980. This should allow prices to drop at a moderate rate during the yeeu. However, basic demand appears just too strong to support any significant price degradation. We still are maintaining our 13-14 percent growth forecast for domestic consumption in 1980 and, if anything, we are getting more optimistic about the outlook for this year. Longer term, we are more and more convinced that a basic shortage in semiconductor parts will once again emerge in 1981 and beyond. This has important implications for 1980 as well as beyond. Let us assure you that large buyers of semiconductors are very concerned about availability of parts over the next 3-5 years. As such, they are less likely to be aggressive in pricing when any softness does develop during the course of 1980, since they are interested in maintaining good relations with the large suppliers. In this regard, it is noteworthy that Hewlett-Packard, which has sited components costs as one of the major depressants of profit margins, has already raised prices in fiscal 1980 by twice as much as they had in all of fiscal 1979. One final point needs emphasizing. Despite the very high profits of the industry, the companies are operating inefficiently. There are large numbers of new employees who have not yet been effectively worked into the system, and many plants are producing far more wafers than they were designed for. One could reasonably make the case that a period of moderation between supply and demand would be a very valuable long term development for the semiconductor industry, as it would allow the companies an opportimity to get yields up and costs down. We see no compelling reasons to anticipate any meaningful contraction in semiconductor profit margins during 1980. PAPER & FOREST PRODUCTS Now that the recession is upon us (?) and paper profits are about to fall off of a cliff, we want to prepare you for a shorter than expected drop, particularly for brown paper. Everyone knows tliat brown paper prices get cut dramatically in the latter Stages of a recession and that profit margins fall accordingly—except things should be different this time around: • Operating rates will probably fall in 1980, but limited capacity additions should keep utilization rates around 94 percent in both 1980 and 1981, which would be far from catastrophic. • Prices are much higher than they were a year ago and we think they are stiU going higher, not lower, near term—expect an 11 percent increase in linerboard prices in February. Even with prices coming down in the second half of 1980, operating margins should be about flat for the full year (higher first half, lower second) and flat again in 1981 (lower first half, higher second). Beginning in late 1981, the brown paper sector - 3 -could move towards two or more years of basieedly sold out conditions and much higher margins. • Underlying our positive attitude is one basic fact—the brown paper sector is consolidating. Four smedler aggressive companies—Hoerner Waldorf, Inland Container, Hudson Pulp & Paper, and Bodcaw—have been bought by larger concerns within the last three years. Generally, prices would be expected to start dropping rapidly in the second half of 1980. If we are right and they do not drop, there may be more converts to our present minority view—namely tliat there are long-term opportunities in the brown sector of the paper business. SMALL COMPUTERS The feedback from our Small Computer Conference held in January is that growth rates in almost all sectors of the market should moderate only slightly in 1980. We do not expect the industry to be significantly affected by a recession, which is good news not only for the small computer suppliers, but also for their suppliers (i.e., the semiconductor companies). Listed below in Table 1 are our growth forecasts for the various segments of this market over the next two years. Some of our estimates are in revenues and others are in if-sold value. We believe that overall small computer revenue growth was about 26 percent in 1979 and expect 23 percent and 25 percent growth in 1980 and 1981, respectively. Table 1 ESTIMATED GROWTH OF SMALL COMPUTER INDUSTRY BY SEGMENT General Purpose Minicomputers Very Small Business Computers Small Business Computers Larger Business Systems Processor Based Terminals Personal Computers 1978/79 30% 114% 17% 41% 22% 60% 1979/80 25% 67% 21% 60% 23% 47% 1980/81 27% 43% 19% 22% 23% 36% Source: DATAQUEST, Inc. General purpose minicomputers (major suppliers: Digital Equipment and Data General) should enjoy somewhat lesser growth in 1980, pifincipsilly because of reduced demand from hardware OEMs. However, as noted in our numbers, the downturn should not be significant and should be bolstered by continued high growth in service revenues. Some acceleration in growth is anticipated in 1981. The rate of growth in this sector may be slowing longer term, but it should remain at very high levels for the next several years. - 4 -DATAQUEST defines very smedl business computers (major products: IBM 5110, Datapoint 1500, and Wang PCS II) to be commercial computers selling in the $5,000-$l5,000 price range. This is a small market, totalling only $300 million in 1979, but we expect this to be one of the major growth segments of the small computer market, reaching $1.4 billion by 1984, a compound growth rate of 35 percent. We define larger business systems to be the products in the $80,000-$200,000 price range. They include the IBM System/38 and 4431, the Hewlett-Packard 3000 Series, the Wang VS Line (the most important part of its computer effort) and most of Prime Computer's products. Our growth forecast for 1980 and 1981 are skewed because of expected initial shipments of the 4331 by IBM in 1980. If one excludes IBM from our data, the other participants should experience growth in the 30-35 percent area in both 1980 and 1981. Small business computers (price range $15-80,000) have somewhat less potential, both near and-longer term, because a high percentage of the first-time users were penetrated in the early and mid-1970s. Major products here are the IBM System/32 and System/34 and the Burroughs B-80 and 90. Personal computers should enjoy rapid growth from a low base. In our view the major commercial opportunity here is in business oriented personal computers sold to larger companies to meet the individual needs of executives and managers. We expect to see increased emphasis on this market by most participants. WORD PROCESSING A meeting at our recent Small Computer Conference between our financial clients and the management of Lanier served to point out some of the opportunities and challenges facing the smaller independent word processing suppliers. Lanier has thus far concentrated exclusively on the stand alone sector of the market, as have CPT and NBI. Despite the probability of a recession, we believe that the stand alone market wiU grow very significantly in 1980, but that the growth rates will start to moderate somewhat after this year. In addition, the level of competition should increase. This wiU be a function of both improved product offerings from Xerox and IBM and competition from small business computer suppliers and other mainframe companies who offer word processing capabilities as part of their total package. As an example, the Datapoint 1800 terminal, used as a smaU business computer, can run the new Dataproducts word processing software. All of this means that the independents need to expand the scope of tlieir product offerings if they expect to maintain high growth rates. This expansion will likely encompass both some integration with data processing and expansion into the Shared resource sector of the market. Both CPT and Lanier have introduced their first clustered terminal systems. Among the most important criteria for evaluating the potential success of the independent suppliers in adapting to the changes in the market will be the strength and sophistication of their marketing organization, the ability to painlessly integrate whatever data processing capability is necessary, and tlie excellence of their software in a more competitive environment. In general, we believe that it is important to have a direct sales force that is capable of making the higher level and more sophisticated sell required for clustered terminals. - 5 -Regarding Lanier specificeilly, its new shared resource word processing system offers a lot more softwsire power tlian its stand alone units and larger storage capability. In particular, it has an equation software package option that, in our opinion, appears superior even to that of NBI. The biggest question we have about the product offering is the larger number of variations in product configuration and the difficulty that a salesperson accustomed to seUing stand alone word processors may have in making this type of sale. Lanier plans on having shared systems specialists who will assist the regular salesmen in making a sale and do some direct marketing themselves. We think that these people wiU be necessary if the product is to succeed. The target at present is for shared systems to contribute 15-20 percent of Lanier's total word processing business by the fourth quarter ol calendar 1980. We expect $2.25 per share in earnings at Lanier in the May 1980 fiscal year versus $1.88 in fiscal 1979. Michael Weisberg RECENT NEWSLETTERS OF NOTE Capital Equipment 1. Farm Tractor Sales Estimates Instrumentation 1/30/80 1. ATE Market for Semiconductor Testing 2. Digital Multimeter Product Review 3. Test Instrument Market Outlook 4. ATE Market Outlook 1/18/80 1/11/80 1/11/80 1/08/80 Computers 1. Board Level Microcomputers 1/22/80 Paper & Forest Products - 1. Norscan Market Pulp Inventories Down, Prices Up 2. The Outlook for Uneoated Free Sheet: 1980-82 1/25/80 1/07/80 Copy i S c Duplicating 1. IBM Announces Copier Price Increases 2. 1979 SICOB Exhibition Report 3. Oce Introduces the 1900 series 1/15/80 12/21/79 12/21/79 - 6 -^. -<r-=-^» RESEARCH , A SubaidJarv of A.C, Nielsen Co. ^ INCORPORATED 1Mb w s u b ^ 1 bH 1 SCIS Code: VoL I Newsletters BOARD-LEVEL MICROCOMPUTERS SDMBfARt PreUmiiMffy estimates indicate that U.S.-based suppliers of board-level micro-computer products had another year of dramatic growth in 1979. Shipmmts of 8-, 12-, and 16-bit bMird-level microcomputers totaled an estimated 186,000 units, with associated revenues estimated at $163 million. These figures represent growth rates of over 90 percent in units and approximately 57 percent in revenues for worldwide shipments by MS. manufacturers. DATAQUEST believes that growth in the coming five years wiU be less e3q)losive, however, although rates of nearly 40 percent in units £Uid over 25 percent in dollars are expected through 1984. By 1984 the market is expected to approach cMie million units annually, with revenues of more than $500 million. Surprisii^ly, the greatest market growth occurred irot in the newer 16-bit products but in the older 8-bit devices. TTiis rather explosive growth, which resulted in a doubling of unit sh^ments in 1979 over 1978, was the result of the proliferation of a new generation of very low cost products. Competition from a variety of new products costii^ $200 and less caused average seUir^ prices to decline by nearly <Hie quarter and catapulted several new competitors into significant positions in the S-rbit board-level market. Tlie 12- and 16-bit market also experienced substsuntial growth in 1979, although the exp^sted penetration of the semiconductor suppliers into a market traditionally domiiuited by minicomputer suppliers was not as extensive as had been forecast. 8-Bit Board-Level Microcomputers Table 1 summarizes estimated worldwide imit shipments and revenues of U.S.-based 8-bit board-level microcomputer manufacturers for 1978 and 1979. The unit figures in this table (and all tables in this newsletter) are for C^U boards only while the revenue figures include supplier revenues from all boards and support products shipped by CPU board manufacturers. In 1979, the 8-bit market grew by more than 100 percent in units and more than 60 percent in revenues. TTte large discrepancy in these two growth rates was due to a drop of approximately 22 percent in average selling prices. Average ,price declines were in turn due to the emergence of a new generation of low-cost products in the 8-bit market. The availability for the first time of board-level products at prices of $200 and less has permitted sales to new markets and customers fop which microcomputer products can now be justified based on price alone. The greatest inroads were made by products based on the STD bus and products based on the KIM biis, Pro-Log and Copyrfeht © 22 January 1980 by DATAQUEST - Reproduction Prohibited The content of this report represents our interpretation and analysis of information generally available to the public or released by responsible inIdividuals in the subject companies, but is not guaranteed as to accuracy or completeness It does not contain material provided to us in confidence by our clients This information Is not furnished in connection with a sale or offer to sell securItIes or in connection with the solicitation of an offer to buv securities This firm and its parent and/or their officers, stockholders, or members of their families may, from time to time, have a long or short posItion in the securitIes mentioned and may sell or buy such securities 19055 Pruneridge Ave. / Cupertino, CA 95014 / (408) 725-1200 / TWX (910) 338-7695 / DATAQUEST CPTO Mostek emerged as major competitors in the marketplace due to their einphasis on the STD bus, while Rockwell, Synertek, and MOS Technology experienced major gains due to the success of products based upon the KIM bus. These products have proved successfiil in industrial and instiumentation environments where {^plications for low-cost, low-pfflfOTmance products abound. European markets and educational markets have also accounted f O T large volumes of these low-priced products. . Table 1 8-KT BOARD-LEVEL MICROCOMPUTEBS ESmiATEn WORLDWIDE SHIPMENTS AND REVENUES U.S.-BASED SUPPUERS Total ; Intel Naticmal Semictaiductor Pro--Log Motorola Rockwell Zilog Synertek Mostek MOS Technok^ Others Unit Shipments (Thousands) 1978 20.0 5.7 2.8 4.2 1.0 2.4 10.0 1.0 10.0 6.9 1979 40.0 9.8 10.0 7.1 15.0 4.7 15.0 9.0 15.0 7.4 Revenues (Millions of Dollars) 1978 $18.5 5.1 3.0 5.0 0.4 2.5 2.5 0.6 2.0 10.4 1979 $32.0 TA 6.0 5.5 5.3 4.3 3.8 3.6 3.0 10.1 - Share of Revenues 1978 37% . 10 6 10 1 5 5 1 4 21 1979 40% 9 7 7 7 5 5 4 4 12 64 , . 133 $ 50 $ 81 100% 100% Source: DATAQUEST, Inc. 12-and 16-Bit Board-Levid Mjeroeomputers ^, «. DATAQUEST estimates that in 1979 the 12- and 16-bit board-level microcom-puter market grew over 60 percent in units and over 50 pereef^t in revenues, as shown in "table 2. Digital Equipment continued to dominate the ^ark;et in 1979 and even gwned^hare di^ to the success of its LSI-ll/2 and its new LSl-11/23 products. Some price erosicxi occurred in 1979 due to the impact of new h^her perfOT-mancae..^' lower priced product introduced by Computer Automation, Data General, and iSigital Equipment diru^ the year. However this price erosion, just over 5 percent, was less than anticipated, primarily because competition from semiconductor su^liers did not occur in 1979 as had been expected, bitel was the only major semiconductor suppli^ to begin quantity shipments of 16-bit board-level products in 1979. hitel's iSBC 86 became g«ieraEy available in 1979, but was sold primarQy as an upgrade product for 8-bit customers rather than as a product competing directly with the minicomputer suppliers. DATAQUEST believes that as Intel expands this product line, and as Zil<:^ and Motorola enter the market with products based upon the Z-8000 and the 68000, significant competition between these two classes of suppliers will become a reality, lliese companies are presently emphasteii^ production of their new - 2 -l6H>it chip-level products, however, and we do not expect significant empliasis on the l6^i>it board niarlcet until 1981. " Table-2 12- AND 16-BIT BOARD-LEVEL MICROCOHPUTERS ESTIMATED WORLDWIDE SHIPMENTS AND REVENUES U.S.-BASED SU^PUERS Digital Equipment Texas Instruments Hewlett-Paclcard Intel Data General Computer Automation Others Total • Unit Shipments (Thousands) 1978 1979 15.0 6.0 ' 2.0 -2.0 1.2 6.8 33 30.0 7.0 2.5 1.5 2.5 1.5 8.0 53 ': - Revenues^ (Millions of Dollars) 1978 1979 $25.0 8.5 8.0 -3.0 2.0 7.5 $ 54 $44.0 9.8 9.8 3.9 3.5 2.2 8.8 $ 82 '•' Share of Revenues 1978 1979 46% 16 15 -6 .- 4 13 100% 54% 12 12 5 4 3 10 100% libricet Forecasts Source: DATAQUEST, Inc. 'i?.' Tables 3 and 4 provide updated forecasts for the 8-bit and the 12- and 16-bit board-level microcomputer. marlcets through 1984. In the 8-bit marlcetplace, we expect that growth will continue to be stimulated by price declines during 1980 and 1981. After 1981 prices should begin to stabilize, and significant growth should continue as these products penetrate a seemingly unlimited variety of new applications in industrial, scientific, and control markets. ' ' ' ' The 12- and 16-bit board-level microcomputer market will experience far more significant price declines due to increased competition during "l98l and 1982. We expect price and performanQe to be key issues in this marketplace daring the forecast period, and new standards of power and performance should be set each' year as this market develops during the first half of the 1980s. . "' Li •tit -i '-: '^' '.f<.' ^' •^'1^- % • • >if. :.'• n.:. .. • • • • • , , • : • i-^:, Gfiht S.'^BkiSfree' i • " • . .. '' •if>{>3!ii.. •y '% •si:t..t.:^i-3; ^•i-'yi: •: 1 • --^. m^ a - ' l , . -J>'-3 -Table 3 ESTIHATED WORLDWIDE MARKET FOR 8-BIT BOABO-LEVEL MICROCOMPUTEBS Compmtnd Annual Growth Rate 1976 1977 1978 1979 1980 1981 1982 1983 1984 1979-1984 lliousands of Annual Units 17 35 64 133 210 300 410 530 660 37.8% Average Systetn Price (Thousands of DoUars) $1.0 $0.9 $0.8 $0.6 $0.5 $0.5 $0.5 $0.4 $0.4 (7.0%) Millions of DoUars $ 17 $ 32 $ 50 $ 81 $110 $150 $190 $230 $280 28.2% Source: DATAQUEST, Inc. Table 4 ESmiATED WORLDWIDE MARKET FOR 12-raT AND 16-BlT BOARD-LEVEL AnCRGCOMPUTERS Compound Armual Growth Rate 1976 1977 1978 1979 1980 1981 1982 1983 1984 1979-1984 Thousands of " Annual Units 10 22 33 53 80 120 180 240 310 42.4% Average System Price (Thousands of Dollars) $1.4 $1.6 $1.6 $1.5 $1.4 $1.2 $1.0 $0.9 $0.8 (12.2%) IVIillions Of DoUars $ 14 $ 35 $ 54 $ 82 $110 $145 $180 $215 $250 25.0% Source: DATAQUEST, Inc. - 4 ' |
189638 | https://www.youtube.com/watch?v=dL1tbrJtFfc | OpenStax: Algebra and Trigonometry - Chapter 1, Section 6 | Rational Expressions
Scalar Learning
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Welcome to Huzefa’s explanation video of OpenStax Algebra and Trigonometry textbook. This is a full walkthrough of Chapter 1, Introduction to Prerequisites, Section 6, Rational Expressions. Watch Huzefa as he reviews exercises 1-57 odd.
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To skip to a particular question, use the chapters below:
00:00 Introduction
00:14 Exercise 1
00:49 Exercise 3
01:14 Exercise 5
01:47 Exercise 7
02:34 Exercise 9
04:13 Exercise 11
04:42 Exercise 13
06:07 Exercise 15
07:17 Exercise 17
09:42 Exercise 19
11:53 Exercise 21
12:40 Exercise 23
14:54 Exercise 25
17:31 Exercise 27
20:16 Exercise 29
23:22 Exercise 31
25:57 Exercise 33
26:26 Exercise 35
27:29 Exercise 37
29:05 Exercise 39
30:40 Exercise 41
31:35 Exercise 43
32:25 Exercise 45
34:07 Exercise 47
35:30 Exercise 49
37:52 Exercise 51
39:07 Exercise 53
39:56 Exercise 55
42:51 Exercise 57
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Introduction [Music] what's up everybody and welcome back to open stacks algebra and trigonometry chapter 1 section 6 rational expressions let's do it how can you use factoring to simplify rational expressions so i'm going to give you an example so you can Exercise 1 see what it's all about so if we have a rational expression this polynomial over this polynomial what we can do is we can factor the top so again we're going to ask what multiplies to 4 and adds to negative 4 that's negative 2 and negative 2. so it's going to factor like so and the bottom one we're going to ask the question what multiplies to negative 8 and adds to positive 2. that's positive 4 and negative 2. so it's going to factor like this and then we can cancel out these two binomials because they're the same in the top and the bottom boom and we've simplified done tell whether the following statement is true or false and explain why you only need to find the Exercise 3 lcd when adding or subtracting rational expressions i would say this is generally true because when you're multiplying or dividing you can just kind of multiply or divide everything through it doesn't matter if you have common denominators or not whereas we're talking about adding or subtracting we need those denominators to be the same before we can add those numerators for this expression we're meant to simplify and all i want you to think about is Exercise 5 factor factor factor obviously we see these are quadratic expressions on the top and bottom so let's do it on the top one let's see what multiplies to 25 and adds to 10 that is 5 and 5. so we got y plus 5 times y plus 5 on the bottom what multiplies to 30 and adds to 11 that's positive 6 and positive 5. now we can see we've got y plus 5 on the top and bottom they cancel out for a final result of y plus five over y plus six boom done here on top we are going to factor once again but first i got a gcf so i'm gonna Exercise 7 factor out that nine out of the entire expression i got b squared plus two b plus one over and here i'm going to factor out a three on the bottom another gcf b plus one now i can factor this inside expression what multiplies to one and adds to 2 that's 1 and 1. so i'm going to factor it as b plus 1 times b plus 1 and on the bottom we're going to leave it as is but check it out i got a b plus 1 and a b plus 1 those cancel out and then i got a 9 over 3 dividing both by 3 and i got 3 and i've got 1. so my final answer is if i redistribute this 3 like so is 3 b plus 3 over 1 but that means i can just kind of remove that denominator here's the final answer done here on top there's no gcf so i'll rewrite it as is Exercise 9 on the bottom we have a gcf of 2 so i'm going to factor out a 2 pull out a 2 and then it's going to be 2x squared plus regular x right 2 times x gives us back to that 2x and then minus 1. so these are leading coefficients so i'm going to use the star method for both so on top i got 2 for the a term the b term is 7 and a times c is 2 times negative 4 is negative 8. so what multiplies to negative 8 and adds to 7 that would be positive 8 and negative 1. and that would mean that i can then reduce this to 1 and 4 right divide the top and bottom by 2. so now the top part factors as follows we have one x plus four times two x minus one so you notice the top number goes with the variable like that the bottom number four goes here as the constant now for the denominator i'm going to do the star method again and i'm going to throw a 2 here a 2 here 2 times negative 1 is negative 2 up top that b value that 1 goes down here what multiplies to negative 2 and adds to 1 that's positive 2 negative 1 cancels out divide both of those by 2 we got 1 and 1. so here are the final expressions and don't forget that 2 stays outside so then we've got 1x plus 1 times x minus one and now check it out we can cancel this and this and then if i were to redistribute that two we'd have for our final expression x plus four over two x plus two done so again we're going to factor this top part and there's no gcf in either Exercise 11 we're going to ask the question what multiplies to 18 what adds to 9 that's 3 and 6. on the bottom we're going to ask the question what multiplies to negative 18 and adds to positive three that would be positive six and negative three check it out we have an a plus six a plus six and then we're left with a plus three over a minus three boom done Exercise 13 here there's no gcf for either so we're going to use the star method for both so on top we've got a of 12 we've got b of negative 29 and we've got a times c of negative 96 so what multiplies to negative 96 and adds to negative 29 that's negative 32 and positive 3. we can reduce both sides divide those by 3 and we've got 4 and 1 and then we can divide both of these by four and we've got three and negative eight so the top becomes three n minus eight times four n plus one and then for the bottom we're going to do the same thing star method again boom boom we've got a is 28 b is negative 5 down here and a times c is negative 84. so what multiplies negative 84 and adds to negative 5 that would be negative 12 and positive 7. this reduces divided by 7 to 4 and 1. this can reduce divide top and bottom by 4 and we've got 7 and negative 3. so now we have seven n minus three four n plus one because we got a positive four and positive one check it out we know we did it right because cancel cancel and we're left with three n minus eight over seven n minus 3 Exercise 15 done now we are multiplying rational expressions but i want you to go back to that same philosophy factor factor factor and you're going to see some cool things unfold so check it out this one we're going to ask what multiplies to negative 24 and adds to 2 so that is going to be positive 6 and negative 4. on the bottom we're going to ask what multiplies 36 adds to 12 that's positive 6 and positive 6 c plus 6 c plus 6. you can already see this is going to cancel out but we're going to wait we're going to do it all at the end then we multiply times what multiplies to 24 and adds to negative 10. that is going to be negative 6 and negative 4 so c minus four c minus six last but not least we'll multiply 16 and adds to negative eight that's gonna be negative four and negative four so we got c minus four and c minus four now once we factor correctly this is the fun part so check it out we've got c plus six c plus six then we've got c minus four c minus four then we got another c minus four c minus four and we're left with c minus six over c plus six boom done here we got a little bit more complex factoring and notice even with these Exercise 17 terms here with the leading coefficients there's no gcf's there's gonna be a lot of star method here we go let's do the top one we're gonna start with our a term of 10 our b term of negative 9 and a times c is negative 90. so what multiplies to negative 90 and adds to negative 9 that's negative 15 and positive 6 reduced by dividing by two and we got five and three and then here we divide by five and we've got two and negative three boom so the top left factors to two h minus three times five h plus three over now we're going to use the star method again so we're gonna have a bunch of star methods here we've got two for the a term we've got b is negative 19 and a times c two times four is 48 so what multiplies to 48 and adds to negative 19. that is going to be negative 3 and negative 16. we can't reduce this side so that's chillin but we got to divide these by 2 so we got 1 and negative 8 boom so the bottom factors to 2h minus 3 times 1h minus 8. that's pretty cool because again you can see the 2h minus 3 is going to cancel out next we got this one this one we don't need the star method because it's got no leading term there so what multiply 64 adds to negative 16 it's gonna be negative eight and negative eight so h minus eight times h minus eight on the bottom here we do need the star method so let's set it up and we're gonna have a 5 for a negative 37 for b and a big number 5 times negative 24 which is negative 120 up top so what multiplies to negative 120 that's the negative 37 that is going to be negative 40 and positive three can't reduce this so we're good reduce this by dividing by five we've got one and negative eight boom so now we can make it like so we can say one h minus eight times five h plus three now it's the fun part we've got h minus eight h minus eight we've got another h minus eight and h minus eight then we got a five h plus three five h plus three and last but not least a two h minus three and a two h minus three so what happens when everything cancels out it's essentially the same thing over the same thing which means you simply get one because anything divided by itself is one so on these top two they're actually almost the same but we're going Exercise 19 to have to use the star method because they got leading coefficients no gcf so let's start with the top left so we got an a term of 2 a b term of 15 and a times c is 50. so what multiplies to 50 and adds to 15 that's 5 and 10 reduce this to 1 and 5. so here's how it factors it's going to be 2 d plus 5 times d plus 5. and instead of doing this denominator i'm going to do this numerator next as well because we're going to need another star method so we got 2 as the a term negative 15 as the b term and 2 times 25 is 50 as the a times c term so here it's going to be 5 and 10 again that multiply to 50 but they're going to be negative because they're adding to negative 15 divide both by 2 and we got 1 and negative 5 reduced boom and boom so now we have 2 d minus 5 d minus 5. now on the bottom it's something special we have difference of perfect squares so when we factor these the way you do it is you take the square root of the first which is 2d square root of 4 is 2 square root of d squared is d and square root of the second which is 5. and you place that here and here and since it's a difference of squares one's going to be plus one's going to be minus likewise over here we've got the square root of 25 and d squared which is five d and then the square root of one which is one and again alternate with that plus minus now you can see we can do a little cross cancellation we got 2d plus 5 on the top and bottom boom boom and then we got a 2d minus 5 here and here and now we're left with these two on top and these two on bottom but i'm gonna go ahead and re-foil them so d plus five times d minus five guess what that's going to get us back to a perfect square because that is exactly how we factor a perfect square so we can combine it to become d squared minus 25 and if you're not sure you can actually foil it and see that it works out to this nice binomial and on the bottom we're going to just recombine those back to 25 d squared minus 1 boom done Exercise 21 once again we're going to start with factoring on the top left which is a difference of squares so that becomes t plus 1 times t minus 1. then on the bottom we're going to see what multiplies to 3 and adds to 4 that is positive 3 and positive 1. on the top right we're going to say what multiplies to negative 15 and adds to positive 2 that is positive 5 and negative 3 and then over here what multiplies to positive 3 and adds to negative 4 is negative one and negative three now is the fun part we're gonna cancel out a t minus three like so a t minus one and a t plus one like so which means now we're left with t plus five over t plus three boom done once again we're going to factor factor factors so on the Exercise 23 top left i notice that it's a difference of squares so i can factor like a typical difference of squares like so square root of 36 is 6 square root of 25 is 5 and of course we need that x squared square root so we got x and x and since the difference of squares we alternate with plus minus on the bottom there's no gcf so we're going to go straight into the star method so we have 6 which is the a's 65 on the bottom which is the b and then 6 times 5 which is a times c is 300 up top so the question is what multiplies to 300 and adds to 65 that would be 5 and 60. then we can divide both of these by 6 and we get 1 10 and those are our binomials so we have 6x plus 5 times 1x plus 10. once again we're going to run the star method so we've got 3 as the a term the b term is 32 and the a times c term up top is 60. so what multiplies to 60 and adds to 32. that would be 30 and 2. here we can divide by three and we get one and ten those are our binomials so we have one x plus ten times three x plus two now on the bottom we're gonna run the star method one more time again no gcf so we're good there always got to check for gcf before you apply the star method and then we've got an 18 like so we've got a b term of 27 and on the bottom we've got a times c which is 180. so what multiplies to positive 180 and adds to 27 that would be 15 and 12. we can reduce both of these divide these by 6 and we get 3 over 2 divide these by 3 and we get six over five boom boom are the binomials so we have six x plus five times three x plus two now the fun part three x plus two three x plus two six x plus five six x plus five and x plus ten x plus ten which leaves us with six x minus five over six x plus five boom done Exercise 25 all right in this case we got more factoring happening but i want you to do something before you factor i want you to address that division because when you divide by fraction it's the same as multiplying by its reciprocal so i'm going to start by rewriting this as follows the first expression stays the same but the second part is going to flip so we got 2p squared on top and then we got the 6p squared minus 11p plus 4 on the bottom now we're going to factor and notice there's no gcfs for any of these so we're just going to go straight to the star method here we go with the top left first a term of 6 b term of 1 right 1 p and then a times c is negative 72 so what multiplies to negative 72 and adds to 1. that is positive 9 negative 8 we reduce by dividing by three that's two three reduce by dividing by two that's three negative four and there are your binomials so we have three p minus four times two p plus 3 over now we got to run the star method again for this guy we've got an a term of 8 b term of 18 and 8 times 9 is 72 up top so we'll multiply 72 and adds a positive 18 that would be 6 and 12. then we're gonna reduce divide by four that's two and three divide by two and that's four and three boom boom and now we have four p plus three times two p plus three times and once again we got more star methods happening so up top we've got two two b term is eleven c term is negative twelve what multiplies negative 12 adds to 11 positive 12 negative 1 reduced by dividing by 2 1 and 6. so we got those and those for the binomial so 1 p plus 6 times 2 p minus 1 over last star method we'll do over here we've got 6 for the a's negative 11 for b and a times c 6 and 4 is 24 up top multiplies 24 adds to negative 11 is negative eight negative three divide by three we got two and negative one and divide by two and we got three and negative four so we've got three p minus four times two p minus one now we cross off two p minus one like that two p plus three like that and three p minus four like so and we're left with p plus six over four p plus three boom done here we're once again going to factor Exercise 27 but first we're going to flip this division into multiplication again it's the same as multiplying by the reciprocal so we're going to rewrite it as follows so notice on the second fraction we've taken the reciprocal so this has gone down here and this has gone up here and we've changed it to multiplication now since there's no gcf for any of these we're going to go ahead and factor using the star method so we're going to start with the top left so we've got 18 and 18 for the a term b term is positive 77 and a times c is negative 324 and a times c is negative 324 so what multiplies negative 324 adds to 77 that is positive 81 and negative four now we're going to simplify that turns divides by two we get nine and negative two here we divide by nine and we get two and nine so this gives us two d plus nine times nine d minus 2. then we run the star method for the bottom left and we've got 27 up top for a negative 15 for b 27 times 2 is 54 for a times c what multiplies 54 adds to negative 15 that's negative 6 and negative 9. simplify simplify divided by 3 we get negative 2 and 9 over here divide by 9 and we get 3 and negative 1 over here which gives us nine d minus two times three d minus one running the star method for the top right we've got nine for the a term negative fifteen for b nine times four is thirty six for c so what multiplies 36 adds to negative 15 that's negative 3 and negative 12. divide by 3 we got 3 negative 1. divide by 3 we got 3 negative 4. so that gives us 3 d minus 1 times 3 d minus 4 over last but not least we're going to do the star method for the bottom right so we've got 3 3 29 for b 3 times negative 44 is negative 132 is a times c so what multiplies negative 132 adds to 29. that is positive 33 and negative 4. divide by 3 divided by 3 we got 1 and eleven boom oh so now we have one d plus eleven times three d minus four now the fun part cross off three d minus four three d minus four nine d minus two and nine d minus two last but not least three d minus one and three d minus one and now we are left with two d plus nine over d plus eleven boom done once again we are going to start by flipping that division into Exercise 29 multiplication as follows so the first part remains the same it's the second part that we flip and again we change that to multiplication so the 36 b squared and all that goes on top while the 18b squared goes on the bottom now in a few of these we actually do have a gcf so we're going to have to address that as well so let's first start by factoring out gcf here everything can be divided by 2 and here everything again can be divided by 2. so now i got 144 b squared minus 25 over 2 times 36 b squared right divide that by 2 minus 3 b divided by 2 minus 5 boom and we're going to divide this by 2 as well and we've got 18 b squared right we're dividing by 2 and we're dividing that 18 by 2 and that's 9 and then dividing 10 by 2 and that's 5. boom over and then this stays the same now we're going to factor and of course this up top is a difference of squares that's really nice so it just becomes 12 b minus 5 right we're taking the square root of each piece times 12 b plus 5 like so over now for the bottom left we're going to run it through the star method we got 36 here and here we've got negative 3 for the b and then negative 5 times 36 is negative 180 for a times c so what multiplies a negative 180 what adds to negative 3. that would be negative 15 and positive 12. now we're going to reduce divide by 3 we get negative 5 and 12 divide by 12 and we get 1 and 3. so now we have 12 b minus 5 times 3 b plus 1. now we're going to run this through the star method so up top right we've got 18 and 18. we've got negative 9 for the b 18 times negative 5 is negative 90. what multiplies to negative 90 adds to negative 9 that would be negative 15 positive 6 divide by 6 1 and 3 boom divide by three we have six and negative five all right so now we have for the top right six b minus five times three b plus one last but not least we run through the star method on the bottom right so we have 18 18 negative 21 on the bottom for the b a times c is 90. what multiplies to 90 adds to negative 21. that is negative 6 and negative 15 divided by 6 we got negative 1 3 and divide by 3 we got 6 and negative 5. so this gives us 3b minus 1 times 6 b minus five now the fun part cancel cancel three b plus one boom and twelve b minus five which leaves us with 12 b plus five over three b minus 1 boom Exercise 31 done all right for this one once again we see we have no gcf so we're going to factor everything using the star method also i'm going to start by converting that division to multiplication as follows so notice the entire expression on the left stays the same where we're going to flip the expression on the right as so now we're going to use the star method starting on the top left and we're going to throw the a term up top like this the b term on the bottom and then a times c 22 times 10 is 220 up top so what multiplies to 220 and adds to 59 that is of course 55 and 4. we can divide the right by 2 we get 11 and 2 the left by 11 and we get two and five so we have two y plus five times eleven y plus two now we're gonna do the bottom left so once again we got 12 for the a term we got the b term of 28 and a times c 12 times negative 5 is negative 60. so what multiplies negative 60 adds to 28. that's going to be 30 and negative 2. so we're going to divide the right by 2 when we get 6 and negative one we're going to divide the left by six and we get two and five so now we have two y plus five and over here we have six y minus one now on the right we're gonna do star method again so we've got 24 up top like this for the a term 24 times 1 that's a times c up top and then the b term of negative 10. so what multiplies to positive 24 adds to negative 10 that's negative 6 negative 4. simplify by dividing both of these by 4 we get 6 negative 1. over here divide both by 6 and we get 4 and negative 1. so up top we have 4y minus 1 times 6y minus 1 over last but not least we're going to do star method for the bottom so again we got 11 for the a term up top we've got 8 times 11 88 up here for a times c and 46 on the bottom so what multiplies the 88 and adds to 46 that's 2 and 44. so we divide by 11 we got 1 and 4 here we can't do anything so we're good to go so now we have 1 y plus 4 over here times 11 y plus 2 and now the fun part so 2 y plus 5 boom gone 11 y plus 2 gone 6 y minus 1 gone and we're left with 4 y minus 1 over y plus 4 done Exercise 33 for these we're meant to add and simplify we can't add unless we have a common denominator so check it out right now i got x under the bottom of that one i got y under the bottom here so to get a common denominator it could be x times y so if i multiply this by y and y multiply this by x and x now i have a common denominator now i can combine so now i have 4 y plus 10 x over x y and that is the winner done to Exercise 35 combine these once again we need a common denominator so they have nothing in common as of now so the way we're going to get a common denominator is i'm going gonna have to multiply this one times that denominator over itself right a minus three over a minus three and then this one i'm gonna have to multiply by a plus one a plus one now we've got common denominators now i can distribute and combine so up top here i have four a minus 12 over here i have five a plus five on the bottom if i foil everything out i get a squared minus three a plus a minus three now i can simplify everything 4a and 5a make 9a negative 12 and 5 make negative 7. on the bottom we have a squared negative 3a and a is negative 2a and minus 3 boom done Exercise 37 once again to get common denominators we're going to have to multiply this denominator times that that denominator times that so check it out y plus three over y minus two plus y minus three over y plus one so i've drawn these a little bit long so we can quickly add the y plus 1 and y plus 1 and then here i'm going to multiply by that denominator of y minus 2 y minus 2. now notice these denominators are the same so we can combine but first let's simplify so up top if we foil we've got y squared plus y plus three y plus three so we got plus y plus three y plus three over here we've got y squared minus 2y negative 3 times y is negative 3y and then negative 3 times negative 2 is positive 6 over and this is going to be a common denominator so we just multiply one same thing y times y is y squared right then we got y times one is y that's negative two y and then negative two times one is negative two now we're going to combine like terms simplify and we'll be done so first we have 2 y squared then we have 4y plus negative 2y is 2y minus 3y is minus y then we have a 3 and 6 and that combines to be a nine over y squared y negative two y make minus y minus two boom done to get common denominators here we're gonna do the Exercise 39 same thing we got z plus one over here as that denominator and then we have z minus two so to get common denominators i gotta multiply this by z minus two on the top and the bottom and this one we're going to multiply by that z plus one and again we have to multiply by z plus one over z plus one so we're not actually changing the fraction because z plus one over z plus one is one all right now we're going to simplify so distribute distribute we've got three z squared minus three z times negative 2 is negative 6z plus and these are going to be over common denominators so we can kind of combine everything into one big numerator so then we're going to foil 2 z squared then we've got 2z times 1 is 2z 5 times z is 5 z and then 5 times 1 is 5 over z times z is z squared and then z times negative 2 is negative 2 z z times 1 is z and then 1 times negative 2 is negative 2. so now we're going to combine the like terms 3 and 2 make 5 z squared negative 6z plus 2z plus five z that's gonna be positive one z right negative six plus two plus five is positive one and then we've just got that lone five out there like that and then on the denominator we got that z squared we got negative 2z and z makes negative z last but not least minus 2 boom done all right we got an x plus 1 and a y plus 1 once again we need common Exercise 41 denominators so let's write it out as follows so to get our common denominators i'm going to multiply this by that denominator which is y plus 1 over y plus 1. and here we're going to multiply by that original denominator which is x plus 1 and of course we need to x plus 1 on the top now we're going to distribute and simplify so we got x y x times one is plus x plus y times x which is another x y y times one is y over and then we're gonna foil so we got x y plus x plus one times y which is y plus one last but not least we're going to simplify by combining like terms so up top we got two x y right those are like terms then we got x and we got y over nothing combines in the denominator so it just stays as is boom done so we've got 2 over a plus 7 over b the Exercise 43 way we're going to get common denominators is this has to multiply by b over b this has to multiply by a over a now we got common denominators of a b so when we combine those now we have 2b plus 7a over a b over b now we can kind of consolidate everything by the way this fraction is really dividing b well guess what dividing by b is the same as multiplying by 1 over b so i'm going to rewrite this as 2 b plus 7 a over a b times 1 over b obviously the one just multiplies this and stays the same b times that gives us a denominator of a b squared up top we still got 2b plus 7a Exercise 45 for the win so again before we can simplify we need to combine these two fractions up top into one fraction the bottom's chilling so we got three over a plus b over six over two b over 3 a so to get a common denominator this needs to multiply by 6 over 6 right because we have a 6 there and this needs to multiply by a and a now we're going to get 18 over 6 a plus a b because i can just combine 3 times 6 is 18 combines with the a b over 6 a over 2 b over 3 a and dividing by this fraction on the bottom is the same as multiplying by its reciprocal so check this out we can say 18 plus a b over 6 a times the reciprocal of this which is 3 a over 2 b now we're going to distribute distribute and multiply there and we're left with 3a times 18 is 54 a plus 3a times a b is 3a squared b right a times a gives us a squared over 2b times 6a is 12 a b we can divide the 54 the 3 and the 12 all by 3 right so that becomes 1 that becomes 4 and this becomes 18. we can also divide everything by a because there's an a in common to all the terms so check this out a goes away that becomes an a to the first and that a goes away divide everything by a so now our final answer is 18 plus 1 a b over 4 b for the when done once again to simplify we need to Exercise 47 combine to have like terms so i'm going to rewrite this as a b minus b over a over and the denominator is already into one fraction over that one denominator so that's chilling so now to get a common denominator we're going to have to have a b so i multiply this by a and a times a up top is going to give me an a squared over here we're going to multiply by b over b and guess what b times b is b squared now we're going to simplify and we have a squared minus b squared over a b over a plus b over a b now we're going to again multiply this times the reciprocal of this because it's again dividing so it's the same as multiplying by the reciprocal so we have a squared minus b squared over a b times the reciprocal a b over a plus b so right off the bat you're going to see that check it out we got this in the numerator and the denominator we can cross cancel and then we've got this over this but you might also recognize that this is a difference of squares so i'm going to simplify it to become or factored i should say to be a minus b times a plus b that's how we factor a difference of squares over a plus b and look how nice that is because once again cancel cancel and we're left with the final expression of a minus b done so in this one once again we need Exercise 49 common denominators c plus 2 times c plus 1 so we're going to rewrite it and the denominator is good to go because this is over one single denominator so to get this to have common denominators we multiply this one by c plus one and this one by c plus two now we're going to distribute here and foil here so on the left we have two c squared plus 2c right 2c times 1 plus then we got c squared c times c c times 2 which is 2c negative 1 times c which is minus c and then negative 1 times 2 is minus 2 over if we distribute this we get c squared plus c and then we've got two times c which is two c plus two times one which is two and this whole expression is still over two c plus one over c plus one but let's leave that for now we're going to first simplify the numerator so now we have 2c squared plus c squared which is 3c squared 2c plus 2c minus c is plus 3c and then minus 2 is chilling out there then we have over c squared plus c plus 2c which is 3c and then plus 2. last but not least we're dividing by this expression but it's the same as multiplying by this reciprocal right so we can just multiply by the reciprocal we flip the c plus 1 on top and 2c plus 1 on the bottom now i'm looking at this and i'm realizing wait a minute if i factor this back to what we had before i'm going to be able to cross cancel so i'm going to go ahead and do that so i'm going to shrink down the work like so so i have more room and here i'm going to factor this again i'm going to leave the top the same 3c squared plus 3c minus 2 over and this goes back to c plus 1 times c plus 2. now these cancel out like so which is pretty cool and then last but not least i'm going to foil this again on the bottom so the top is going to stay the same 3c squared plus 3c minus 2 on the bottom we've got that times that which is 2c squared plus c plus 4c and then plus 2 times 1 which is plus 2. we're going to combine like terms and we end with 3c squared plus 3c minus 2 over 2c squared plus five c plus two for the Exercise 51 win done brenda is placing tile on her bathroom floor the area of the floor is 15x squared minus eight x minus seven the area of one tile is x squared minus two x plus one to find the number of tiles simplify the rational expression so of course what we're going to do here is we're going to factor and here on top we need that star method because of the leading coefficient so once again recognize that there's no gcf which is what we need otherwise you have to factor out the gcf first then you factor so 15 goes up top for the a value negative 8 is my b value and negative 7 times 15 which is negative 105 is a times c let me ask the question what multiplies to negative 105 and adds to negative 8. that is of course negative 15 and positive 7. this is going to simplify to 1 over negative 1 and there are our two binomials so now we have one x minus one times fifteen x plus seven on the bottom we're gonna factor more easily because we've got no leading coefficient so we got x and x here what multiplies to one adds to negative two that's negative 1 and negative 1. then we can cancel cancel and our final answer is 15 x plus 7 over x minus 1 boom done aaron wants to mulch his Exercise 53 garden his garden is x squared plus 18 18x plus 81. one bag of mulch covers x squared minus 81. divide the expressions and simplify to find out how many bags of mulch air needs to mulch this garden so i'm going to write the first one on top of the second one and then simplify so once again we're going to start by factoring so i'm going to factor these two so we're going to start here what multiplies to 81 and adds to 18. that is 9 and 9 positive and then here we got a difference of squares so that becomes x minus 9 x plus nine right to factor a difference of squares we take the square root of this place that here take the square root of this and place that here and of course we alternate with minus plus then we cancel cancel and our final answer is x plus 9 over x minus 9 done in this one we got quite a lot Exercise 55 going on but we're going to start with the same protocol a factor factor factor so we're going to go top left and all the way around until we get to the end and these are all have leading terms none of these have gcf so we're going to go straight into the star method starting up top so let's check it out we got an a term of 3 we got a b term of negative 10 and then a times c of 9. so what multiplies to positive 9 adds to negative 10 that's negative 1 and negative 9 and we simplify simplify divide them both by 3 that's 1 and negative 3. here are the values for the binomial so this is 3y minus 1 times y minus three over and then we got this one here we got the star method again we've got a a value of three up top here and here we've got a b value of five and a times c three times negative two which is negative 6. what multiplies the negative 6 adds to positive 5. positive 6 and negative 1. now we're going to divide by 3 here and here and we simplify to 1 and 2 there are our coefficients so now we've got 1y plus two times three y minus one over here we're gonna run the star method again we've got a terms of two two b term of negative three and then we got a times c two times negative twenty which is negative 40. what multiplies the negative 40 adds to negative 3 that's negative 8 and positive 5 reduce reduce divided by 2 1 and negative 4 those are our values and then so up top we've got 2 y plus 5 times 1 y or just y minus 4. so once again we're going to run the star method one more time we've got 2 for the a term here we've got a negative 1 for the b term and then 2 times negative 15 is negative 30. so what multiplies the negative 30 adds to negative one we got negative six and positive five divided by two one divided by two negative three so we got this and this so we got two y right two on the y value and then plus five times one y minus three y minus three and i know we got this all over y minus four but we're gonna get back to that so first let's go ahead and do the fun part cancels out two y plus five two y plus five cancels out y minus 3 y minus 3. cancel out 3y minus 1 and 3y minus 1. now we're left with y minus 4 over y plus 2 over y minus 4. so this fraction is now being divided by this expression alternatively you can think about this fraction multiplying the reciprocal of this so check it out y minus 4 over y plus 2 times the reciprocal of that which is 1 over y minus four once again these cancel cancel right cross canceling which leads us to the final answer one over y plus two for the win Exercise 57 done all right we got a lot of stuff going on here so the first thing we need to do is switch all these divisions to multiplications so first things first i'm going to flip this as follows so we notice we leave the first expression alone but since we're dividing we flip this one and the 8x squared goes on top and the 3x squared expression goes on the bottom as follows so i'm going to follow the order of operations i'm going to go left to right with the multiplication these are all equal footing but again we go left to right when it's the same operation or the same level so let's start there and then we'll bring this into the mix start again with factoring so i'm going to factor this on top what multiplies to 12 and adds to 7 that would be 4 and 3. on the bottom what multiplies to negative 6 adds to positive 1 it's going to be positive 3 and negative 2. now here we would use star method but we do have a gcf so the first thing i'm going to do is i'm going to factor out a 4. all of these are divisible by 4. so i have 4 times 2x squared minus x minus 6. right i'm dividing each of these by 4 to get what's remaining inside so now when i do run the star method it's going to have 2 for the a term negative 1 for the b term and then 2 times negative 6 is negative 12 up top what multiplies negative 12 adds to negative 1 negative 4 positive 3. simplify simplify 1 negative 2 and we go like this and we go like this so now up top we have that 4 kind of stuck in front and then we have this factored form of one x minus two times two x plus three now on the bottom there is no gcf so we're gonna run the star method with just these values so we've got three for the a term 19 for the b term and then we got 3 times 28 which is 84 that's for the a times c term then what multiplies to 84 adds to 19 that's 7 and 12. simplify by dividing by 3 we have 1 and 4. boom and boom so now we have one x plus four times three x plus seven now we're gonna cancel as follows x plus four x plus four then we got x minus two x minus two we've got x plus three x plus three and we're left with four times two x plus three over three x plus seven now this is divided by this final expression so i'm gonna flip that to multiplication and then take the reciprocal of this last expression which is three x squared plus four x minus seven on top two x squared plus x minus three on the bottom now i'm gonna take this and i'm going to factor both of these with the star method notice there is no gcf not like up here where we could divide by four so for the top right we've got 3 for the a term positive 4 for the b term 3 times negative 7 is negative 21 for a times c well multiplies to negative 21 adds to four positive seven negative three divide by three boom boom one and negative one so now top we've got one x minus one times three x plus seven on the bottom we'll run the star method one more time we've got a two and a two we've got one on the bottom for the b term and then a times c two times negative three is negative six up top so what multiplies to negative six adds to one that's positive three and negative two and we simplify by dividing by two we got one and negative one and then we've got two x plus three times one x minus one now we're gonna simplify one more time we got three x plus seven three x plus seven two x plus three two x plus three and finally x minus one x minus one and we're left with just four for the win done i hope you guys enjoyed this video and if you did please click that like button if you wanna see more from the scalar learning channel make sure to click subscribe thank you guys so much for joining i'll see you 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189639 | https://www.sciencedirect.com/topics/agricultural-and-biological-sciences/cervical-mucus | Skip to Main content
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Female Reproduction
Cervical mucus
Cervical mucus is a hydrogel consisting of 90–95% water and a heterogeneous mixture of mucin glycoproteins. The physical properties and the biochemical composition of cervical mucus change during the menstrual cycle. When the ovulation approaches, cervical mucus becomes thinner and more watery and is so-called “egg white cervical mucus”, as it resembles raw egg white. Egg white cervical mucus is believed to be preferable mucus for conception, as it provides an easy pathway for the sperm to swim through.
The cervical mucus layer on the surface of the cervix works as barrier to prevent infection. Cell-surface (MUC1, MUC4 and MUC16) and gel-forming (MUC5B, MUC5AC, MUC6) mucins produced by endocervical epithelium contribute to the formation of the mucus layer in the cervical canal (Andersch-Bjorkman et al., 2007). In addition, the quality of cervical mucus significantly influences the fertility, as interactions with cervical mucus affect the penetration of spermatozoa into the uterine cavity (Martyn et al., 2014). Cervical mucus also works as lubricant during sexual intercourse.
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Reference work2018, Encyclopedia of Reproduction (Second Edition)Takeshi Kurita
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Contraception
2014, Human Reproductive Biology (Fourth Edition)Richard E. Jones PhD, Kristin H. Lopez PhD
Cervical Mucus Method
The amount and consistency of the cervical mucus change throughout the menstrual cycle (see Chapter 3). During the “wet days,” immediately before and after ovulation, the mucus becomes more abundant, becomes clear and slippery (like raw egg white), and has a high degree of threadability as detected by placing it between two fingers. A woman is most fertile at this time. Before this stage, the mucus is a cloudy yellow or white and sticky. After the wet days, the mucus volume decreases, and it is again cloudy. Coitus should be avoided from the time that the wet days begin until the fourth day after the wet days end. This cervical mucus method is very inefficient, with a high failure rate.
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Book2014, Human Reproductive Biology (Fourth Edition)Richard E. Jones PhD, Kristin H. Lopez PhD
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Volume II
2016, Endocrinology: Adult and Pediatric (Seventh Edition)Frank J. Broekmans, Bart C.J.M. Fauser
Assessment of Cervical Mucus–Sperm Interaction
In some mammals such as the horse, after intercourse, semen is ejected directly into the uterus. In contrast, in the human, semen is deposited in the posterior fornix of the vagina. The cervix is believed to play an important role in reproduction by allowing the sperm to enter the uterine cavity.
A number of specific functions of cervical mucus have been identified, including protecting the sperm from the hostile acidic milieu in the vagina, allowing the sperm to enter the cervix, supporting energy requirements for sperm motility, and filtering morphologically abnormal sperm. Before ovulation, cervical mucus is produced in large quantities, allowing easy sperm access at the most appropriate moment during the menstrual cycle. The prognostic performance of cervical mucus tests, the incidence of cervical factor infertility (“cervical hostility”), and the validity of treatment options to correct disturbed cervical mucus–sperm interactions remain highly controversial.
Postcoital Test
This test, which involves appraisal of the presence of motile sperm in cervical mucus, after intercourse during the late follicular phase of the menstrual cycle, was originally described in 1866 by Sims and was reemphasized in 1913 by Huhner. There is no agreement regarding the preferred interval between intercourse and the test, nor the cutoff between a normal and an abnormal test result. The threshold is somewhere between one and five spermatozoa per high-power magnification (i.e., 10 × 40) field. Although the test has been widely applied in Europe, questions have accumulated regarding the diagnostic and prognostic power of the test.90
A systematic review of 11 well-designed studies indicated that the discriminating ability of the postcoital test is poor, regardless of the applied criteria for normality.91,92 A subsequent systematic prospective evaluation indicated that the inclusion of a postcoital test in the routine evaluation of new couples only results in additional interventions.91 Several national and international bodies (such as the American Society of Reproductive Medicine, the European Society of Human Reproduction, and the Royal College of Obstetrics and Gynaecology) currently advise against performing the postcoital test in routine infertility evaluation. In addition, earlier tests used to evaluate the quality of the cervical mucus, along with several in vitro tests of interactions between cervical mucus and sperm, have been abandoned.
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Book2016, Endocrinology: Adult and Pediatric (Seventh Edition)Frank J. Broekmans, Bart C.J.M. Fauser
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Assisted Reproduction
2018, Encyclopedia of Reproduction (Second Edition)Grace M. Centola
Postcoital Test
A PCT is performed by the gynecologist or reproductive endocrinologist to determine if the midcycle cervical mucus is conducive to sperm penetration. Instructions are provided for ovulation timing with the assumption that at, or right before midcycle, the cervical mucus is receptive to sperm penetration and survival. The couple is instructed to have intercourse, and the female partner to appear at the physician’s office 3–4 h after intercourse. Alternately, the couple is instructed to have intercourse the night before the scheduled test, and the cervical mucus is checked at the physician’s office the next morning (WHO, 2010).
A smear of the cervical mucus is taken by the physician and examined under a microscope. There should be an adequate amount or volume of the cervical mucus, and the consistency should be watery minimally viscous midcycle mucus (Moghissi, 1976; WHO, 2010). The cervical mucus should show adequate stretching, Spinnbarkeit, and is scored as 0 (low stretchability) to 3 (9 cm or more stretching). Ferning is scored after a sample of mucus is air dried on a glass slide. Once mucus has dried on the slide, crystallization presents as a fern-like appearance, with branching of the “ferns.” Ferning is scored on a scale of 0 (no fern formation) to 3 (significant fern stems) (Moghissi, 1976; WHO, 2010). The cervical mucus is rated as good mucus which favors sperm penetration, or unfavorable (Moghissi, 1976; Bush et al., 1997; WHO, 2010).
The mucus smear is also examined for the presence of sperm. It is desirable to see 10 or more sperm per high power field examined. Additionally, the motility of the sperm in the mucus is rated as progressive, motile but nonprogressive, or immotile. The PCT is negative if no sperm are found in the mucus. Rapidly motile sperm seen in the cervical mucus some 9–14 h after intercourse indicates that the cervical mucus is good quality and not hostile to sperm. It is then assumed that sperm would sufficiently progress through the cervix and into the uterus and fallopian tubes (Moghissi, 1976; Bush et al., 1997; WHO, 2010). Considering the results, the physician will interpret a negative PCT to result from incorrect midcycle timing, possible lack of intravaginal ejaculation, ejaculatory dysfunction, and abnormal semen analysis (if an analysis had not been previously performed). A negative PCT should be repeated to confirm these findings.
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Reference work2018, Encyclopedia of Reproduction (Second Edition)Grace M. Centola
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How to set up an andrology laboratory for a fertility center?
2024, Handbook of Current and Novel Protocols for the Treatment of InfertilityDe Munck Neelke, Ibrahim El-Khatib
Cervical mucus/sperm interaction assay
This is a simple test that provides important information about female hormonal status and sperm function. An aspirate of cervical mucus is retrieved within 30 min of intercourse at midcycle. The mucus is then examined microscopically for sperm count and motility, and mucus features such as viscosity and ferning.
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Book2024, Handbook of Current and Novel Protocols for the Treatment of InfertilityDe Munck Neelke, Ibrahim El-Khatib
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Assisted Reproduction
2018, Encyclopedia of Reproduction (Second Edition)Grace M. Centola
Introduction
Determination of the capacity of the sperm to pass through the woman’s cervical mucus at the time of intercourse is an important adjunct for clinicians to use in diagnosis and management of the infertile couple. The choice of which additional test(s) to perform, and when to perform them, are dependent on the initial evaluation of the male and female partners.
With natural conception, the sperm are deposited at the cervix, must swim through the cervical mucus into the uterus, and pass into the oviducts or fallopian tubes to arrive at the site of fertilization. Since the cervical mucus is the first barrier for the sperm entering the female reproductive tract, assessment of the interaction between the sperm and the cervical mucus can be an important step in fertility diagnostics.
An in vivo test of sperm–cervical mucus interaction is referred to as the postcoital test (PCT), Sims test, Sims–Huehner test, or Huehner test. In vitro laboratory assessment of sperm–cervical mucus interaction is referred to simply as a simple slide test or Kremer Test, and the capillary tube test or Kurzrock–Miller test (Mortimer, 1994; WHO, 2010).
Cervical mucus is conducive to sperm penetration only for a short time at the middle part of the female’s ovulation cycle, from approximately day 9 of a normal 28-day cycle to the day of ovulation (WHO, 2010). At most times during a woman’s cycle, the cervical mucus is thick and does not allow easy penetration by motile sperm. However, at midcycle, under the influence of hormones such as estrogen, the cervical mucus changes, becoming thinner and more abundant allowing easy passage of the motile sperm (WHO, 2010). It is at the midcycle time when both the quality of the cervical mucus and the activity of the sperm can be assessed. “Spinnbarkeit” is a term used to describe the elasticity or stretchability of the mucus, and “ferning” is the visual appearance of midcycle cervical mucus that is dried on a glass slide. Both Spinnbarkeit and ferning show characteristic patterns in midcycle cervical mucus as compared to other times during a woman’s cycle. Abnormal amount and quality of midcycle cervical mucus is a cause for concern. Abnormal numbers and/or motility of sperm in normal midcycle cervical mucus are also a cause for concern. Both may be indications to attempt to improve the mucus with medications, or bypass the hostile cervical mucus to deposit motile sperm directly into the uterus (intrauterine insemination; IUI) or other forms of assisted reproduction which are very common treatment options.
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Reference work2018, Encyclopedia of Reproduction (Second Edition)Grace M. Centola
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Female Reproduction
2018, Encyclopedia of Reproduction (Second Edition)Mala Mahendroo, Shanmugasundaram Nallasamy
In Non-pregnancy
The cervical epithelium functions to provide a structural and an immunoprotective barrier as well as produce a cycle specific mucosal composition to regulate fertility. The epithelium produces junctional barrier proteins, cytokines, chemokines, antimicrobials, pattern recognition receptors and protease inhibitors to achieve these functions. Epithelial cell proliferation and the properties of their mucosal secretions undergoes significant changes during the menstrual cycle. These properties of mucus influence sperm motility and survival within the female reproductive tract thus influencing overall fertility (Martyn et al., 2014). The mucus is mostly composed of water, mucins, ions, antimicrobials and various other factors. Mucins are large glycosylated polymers that alter viscoelastic properties of the cervical mucus. Five different mucin proteins are known to be secreted by the cervical epithelia (Martyn et al., 2014). At the time of ovulation, the cervical mucus has low viscosity with marked spinnbarkeit and a high ionic concentration capable of forming a clear fern pattern. During this time, mucin polymers are arranged in such a way to permit sperm movement. The mucus turns highly viscous with low spinnbarkeit and exhibits no fern pattern at other stages of cycle to prevent sperm entry (Jequier, 2009) (Fig. 3). The functions of the cervical epithelia and its mucus are well conserved between species including human and mice.
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Reference work2018, Encyclopedia of Reproduction (Second Edition)Mala Mahendroo, Shanmugasundaram Nallasamy
Chapter
Human Papillomavirus (HPV)
2014, Animal BiotechnologyMausumi Bharadwaj Dr, ... Ravi Mehrotra Prof.
Cervical Cancer
Anatomy of the Female Pelvis
The cervix (from the Latin for “neck”) connects the upper body of the uterus to the vagina. The cervix is the lower one-third of the uterus, and is composed of dense, fibromuscular tissue lined by two types of epithelium: squamous epithelium and columnar epithelium. It is about 3 cm in length and 2.5 cm in diameter. The endocervix (upper part close to the uterus) is covered by glandular cells, and the ectocervix (lower part close to the vagina) is covered by squamous cells. The stratified squamous epithelium covers most of the ectocervix and vagina. It’s lowest (basal) layer, composed of rounded cells, is attached to the basement membrane, which separates the epithelium from the underlying fibromuscular stroma. The columnar epithelium lines the cervical canal and extends outwards to a variable portion of the ectocervix. The transformation zone refers to the place where these two regions of the cervix meet. The original squamocolumnar junction (SCJ) appears as a sharp line, with a step produced by the different thicknesses of the columnar and squamous epithelia. The cervix produces cervical mucus that changes in consistency during the menstrual cycle to prevent or promote pregnancy. During childbirth, the cervix dilates to allow the baby to pass through. During menstruation, the cervix opens a small amount to permit passage of menstrual flow.
Cervical cancer forms in the cervix, the lower end of the uterus, and is preceded by a precancerous condition called cervical intraepithelial neoplasia (CIN), which may or may not develop into cancer (Das et al., 2008). The progression of cervical cancer is a multi-step process. Initially, normal cells undergo precancerous changes and ultimately develop into cancer cells. These precancerous conditions include cervical intraepithelial neoplasia (CIN), squamous intraepithelial lesion (SIL), and dysplasia. It takes several years to develop into an invasive cancer, and is preventable if detected early (Figure 6.1). Thus, cervical cancer provides an excellent human model for studying the process of carcinogenesis in vivo.
Historical Overview
Cervical cancer is a major health concern for all women. In most developing countries, cervical cancer is the leading female malignancy and a common cause of death among middle-aged women. In developed populations with good awareness and screening options, invasive cervical cancer is a relatively rare condition, whereas its precursors and the equivocal cytological results represent a major health burden (zur Hausen, 1982; zur Hausen, 2002; Parkin and Bray, 2006; Heins Jr. et al., 1958; Gasparini and Panatto, 2009).
The disease has been known since ancient times, however, the cause was unknown. In 400 BCE, the Greek physician Hippocrates wrote about the disease and even attempted to treat the cancer with a procedure known as the trachelectomy, but could not eradicate the cancer.
Mistaken Theories of Causation
Epidemiologists working in the early 20th century noted that cervical cancer behaved like a sexually transmitted disease and summarized it as follows:
1.
: Cervical cancer was common in female sex workers.
2.
: For centuries, doctors were confused by the cause of cervical cancer. The first theory rose to prominence in 1842 in Florence, when a doctor noticed that married women and prostitutes were susceptible to cervical cancer, but nuns had a very low incidence of the cancer (Rigoni in 1841). However, because nuns did suffer from breast cancer, it was incorrectly determined that the cause of both diseases was tight corsets.
3.
: It was more common in the second wives of men whose first wives had died from cervical cancer.
4.
: It was rare in Jewish women.
5.
: In 1935, Syverton and Berry discovered a relationship between rabbit papillomavirus (RPV) and skin cancer in rabbits (HPV is species-specific, and therefore cannot be transmitted to rabbits).
This led to the suspicion that cervical cancer could be caused by a sexually transmitted agent. Initial research in the 1940s and 1950s put the blame on smegma. For example, (Heins Jr. et al., 1958) during the 1960s and 1970s it was suspected that infection with herpes simplex virus was the cause of the disease. HSV was seen as a likely cause because it was known to survive in the female reproductive tract, and to be transmitted sexually in a way compatible with known risk factors, such as promiscuity and low socioeconomic status. Herpes viruses were also implicated in other malignant diseases, including Burkitt’s lymphoma, nasopharyngeal carcinoma, Marek’s disease, and Lucké renal adenocarcinoma. HSV was recovered from cervical tumor cells. In the 1970s, the prevailing thought in American medicine was that cervical cancer was linked to herpes, which was also incorrect (Heins Jr. et al., 1958; Gasparini and Panatto, 2009; Scotto and Bailar 3rd, 1969; Syverton and Berry, 1935).
The First Breakthrough
While the majority of doctors were completely in the dark, in the 1930s, Dr. Richard Shope of the Rockefeller University studied wild rabbits that had developed “horns,” which upon further analysis, was caused by a virus that could be transmitted. This research eventually led to the discovery that cervical cancer was caused by a papillomavirus.
Dr. George Papanicolaou’s famous smear test was developed in the United States and was introduced into practice in the 1940s. He developed his cervical cytology research into an effective screening test, it entered widespread use in the UK as early as the 1950s, and a national cervical screening program was introduced in the UK in 1988; this effectively solved the screening problem. In 1951, the first successful in vitro cell line (HeLa) was derived from biopsies of the cervical cancer of Henrietta Lacks (Gasparini and Panatto, 2009; Syverton and Berry, 1935; Walboomers et al., 1999).
Nobel Prize for Discovering HPV
Dr. Shope paved the way for Dr. Harald zur Hausen’s work in the 1980s. The link between genital HPV infections and cervical cancer was first demonstrated in the early 1980s by Harlad zur Hausen, a German virologist who cloned two of the most important high-risk HPV types (16 and 18) and showed the association between HPV infection and cervical cancer (Gasparini and Panatto, 2009). He did tremendous research on cancer of the uterine cervix (zur Hausen, 2002) and received the Nobel Prize in Physiology or Medicine (2008) for his discovery of HPV. This association is now well established by a large number of clinicoepidemiological, molecular, and experimental studies on HPV.
In 1988, the Bethesda System for reporting Pap results was developed, and in 2006 the first HPV vaccine was approved by the FDA (Das et al., 2008; Donnelly et al., 2005; Frazer, 2004; McMurray et al., 2001).
Cancer research is becoming multidisciplinary. Complex structural and therapeutic problems require synergistic approaches employing an assortment of molecular cancer biologies that synthesize the findings of three decades of recent cancer research and propose a conceptual framework that illuminates the conclusions of these discoveries. In the following sections, this chapter will continue to provide a detailed overview of various processes, and will cover the recent trends in the field of cervical cancer management, including the technologies available for early detection and cures. It also describes HPV biology, including the role of tumor suppressor genes and oncogenes used in the diagnosis and prognosis determination of cervical cancer. It will update various methods of cytology screening, including visual inspection of the cervix, the Pap test, colposcopy, detection of high-risk HPV16 and -18, and treatment with ultimate success in reducing cervical cancer mortality (zur Hausen, 2002; Hussain et al., 2012). Finally, development of the HPV vaccine is outlined.
Most importantly, the world has witnessed decreased incidence rates for cervical cancer in countries with organized screening. However, increased rates of cervical cancer have been reported in several populations due to failure to implement cytology-based screening programs. Therefore, complete awareness and knowledge of current diagnostic approaches of cervical cancer are important for tackling this fatal disease. Keeping this in mind, the following sections will certainly help clinicians, virologists, cytologists, epidemiologists, and public health specialists in understanding all clinical, molecular, and epidemiological aspects of cervical cancer. Offered are many pedagogical features such as cervical cancer epidemiology, screening, HPV biology, and vaccine development, which should help readers hone their analytical abilities and think objectively about a number of complex biological processes.
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Book2014, Animal BiotechnologyMausumi Bharadwaj Dr, ... Ravi Mehrotra Prof.
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Campylobacter
1990, Diagnostic Procedure in Veterinary Bacteriology and Mycology (Fifth Edition)J.F. Prescott
Collection of Cervical Mucus
The test is convenient and accurate if animals are tested between 2 and 7 months after infection, are not in estrus, and no blood is present. The test is done on a herd basis, so that 10 cows in the above category are tested, or 20 if no such selection is possible.
A number of methods have been described. The following simple procedure is given by Laing and associates (6). The mucus is collected by means of a glass tube about 50 cm in length and 1 cm in diameter. This pipette has a slight bend about 10 cm from one end, which is lightly plugged with cotton wool at one end; the other end is also lightly plugged with cotton wool, to act as a stop for the mucus. Before use, the pipettes are wrapped in greaseproof paper and sterilized by autoclaving.
A piece of rubber tubing about 50 cm long is attached to the straight end of the pipette, the plug at the bent end is removed, and this end is passed into the vagina as far as the cervix. Then by sucking on the free end of the rubber tubing and moving the pipette backward and forward in the vagina, one can loosen a portion of mucus and draw it into the pipette. The suction is maintained as the pipette is withdrawn from the vagina; a small, sterile rubber stopper is inserted into the pipette and a label identifying the animal is attached. In the laboratory, the mucus is forced from the pipette into a test tube by applying pressure on the cotton wool plug at the straight end of the pipette with a length of flexible wire.
Hoerlein and Kramer (7) describe the collection of cervical mucus using sterile artificial insemination pipettes (large bore 1.5 ml) introduced through a 12-in-long (8-mm diameter) Pyrex® speculum. The mucus is drawn into the pipette by means of a small syringe attached by a short length of rubber tubing. If mucus cannot be cultured within 4 hr after collection, it is recommended that it be frozen on dry ice while in transit to the laboratory.
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Book1990, Diagnostic Procedure in Veterinary Bacteriology and Mycology (Fifth Edition)J.F. Prescott
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Female Reproduction
2018, Encyclopedia of Reproduction (Second Edition)Mala Mahendroo, Shanmugasundaram Nallasamy
In Pregnancy
The cervical epithelium serves as a physical barrier of protection, provides immune surveillance and modulates the local tissue steroid environment to maintain pregnancy or initiate cervical ripening for parturition (Timmons et al., 2010). Through pregnancy, the epithelium undergoes extensive proliferation followed by differentiation (Fig. 4). In the latter part of pregnancy, the upper layers of terminally differentiated epithelia are laden with mucin – secreting vacuoles. In mice, the thickness of this mucosal epithelium reaches a maximum at the time of birth on day 19 of gestation and regresses during the postpartum period. Mucus provides a physical and immune- barrier, while epithelial cell junctions such as tight junctions, adherens junctions and desmosomes are formed between adjacent cells in the pericellular space and serve to regulate the movement of molecules between cells (Timmons et al., 2010). Further, the barrier function of epithelium is complemented by the structure of the pericellular matrix and its constituents. In addition, the cervical epithelia play a role in tissue hydration through the expression of aquaporins. Similar to non-pregnancy, the epithelium at pregnancy also produces cytokines, chemokines, antimicrobials, pattern recognition receptors and proteases inhibitors to achieve its functions. While the cervical epithelia and the mucus it secretes have a similar function in most species, primates including humans are unique in that during pregnancy, the cervical glands and epithelium secrete a thick mucus which fills the endocervical canal to form a plug. The cervical mucus plug is present till term and will be shed only around the time of parturition. Its unique composition provides physical as well as immunological barrier function (Becher et al., 2009).
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Reference work2018, Encyclopedia of Reproduction (Second Edition)Mala Mahendroo, Shanmugasundaram Nallasamy
Related terms:
Progesterone
Luteinizing Hormone
Monospecific Antibody
Progestin
Cervix
Menstrual Cycle
Ovulation
Phytoestrogen
Contraceptives
Semen
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189640 | https://pmc.ncbi.nlm.nih.gov/articles/PMC9605318/ | Factors Influencing Personalized Management of Vestibular Schwannoma: A Systematic Review - PMC
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Factors Influencing Personalized Management of Vestibular Schwannoma: A Systematic Review
Bruno Sergi
Bruno Sergi
1 Department of Head, Neck and Sensory Organs, Università Cattolica del Sacro Cuore, 00168 Rome, Italy
2 Unit of Otorhinolaryngology-Head and Neck Surgery, Fondazione Policlinico Universitario A. Gemelli IRCCS, 00168 Rome, Italy
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1,2, Stefano Settimi
Stefano Settimi
1 Department of Head, Neck and Sensory Organs, Università Cattolica del Sacro Cuore, 00168 Rome, Italy
2 Unit of Otorhinolaryngology-Head and Neck Surgery, Fondazione Policlinico Universitario A. Gemelli IRCCS, 00168 Rome, Italy
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1,2,, Gaia Federici
Gaia Federici
3 Department of Otolaryngology-Head and Neck Surgery, University Hospital of Modena, University of Modena and Reggio Emilia, 41125 Modena, Italy
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Costanza Galloni
3 Department of Otolaryngology-Head and Neck Surgery, University Hospital of Modena, University of Modena and Reggio Emilia, 41125 Modena, Italy
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Carla Cantaffa
3 Department of Otolaryngology-Head and Neck Surgery, University Hospital of Modena, University of Modena and Reggio Emilia, 41125 Modena, Italy
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Eugenio De Corso
2 Unit of Otorhinolaryngology-Head and Neck Surgery, Fondazione Policlinico Universitario A. Gemelli IRCCS, 00168 Rome, Italy
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Daniela Lucidi
3 Department of Otolaryngology-Head and Neck Surgery, University Hospital of Modena, University of Modena and Reggio Emilia, 41125 Modena, Italy
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1 Department of Head, Neck and Sensory Organs, Università Cattolica del Sacro Cuore, 00168 Rome, Italy
2 Unit of Otorhinolaryngology-Head and Neck Surgery, Fondazione Policlinico Universitario A. Gemelli IRCCS, 00168 Rome, Italy
3 Department of Otolaryngology-Head and Neck Surgery, University Hospital of Modena, University of Modena and Reggio Emilia, 41125 Modena, Italy
Correspondence: stefano.settimi@unicatt.it; Tel.: +39-0630154439
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Dueng-Yuan Hueng: Academic Editor
Received 2022 Jul 23; Accepted 2022 Sep 25; Collection date 2022 Oct.
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PMCID: PMC9605318 PMID: 36294756
Abstract
Management of vestibular schwannoma (VS) is a complex process aimed at identifying a clinical indication for fractionated stereotactic radiotherapy (sRT) or microsurgical resection or wait and scan (WS). The aim of the review was to clarify which patient and tumor parameters may lead to different therapeutic choices, with a view to a personalized VS approach. A systematic review according to Preferred Reporting Items for Systematic Review and Meta-Analysis criteria was conducted between February and March 2022. The authors defined six parameters that seemed to influence decision-making in VS management: 1-incidental VS; 2-tumor size; 3-tumor regrowth after sRT; 4-subtotal resection; 5-patients’ age; 6-symptoms. The initial search yielded 3532 articles, and finally, 812 articles were included. Through a qualitative synthesis of the included studies, management strategies were evaluated and discussed. An individualized proposal of procedures is preferable as compared to a single gold-standard approach in VS decision-making. The most significant factors that need to be considered when dealing with a VS diagnosis are age, tumor size and hearing preservation issues.
Keywords: vestibular schwannoma, acoustic neuroma, translabyrinthine, retrosigmoid, middle cranial fossa, stereotactic radiotherapy, radiosurgery, gamma knife, quality of life
1. Introduction
Vestibular schwannomas (VS) account for 8%–10% of all intracranial neoplasms and are the most common tumors of the cerebellopontine angle . Current management strategies vary considerably across centers and countries and decision-making has progressively become more complex [2,3]. Tumor parameters, including initial size and interval growth on serial imaging (often >2 mm between images), are commonly associated with the decision for treatment. Major advancements have been made in VS therapy: fractionated stereotactic radiotherapy or radiosurgery (sRT) provides a treatment option, alternative to the microsurgical resection in selected cases. Microsurgery, however, remains the mainstay of treatment for large tumors, the main approaches being the translabyrinthine and the retrosigmoid ones. Retrospective studies of large cohorts (up to 8330 patients collected on a 7-year US registry analysis) demonstrated that 48–59% of patients underwent microsurgery and 21–24% underwent radiotherapy, with surgical resection correlating with younger age and larger tumor size [4,5,6].
Increasing interest in quality of life (QoL) measurements arose in VS treatment in the past decade [7,8]. Several reports indicated that surgical intervention for VS has a significant impact on social functioning. Most VS patients have, in fact, minimal preoperative disability and treatment of VS is aimed at dealing with the disease, rather than patient symptoms per se. Adequate counseling is necessary and it must give realistic expectations. Although several cornerstones of diagnosis and therapy are shared among different centers, there are still controversies related to the characteristics of tumors and patients, as well as institutional preferences. Personalized medicine is a medical model that separates patients into different groups, with final strategies being tailored to the individual patient, based on their predicted response. The aim of the present review was to clarify which patient and tumor’s parameters may lead to different therapeutic choices, with a view to a personalized approach.
2. Materials and Methods
This review was conducted in accordance with the Preferred Reporting Items for Systematic Review and Meta-Analysis (PRISMA) process to identify published clinical articles regarding VS management. Manuscripts were screened by MEDLINE database, Cochrane review, LILACS, Web of Science and Google Scholar. Parentheses and Boolean operators (AND, OR) were applied to create conjunctions. The search was performed between February and March 2022 based on MeSH terms, as follows: [(acoustic schwannoma[MeSH Terms]) OR (acoustic neurinoma[MeSH Terms]) OR (acoustic neuroma[MeSH Terms])) AND ((surgical[MeSH Terms]) OR (surgery[MeSH Terms]) OR (radiotherapy[MeSH Terms]) OR (cyberknife radiosurgery[MeSH Terms]) OR (gamma knife radiosurgery[MeSH Terms]) OR (radiosurgery, stereotactic[MeSH Terms]) OR (retrosigmoid[All Fields]) OR (translabyrinthine[All Fields]) OR (fossa, middle cranial[MeSH Terms]) OR (observation[MeSH Terms])].
In the first screening, authors independently read the titles and abstracts of all articles performing the first selection, being as inclusive as possible. Any disagreements were resolved by consensus. In the second phase, the full articles were collected for the analysis, based on the following exclusion criteria: papers with no full text available, those written in languages other than English, Italian, French and Spanish, those regarding Neurofibromatosis 1-2 (NF 1-2) or other histological entities different from Schwannoma and affecting the internal auditory canal (IAC), those regarding Schwannomas of the seventh cranial nerves, case reports, systematic reviews, metanalysis, editorial letters, anatomical studies, surgical/technical notes, basic sciences and animal model studies. Moreover, only studies published from January 2001 to April 2022 were screened.
We excluded all the articles that did not meet the inclusion criteria or deal directly with the issue investigated. Additional studies were manually identified from the reference lists of retrieved literature. The authors extracted data from included articles using a standardized template and collected them into a computerized database. The authors, through a qualitative synthesis of the included studies, defined six parameters that seemed to influence decision-making in VS management, as follows: 1-incidental VS; 2-tumor size; 3-tumor regrowth after sRT; 4-subtotal resection; 5-patients’ age; 6-symptoms. Management strategies according to these issues were carefully evaluated and discussed.
3. Results and Discussion
In total, our search yielded 3532 articles. A further manual check of the references included in the articles was performed, adding 75 articles. We excluded 703 articles for not dealing directly with the investigated issue, 931 articles for publication year < 2001, 177 records for full text not available, and 98 for language different than the included ones. Finally, 1698 full text articles were assessed for eligibility and 154 of those were excluded for describing NF 1–2 cases, 95 for histologic features different from Schwannoma, 11 for describing Schwannomas of the seventh cranial nerves and 626 for article type different from the included ones. The details of the systematic search are shown in Figure 1.
Figure 1.
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Flowchart of article search and selection according to the PRISMA criteria.
3.1. Incidental VS
The estimated incidence of incidental VS is around 0.2–0.3%, while it is higher in autoptical studies (around 1–2.4%) . A completely asymptomatic VS found in a brain scanning performed for other reasons represents a clinical challenge . On one hand, several studies proved that small, asymptomatic VS do not usually tend to grow, compared with larger and symptomatic ones, as described by Carlson et al. on a 38-patients’ cohort . On the other hand, the best surgical results in terms of both facial function and hearing preservation are obtained in the population affected by small, asymptomatic VS, as demonstrated on a subset of 153 patients operated on by retrosigmoid approach . The growth rate and time to treatment does not seem to differ between asymptomatic small VS versus symptomatic and larger ones, The survival-free tumor growth/treatment was 54% after 5 years. Despite this growth, very few patients experienced new symptoms. Moreover, as discussed below in the text, there is a paucity of prognostic factors that can predict growth and symptoms progression .
3.2. Tumor Size
Koos classification includes Grade I or intracanalicular tumor; Grade II orsmall tumor protruding at CPA, up to 20 mm; Grade III or tumor occupying the CPA, with no displacement of the cerebral trunk, up to 30 mm; Grade IV or large tumors, with displacement of the trunk or cranial nerves, >30 mm. Even though the VS incidence has not significantly increased over the last decade, what surely has increased is the rate of small VS at diagnosis; this is mainly attributable to recent improvements in imaging techniques, particularly contrast-enhanced MRI, which is nowadays capable of detecting tumors as small as 2–3 mm ; this led to a trend change in VS management towards an increasingly conservative approach . A recent retrospective analysis of the US Surveillance, Epidemiology, and End Results (SEER) database revealed that the rate of VS managed by means of watchful waiting has increased over time, especially concerning older patients and those with smaller tumors, and predicted that by the year 2026, half of newly diagnosed VS will be initially approached with observation alone .
According to the EANO guidelines, watchful waiting with serial MRI scans is the preferable option for incidental and asymptomatic VS . Of note, tumor size is not among the factors dictating treatment versus observation. Of course, one must bear in mind that the larger the lesion is, the higher the probability to cause symptoms. One of the main arguments urged by those who favor observation is the fact that approximately 58 to 71% of small VS are stable in size over time, as demonstrated by Fieux et al. on an 1105 cohort of VS patients discussed in multidisciplinary meetings . Also, tumor growth does not necessarily prompt switching to active treatment, in fact, failure of conservative treatment for intracanalicular VS is reported to be as low as 15% even in studies with 10-year follow-up .
One recent retrospective study reported that a tumor size larger than 7 mm at diagnosis was associated with an increased risk of tumor growth during observation . Many reports investigated the influence of initial tumor size on the extent of tumor growth over time, however, not all of them agreed that larger tumor size at diagnosis is associated with a higher risk of growth and those that do often use different cutoff sizes to define the association [18,19].
Other predictors of VS growth known from the literature include IAC filling, cystic and hemorrhagic features within the tumor, hormonal treatment, extracanalicular component greater than 20 mm, young age at diagnosis and NF-2. Most authors suggest to adopt a watchful waiting approach for small, asymptomatic lesions and switch to active treatment in case of tumor growth greater than 2–3 mm per year and/or significant worsening of symptoms. Interestingly, it has been demonstrated that the rate of post-operative complications is not significantly different when comparing patients undergoing primary surgery and those undergoing surgery due to failure of conservative management as demonstrated in an epidemiological study by Schmidt et al. . On the other hand, advocates of upfront surgical treatment for small VS argue that post-operative functional outcomes are far better for small lesions with respect to larger ones. In fact, small tumor size is a well-known favorable prognostic factor for both facial nerve (FN) function and serviceable hearing preservation [11,14,21,22,23,24].
Comparative studies on the three viable management options for small VS, namely observation, radiosurgery and microsurgery, have shown similar results in terms of tumor control and FN function preservation. As far as hearing function is concerned, while it is generally agreed upon that short-term hearing preservation in small VS is better in patients undergoing a conservative management than in patients subjected to active treatment, whether it is surgery or stereotactic radiotherapy [25,26], data on long- term hearing preservation are more debatable, with some studies showing that hearing function decline is faster in the observation group after the first 2 years of follow up, while it predictably remains stable over time after surgery, as measured at 10 and 15 years .
sRT is a viable treatment option for small (Koos grade I and II) VS as an alternative to microsurgery and it has been suggested to be associated with a lower risk of treatment-related morbidity for small and medium-sized VS as compared to microsurgery [27,28].
Conservative management is not a viable option for large VS, nor is sRT, especially if a mass effect is present. There have been, however, reports on the outcomes of sRT for large VS that are not candidate to surgical excision. Results are variable across the literature, with tumor control rates being directly associated to tumor size. For instance, in a retrospective study by Huang and colleagues on 35 patients affected by large VS large treated by gamma knife radiosurgery, it was observed that tumor volume equal to or larger than 3 cm was a significant factor predictive of treatment failure .
3.3. Tumor Regrowth after sRT
Gamma knife stereotactic radiosurgery and fractionated stereotactic radiotherapy (sRT) have proved as valuable alternatives to microsurgical excision since the early 1990s. Nevertheless, these options have different goals: microsurgery aims at complete tumor removal, while radiation therapy aims at tumor control, and growth prevention . Nakamura et al. suggest a follow-up neuroimaging based on MRI contrast-enhanced (T1- and T2-weighted sequences) at 3, 6 and 12 months during the first year, every 6 months during the second year and yearly thereafter. According to Yomo et al. , response to radiation therapy can be classified as: (1) regression: more than 10% volume reduction; (2) stabilization: volume variation within 10%; (3) enlargement: more than 10% volume increase, not requiring further intervention; (4) failure: uncontrollable tumor growth requiring further intervention and/or appearance of disabling side effects.
In a series of 78 patients who underwent sRT for VS and were observed up to 63 months, Nakamura et al. classify changes in tumor volume as: (1) temporary enlargement (41%); (2) no change or sustained regression (34%); (3) alternating enlargement and regression (13%); (4) continuous enlargement (12%). Alternating enlargement and regression can be explained by repeated extension and collapse of the cystic component of the tumor. The VS enlargement can be temporary, in this case, tumor tends to growth within the first post-radiation year, regressing spontaneously within 2 years .
There are three main factors involved in tumor enlargement after radiation therapy: solid expansion of the tumor, tumor necrosis and tumor cyst formation. Therefore, it is strongly recommended [30,31,33] to try to avoid reintervention during the first 2 years after radiation therapy. As a matter of fact, cranial nerves are more susceptible to surgical damage during the first year. Moreover, the interpretation of MR images in the early period after radiation therapy can be confusing.
Obviously, surgery is inevitable in case of significant complications associated with tumor growth or radiation toxicity, such as brainstem compression or hydrocephalus, as illustrated by Slattery et al. in a review regarding the House Ear Clinic experience . In case of failure after radiation therapy for VS, microsurgical resection is advocated. Translabyrinthine approach is usually preferred, as the chance of preserving hearing in a patient who has undergone radiation therapy is very poor . In a study by Roche et al. the difficulties observed during 23 surgical resections after failed radiation therapy were analyzed, and the authors reported that tumors were more difficult to dissect in 43% of cases in comparison with size-matched naïf tumors. Severe FN and brainstem adherences were the main difficulties encountered during surgery. Moreover, lack of color change between FN and tumor contributes to make dissection harder . Therefore, it is not surprising that several studies have demonstrated how cranial nerve outcomes for patients undergoing microsurgery after prior radiosurgery are relatively poor [33,35,36].
3.4. Planned Sub-Total Resection and Residual Tumor Management
The introduction of sRT allows the surgeon to better control tumor growth while avoiding the morbidity associated with surgery. In this scenario, treatment of large and adherent tumors can consist of surgery with the aim of at least reducing the tumor to a size suitable for sRT and removing as much tumor as can be safely removed, paying particular attention to preventing FN iatrogenic injury [37,38,39,40,41,42].
Current goals of modern treatment include both maintaining long-term tumor control and maximizing FN function and QoL. FN dysfunction after surgery, in fact, has a significant impact on patients’ QoL and more emphasis is now being placed on preserving FN function at the cost of leaving residual tumors behind [8,43,44,45,46].
The strategy of sub-total resection (STR) aims to debulk enough tumor volume to relieve symptoms caused by mass effect and provide a more favorable target size for adjuvant sRT . A less frequently reported outcome is the near-total resection (NTR) where the residual tumor volume is microscopic in size [48,49]. Chen et al. defined STR as when 2–5% of the tumor is left behind during surgery as noted by the surgeon and if evident on 1-yr postoperative MRI; furthermore, they defined NTR as <2% of the tumor or tumor capsule left behind during surgery, as evident from the surgeon’s subjective observation and if it is manifest or absent on 1-yr postoperative MRI. Although it has been reported that some residual tumors do not grow, progressive tumor growth is a concern in patients who have STR [37,41,51,52,53,54,55,56,57].
STR and NTR in most centers are sometimes planned event, but in most of cases they represent a decision made intraoperatively as to avoid the risk of a cranial nerve or brain stem injury. Few published studies have examined the growth rates of residual tumors left in the surgical bed. Rosenberg et al. reported a postoperative growth rate of 0.35 mm/year for subtotal resection (STR) compared with 0.90 mm/year for patients who did not undergo surgical intervention, as measured on an 80 patients’ cohort during a 25-year observation. Of the residual VS, the authors reported that 68% did not grow or regressed compared with 42% in the non-surgical group. Bloch et al. compared patients having undergone NTR versus STR; they reported a significant difference in recurrence, with a 3% recurrence rate in the NTR group compared with 32% in the STR group. The mean time to recurrence was 3 years. The authors concluded that STR should be avoided when possible due to the higher rate of recurrence. Syed et al. described that VS recurrence was seen in 3 out of 42 treated patients (7.1%) and all had undergone an STR. No recurrence was registered in the sub-group of patients treated with NTR. The mean growth rate for these 3 cases was 0.77 mm/year. Two patients demonstrated significant regrowth within a 2-year period. The third patient showed minimal regrowth only after >8 years of follow-up. Finally, Strickland et al. reported in their recent re-examination that, among patients treated with STR, regrowth was observed in 12 patients (36.3%), at an average of 23.7 months (range, 6–44 months). The NTR cohort did not experience tumor recurrence in their experience. At the time of regrowth, the tumor size increased at an average of 3.83 mm when compared with the most recent stable imaging (range, 2–8 mm). Despite the intentional STR trend, the authors stated that their philosophy is to maximize surgical resection to achieve a microscopic gross total resection whenever possible, and reserve STR or NTR for those tumors that, because of cranial nerve adherence, represent a risk for facial nerve preservation in case of further removal .
Concerning the functional outcomes, and focusing on the postoperative FN function, Bloch et al. reported House–Brackmann score of I–II in 81% of the 79 treated patients (opered by retrosigmoid, translabirinthine and middle cranial fossa approaches), with no significant differences between NTR and STR. Starnoni et al. reported in their recent meta-analysis the follow-up clinical data on FN function from eight included studies [62,63,64,65,66,67,68,69] and a random-effects pooled analysis showed an FN preservation rate (HB grade I–II) of 96.1% (95% CI 93.7–98.5%) after a combined microsurgical (STR) and sRT approach. Chen and colleagues concluded that the decision to leave behind a tumor attached to the FN can be justified if the incidence and the rate of tumor regrowth are acceptably low (based on tumor site, amount of tumor left behind, tumor vascularization and age) and if there is a significant benefit in terms of FN preservation. Most authors [50,59,60,61,65,66] suggest that, given the good growth control, the FN preservation and the low number of complications, the surgical approach including STR or NTR, followed by sRT in case of documented regrowth, has an excellent clinical and functional outcome, while still achieving a tumor control rate comparable to that of total surgical resection.
3.5. Patient’s Age
Many authors suggest the need for personalized counselling on VS management, taking into account age, comorbidities, life expectancy, and the risk of any short- or long-term side effects . Varieties of demographic factors, especially age, are linked to VS size at diagnosis and to the initial treatment plan offered. Older age is associated with smaller tumors, with an observational approach when feasible, and, when pursuing treatment, with candidacy to radiation therapy . While surgery may cause sudden neurologic impairment, radiation can affect neurologic function even after many years. For this reason and in the event of a tumor regrowth or a malignant transformation, some authors recommend radiation therapy only in older patients [3,72,73,74].
In some cases, surgery is necessary even in elderly patients: the most common indications are progressive tumor growth up to large size causing brainstem compression and disabling neurological symptoms, and regrowth after previous treatment (both radiosurgery and STR). Recent evidence suggests that this population can be subdivided by age or overall health status or frailty. The concept of frailty has gained much traction in recent years as studies have identified its use to be more predictive of postoperative outcomes, compared to age alone. The analysis found that the frail group had statistically significant higher rates of readmission, postoperative infection, facial paralysis, urinary tract infection, and hydrocephalus . If elderly patients are more prone to develop general complications after surgery (including acute cardiac events, stroke, bleeding, postoperative delirium, prolonged inpatient stays as well as mortality), complications specific to VS and its removal, including cerebrospinal fluid leak or FN dysfunction, were not shown to be significantly higher, as shown on a population of 452 patients divided by age cutoff > 70 years [76,77]. sRS results proved particularly favorable in elderly patients in terms of overall outcome and reliable tumor control. A study by Sergi et al. recently described an algorithm for tumor management, which considered an age cutoff > 65 years for sRT candidacy in patients with growing tumors (Figure 2) .
Figure 2.
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Algorithm proposed by Sergi et al. to predict individualized decision-making in VS management.
3.6. Symptoms
3.6.1. Dizziness
Vestibular symptoms are present in 40–75% of VS patients at the time of the diagnosis [78,79], but they are rarely the presenting symptom. Compensatory mechanisms mediated by vision and contralateral vestibular apparatus probably play a crucial role in delayed presentation . Vestibular symptoms in VS can be due both to vestibular nerve dysfunction and to brainstem compression, in case of tumor growth in cerebello-pontine angle. A classification system was proposed at the Consensus Meeting on Systems for Reporting Results in Acoustic Neuroma (Tokyo, Japan, 2001) : grade I: normal, no dizziness; grade II: occasional and slight dizziness or disequilibrium; grade III: moderate or persistent dizziness or disequilibrium; grade IV: severe, persistent or almost persistent dizziness or disequilibrium, incapacitating and severely affecting the quality of daily life.
Andersen et al. , in a series of 434 patients, described how vestibular symptoms change with tumor size. Smallest tumors tend to be asymptomatic because nerve function is completely preserved. Medium-sized tumors tend to determine an increasing neuropathy, with consequent worsening dizziness and vertigo. Finally, larger tumors are associated with a more complete and stable peripheral loss, allowing better central compensation. In a study by Kentala et al. , in a population of 122 VS patients, 49% of patients had vertigo attacks and 69% of these attacks were mild to moderate. Moreover, this study shows how vertigo secondary to VS differs from vertigo in other peripheral diseases by the absence (63%) or low intensity (18%) of nausea. Nevertheless, there is plenty of evidence in the literature that vestibular symptoms are the most debilitating ones and have a strong negative impact on a patient’s QoL [78,80,82,83]. It is mandatory, therefore, that vestibular symptoms are taken into consideration in the therapeutic management of VS Vestibular symptoms tend to worsen when VS increases in dimensions, while seem to remain stable in case of unchanged tumor dimensions [83,84]; this indicates a favorable prognosis regarding vestibular symptoms in patients with non-growing VS. However, even in case of mild dizziness or unsteadiness, appropriate vestibular rehabilitation it is mandatory .
A metanalysis by Kim et al. indicates that both microsurgery and radiotherapy can lead to improvement in balance outcomes in VS patients, therefore there is no significant advantage relative to vestibular symptoms between these therapeutic options. Similarly, a systematic review showed that overall Dizziness Handicap Inventory (DHI) scores were not statistically influenced by intervention, irrespective of modality (surgery VS sRT). Vestibular ablation, including intratympanic gentamicin and transmastoid labyrinthectomy, could be considered in order to cope with disabling vertigo in patients with VS candidate for observation, at the possible expense of hearing loss . Moreover, intratympanic gentamicin could be performed even before surgery, in order to “pre-habilitate” patients with remaining vestibular function to vestibular loss, reducing postoperative malaise and speed up recovery. The gradual reduction of vestibular function that follows gentamicin instillations allows patients to better get used to it, compared to a sudden complete loss of function as in case of surgical removal . In a study by Yang et al. evaluating intratympanic gentamicin treatment in patients with small VS and intractable vertigo, DHI score decreased significantly after treatment. Though patients experienced residual unsteadiness, they reported excellent relief of stress and depression related to their disabling vertigo.
3.6.2. Tinnitus
The incidence of tinnitus in patients with a diagnosis of VS is reported to vary from 63% to 75%. It is the third most common symptom leading to VS diagnosis, following hearing loss and dizziness, according to a recently published survey by Peris-Celda et al. on a cohort of 1304 patients . While it is clear that hearing impairment is implicated in the pathogenesis of tinnitus not associated to VS, the association of hearing impairment and tinnitus in VS patients is debated. Tumor size seems to be inversely correlated with the incidence of tinnitus and patients with larger tumor size seem to have a higher chance at tinnitus resolution after surgery [90,91].
Lately, as the focus of VS management shifts towards maintaining patients’ QoL, tinnitus has received a great deal of attention, as it is one of the symptoms with the greatest impact on psychological well-being. The presence of tinnitus should be therefore taken into account in the decision-making process . In fact, there have been a number of reports claiming that active treatment, irrespective of the modality, is associated to higher rates of tinnitus improvement/resolution with respect to observation [93,94]. For instance, a study on tinnitus outcome after translabyrinthine surgery reported a statistically significant decrease in the Tinnitus Handicap Inventory (THI) score and in the Visual Analogue Scale severity of tinnitus . However, these results are not consistent across the existing literature up to date. Other studies, in fact, have shown that tinnitus outcome after surgery is unpredictable, as they may stay unchanged or even worsen in a variable proportion of patients. Preservation of preoperative hearing and neurectomy of the cochlear nerve were independently associated with higher rates of tinnitus resolution after surgery in a study by Chovanec and colleagues . Accordingly, Kohno et al. have reported that the prognosis for tinnitus was significantly worse in patients with anatomically preserved cochlear nerves without useful hearing than in the group with severed cochlear nerves and that severing the cochlear nerve was associated with significant efficacy in resolving tinnitus .
Comparisons between hearing sparing versus non-hearing sparing approaches have shown that tinnitus outcomes are better in patients treated by a translabyrintine approach than in those treated by a retrosigmoid approach, confirming the hypothesis that cochlear nerve interruption is a positive predictor of tinnitus resolution Conversely, other studies deny the existence of an association between type of surgery and tinnitus resolution, suggesting that the maintenance mechanism of tinnitus is to be traced to the brainstem and central nervous system above the brainstem and not to the more peripheral structures [91,99,100]. Other factors seemingly associated with a higher likelihood of either tinnitus resolution or improvement include age > 50 years and nonserviceable preoperative hearing. Hearing preservation and cochlear nerve status did not correlate with the prognosis of postoperative tinnitus .
3.6.3. Hearing Function
It has been shown that hearing loss in VS untreated patients can occur gradually or suddenly, regardless of tumor size and that 10-years hearing preservation rate after sRT is around 23% . The treatment options of VS can be divided in three main categories: observation, radiation therapy and surgery. A recent review on 3652 patients from 26 studies, and a mean follow-up of 49.2 months demonstrated consistent patterns in progression of hearing loss during observation. The authors suggest the following benchmark for those presenting with serviceable hearing (SH) at diagnosis: approximately 75% retain SH at 3 years, 60% at 5 years, and 40% at 10 years .
Hearing preservation after surgery varies from 18 to 82% . Among surgical treatments, retrosigmoid and middle cranial fossa treatments are the only viable options for hearing preservation, without any significant differences in terms of SH preservation in the long term. A selection of patients that are candidates for surgical removal and hearing preservation is mandatory. The most commonly accepted criteria are:
Age (usually less than 65–70 years old)
Tumor size (usually <2.5 cm, with best results when tumor <1 cm with ≥80% hearing preservation) [46,106,107].
The preoperative hearing class, despite the size of the VS, correlates with postoperative hearing results .
Degree of fundus filling: Tringali et al., using regression analysis, demonstrated that the degree of IAC involvement was the most correlated predictor of successful hearing preservation. When the fundus was completely involved, the possibility of preserving hearing dropped significantly, in absolute terms and also compared to all other degrees of IAC filling .
Other factors to be considered for hearing preservation treatments are patient’s general health, tumor growth pattern and characteristics, contralateral hearing, NF 2, and clinician’s experience . The cornerstone in hearing preservation during surgery is the use of intraoperative monitoring techniques , usually ABR and/or direct eight nerve monitoring (DENM), also called CNAPs (Cochlear Nerve Action Potentials) . The ABR shows some disadvantages, like being a far field technique and not having a real-time feedback on the VIII nerve status; DENM/CNAPs instead is a near field system where the electrodes are placed directly on the cochlear nerve; the signal is reproduced in a few seconds . Notably, the surgeon must also be careful in preserving the labyrinthine artery, that is a terminal branch.
Despite the type of surgical approach, the highest chance of hearing preservation are shown by patients with intracanalicular VS and class A pre-opeative hearing, compared with extrameatal tumors and class B hearing or lower .
As far as sRT is concerned, studies report the preservation of SH in 85–87% of cases [111,112]. A recent systematic review has demonstrated differences in terms of hearing preservation comparing stereotactic radiosurgery versus fractionated radiotherapy, with slightly better results obtained by the latter (49% vs. 45% of average deterioration for patients with SH, respectively) . The major bias in the reviewed articles is the length of patients’ follow up, which is usually around 5 years, not enough to anticipate 10 or 20 years behavior of SH, neither for conservative observation, nor after radiation therapy, nor after preservation surgery.
3.7. Multidisciplinary and Personalized Management of VS in Our Experience
In our experience, the MDT is composed of an otolaryngologist, neurosurgeon, and radiotherapist and is held once/twice a month. In a previously published paper , we described the results of a retrospective study on 107 consecutive patients treated by our vestibular schwannoma MDT from June 2016 to December 2019. The analysis included patient age, tumor size, hearing level, facial nerve function, tumor control, complications, and quality of life questionnaires. The median follow-up time was 30 months (range: 12–54). The median pre-treatment Koos grading was 2 (range: 1–4) and all patients had pre-treatment grade I facial nerve function. For what concerns the outcomes, according to treatment modality, in the MS group (22 patients) all subjects underwent a complete removal of the tumor; 18% of patients showed postoperative facial nerve dysfunction and no serviceable hearing (AAO-HNS Class > B) was present after surgery. In the sRT group (11 patients), one patient complained of facial paresthesia and postural instability after treatment, spontaneously resolved in 2 weeks, and one patient had posttreatment hearing worsening (class B to class D). The tumor control rate was 100%, and the mean volume reduction was 6.3 mm (range: 4–8.7 mm). Among those patients, 3 had transitioned from stage III Koos to stage II Koos, while 8 out of 22 patients had unchanged Koos stage after treatment. Finally, in the WS group (74 patients), during follow-up time hearing class worsened in 5 patients. No further symptoms occurred during observation and tumor size remained unchanged at subsequent MRI examinations in all cases.
About quality of life, we administered the Short Form-12 (SF-12), a multipurpose measure of health status composed of 2 main items: the Physical Component Summary-12 (PCS-12) score and the Mental Component Score-12 (MCS-12) score. Significant differences between groups were detected in the PCS-12 item, with higher scores in the WS group compared with the MS and sRT groups (p< 0.05 in both comparisons).
The review of the literature described in this paper has focused our attention on the problem of age and on the possible worst surgical outcome in elderly patients. However, a clear cutoff for age is missing, as many studies refer nonspecifically to the concept of “frailty”; this finding led us to the decision to stratify patients according to the cutoff > 65 years, based on data reported above.
4. Conclusions
Decision-making in VS management has progressively become more challenging. An individualized proposal of procedures is preferable as compared to a single gold-standard approach. The present review analyzed which patient and tumor’s factors need to be considered when dealing with a VS diagnosis, the most significant being age, tumor size and hearing preservation.
Author Contributions
Conceptualization: B.S., S.S., E.D.C. and D.L.; methodology: B.S., G.F., C.C. and C.G.; software: G.F., C.C. and C.G.; validation: G.F., C.C., C.G. and D.L.; formal analysis, G.F., C.C., C.G. and D.L.; writing—original draft preparation, B.S., S.S. and D.L; writing—review and editing, E.D.C., D.L. and C.C. All authors have read and agreed to the published version of the manuscript.
Data Availability Statement
Data are available upon reasonable request.
Conflicts of Interest
The authors declare no conflict of interest.
Funding Statement
This research received no external funding.
Footnotes
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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189641 | https://www.studocu.com/en-za/messages/question/12671398/what-is-the-relationship-between-radius-and-diameter-in-the-context | [Solved] what is the relationship between radius and diameter in the - Maths literacy - Studocu
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Sehunelo Secondary School
Maths literacy
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what is the relationship between radius and diameter in the
Sehunelo Secondary School
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Anonymous Student
4 months ago
what is the relationship between radius and diameter in the context above
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1 Maths Grade 8 Workbook - Engaging Exercises and Concepts for 2024 Mathematics Summaries 83%(6)
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Answer Created with AI
4 months ago
Relationship Between Radius and Diameter
In geometry, the radius and diameter are two fundamental measurements of a circle. Here’s how they relate to each other:
The radius is the distance from the center of the circle to any point on its circumference.
The diameter is the distance across the circle, passing through the center, and is equal to two times the radius.
Mathematical Relationship
The relationship can be expressed with the following formulas:
Diameter (D):
js
D = 2 r
Radius (r):
js
r = D / 2
This relationship is crucial because the diameter is essentially a line that divides the circle into two equal parts, and it is always twice the length of the radius. This is expressed in the formula: (d = 2r).1
Summary
If you know the radius, you can find the diameter by multiplying by 2.
If you know the diameter, you can find the radius by dividing by 2.
Example
If the radius of a circle is 5 units, the diameter would be:
js
D = 2 5 = 10 units
Conversely, if the diameter is 10 units, the radius would be:
js
r = 10 / 2 = 5 units
This relationship is crucial in various applications, including calculations involving the area and circumference of circles. For instance, the circumference of a circle can be calculated using the diameter with the formula (C = \pi D), where (\pi) is approximately 3.14159.2 This demonstrates the importance of understanding the relationship between the radius and diameter in practical applications.
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189642 | https://arxiv.org/pdf/1801.03158 | Stabbing Pairwise Intersecting Disks by Five Points ∗
Sariel Har-Peled 1, Haim Kaplan 2, Wolfgang Mulzer 3, Liam Roditty 4,Paul Seiferth 3, Micha Sharir 2, and Max Willert 3
1
Department of Computer Science, University of Illinois, Urbana, IL 61801, USA, sariel@illinois.edu
2
School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel, {haimk,michas}@tau.ac.il
3
Institut für Informatik, Freie Universität Berlin, 14195 Berlin, Germany,
{mulzer,pseiferth,willerma}@inf.fu-berlin.de
4
Department of Computer Science, Bar Ilan University, Ramat Gan 5290002, Israel, liamr@macs.biu.ac.il
Abstract
Suppose we are given a set D of n pairwise intersecting disks in the plane. A planar point set P
stabs D if and only if each disk in D contains at least one point from P . We present a deterministic algorithm that takes O(n) time to find five points that stab D. Furthermore, we give a simple example of 13 pairwise intersecting disks that cannot be stabbed by three points. Moreover, we present a simple argument showing that eight disks can be stabbed by at most three points. This provides a simple—albeit slightly weaker—algorithmic version of a classical result by Danzer that such a set D can always be stabbed by four points.
1 Introduction
The maximum clique problem is a classic problem in combinatorial optimization : given a simple graph
G = ( V, E ), find a maximum-cardinality set C ⊆ V of vertices such that any two distinct vertices in C
are adjacent. In 1972, Karp proved that the maximum clique problem is NP-hard . Even worse, a subsequent line of research showed that the maximum clique problem is hard to approximate. In particular, we now know that for any fixed ε > 0, if there is a polynomial-time algorithm that approximates maximum clique in an n-vertex graph up to a factor of n1−ε, then P = NP However, if the input graph has additional structure, the problem can become easier. For example, if the input is the intersection graph of a set of disks in the plane, the maximum clique problem admits efficient (approximation) algorithms: for unit disk graphs, it can be solved in polynomial time , while for general disk intersection graphs, there is a randomized EPTAS . Earlier, Ambühl and Wagner presented a polynomial-time algorithm that computes a τ / 2-approximation for the maximum clique in a general disk intersection graph, where τ is the minimum stabbing number of any arrangement of pairwise intersecting disks in the plane, i.e., the minimum number of points that are needed to stab every disk in such an arrangement. Motivated by this application, our goal here is to understand this stabbing number better. Let D be a set of n disks in the plane. If every three disks in D intersect, then Helly’s theorem shows that the whole intersection ⋂ D of D is nonempty [13, 14, 17]. In other words, there is a single point p
that lies in all disks of D, that is, p stabs D. More generally, when we know only that every pair of disks
∗
A preliminary version appeared as S. Har-Peled, H. Kaplan, W. Mulzer, L. Roditty, P. Seiferth, M. Sharir, and M. Willert.
Stabbing Pairwise Intersecting Disks by Five Points. Proc. 29th ISAAC, pp. 50:1–50:12. SHP was supported by a NSF AF awards CCF-1421231, and CCF-1217462. WM was supported by DFG grant MU/3501/1 and ERC STG 757609. PS was supported by DFG grant MU/3501/1. MS was supported by ISF grant 892/13 and 260/18, by the Israeli Centers of Research Excellence (I-CORE) program (Center No. 4/11), and by the Blavatnik Research Fund in Computer Science at Tel Aviv University. HK was supported by ISF grant 1595-19 and the Blavatnik Family Foundation. Work on this paper was supported in part by grant 1367/2016 and 1161/2011 from the German-Israeli Science Foundation (GIF).
1
arXiv:1801.03158v3 [cs.CG] 28 Apr 2021
D1D2L1,3 L1,2 L2,3 c2c3c1wD3uvD1c1D2c2cEqp`Figure 1: Left: At least one lens angle is large. Right: D1 and E have the same radii and lens angle 2π/ 3.By Lemma 2.2, D2 is a subset of E. {c1, c, p, q } is the set P from Lemma 2.4. in D intersect, there must be a point set P of constant size such that each disk in D contains at least one point in P – the minimum cardinality of P is the stabbing number of D. It is indeed not surprising that
D can be stabbed by a constant number of points, but for some time, the exact bound remained elusive. Eventually, in July 1956 at an Oberwolfach seminar, Danzer presented the answer: four points are always sufficient and sometimes necessary to stab any finite set of pairwise intersecting disks in the plane. Danzer was not satisfied with his original argument, so he never formally published it. In 1986, he presented a new proof . Previously, in 1981, Stachó had already given an alternative proof , building on a previous construction of five stabbing points . This line of work was motivated by a result of Hadwiger and Debrunner, who showed that three points suffice to stab any finite set of pairwise intersecting unit
disks . In later work, these results were significantly generalized and extended, culminating in the celebrated (p, q )-theorem that was proven by Alon and Kleitman in 1992 . See also a recent paper by Dumitrescu and Jiang that studies generalizations of the stabbing problem for translates and homothets of a convex body . Danzer’s published proof is fairly involved. It uses a compactness argument that does not seem to be constructive, and one part of the argument relies on an underspecified verification by computer. Therefore, it is quite challenging to check the correctness of the argument, let alone to derive any intuition from it. There seems to be no obvious way to turn it into an efficient algorithm for finding a stabbing set of size four. The proof of Stachó is simpler, but it is obtained through a lengthy case analysis that requires a very disciplined and focused reader. Here, we present a new argument that yields five stabbing points. Our proof is constructive, and it lets us find the stabbing set in deterministic linear time. Following the conference version of this paper, Carmi, Katz, and Morin published a manuscript in which they present an algorithm that can find four stabbing points in linear time . As for lower bounds, Grünbaum gave an example of 21 pairwise intersecting disks that cannot be stabbed by three points . Later, Danzer reduced the number of disks to ten . This example is close to optimal, because every set of eight disks can be stabbed by three points, as mentioned by Stachó and formally proved in Section 5 below. However, it is hard to verify Danzer’s lower bound example—even with dynamic geometry software, the positions of the disks cannot be visualized easily. We present a new and simple proof that shows that the stabbing number of D is upper bounded by 5.Moreover, we obtain a linear time algorithm that can find these 5 stabbing points. Finally, we present a simple construction of 13 pairwise intersecting disks that cannot be stabbed by 3 points, and work out a proof of Stachó’s eight-disk claim.
2 The Geometry of Pairwise Intersecting Disks
Let D be a set of n pairwise intersecting disks in the plane. A disk Di ∈ D is given by its center ci and its radius ri. To simplify the analysis, we make the following assumptions: (i) the radii of the disks are pairwise distinct; (ii) the intersection of any two disks has a nonempty interior; and (iii) the intersection of any three disks is either empty or has a nonempty interior. A simple perturbation argument can then handle the degenerate cases. 2The lens of two disks Di, D j ∈ D is the set Li,j = Di ∩ Dj . Let u be any of the two intersection points of the boundary of Di and the boundary of Dj . The angle ∠ciuc j is called the lens angle of Di
and Dj . It is at most π. A finite set C of disks is Helly if their common intersection ⋂ C is nonempty. Otherwise, C is non-Helly . We present some useful geometric lemmas.
Lemma 2.1. Let {D1, D 2, D 3} be a set of three pairwise intersecting disks that is non-Helly. Then, the set contains two disks with lens angle larger than 2π/ 3.Proof. Since {D1, D 2, D 3} is non-Helly, the lenses L1,2, L1,3 and L2,3 are pairwise disjoint. Let u be the vertex of L1,2 nearer to D3, and let v, w be the analogous vertices of L1,3 and L2,3 (see Figure 1, left). Consider the simple hexagon c1uc 2wc 3v, and write ∠u, ∠v, and ∠w for its interior angles at u, v, and w.The sum of all interior angles is 4π. Thus, ∠u + ∠v + ∠w < 4π, so at least one angle is less than 4π/ 3. It follows that the corresponding lens angle, which is the exterior angle at u, v, or w must be larger than
2π/ 3.
Lemma 2.2. Let D1 and D2 be two intersecting disks with r1 ≥ r2 and lens angle at least 2π/ 3. Let E
be the unique disk with radius r1 and center c, such that (i) the centers c1, c2, and c are collinear and c lies on the same side of c1 as c2; and (ii) the lens angle of D1 and E is exactly 2π/ 3 (see Figure 1, right). Then, if c2 lies between c1 and c, we have D2 ⊆ E.Proof. Let x ∈ D2. Since c2 lies between c1 and c, the triangle inequality gives
|xc | ≤ | xc 2| + |c2c| = |xc 2| + |c1c| − | c1c2|. (1) Since x ∈ D2, we get |xc 2| ≤ r2. Also, since D1 and E have radius r1 each and lens angle 2π/ 3, it follows that |c1c| = √3 r1. Finally, |c1c2| = √r21 + r22 − 2r1r2 cos α, by the law of cosines, where α is the lens angle of D1 and D2. As α ≥ 2π/ 3 and r1 ≥ r2, we get cos α ≤ − 1/2 = ( √3 − 3/2) − √3 + 1 ≤
(√3 − 3/2) r1/r 2 − √3 + 1 , As such, we have
|c1c2|2 = r21 + r22 − 2r1r2 cos α ≥ r21 + r22 − 2r1r2
((√3 − 3/2) r1
r2
− √3 + 1
)
= r21 − 2(√3 − 3/2)r21 + 2( −√3 + 1) r1r2 + r22
= (1 − 2√3 + 3) r21 + 2( −√3 + 1) r1r2 + r22 = (r1(√3 − 1) + r2
)2.
Plugging this into Equation 1 gives |xc | ≤ r2 + √3r1 − (r1
(√3 − 1) + r2
) = r1, i.e., x ∈ E.
Lemma 2.3. Let D1 and D2 be two intersecting disks with equal radius r and lens angle 2π/ 3. There is a set P of four points so that any disk F of radius at least r that intersects both D1 and D2 contains a point of P .Proof. Consider the two tangent lines of D1 and D2, and let p and q be the midpoints on these lines between the respective two tangency points. We set P = {c1, c 2, p, q }; see Figure 2. Given the disk F that intersects both D1 and D2, we shrink its radius, keeping its center fixed, until either the radius becomes r or until F is tangent to D1 or D2. Suppose the latter case holds and F is tangent to D1. We move the center of F continuously along the line spanned by the center of F and c1
towards c1, decreasing the radius of F to maintain the tangency. We stop when either the radius of F
reaches r or F becomes tangent to D2. We obtain a disk G ⊆ F with center c = ( cx, c y ) so that either: (i) radius (G) = r and G intersects both D1 and D2; or (ii) radius (G) ≥ r and G is tangent to both D1
and D2. Since G ⊆ F , it suffices to show that G ∩ P 6 = ∅.We introduce a coordinate system, setting the origin o midway between c1 and c2, so that the y-axis passes through p and q. Then, as in Figure 2, we have c1 = ( −√3 r/ 2, 0) , c2 = ( √3 r/ 2, 0) , q = (0 , r ),and p = (0 , −r).3D22D21pc2qD2D1c1γQt1t2s1s2Figure 2: Left: P = {c1, c 2, p, q } is the stabbing set. The green arc γ = ∂D 21 ∩ Q is covered by D2 ∪ Dq .D2qpkk+k−c1cc2ED1xyD2qpkk+k−c1cc2ED1x
Figure 3: Proof of Lemma 2.4. Left (Case (i)): x is an arbitrary point in D2 ∩ F \ k+ and y is an arbitrary point in D1 ∩ F . Right (Case (ii)): x is an arbitrary point in D2 ∩ F ∩ k+. The angle at c in the triangle
∆xcc 2 is ≥ π/ 2.For case (i), let D21 be the disk of radius 2r centered at c1, and D22 the disk of radius 2r centered at c2.Since G has radius r and intersects both D1 and D2, its center c has distance at most 2r from both c1
and c2, i.e., c ∈ D21 ∩ D22 . Let Dp and Dq be the two disks of radius r centered at p and q. We will show that D21 ∩ D22 ⊆ D1 ∪ D2 ∪ Dp ∪ Dq . Then it is immediate that G ∩ P 6 = ∅. By symmetry, it is enough to focus on the upper-right quadrant Q = {(x, y ) | x ≥ 0, y ≥ 0}. We show that all points in D21 ∩ Q are covered by D2 ∪ Dq . Without loss of generality, we assume that r = 1 . Then, the two intersection points of D21 and Dq are t1 = ( 5√3−2√87 28 , 38+3 √29 28 ) ≈ (−0.36 , 1.93) and t2 = ( 5√3+2 √87 28 , 38 −3√29 28 ) ≈ (0 .98 , 0.78) ,and the two intersection points of D21 and D2 are s1 = ( √32 , 1) ≈ (0 .87 , 1) and s2 = ( √32 , −1) ≈ (0 .87 , −1) .Let γ be the boundary curve of D21 in Q. Since t1, s 2 6 ∈ Q and since t2 ∈ D2 and s1 ∈ Dq , it follows that
γ does not intersect the boundary of D2 ∪ Dq and hence γ ⊂ D2 ∪ Dq . Furthermore, the subsegment of the y-axis from o to the start point of γ is contained in Dq , and the subsegment of the x-axis from o to the endpoint of γ is contained in D2. Hence, the boundary of D21 ∩ Q lies completely in D2 ∪ Dq , and since D2 ∪ Dq is simply connected, it follows that D21 ∩ Q ⊆ D2 ∪ Dq , as desired. For case (ii), since G is tangent to D1 and D2, the center c of G is on the perpendicular bisector of c1
and c2, so the points p, o, q and c are collinear. Suppose without loss of generality that cy ≥ 0. Then, it is easily checked that c lies above q, and radius (G) + r = |c1c| ≥ | oc | = r + |qc |, so q ∈ G.
Lemma 2.4. Consider two intersecting disks D1 and D2 with r1 ≥ r2 and lens angle at least 2π/ 3. Then, there is a set P of four points such that any disk F of radius at least r1 that intersects both D1 and D2
contains a point of P .Proof. Let be the line through c1 and c2. Let E be the disk of radius r1 and center c ∈ that satisfies the conditions (i) and (ii) of Lemma 2.2. Let P = {c1, c, p, q } as in the proof of Lemma 2.3, with respect to D1 and E (see Figure 1, right). We claim that
D1 ∩ F 6 = ∅ ∧ D2 ∩ F 6 = ∅ ⇒ E ∩ F 6 = ∅. () 4Once () is established, we are done by Lemma 2.3. If D2 ⊆ E, then () is immediate, so assume that
D2 6 ⊆ E. By Lemma 2.2, c lies between c1 and c2. Let k be the line through c perpendicular to `, and let k+ be the open halfplane bounded by k with c1 ∈ k+ and k− the open halfplane bounded by k with
c1 6 ∈ k−. Since |c1c| = √3 r1 > r 1, we have D1 ⊂ k+; see Figure 3. Recall that F has radius at least r1
and intersects D1 and D2. We distinguish two cases: (i) there is no intersection of F and D2 in k+, and (ii) there is an intersection of F and D2 in k+; see Figure 3 for the two cases. For case (i), let x be any point in D1 ∩ F . Since we know that D1 ⊂ k+, we have x ∈ k+. Moreover, let y be any point in D2 ∩ F . By assumption, y is not in k+, but it must be in the infinite strip defined by the two tangents of D1 and E. Thus, the line segment xy intersects the diameter segment k ∩ E. Since F
is convex, the intersection of xy and k ∩ E is in F , so E ∩ F 6 = ∅.For case (ii), fix x ∈ D2 ∩ F ∩ k+ arbitrarily. Consider the triangle ∆xcc 2. Since x ∈ k+, the angle at
c is at least π/ 2. Thus, |xc | ≤ | xc 2|. Also, since x ∈ D2, we know that |xc 2| ≤ r2 ≤ r1. Hence, |xc | ≤ r1,so x ∈ E and () follows, as x ∈ E ∩ F .
3 Existence of Five Stabbing Points
With these tools we can now show that there is a stabbing set with five points.
Theorem 3.1. Let D be a set of n pairwise intersecting disks in the plane. There is a set P of five points such that each disk in D contains at least one point from P .Proof. If D is Helly, there is a single point that lies in all disks of D. Thus, assume that D is non-Helly, and let D1, D 2, . . . , D n be the disks in D ordered by increasing radius. Let i∗ be the smallest index with ⋂
i≤i∗
Di = ∅. By Helly’s theorem [13, 14, 17], there are indices j, k < i ∗ such that {Di∗ , D j , D k} is non-Helly. By Lemma 2.1, two disks in {Di∗ , D j , D k} have lens angle at least 2π/ 3. Applying Lemma 2.4 to these two disks, we obtain a set P ′ of four points so that every disk Di with i ≥ i∗ contains at least one point from P ′. Furthermore, by definition of i∗, we have ⋂
i<i ∗
Di 6 = ∅, so there is a point q that stabs every disk Di with i < i ∗. Thus, P = P ′ ∪ { q} is a set of five points that stabs every disk in D, as desired.
Remark. A weakness in our proof is that it combines two different stages, one of finding the point q
that stabs all the small disks, and one of constructing the four points of Lemma 2.4 that stab all the larger disks. It is an intriguing challenge to merge the two arguments so that altogether they only require four points. The proof of Carmi et al. uses a different approach.
4 Algorithmic Considerations
The proof of Theorem 3.1 leads to a simple O(n log n) time algorithm for finding a stabbing set of size five. For this, we need an oracle that decides whether a given set of disks is Helly. This has already been done by Löffler and van Kreveld , in a more general context:
Lemma 4.1 (Theorem 6 in ) . Given a set of n disks, the problem of choosing a point in each disk such that the smallest enclosing circle of the resulting point set has minimum radius can be solved in O(n)
deterministic time.
Now, an O(n log n)-time algorithm for finding the five stabbing points is based on the analysis in the proof of Theorem 3.1. It works as follows: first, we sort the disks in D by increasing radius. This takes
O(n log n) time. Let D = 〈D1, . . . , D n〉 be the resulting order. Next, we use binary search with the oracle from Lemma 4.1 to determine the smallest index i∗ such that the prefix {D1, . . . , D i∗ } is non-Helly. This yields the disk Di∗ . We have to invoke the oracle O(log n) times, which gives a total time of O(n log n)
for this step. After that, we use another binary search with the oracle from Lemma 4.1 to determine the smallest index k < i ∗ such that {Di∗ , D 1, . . . , D k} is non-Helly. This costs O(n log n) time as well. Then, we perform a linear search to find an index j < k such that {Dj , D k, D i∗ } is a non-Helly triple. This step 5works in O(n) time. Finally, we use Lemma 4.1 to obtain in O(n) time a stabbing point q for the Helly set {D1, . . . , D i∗−1} and the method from the proof of Theorem 3.1 to extend q to a stabbing set for the whole set D. This last step works in O(1) time since the result depends solely on {Dj , D k, D i∗ }. Hence, we can state our claimed theorem.
Theorem 4.2. Given a set D of n pairwise intersecting disks in the plane, we can find in O(n log n)
time a set P of five points such that every disk of D contains at least one point of P .
The proof of Lemma 4.1 uses the LP-type framework by Sharir and Welzl [6, 19]. As we will see next, a more sophisticated application of the framework directly leads to a deterministic linear time algorithm to find a stabbing set with five points.
The LP-type framework. An LP-type problem (H, w, ≤) is an abstract generalization of a low-dimensional linear program. It consists of a finite set of constraints H, a weight function w : 2 H → W ,and a total order (W, ≤) on the weights. The weight function w assigns a weight to each subset of constraints. It must fulfill the following two axioms:
• Monotonicity : for any H′ ⊆ H and H ∈ H , we have w(H′ ∪ { H}) ≤ w(H′);
• Locality: for any B ⊆ H ′ ⊆ H with w(B) = w(H′) and for any H ∈ H , we have that if
w(B ∪ { H}) = w(B), then also w(H′ ∪ { H}) = w(H′).Given a subset H′ ⊆ H , a basis for H′ is an inclusion-minimal set B ⊆ H ′ with w(B) = w(H′). The
combinatorial dimension of (H, w, ≤) is the maximum size of any basis of any subset of H. The goal in an LP-type problem is to determine w(H) and a corresponding basis B for H. Next, given a set B ⊆ H
and a constraint H ∈ H , we say that H violates B if w(B ∪ { H}) < w (B).A generalization of Seidel’s algorithm for low-dimensional linear programming [18, 19] shows that we can solve an LP-type problem in O(|H| ) expected time, provided that a constant time algorithm for the following problem is available. Here and below, the constant factor in the O-notation may depend on the combinatorial dimension.
• Violation test: Given a basis B and a constraint H ∈ H , determine whether H violates B and return an error message if B is not a basis for any H′ ⊆ H .1
For a deterministic solution, we need an additional computational assumption. Let B ⊆ H be a basis of any subset H′ ⊆ H , we use vio (B) to denote the set of all constraints H ∈ H that violate B, i.e., that have w(B ∪ { H}) < w (B). Consider the range space (H, R = {vio (B) | B is a basis for some H′ ⊆ H} ).For a subset Y ⊆ H , we let (Y, RY ) be the induced range space , that is, RY = {Y ∩ R | R ∈ R} . Chazelle and Matoušek have shown that an LP-type problem can be solved in O(|H| ) deterministic time if there is a constant-time violation test as stated above and the following computational assumption holds:
• Oracle: Given a subset Y ⊆ H , we can compute some superset R′ ⊇ R Y in time |Y| O(1) .During the following discussion, we will show that the problem of finding a non-Helly triple as in Theorem 3.1 is LP-type and fulfills the four requirements for the algorithm of Chazelle and Matoušek.
Remark. Löffler and van Kreveld provide proofs that the underlying problem in Lemma 4.1 is of LP-type, but they do not give arguments for the two computational assumptions, see . However, it is not difficult to also verify the two missing statements.
1Here, we follow the presentation of Chazelle and Matoušek . Sharir and Welzl use a violation test without the error message. Instead, they need an additional basis computation primitive: given a basis Band a constraint H∈ H , find a basis for B ∪ { H}. If a violation test with error message exists and if the combinatorial dimension is a constant, a basis computation primitive can easily be implemented by brute-force enumeration.
6D2D1D3D4D∞vFigure 4: Left: The disks D3 and D4 are destroyers of the Helly set {D1, D 2}. Moreover, D3 is the smallest destroyer of the whole set {D1, D 2, D 3, D 4}. Right: The disks without D∞ form a Helly set C. The smallest destroyer of C is D∞ and the point v is the extreme point for C and D∞, i.e., dist (C) = d(v, D ∞).
Geometric observations. The distance between two closed sets A, B ⊆ R2 is defined as d(A, B ) = min {| ab | | a ∈ A, b ∈ B}. From now on, we assume that all points in ⋃ D have positive y-coordinates. This can be ensured with linear overhead by an appropriate translation of the input. We denote by D∞
the closed halfplane below the x-axis. It is interpreted as a disk with radius ∞ and center at (0 , −∞ ).First, observe that for any subsets C1 ⊆ C 2 ⊆ D ∪ { D∞}, we have that if C1 is non-Helly, then C2 is non-Helly. For any C ⊆ D ∪ { D∞}, we say that a disk D destroys C if C ∪ { D} is non-Helly. Observe that
D∞ destroys every non-empty subset of D. Moreover, if C is non-Helly, then every disk is a destroyer. See Figure 4 for an example. We can make the following two observations.
Lemma 4.3. Let C ⊆ D be Helly and D a destroyer of C. Then, the point v ∈ ⋂ C with minimum distance to D is unique. Proof. Suppose there are two distinct points v 6 = w ∈ ⋂ C with d(v, D ) = d( ⋂ C, D ) = d(w, D ). Since ⋂ C is convex, the segment vw lies in ⋂ C. Now, if D 6 = D∞, then every point in the relative interior of
vw is strictly closer to D than v and w. If D = D∞, then all points in vw have the same distance to D,but since ⋂ C is strictly convex, the relative interior of vw lies in the interior of ⋂ C, so there must be a point in ⋂ C that is closer to D than v and w. In either case, we obtain a contradiction to the assumption
v 6 = w and d(v, D ) = d( ⋂ C, D ) = d(w, D ). The claim follows. Let C ⊆ D be Helly and D a destroyer of C. The unique point v ∈ ⋂ C with minimum distance to D
is called the extreme point for C and D (see Figure 4, right).
Lemma 4.4. Let C1 ⊆ C 2 ⊆ D be two Helly sets and D a destroyer of C1 (and thus of C2). Let
v ∈ ⋂ C1 be the extreme point for C1 and D. We have d( ⋂ C1, D ) ≤ d( ⋂ C2, D ). In particular, if
v ∈ ⋂ C2, then d( ⋂ C1, D ) = d( ⋂ C2, D ) and v is also the extreme point for C2 and D. If v 6 ∈ ⋂ C2, then
d( ⋂ C1, D ) < d ( ⋂ C2, D ).Proof. The first claim holds trivially: let w ∈ ⋂ C2 be the extreme point for C2 and D. Since C1 ⊆ C 2,it follows that w ∈ ⋂ C1, so d( ⋂ C1, D ) ≤ d(w, D ) = d( ⋂ C2, D ). If v ∈ ⋂ C2, then d( ⋂ C1, D ) ≤
d( ⋂ C2, D ) ≤ d(v, D ) = d( ⋂ C1, D ), so v = w, by Lemma 4.3. If v / ∈ ⋂ C2, then d( ⋂ C1, D ) < d ( ⋂ C2, D ),by Lemma 4.3 and the fact that C1 ⊆ C 2. See Figure 5. Let C be a subset of D. For 0 < r ≤ ∞ we define C<r as the set of all disks in C with radius smaller than r. Recall that we assume that all the radii are pairwise distinct. A disk D with radius r, 0 < r ≤ ∞ ,is called smallest destroyer of C if (i) D ∈ C or D = D∞, (ii) D destroys C<r , and (iii) there is no disk 7D2D1D4D3vD2D1D4D3vwFigure 5: Left: The disk D4 is a destroyer for the Helly sets {D1, D 2} and {D1, D 2, D 3}. The extreme point v for {D1, D 2} is also the extreme point for {D1, D 2, D 3}. Right: The disk D4 is a destroyer for the Helly sets {D1, D 2} and {D1, D 2, D 3}. The extreme point v for {D1, D 2} is not in D3. The distance to D4 increases. D2D1ED3D2D1D3E
Figure 6: Monotonicity: In both cases, {D1, D 2, D 3} is non-Helly with smallest destroyer D3. Adding a disk E either decreases the radius of the smallest destroyer (left) or increases the distance to the smallest destroyer (right).
D′ ∈ C <r that destroys C<r . Observe that Property (iii) is the same as saying that C<r is Helly. See Figure 4 for an example. Let C be a subset of D and D the smallest destroyer of C. We write rad (C) for the radius of D and
dist (C) for the distance between D and the set ⋂ C<rad( C), i.e., dist (C) = d( ⋂ C<rad( C), D ). Now, if C is Helly, then D = D∞ and thus rad (C) = ∞. If C is non-Helly, then D ∈ C and thus rad (C) < ∞. In both cases, dist (C) is the distance between D and the extreme point for C<rad( C) and D. We define the weight of C as w(C) = ( rad (C), − dist (C)) , and we denote by ≤ the lexicographic order on R2. Chan observed, in a slightly different context, that (D, w, ≤) is LP-type . However, Chan’s paper does not contain a detailed proof for this fact. Thus, in the following lemmas, we show the two LP-type axioms, present a constant time violation test, and a polynomial-time oracle. We start with the monotonicity axiom followed by the locality axiom.
Lemma 4.5. For any C ⊆ D and E ∈ D , we have w(C ∪ { E}) ≤ w(C).Proof. Set C∗ = C ∪ { E}. Let D be the smallest destroyer of C, and let r = rad (C) be the radius of D.Since D destroys C<r , the set C<r ∪ { D} is non-Helly. Moreover, since C<r ∪ { D} ⊆ C ∗
<r
∪ { D}, we know that C∗
<r
∪ { D} is also non-Helly. Therefore, D destroys C∗
<r
and we can derive rad (C∗) ≤ rad (C). If we have rad (C∗) < rad (C), we are done. Hence, assume that rad (C∗) = rad (C). Then D is the smallest destroyer of C∗, and Lemma 4.4 gives − dist (C∗) = −d( ⋂ C∗
<r
, D ) ≤ − d(⋂ C<r , D ) = − dist (C). Hence,
w(C∗) ≤ w(C). See Figure 6 for an illustration. 8FDD∞EvvvD∞EEFFigure 7: A basis can either be a non-Helly triple (left), a pair of intersecting disks E and F where the point of minimum y-coordinate in E ∩ F is a vertex (middle), or a single disk (right).
Lemma 4.6. Let B ⊆ C ⊆ D with w(B) = w(C) and let E ∈ D . Then, if w(B ∪ { E}) = w(B), we also have w(C ∪ { E}) = w(C).Proof. Set C∗ = C ∪ { E}, B∗ = B ∪ { E}. Let r = rad (C) and D be the smallest destroyer of C. Since
w(C) = w(B) = w(B∗), we have that D is also the smallest destroyer of B and of B∗. If the radius of E is larger than r, then E cannot be the smallest destroyer of C∗, so w(C∗) = w(C). Thus, assume that E
has radius less than r. Let v be the extreme point of C<r and D. Since w(B∗) = w(B), we know that
d( ⋂ B<r , D ) = d( ⋂ B∗
<r
, D ) = d(v, D ). Now, Lemma 4.4 implies that v ∈ E, since E ∈ B ∗
<r
. Thus, the set C∗
<r
= C<r ∪ { E} is Helly and therefore, there is no disk D′ ∈ C ∗
<r
that destroys C∗
<r
. Furthermore, since D destroys C<r and C<r ⊂ C ∗
<r
, the disk D also destroys C∗
<r
. Therefore, D is also the smallest destroyer of C∗, so rad( C∗) = r = rad( C). Finally, since B∗
<r
⊆ C ∗
<r
we can use Lemma 4.4 to derive
d
( ⋂ C<r , D
)
= d
( ⋂ B∗
<r
, D
)
≤ d
( ⋂ C∗
<r
, D
)
≤ d(v, D ) = d
( ⋂ C<r , D
)
.
The claim follows. Next, we are going to describe the violation test for (D, w, ≤): given a basis B ⊆ D and a disk E ∈ D ,check whether E violates B, i.e., whether w(B ∪ { E}) < w (B), and return an error message if B is not a basis. But first, we show that the combinatorial dimension of (D, w, ≤) is at most 3.
Lemma 4.7. For each C ⊆ D , there is a set B ⊆ C with |B| ≤ 3 and w(B) = w(C).Proof. Let D be the smallest destroyer of C. Let r = rad (C) be the radius of D, and let v ∈ ⋂ C<r be the extreme point for C<r and D. First of all, we observe that v cannot be in the interior of ⋂ C<r , since
v minimizes the distance to D. Thus, there has to be a non-empty subset A ⊆ C <r such that v lies on the boundary of each disk of A. Let A be a minimal set such that d(⋂ A, D ) = d(v, D ). It follows that
|A| ≤ 2. See Figure 7 for an illustration. First, assume that A = {E}. Then, since d(E, D ) = d(v, D ) > 0, we know that E ∩D = ∅. As the disks in C intersect pairwise, we derive D / ∈ C and hence D = D∞. Setting B = A, we get rad (C) = ∞ = rad (B)
and dist( C) = d(v, D ) = d(E, D ) = dist( B). Thus, |B| ≤ 3 and w(B) = w(C).Second, assume that A = {E, F }. Then, v is one of the two vertices of the lens L = E ∩ F . Next, we show that d(L, D ) ≥ d(v, D ). Assume for the sake of contradiction that there is a point w ∈ L with
d(w, D ) < d (v, D ). By general position and since v is the intersection of two disk boundaries, there is a relatively open neighborhood N around v in ⋂ C<r such that N is also relatively open in L. Since L
is convex, there is a point x ∈ N that also lies in the relative interior of the line segment wv . Then,
d(x, D ) < d (v, D ) and x ∈ ⋂ C<r . This yields a contradiction, as v is the extreme point for C<r and D.Thus, we have d(L, D ) ≥ d(v, D ) which also shows hat D ∩ E ∩ F = ∅.We set B = {E, F }, if C is Helly (i.e., D = D∞), and B = {D, E, F }, if C is non-Helly (i.e., D ∈ C ). In both cases, we have B ⊆ C and |B| ≤ 3. Moreover, we can conclude that D destroys B<r = {E, F },and since B<r is Helly, D is the smallest destroyer of B. Hence, we have rad( C) = r = rad( B).9To obtain dist (B) = dist (C), it remains to show d(⋂ B<r , D ) = d(⋂ C<r , D ). Since B<r ⊆ C <r , we can use Lemma 4.4 as well as d(L, D ) ≥ d(v, D ) to derive
d
( ⋂ C<r , D
)
≥ d
( ⋂ B<r , D
)
, = d(L, D ) ≥ d(v, D ) = d
( ⋂ C<r , D
)
as desired. We conclude that w(B) = w(C).We remark that the set B is actually a basis for C: if B is a non-Helly triple, then removing any disk from B creates a Helly set and increases the radius of the smallest destroyer to ∞. If |B| ≤ 2, then D∞ is the smallest destroyer of B and the minimality follows directly from the definition. Following the argument of the last proof, the violation test is now immediate. We present pseudo-code in Algorithm 1. It obviously needs constant time. Finally, to apply the algorithm of Chazelle and Matoušek, we still need to check that there is a polynomial-time oracle that computes a superset of RY
for a given set of disks Y.
Algorithm 1 The violation test.
1:
procedure violates (set B ⊆ D , disk E ∈ D with radius r′)
2:
if |B| > 3 or |B| = 3 and B is Helly then return “ B is not a basis.”
3:
if |B| = 2 and the y-minimum of ⋂ B is also the y-minimum of a single disk of B then
4:
return “ B is not a basis.”
5:
if B = {D1} then
6:
if the y-minimum in E ∩ D1 differs from the y-minimum in D1 then
7:
return “ E violates B.”
8:
else return “ E does not violate B.”
9:
if B = {D1, D 2} then
10:
v = argmin {wy | w ∈ D1 ∩ D2}
11:
if v / ∈ E then return “ E violates B.”
12:
else return “ E does not violate B.”
13:
else . B is of size 3, non-Helly, and does not contain D∞.
14:
D = smallest destroyer of B
15:
{D1, D 2} = B \ { D}
16:
r = rad( B)
17:
if r′ > r then return “ E does not violate B.”
18:
else
19:
v = argmin {d(w, E ) | w ∈ D1 ∩ D2}
20:
if v / ∈ E then return “ E violates B.”
21:
else return “ E does not violate B.” Lemma 4.8. Given a set Y ⊆ D of disks, we can compute a superset of RY in time O(|Y| 4).Proof. Let v ∈ R2 and r > 0. First, we let Rv = {D ∈ Y | v / ∈ D} be the range of all disks that do not contain v. Second, let Rv,r be the range of all disks of diameter smaller than r that do not contain the point v, i.e., Rv,r = {D ∈ Y | v / ∈ D and rD < r }. We define R′ to be the set of all ranges Rv over all v and subsequently, we let R′′ be the set of all ranges Rv,r over all v and r, that is,
R′′ = {Rv,r | v ∈ R2 and r > 0}.The discussion from the previous lemmas shows that for any basis B, there is a point vB ∈ R2 and a radius rB > 0 such that a disk E ∈ D with radius rE violates B if and only if vB 6 ∈ E and rE < r B. Hence, we have R′′ ⊇ R Y . We show how to compute R′′ in polynomial time. For this, we first construct R′.For the given set Y of disks, we compute the arrangement A(Y) and then focus on the facets of
A(Y). Since the arrangement has O(|Y| 2) facets, we can compute A(Y) in time O(|Y| 3) using a simple brute-force approach (faster algorithms exist, but are not needed here). Clearly, for two points v and w
of the same facet of A(Y), we have Rv = Rw. Therefore, for a given facet f , we pick an arbitrary point 10 v ∈ f , and we compute Rv by a linear scan of Y. Summing over all facets, we can thus compute R′ in time O(|Y| 3).Finally, to compute R′′ , we iterate over all O(|Y| 2) ranges in R′. Given a range Rv ∈ R ′, we get all
Rv,r for r > 0 by first sorting Rv by increasing radii and then taking every prefix of the sorted list of disks. For a fixed v, this can be done in time O(|Y| 2). Hence, R′′ can be computed in O(|Y| 4) time. The claim follows. The following lemma summarizes the discussion so far.
Lemma 4.9. Given a set D of n pairwise intersecting disks in the plane, we can decide in O(n)
deterministic time whether D is Helly. If so, we can compute a point in ⋂ D in O(n) deterministic time. If not, we can compute the smallest destroyer D of D and two disks E, F ∈ D <r that form a non-Helly triple with D. Here, r is the radius of D.Proof. Since (i) (D, w, ≤) is LP-type, (ii) the violation test needs constant time, and (iii) the oracle needs polynomial time, we can apply the deterministic algorithm of Chazelle and Matoušek to compute w(D) = ( rad (D), − dist (D)) and a corresponding basis B in O(n) time. Then, D is Helly if and only if rad (D) = ∞. If D is Helly, then |B| ≤ 2. We compute the unique point v ∈ ⋂ B with
d(v, D ∞) = d( ⋂ B, D ∞
). Since B ⊆ D and d( ⋂ B, D ∞
) = d( ⋂ D, D ∞
), we have v ∈ ⋂ D by Lemma 4.4. We output v. If D is non-Helly, we simply output B, because B is a non-Helly triple with the smallest destroyer D of D and two disks E, F ∈ D <r , where r is the radius of D.
Theorem 4.10. Given a set D of n pairwise intersecting disks in the plane, we can find in deterministic
O(n) time a set P of five points such that every disk of D contains at least one point of P .Proof. Using the algorithm from Lemma 4.9, we decide whether D is Helly. If so, we return the extreme point computed by the algorithm. Otherwise, the algorithm gives us a non-Helly triple {D, E, F }, where
D is the smallest destroyer of D and E, F ∈ D <r , with r being the radius of D. Since D<r is Helly, we can obtain in O(n) time a stabbing point q ∈ ⋂ D<r by using the algorithm from Lemma 4.9 again. Next, by Lemma 2.1, there are two disks in {D, E, F } whose lens angle is at least 2π/ 3. Let P ′ be the set of four points from the proof of Lemma 2.4. Then, P = P ′ ∪ { q} is a set of five points that stabs every disk in D.
5 Simple Bounds
We now provide some easy lower and upper bounds on the number of disks for which a certain number of stabbing points is necessary or sufficient.
Eight disks can be stabbed by three points. For the proof that any set of eight pair-wise intersecting disks can be stabbed by at most three points, we show the following lemma.
Lemma 5.1. Let D be a set of at least 5 pairwise intersecting disks. Then, D contains a Helly-triple. Proof. Let D be a set of exactly 5 pairwise intersecting disks. We assume that no three centers of the disks are on a line, since otherwise these three disks are a Helly-triple. Since the complete graph K5
does not have a planar embedding, there have to be four different disks D1, . . . , D 4 ∈ D with centers
c1, . . . , c 4 and radii r1, . . . , r 4 such that the line segments c1c3 and c2c4 intersect, see Figure 8. Let x be the intersection point. Moreover, let α (resp., β) be the intersection of the lens L1,3 (resp., L2,4) and the line segment c1c3 (resp., c2c4). If x is in α or β, we are done. Otherwise, let y be the point of α that is closest to x and let z be the point of β closest to x. We can assume without loss of generality that
|xy | ≤ | xz | and x / ∈ D4. Using the triangle inequality, We can derive
|c2y| ≤ | c2x| + |xy | ≤ | c2x| + |xz | ≤ r2
to conclude that y ∈ D1 ∩ D2 ∩ D3.11 c4c2c1c3xαβyzFigure 8: Proof of Lemma 5.1. Now consider a set D of 8 pairwise intersecting disks. Using Lemma 5.1, we can find a Helly-triple in
D. Among the remaining 5 disks, we find a second Helly-triple. The remaining two disks can be stabbed by one point. This reasoning yields the following corollary, which was already mentioned by Stachó .
Corollary 5.2. Every set D of at most 8 pairwise intersecting disks can be stabbed by 3 points.
13 disks with 4 stabbing points. Danzer presented a set of 10 pairwise intersecting pseudo-disks with stabbing number four . However, it is not clear to us how these 10 pseudo-disks can be realized as pairwise intersecting Euclidean disks achieving the same stabbing number. Moreover, it is another open problem whether 9 pairwise intersecting disks can be stabbed by three points. Instead, we want to describe a set of 13 pairwise intersecting disks in the plane such that no point set of size three can pierce all of them. The construction begins with an inner disk A of radius 1 and three larger disks D1, D2, D3 of equal radius, so that each pair of disks in {A, D 1, D 2, D 3} is tangent. For i = 1 , 2, 3, we denote the contact point of A and Di by ξi.We add six more disks as follows. For i = 1 , 2, 3, we draw the two common outer tangents to A and
Di, and denote by T −
i
and T +
i
the halfplanes that are bounded by these tangents and are openly disjoint from A. The labels T −
i
and T +
i
are chosen such that the points of tangency between A and T −
i
, Di, and
T +
i
, appear along the boundary of A in this counterclockwise order. One can show that the nine points of tangency between A and the other disks and tangents are pairwise distinct (see Figure 9). We regard the six halfplanes T −
i
, T +
i
, for i = 1 , 2, 3, as (very large) disks; in the end, we can apply a suitable inversion to turn the disks and halfplanes into actual disks, if so desired. Finally, we construct three additional disks A1, A2, A3. To construct Ai, we slightly expand A into a disk A′
i
of radius 1 + ε1, while keeping the tangency with Di at ξi. We then roll A′
i
clockwise along Di,by a tiny angle ε2 ε1, to obtain Ai.This gives a set of 13 disks. For sufficiently small ε1 and ε2, we can ensure the following properties for each Ai: (i) Ai intersects all other 12 disks; (ii) the nine intersection regions Ai ∩ Dj , Ai ∩ T −
j
, Ai ∩ T +
j
,for j = 1 , 2, 3, are pairwise disjoint; and (iii) ξi /∈ Ai.
Theorem 5.3. The construction yields a set of 13 disks that cannot be stabbed by 3 points. Proof. Consider any set P of three points. Set A∗ = A ∪ A1 ∪ A2 ∪ A3. If P ∩ A∗ = ∅, we have unstabbed disks, so suppose that P ∩ A∗ 6 = ∅. For p ∈ P ∩ A∗, property (ii) implies that p stabs at most one of the nine remaining disks Dj , T +
j
and T −
j
, for j = 1 , 2, 3. Thus, if P ⊂ A∗, we would have unstabbed disks, so we may assume that |P ∩ A∗| ∈ { 1, 2}.Suppose first that |P ∩ A∗| = 2 . As just argued, at most two of the remaining disks are stabbed by
P ∩ A∗. The following cases can then arise. (a) None of D1, D2, D3 is stabbed by P ∩ A∗. Since {D1, D 2, D 3} is non-Helly and a non-Helly set must be stabbed by at least two points, at least one disk remains unstabbed. 12 D1D3AD2T −
1T +
1Figure 9: Each common tangent ` between A and Di represents a very large disk, whose interior is disjoint from A. The nine points of tangency are pairwise distinct. (b) Two disks among D1, D2, D3 are stabbed by P ∩ A∗. Then the six unstabbed halfplanes form many non-Helly triples, e.g., T −
1
, T −
2
, and T −
3
, and again, a disk remains unstabbed. (c) The set P ∩ A∗ stabs one disk in {D1, D 2, D 3} and one halfplane. Then, there is (at least) one disk Di such that Di and its two tangent halfplanes T −
i
, T +
i
are all unstabbed by P ∩ A∗. Then,
{Di, T −
i
, T +
i
} is non-Helly, and at least 2 more points are needed to stab it. Suppose now that |P ∩ A∗| = 1 , and let P ∩ A∗ = {p}. We may assume that p stabs all four disks A, A1,
A2, A3, since otherwise a disk would stay unstabbed. By property (iii), we can derive p 6 ∈ { ξ1, ξ 2, ξ 3}.Now, since p ∈ A \ { ξ1, ξ 2, ξ 3}, the point p does not stab any of D1, D2, D3. Moreover, by property (ii), the point p can only stab at most one of the remaining halfplanes. Since {D1, D 2, D 3} is non-Helly, it requires two stabbing points. Moreover, since |P \ { p}| = 2 , it must be the case that one point q of
P \ A∗ is the point of tangency of two of these disks, say q = D2 ∩ D3. Then, q stabs only two of the six halfplanes, say, T −
1
and T +1 . But then, {D1, T +2 , T −
3
} is non-Helly and does not contain any point from
{p, q }. At least one disk remains unstabbed.
6 Conclusion
We gave a simple linear-time algorithm, based on techniques for solving LP-type problems, to find five stabbing points for a set of pairwise intersecting disks in the plane. The arXiv manuscript by Carmi, Katz, and Morin claims a similar linear-time algorithm for finding four stabbing points. It would now be interesting to see whether these results, the ones by Danzer, Stachó, and ours, could be used to find new deterministic approximation algorithms for computing large cliques in disk graphs; refer to [2, 3] for the known algorithms. On the lower-bound side, it is still not known whether nine disks can always be stabbed by three points or not. For eight disks, we provided a proof that three points always suffice, as already mentioned by Stachó . The lower bound construction of Danzer with ten disks can easily be verified for pseudo-disks. However, the example is not easy to draw, even with the help of geometry processing software. Until now, we were not able to check whether his pseudo-disk arrangement can be realized as a Euclidean disk arrangement. 13 References
N. Alon and D. J. Kleitman. Piercing convex sets and the Hadwiger-Debrunner (p, q )-problem. Adv. Math. , 96(1):103–112, 1992. C. Ambühl and U. Wagner. The clique problem in intersection graphs of ellipses and triangles.
Theory of Computing Systems , 38(3):279–292, 2005. M. Bonamy, E. Bonnet, N. Bousquet, P. Charbit, and S. Thomassé. EPTAS for max clique on disks and unit balls. In Proc. 59th Annu. IEEE Sympos. Found. Comput. Sci. (FOCS) , pages 568–579, 2018. P. Carmi, M. J. Katz, and P. Morin. Stabbing pairwise intersecting disks by four points.
arXiv:1812.06907 , 2018. T. M. Chan. An optimal randomized algorithm for maximum Tukey depth. In Proc. 15th Annu. ACM-SIAM Sympos. Discrete Algorithms (SODA) , pages 430–436, 2004. B. Chazelle. The Discrepancy Method—Randomness and Complexity . Cambridge University Press, Cambridge, 2001. B. Chazelle and J. Matoušek. On linear-time deterministic algorithms for optimization problems in fixed dimension. J. Algorithms , 21(3):579–597, 1996. B. N. Clark, C. J. Colbourn, and D. S. Johnson. Unit disk graphs. Discrete Mathematics , 86(1-3):165–177, 1990. L. Danzer. Zur Lösung des Gallaischen Problems über Kreisscheiben in der Euklidischen Ebene.
Studia Sci. Math. Hungar. , 21(1-2):111–134, 1986. A. Dumitrescu and M. Jiang. Piercing translates and homothets of a convex body. Algorithmica ,61(1):94–115, 2011. B. Grünbaum. On intersections of similar sets. Portugal. Math. , 18:155–164, 1959. H. Hadwiger and H. Debrunner. Ausgewählte Einzelprobleme der kombinatorischen Geometrie in der Ebene. Enseignement Math. (2) , 1:56–89, 1955. E. Helly. Über Mengen konvexer Körper mit gemeinschaftlichen Punkten. Jahresbericht der Deutschen Mathematiker-Vereinigung , 32:175–176, 1923. E. Helly. Über Systeme von abgeschlossenen Mengen mit gemeinschaftlichen Punkten. Monatshefte für Mathematik , 37(1):281–302, 1930. R. M. Karp. Reducibility among combinatorial problems. In Proceedings of a symposium on the Complexity of Computer Computations , pages 85–103, 1972. M. Löffler and M. van Kreveld. Largest bounding box, smallest diameter, and related problems on imprecise points. Comput. Geom. , 43(4):419–433, 2010. J. Radon. Mengen konvexer Körper, die einen gemeinsamen Punkt enthalten. Mathematische Annalen , 83(1):113–115, 1921. R. Seidel. Small-dimensional linear programming and convex hulls made easy. Discrete Comput. Geom. , 6:423–434, 1991. M. Sharir and E. Welzl. A combinatorial bound for linear programming and related problems. Proc. 9th Sympos. Theoret. Aspects Comput. Sci. (STACS) , pages 567–579, 1992. L. Stachó. Über ein Problem für Kreisscheibenfamilien. Acta Sci. Math. (Szeged) , 26:273–282, 1965. 14 L. Stachó. A solution of Gallai’s problem on pinning down circles. Mat. Lapok , 32(1-3):19–47, 1981/84. D. Zuckerman. Linear degree extractors and the inapproximability of max clique and chromatic number. In Proc. 38th Annu. ACM Sympos. Theory Comput. (STOC) , pages 681–690, 2006. 15 |
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Trigonometry
Trigonometry is the study of relations between the side lengths and angles of triangles through the trigonometric functions. It is a fundamental branch of mathematics, and its discovery paved the way towards countless famous results.
In contest math, trigonometry is an integral subfield of both geometry and algebra. Many essential results in geometry are written in terms of the trigonometric functions, such as the Law of Sines and the Law of Cosines; many more, such as Stewart's Theorem, are most easily proven using trigonometry. In algebra, expressions involving the trigonometric functions appear frequently on contests. These are solved by clever usage of the trigonometric functions' countless identities, which can simplify otherwise unwieldy equations.
Outside of competition math, trigonometry is the backbone of much of analysis. In particular, Fourier Analysis is written almost entirely in the language of the trigonometric functions.
Contents
[hide]
1 Definitions
1.1 Right triangle definition
1.2 Unit circle definition
1.3 Taylor series definition
2 Applications in Geometry
2.1 Law of Sines
2.2 Law of cosines
3 Trigonometric identities
4 See also
Definitions
The trigonometric functions can be defined in several equivalent ways. The definition usually taught first is the right triangle definition, for its ease of access. An intermediate to olympiad geometry course usually uses the unit circle definition of trigonometry. Beyond the scope of contest math, the Taylor series definition of trigonometry is preferred in order to extend trigonometry to a complex domain.
Right triangle definition
The right triangle definition of trigonometry involves the ratios between edges of a right triangle, with respect to a given angle. The definitions below will be referring to angle , with side lengths specified in the diagram. Because angle must be less than for the triangle to stay right, these definitions only work for acute angles.
Sine: The sine of angle , denoted , is defined as the ratio of the side opposite to the hypotenuse.
Cosine: The cosine of angle , denoted , is defined as the ratio of the side adjacent to the hypotenuse.
Tangent: The tangent of angle , denoted , is defined as the ratio of the side opposite to the side adjacent to .
A common mnemonic to remember this is SOH-CAH-TOA, where Sine = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, and Tangent = Opposite / Adjacent
More uncommon are the reciprocals of the trigonometric functions, listed below.
Cosecant: The cosecant of angle , denoted , is defined as the reciprocal of the sine of .
Secant: The secant of angle , denoted , is defined as the reciprocal of the cosine of .
Cotangent: The cotangent of angle , denoted , is defined as the reciprocal of the tangent of .
The right triangle definition is most commonly taught in introductory geometry classes for its simplicity. However, it has its limitations. It only works if is right, which means that the trigonometric functions are only defined when angle is acute.
Even though it is defined using right triangles, trigonometry is just as useful when used on acute and obtuse triangles. The Law of Sines and Law of Cosines mentioned below generalize the right triangle definition to include all triangles.
Unit circle definition
Consider the unit circle, the circle with radius one centered at the origin. Starting at , walk a distance counterclockwise around the unit circle, as shown in the diagram. The coordinates of this point are defined to be .
As for the other trigonometric functions, is defined to be the ratio of to , and cosecant, secant, and cotangent are defined to be the reciprocals of sine, cosine, and tangent, respectively.
The benefit of this definition is that it matches the right triangle definition for acute angles, but extends their domain from acute angles to all real-valued angles. As such, this definition is usually preferred in intermediate to olympiad geometry settings.
Taylor series definition
The Taylor series for sine and cosine are used as their definitions in all higher mathematics. This meets the rigorous standards of real analysis, and gives a concrete way to extend the definitions of trigonometric functions from the real numbers to the full complex plane. The Taylor series for sine and cosine are shown below: These formulas are not used in high school math competitions. However, they do appear on the Putnam and other undergraduate competitions.
Applications in Geometry
While trigonometry is useful at any level, intermediate competitions are particularly fond of geometry problems demanding trigonometry. In addition to those mentioned, here are some highlights of the applications of trigonometry to geometry:
Law of Sines
The Law of Sines states that in any , where is the side opposite to , opposite to , opposite to , and is the circumradius of . The law of sines is particularly handy in problems involving the circumradius, seeing extremely wide usage in intermediate geometry.
Law of cosines
The Law of Cosines states that in any , where is the side opposite to , opposite to , and opposite to . It is a generalization of the Pythagorean Theorem and is used to prove several famous results, such as Heron's Formula and Stewart's Theorem. However, it sees limited applicability compared to the Law of Sines, as usage of the Law of Cosines can get algebra-heavy. It is helpful to memorize common, "nicer" values of sine and cosine as it can come in handy in contests, especially if you wish to apply either this or the Law of Sines to problems.
Trigonometric identities
Trigonometric identities are expressions true for all inputs involving the trigonometric functions. Due to the natural relationship between their definitions, these identities run numerous. In contest math, the most useful of these are:
Pythagorean identities
Angle addition identities
Double angle identities
Half angle identities
Sum-to-product identities
Product-to-sum identities
See also
Trigonometric identities
Law of Sines
Law of Cosines
Stewart's Theorem
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1.1 Examples
2 Related calculations
3 Related pages
4 References
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From Simple English Wikipedia, the free encyclopedia
The Simple English Wiktionary has a definition for: mean.
In mathematics and statistics, the mean is a kind of average. Besides the mean, there are other kinds of average, and there are also a few kinds of mean. While arithmetic mean is the most commonly used mean, there are various other means and they are calculated differently. It is important to know the difference as many websites and authors have got this wrong.
Mean of some values under an operations can be thought of as the value by which we can replace all the previous values and still get the same accumulation over the operation. Here, operation is important as it determines the way accumulation is calculated and in turn what kind of mean is the actual representative of the problem at the hand.
For example, if the operation is addition, then the mean would be arithmetic mean, if the operation is product then the mean would be the geometric mean, and so on.
Arithmetic mean is calculated by adding all of the values together, then dividing by the number of values. For example, if 1, 2, 2, 100, 100 is a set of numbers or scores. If we add all the numbers, the answer is 205. By dividing this number by the number of numbers (5), we find that the mean is 41. The difficulty with this particular set of numbers is that no one in this group scored anything like a 41, and it does not tell us much about what kind of scores these numbers represent.
Calculation details
[change | change source]
In general, to find the average of numbers, the numbers are added and the total is divided by .
In symbols, if the numbers are , , , ... , the total is:
The total is divided by to make the average:
If , , , ..., are all the numbers in a sample , then this average is also called the sample mean of , and represented by the symbol .
Examples
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Lucy is 5 years old. Tom is 6 years old. Emily is 7 years old. To find the average age:
Add the three numbers :
: The total is 18. Divide the total 18 by three:
The average of the three numbers is 6.
: Therefore, the average age of Lucy, Tom and Emily is 6 years.
Related calculations
[change | change source]
The idea behind the mean is to represent a number of measurements, or values, by one value only. But there are different ways to calculate such a representing value.
The median is the number that divides all the samples in such a way that half of the samples are below it, and the other half above. Example: 1, 10, 50, 100, 100 is a set of numbers or scores. If we look at these scores, we discover that the number 50 falls in the middle of the range of numbers, which tells us that half the numbers or scores are above this number, and half the numbers and scores are below this number. This is more information, depending on what you are trying to find out about this group of numbers, to help you find out what you want to know. It is not always possible to make the higher and lower group each exactly half of the total (for example, the equal division fails for the list 1, 2, 2).
The modus or mode is the number that occurs most often. Example: 1, 2, 2, 100, 200 is a set of numbers or scores. If we look at the numbers we discover that the number 2 recurs most often and would tell us that the number or score of 2 is the most common score or number in the group.
The arithmetic mean is just the average, the value that is the sum of all values, divided by their number. This is what is most often referred to as mean.
The geometric mean is the root of the product of all values. For example, the geometric mean of 4, 6, and 9 is 6, because 4 times 6 times 9 is 216, and the cube root (because there are three values) of 216 is 6.
The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals. It is often used when people want a mean of rates or percentages.
The root mean square (or quadratic mean) is the square root of the arithmetic mean of the squares of the values. The root mean square is at least as high as the arithmetic mean, and usually higher.
If people do many different measurements, they will get many different results. Those results have a certain distribution, and they can also be centered around an average value. This average value is what mathematicians call arithmetic mean.
Mean can also stand for expected value. For a random variable , this is represented by the symbol .
Related pages
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Standard deviation
References
[change | change source]
↑ 1.0 1.1 "List of Probability and Statistics Symbols". Math Vault. 2020-04-26. Retrieved 2020-08-21.
↑ 2.0 2.1 "Mean | mathematics". Encyclopedia Britannica. Retrieved 2020-08-21.
↑ Weisstein, Eric W. "Mean". mathworld.wolfram.com. Retrieved 2020-08-21.
| v t e Statistics |
| Outline Index |
| | Descriptive statistics | | | | | | | | | | | --- --- --- --- | | Continuous data | | | | --- | | Center | Mean + arithmetic + geometric + harmonic + cubic + generalized/power Median Mode | | Dispersion | Variance Standard deviation Average absolute deviation Coefficient of variation Percentile Range Interquartile range | | Shape | Central limit theorem Moments + Skewness + Kurtosis + L-moments | | | Count data | Index of dispersion | | Summary tables | Grouped data Frequency distribution Contingency table | | Dependence | Pearson product-moment correlation Rank correlation + Spearman's ρ + Kendall's τ Partial correlation Scatter plot | | Graphics | Bar chart Biplot Box plot Control chart Correlogram Fan chart Forest plot Histogram Pie chart Q–Q plot Run chart Scatter plot Stem-and-leaf display Radar chart Violin plot | | |
| | Data collection | | | | | --- | | Study design | Population Statistic Effect size Statistical power Optimal design Sample size determination Replication Missing data | | Survey methodology | Sampling + stratified + cluster Standard error Opinion poll Questionnaire | | Controlled experiments | Scientific control Randomized experiment Randomized controlled trial Random assignment Blocking Interaction Factorial experiment | | Adaptive Designs | Adaptive clinical trial Up-and-Down Designs Stochastic approximation | | Observational Studies | Cross-sectional study Cohort study Natural experiment Quasi-experiment | | |
| | Statistical inference | | | | | --- | | Statistical theory | Population Statistic Probability distribution Sampling distribution + Order statistic Empirical distribution + Density estimation Statistical model + Model specification + Lp space Parameter + location + scale + shape Parametric family + Likelihood (monotone) + Location–scale family + Exponential family Completeness Sufficiency Statistical functional + Bootstrap + U + V Optimal decision + loss function Efficiency Statistical distance + divergence Asymptotics Robustness | | Frequentist inference | | | | --- | | Point estimation | Estimating equations + Maximum likelihood + Method of moments + M-estimator + Minimum distance Unbiased estimators + Mean-unbiased minimum-variance - Rao–Blackwellization - Lehmann–Scheffé theorem + Median unbiased Plug-in | | Interval estimation | Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling + Bootstrap + Jackknife | | Testing hypotheses | 1- & 2-tails Power + Uniformly most powerful test Permutation test + Randomization test Multiple comparisons | | Parametric tests | Likelihood-ratio Score/Lagrange multiplier Wald | | | Specific tests | | | | Z-test (normal) Student's t-test F-test | | Goodness of fit | Chi-squared G-test Kolmogorov–Smirnov Anderson–Darling Lilliefors Jarque–Bera Normality (Shapiro–Wilk) Likelihood-ratio test Model selection + Cross validation + AIC + BIC | | Rank statistics | Sign + Sample median Signed rank (Wilcoxon) + Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova + 1-way (Kruskal–Wallis) + 2-way (Friedman) + Ordered alternative (Jonckheere–Terpstra) | | | Bayesian inference | Bayesian probability + prior + posterior Credible interval Bayes factor Bayesian estimator + Maximum posterior estimator | | |
| | Correlation Regression analysis | | | | | --- | | Correlation | Pearson product-moment Partial correlation Confounding variable Coefficient of determination | | Regression analysis | Errors and residuals Regression validation Mixed effects models Simultaneous equations models Multivariate adaptive regression splines (MARS) | | Linear regression | Simple linear regression Ordinary least squares General linear model Bayesian regression | | Non-standard predictors | Nonlinear regression Nonparametric Semiparametric Isotonic Robust Heteroscedasticity Homoscedasticity | | Generalized linear model | Exponential families Logistic (Bernoulli) / Binomial / Poisson regressions | | Partition of variance | Analysis of variance (ANOVA, anova) Analysis of covariance Multivariate ANOVA Degrees of freedom | | |
| | Categorical / Multivariate / Time-series / Survival analysis | | | | | --- | | Categorical | Cohen's kappa Contingency table Graphical model Log-linear model McNemar's test Cochran-Mantel-Haenszel statistics | | Multivariate | Regression Manova Principal components Canonical correlation Discriminant analysis Cluster analysis Classification Structural equation model + Factor analysis Multivariate distributions + Elliptical distributions - Normal | | Time-series | | | | --- | | General | Decomposition Trend Stationarity Seasonal adjustment Exponential smoothing Cointegration Structural break Granger causality | | Specific tests | Dickey–Fuller Johansen Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey | | Time domain | Autocorrelation (ACF) + partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional heteroskedasticity (ARCH) Vector autoregression (VAR) | | Frequency domain | Spectral density estimation Fourier analysis Wavelet Whittle likelihood | | | Survival | | | | --- | | Survival function | Kaplan–Meier estimator (product limit) Proportional hazards models Accelerated failure time (AFT) model First hitting time | | Hazard function | Nelson–Aalen estimator | | Test | Log-rank test | | | |
| | | | | | | --- | | Biostatistics | Bioinformatics Clinical trials / studies Epidemiology Medical statistics | | Engineering statistics | Chemometrics Methods engineering Probabilistic design Process / quality control Reliability System identification | | Social statistics | Actuarial science Census Crime statistics Demography Econometrics Jurimetrics National accounts Official statistics Population statistics Psychometrics | | Spatial statistics | Cartography Environmental statistics Geographic information system Geostatistics Kriging | | |
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189645 | https://www.nagwa.com/en/videos/293139814842/ | Question Video: Stating the Parity of a Function Mathematics • Second Year of Secondary School
Is the function 𝑓(𝑥) = 𝑥⁵ tan⁴ (6𝑥) even, odd, or neither even nor odd?
Video Transcript
Is the function 𝑓 of 𝑥 equals 𝑥
to the fifth power times tan of six 𝑥 to the fourth power even, odd, or neither
even nor odd?
Let’s recall how we check the
parity of a function. The first thing we do is check the
domain of the function. We need that to be centered at 𝑥
equals zero. Then, if the answer is no, we can
say that the function is neither even nor odd without performing any further
tests. If the answer is yes, though, we
say that it will be even if it satisfies 𝑓 of negative 𝑥 equals 𝑓 of 𝑥. And it will be odd if it satisfies
𝑓 of negative 𝑥 equals negative 𝑓 of 𝑥. Then, of course, if it satisfies
neither of these, it will be neither even nor odd.
So let’s think about the domain of
our function. Our function is the product of two
functions. It’s the product of 𝑥 to the fifth
power and tan of six 𝑥 to the fourth power. And so the domain of 𝑓 of 𝑥 will
be the intersection of the domains of the respective parts of the function. Well, 𝑥 to the fifth power is a
polynomial, so its domain is the set of real numbers or the open interval from
negative ∞ to ∞. But what about the domain of the
trigonometric part? Well, it’s all real numbers, except
those that make cos of six 𝑥 equal to zero. But since the values of 𝑥 that
make cos of six 𝑥 equal to zero are symmetrical about the 𝑦-axis, then we can say
that the domain of tan of six 𝑥 to the fourth power must be centered at 𝑥 equals
zero.
Since both domains are centered at
𝑥 equals zero, then we can answer yes to this first question, and we’re able to
move on. We now see that it’s even if 𝑓 of
negative 𝑥 is equal to 𝑓 of 𝑥 and odd if it’s equal to negative 𝑓 of 𝑥. And so let’s evaluate 𝑓 of
negative 𝑥. To do so, we replace each instance
of 𝑥 in our original function with negative 𝑥. And we get 𝑓 of negative 𝑥 is
negative 𝑥 to the fifth power times tan of negative six 𝑥 to the fourth power. We’ll evaluate each part in
turn. Let’s begin with negative 𝑥 to the
fifth power. Since the exponent is odd, when we
multiply this out, we’re going to get a negative result. Negative 𝑥 to the fifth power is
as shown.
But what about the tan
function? Well, we can actually quote the
result that tan of 𝑥 is odd, meaning that tan of negative 𝑥 is equal to negative
tan of 𝑥 and, in turn, the tan of negative six 𝑥 is equal to negative tan of six
𝑥. But of course, we’re raising this
to the fourth power. We’re raising it to an even
exponent. And we know when we raise a
negative number to an even exponent, the result is positive. And so tan of negative six 𝑥 to
the fourth power is just tan of six 𝑥 to the fourth power.
And so 𝑓 of negative 𝑥 is
therefore equal to negative 𝑥 to the fifth power times tan of six 𝑥 to the fourth
power. So does this satisfy either of our
criteria, is it even or odd? Well, yes. If we look at it carefully, we see
it’s the same as negative 𝑓 of 𝑥. 𝑓 of negative 𝑥 is equal to
negative 𝑓 of 𝑥. And so the function must be
odd.
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189646 | http://www.grad.hr/geomteh3d/skripta/konj_promjeri_eng.html | Conjugated diameters of a conic
| | | | | |
--- ---
| A line between two points of a conic is called a chord.Midpoints of parallel chords of a conic are collinear points and the line connecting them is called a diameter of a conic. We say this diameter is conjugate to this direction of parallel chords. Tangent lines that pass through real intersections of a diameter and a conic are always parallel and have the same direction as the chords conjugate to that diameter. Every conic has infinitely many diameters and they pass through one point called the center of the conic. Parabola's center is a point at infinity that lies on its axis. Look at all chords parallel to one diameter. Midpoints of this chords lie on another diameter that has the same direction as the chords conjugate to the first diameter. Such two diameters are called conjugate diameters. Two diameters are conjugate if each bisects the chords parallel to the other diameter. The following is important: - Both conjugate diameters intersect an ellipse in real points. - One diameter intersects a hyperbola in real points while its conjugate diameter intersects this hyperbola in a pair of conjugate imaginary points. - All diameters of a parabola are parallel to its axis and the line at infinity is conjugate to all of them. Since the tangents at the intersections of a diameter and a conic are parallel and every diameter of an ellipse intersects it in real points, the following holds for conjugate diameters of an ellipe: Two diameters of an ellipse are conjugate if the tangents at intersections of one diameter and this ellipse are parallel to the other diameter. Generally, conjugate diameters of an ellipse or a hyperbola are not perpendicular. However, for these conics exists exactly one pair of perpendicular conjugate diameters. Pair of perpendicular conjugate diameters of an ellipse or a hyperbola are called axes of that conic. Lines that carry the axes of an ellipse or a hyperbola are axes of symmetry of these curves. Parabola has only one axis of symmetry. Intersection points of a conic and its axes are called vertices of a conic. Ellipse has four vertices, hyperbola two and parabola one. A circle, a special case of an ellipse, has some interesting properties. We recall from elementary school that a circle has infinitely many axes of symmetry (it is symmetrical with respect to any line passing through its center) and that in every point on a circle, the tangent at that point is perpendicular to the diameter that passes through that point. Therefore, the following holds: Every pair of perpendicular diameters of a circle are conjugate. | | | --- | | | | Figure 9 | | | --- | | | | Figure 10 Created by Sonja Gorjanc, translated by Helena Halas and Iva Kodrnja - 3DGeomTeh - Developing project of the University of Zagreb | |
189647 | https://dcbeportfolio.weebly.com/uploads/2/4/6/1/24615843/day_8_-_exponential_functions.pdf | Day 8 – Exponential Functions Lesson Plan Name:__Diane Baker____ Grade: 9th_ Subject: Algebra I______ Planned Lesson Date: _March 3, 2015 _ Lesson Objectives • 2 or 3 student outcomes • Begin with verb Learning Objective • Evaluate and graph exponential functions. Nat’l / State Standards • AL College & Career Ready Course of Study -‐ Common Core • Learning Targets / District Standards • National Standards (NCTM; NCTE; etc) Alabama Course of Study Objective • Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. [F.IF.7.e] Learning Target • I can evaluate and graph an exponential function. Pre-‐Instructional Activities • Review • Formative Assessment • Introductory Set • Prior Knowledge • Essential Questions • Problem Question • Writing Prompts • Predictions / Purpose • Vocabulary Take attendance. Return graded work. Prior Knowledge • Bell ringer: End-‐of-‐Course Test Practice Simplify the radical expression given an integer value for the variable. Review • Post answer keys for Page 450, 11 – 35 odd and Section 7-‐5: Rational Exponents and Radicals Worksheet • Question and answer period Essential Questions • How do you evaluate an exponential function? • How do you graph an exponential function? Vocabulary • Present the Chapter 7 – Section 6 Exponential Functions PPT. • Depict an exponential function and label the parts. Students copy the picture and label the parts. • Compare/contrast an exponential function to a linear function. Using prior knowledge, students make the connection that exponential functions are similar to linear functions in many ways, but their graphs are different. • Graphically depict an exponential function. Class discussion concerning the graph of an exponential function, i.e. y-‐intercept, asymptote, and end behavior, etc. • Compare/contrast the graph of an exponential function to its representation in data table. Students make the connection that graphs and tables are two different ways of displaying the same information. Teaching • Direct Teaching • Graphic Organizers • Reading Instruction • Tech Integration • Teacher Demonstration • Guided Practice • Independent Practice • Small Group Activities • Experiential Activities • Research / Study • Simulations • Problem Solving Activities • Differentiated Instruction • Accommodations • Ongoing Assessment Guided Practice/Class Discussion • Distribute the student copy of “Alice in Wonderland”, the Graphing Exponential Functions Rubric, and several copies of the First Quadrant Graph Paper to each student. • Students read “The Situation of Alice”. • Ask open-‐ended questions so students make the connection that Alice is shrinking exponentially when she takes a drink and growing exponentially when she eats the cake. • Students read “The Questions”. • Working with the students, answer the five questions and have the students take notes. • Create a table to represent Alice’s height after she eats each ounce of cake. Create a second table to represent Alice’s height after she drinks each ounce of beverage. Encourage students to copy the tables so they have the information for their assignment. Reading Instruction • Read through the directions for “Homework 1: Graphing Alice” with the students. • Identify the assumption that Alice is initially 1 foot tall. • Walk through the procedure for setting up problems 1a and 1b as well as 2a and 2b. • Briefly read through problems 3 and 4 and answer questions and/or clarify points of confusion. • Walk through each of the questions listed under problem 5 and discuss the answers to each question. Independent Practice • Assignment: Homework 1: Graphing Alice. The project is due in one week and will count as a quiz grade. Tech Integration • Chapter 7 – Section 6 – Exponential Functions PPT, student copy of “Alice in Wonderland”, Graphing Exponential Functions Rubric, and First Quadrant Graph Paper are posted on the class Edmodo page. • Students may take snapshots of the class notes with their electronic devices. • Students may use scientific calculators for problem solving. Differentiated Instruction • While some students could have completed the project with only minimal guidance, most students require varying degrees of assistance to complete this project. A step-‐by-‐step walkthrough of the procedure required for the first half of the project is presented to the students so that everyone has a common understanding of how to calculate the changes in Alice’s height when she eats the cake or drinks the beverage. To deepen the students’ understanding, data table are created to summarize the results and students can use this information to create their graphs. Problem 5 is addressed through the class discussion so that everyone has a clear picture of their expected results should be. Closure • Summary / Conclusions • Re-‐teaching • Formative Assessment • Review • Reflection Summary/Conclusions • Remind students to use their class notes and the Chapter 7 – Section 6 – Exponential Functions PPT on the class Edmodo page to help them complete the project. • Encourage students to work together on the project outside of class and use other resources, such as their textbook and online graphing applications, for help. Materials Needed: Bell Ringer – End of Course Test Practice Chapter 7 – Section 6 – Exponential Functions PPT Chapter 7 – Section 6 – Alice in Wonderland – Teacher Notes Chapter 7 – Section 6 – Alice in Wonderland – Student Copy Chapter 7 – Section 6 – Graphing Exponential Functions Rubric Chapter 7 – Section 6 – Individual Grading Rubrics Chapter 7 – Section 6 – First Quadrant Graph Paper Chapter 7 – Section 6 – Homework 1 – Graphing Alice – Answer Key Chapter 7 – Section 6 – Exponential Function Graphs – Answer Key Resources: Interactive Mathematics Program – Year 2 (1998) Pearson’s Algebra I Common Core textbook (2012) Teacher Reflection: The students were excited about this project. Almost everyone is familiar with story of Alice in Wonderland and could visualize the changes to Alice’s height during the class discussion about exponential growth and shrinkage. Students did not have any problems summarizing the data in a table. However, they were hesitant to graph the information. Having an extra day to work on this project in class would benefit many students so they could work together in cooperative groups. |
189648 | https://www.youtube.com/watch?v=YtkIThSpwyw | Finding the imaginary part of a complex number.
The Mathmagic Show
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Posted: 22 Feb 2020
🚀 In this video, we explore how to find the imaginary part of a complex number, Z, using a simple formula (Z - Z̅) / 2i. 🎓✨
We'll start by representing Z as x + iy, where x is the real part and y is the imaginary part of the complex number. We'll then calculate Z̅, the conjugate of Z, which is x - iy. By following the formula, we'll subtract Z̅ from Z and divide the result by 2i. 🧠🔢
After simplifying the expression, we'll see that the formula leaves us with the imaginary part, y, of the complex number Z. 🎉💡
We'll also provide a visual representation of the complex number Z on the real and imaginary axes, helping you understand the concept even better. 📊👁️
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How do I find the imaginary part of a complex number?
What is the formula for finding the imaginary part of a complex number?
How do I represent complex numbers using X + iY notation?
How do I simplify a complex number expression?
What is the difference between real and imaginary parts of a complex number?
How do I plot a complex number on the complex plane?
What is the purpose of the imaginary axis on the complex plane?
How do I add, subtract, multiply, or divide complex numbers?
Are there any real-life applications for complex numbers?
How do I calculate the magnitude and phase angle of a complex number?
4 comments
Transcript:
I just want to convince ourselves that following is to an imaginary part of a complex number Z is defined to be essentially you can find it by doing Z minus Z bar divided by 2 I let's go and actually confirm this so first just introduce X plus iy to represents Z keep the - and does D bar it is X plus y I just change the sign in the middle - it negative so it becomes X minus iy / - I write it better so now distribute that negative to each term here so I have X plus I Y - X plus iy the whole thing is divided by 2 I continue here cancel off what you can so specifically notice that X and negative x are opposites so basically erase them away and that gives you then the following iy + iy / - I continue so now this is going to give you 2 y I over 2i and now I hope you see why you need to have and the denominated entire time - why because this has to cancel it with this this cancels with that and it leaves Y and this is the imaginary part of the number Z so in other words in terms of a picture roughly speaking what it's doing for us is this let me fix that so so it's straighter okay that's a bit better here we are so this is the number Z right here which is X plus I Y so this is the real axis in this context the imaginary axis most context then the y part of the number that would be right here that's your imaginary part right here and that is what this allows you to find for a complex number Z thanks so much I'll see you another video give a like and subscribe |
189649 | https://phys.libretexts.org/Bookshelves/College_Physics/College_Physics_1e_(OpenStax)/02%3A_Kinematics/2.03%3A_Time_Velocity_and_Speed | 2.3: Time, Velocity, and Speed - Physics LibreTexts
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2: Kinematics
College Physics 1e (OpenStax)
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2.3: Time, Velocity, and Speed
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2. Bookshelves
3. College Physics
4. College Physics 1e (OpenStax)
5. 2: Kinematics
6. 2.3: Time, Velocity, and Speed
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College Physics 1e (OpenStax)
Front Matter
1: The Nature of Science and Physics
2: Kinematics
3: Two-Dimensional Kinematics
4: Dynamics- Force and Newton's Laws of Motion
5: Further Applications of Newton's Laws- Friction, Drag, and Elasticity
6: Uniform Circular Motion and Gravitation
7: Work, Energy, and Energy Resources
8: Linear Momentum and Collisions
9: Statics and Torque
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11: Fluid Statics
12: Fluid Dynamics and Its Biological and Medical Applications
13: Temperature, Kinetic Theory, and the Gas Laws
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17: Physics of Hearing
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19: Electric Potential and Electric Field
20: Electric Current, Resistance, and Ohm's Law
21: Circuits, Bioelectricity, and DC Instruments
22: Magnetism
23: Electromagnetic Induction, AC Circuits, and Electrical Technologies
24: Electromagnetic Waves
25: Geometric Optics
26: Vision and Optical Instruments
27: Wave Optics
28: Special Relativity
29: Introduction to Quantum Physics
30: Atomic Physics
31: Radioactivity and Nuclear Physics
32: Medical Applications of Nuclear Physics
33: Particle Physics
34: Frontiers of Physics
Back Matter
2.3: Time, Velocity, and Speed
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2.2: Vectors, Scalars, and Coordinate Systems
2.4: Acceleration
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Table of contents
1. Time
2. Velocity
3. Speed
4. Summary
5. Glossary
Learning Objectives
By the end of this section, you will be able to:
Explain the relationships between instantaneous velocity, average velocity, instantaneous speed, average speed, displacement, and time.
Calculate velocity and speed given initial position, initial time, final position, and final time.
Derive a graph of velocity vs. time given a graph of position vs. time.
Interpret a graph of velocity vs. time.
There is more to motion than distance and displacement. Questions such as, “How long does a foot race take?” and “What was the runner’s speed?” cannot be answered without an understanding of other concepts. In this section we add definitions of time, velocity, and speed to expand our description of motion.
Figure 2.3.1: The motion of these racing snails can be described by their speeds and their velocities. (credit: tobitasflickr, Flickr)
Time
As discussed in Physical Quantities and Units, the most fundamental physical quantities are defined by how they are measured. This is the case with time. Every measurement of time involves measuring a change in some physical quantity. It may be a number on a digital clock, a heartbeat, or the position of the Sun in the sky. In physics, the definition of time is simple—time is change, or the interval over which change occurs. It is impossible to know that time has passed unless something changes.
The amount of time or change is calibrated by comparison with a standard. The SI unit for time is the second, abbreviated s. We might, for example, observe that a certain pendulum makes one full swing every 0.75 s. We could then use the pendulum to measure time by counting its swings or, of course, by connecting the pendulum to a clock mechanism that registers time on a dial. This allows us to not only measure the amount of time, but also to determine a sequence of events.
How does time relate to motion? We are usually interested in elapsed time for a particular motion, such as how long it takes an airplane passenger to get from his seat to the back of the plane. To find elapsed time, we note the time at the beginning and end of the motion and subtract the two. For example, a lecture may start at 11:00 A.M. and end at 11:50 A.M., so that the elapsed time would be 50 min.Elapsed timeΔt is the difference between the ending time and beginning time,
Δt=t f−t 0,
where Δt is the change in time or elapsed time, t f is the time at the end of the motion, and t 0 is the time at the beginning of the motion. (As usual, the delta symbol, Δ, means the change in the quantity that follows it.)
Life is simpler if the beginning time t 0 is taken to be zero, as when we use a stopwatch. If we were using a stopwatch, it would simply read zero at the start of the lecture and 50 min at the end. If t 0=0, then
(2.3.1)Δt=t f≡t.
In this text, for simplicity’s sake,
motion starts at time equal to zero (t 0=0)
the symbol t is used for elapsed time unless otherwise specified (Δt=t f≡t)
Velocity
Your notion of velocity is probably the same as its scientific definition. You know that if you have a large displacement in a small amount of time you have a large velocity, and that velocity has units of distance divided by time, such as miles per hour or kilometers per hour.
Definition: AVERAGE VELOCITY
Average velocityis displacement (change in position) divided by the time of travel,
(2.3.2)v¯=Δx Δt=x f−x 0 t f−t 0.
where v¯ is the average (indicated by the bar over the v) velocity, Δx is the change in position (or displacement), and x f and x 0 are the final and beginning positions at times t f and t 0, respectively. If the starting time t 0 is taken to be zero, then the average velocity is simply
(2.3.3)v¯=Δx t.
Notice that this definition indicates that velocity is a vector because displacement is a vector. It has both magnitude and direction. The SI unit for velocity is meters per second or m/s, but many other units, such as km/h, mi/h (also written as mph), and cm/s, are in common use. Suppose, for example, an airplane passenger took 5 seconds to move −4 m (the negative sign indicates that displacement is toward the back of the plane). His average velocity would be
(2.3.4)v¯=Δx t=−4 m 5 s=−0.8 m/s.
The minus sign indicates the average velocity is also toward the rear of the plane.
The average velocity of an object does not tell us anything about what happens to it between the starting point and ending point, however. For example, we cannot tell from average velocity whether the airplane passenger stops momentarily or backs up before he goes to the back of the plane. To get more details, we must consider smaller segments of the trip over smaller time intervals.
Figure 2.3.2: A more detailed record of an airplane passenger heading toward the back of the plane, showing smaller segments of his trip.
The smaller the time intervals considered in a motion, the more detailed the information. When we carry this process to its logical conclusion, we are left with an infinitesimally small interval. Over such an interval, the average velocity becomes the instantaneous velocity or the velocity at a specific instant. A car’s speedometer, for example, shows the magnitude (but not the direction) of the instantaneous velocity of the car. (Police give tickets based on instantaneous velocity, but when calculating how long it will take to get from one place to another on a road trip, you need to use average velocity.) Instantaneous velocityv is the average velocity at a specific instant in time (or over an infinitesimally small time interval).
Mathematically, finding instantaneous velocity, v, at a precise instant t can involve taking a limit, a calculus operation beyond the scope of this text. However, under many circumstances, we can find precise values for instantaneous velocity without calculus.
Speed
In everyday language, most people use the terms “speed” and “velocity” interchangeably. In physics, however, they do not have the same meaning and they are distinct concepts. One major difference is that speed has no direction. Thus speed is a scalar. Just as we need to distinguish between instantaneous velocity and average velocity, we also need to distinguish between instantaneous speed and average speed.
Instantaneous speed is the magnitude of instantaneous velocity. For example, suppose the airplane passenger at one instant had an instantaneous velocity of −3.0 m/s (the minus meaning toward the rear of the plane). At that same time his instantaneous speed was 3.0 m/s. Or suppose that at one time during a shopping trip your instantaneous velocity is 40 km/h due north. Your instantaneous speed at that instant would be 40 km/h—the same magnitude but without a direction. Average speed, however, is very different from average velocity. Average speedis the distance traveled divided by elapsed time.
We have noted that distance traveled can be greater than displacement. So average speed can be greater than average velocity, which is displacement divided by time. For example, if you drive to a store and return home in half an hour, and your car’s odometer shows the total distance traveled was 6 km, then your average speed was 12 km/h. Your average velocity, however, was zero, because your displacement for the round trip is zero. (Displacement is change in position and, thus, is zero for a round trip.) Thus average speed is not simply the magnitude of average velocity.
Figure 2.3.3: During a 30-minute round trip to the store, the total distance traveled is 6 km. The average speed is 12 km/h. The displacement for the round trip is zero, since there was no net change in position. Thus the average velocity is zero.
Another way of visualizing the motion of an object is to use a graph. A plot of position or of velocity as a function of time can be very useful. For example, for this trip to the store, the position, velocity, and speed-vs.-time graphs are displayed in Figure 2.3.4. (Note that these graphs depict a very simplified model of the trip. We are assuming that speed is constant during the trip, which is unrealistic given that we’ll probably stop at the store. But for simplicity’s sake, we will model it with no stops or changes in speed. We are also assuming that the route between the store and the house is a perfectly straight line.)
Figure 2.3.4: Position vs. time, velocity vs. time, and speed vs. time on a trip. Note that the velocity for the return trip is negative.
MAKING CONNECTIONS: TAKE-HOME INVESTIGATION - GETTING A SENSE OF SPEED
If you have spent much time driving, you probably have a good sense of speeds between about 10 and 70 miles per hour. But what are these in meters per second? What do we mean when we say that something is moving at 10 m/s? To get a better sense of what these values really mean, do some observations and calculations on your own:
calculate typical car speeds in meters per second
estimate jogging and walking speed by timing yourself; convert the measurements into both m/s and mi/h
determine the speed of an ant, snail, or falling leaf
Exercise 2.3.1
A commuter train travels from Baltimore to Washington, DC, and back in 1 hour and 45 minutes. The distance between the two stations is approximately 40 miles. What is
the average velocity of the train, and
the average speed of the train in m/s?
Answer
(a) The average velocity of the train is zero because x f=x 0; the train ends up at the same place it starts.
(b) The average speed of the train is calculated below. Note that the train travels 40 miles one way and 40 miles back, for a total distance of 80 miles.
distance time=80miles 105minutes
80miles 105minutes×5280feet 1mile×1meter 3.28feet×1minute 60seconds=20m/s
Summary
Time is measured in terms of change, and its SI unit is the second (s). Elapsed time for an event is Δt=t f−t 0, where t f is the final time and t 0 is the initial time. The initial time is often taken to be zero, as if measured with a stopwatch; the elapsed time is then just t.
Average velocity v¯ is defined as displacement divided by the travel time. In symbols, average velocity is v¯=Δx Δt=x f−x 0 t f−t 0.
The SI unit for velocity is m/s.
Velocity is a vector and thus has a direction.
Instantaneous velocity v is the velocity at a specific instant or the average velocity for an infinitesimal interval.
Instantaneous speed is the magnitude of the instantaneous velocity.
Instantaneous speed is a scalar quantity, as it has no direction specified.
Average speed is the total distance traveled divided by the elapsed time. (Average speed is not the magnitude of the average velocity.) Speed is a scalar quantity; it has no direction associated with it.
Glossary
average speeddistance traveled divided by time during which motion occursaverage velocitydisplacement divided by time over which displacement occursinstantaneous velocityvelocity at a specific instant, or the average velocity over an infinitesimal time intervalinstantaneous speedmagnitude of the instantaneous velocitytimechange, or the interval over which change occursmodelsimplified description that contains only those elements necessary to describe the physics of a physical situationelapsed timethe difference between the ending time and beginning time
This page titled 2.3: Time, Velocity, and Speed is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.
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Trigonometric identities
In trigonometry, trigonometric identities are equations involving trigonometric functions that are true for all input values. Trigonometric functions have an abundance of identities, of which only the most widely used are included in this article.
Contents
[hide]
1 Pythagorean identities
2 Angle addition identities
3 Double-angle identities
3.1 Cosine double-angle identity
4 Half-angle identities
5 Product-to-sum identities
6 Sum-to-product identities
7 Other identities
7.1 Triple-angle identities
7.2 Even-odd identities
7.3 Conversion identities
7.4 Euler's identity
7.5 Miscellaneous
8 Resources
9 See also
Pythagorean identities
The Pythagorean identities state that
Using the unit circle definition of trigonometry, because the point is defined to be on the unit circle, it is a distance one away from the origin. Then by the distance formula, . To derive the other two Pythagorean identities, divide by either or and substitute the respective trigonometry in place of the ratios to obtain the desired result.
Angle addition identities
The trigonometric angle addition identities state the following identities:
There are many proofs of these identities. For the sake of brevity, we list only one here.
Euler's identity states that . We have that By looking at the real and imaginary parts, we derive the sine and cosine angle addition formulas.
To derive the tangent addition formula, we reduce the problem to use sine and cosine, divide both numerator and denominator by , and simplify. as desired.
Double-angle identities
The trigonometric double-angle identities are easily derived from the angle addition formulas by just letting . Doing so yields:
Cosine double-angle identity
Here are two equally useful forms of the cosine double-angle identity. Both are derived via the Pythagorean identity on the cosine double-angle identity given above.
In addition, the following identities are useful in integration and in deriving the half-angle identities. They are a simple rearrangement of the two above.
Half-angle identities
The trigonometric half-angle identities state the following equalities:
The plus or minus does not mean that there are two answers, but that the sign of the expression depends on the quadrant in which the angle resides.
Consider the two expressions listed in the cosine double-angle section for and , and substitute instead of . Taking the square root then yields the desired half-angle identities for sine and cosine. As for the tangent identity, divide the sine and cosine half-angle identities.
Product-to-sum identities
The product-to-sum identities are as follows:
They can be derived by expanding out and or and , then combining them to isolate each term.
Sum-to-product identities
Substituting and into the product-to-sum identities yields the sum-to-product identities.
Other identities
Here are some identities that are less significant than those above, but still useful.
Triple-angle identities
All of these expansions can be proved using trick and perform the angle addition identities. Same for and for .
Even-odd identities
The functions , , , and are odd, while and are even. In other words, the six trigonometric functions satisfy the following equalities:
These are derived by the unit circle definitions of trigonometry. Making any angle negative is the same as reflecting it across the x-axis. This keeps its x-coordinate the same, but makes its y-coordinate negative. Thus, and .
Conversion identities
The following identities are useful when converting trigonometric functions.
All of these can be proven via the angle addition identities.
Euler's identity
Euler's identity is a formula in complex analysis that connects complex exponentiation with trigonometry. It states that for any real number , where is Euler's constant and is the imaginary unit. Euler's identity is fundamental to the study of complex numbers and is widely considered among the most beautiful formulas in math.
Similar to the derivation of the product-to-sum identities, we can isolate sine and cosine by comparing and , which yields the following identities:
They can also be derived by computing and . These expressions are occasionally used to define the trigonometric functions.
Miscellaneous
These are the identities that are not substantial enough to warrant a section of their own.
Resources
Table of trigonometric identities
List of Trigonometric Identities
See also
Trigonometry
Trigonometric substitution
Proofs of trig identities
Retrieved from "
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Trigonometry
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189651 | https://arxiv.org/abs/2101.09350 | [2101.09350] Eigenvalue bounds and spectral stability of Lamé operators with complex potentials
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arXiv:2101.09350 (math)
[Submitted on 22 Jan 2021]
Title:Eigenvalue bounds and spectral stability of Lamé operators with complex potentials
Authors:Biagio Cassano, Lucrezia Cossetti, Luca Fanelli
View a PDF of the paper titled Eigenvalue bounds and spectral stability of Lam\'e operators with complex potentials, by Biagio Cassano and 2 other authors
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Abstract:This paper is devoted to providing quantitative bounds on the location of eigenvalues, both discrete and embedded, of non self-adjoint Lamé operators of elasticity -\Delta^\ast + Vin terms of suitable norms of the potential V. In particular, this allows to get sufficient conditions on the size of the potential such that the point spectrum of the perturbed operator remains empty. In three dimensions we show full spectral stability under suitable form-subordinated perturbations: we prove that the spectrum is purely continuous and coincides with the non negative semi-axis as in the free case.
Subjects:Spectral Theory (math.SP); Mathematical Physics (math-ph); Analysis of PDEs (math.AP)
Cite as:arXiv:2101.09350 [math.SP]
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189652 | https://en.wikibooks.org/wiki/Timeless_Theorems_of_Mathematics/Mid_Point_Theorem | Timeless Theorems of Mathematics/Mid Point Theorem - Wikibooks, open books for an open world
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1 ProofToggle Proof subsection
1.1 Statement
1.2 Proof with the help of Congruent Triangles
1.3 Proof with the help of Coordinate Geometry
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From Wikibooks, open books for an open world
<Timeless Theorems of Mathematics
In this right triangle, A D=C D,B E=C E,D E=1 2 A B{\displaystyle AD=CD,BE=CE,DE={\frac {1}{2}}AB}and D E∥A B{\displaystyle DE\parallel AB} according to the Mid Point Theorem
The midpoint theorem is a fundamental concept in geometry that establishes a relationship between the midpoints of a triangle's sides. This theorem states that when you connect the midpoints of two sides of a triangle, the resulting line segment is parallel to the third side. Additionally, this line segment is precisely half the length of the third side.
Proof
[edit | edit source]
Statement
[edit | edit source]
In a triangle, if a line segment connects the midpoints of two sides, then this line segment is parallel to the third side and half its length.
Proof with the help of Congruent Triangles
[edit | edit source]
The construction for the mid-point theorem's proof with similar triangles
Proposition: Let D{\displaystyle D} and E{\displaystyle E} be the midpoints of A C{\displaystyle AC} and B C{\displaystyle BC} in the triangle A B C{\displaystyle ABC}. It is to be proved that,
D E∥A B{\displaystyle DE\parallel AB} and;
D E=1 2 A B{\displaystyle DE={\frac {1}{2}}AB}.
Construction: Add D{\displaystyle D} and E{\displaystyle E}, extend D E{\displaystyle DE} to F{\displaystyle F} as E F=D E{\displaystyle EF=DE}, and add B{\displaystyle B} and F{\displaystyle F}.
Proof: In the triangles Δ C D E{\displaystyle \Delta CDE} and Δ E B F,{\displaystyle \Delta EBF,}
C E=B E{\displaystyle CE=BE}; [Given]
D E=E F{\displaystyle DE=EF}; [According to the construction]
∠C E D=∠A E F{\displaystyle \angle CED=\angle AEF}; [Vertical Angles]
∴ Δ C D E≅Δ E B F{\displaystyle \Delta CDE\cong \Delta EBF}; [Side-Angle-Side theorem]
So, ∠C D E=∠B F E{\displaystyle \angle CDE=\angle BFE}
∴ C D∥B F{\displaystyle CD\parallel BF}
Or, A D∥B F{\displaystyle AD\parallel BF} and C D=B F=D A{\displaystyle CD=BF=DA}
Therefore, A D F B{\displaystyle ADFB} is a parallelogram.
∴ D F∥A B{\displaystyle DF\parallel AB} or D E∥A B{\displaystyle DE\parallel AB}
D F=A B{\displaystyle DF=AB}
Or D E+E F=A B{\displaystyle DE+EF=AB}
Or, D E+D E=A B{\displaystyle DE+DE=AB} [As, Δ C D E≅Δ E B F{\displaystyle \Delta CDE\cong \Delta EBF}]
Or, 2 D E=A B{\displaystyle 2DE=AB}
Or, D E=1 2 A B{\displaystyle DE={\frac {1}{2}}AB}
∴ In the triangle Δ A B C,{\displaystyle \Delta ABC,}D E∥A B{\displaystyle DE\parallel AB} and D E=1 2 A B{\displaystyle DE={\frac {1}{2}}AB}, where D{\displaystyle D} and E{\displaystyle E} are the midpoints of A C{\displaystyle AC} and B C{\displaystyle BC}. [Proved]
Proof with the help of Coordinate Geometry
[edit | edit source]
Proposition: Let D{\displaystyle D} and E{\displaystyle E} be the midpoints of A C{\displaystyle AC} and A B{\displaystyle AB} in the triangle A B C{\displaystyle ABC}, where the coordinates of A,B,C{\displaystyle A,B,C} are A(x 1,y 1),B(x 2,y 2),C(x 3,y 3){\displaystyle A(x_{1},y_{1}),B(x_{2},y_{2}),C(x_{3},y_{3})}. It is to be proved that,
D E=1 2 B C{\displaystyle DE={\frac {1}{2}}BC} and
D E∥B C{\displaystyle DE\parallel BC}
Proof: The distance of the segment B C=(x 3−x 2)2+(y 3−y 2)2{\displaystyle BC={\sqrt {(x_{3}-x_{2})^{2}+(y_{3}-y_{2})^{2}}}}
The midpoint of A(x 1,y 1){\displaystyle A(x_{1},y_{1})} and C(x 3,y 3){\displaystyle C(x_{3},y_{3})} is D(x 1+x 3 2,y 1+y 3 2){\displaystyle D({\frac {x_{1}+x_{3}}{2}},{\frac {y_{1}+y_{3}}{2}})}.
In the same way, The midpoint of A(x 1,y 1){\displaystyle A(x_{1},y_{1})} and B(x 2,y 2){\displaystyle B(x_{2},y_{2})} is E(x 1+x 2 2,y 1+y 2 2){\displaystyle E({\frac {x_{1}+x_{2}}{2}},{\frac {y_{1}+y_{2}}{2}})}
∴ The distance of D E=(x 1+x 3 2−x 1+x 2 2)2+(y 1+y 3 2−y 1+y 2 2)2{\displaystyle DE={\sqrt {({\frac {x_{1}+x_{3}}{2}}-{\frac {x_{1}+x_{2}}{2}})^{2}+({\frac {y_{1}+y_{3}}{2}}-{\frac {y_{1}+y_{2}}{2}})^{2}}}}
=(x 1+x 3−x 1−x 2 2)2+(y 1+y 3−y 1−y 2 2)2{\displaystyle ={\sqrt {({\frac {x_{1}+x_{3}-x_{1}-x_{2}}{2}})^{2}+({\frac {y_{1}+y_{3}-y_{1}-y_{2}}{2}})^{2}}}}
=(x 3−x 2)2 4+(y 3−y 2)2 4{\displaystyle ={\sqrt {{\frac {(x_{3}-x_{2})^{2}}{4}}+{\frac {(y_{3}-y_{2})^{2}}{4}}}}}
=(x 3−x 2)2+(y 3−y 2)2 4{\displaystyle ={\sqrt {\frac {(x_{3}-x_{2})^{2}+(y_{3}-y_{2})^{2}}{4}}}}
=(x 3−x 2)2+(y 3−y 2)2 2{\displaystyle ={\frac {\sqrt {(x_{3}-x_{2})^{2}+(y_{3}-y_{2})^{2}}}{2}}}
=1 2 B C{\displaystyle ={\frac {1}{2}}BC}; [As, B C=(x 3−x 2)2+(y 3−y 2)2{\displaystyle BC={\sqrt {(x_{3}-x_{2})^{2}+(y_{3}-y_{2})^{2}}}}]
The slope of B C,{\displaystyle BC,}m 1=y 2−y 3 x 2−x 3{\displaystyle m_{1}={\frac {y_{2}-y_{3}}{x_{2}-x_{3}}}}
The slope of D E,{\displaystyle DE,}m 2=y 1+y 2 2−y 1+y 3 2 x 1+x 2 2−x 1+x 3 2{\displaystyle m_{2}={\frac {{\frac {y_{1}+y_{2}}{2}}-{\frac {y_{1}+y_{3}}{2}}}{{\frac {x_{1}+x_{2}}{2}}-{\frac {x_{1}+x_{3}}{2}}}}}=y 1+y 2−y 1−y 3 2 x 1+x 2−x 1−x 3 2{\displaystyle ={\frac {\frac {y_{1}+y_{2}-y_{1}-y_{3}}{2}}{\frac {x_{1}+x_{2}-x_{1}-x_{3}}{2}}}}=y 2−y 3 2 x 2−x 3 2{\displaystyle ={\frac {\frac {y_{2}-y_{3}}{2}}{\frac {x_{2}-x_{3}}{2}}}}=y 2−y 3 x 2−x 3{\displaystyle ={\frac {y_{2}-y_{3}}{x_{2}-x_{3}}}}=m 1{\displaystyle =m_{1}}; [As, m 1=y 2−y 3 x 2−x 3{\displaystyle m_{1}={\frac {y_{2}-y_{3}}{x_{2}-x_{3}}}}]
Therefore, D E∥B C{\displaystyle DE\parallel BC}
∴ In the triangle Δ A B C,{\displaystyle \Delta ABC,}D E∥B C{\displaystyle DE\parallel BC} and D E=1 2 B C{\displaystyle DE={\frac {1}{2}}BC}, where D{\displaystyle D} and E{\displaystyle E} are the midpoints of A C{\displaystyle AC} and A B{\displaystyle AB}. [Proved]
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189653 | https://e-century.us/files/ijcem/9/12/ijcem0029971.pdf | Int J Clin Exp Med 2016;9(12):23734-23737 www.ijcem.com /ISSN:1940-5901/IJCEM0029971 Case Report Subungual glomus tumor causing 15 years of pain: a case report Ying-Hao Jiang1, Hang Zhang1, Kai-Bo Chen1, Jing-Hong Xu2, Jie Xia1, Yang Chen1, Yi-Qiao Lu1, Hua Tian1, Xiao-Li Jin1, Zhi-Wei Wu1, Di-Ke Shi1, Li Chen1 1Department of General Surgery, The Second Affiliated Hospital, College of Medicine, Zhejiang University, Hangzhou, China; 2Department of Pathology, The Second Affiliated Hospital, College of Medicine, Zhejiang University, Hangzhou, China. Equal contributors.
Received April 6, 2016; Accepted September 16, 2016; Epub December 15, 2016; Published December 30, 2016 Abstract: Subungual glomus tumors are rare benign tumors arising from glomus body, which often present with pinpoint pain under the nail. A case of 36-year-old female patient presented with intense pain over the right middle fingertip for 15 years is reported here. A transungular approach was taken to excise the tumor mass under local anesthesia, and histopathology reported a subungual glomus tumor. Complete removal of the tumor mass is critical to reduce the nail bed damage and deformity. Characteristic clinical features of excruciating pain, localized tender ness and coldsensitivity are importantto make correct diagnosis. Physical examination and imageology can help to confirm the diagnosis and locate the tumor mass.
Keywords: Glomus tumor, subungual, surgical excision, diagnosis, pain Introduction Glomus tumors are relatively rare tumors found all over the body. About 80% of the tumors are located in the upper extremities, especially subungual areas, accounting for about 2% of all hand tumors . Glomus tumors are closely related with hyperplasia of glomus bodies , which are supposed to function in thermoregu lation and blood circulation of the skin.
Glomus tumors require careful assessment for differential diagnosis to avoid misdiagnosed and unsuitable treatments, which may leave patients with years of chronic pain. Complete removal of the tumor mass is very effective to cure the pain and avoid recurrence. Typical glo mus tumors present characteristic clinical fea tures of excruciating pain, localized tenderness and cold sensitivity. These features strongly indicate the diagnosis of subungual glomus tumor. Imaging examinations such as magn-etic resonance imaging (MRI) and ultrasonogra phy also have been suggested to confirm the diagnosis.
Case report A 36-year-old patient was admitted to our hos pital with complain of excruciating pain over the right middle fingertip for 15 years. No trauma happened prior to onset of symptom. The pain was intensified by mild touchor cold stimula tion, torturing her even at sleep time. No rele vant past medical history or family history was mentioned. She suffered the pain for such a long period, and pain gradually intensified in recent years, however no accurate diagnosis could be confirmed by any previous hospitals.
Physical examination revealed obvious point tenderness over the tip of the right middle fin ger. There were no visible masses, no color change of skin and finger nail, no feeling of numbness, which differentiated from Raynaud’s phenomenon. The pain was aggravated by immersing the hand in cold water. Love’s test and Hildreth’s test were both positive. Ultrasound revealed a sheet hypoechoic mass (diameter: 4.92.9 mm) beneath the subcuta neous soft tissues with clear boundaries and CDFI (color Doppler flow imaging) showed rich blood flows inside the mass.
Before surgery, the most fierce tenderness area was marked (Figure 1A), and a rubber band was fixed to the finger root to exsanguinate the digit. The mass was located at the lower central Subungual glomus tumor causing years of pain 23735 Int J Clin Exp Med 2016;9(12):23734-23737 subungual region. A transungular approach was performed to excise the mass under the nerve block anesthesia of the finger root. Firstly a separation of nail was made by a sharp scalpel along the bilateral nail groove. After removing the nail plate, anapproximately 3 mm mass was well exposed (Figure 1B) and then completely excised (Figure 1C). The germinal matrix should be taken excellent care of during the whole pro cedure. Later histopathological report demon strated a subungual glomus tumor (Figure 2).
The patient recovered well during the follow-ups of 3 months, 6 months, and 1 year after deformed nails, subungual discoloration, hypo esthesia or other symptoms. Recently, it’s wide ly accepted that the pain of glomus tumor referred to the rich unmyelinated sensory nerve fibers in the tumor. Additionally, hypotheses of increased intracapsular pressure sensitivity to stress and algogenic substance released by mast cells also need to be further testified .
The clinical diagnosis of glomus tumors usually based on the classic triad, assisted with Love’s test, Hildreth’s test, cold sensitivity test and trans-illumination. Love’s test is applied by pressing the suspicious area with a pin head or Figure 1. Macroscopic view of the tumor. A. Fingers before the surgery. B. Glomus tumor exposed on the nail bed. C. Excised tumor tissue. D. A follow-up of 3 months after the surgery. E. A follow-up of 1 year after the surgery.
the surgery (Figure 1D, 1E). No recurrence was observed in the latest follow-up, even though there was as light deformity of the nail. Discussion Glomus tumor is a rare benign tumor, whose pathological fea tures were first described by Masson in 1924 . Glomus tumor is mainly caused by hyperplasia of the glomus body. Glomus bodies locate in the dermal retinacular layers and directly connect arteriovenous structures, consisting of affer ent artery, vascular anastomo sis, venous pooling, intraglo merular reticulum and capsular portion. Normal glomus bodies are found in trunk, neck as well as extremities, which are sup posed to function in thermoreg ulation andblood circulation of the skin. Glomus tumors are mostly seen in female ranging from 30 to 50 years old, with diameters gen erally less than 1 cm. Although glomustumors can be found all over the body, even in the stom ach , it usually occurred in the extremities, accounting for 1-5% of all hand tumors and 75% are subungual. The clinical features include a classic triad of excruciating pain, localized tenderness and cold sensitivity. Sometimes it may presents as Subungual glomus tumor causing years of pain 23736 Int J Clin Exp Med 2016;9(12):23734-23737 with clear boundaries and rich blood flow signal inside. X-ray test can show tumor pressure trace and bone erosion for those with relatively large size. While MRI (magnetic resonance imaging) (T2 phase) displays a local signal enhancement. MRI has a sensitivity of 90% for glomus tumor, but only 50% in specificity . In addition, MRI can also be helpful to locate the tumor . Therefore, in patients with typical clinical manifestations, ultrasonography and MRI are routinely recommended as the most helpful tools for the preoperative accurate diagnosis. MDCT (multidetector computed to-mography) has an advantage in showing a sub ungual nodule and a depression of the distal phalanx more directly and helps to locate the tumor . However, the average time to make right diagnosis of subungual tumor is 7 year , and lack of awareness to this rare dise-ase is the major problem for misdiagnoses as neuralgia, paronychia, or arthritis, which leads toineffective treatment and causes intolerant anxiety of patients for many years.
Complete surgicalexcision is the only effective way to cure glomus tumor. Love’s test or trans-illumination test should be done preoperatively to locate the tumor. Theproximal phalanx should be fully exsanguinated by binding tourni quet to the root of digits to clear surgical field. One more tourniquet on the upper limb may be chosen in case of poor exsanguinating effect.
There are two major surgical approaches to excise subungual glomus tumor. The traditi-onal approach is transungual excision, which removes part or entire nail plate, and cuts through the nail bed to guarantee good tumor exposure. Complete removal is relatively easy, but damage to the nail bed is obvious more serious, with higher incidence of postopera-tive nail deformity. Another commonly used approach is lateral incision, which makes an L-shaped incision along the edge of the nail, and lifts the entire nail bed and nail plate to expose the tumor. This approach leaves small er damage, and preserves the wholeness of the nail bed, reducing the risk of postopera-tive nail deformity. But with a smaller exposed surgicalfield, it is restrictedby the location of tumor, and requires more skills if the tumor is located on the central nail bed, and may even damage digital nerves. Hence this approach is usually reserved for laterally located tumors [9, a ball point pen. A severe pain with hand retrac tion indicates positive (Figure 3). The sensitivity of Love’s test is 100%, but its specificity is not high enough, because some diseases can also cause the similar pain, such as onychia, peri onychia, and subungual hematoma. Hildreth’s test is fastening the elevated limb with tourni quet to eliminate pain, whose specificity is 91% to 100%. Therefore, clinical features with posi tive Hildreth’s test are of great diagnosis value to glomus tumor.
Imaging examination can also contribute to the diagnosis. High frequency (40 MHz) ultrasonog raphy can detect >2 mm subcutaneous homo geneous hypoechoicmasses, often presented Figure 2. Histopathology examination of the tumor. The tumor has multiple dilated blood vessels sur rounded by clusters of glomus cells. The tumor cell contains round nucleus with amphophilic or pale eosinophilic cytoplasm (Haematoxylin-Eosin stain, ×400).
Figure 3. Love’s test for patients. Pressing the suspi cious area will trigger a severe pain and retraction re sponse, which indicates positive sign to Love’s test.
Subungual glomus tumor causing years of pain 23737 Int J Clin Exp Med 2016;9(12):23734-23737 10]. Garg proposed a modified lateral subperi osteal approach, which curves around the pulp, dissects to the periosteum, and raises a dorsal flap of nail matrix to expose the tumor . This approach avoids damage to the nail bed and nail plate without restriction of tumor location.
More and more modified surgical approaches and new techniques have been introduced. Roan reported a case of nail bed complex inci sion without extracting the nail . The follow-ups returned a significant lower rate of postop erative nail deformity . Microscopic assist ed surgery has also been reported in glomus tumors for its blood-less procedure, and little damage to the nail matrix with larger assurance of complete excision of tumor . A 12-year follow-up reported that microscopic excision of subungual glomus tumors were as safe as tra ditional surgery excision, and had advantages in little damage and low rate of recurrence and nail deformity .
In this report, we showed a patient with chronic pain in right middle fingertip for 15 years, and most patients with subungual glomus tumors also have a long history. They may have con sulted many doctors, but still being misdiag nosed and treated with ineffective conserva tive treatment for many years. Some of these patients cannot tolerant such pain and resort to nerve block, even amputation or other inap propriate treatment. Surgical excision is the only effective treatment method to terminate the suffering. The principle is complete removal of the tumormass and reducing the nail bed damage. Once a doctor has mind of this rare subungual disease, it would be not that difficult to make correct diagnosis with the characteris tic clinical features.
Disclosure of conflict of interest None.
Address correspondence to: Li Chen, Department of General Surgery, The Second Affiliated Hospital, College of Medicine, Zhejiang University, 88 Jiefang Road, Shangcheng District, Hangzhou 310000, China. Tel: +86-13606808530; E-mail: chenli_hz@ yahoo.com References Gombos Z and Zhang PJ. Glomus tumor. Arch Pathol Lab Med 2008; 132: 1448-1452.
Masson P. Le glomus neuromyo-arteriel des regions tactiles et ses tumeurs. Lyon Chi 1924; 21: 257-280.
Chen KB and Chen L. Glomus tumor in the stomach: A case report and review of the litera ture. Oncol Lett 2014; 7: 1790-1792.
Won L, Soon BK, Sang HC, Eo SR, Kwon C. Glo mus Tumor of the Hand. Arch Plast Surg 2015; 42: 295-301.
Al-Qattan MM, Al-Namla A, Al-Thunayan A, Al-Subhi F and El-Shayeb AF. Magnetic resonance imaging in the diagnosis of glomus tumours of the hand. J Hand Surg Br 2005; 30: 535-540.
Matloub HS, Muoneke VN, Prevel CD, Sanger JR and Yousif NJ. Glomus tumor imaging: use of MRI for localization of occult lesions. J Hand Surg Am 1992; 17: 472-475.
Xia J, Cai YX, Jin ZQ, He XZ and Fan YM. Preop erative evaluation of a subungual glomus tu mor case using multidetector computed to mography angiography. Ann Dermatol 2015; 27: 226-227.
Newman MJ, Pocock G and Allan P. Glomus tu mour: a rare differential for subungual lesions. BMJ Case Rep 2015; 2015.
Vasisht B, Watson HK, Joseph E and Lionelli GT. Digital glomus tumors: a 29-year experi ence with a lateral subperiosteal approach. Plast Reconstr Surg 2004; 114: 1486-1489.
Lee SH, Roh MR and Chung KY. Subungual glo mus tumors: surgical approach and outcome based on tumor location. Dermatol Surg 2013; 39: 1017-1022.
Garg B, Machhindra MV, Tiwari V, Shankar V and Kotwal P. Nail-preserving modified lateral subperiosteal approach for subungual glomus tumour: a novel surgical approach. Musculo skelet Surg 2016; 100: 43-8.
Roan TL, Chen CK, Horng SY, Hsieh JH, Tai HC, Hsieh MH, Chien HF and Tang YB. Surgical technique innovation for the excision of subun gual glomus tumors. Dermatol Surg 2011; 37: 259-262.
Wang PJ, Zhang Y and Zhao JJ. Treatment of subungual glomus tumors using the nail bed margin approach. Dermatol Surg 2013; 39: 1689-1694.
Huang HP, Tsai MC, Hong KT, Chang SC, Wang CH, Li CC, Chiu WK and Chen SG. Outcome of microscopic excision of a subungual glomus tumor: a 12-year evaluation. Dermatol Surg 2015; 41: 487-492. |
189654 | https://www.uptodate.com/contents/catatonia-in-adults-epidemiology-clinical-features-assessment-and-diagnosis/abstract/14 | Medline ® Abstract for Reference 14 of 'Catatonia in adults: Epidemiology, clinical features, assessment, and diagnosis' - UpToDate
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Medline ® Abstract for Reference 14 of 'Catatonia in adults: Epidemiology, clinical features, assessment, and diagnosis'
14PubMed|TI Catatonic syndrome in a general psychiatric inpatient population: frequency, clinical presentation, and response to lorazepam.AU Rosebush PI, Hildebrand AM, Furlong BG, Mazurek MF SO J Clin Psychiatry. 1990;51(9):357.
In a prospective open trial conducted on a general psychiatric ward, the authors diagnosed catatonic syndrome 15 times in 12 patients over a 1-year period. These 12 patients represented 9% of all admissions. The following signs were present in two thirds or more of the episodes studied: immobility (100%), staring (92%), mutism (85%), withdrawal/refusal to eat (78%), posturing/grimacing (73%), and rigidity (66%). Other signs of catatonia were seen less frequently. Lorazepam 1 to 2 mg was administered in every case, and patients were evaluated at hourly intervals. Of the 15 episodes, 12 responded completely and dramatically to lorazepam treatment within 2 hours, 1 responded partially, and 2 had no response. Adverse effects were infrequent. A CNS abnormality or dysfunction was evident in 8 of the 12 responders, suggesting that a beneficial response to lorazepam is not limited to patients with pure psychogenic catatonia. The prompt recognition and treatment of catatonia may reduce morbidity in and length of stay for hospitalized psychiatric patients.
AD Department of Psychiatry, McMaster University, Hamilton, Ontario, Canada.PMID2211547
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Medical Trash Bags: Compliance, Color Coding, and Safety Standards
September 8, 2025
Posted byman good
08 Sep
Table of Contents
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More Than Just a Trash Bag
A Brief History of Medical Waste Management
What Are Medical Trash Bags?
Types of Medical Waste and Corresponding Bags
Infectious Waste
Pathological Waste
Sharps Waste
Pharmaceutical Waste
General Medical Waste
Color Coding Around the World
Regulations in Detail
U.S. Framework
International Standards
Risks of Using Poor Medical Trash Bags
Case Studies
Case 1: Outbreak from a Broken Bag
Case 2: Compliance Saves Millions
Case 3: Public Image at Risk
Step-by-Step Guide: Setting Up a Medical Waste Bag Program
Sustainability in Medical Trash Bags
The Future of Medical Trash Bags
How TP Plastic USA Ensures Safety and Compliance
Conclusion: A Bag That Saves Lives
More Than Just a Trash Bag
Medical waste is one of the most sensitive waste streams in the world. It carries infectious risks, regulatory oversight, and environmental challenges. While to the untrained eye a trash bag is just a bag, in healthcare, medical trash bags are compliance tools, safety barriers, and environmental safeguards.
Hospitals generate tons of waste every day — much of it harmless, but a significant portion hazardous. Choosing the wrong bag can lead to leaks, infections, fines, and reputational harm. That’s why understanding medical trash bags is critical for healthcare leaders, procurement managers, and even frontline staff.
At TP Plastic USA, we help facilities make the right choice with bags designed to meet U.S. and international standards.
A Brief History of Medical Waste Management
Before the 1980s: Most hospital waste was disposed like regular trash. Incineration was common but unregulated.
1988: The U.S. passed the Medical Waste Tracking Act after syringes and biohazards washed up on East Coast beaches. This highlighted the dangers of poor disposal.
1990s–2000s: Segregation systems (color-coded bags, sharps containers) became the global norm.
Today: Strict laws (OSHA, EPA, FDA, DOT) govern every stage: from the bag a nurse uses to the truck that transports waste.
The simple trash bag became a critical piece of compliance infrastructure.
What Are Medical Trash Bags?
Medical trash bags are specially designed to:
Contain infectious and hazardous waste.
Prevent leaks, punctures, and exposure.
Follow strict color-coding and labeling rules.
Support safe transport, storage, and disposal.
Common materials: HDPE, LDPE, or blended polyethylene, often thicker and more durable than household bags.
Types of Medical Waste and Corresponding Bags
Infectious Waste
Bandages, gowns, swabs contaminated with blood.
Red biohazard bags required.
Pathological Waste
Human tissues, body parts, specimens.
Typically in yellow bags or containers.
Sharps Waste
Needles, scalpels, broken glass.
Placed in puncture-proof sharps containers, then secondary bags if needed.
Pharmaceutical Waste
Expired medicines, vaccines, chemotherapy drugs.
Blue or white bags, depending on country.
General Medical Waste
Packaging, paper, kitchen waste from hospitals.
Disposed in black bags.
Color Coding Around the World
| Region | Red | Yellow | Black | Blue/White |
--- ---
| U.S. | Infectious/biohazard | Pathological waste | General medical | Pharmaceuticals |
| EU | Biohazard waste | Infectious liquids | Domestic-like waste | Medicines, recyclables |
| Asia | Infectious waste | Pathological & sharps | Non-hazardous waste | Drug/pharma waste |
While exact systems differ, the principle is always segregation for safety.
Regulations in Detail
U.S. Framework
OSHA: Requires biohazard labeling, staff training, PPE use.
EPA: Oversees hazardous medical waste disposal.
FDA: Regulates any medical device bags.
DOT: Governs transport of medical waste across states.
Violations can cost up to $70,000 per incident in OSHA fines.
International Standards
WHO: Issues global guidelines for medical waste handling.
EU EN 13432: Standards for waste management packaging.
ISO 16603: Resistance of protective clothing/material to blood penetration.
Healthcare facilities worldwide must keep up to avoid penalties.
Risks of Using Poor Medical Trash Bags
Leakage and Spills: Thin bags allow blood or fluids to escape.
Staff Infections: Exposure to pathogens like Hepatitis B, C, or HIV.
Environmental Contamination: Improper bags increase landfill hazards.
Legal Penalties: Misuse of color codes or thickness standards can trigger fines.
Patient Confidence: Patients equate waste handling with overall hospital quality.
Case Studies
Case 1: Outbreak from a Broken Bag
A Southeast Asian hospital used thin, non-compliant red bags. When one tore, janitorial staff were exposed to infectious waste, leading to two staff infections. Cost: lawsuits + $200,000 in penalties.
Case 2: Compliance Saves Millions
A U.S. hospital group standardized with star-sealed red biohazard bags. Over 3 years, bag failure rates dropped 60%, saving $2.5 million in cleanup, labor, and liability costs.
Case 3: Public Image at Risk
In India, media reported images of yellow medical bags mixed with household trash. Public outrage forced government audits, leading to hospital suspensions.
Step-by-Step Guide: Setting Up a Medical Waste Bag Program
Identify Waste Streams: Infectious, pharmaceutical, general.
Assign Color Codes: Follow local/national regulations.
Train Staff: Nurses, janitors, and transport staff must all know the codes.
Use Star-Sealed Bags: To prevent leaks.
Don’t Overfill: Bags should only reach 75% capacity.
Double-Bag When Necessary: For heavy infectious waste.
Label Clearly: Include biohazard symbols and facility ID.
Audit Regularly: Check compliance monthly.
Sustainability in Medical Trash Bags
Medical waste can’t all be recycled due to infection risks. But sustainability plays a role in:
Non-infectious waste bags: Using recycled content.
Biodegradable liners: For non-hazardous medical waste.
Segregation efficiency: Proper sorting reduces the amount of waste needing incineration.
Kaiser Permanente reports saving $5 million annually by improving waste segregation and using eco-friendly general medical bags.
The Future of Medical Trash Bags
Smart Bags with RFID Labels: Track waste from generation to incineration.
AI-Integrated Sorting: Robots assist staff in segregating waste.
Compostable Medical Bags: Early-stage research for non-infectious categories.
Global Harmonization: Movement toward unified color coding worldwide.
These innovations will reshape compliance and sustainability in the next decade.
How TP Plastic USA Ensures Safety and Compliance
We manufacture:
Red Biohazard Bags (OSHA-compliant, star-sealed).
Yellow Pathological Bags (durable, puncture-resistant).
Black General Waste Bags (economical, high capacity).
Blue/White Pharmaceutical Bags (customizable for pharmacies and hospitals).
Our advantages:
High-grade HDPE/LDPE blends.
Star-sealed designs to prevent leaks.
OEM/ODM services for custom branding and sizes.
Compliance with U.S., EU, and WHO standards.
Conclusion: A Bag That Saves Lives
In healthcare, waste management isn’t optional — it’s life-saving. Medical trash bags are more than plastic; they’re a frontline defense against infection, a compliance tool, and a sustainability challenge.
Facilities that invest in the right medical trash bags save money, protect staff, and reassure patients. At TP Plastic USA, we make that possible with durable, compliant, and customizable solutions.
Because in medicine, the right bag is part of the cure.
TP Plastic – The quality you can trust!
Zalo/WhatsApp: (+84) 915 871 722 / (+1) 818 914 – 0351
Website: tpplasticusa.com
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189656 | https://arupconsult.com/content/paraneoplastic-pemphigus | Paraneoplastic Pemphigus | Choose the Right Test
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Paraneoplastic Pemphigus
Last Literature Review: October 2020 Last Update: July 2025
Related Algorithms
Immunobullous Diseases Testing Algorithm - Epithelial Antibody Associated
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Leiferman
Kristin M. Leiferman, MD
Co-Director, Immunodermatology Laboratory, Professor of Dermatology, and Adjunct Professor of Pathology, University of Utah
Medical Director, Immunodermatology, ARUP Laboratories
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John J. Zone, MD
Professor and Chairman Emeritus, Dermatology, and Adjunct Professor of Pathology, University of Utah
Co-Director, Immunodermatology Laboratory, ARUP Laboratories
Paraneoplastic pemphigus, also referred to as paraneoplastic autoimmune multiorgan syndrome, is a severely debilitating blistering disease that affects skin and mucous membranes and nearly always involves an underlying neoplasm.1
Kappius RH, Ufkes NA, Thiers BH. Paraneoplastic pemphigus. In: StatPearls. Treasure Island (FL). StatPearls Publishing; 2020.
cite Paraneoplastic pemphigus is much less common than some other forms of pemphigus, such as pemphigus foliaceus and pemphigus vulgaris. Diagnosis can be challenging because of the tendency of paraneoplastic pemphigus to mimic other cutaneous diseases.1
Kappius RH, Ufkes NA, Thiers BH. Paraneoplastic pemphigus. In: StatPearls. Treasure Island (FL). StatPearls Publishing; 2020.
Accurate diagnosis requires assessment of clinical characteristics and histopathologic features, along with the detection of disease-specific autoantibodies in tissue and/or serum using methodologies such as direct immunofluorescence (DIF) microscopy, indirect immunofluorescence (IIF) testing, and enzyme-linked immunosorbent assays (ELISAs).2
Kershenovich R, Hodak E, Mimouni D. Diagnosis and classification of pemphigus and bullous pemphigoid. Autoimmun Rev. 2014;13(4-5):477‐481.
The variousimmunobullous diseases associated with epithelial antibodies have overlapping clinical presentations, and broad serologic screening is recommended to establish a diagnosis unless a specific disease is suspected and/or supported by characteristic findings.
Quick Answers for Clinicians
What are some clinical indications that testing for paraneoplastic pemphigus may be appropriate?
Paraneoplastic pemphigus is associated with a variety of lesion types, including flaccid and/or tense bullae, erosions, urticarial lesions, erythema multiforme-like lesions, lichen planus-like lesions, and flat scaly papules.3
Witte M, Zillikens D, Schmidt E. Diagnosis of autoimmune blistering diseases.Front Med (Lausanne). 2018;5:296.
Widespread, severe mucosal lesions occur in nearly all patients,1
Kappius RH, Ufkes NA, Thiers BH. Paraneoplastic pemphigus. In: StatPearls. Treasure Island (FL). StatPearls Publishing; 2020.
usually on oral surfaces.3
Witte M, Zillikens D, Schmidt E. Diagnosis of autoimmune blistering diseases.Front Med (Lausanne). 2018;5:296.
The disease can affect various types of epithelia and can therefore lead to involvement of various organs, for example, the eyes, lungs, gastrointestinal tract, kidney, and thyroid.1
Kappius RH, Ufkes NA, Thiers BH. Paraneoplastic pemphigus. In: StatPearls. Treasure Island (FL). StatPearls Publishing; 2020.
Some patients develop bronchiolitis obliterans or myasthenia gravis (both of which are associated with increased mortality rates).4
Wang L, Nong L, Li F, et al. Predominant stroma-rich feature in hyaline vascular variant of Castleman disease Is associated with paraneoplastic pemphigus. Am J Clin Pathol. 2020;154(3):403-413.
Because an underlying neoplasm is almost always present, any patient suspected of having paraneoplastic pemphigus but no previously detected neoplasm should undergo an immediate and thorough evaluation for malignancy.1
Kappius RH, Ufkes NA, Thiers BH. Paraneoplastic pemphigus. In: StatPearls. Treasure Island (FL). StatPearls Publishing; 2020.
What is challenging about diagnosing paraneoplastic pemphigus?
Paraneoplastic pemphigus can present similarly to other cutaneous diseases, so much so that the five major subtypes of paraneoplastic pemphigus are referred to as bullous pemphigoid-like, erythema multiforme-like, graft-versus-host-disease-like, lichen planus-like, and pemphiguslike.1
Kappius RH, Ufkes NA, Thiers BH. Paraneoplastic pemphigus. In: StatPearls. Treasure Island (FL). StatPearls Publishing; 2020.
Moreover, drug reactions can have analogous presentations. Because of similarities and overlap in clinical presentation among blistering autoimmune diseases, broad serologic screening is generally recommended during initial evaluation.
Which neoplasms are most commonly associated with paraneoplastic pemphigus?
The most common neoplasms in paraneoplastic pemphigus are lymphoproliferative, e.g., non-Hodgkin lymphoma, chronic lymphocytic leukemia, and Castleman disease,5
Ohzono A, Sogame R, Li X, et al. Clinical and immunological findings in 104 cases of paraneoplastic pemphigus. Br J Dermatol. 2015;173(6):1447-1452.
in particular, certain subtypes of Castleman disease.4
Wang L, Nong L, Li F, et al. Predominant stroma-rich feature in hyaline vascular variant of Castleman disease Is associated with paraneoplastic pemphigus. Am J Clin Pathol. 2020;154(3):403-413.
Other associated malignancies include sarcomas, thymomas, squamous cell carcinomas, and carcinomas of the colon, lung, and stomach.1
Kappius RH, Ufkes NA, Thiers BH. Paraneoplastic pemphigus. In: StatPearls. Treasure Island (FL). StatPearls Publishing; 2020.
Where can I find information on testing for other epithelial-antibody associated immunobullous diseases?
ARUP Consult has an overview of Immunobullous Diseases (Epithelial Antibody Associated), as well as specific information on other forms of pemphigus, along with information on pemphigoid, pemphigoid gestationis, epidermolysis bullosa acquisita (EBA), linear IgA disease, and dermatitis herpetiformis. Visit our algorithms for testing steps for the various diseases.
Indications for Testing
Testing for pemphigus is appropriate in patients with suspected malignancy (a neoplasm typically precedes skin disease) or cutaneous manifestations that are consistent with paraneoplastic pemphigus (see Quick Answers for Clinicians) and are not attributable to a more common cutaneous disorder. Strong clinical suspicion for paraneoplastic pemphigus in the absence of known cancer should prompt a thorough evaluation for possible malignancy.1
Kappius RH, Ufkes NA, Thiers BH. Paraneoplastic pemphigus. In: StatPearls. Treasure Island (FL). StatPearls Publishing; 2020.
Laboratory Testing
Diagnosis
Diagnosis of paraneoplastic pemphigus is based on supportive histopathologic findings on examination of formalin-fixed tissue, immunopathologic features, with demonstration on DIF microscopy of characteristic immunoglobulin G (IgG) and/or complement component 3 (C3) reactivity patterns, detection of autoantibodies to epithelial components in serum, and compatible clinical features.
Immunopathology
DIF microscopy, used to detect tissue-bound autoantibodies, is performed on perilesional skin biopsy tissue and is an important part of an evaluation for paraneoplastic pemphigus.2
Kershenovich R, Hodak E, Mimouni D. Diagnosis and classification of pemphigus and bullous pemphigoid. Autoimmun Rev. 2014;13(4-5):477‐481.
,3
Witte M, Zillikens D, Schmidt E. Diagnosis of autoimmune blistering diseases.Front Med (Lausanne). 2018;5:296.
The disease is characterized by cell surface IgG antibody staining and intercellular C3 deposition2
Kershenovich R, Hodak E, Mimouni D. Diagnosis and classification of pemphigus and bullous pemphigoid. Autoimmun Rev. 2014;13(4-5):477‐481.
,3
Witte M, Zillikens D, Schmidt E. Diagnosis of autoimmune blistering diseases.Front Med (Lausanne). 2018;5:296.
and may demonstrate granular or linear IgG basement membrane zone (BMZ) antibodies at the dermal-epidermal junction.1
Kappius RH, Ufkes NA, Thiers BH. Paraneoplastic pemphigus. In: StatPearls. Treasure Island (FL). StatPearls Publishing; 2020.
A combination of cell surface plus BMZ IgG autoantibody reactivity characteristically is observed in paraneoplastic pemphigus. IgA autoantibodies (cell surface or BMZ) are rarely identified in this disease and may be found in an IgA variant of paraneoplastic pemphigus.
Serum Tests
In addition to tissue evaluation using DIF microscopy, assessment for pemphigus involves detection and identification of circulating autoantibodies in serum. Various serum epithelial autoantibodies and combinations of autoantibodies may develop in paraneoplastic pemphigus. IgG antibodies specifically associated with paraneoplastic pemphigus include autoantibodies against envoplakin, periplakin, and desmogleins 1 and 3, as well as autoantibodies against desmoplakin, plectin, desmocollins 1, 2, and 3, alpha (α)-2 macroglobulin-like protein 1 (A2ML1), epiplakin, BP230, BP180, and laminin-332.1
Kappius RH, Ufkes NA, Thiers BH. Paraneoplastic pemphigus. In: StatPearls. Treasure Island (FL). StatPearls Publishing; 2020.
,6
Otten JV, Hashimoto T, Hertl M, et al. Molecular diagnosis in autoimmune skin blistering conditions.Curr Mol Med. 2014;14(1):69-95.
The plakins are predominant antigenic targets in paraneoplastic pemphigus, especially envoplakin and periplakin. A study of 104 patients with paraneoplastic pemphigus found autoantibodies against desmoglein 3; desmocollins 1, 2, or 3; and A2ML1 in a majority of patients (78%, 71%, and 60%, respectively).5
Ohzono A, Sogame R, Li X, et al. Clinical and immunological findings in 104 cases of paraneoplastic pemphigus. Br J Dermatol. 2015;173(6):1447-1452.
Available serum tests include IIF testing and ELISAs. With IIF testing, the patient serum is incubated with epithelial tissue substrates (e.g., rodent substrates such as rat bladder4
Wang L, Nong L, Li F, et al. Predominant stroma-rich feature in hyaline vascular variant of Castleman disease Is associated with paraneoplastic pemphigus. Am J Clin Pathol. 2020;154(3):403-413.
,5
Ohzono A, Sogame R, Li X, et al. Clinical and immunological findings in 104 cases of paraneoplastic pemphigus. Br J Dermatol. 2015;173(6):1447-1452.
) to detect autoantibodies that react with the target proteins expressed in the substrate tissues. Binding of IgG autoantibodies to the transitional epithelium in rodent bladder tissue is a characteristic finding because of the greater concentration of plakins in bladder tissue.6
Otten JV, Hashimoto T, Hertl M, et al. Molecular diagnosis in autoimmune skin blistering conditions.Curr Mol Med. 2014;14(1):69-95.
IIF testing in patients with paraneoplastic pemphigus typically reveals serum IgG autoantibodies that bind in an intercellular pattern to the surface of epithelial cells and also to the epithelial BMZ.6
Otten JV, Hashimoto T, Hertl M, et al. Molecular diagnosis in autoimmune skin blistering conditions.Curr Mol Med. 2014;14(1):69-95.
Patterns of antibody reactivity visualized by IIF have good clinical utility to support a diagnosis of paraneoplastic pemphigus.7
Helou J, Allbritton J, Anhalt GJ. Accuracy of indirect immunofluorescence testing in the diagnosis of paraneoplastic pemphigus. J Am Acad Dermatol. 1995;32(3):441-447.
ELISA tests both detect and semiquantify autoantibodies.3
Witte M, Zillikens D, Schmidt E. Diagnosis of autoimmune blistering diseases.Front Med (Lausanne). 2018;5:296.
ELISA testing for paraneoplastic pemphigus includes autoantibodies against envoplakin, desmoglein 1 and 3, BP230, and BP180, which may aid in diagnosis and in monitoring the disease. Of these antigenic targets, envoplakin is among the most specific for paraneoplastic pemphigus.
If an autoantibody screen yields positive results in patients without a known malignancy, an aggressive evaluation for malignancy is warranted.1
Kappius RH, Ufkes NA, Thiers BH. Paraneoplastic pemphigus. In: StatPearls. Treasure Island (FL). StatPearls Publishing; 2020.
ARUP Laboratory Tests
Additional detail about the tests below can be found in the ARUP Immunobullous Disease Testing Comparison table.
Recommended Serologic Test
Preferred expanded panel to assess and monitor paraneoplastic pemphigus
Includes IgG envoplakin antibodies by ELISA and IgG antibodies by IIF
Testing should be correlated initially with concurrent DIF biopsy, histopathological examination of formalin-fixed tissue, and assessment of other epithelial antibodies
Consider ordering concurrently with Immunobullous Disease Antibody Panel for broad epithelial antibody assessment
If other more common types of pemphigus are diagnostic considerations, concurrently order Pemphigus Antibody Panel, IgG with or without the rarer IgA pemphigus variant test
3016534
Paraneoplastic Pemphigus (Paraneoplastic Autoimmune Multiorgan Syndrome) Expanded Antibody Panel by IIF With ELISA 3016534
Method
Semi-Quantitative Indirect Immunofluorescence (IIF)/Semi-Quantitative Enzyme-Linked Immunosorbent Assay (ELISA)
Use to assess and monitor paraneoplastic pemphigus, a rare paraneoplastic disease associated with lymphoproliferative disorders/malignancies and demonstrating clinical features of severe pemphigus
Testing should be correlated initially with concurrent DIF biopsy, histopathological examination of formalin-fixed tissue, and assessment of other epithelial antibodies
Consider ordering concurrently with Immunobullous Disease Antibody Panel for broad epithelial antibody assessment
If other more common types of pemphigus are diagnostic considerations, order Pemphigus Antibody Panel, IgG with or without the rarer IgA pemphigus variant test, concurrently with this test
0092107
Paraneoplastic Pemphigus (Paraneoplastic Autoimmune Multiorgan Syndrome) Screening Antibodies by IIF
0092107
Method
Semi-Quantitative Indirect Immunofluorescence (IIF)
Use in conjunction with Paraneoplastic Pemphigus (Paraneoplastic Autoimmune Multiorgan Syndrome) Screening Antibodies by IIF to aid in the diagnosis of paraneoplastic pemphigus
Testing should be correlated initially with concurrent DIF biopsy, histopathological examination of formalin-fixed tissue, and assessment of other epithelial antibodies
May be used to monitor disease in individuals with increased IgG envoplakin antibody levels
3016533
Envoplakin Antibody, IgG by ELISA 3016533
Method
Semi-Quantitative Enzyme-Linked Immunosorbent Assay (ELISA)
Immunopathologic Test (DIF)
Use with serum immunobullous disease/epithelial antibody testing and formalin-fixed tissue histopathology for assessment of pruritic, urticarial, blistering, and/or erosive disorders
Use with formalin-fixed tissue histopathology for assessment of inflammatory, immune-mediated cutaneous disease
Optimal specimen location and complementary serum testing and/or histopathology examination vary according to disease type; note that specimen location and transport medium/fixative are different for direct immunofluorescence testing and fixed-tissue histopathology
0092572
Direct Immunofluorescence, Tissue Biopsy (Cutaneous, Mucosal, Epithelial)
0092572
Method
Direct Immunofluorescence
Other Serologic Tests
Use as initial comprehensive testing panel to aid in the diagnosis of and distinguishing among skin and mucous membrane disorders that present with blistering, erosions, eczema, pruritus, and/or urticaria
Use for assessment of suspected epithelial antibody-associated immunobullous diseases, pemphigoid and pemphigus and their variants, that are not clinically distinguishable, have nonspecific features, potentially express overlapping epithelial antibodies, and/or are indicated by concurrent DIF biopsy
3001409
Immunobullous Disease Antibody Panel 3001409
Method
Semi-Quantitative Indirect Immunofluorescence (IIF)/Semi-Quantitative Enzyme-Linked Immunosorbent Assay (ELISA)
Components: BMZ antibodies, IgG by IIF; BMZ antibodies, IgA by IIF; BP180 and BP230 antibodies, IgG by ELISA; collagen type VII antibodies, IgG by ELISA; cell surface antibodies, IgG by IIF; desmoglein 1 and 3 antibodies, IgG by ELISA; cell surface antibodies, IgA by IIF
Use as the preferred serum antibody panel to assess and monitor IgG pemphigus variants (includes pemphigus foliaceus and pemphigus vulgaris), which present with blistering and erosive disease affecting skin and mucous membranes
Testing should be correlated initially with concurrent DIF biopsy
0090650
Pemphigus Antibody Panel, IgG 0090650
Method
Semi-Quantitative Indirect Immunofluorescence (IIF) / Semi-Quantitative Enzyme-Linked Immunosorbent Assay (ELISA)
Components: cell surface antibodies, IgG by IIF; desmoglein 1 and desmoglein 3 antibodies, IgG by ELISA
Use as the preferred initial diagnostic panel for suspected BMZ antibody-associated skin and mucous membrane disorders that present with blistering, erosions, eczema, urticaria, pruritus, and/or mucositis
May be indicated by concurrent DIF biopsy
Alternatively, order the comprehensive Immunobullous Disease Antibody Panel for initial serum diagnostic assessment of epithelial antibody-associated diseases, pemphigoid, pemphigus, and their variants
3001410
Basement Membrane Zone Antibody Panel 3001410
Method
Semi-Quantitative Indirect Immunofluorescence (IIF)/Semi-Quantitative Enzyme-Linked Immunosorbent Assay (ELISA)
Components: BMZ antibodies, IgG by IIF; BMZ antibodies, IgA by IIF; BP180 and BP230 antibodies, IgG by ELISA; collagen type VII antibodies, IgG by ELISA
Use to assess and monitor epithelial antibody expression in paraneoplastic pemphigus
0092566
Bullous Pemphigoid (BP180 and BP230) Antibodies, IgG by ELISA 0092566
Method
Semi-Quantitative Enzyme-Linked Immunosorbent Assay (ELISA)
0090649
Desmoglein 1 and Desmoglein 3 (Pemphigus) Antibodies, IgG by ELISA 0090649
Method
Semi-Quantitative Enzyme-Linked Immunosorbent Assay (ELISA)
0092001
Pemphigoid Antibody Panel 0092001
Method
Semi-Quantitative Indirect Immunofluorescence (IIF) / Semi-Quantitative Enzyme-Linked Immunosorbent Assay (ELISA)
Components: BMZ antibodies, IgG by IIF; BMZ antibodies, IgA by IIF; BP180 and BP230 antibodies, IgG by ELISA
Use to monitor linear IgG and IgA BMZ antibody-associated diseases and IgG and IgA cell surface antibody-associated diseases in which antibody levels by ELISAs may not be increased and/or to assess for changing patterns of epithelial antibody expression
May be used as general initial serum test for immunobullous diseases; however, for more sensitive and specific serum testing with ELISAs for pemphigoid and EBA or for IgG variant pemphigus, refer to Basement Membrane Zone Antibody Panel or Pemphigus Antibody Panel, IgG
0090299
Basement Membrane Zone and Cell Surface (Epithelial) Antibodies, IgG and IgA by IIF 0090299
Method
Semi-Quantitative Indirect Immunofluorescence (IIF)
Components: BMZ antibodies, IgG by IIF; BMZ antibodies, IgA by IIF; cell surface antibodies, IgG by IIF; cell surface antibodies, IgA by IIF
References
31536300
Kappius RH, Ufkes NA, Thiers BH. Paraneoplastic pemphigus. In: StatPearls. Treasure Island (FL). StatPearls Publishing; 2020.
24424192
Kershenovich R, Hodak E, Mimouni D. Diagnosis and classification of pemphigus and bullous pemphigoid. Autoimmun Rev. 2014;13(4-5):477‐481.
30450358
Witte M, Zillikens D, Schmidt E. Diagnosis of autoimmune blistering diseases.Front Med (Lausanne). 2018;5:296.
32459333
Wang L, Nong L, Li F, et al. Predominant stroma-rich feature in hyaline vascular variant of Castleman disease Is associated with paraneoplastic pemphigus. Am J Clin Pathol. 2020;154(3):403-413.
26358412
Ohzono A, Sogame R, Li X, et al. Clinical and immunological findings in 104 cases of paraneoplastic pemphigus. Br J Dermatol. 2015;173(6):1447-1452.
24160488
Otten JV, Hashimoto T, Hertl M, et al. Molecular diagnosis in autoimmune skin blistering conditions.Curr Mol Med. 2014;14(1):69-95.
7868713
Helou J, Allbritton J, Anhalt GJ. Accuracy of indirect immunofluorescence testing in the diagnosis of paraneoplastic pemphigus. J Am Acad Dermatol. 1995;32(3):441-447.
Additional Resources
30103046
Amber KT, Valdebran M, Grando SA. Paraneoplastic autoimmune multiorgan syndrome (PAMS): beyond the single phenotype of paraneoplastic pemphigus. Autoimmun Rev. 2018;17(10):1002-1010.
24434358
Baum S, Sakka N, Artsi O, et al.Diagnosis and classification of autoimmune blistering diseases. Autoimmun Rev. 2014;13(4-5):482‐489.
27878477
Kartan S, Shi VY, Clark AK, et al. Paraneoplastic pemphigus and autoimmune blistering diseases associated with neoplasm: characteristics, diagnosis, associated neoplasms, proposed pathogenesis, treament.Am J Clin Dermatol. 2017;18(1):105-126.
25474518
Kelly S, Culican S, Silvestrini RA, et al. Comparative study of five serological assays for the diagnosis of paraneoplastic pemphigus. Pathology. 2015;47(1):58-61.
28492232
Kasperkiewicz M, Ellebrecht CT, Takahashi H, et al. Pemphigus.Nat Rev Dis Primers. 2017;3:17026.
29186863
Paolino G, Didona D, Magliulo G, et al. Paraneoplastic pemphigus: insight into the autoimmune pathogenesis, clinical features and therapy. Int J Mol Sci. 2017;18(12):2532.
17434044
Taintor AR, Leiferman KM, Hashimoto T, et al. A novel case of IgA paraneoplastic pemphigus associated with chronic lymphocytic leukemia.J Am Acad Dermatol. 2007;56(5 Suppl):S73-S76.
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189657 | https://builtin.com/hardware/gb | Expert Contributors
What Is a GB (Gigabyte)?
A gigabyte (GB) is a form of digital measurement used to describe the size of information on a system or the capacity of storage available on a disk or other digital storage media. A gigabyte is equal to one billion bytes.
Written by
Katlyn Gallo
Image: Shutterstock / Built In
UPDATED BY
Brennan Whitfield | May 08, 2025
Summary:
A gigabyte (GB) is a digital unit of measurement equal to one billion bytes, commonly used to describe file sizes and storage capacity on devices like computers, smartphones and cloud platforms. It helps users understand how much digital space is available or used.
more
A gigabyte (GB) is a digital unit of measurement equal to one billion bytes, commonly used to describe file sizes and storage capacity on devices like computers, smartphones and cloud platforms. It helps users understand how much digital space is available or used.
A gigabyte (GB) is a unit of digital measurement used to describe the size of files and the capacity of storage devices like hard drives, smartphones and cloud platforms. In decimal terms, a gigabyte is equal to one billion bytes in data size or storage capacity.
From day to day, there are many units of measurement we come across, whether measuring the length or width of an object, weighing how light or heavy something is, or describing the temperature outside. Like tangible items, things in our digital realm have units of measure — like gigabyte — that we use to describe their sizes as well.
How Many MB Are in a GB?
In decimal measurement, there are 1,000 megabytes (MB) in one gigabyte (GB). You can do additional conversions using simple math.
1,000 bytes = 1 kilobyte (KB)
1,000 kilobytes (KB) = 1 megabyte (MB)
1,000 megabytes (MB) = 1 gigabyte (GB)
1,000 gigabytes (GB) = 1 terabyte (TB)
1,000 terabytes (TB) = 1 petabyte (PB)
1,000 petabytes (PB) = 1 exabyte (EB)
How Many Bytes Are in a Gigabyte? | Video: Jared Owen
Why Do We Use GB?
In general, we use units of measure to define the magnitude of something in a consistent way. The same holds true for gigabytes, which we use as a consistent way to measure the size of a file, program or digital storage capacity.
If you consider your personal computer, you’re likely aware that your hard drive, where you save files, has a maximum amount of storage. You’ll notice that your system’s capacity is typically described in gigabytes, which helps you understand how much available space remains. A standard computer may have around 250 GB of available space. Each time you download a file or program to your computer, some of that available capacity will be used.
More From Katlyn GalloCSPM: An Introduction to Cloud Security Posture Management
What Are Alternatives to GBs?
Like other units of measurement, we can convert gigabytes into larger or smaller units depending on the use case. If you’re referring to a tiny amount of digital information, it may not make sense to present the size in gigabytes. Similarly, other units of measure are better suited for describing a large amount of digital information.
Some alternate units of digital measurement include:
Kilobyte (KB)
Megabyte (MB)
Terabyte (TB)
Petabyte (PB)
Exabyte (EB)
What Are GB in Phone Storage?
As mentioned earlier, one example use case for a gigabyte is to describe the capacity of a computer’s hard drive. However, there are many other situations where we use gigabytes to understand the size of a digital object or storage capacity.
A common example many will be familiar with is a smartphone. Today’s smartphones typically have 64 or more gigabytes of storage capacity available for use. Each time you send and receive texts, take photos and videos or install mobile applications, you’re using available storage.
Consider an iPhone. You can view the phone’s storage in Settings under the “General” menu. The image below shows how Apple uses the gigabyte unit of measure to describe that, of the 128 gigabytes of space available, 70.1 of those gigabytes are used by mobile apps, the operating system (iOS), photos, system data and more.
What Are GB in Cloud Storage?
Another popular use case is the use of gigabytes to describe cloud storage, like iCloud or Google cloud storage. Those who have Gmail accounts will notice when you log into your email account, you can see a display showing the amount of cloud storage available. The below image is an example of how Google storage displays the capacity of a cloud storage account. This particular account has used minimal storage, which is shown in megabytes, of the 15 available gigabytes. Knowing there are 1,000 megabytes in a gigabyte, 32.2 megabytes can be converted to gigabytes by dividing it by 1,000. So, this person has used 0.0322 gigabytes of Google storage.
Frequently Asked Questions
What is a gigabyte (GB)?
A gigabyte (GB) is a unit of digital measurement equal to one billion bytes, used to describe file sizes or storage capacity.
How many megabytes are in a gigabyte?
There are 1,000 megabytes (MB) in one gigabyte (GB).
What units are smaller or larger than a gigabyte?
Smaller units of digital measurement than a gigabyte include:
Bytes (1,000,000,000 bytes = 1 GB)
Kilobytes or KB (1,000,000 KB = 1 GB)
Megabytes or MB (1,000 MB = 1 GB)
Larger units of digital measurement than a gigabyte include:
Terabytes or TB (1,000 GB = 1 TB)
Petabytes or PB (1,000,000 GB = 1 PB)
Exabytes or EB (1,000,000,000 GB = 1 EB)
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189658 | https://www.calculatorsoup.com/calculators/discretemathematics/permutations.php | skip to calculator
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Calculator Soup®
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Basic Calculator
Calculators
Discrete Math
Permutations Calculator nPr
Permutations Calculator nPr
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© Calculator Soup
Like the
Combinations Calculator the
Permutations Calculator finds the number of subsets that can be taken from a larger set. However, the order of the subset matters. The Permutations Calculator finds the number of subsets that can be created including subsets of the same items in different orders.
Factorial
: There are n! ways of arranging n distinct objects into an ordered sequence, permutations where n = r.
Combination
: The number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.
Permutation
: The number of ways to choose a sample of r elements from a set of n distinct objects where order does matter and replacements are not allowed. When n = r this reduces to n!, a simple factorial of n.
Combination Replacement
: The number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are allowed.
Permutation Replacement
: The number of ways to choose a sample of r elements from a set of n distinct objects where order does matter and replacements are allowed.
n
: the set or population
r
: subset of n or sample set
Permutations Formula:
P(n,r)=n!(n−r)!
For n ≥ r ≥ 0.
Calculate the permutations for P(n,r) = n! / (n - r)!. "The number of ways of obtaining an ordered subset of r elements from a set of n elements."
Permutation Problem 1
Choose 3 horses from group of 4 horses
In a race of 15 horses you beleive that you know the best 4 horses and that 3 of them will finish in the top spots: win, place and show (1st, 2nd and 3rd). So out of that set of 4 horses you want to pick the subset of 3 winners and the order in which they finish. How many different permutations are there for the top 3 from the 4 best horses?
For this problem we are looking for an ordered subset of 3 horses (r) from the set of 4 best horses (n). We are ignoring the other 11 horses in this race of 15 because they do not apply to our problem. We must calculate P(4,3) in order to find the total number of possible outcomes for the top 3 winners.
P(4,3) = 4! / (4 - 3)! = 24 Possible Race Results
If our 4 top horses have the numbers 1, 2, 3 and 4 our 24 potential permutations for the winning 3 are {1,2,3}, {1,3,2}, {1,2,4}, {1,4,2}, {1,3,4}, {1,4,3}, {2,1,3}, {2,3,1}, {2,1,4}, {2,4,1}, {2,3,4}, {2,4,3}, {3,1,2}, {3,2,1}, {3,1,4}, {3,4,1}, {3,2,4}, {3,4,2}, {4,1,2}, {4,2,1}, {4,1,3}, {4,3,1}, {4,2,3}, {4,3,2}
Permutation Problem 2
Choose 3 contestants from group of 12 contestants
At a high school track meet the 400 meter race has 12 contestants. The top 3 will receive points for their team. How many different permutations are there for the top 3 from the 12 contestants?
For this problem we are looking for an ordered subset 3 contestants (r) from the 12 contestants (n). We must calculate P(12,3) in order to find the total number of possible outcomes for the top 3.
P(12,3) = 12! / (12-3)! = 1,320 Possible Outcomes
Permutation Problem 3
Choose 5 players from a set of 10 players
An NFL team has the 6th pick in the draft, meaning there are 5 other teams drafting before them. If the team believes that there are only 10 players that have a chance of being chosen in the top 5, how many different orders could the top 5 be chosen?
For this problem we are finding an ordered subset of 5 players (r) from the set of 10 players (n).
P(10,5)=10!/(10-5)!= 30,240 Possible Orders
References
For more information on permutations and combinations please see
Wolfram MathWorld: Permutation.
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189659 | https://engineering.purdue.edu/~wassgren/teaching/ME30800/NotesAndReading/BuoyantForce_Reading.pdf | Notes on Thermodynamics, Fluid Mechanics, and Gas Dynamics 2.4. Buoyant Force and Center of Buoyancy When an object is submerged in a fluid, the pressure acting on the object deeper in the fluid (i.e., in the direction of gravity) will be larger than the pressure acting on the object shallower in the fluid. As a result, there will be a net pressure force acting on the object. This net pressure force is known as the buoyant force.
To derive the value of the buoyant force, consider the vertical pressure forces acting on a narrow cylinder with cross-sectional area dA within a fully-submerged object as shown in Figure 2.17.
Figure 2.17. Pressure forces on a thin cylinder of cross-sectional area dA and height l from within a fully-submerged object.
The net pressure force in the vertical direction on the narrow cylinder, assuming an incompressible fluid, is, dFp,net = (p + ⇢fluidgl)dA −pdA = ⇢fluidgldA (acting opposite to gravity).
(2.78) The total net pressure force acting on the object is found by integrating these small bits of pressure force over the entire cross-sectional area of the object, Fp,net = ˆ A dFp,net = ˆ A ⇢fluidgldA (acting opposite to gravity).
(2.79) Since the density and gravity are assumed constant here, they may be pulled outside the integral, Fp,net = ⇢fluidg ˆ A ldA (acting opposite to gravity), (2.80) = ⇢fluidg ˆ V dV (acting opposite to gravity), (2.81) Fp,net = FB = ⇢fluidgVsubmerged object (acting opposite to gravity), (2.82) where the integral is simply the volume of the submerged object. This net pressure force acting on the object is referred to as the buoyant force.
Notes: (1) Equation (2.82) states that the buoyant force is equal to the weight of the fluid that’s been displaced by the submerged object. This relationship is also known as Archimede’s Principle.
(2) The same analysis can be used for partially submerged objects. In that case, the pressure acting on the top of the object is atmospheric pressure while the pressure at the bottom is patm + ⇢fluidgl0, where l0 is the length of the narrow cylinder that’s submerged in the fluid (Figure 2.18). After integrating over the objects cross-sectional area (similar to Eq. (2.80), we would arrive at exactly the same relation as in Eq. (2.82) except that the Vsubmerged object refers to just that volume that is submerged in the fluid.
C. Wassgren 157 2021-12-15 Notes on Thermodynamics, Fluid Mechanics, and Gas Dynamics Figure 2.18. Pressure forces on a thin cylinder of cross-sectional area dA. The depth of the cylinder below the free surface is l0.
(3) There is no net pressure force on the object in the directions perpendicular to gravity since the pressure only varies parallel to the gravitational vector.
The resultant buoyant force acts at the center of buoyancy. The center of buoyancy is found by equating the moment caused by the resultant buoyant force acting at the center of buoyancy to the distributed moment caused by the distributed pressure forces. Consider moments about the z axis in Figure 2.19.
Figure 2.19. Moments about the z axis due to the pressure forces acting on a thin cylinder of cross-sectional area dA and height l from within a fully-submerged object.
xCBˆ i ⇥⇢gV ˆ j | {z } buoyant force = ˆ A xˆ i ⇥ ⇢gldAˆ j | {z } net pressure force on cylinder , (2.83) xCB⇢gV ˆ k = ⇢gˆ k ˆ A xdV (dV = ldA), (2.84) xCB = 1 V ˆ V xdV, (2.85) which is the center of displaced volume. Performing similar analyses about the x and y axes produces similar results. Thus, the center of buoyancy is located at the center of the displaced volume. This is true for both fully submerged and partially submerged objects.
C. Wassgren 158 2021-12-15 Notes on Thermodynamics, Fluid Mechanics, and Gas Dynamics 2.5. Stable Orientation of a Submerged Object Submerged objects will be in an equilibrium orientation when the forces acting on the object are such that there is no net moment on the object. Considering only the object weight and a buoyant force, an equilibrium orientation will only occur when the two forces are co-linear, as shown in Figure 2.20. Neither object experiences a net moment.
Figure 2.20. The buoyant force, acting at the center of buoyancy, and weight, acting at the center of gravity, for two fully-submerged objects in equilibrium. The object on the left is stable, but the object on the right is unstable.
The object on the left is in a stable equilibrium while the object on the right is in an unstable equilibrium.
The reason for the di↵erence is that if each object is rotated slightly, the object on the left will experience a moment that restores it back to its original configuration. However, a small perturbation to the right-hand object will result in a moment that will cause the object to move away from its initial configuration.
The stability of partially submerged objects is a particularly important topic when considering the design of ships. The Swedish ship Vasa is a famous example of a ship that was unstable and “turtled” shortly after setting sail for the first time. Unfortunately, stability analysis of partially submerged objects can be complicated since the submerged volume and center of buoyancy changes as the orientation of the object rotates. For example, consider the stability of the simple shape shown in Figure 2.21 (CG is the center of gravity and CB is the center of buoyancy). The initial configuration of the object (on the left) appears to be Figure 2.21. The center of buoyancy and center of gravity for a partially-submerged object.
The center of buoyancy changes location as the submerged volume changes.
in unstable equilibrium with the center of gravity above the center of buoyancy. However, when the object is tilted (on the right), the center of buoyancy shifts to one side such that it acts to restore the object to its initial configuration. Hence, the object is actually initially in stable equilibrium.
C. Wassgren 159 2021-12-15 statics_02 Page 1 of 2 A tank is divided by a wall into two independent chambers. The left chamber is filled to a depth of HL=6m with water (rH20=1000 kg/m3) and the right side if filled to a depth of HR=5m with an unknown fluid. A wooden cube (SGwood=0.6) with a length of L=0.20m on each side floats half submerged in the unknown fluid. Air (rair=1.2 kg/m3) fills the remainder of the container above each fluid. The right container has a pipe that is vented to the atmosphere while the left container is sealed from the atmosphere. A manometer using mercury as the gage fluid (SGHg=13.6) connects the two chambers and indicates that h=0.150 m. a. Determine the density of the unknown fluid. b. Determine the magnitude of the force (per unit depth into the page) acting on the dividing wall due to the unknown fluid. c. Determine the magnitude of the force (per unit depth into the page) acting on the dividing wall due to the water. SOLUTION: Balance forces on the wooden cube. (1) (2) Using the given data: SGwood = 0.6 rH2O = 1000 kg/m3 Þ rfluid = 1200 kg/m3 ( ) 2 3 1 fluid wood 2 0 y F g L L gL r r = = -å 2 fluid wood wood H O 2 2SG r r r \ = = wooden cube (SGwood=0.6) of length L on a side h HL water unknown fluid L ½ L HR air air mercury (SGHg=13.6) dividing wall vent to the atmosphere (patm = 101 kPa (abs)) Notes on Thermodynamics, Fluid Mechanics, and Gas Dynamics C. Wassgren 160 2021-12-15 statics_02 Page 2 of 2 Now determine the force acting on the wall due to the unknown fluid. (3) (4) Using the given data: patm = 101 kPa (abs) HR = 5 m rfluid = 1200 kg/m3 g = 9.81 m/s2 Þ Fp,R = 506 kN/m Now find the pressure force due to the water. (5) (6) where pL is the (absolute) pressure acting on the free surface of the water. This pressure may be found using the manometer. (7) Substitute Eqn. (7) into Eqn. (6). (8) Using the given data: patm = 101 kPa (abs) SGHg = 13.6 rH2O = 1000 kg/m3 g = 9.81 m/s2 h = 0.150 m HL = 6 m Þ Fp,L = 903 kN/m ( ) ( ) ( ) !
, atm fluid 0 abs 1 R y H p R y dA p F p gy dy r = = = = = + ò "## $## % 2 1 , atm fluid 2 p R R R F p H gH r \ = + ( ) ( ) ( ) !
2 , H O 0 abs 1 L y H p L L y dA p F p gy dy r = = = = = + ò "# # $## % 2 2 1 , H O 2 p L L L L F p H gH r \ = + H O 2 atm Hg atm Hg L p p gh p SG gh r r = + = + ( ) H O 2 2 2 1 , atm Hg H O 2 p L L L F p SG gh H gH r r \ = + + h mercury (SGHg=13.6) patm pL Notes on Thermodynamics, Fluid Mechanics, and Gas Dynamics C. Wassgren 161 2021-12-15 buoyancy_10 Page 1 of 1 A hydrometer is a specific gravity indicator, the value being indicate by the level at which the free surface intersects the stem when floating in a liquid. The 1.0 mark is the level when in distilled water. For the unit shown, the immersed volume in distilled water is 15 cm3. The stem is 6 mm in diameter. Find the distance, h, from the 1.0 mark to the surface when the hydrometer is placed in a nitric acid solution of specific gravity 1.5. SOLUTION: Since the hydrometer is in equilibrium, its weight and the buoyant force should equal each other. When submerged in distilled water, ! = #!"#$% $%&',!"# = #!"#$ℎ ) '" => ℎ= + ,!"#-$ %$", (1) where A is the hydrometer’s cross-sectional area. The height h is the location where the mark is made for distilled water. When submerged in nitric acid, ! = #!.#&$ ) '"(ℎ+ Δℎ) => ℎ+ Δℎ= + ,!'#&-$ %$" = + /0!'#&,!"#-$ %$". (2) Combining Eqs. (1) and (2), + ,!"#-$ %$" + Δℎ= + /0!'#&,!"#-$ %$", (3) Δℎ= + /0!'#&,!"#-$ %$" − + ,!"#-$ %$", (4) Δℎ= + ,!"#-$ %$" -1 /0!'#& −1/, (5) Δℎ= ,!"#-2()+,!"# ,!"#-$ %$" -1 /0!'#& −1/, (6) Δℎ= 2()+,!"# $ %$" -1 /0!'#& −1/. (7) Using the given data, Vdisp,H2O = 15 cm3, d = 0.6 cm, SGHNO3 = 1.5, => Dh = -17.7 cm. The hydrometer moves upward a distance of 17.7 cm from where the distilled water mark is located. Solution: We will apply the hydrostatics equations to this system.
Governing Equations: Fbuoy ρ g ⋅ Vd ⋅ = (Buoyant force is equal to weight of displaced fluid) Assumptions: (1) Static fluid (2) Incompressible fluid Taking a free body diagram of the hydrometer: ΣFz 0 = M − g ⋅ Fbuoy + 0 = Solving for the mass of the hydrometer: M Fbuoy g = ρ Vd ⋅ = When immersed in water: M ρw Vw ⋅ = When immersed in nitric acid: M ρn Vn ⋅ = Since the mass of the hydrometer is the same in both cases: ρw Vw ⋅ ρn Vn ⋅ = When the hydrometer is in the nitric acid: Vn Vw π 4 d2 ⋅ h ⋅ − = ρn SG ρw ⋅ = Therefore: ρw Vw ⋅ SG ρw ⋅ Vw π 4 d2 ⋅ h ⋅ − § ¨ © · ¸ ¹ ⋅ = Solving for the height h: Vw SG Vw π 4 d2 ⋅ h ⋅ − § ¨ © · ¸ ¹ ⋅ = Vw 1 SG − ( ) ⋅ SG − π 4 ⋅ d2 ⋅ h ⋅ = h Vw SG 1 − SG § ¨ © · ¸ ¹ ⋅ 4 π d2 ⋅ ⋅ = h 15 cm3 ⋅ 1.5 1 − 1.5 § ¨ © · ¸ ¹ u 4 π 6 mm ⋅ ( )2 u u 10 mm ⋅ cm § ¨ © · ¸ ¹ 3 u = h 177 mm ⋅ = Notes on Thermodynamics, Fluid Mechanics, and Gas Dynamics C. Wassgren 162 2021-12-15 buoyancy_08 Page 1 of 1 A uniform block of steel (with a specific gravity of 7.85) will “float” at a mercury-water interface as shown in the figure. What is the ratio of the distances a and b? SOLUTION: Balance forces in the vertical direction, , (1) where the buoyant forces are equal to the weights of the displaced fluids. Re-writing in terms of the lengths a and b and the block’s cross-sectional area Ablock, , (2) , (3) , (4) , (5) . (6) Using the given data, SGHg = 13.6 SGsteel = 7.85 Þ a/b = 0.83 Note that we could also solve this problem by balancing the block’s weight with the pressure forces acting on the top and bottom block surfaces. , (7) where H is the depth of the water-mercury interface. Simplifying this equation gives, , (8) , (9) which is exactly the same as Eq. (3). F V ∑ = 0 = −Wblock + F B,Hg + F B,H2O = −ρblockVblockg + ρHgVblock, in Hg g + ρH2OVblock, in H2O g −ρblockAblock a + b ( )+ ρHgAblockb + ρH2OAblocka = 0 −ρsteel a + b ( )+ ρHgb + ρH2Oa = 0 −ρH2OSGsteelb a b +1 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟+ ρH2OSGHg + ρH2Ob a b = 0 −SGsteel a b +1 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟+ SGHg + a b = 0 a b = SGHg −SGsteel SGsteel −1 F V ∑ = 0 = −Wblock + Fp,H2O + Fp,Hg = −ρblockAblock a + b ( )g −ρH2Og H −a ( )Ablock + ρH2OgH + ρHggb ( )Ablock −ρblock a + b ( )−ρH2O H −a ( )+ ρH2OH + ρHgb = 0 −ρblock a + b ( )+ ρH2Oa + ρHgb = 0 a b water mercury steel block Notes on Thermodynamics, Fluid Mechanics, and Gas Dynamics C. Wassgren 163 2021-12-15 buoyancy_04 Page 1 of 1 Archimedes principle states that the buoyant force acting on a submerged object is equal to the weight of the fluid displaced by that object. Is this true for compressible fluids? SOLUTION: Consider an arbitrary object immersed in a compressible fluid as shown in the figure below. Determine the net pressure force acting on a parallelpiped of the material with a differential cross-sectional area, , (1) where, , (2) and, , (3) where r is the density of the fluid (not the object). Equation (1) becomes, , (4) . (5) The net pressure force acting over the entire object, i.e., the buoyant force, is, . (6) Assuming that the gravitational acceleration is constant (usually a good assumption), , (7) Note that the integrals in the previous equation give the mass of the fluid displaced by the object, i.e., . (8) Thus, just as with the incompressible case, the buoyant force in a compressible fluid is equal to the weight of the fluid displaced by the object, . (9) ( ) 1 2 P dF p p dA = - p1 = pz=0 + ρg dz z=0 z=z1 ∫ p2 = pz=0 + ρg dz z=0 z=z2 ∫ dFP = pz=0 + ρg dz z=0 z=z1 ∫ −pz=0 − ρg dz z=0 z=z2 ∫ ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ dA 1 2 z z P z z dF dA gdz r = = = ò 1 2 z z P P A A z z F dF gdzdA r = = = = ò ò ò FP = g ρ dz z=z2 z=z1 ∫ A ∫ dA Mfluid displaced by object = ρ dz z=z2 z=z1 ∫ A ∫ dA Fp = Mfluid displaced by object g p1dA p2dA dA g z Notes on Thermodynamics, Fluid Mechanics, and Gas Dynamics C. Wassgren 164 2021-12-15 statics_20 Page 1 of 1 Consider an ice cube with initial volume Vice,0 floating in a cup of water of initial volume Vwater,0. The specific gravity of ice is SGice. Show mathematically that, as the ice cube melts, the water level in the cup remains unchanged. SOLUTION: If a mass of ice, Dmice, melts (Dmice < 0), it will correspond to an equal increase in water, Dmwater, i.e., . (1) Expressed in terms of volumes, , (2) . (3) The volume of water displaced by the ice is found by equating the weight of the displaced water to the weight of the ice (Archimedes Law), , (4) . (5) Thus, if a volume of ice melts, DVice, then the amount of water displaced, in order to balance the new ice weight, is, . (6) Note that if the ice melts (DVice < 0) , less water needs to be displaced to support the (smaller) ice weight (DVwater,disp < 0). Thus, the sum of the volume of water added due to melting and the change in displaced water volume due to a change in the weight of the ice is, . (7) The increase in water volume is exactly balanced by a decrease in the displaced water volume, which means that the water level height won’t change! This fact has important implications regarding the rise in sea level due to melting ice. Melting free-floating ice, e.g., icebergs, won’t result in an increase in sea level. However, ice that was originally supported by land, e.g., glaciers, will contribute to an increase in sea levels. !Δmwater = −Δmice !ρwaterΔVwater = −ρiceΔVice = −SGiceρwaterΔVice !ΔVwater = −SGiceΔVice !ρwaterVwater,dispg = ρiceViceg = SGiceρwaterViceg !Vwater,disp = SGiceVice !ΔVwater,disp = SGiceΔVice !ΔVwater + ΔVwater,disp = −SGiceΔVice + SGiceΔVice = 0 Notes on Thermodynamics, Fluid Mechanics, and Gas Dynamics Video solution: C. Wassgren 165 2021-12-15 statics_19 Page 1 of 3 Consider the system shown below. A wooden sphere of radius R and specific gravity SGwood is half submerged in an unknown liquid, referred to as liquid A. Liquid A, which has a depth HA, is separated from a pool of water, which has a depth HH2O, by a hinged gate tilted at an angle q with respect to the horizontal. The gate has a width b into the page. a. What is the density of liquid A, rA, in terms of the specific gravity of the wooden sphere (SGwood) and the density of water (rH20)? b. What is the pressure force liquid A exerts on the inclined gate in terms of (a subset of) rA, HA, g, b, and q? Write this force as a vector. c. Assuming the gate has negligible mass and the angle q is 90° so the gate is vertical (figure shown below), at what height HH20 will the gate just start to rotate about its hinge? Write this height in terms of (a subset of) rA, rH20, HA, g, and b. SOLUTION: The density of liquid A may be found by balancing the weight of the wooden sphere with the buoyant force acting on it, , (1) . (2) The force that liquid A exerts on the gate may be found by integrating pressure forces along the length of the gate, , (3) where, (gage pressure), (4) , (5) F W = F B ⇒ρwood 4 3π R3g = ρA 1 2 4 3π R3 half of the sphere is submerged g ⇒ρA = 2ρwood ρA = 2SGwoodρH20 FA on gate = −pdA A ∫ p = ρAgy dA = bdyˆ i −bdxˆ j R R HA q HH20 hinge liquid A water y x dx dy q L HA g HA HH20 Notes on Thermodynamics, Fluid Mechanics, and Gas Dynamics C. Wassgren 166 2021-12-15 statics_19 Page 2 of 3 so that, . (6) Note that, and , (7) so that Eq. (6) becomes, , (8) . (9) Another approach to calculating the force on the gate is to balance forces on the triangular block of liquid shown in the figure below. , (10) , (11) where Eq. (7) has been used. Note that since FA on gate = -Fgate on A, the final result is the same as what was found in Eq. (9)! For the specific case when q = 90° (figure shown below), the moments about the hinge are, , (12) , (13) , (14) FA on gate = −ρAgy ( ) bdyˆ i −bdxˆ j ( ) A ∫ = ρAgb −ˆ i ydy y=0 y=HA ∫ + ˆ j ydx x=0 x=L ∫ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ y = x tanθ H A = L tanθ FA on gate = ρAgb −ˆ i ydy y=0 y=HA ∫ + ˆ j x tanθ dx x=0 x=HA tanθ ∫ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ FA on gate = −1 2 ρAgbH A 2ˆ i + 1 2 ρAgb H A 2 tanθ ˆ j F ∑ = 0 = −ρAgy ( ) dybˆ i ( ) y=0 y=HA ∫ pressure force on side of fluid block +ρAg 1 2 LH Abˆ j weight of fluid block + F gate on A force gate exerts on block F gate on A = 1 2 ρAgbH A 2ˆ i −1 2 ρAg H A 2 tanθ bˆ j M hinge,z ∑ = 0 = − ′ y + H A −H H2O ( ) ⎡ ⎣ ⎤ ⎦ρH20g ′ y ( ) bd ′ y ( ) ′ y =0 ′ y =HH20 ∫ + y ρAgy ( ) bdy ( ) y=0 y=HA ∫ 0 = gb −ρH20 ′ y 2 + H A −H H2O ( ) ′ y ⎡ ⎣ ⎤ ⎦d ′ y ′ y =0 y=HH2O ∫ + ρA y2 dy y=0 y=HA ∫ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ρH20 1 3 H H2O 3 + 1 2 H A −H H20 ( )H H2O 2 ⎡ ⎣ ⎤ ⎦= 1 3 ρAH A 3 y x q L HA Fgate on A weight x HA HH2O hinge y y’ Notes on Thermodynamics, Fluid Mechanics, and Gas Dynamics C. Wassgren 167 2021-12-15 statics_19 Page 3 of 3 , (15) , (16) . (17) This equation could be solved numerically for HH20/HA given a value for rA/rH20. The following plot shows example solutions. An alternate approach for deriving Eq. (17) is to sum moments about the hinge, but make note of the fact that the center of pressure on each wall is one-third of the liquid depth from the bottom of the wall, , (18) , (19) , (20) , (21) which is the same as Eq. (17). H H20 H A ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 3 + 3 2 1− H H20 H A ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ H H20 H A ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2 = ρA ρH20 H H20 H A ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 3 + 3 2 H H20 H A ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2 −3 2 H H20 H A ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 3 = ρA ρH20 H H20 H A ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 3 −3 H H20 H A ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2 + 2 ρA ρH20 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟= 0 M hinge,z ∑ = 0 = − H A −HH2O ( )+ 2 3 HH2O ⎡ ⎣ ⎤ ⎦ 1 2 ρH2OgbH H2O 2 ( )+ 2 3 H A ( ) 1 2 ρAgbH A 2 ( ) 1 2 ρH2OH H2O 2 H A −1 6 ρH2OH H2O 3 = 1 3 ρAH A 3 3 H H2O H A ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2 − H H2O H A ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 3 = 2 ρA ρH2O ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ H H2O H A ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 3 −3 H H2O H A ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2 + 2 ρA ρH2O ⎛ ⎝ ⎜ ⎞ ⎠ ⎟= 0 Notes on Thermodynamics, Fluid Mechanics, and Gas Dynamics C. Wassgren 168 2021-12-15 statics_03 Page 1 of 2 James Bond is trapped on a small raft in a steep walled pit filled with water as shown in the figure. Both the raft and pit have square cross-sections with a side length of l=3 ft for the raft and L=4 ft for the pit. In the raft there is a steel anchor (SGA=7.85) with a volume of VA=1 ft3. In the current configuration, the distance from the floor of the raft to the top of the pit is H=7.5 ft. Unfortunately, Bond can only reach a distance of R=7 ft from the floor of the raft. In order for Bond to escape, would it be helpful for him to toss the anchor overboard? Justify your answer with calculations. (Hint: The mass of water is conserved in this problem.) SOLUTION: Consider the cases when the anchor is in the raft and out of the raft as shown in the figures below. First consider the change in the position of the raft floor relative to the free surface of the water. Case (a): (1) Case (b): (2) mraft+Bond + manchor ( )g weight of raft & contents = ρH2Ogl2h weight of displaced water mraft+Bond ( )g weight of raft & contents = ρH2Ogl2 h + Δh ( ) weight of displaced water l L (a) h D l L D + DD h + Dh (b) H H + DH H R l L James Bond anchor with volume VA and specific gravity, SGA water Notes on Thermodynamics, Fluid Mechanics, and Gas Dynamics C. Wassgren 169 2021-12-15 statics_03 Page 2 of 2 Subtract Eqn. (2) from Eqn. (1) and simplify. (3) (4) (5) (6) Note that since Vanchor > 0, Dh < 0 and thus the raft moves up relative to the free surface. However, the free surface will also move so we still don’t yet know whether Bond moves up or down relative to the surface of the pit. We must now consider the movement of the free surface of the water. Case (a): (7) Case (b): (8) Since the volume of water is conserved, Eqns. (7) and (8) must be equal. (9) (10) (where Eqn. (6) has been utilized) (11) Note that since SGanchor > 1, DD < 0, i.e. the free surface moves downward. Combine the expressions for Dh and DD to determine the movement of the raft bottom relative to the pit walls. (12) (13) (14) (15) Use the given data to determine DH. Vanchor = 1 ft3 L = 4 ft SGanchor = 7.85 l = 3 ft Þ DH = -0.44 ft (The raft moves closer to the top of the pit.) Recall that H = 7.5 ft and Bond can only reach R = 7 ft. After tossing the anchor overboard, the bottom of the raft is H + DH = 7.06 ft > R = 7 ft. Hence, Bond still can’t reach the top of the pit. Goodbye, Mr. Bond. ( ) ( ) ( ) 2 2 2 2 raft+Bond anchor raft+Bond H O H O m m g m g gl h gl h h r r + -= -+ D 2 2 anchor H O m l h r = -D 2 anchor 2 H O m h l r D = -anchor anchor 2 SG V h l \D = - VH2O = L 2D volume of H2O in pit − l2h volume of raft in H2O VH2O = L 2 D + ΔD ( ) volume of H2O in pit −l2 h + Δh ( ) volume of raft in H2O −Vanchor ( ) ( ) 2 2 2 2 anchor L D D l h h V L D l h + D -+ D -= -2 2 anchor 0 L D l h V D -D -= 2 anchor 2 l h V D L D + \D = ( ) anchor anchor 2 1 SG V D L -\D = ( ) ( ) ( ) D H h D D H H h h + -= + D + + D -+ D H D h D = -D + D ( ) anchor anchor anchor anchor 2 2 1 SG V SG V H L l -D = --2 anchor anchor 2 2 1 1 V L H SG L l é ù æ ö \D = --ê ú ç ÷ è ø ë û Notes on Thermodynamics, Fluid Mechanics, and Gas Dynamics C. Wassgren 170 2021-12-15 statics_17 Page 1 of 3 A cylindrical log of radius R and length L rests against the top of a dam. The water is level with the top of the log and the center of the log is level with the top of the dam. You may assume that the contact point with the dam is frictionless. Obtain expressions for a. the mass of the log, and b. the contact force between the log and dam. Express your answers in terms of (a subset of) rH2O, g, L, and R. SOLUTION: The mass of the log, m, may be found by performing a force balance in the vertical direction, , (1) where g is the acceleration due to gravity. Note that the point of contact with the dam is assumed to be frictionless. The net vertical pressure force, FP,y, is found by integrating the vertical component of the pressure force around the log, , (2) , (3) , (4) where r is the density of the water. Evaluating the integral in Eq. (4) gives, , (5) . (6) Substituting into Eq. (1) and solving for m gives, F y ∑ = 0 = mg + F P,y F P,y = psinθ dA θ=π 2 θ=2π ∫ = ρgy =p sinθ Rdθ L ( ) =dA θ=π 2 θ=2π ∫ F P,y = ρg R −Rsinθ ( ) =y sinθRdθ L ( ) θ=π 2 θ=2π ∫ = ρgR2L 1−sinθ ( )sinθ dθ θ=π 2 θ=2π ∫ F P,y = ρgR2L sinθ −sin2θ ( )dθ θ=π 2 θ=2π ∫ F P,y = ρgR2L −cosθ θ=π 2 θ=2π − 1 2θ −1 4 sin 2θ ( ) ⎡ ⎣ ⎤ ⎦θ=π 2 θ=2π { } = ρgR2L −1−1 2 2π −π 2 ( ) ⎡ ⎣ ⎤ ⎦ F P,y = −1+ 3π 4 ( )ρgR2L gravity, g y q R x Fw mg R Notes on Thermodynamics, Fluid Mechanics, and Gas Dynamics Video solution: C. Wassgren 171 2021-12-15 statics_17 Page 2 of 3 . (7) An alternate, easier method for determining the vertical pressure force acting on the log is to note that the vertical surface forces acting along a horizontal plane at the bottom of the log is, , (8) , (9) , (10) which is the same result found in Eq. (7). An even easier method is to use a buoyant force, although one must recognize the appropriate volume to use to determine the displaced volume. A vertical force balance for the log gives, Þ , (11) where FB is the buoyant force, which is the weight of the displaced fluid. Note that in this case, the displaced volume of fluid is the volume of the log, plus the volume above the right, upper quadrant of the log as shown in the figure below, , (12) Combining Eqs. (11) and (12) gives the mass of the log, , (13) which is exactly the same result as found in the previous two methods. m = 1+ 3π 4 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ρR2L F y ∑ = 0 = ρg 2R ( ) 2RL ( ) pressure force at bottom −mg log weight −ρgL 3 4 4R2 −π R2 ( ) weight of water = 4ρgLR2 −mg −ρgL 3 4 4R2 −π R2 ( ) mg = ρgLR2 4 −3 4 4 −π ( ) ⎡ ⎣ ⎤ ⎦= ρgLR2 4 −3+ 3 4 π [ ] m = ρR2L 1+ 3π 4 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ F y ∑ = 0 = −mg + F B m = F B g F B = ρgVdisplaced = ρg 3 4 π R2 + R2 ( )L = ρgR2L 3π 4 +1 ( ) m = ρR2L 3π 4 +1 ( ) y q R x Fw mg mH2Og y R x Notes on Thermodynamics, Fluid Mechanics, and Gas Dynamics Video solution: C. Wassgren 172 2021-12-15 statics_17 Page 3 of 3 Now consider a horizontal force balance for the log. , (14) where Fw is the horizontal force exerted by the wall on the wall and FP,x is the horizontal component of the net pressure force acting on the log due to the water. The net horizontal pressure force is given by, , (15) . (16) Evaluate the integrals in Eq. (16), , (17) . (18) Substitute into Eq. (14) and solve for the wall force. . (19) Another, much simpler method for finding the wall force is to note that the horizontal pressure force acting on the log will simply be the pressure force acting on the horizontally projected area. , (20) which is precisely the same result found in Eq. (18). Note that the horizontal pressure force is only evaluated from y = 0 to y = R since on the bottom half of the log, the pressure forces from either side of the log cancel each other out. F x ∑ = 0 = −F w + F P,x F P,x = −pcosθ dA θ=π 2 θ=2π ∫ = −ρgy ( ) =p cosθ RdθL ( ) =dA θ=π 2 θ=2π ∫ = −ρg R −Rsinθ ( ) =y ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥cosθ RdθL ( ) θ=π 2 θ=2π ∫ F P,x == −ρgR2L 1−sinθ ( )cosθ dθ θ=π 2 θ=2π ∫ = −ρgR2L cosθ −sinθ cosθ ( )dθ θ=π 2 θ=2π ∫ F P,x = −ρgR2L sinθ θ=π 2 θ=2π −1 2 sin2θ θ=π 2 θ=2π ⎡ ⎣ ⎢ ⎤ ⎦ ⎥= −ρgR2L sinθ θ=π 2 θ=2π −1 2 sin2θ θ=π 2 θ=2π ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ F P,x = −ρgR2L −1+ 1 2 [ ] = 1 2 ρgR2L F w = 1 2 ρgR2L F P,x = pdA y=0 y=R ∫ = ρgy ( ) =p dyL =dA y=0 y=R ∫ = ρgL ydy y=0 y=R ∫ = 1 2 ρgR2L y q R x Fw mg Notes on Thermodynamics, Fluid Mechanics, and Gas Dynamics Video solution: C. Wassgren 173 2021-12-15 |
189660 | https://link.springer.com/article/10.3758/s13428-020-01420-5 | Change that occurs in distinct phases or regimes can be modeled using piecewise (spline) functions (see, e.g., Gallant & Fuller, 1973; Seber & Wild, 1989, Chapter 9) where the overall piecewise regression model is a complex amalgamation of submodels, each of which is associated with a distinct interval of time (see, e.g., Cudeck & Klebe, 2002). Because the functional form in each segment can be tailored to fit the localized data (Cudeck & Harring, 2010), the piecewise growth model is quite flexible and can accommodate a variety of modeling scenarios that are not adequately captured by mathematical functions for single-stage change processes (Grimm et al., 2011; Ram & Grimm, 2009; Sterba, 2014) and/or often yield parameters with more meaningful and substantive interpretations.
For example, consider the two-phase linear-linear piecewise model depicted in Fig.1. The changepoint distinguishes between two phases comprising the overall change process. On the left-hand side of the changepoint are the localized data corresponding to phase 1 in which a linear function is superimposed. The data in this phase also suggests that some curvilinear function in _t_, such as a quadratic function, may also be appropriate. The localized data to the right of the changepoint represent the change process across the second phase. It is clear from the graph that change appears constant across larger values of _t_ and might be best characterized by a linear function where the rate of change is assumed to be zero.
Fig. 1
A generic piecewise model with two phases and a single changepoint
Full size image
Specification and estimation of piecewise growth models within a mixed-effects modeling framework has been thoroughly discussed in several articles (see, e.g., Cudeck & Klebe, 2002; Naumova et al.,, 2001) and book chapters (see, e.g., Fitzmaurice et al.,, 2011; Hoffman, 2015; Verbeke & Molenberghs, 2000). Cudeck and Klebe (2002), for example, fit a quadratic-linear mixed-effects model with zero- and first-order continuity constraints (Seber & Wild, 1989) to nonverbal performance data obtained from a life span study. Even though a polynomial was fit to each of the two segments comprising the growth model, the changepoint marking the shift from the first phase to the second phase was an unknown, subject-specific coefficient to be estimated from the data, thereby making the overall function intrinsically nonlinear.Footnote 1 These authors, and others (see, e.g., Grimm et al.,, 2017), demonstrated how this piecewise mixed-effects model could be fitted using SAS PROC NLMIXED—a module that allows user-defined conditional or Boolean logic programming statements (e.g., _if-then_ statements) and integration of SAS PROC IML functions—allowing the estimation algorithm to parse an individuals’ data to fit one segment or another in a straightforward manner. If the changepoint denoting the transition from one phase to another does not vary from person to person or has a known value, then conventional multilevel modeling software, like SAS PROC MIXED (see, e.g., Hoffman, 2015; Verbeke & Molenberghs, 2000) or the _lmer_ function in the lme4 package in R can be used.
Although the implementation of piecewise growth models as mixed-effects models is relatively straightforward, fitting these same models as latent growth models using structural equation modeling (SEM) software programs has proven to be more challenging because SEM software generally does not allow user-defined programming statements. However, the majority of SEM programs do have the facility to implement nonlinear constraints on model parameters, which permits, for example, the elements of the factor loading matrix to be expressed as nonlinear functions of growth model parameters and constants (see, e.g., Blozis et al.,, 2008; Grimm & Ram, 2009; Preacher & Hancock, 2012; Preacher & Hancock, 2015). It is precisely this nonlinear constraint functionality that allows one to fit piecewise latent growth models with SEM software. Harring et al., (2006) discuss how a conditionally-linear form of a bilinear (linear-linear) piecewise LGM could be implemented in SEM software by reparameterizing the model to a form that can take advantage of the nonlinear constraints of the program. This is accomplished using a variant of the minimum/maximum function for monotonic (i.e., always non-decreasing or non-increasing) functional relations between the response and time (see, Harring et al.,, 2006, for a complete description). This reparameterization permitted newly derived parameters to be recast from regression parameters of the original linear-linear growth function. One drawback of this approach at that time was that the reparameterized coefficients—simple functions of the original parameters—no longer related directly to the underlying developmental process and therefore lacked meaningful substantive interpretation, thus requiring back transformation of the model parameters. Modules in contemporary SEM software (e.g., the NEW command in M _plus_) that allow new parameters to be derived from those estimated as part of the model now make this latter point moot.
Numerous examples exist in the methodological literature demonstrating how various nonlinear growth functions can be formulated in a latent growth modeling framework and implemented utilizing nonlinear constraints (see, e.g., Blozis et al.,, 2008; Choi et al.,, 2009; Grimm and Ram, 2009; Grimm et al.,, 2017; Preacher & Hancock, 2015; Sterba, 2014). The bilinear piecewise latent growth model introduced by Harring et al., (2006), for instance, has been extended to second-order factor structures (Kohli and Harring, 2013), growth mixture models (Kohli et al., 2013; Kohli et al., 2015; Kohli et al., 2016), and random changepoints (Feng et al., 2019; Grimm et al., 2017; Preacher & Hancock, 2015). Other methodological advances include extending piecewise LGMs to repeated measures data with measurement occasions that may vary across individuals in placement and/or number (Sterba, 2014) and to empirically determine the number and locations of changepoints in a dataset using an automated search algorithm (Marcoulides, 2018). These latter two methods impose the rather strict assumptions that changepoints are _known_ (Sterba, 2014) and the _same_ for all subjects (Marcoulides, 2018; Sterba, 2014). These methodological elaborations notwithstanding, applications of piecewise LGMs _beyond_ two-phase monotonic, polynomial processes with known and/or fixed changepoints are scarce and may reflect the apparent difficulty in implementing such models in standard SEM software. To address this methodological gap, we demonstrate through three empirical examples how M _plus_ (version 8.1; Muthén & Muthén, 1998) and lavaan in R (version 0.6-5; Rosseel, 2012)—popular mainstream SEM software—can be utilized to fit a broader class of piecewise LGMs to describe non-polynomial growth within a given phase, non-monotonic growth over the entire measurement period, growth that encompasses more than two phases, and that allows the changepoints to be unknown (freely estimated from the data) and/or to vary across individuals.
As was pointed out previously (see, e.g., Blozis, 2007; Blozis et al.,, 2008; Grimm et al.,, 2017; Harring et al.,, 2006; Harring et al.,, 2012), SEM programs such as M _plus_, LISREL, and laavan in R, remain the tools of choice of many researchers for analyzing a wide range of models. This is especially pertinent given recent advancements of SEM software to fit multilevel models to nested data structures, finite mixture models to account for population heterogeneity, and longitudinal models for intensive data collection designs. Yet, it is the most basic functionality of SEM programs—specification of _latent_ repeated outcomes (i.e., second-order latent growth models; Hancock et al.,, 2001), incorporation of measured and latent variable covariates (Blozis & Cudeck, 1999), extensions to multiple group structures (McArdle & Nesselroade, 2014), accommodation of multivariate repeated measures (Blozis, 2004), and use of well-understood indices of model fit that make keeping analyses within the same software environment attractive.
In the remainder of this manuscript, we first review how piecewise growth models can be formulated in the latent growth modeling framework. Then, building off of the oft-utilized bilinear piecewise LGM, we extend the piecewise LGM framework to segmented polynomials and inherently nonlinear functions in subsequent sections. Finally, we shift to modeling a three-phase longitudinal process. As the elaborations are introduced, analytic decision points will be discussed such as whether (a) the segments join at the changepoint and how to incorporate this information into model specification; (b) the growth factors, including the changepoints, are random or fixed and how this decision impacts the model specification in the software; and (c) the inclusion of latent variable covariates as time-invariant predictors of piecewise growth.
Piecewise growth models
Specifying piecewise functions in a latent growth modeling framework follows, at least initially, the notation exploited by Cudeck and Klebe (2002). Let _y_ _i_ _j_ denote the response of the _i_ th individual on the _j_ th occasion with (j = 1,2,\dotsc ,n_{i}). The occasion of the measurement or the elapsed time from the beginning of the study to the _j_ th assessment is _t_ _j_. The collection of responses for individual _i_ is denoted by (\mathbf {y}_{i}=(y_{1},\dotsc ,y_{n_{i}})^{\prime }), which is to be evaluated according to a given set of time points (\mathbf {t}_{i}=(t_{1},\dotsc ,t_{n_{i}})^{\prime }), where _n_ _i_ is the total number of measures for the individual. In contrast to the specification typical of mixed effect models, latent growth models are frequently, but not always, applied to a time-structured design in which measurement occasions are fixed across all individuals (McNeish & Matta, 2018). The _i_ subscript on _n_ is included to allow for the possibility that the length of and elements that comprise t_i_ may vary across individuals (see, e.g., Blozis & Harring, 2015; Sterba, 2014). For the individual, the piecewise growth model can be written as
$$ \mathbf{y}_{i} = f(\mathbf{t}_{i}, \boldsymbol{\theta}_{i}) + \mathbf{e}_{i}, $$
(1)
where _f_ defines the functional form of the growth model as a function of time (t_i_) and individual growth coefficients, _θ__i_, and (\mathbf {e}_{i}=(e_{i1},\dotsc ,e_{in_{i}})^{\prime }) is the set of time-specific residuals induced by imperfectly capturing the trajectory of y_i_ through _f_. In their simplest form, the individual coefficients are decomposed into the sum of fixed effects (_θ_) and random effects (u_i_), respectively
$$ \boldsymbol{\theta}_{i} = \boldsymbol{\theta} + \mathbf{u}_{i}. $$
The fixed effects (_θ_) are growth parameters for the typical individual. The random effects (u_i_) and time-specific residuals (e_i_) are assumed to be independent [i.e., (cov(\mathbf {u}_{i},\mathbf {e}_{i}^{\prime })=\mathbf {0}]) and each vector is multivariate normal such that
$$ \mathbf{u}_{i} \sim MVN(\mathbf{0}, \boldsymbol{\Psi}) {\kern24pt} \text{and} {\kern24pt} \mathbf{e}_{i} \sim MVN(\mathbf{0}, \boldsymbol{\Theta}_{i}). $$
Here, Ψ is a symmetric covariance matrix of the random effects and is often assumed to be unstructured so as to not impose restrictions on (a) the extent to which growth factors vary across individuals, nor on (b) the direction and degree to which individual growth factors covary. The time-specific residual variances and their covariances across time are summarized in the _n_ _i_ × _n_ _i_ covariance matrix Θ_i_. When coupled with the random effects covariance structure (Ψ), this residual covariance matrix (Θ_i_) often takes on a simple structure, such as (\boldsymbol {\Theta }_{i}=\mathbf {I}_{n_{i}}\sigma ^{2}) or (\boldsymbol {\Theta }_{i}=\mathbf {I}_{n_{i}}{\sigma _{j}^{2}}), where (j=1,\dotsc ,n_{i}), and where (\mathbf {I}_{n_{i}}) is an identity matrix of dimension _n_ _i_. Other structures are certainly possible (see, e.g., Fitzmaurice et al.,, 2011; Grimm & Widaman, 2010; Jennrich & Schluchter, 1986), and the choice of a particular structure should be theoretically defensible or empirically driven by a thorough exploration of the data.
The oft-cited linear-linear growth model is one possible form of _f_(t_i_,_θ__i_) and is defined in Eq.2:
$$ \begin{array}{@{}rcl@{}} f(\mathbf{t}_{i},\boldsymbol{\theta}_{i}) = \begin{cases} \alpha_{1i}+\alpha_{2i}t_{ij} & {\kern.75em} t_{ij} \leq \gamma_{i} \ \alpha_{3i}+\alpha_{4i}t_{ij} & {\kern.75em} t_{ij} > \gamma_{i} \end{cases}, \end{array} $$
(2)
where _α_ 1 _i_ and _α_ 2 _i_ are the intercept and slope of the first phase and _α_ 3 _i_ and _α_ 4 _i_ are the intercept and slope of the second phase, respectively. Because there are only two phases, there is only one changepoint (_γ_ _i_). For this function, the set of model coefficients for the _i_ th individual is (\boldsymbol {\theta }_{i}=(\alpha _{1i},\alpha _{2i},\alpha _{3i},\alpha _{4i},\gamma _{i})^{\prime }). The inclusion of the subscript _i_ on each growth factor in Eq.2 implies that each growth factor—including the changepoint—is allowed to vary across individuals. In other words, individuals may transition from phase 1 to phase 2 at different times, and individual trajectories within a phase might look quite different from the bilinear trajectory for the typical individual.
Behavior at the changepoint
Most applications using the bilinear piecewise growth model assume that the two linear segments join at the changepoint,Footnote 2 although exceptions have been noted (see, e.g., Cudeck & Codd, 2012; Cudeck & Harring, 2010; Cudeck & Klebe, 2002; Hoffman, 2015). To ensure continuity between adjoining segments, the two functions must be continuous and fulfill the condition
$$ \alpha_{1i}+\alpha_{2i}\gamma_{i} = \alpha_{3i}+\alpha_{4i}\gamma_{i}. $$
(3)
The equality constraint in Eq.3 requiring the values of the phase 1 and phase 2 functions to be equal at the changepoint (i.e., when _t_ _i_ _j_ = _γ_ _i_) has been termed zero-order continuity (Seber & Wild, 1989) and guarantees that the two linear functions will meet resulting in an abrupt elbow-like transition from one phase to the next. With this constraint, one of the parameters is redundant and the bilinear piecewise function in Eq.2 can be re-expressed, for example, by parameterizing the second phase intercept, _α_ 3 _i_, in terms of the other model parameters as
$$ \begin{array}{@{}rcl@{}} f(\mathbf{t}_{i},\boldsymbol{\theta}_{i})= \begin{cases} \alpha_{1i}+\alpha_{2i}t_{ij} & t_{ij} \leq \gamma_{i} \ \alpha_{1i}+\alpha_{2i}\gamma_{i}+\alpha_{4i}(t_{ij}-\gamma_{i}) & t_{ij} > \gamma_{i} \end{cases}. \end{array} $$
(4)
The resulting function now has three growth parameters, _α_ 1 _i_,_α_ 2 _i_, _α_ 4 _i_, and single changepoint, _γ_ _i_. If a more gradual and smooth transition between phases better captures the underlying behavior of the phenomenon around the changepoint, then higher-order continuity conditions can be implemented (see, e.g., Cudeck & Klebe, 2002, for a thorough description and discussion). This requires, however, that the functions for the segments be of sufficient complexity with a greater number of parameters. We demonstrate how this is accomplished in the empirical examples forthcoming.
Fitting the piecewise growth model in Eq.4 as a mixed-effects model requires writing an _if-then_ statement such as
$$ \begin{array}{@{}rcl@{}} &&~~~~~~~~~~~\text{if~} t \le \gamma \text{~then~} f = \alpha_{1}+\alpha_{2} \cdot t\ &&\text{else~if~} t > \gamma \text{~then~} f = \alpha_{1}+\alpha_{2}\gamma + \alpha_{4i}(t - \gamma), \end{array} $$
using software, such as SAS or R, that allows conditional programming statements. The challenge of fitting this same model in SEM software is to re-express _f_(t_i_,_θ__i_) as a linear combination of a factor loading matrix and latent growth factors, Λ_i__η__i_, the cornerstone of the latent growth modeling framework (Bollen & Curran, 2006; Meredith & Tisak, 1990).
Specifying piecewise models in an LGM framework
Two-phase growth models can be specified in a number of ways. In some cases, the functions that define the different segments include only linear parameters, such as a model based on a linear-linear or quadratic-linear function, and the only nonlinear parameter is the changepoint. If the changepoint is known a priori and is fixed across individuals—such as may be the case when an intervention is delivered at a specific time—the discontinuity in the overall pattern can be easily treated through adding a second linear growth factor and setting elements of the factor loading matrix to pre-specified values. For a linear-linear function, the second latent growth factor can either be interpreted as the linear slope of the second phase (see the left panel of Fig.2) or as the difference between the linear slopes of phase two and phase one (see the right panel of Fig.2) depending on how the factor loading matrix is specified (see, e.g., Hancock et al.,, 2013).
Fig. 2
The left panel shows a bilinear piecewise LGM with an explicit second phase slope. The right panel shows a bilinear piecewise LGM parameterized with a difference in linear slopes between phase 2 and phase 1
Full size image
In other cases, one or both of the functions that define the segments include a nonlinear parameter, such as a model based on a combination of a linear and an exponential function. Typically, one or more of the growth parameters that enter the model in a linear way are random. Nonlinear growth parameters may be random or fixed. If fixed, then the model falls within the framework of a conditionally linear model. For instance, in a linear-exponential growth model, the nonlinear parameter of the exponential function would be fixed and the rate of change therefore held constant across individuals. In a very different formulation of a piecewise model, a nonlinear growth function is defined by a first-order Taylor polynomial, and as such, the weights of the polynomial are random and the nonlinear growth parameter is fixed. This latter type of model is known as a structured latent curve model (SLCM; Browne, 1993; Browne & du Toit, 1991). A third formulation of the model is one in which the nonlinear growth function is random, such as in a fully nonlinear mixed-effects model (see, e.g., Cudeck, 1996; Davidian & Giltinan, 1995; Davidian & Giltinan, 2003). Of these three formulations, only the first two may be fit within an SEM framework.
Structured latent curve model approach
Before delving into the specifics of the modeling extensions and empirical examples, we provide a very brief overview of the SLCM (readers familiar with the SLCM can skip this section without loss of continuity). Formulation of a structured latent curve model begins with the mean response that is assumed to follow a particular _target function_, _f_(t_i_,_θ_). To be clear, a target function is simply a mathematical function of time describing a trajectory of the mean response. For now, this target function is arbitrary, but represents any nonlinear growth function in which at least one parameter enters _f_ in a nonlinear manner. For individual _i_, a generic four-parameter target function can be re-expressed as a first-order Taylor series expansion of the target function (see, e.g., Blozis & Harring, 2016; Browne, 1993; Preacher & Hancock, 2015)
$$ \begin{array}{@{}rcl@{}} \mathbf{y}_{i} &=& \mathbf{f}(\mathbf{t}_{i},\boldsymbol{\theta}) + z_{1i}\mathbf{f}_{1}^{\prime}(\mathbf{t}_{i},\boldsymbol{\theta})+ z_{2i}\mathbf{f}_{2}^{\prime}(\mathbf{t}_{i},\boldsymbol{\theta})+ z_{3i}\mathbf{f}_{3}^{\prime}(\mathbf{t}_{i},\boldsymbol{\theta})\ &&+ z_{4i}\mathbf{f}_{4}^{\prime}(\mathbf{t}_{i},\boldsymbol{\theta}) + \mathbf{e}_{i} \end{array} $$
(5)
where (\mathbf {f}_{k}^{\prime }(\mathbf {t}_{i},\boldsymbol {\theta })) is a vector of first partial derivatives (known as a _basis function_, Browne, 1993; Meredith & Tisak, 1990) with respect to the _k_ th growth parameter and is evaluated at the _n_ _i_ time points in t_i_ and parameters in _θ_. The basis functions are weighted by random effects, _z_ _k_ _i_, individual-level deviations from the growth parameters in _θ_ with means equal to zero. With the additional assumption that the residuals in e_i_ have means of zero as well implies that _E_[y_i_] = _μ_ = f(t_i_,_θ_).
The basis functions comprise the columns of the factor loading matrix, Λ_i_(t_i_,_θ_),
$$ \begin{array}{@{}rcl@{}} \boldsymbol{\Lambda}_{i}(\mathbf{t}_{i},\boldsymbol{\theta})= \begin{bmatrix} \frac{\partial f(t_{1},\boldsymbol{\theta})}{\partial\theta_{1}} & {\cdots} & \frac{\partial f(t_{1},\boldsymbol{\theta})}{\partial\theta_{4}} \ \frac{\partial f(t_{2},\boldsymbol{\theta})}{\partial\theta_{1}} & {\cdots} & \frac{\partial f(t_{2},\boldsymbol{\theta})}{\partial\theta_{4}}\ {\vdots} & {\ddots} & {\vdots} \ \frac{\partial f(t_{n_{i}},\boldsymbol{\theta})}{\partial\theta_{1}} & {\cdots} & \frac{\partial f(t_{n_{i}},\boldsymbol{\theta})}{\partial\theta_{4}}\ \end{bmatrix}. \end{array} $$
(6)
Under an SLCM, the mean function is assumed to be invariant to a constant scaling factor (see, Shapiro & Browne, 1987, Condition 2). As a consequence, the target function f(t_i_,_θ_) can be rewritten as Λ_i_(t_i_,_θ_)_α_, where some of the elements of _α_ may need to be set to zero (see, Blozis & Harring, 2016, for a discussion of how this is determined). Then in the individual-level model, Λ_i_(t_i_,_θ_)_α_ replaces the target function and the model in Eq.5 can be rewritten as
$$ \mathbf{y}_{i} = \boldsymbol{\Lambda}_{i}(\mathbf{t}_{i},\boldsymbol{\theta})\boldsymbol{\alpha} + \boldsymbol{\Lambda}_{i}(\mathbf{t}_{i},\boldsymbol{\theta})\mathbf{z}_{i} + \mathbf{e}_{i}. $$
(7)
Letting _η__i_ = _α_ + z_i_, the model in Eq.7 can be written as
$$ \mathbf{y}_{i} = \boldsymbol{\Lambda}_{i}(\mathbf{t}_{i},\boldsymbol{\theta})\boldsymbol{\eta}_{i} + \mathbf{e}_{i}. $$
(8)
The random effects and residuals are assumed to follow multivariate normal distributions, (\mathbf {z}_{i} \sim N(\mathbf {0}, \boldsymbol {\Psi })) and (\mathbf {e}_{i} \sim N(\mathbf {0}, \boldsymbol {\Theta }_{i})), respectively. The SLCM model in Eq.8 can include time-invariant observed or latent covariates by augmenting the expression of individual growth factors, _η__i_ = _α_ + _Γ__1_x_i_ + _Γ__2__ξ__i_ + z_i_, where coefficients in Γ1 correspond to the measured covariates in x_i_, and
coefficients in Γ2 correspond to the latent covariates in _ξ__i_ which are related to a set indicator variables, w_i_, through a common factor model. The model-implied mean and covariance structures of the repeated measures for this conditional SLCM would be
$$ E[\mathbf{y}_{i}] =\boldsymbol{\mu}_{i}= \boldsymbol{\Lambda}_{i}(\mathbf{t}_{i},\boldsymbol{\theta})(\boldsymbol{\alpha}+ \boldsymbol{\Gamma}_{1}\boldsymbol{\mu}_{x} + \boldsymbol{\Gamma}_{2}\boldsymbol{\kappa}), $$
and
$$ \begin{array}{@{}rcl@{}} Var[\mathbf{y}_{i}] &=&\boldsymbol{\Sigma}_{i}= \boldsymbol{\Lambda}_{i}(\mathbf{t}_{i},\boldsymbol{\theta})(\boldsymbol{\Gamma}_{1}\boldsymbol{\Phi}_{x}\boldsymbol{\Gamma}_{1}^{T} + \boldsymbol{\Gamma}_{2}\boldsymbol{\Phi}_{\xi}\boldsymbol{\Gamma}_{2}^{T} + \boldsymbol{\Psi})\ &&\boldsymbol{\Lambda}_{i}(\mathbf{t}_{i},\boldsymbol{\theta})^{T} + \boldsymbol{\Theta}_{i}, \end{array} $$
where _μ__x_ and _κ_ are the mean vectors of the observed and latent covariates and Φ_x_ and Φ_ξ_ are the covariance matrices of the observed and latent covariates, respectively.
Readers who want a more thorough discussion of the distinctions between the SLCM and nonlinear mixed-effects model are encouraged to read Blozis and Harring (2016) and Grimm et al., (2017), while Preacher and Hancock (2012) and Preacher and Hancock (2015) provide a full description of how the bilinear piecewise growth model fits within the SLCM framework.
Conditionally linear model
An SLCM is formulated by taking a first-order Taylor-series polynomial of a nonlinear growth function where polynomial terms are weighted by individual random effects. The nonlinear growth parameter(s) are fixed. An alternative to an SLCM for fitting nonlinear latent growth models is a slightly more restrictive version of the fully nonlinear mixed-effects model, a conditionally-linear LGM (see, e.g., Blozis & Cudeck, 1999; Harring et al.,, 2006; Harring et al.,, 2012). Individual-specific growth parameters that enter the function in a nonlinear fashion are fixed across individuals, whereas parameters that enter the function in a linear fashion are permitted to vary across individuals. Initial or potential (i.e., asymptotic) performance in developmental learning processes, for example, are often modeled as linear parameters in many nonlinear functions (Bates & Watts, 1988) and display considerable heterogeneity in the sample; conversely, a parameter relating to the rate of change, often a nonlinear parameter, varies markedly less.
The linear-linear function in Eq.4 can be cast as a conditionally-linear model by eliminating the _i_ subscript on the changepoint—the sole nonlinear parameter—as
$$ \begin{array}{@{}rcl@{}} f(\mathbf{t}_{i},\boldsymbol{\theta}_{i})= \begin{cases} \alpha_{1i}+\alpha_{2i}t_{ij} & t_{ij} \leq \gamma \ \alpha_{1i}+\alpha_{2i}\gamma_{i}+\alpha_{4i}(t_{ij}-\gamma) & t_{ij} > \gamma \end{cases}. \end{array} $$
Note, that growth parameters _α_ 1 _i_,_α_ 2 _i_, and _α_ 4 _i_ that enter the piecewise function in a linear manner retain the _i_ subscript and are allowed to vary across individuals. This conditionally-linear piecewise function fits into the LGM framework by writing _f_ as
$$ f(\mathbf{t}_{i},\boldsymbol{\theta}_{i}) = \boldsymbol{\Lambda}_{i}(\mathbf{t}_{i},\boldsymbol{\theta})\boldsymbol{\eta}_{i} $$
where Λ_i_(t_i_,_θ_) contains possibly nonlinear functions of _θ_ = _γ_, incorporates covariates that explain the growth characteristics of (\boldsymbol {\eta }_{i}^{\prime } = (\alpha _{1i},\alpha _{2i},\alpha _{4i})), and includes measurements of time. For each of the empirical examples that follow, computer code for both the SLCM and conditionally-linear model will be provided.Footnote 3
Segmented polynomials as LGMs
We begin this section by revisiting the bilinear model defined in Eq.4, which is reproduced here as the target function defined in Eq.5 for clarity,
$$ \begin{array}{@{}rcl@{}} f(\mathbf{t}_{i},\boldsymbol{\theta})= \begin{cases} \alpha_{1}+\alpha_{2}t_{ij} & t_{ij} \leq \gamma \ \alpha_{1}+\alpha_{2}\gamma+\alpha_{4}(t_{ij}-\gamma) & t_{ij} > \gamma \end{cases}. \end{array} $$
(9)
where (\boldsymbol {\theta } = (\alpha _{1}, \alpha _{2}, \alpha _{4}, \gamma )^{\prime }). To fit this function as an SLCM, Preacher and Hancock (2015) followed the tact introduced by Harring et al., (2006), namely rewriting the bilinear piecewise function using the minimum/maximum function applied to the two line segments, but allowing the changepoint to vary randomly across individuals. A related, but alternative approach can be used instead—providing greater flexibility to fit higher-order polynomials, inherently nonlinear functions (i.e., exponential), as well as to more than two phases with the caveat that the functions of adjacent segments need not be monotonic.
Instead of using the minimum/maximum function applied to the segments themselves, the bilinear piecewise function of Eq.9 can be formulated as an SLCM by coding the _j_ th row of Λ_i_(t_i_,_θ_) using the minimum/maximum function, but applied directly to values of time, _t_ _i_ _j_ and the mean of the changepoint, which is expressed here as _γ_. Following Seber and Wild (1989, Section 9.4.2), the minimum and maximum functions are defined as: (\min \limits (u,v)=\frac {1}{2}[ u + v - \sqrt {(u-v)^{2}}]) and (\min \limits (u,v)=-\max \limits (-u,-v)) implying (\max \limits (u,v)=\frac {1}{2}[ u + v + \sqrt {(v-u)^{2}}]), where _u_,_v_ ∈I R. These expressions are equivalent to the min() and max() functions found in many statistical software packages. The min(u,v) function in SAS PROC IML, for instance, evaluates arguments _u_ and _v_ and returns the minimum of the two. So does (\min \limits (u,v)=\frac {1}{2}[ u + v - \sqrt {(u-v)^{2}}]). Thus, the elements for the _j_ th row of Λ_i_(t_i_,_θ_) can be expressed as
$$ \left[ \boldsymbol{\Lambda}_{i}(\mathbf{t}_{i}, \boldsymbol{\theta}) \right]_{j \cdot} = \left[ 1 {\kern4pt} \min(t_{ij},\gamma) {\kern4pt} \max(t_{ij}-\gamma,0) {\kern4pt} (\alpha_{2} - \alpha_{4}) \left( \frac{\max(t_{ij}-\gamma,0)}{t_{ij}-\gamma}\right) \right], $$
(10)
It may not be readily apparent that the column-wise elements represented in Eq.10 are the partial derivatives of the target function in Eq.9 with respect to each parameter evaluated at the _j_ th time point. To make this connection, the partial derivatives of piecewise functions comprising _f_ are evaluated before and after the changepoint and then combined to create each column across the values, _t_ _i_ _j_. To make this concrete, suppose that six time points for individual _i_ be (\mathbf {t}_{i}=(0,1,2,5,6,10)^{\prime }) and the single changepoint occurs at _γ_ = 3. The partial derivative of _f_ with respect to _α_ 1, the first entry in Eq.10, at each time point before the changepoint (i.e., at 0, 1, and 2) is 1. For times after the changepoint (i.e., at 5, 6, and 10), the partial derivative is also 1. That is,
$$ \begin{array}{@{}rcl@{}} &&\frac{\partial}{\partial\alpha_{1}} \left[\alpha_{1}+\alpha_{2}t_{ij} \right] = 1 {\kern6pt} \text{when} {\kern6pt} t_{ij} \le \gamma \ &&\text{and} {\kern6pt} \frac{\partial}{\partial\alpha_{1}} \left[ \alpha_{1}+\alpha_{2}\gamma+\alpha_{4}(t_{ij}-\gamma) \right] = 1 {\kern6pt} \text{when} {\kern6pt} t_{ij} > \gamma. \end{array} $$
The partial derivative of _f_ with respect to _α_ 2, the second entry in Eq.10, can be computed in a similar manner. For the first linear function—when _t_ _i_ _j_ ≤ _γ_—the partial derivative is _t_ _i_ _j_. When _t_ _i_ _j_>_γ_, then the partial derivative is _γ_. This is exactly what the operator, (\min \limits (t_{ij},\gamma )), does. Consequently, the second column of the hypothetical example evaluated at times t_i_ would be
$$ \frac{\partial{f(\mathbf{t}_{i},\boldsymbol{\theta})}}{\partial{\alpha_{2}}} = \min(t_{ij},\gamma) = (0,1,2,3,3,3)^{\prime}. $$
In the event that a particular parameter in _θ_ does not appear in one of the piecewise segments in _f_, then it will take on the value of 0. The last two entries (i.e., for _α_ 4 and _γ_) in Eq.10 have this characteristic. Take (\max \limits (t_{ij}-\gamma ,0)), the partial derivative of _f_ with respect to _α_ 4. When the value of _t_ _i_ _j_ − _γ_> 0, then the (\max \limits ()) function returns the evaluated number, otherwise the entry is 0. For the running hypothetical example, the elements corresponding to the six time points would be (0, 0, 0, 2, 3, 7). Similarly, the first three elements of the partial derivative of _f_ with respect to _γ_ would be (0,0,0) while the second three elements take on the same value, _α_ 2 − _α_ 4. In our hypothetical example, the value of the changepoint is known—and thus it is apparent when the transition from 0 to _α_ 2 − _α_ 4 occurs. In most practical situations, the changepoint will be an unknown parameter to be estimated. As a consequence, a practical challenge to implementing this method in contemporary SEM software is to automate this type of _on/off_ switch behavior. We accomplish this by including the term ([\max \limits (t_{ij}-\gamma )]) /(_t_ _i_ _j_ − _γ_). This acts as an indicator function taking on the value of 0 when _t_ _i_ _j_ − _γ_ ≤ 0 and taking on the value of 1 when _t_ _i_ _j_ − _γ_> 0. We now show how this alternative approach can be implemented for other piecewise functions.
Quadratic-linear piecewise growth
A quadratic-linear piecewise function can be written as
$$ \begin{array}{@{}rcl@{}} f(\mathbf{t}_{i},\boldsymbol{\theta}_{i})= \begin{cases} \alpha_{1i}+\alpha_{2i}t_{ij} +\alpha_{3i}t_{ij}^{2} & {\kern.75em} t_{ij} \leq \gamma_{i} \ \alpha_{4i}+\alpha_{5i}t_{ij} & {\kern.75em} t_{ij} > \gamma_{i} \end{cases}. \end{array} $$
(11)
For the polynomial segments to meet at the changepoint with a smooth transition requires both zero- and first-order continuity constraints. This means
$$ \alpha_{1i}+\alpha_{2i}t_{ij} +\alpha_{3i}t_{ij}^{2}t_{ij} \Big|_{t_{ij}=\gamma_{i}} = \alpha_{4i}+\alpha_{5i}t_{ij} \Big|_{t_{ij}=\gamma_{i}}, $$
and
$$ \frac{\partial}{\partial t_{ij}} (\alpha_{1i}+\alpha_{2i}t_{ij} +\alpha_{3i}t_{ij}^{2}) \Big|_{t_{ij}=\gamma_{i}} = \frac{\partial}{\partial t_{ij}} (\alpha_{4i}+\alpha_{5i}t_{ij}) \Big|_{t_{ij}=\gamma_{i}}. $$
With these two restrictions, two of the parameters in Eq.11 are redundant and can be re-expressed in terms of other model parameters. By eliminating _α_ 1 _i_ and _α_ 2 _i_, for example, the quadratic-linear function can be rewritten as
$$ \begin{array}{@{}rcl@{}} f(\mathbf{t}_{i},\boldsymbol{\theta}_{i})= \begin{cases} \alpha_{4i}+\alpha_{5i}t_{ij} +\alpha_{3i}(\gamma_{i}-t_{ij})^{2} & {\kern.75em} t_{ij} \leq \gamma_{i} \ \alpha_{4i}+\alpha_{5i}t_{ij} & {\kern.75em} t_{ij} > \gamma_{i} \end{cases}. \end{array} $$
(12)
Using the same approach when specifying the bilinear piecewise growth model, the quadratic-linear piecewise function in Eq.12 used as the target function (by eliminating the _i_ subscript on _θ__i_) would be fit as an SLCM by coding the factor loading matrix as
$$ \left[ \boldsymbol{\Lambda}_{i}(\mathbf{t}_{i}, \boldsymbol{\theta}) \right]_{j \cdot}= \begin{bmatrix} 1 {\kern10pt} t_{ij} {\kern10pt} \max(\gamma-t_{ij},0)^{2} {\kern10pt} 2\alpha_{3}\max(\gamma-t_{ij},0) \end{bmatrix}. $$
(13)
We now show how these methods can be implemented not only for the quadratic-linear piecewise LGM in Eq.12, but also for other piecewise functions as well.
Empirical examples
Three different piecewise LGMs will be fitted to two empirical datasets. Data from a psychological experiment constitutes the second empirical example, in which the response is the number of words that were recalled across 10 trials. Interestingly, performance exhibits three phases where a distinct linear function is hypothesized in each phase. Transition from one phase to the next is abrupt but connected implying that two changepoints will be needed to _glue_ the three segments together. A more complete description of the data is given next followed by reporting the results of each analysis.Footnote 4 The second dataset comes from a learning study in which verbal skill acquisition was assessed. Response times across 12 trial blocks showed a fairly steep, curvilinear decline (learning taking place) during earlier trials. Learning continued across later trials but slowed, and eventually decreased at a constant rate through the last trial. We fit two piecewise growth models to these data: (1) a quadratic-linear function as described earlier and (2) an exponential-linear model that uses an intrinsically nonlinear function—as opposed to a higher-order polynomial—to model the steep decline in the first phase.
Word recall data
The repeated measures data plotted in Fig.3 are the number of words out of 15 possible that were recalled by a sample of college students over ten 30-sec trials of a single-session experiment (Smith & Klebe, 1997, June). The trials are recorded as (t_{ij}=t_{j}=(0,\dotsc ,9)^{\prime }). A random subset of 20 of the full sample (_N_ = 103) are included in the spaghetti plot. As always, individual differences are appreciable. The number of words recalled on the initial trial varied between 3 and 10, whereas at the final trial the range was from 11 to 15. Most participants showed rapid and linear improvement up to Trial 3, after which there was a second phase in which more gradual improvement occurred until approximately trial 6, then little, if any, individual change in the number of words recalled for the final 2 to 3 trials. Here, we fit this data using a linear-linear-linear piecewise LGM across trials. The changepoints marking the shift from one phase to another are unknown parameters to be estimated. It appears that the changepoints are roughly similar for every participant, and thus, these parameters may need to be constrained to be identical for all subjects. This type of hypothesis can be adjudicated by performing a _χ_ 2 difference test under maximum likelihood estimation using an appropriate 50:50 mixture _χ_ 2 distribution (Stoel et al., 2006). The mixture distribution is recommended as the reference distribution to adjudicate the hypothesis test of the variance component of (\psi _{\gamma _{1}} = var(z_{\gamma _{1i}})) whose value under the null distribution is on the edge of parameter space.
Fig. 3
A spaghetti plot with a 20% random sample (_N_ = 103) of the number of words recalled across 10 trials
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The segmented polynomial extends in a straightforward manner to more than two phases. Through some preliminary analyses, it was observed that the two changepoints did not vary across individuals and thus, a conditionally-linear LGM specification in which _γ_ _k_ _i_ = _γ_ _k_ for _k_ = 1,2, was used for the analyses with imposed zero-order continuity (i.e., segments meet at the changepoints, but the transition is abrupt).
$$ \begin{array}{@{}rcl@{}} f(\mathbf{t}_{i},\boldsymbol{\theta}_{i})= \begin{cases} \alpha_{1i}+\alpha_{2i}t_{ij} & {\kern.75em} t_{ij} \leq \gamma_{1} \ \alpha_{3i}+\alpha_{4i}t_{ij} & {\kern.75em} \gamma_{1} < t_{ij} \leq \gamma_{2} \ \alpha_{5i}+\alpha_{6i}t_{ij} & {\kern.75em} \gamma_{2} < t_{ij} \end{cases}. \end{array} $$
(14)
With the imposed zero-order continuity restriction, the three-phase linear LGM in Eq.14 can be rewritten as
$$ \begin{array}{@{}rcl@{}} &&f(\mathbf{t}_{i},\boldsymbol{\theta}_{i})\ &&=\begin{cases} \alpha_{1i}+\alpha_{2i}t_{ij} & {\kern.75em} t_{ij} \leq \gamma_{1} \ \alpha_{1i}+\alpha_{2i}\gamma_{1} + \alpha_{4i}(t_{ij}-\gamma_{1}) & {\kern.75em} \gamma_{1} \leq t_{ij} \leq \gamma_{2} \ \alpha_{1i}+\alpha_{2i}\gamma_{1} + \alpha_{4i}(\gamma_{2}-\gamma_{1})+\alpha_{6i}(t_{ij}-\gamma_{2}) & {\kern.75em} t_{ij} > \gamma_{2} \end{cases}. \ \end{array} $$
(15)
The factor loading matrix for an LGM for the linear-linear-linear piecewise function would be parameterized with four columns corresponding to the four linear individual-specific parameters using Eq.15.
$$ \begin{array}{@{}rcl@{}} \left[ \boldsymbol{\Lambda}_{i}(\mathbf{t}_{i}, \boldsymbol{\theta}) \right]_{j \cdot}&=& \left[ 1 ~\min(t_{ij},\gamma_{1})~\min(\max(0,t_{ij}-\gamma_{1}), \gamma_{2}-\gamma_{1})\right.\ && ~~~\left. \max(0,t_{ij}-\gamma_{2})\right]. \end{array} $$
Results
Table1 shows the results from fitting the piecewise linear-linear-linear latent growth model using maximum likelihood estimation and appeared to have satisfactory model-data fit [_χ_ 2(48) = 67.06,_p_ = 0.036, RMSEA 90% CI (0.017, 0.095), and SRMR = 0.083].
Table 1 Maximum likelihood estimates and standard errors for the conditionally-linear, three-phase linear piecewise LGM
Full size table
The estimated intercept of the linear function in phase 1, (\hat {\alpha }_{1} = 5.45), is interpreted as the average number of words recalled at the beginning of the experiment—approximately 5.5 words. The estimated slope of the linear function in phase 1, (\hat {\alpha }_{2} = 2.82) is the expected increase in words recalled for each additional trial. The estimated slope of the second phase is (\hat {\alpha }_{4}=1.23) and represents the expected increased in the number of words recalled in phase 2. Compared to the constant rate of change in phase 1, the rate of word recall for the average individual in the second phase is slowing. The last estimated growth parameter, (\hat {\alpha }_{6} = 0.22), is the average linear growth rate of phase 3. The changepoints occur between the second and third trial ((\hat {\gamma }_{1}=1.42)) while the second shift occurs between the fourth and fifth trials ((\hat {\gamma }_{2}=3.49)). To see this more clearly, the fitted mean trajectory with fitted changepoints highlighted and superimposed is displayed in Fig.4.
Fig. 4
Fitted mean trajectory for the linear-linear-linear piecewise LGM superimposed on a random sample of _N_ = 10 individuals. The estimated changepoints are highlighted with arrows
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Central to any analysis of latent growth models is characterizing individual behavior of the phenomena underlying the repeated measures data. Examining individual fitted functions can provide valuable insight into understanding the myriad ways the phenomena changes according to the time-response relation. Figure5 illustrates how the model performs for three specific individuals. Note that while each individual transitions at the same junctures from one phase to the next, their linear functions—one in each phase—is specific to the individual (i.e., linear parameters have corresponding random effects).
Fig. 5
Three individuals’ fitted linear-linear-linear trajectories. Estimates of common changepoints are represented by vertical solid lines
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Procedural learning task
The next two examples involve data that were obtained from a learning studyFootnote 5 in which researchers were interested in assessing performance on two procedural tasks. The repeated outcome variable used here is response time corrected for accuracy, taken to assess verbal skill acquisition. Quantitative and spatial skill acquisition were also evaluated. For each task, study participants were required to learn a set of declarative rules for assessing attributes of visual stimuli presented in series. Tasks were given together in blocks, with the administration order varied within blocks to avoid order effects. Both response times and accuracy scores were recorded. Data for a sample of _N_ = 228 individuals whose average accuracy score across trial blocks was 80% or better on the task is considered here. The sample was restricted in this manner to lessen the impact of a speed – accuracy trade-off on response time. Response times for the procedural task were aggregated separately into 12 blocks of 32 trials each, where the median time to respond within blocks was used as the aggregate. For the interested reader, a more comprehensive description of data can be found in Blozis (2004).
As is apparent in Fig.6, response times decreased rapidly across earlier trials where at approximately trial 4 or 5, response times continued to decline but at a constant rate. Among several alternative functions fitted to this data, two piecewise functions were finally chosen based on model-data fit, parameter interpretability and the belief that the underlying process occurs in two distinct phases. The first piecewise function is a quadratic-linear piecewise LGM. The two segments join and a smooth transition between quadratic and linear phase is expected. The quadratic-linear LGM explicated in Eq.12 were fit to these data as a structured latent curve model. In a subsequent section, an exponential-linear piecewise LGM is fitted to the same repeated measures data. The first-phase exponential function is aligned with analyses performed in other studies (see, e.g., Blozis, 2004; Harring et al.,, 2012).
Fig. 6
A spaghetti plot with a 10% random sample (_N_ = 228) of response times across 12 trial blocks
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Results
Table2 presents maximum likelihood estimates and corresponding standard errors obtained from fitting the quadratic-linear LGM in M _plus_ (Muthén and Muthén, 1998). For the growth parameters, examination of the fixed effects estimates shows that the average individual has a convex pattern of quadratic change ((\hat {\alpha }_{3}=0.35)) across trial blocks until trial block 5 ((\hat {\gamma } = 5.22)), the estimated changepoint for the average individual where decline shifts to a constant rate of change that is more gradual. The linear slope of the second phase is (\hat {\alpha }_{5}=-0.17), and represents the expected decrease in reaction time in tenths of a second for each trial block increase while the intercept is (\hat {\alpha }_{4}=8.20). The intercept is the average reaction time in tenths of a second at the initial trial block (i.e., _t_ _j_ = _t_ 1 = 0). Centering time to another trial block in the second phase such as _t_ _j_ = _t_ 12 = 11 or at the changepoint (t_{j}=\hat {\gamma }) would make its value more interpretable (see, Hoffman, 2015, Chapter 6). The estimated fixed effects of the growth parameters were all large relative to their estimated standard errors and thus hypothesis tests using a Wald-like ratio of the estimate to its standard error could be used to establish statistical significance.
Table 2 Maximum likelihood estimates and standard errors for the quadratic-linear piecewise LGM
Full size table
Individual differences in all aspects of learning can be ascertained by examining the variances and covariances of the random coefficients. From Table2, the variance estimates of the random coefficients are all large relative to their standard errors. The correlation between individuals’ second phase intercepts, _α_ 4 _i_ and their changepoints, _γ_ _i_, for example, is
$$ \begin{array}{@{}rcl@{}} corr(z_{\alpha_{4i}}, z_{\gamma_{i}}) &=& \frac{-0.64}{\sqrt{4.61 \cdot 0.46}} \ &=& -0.44, \end{array} $$
indicating a moderate negative linear trend. Thus, individuals who start the second phase at higher initial reaction times (slower reaction) will transition to the second phase at earlier trial blocks compared to those individuals whose initial reaction times are faster. To give some indication of how well the mean curve fits the data, a graph of the mean trajectory is displayed in Fig.7 superimposed on line plots of a random sample of individuals’ data.
Fig. 7
Fitted mean curve for the quadratic-linear piecewise LGM superimposed on a random sample of _N_ = 10 individuals. The estimated changepoint occurs a little after the trial block 5: (\hat {\gamma }=5.11) and is denoted by the vertical dashed line
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Procedural learning task revisited
The last empirical example again utilizes the procedural learning task dataset (see Fig.3 for longitudinal profiles of a random sample of individuals). As is the case with curvilinear repeated measures data, many mathematical functions with parameterizations tailored to the scientifically-relevant features of underlying process may fit the data equally well. In past studies, for example, these data have been fitted with an exponential function in a structured latent curve modeling context (see, e.g., Blozis, 2004), a linear-linear piecewise LGM (Harring et al., 2012; Kohli & Harring, 2013) in a growth mixture modeling context as well as to a quadratic-linear piecewise function, also fitted as a structured latent curve model discussed previously. As a final extension, a two-phase model that assumes an exponential decaying response from the initial trial block to approximately the fifth trial block or so after which the form of change conforms to a linear function with slow, constant decremented change across the later trials.
The approach using the min() and max() functions with time and changepoint arguments can be utilized to fit segments that have at least one parameter of the piecewise growth function that enters in a nonlinear manner (e.g., exponential function) beyond the changepoint. If the functions meet at the changepoint and if a smooth transition is required when moving from one phase to the next, then zero-, first-, and even second-order continuity constraints may be applied given that the functions are of sufficient complexity. For example, the exponential-linear function used in the forthcoming analysis imposes both zero- and first-order continuity conditions. The two-phase piecewise function is defined as
$$ \begin{array}{@{}rcl@{}} f(\mathbf{t}_{i},\boldsymbol{\theta}_{i})= \begin{cases} \alpha_{1i}+ \alpha_{2i}\exp(\alpha_{3i}t_{ij}) & {\kern.75em} t_{ij} \leq \gamma_{i} \ \alpha_{4i} + \alpha_{5i}t_{ij} & {\kern.75em} t_{ij} > \gamma_{i} \end{cases}. \end{array} $$
(16)
In Eq.16, _α_ 1 _i_ is the limiting asymptotic performance (i.e., as (t_{ij} \rightarrow \infty )), _α_ 2 _i_ is a scaling factor and represents the distance from the asymptote to the initial value [i.e., _t_ _i_ _j_ = 0, _f_(t_i_,_θ__i_) = _α_ 1 _i_ + _α_ 2 _i_]. The rate of decay is governed by _α_ 3 _i_, an intrinsically nonlinear parameter of the exponential function, whose values are less than zero, _α_ 3 _i_< 0. Note that if instead, exponential _growth_ in the first phase was posited, then _α_ 3 _i_> 0. Assuming zero-order continuity at the changepoint (i.e., assuming the two segments join at _t_ _i_ _j_ = _γ_ _i_), results in one redundant parameter. Here, we chose to write the intercept of phase 2, _α_ 4 _i_, in terms of other model parameters
$$ \begin{array}{@{}rcl@{}} \alpha_{1i}+ \alpha_{2i}\exp(\alpha_{3i}\gamma_{i}) &=& \alpha_{4i} + \alpha_{5i}\gamma_{i} \ \alpha_{1i}+ \alpha_{2i}\exp(\alpha_{3i}\gamma_{i}) - \alpha_{5i}\gamma_{i} &=& \alpha_{4i}. \end{array} $$
(17)
Further assuming first-order continuity at the changepoint (i.e., assuming the transition from phase 1 (exponential decay) to phase 2 (linear decay) is smooth rather than abrupt), the first-order partial derivatives of each function with respect to time are set equal to one another allowing to eliminate another growth parameter, in this case, linear slope of phase 2
$$ \alpha_{2i}\alpha_{3i}\exp{\alpha_{3i}\gamma_{i}} = \alpha_{5i}. $$
(18)
Together, zero- and first-order continuity defined in Eqs.17 and18 imply
$$ \begin{array}{@{}rcl@{}} \alpha_{4i} &=& \alpha_{1i} + \alpha_{2i}\exp{\alpha_{3i}\gamma_{i}} - \alpha_{2i}\alpha_{3i}\exp{\alpha_{3i}\gamma_{i}}\gamma_{i} \ &=& \alpha_{1i} + (1 - \alpha_{3i} \gamma_{i}) \alpha_{2i}\exp{\alpha_{3i}\gamma_{i}}. \end{array} $$
(19)
The result of plugging Eqs.18 and19 into Eq.16, is
$$ \begin{array}{@{}rcl@{}} f(\mathbf{t}_{i},\boldsymbol{\theta}_{i})= \begin{cases} \alpha_{1i}+ \alpha_{2i}\exp(\alpha_{3i}t_{ij}) & {\kern.75em} t_{ij} \leq \gamma_{i} \ \alpha_{1i} + (1 - \alpha_{3i} \gamma_{i} + \alpha_{3i}t_{ij}) \alpha_{2i}\exp{\alpha_{3i}\gamma_{i}}& {\kern.75em} t_{ij} > \gamma_{i} \end{cases}, \ \end{array} $$
(20)
with four unknown parameters, (\boldsymbol {\theta }_{i}=(\alpha _{1i}, \alpha _{2i}, \alpha _{3i}, \gamma _{i})^{\prime }), each of which may vary across individuals. Note that both the asymptote (_α_ 1 _i_) and scale parameter (_α_ 2 _i_) in phase 1 enter the function linearly while the rate of exponential decay (_α_ 3 _i_) in phase 1 and the changepoint (_γ_ _i_) enter the model in a nonlinear manner. If a conditionally-linear LGM is sought, then only two columns in the factor loading matrix would need to be specified. The nonlinear parameters would be fixed across subjects and would be specified using the nonlinear constraints feature in the software program. If on the other hand, a structured latent curve model is to be fitted in which all parameters—those that enter the function linearly as well as those that enter in a nonlinear fashion—are allowed to vary across individuals, then the factor loading matrix would be comprised of four columns. In the latter case, the columns are made up of first-partial derivatives of the target function with respect to each parameter. The mean vector would set those elements corresponding to nonlinear parameters to zero, although other possibilities exist (see, e.g., Preacher & Hancock, 2015).
The factor loading matrix for the conditionally-linear LGM is
$$ \left[ \boldsymbol{\Lambda}_{i}(\mathbf{t}_{i}, \boldsymbol{\theta}) \right]_{j \cdot} = [1, \exp(\alpha_{3} \cdot \min(t_{ij},\gamma)) \cdot (1 + \alpha_{3} \cdot \max(t_{ij}-\gamma,0))], $$
where (\boldsymbol {\theta }^{\prime } = (\alpha _{3}, \gamma )). The factor loading matrix for the structured latent curve model is
$$ \begin{array}{@{}rcl@{}} \left[ \boldsymbol{\Lambda}_{i}(\mathbf{t}_{i}, \boldsymbol{\theta}) \right]_{j \cdot} &=& [1, \ && \exp[\alpha_{3} \cdot \min(t_{ij},\gamma)] \cdot {1 + \alpha_{3} \cdot \max(t_{ij}-\gamma,0)}, \ && \alpha_{2}\exp{\alpha_{3} \cdot \min(t_{ij},\gamma)} (\alpha_{3}\gamma \cdot \max(t_{ij},\gamma)-\alpha_{3}\gamma^{2}+t_{ij}), \ && {\alpha_{3}^{2}} \cdot \max(t_{ij}-\gamma,0)\alpha_{2}\exp{\alpha_{3}\gamma} ]. \end{array} $$
Results
We fit the exponential-linear piecewise LGM using both the conditionally-linear LGM as well as treating the model as a structured latent curve model. For each model, the residual covariance structure was specified to a homogeneous, mutually-independent structure, Θ_i_ = I_n_ _σ_ 2 as there were no missing data. Maximum likelihood estimates for the conditionally-linear LGM were
$$ \begin{array}{@{}rcl@{}} \hat{\boldsymbol{\theta}} &=& (\hat{\alpha}_{1}, \hat{\alpha}_{2}, \hat{\alpha}_{3}, \hat{\gamma}) \ &=& (6.83, 14.65, -0.64, 6.32), \end{array} $$
$$ \begin{array}{@{}rcl@{}} \hat{\boldsymbol{\Psi}} = \begin{pmatrix} 1.87 & \ 5.16 & 84.95 \end{pmatrix} \hat{\sigma}^{2}=2.43. \end{array} $$
The estimated changepoint occurred between a bit after the seventh trial block, (\hat {\gamma }_{1}=6.32). One reason the changepoint was estimated at this juncture was due to the requirement of equality of the segment functions first-order derivatives. If only the zero-order constraint was implemented, the changepoint would have occurred at an earlier trial block. This disparity in placement of the changepoint is well-known (see, Cudeck & Harring, 2010) and can be directly attributed to what is assumed about the behavior (i.e., abrupt or smooth) of the process near the changepoint. In general, adopting higher-order continuity conditions provides greater degrees of smoothness of the transition between phases at the changepoints, which often has the effect of delaying when the transition occurs.
Maximum likelihood estimates for the structured latent curve model were
$$ \begin{array}{@{}rcl@{}} \hat{\boldsymbol{\theta}} &=& (\hat{\alpha}_{1}, \hat{\alpha}_{2}, \hat{\alpha}_{3}, \hat{\gamma}) \ &=& (7.28, 13.25, -0.89, 4.48), \end{array} $$
$$ \begin{array}{@{}rcl@{}} \hat{\boldsymbol{\Psi}} = \begin{pmatrix} 1.80 &&& \ 5.40 & 101.52 && \ 0 & 37.08 & 99.01 & \ 0 & 14.12 & 26.12 & 7.19 \end{pmatrix} \hat{\sigma}^{2}=1.01. \end{array} $$
Using the New() function in the Model Constraint module in M _plus_ permits estimating the intercept and slope of the second phase for the average individual based on estimates of model parameters.Footnote 6 These were estimated to be (\hat {\alpha }_{4}=8.51) and (\hat {\alpha }_{5}=-0.22), respectively. Time was not centered in any way. Therefore, the interpretation of the intercept is the expected reaction time in tenths of seconds at _t_ _i_ _j_ = 0. The slope has a standard regression interpretation that for each additional trial block after the fifth trial, average reaction time would decrease nearly a quarter of a tenth of a second. From initial fitting of the model, it was determined that the covariances between asymptote and exponential decay rate and between asymptote and changepoint were approximately zero, and were then set to zero, producing the final estimates. Each of the four parameters showed statistically significant between-individual variation (i.e., the diagonal elements of (\hat {\boldsymbol {\Psi }})). Unsurprisingly, the correlation between exponential decay rate and changepoint random effects was strong and positive, (\hat {\rho }_{43}=26.12/ \sqrt {99.01 \cdot 7.19} \approx 0.98).
A plot of the fitted mean exponential-linear piecewise functions using the two approaches is shown in Fig.8. The fitted conditionally-linear piecewise LGM seemed to adhere to the empirical means at each time point quite closely. In contrast, the fitted SLCM in which the exponential rate of decay and the changepoint were allowed to vary across individuals, demonstrated slightly different fit. The mean changepoint occurred at a much earlier trial than did the changepoint from the conditionally-linear piecewise model. To be clear, our intention here, rather than attempting to reach substantive conclusions regarding the underlying procedural learning task response process, is to illustrate how an intrinsically nonlinear piecewise LGM may be used to articulate many interesting aspects and types of longitudinal change that exhibit distinct phases.
Fig. 8
Fitted functions for the average exponential-linear change process for the conditionally-linear LGM (solid line) and the structured latent curve model (dotted line)
Full size image
Discussion
Many alternatives exist to describe curvilinear patterns of repeated measures data. An appealing option, a piecewise growth model, is flexible, can effectively summarize behaviors that display distinct phases, and permits for estimation of the changepoint from one phase to the next. Estimating piecewise growth models as mixed effects models is fairly straightforward using software modules that allow the user to explicitly define the function in each phase using programming statements. For LGMs, estimating even the most basic piecewise growth model, the two-phase linear-linear model, is challenging; and perhaps as a consequence, published studies using other functional forms for the segments or allowing for multiple changepoints, are rare. As one reviewer rhetorically asked, why specify piecewise growth models in an SEM framework when a mixed effects modeling version already exists? There are many reasons to justify approaching this type of growth modeling from an SEM perspective. As was previously argued, SEM software like M _plus_ and lavaan can not only handle basic and advanced nonlinear growth models (Preacher & Hancock, 2015; Ram & Grimm, 2009), but with a few extra lines of code can extend these models to accommodate nested data structures and complex sampling designs, to account for population heterogeneity, and to incorporate intensive data collection design facets among other modeling elaborations. More importantly, using latent variables as longitudinal responses, time-varying covariates, determinants of change, and even distal outcomes—basic tenets of longitudinal SEM methods (Grimm & Marcoulides, 2016; McArdle & Nesselroade, 2014)—can be handled rather easily in SEM software ensuring that executing a piecewise growth modeling analysis within this environment will be worth the extra effort.
A central goal of this article was to show how a broader class of piecewise latent growth models could be fitted utilizing the nonlinear constraint module found in most modern SEM software. To this end, we extended the oft-used linear-linear piecewise latent growth model in three ways. The first elaboration was to a three-phase linear process. Two changepoints were needed to specify the model and were fixed across subjects in the real data example involving word recall. This type of conditionally-linear specification means that while some aspects of the change process operationalized with a piecewise function (i.e., the intercept and slope of the first phase) are specific to the individual, the points of transition of adjacent phases are not. This is not a limitation of the general piecewise LGM system, but arguably one of its most attractive features—tailoring its specification to adapt to characteristics of the particular study behavior. This is best accomplished based on theoretical considerations of the longitudinal design and data attributes as well as a deep understanding of the evolution of the underlying process. Of course, decisions made throughout the modeling process are also informed through the empirical investigation. The second elaboration was to higher-order polynomial functions for data that exhibit two distinct phases. Continuity constraints were incorporated and we demonstrated how the min() and max() functions could be used on time points and changepoints instead of the line segments used in past studies. Columns of the factor loading matrix of the piecewise LGM could then be specified using the nonlinear constraint module in popular SEM software.
The last modeling embellishment was to intrinsically nonlinear functions as was demonstrated in the analysis of the procedural learning task dataset. An exponential-linear piecewise LGM was specified in which the rate of the first phase and the changepoint—individual-specific parameters—enter the function in a nonlinear manner. Analyses using both conditionally-linear and structured latent curve modeling frameworks were performed. Allowing the nonlinear parameters to vary among individuals had the effect of moving the transition from the first to the second phase at an earlier trial. These models are complex with many analytic decision points to be made throughout: (1) should nonlinear parameters be fixed across subjects or should they be allowed to vary? and (2) what type of piecewise function is suggested by the theory of the underlying change process or through an empirical investigation? And, although our analyses did not include investigation of residual covariance structures or augmentation of the model with time-invariant covariates, these nuances as well as the many others naturally encountered when fitting latent growth models are just as applicable when piecewise functions are used.
The piecewise LGMs fitted in this article utilized the min()/max() functions on the time points and changepoints instead of applying these functions on the line segments themselves as Harring et al., (2006) and Preacher and Hancock (2015) have previously demonstrated. This methodological nuance permits the specification of adjacent growth trajectories to be non-monotonic and extends to higher-order polynomials and intrinsically nonlinear functions using the same basic tools (i.e., structured latent curve and conditionally-linear models) when fitting the popular linear-linear piecewise function. The functionality that makes fitting these extended piecewise LGMs in SEM software possible is the nonlinear constraint module found in most mainstream programs, like M _plus_. As others have pointed out (see, e.g., Choi et al.,, 2009; Feng et al.,, 2019; Preacher & Hancock, 2012; Ram & Grimm, 2009), fitting nonlinear latent growth models in software designed to estimate linear relations among measured and latent variables can be challenging. This may be due in part by working with nonlinear functions themselves, which seem a bit more intimidating algebraically. However, as many researchers have pointed out (see, e.g., Cudeck & du Toit, 2002; Davidian & Giltinan, 2003; Pinheiro & Bates, 2000), nonlinear functions can often be tailored so that parameters have a natural, physical interpretation that corresponds directly to substantive characteristics of the research situation without sacrificing model-data fit. This should be sufficient incentive to belay concerns regarding the extra effort required to fit such models especially when continuous repeated measures data exhibit multiple phases.
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Twin Pregnancy: Ultrasound Evaluation and Monitoring
CLINICAL ACTIONS:
Twin pregnancies are followed more closely than singleton pregnancies due to higher risk for complications such as twin-twin transfusion syndrome, selective fetal growth restriction, and preterm labor. Ultrasound is a non-invasive and highly useful tool for screening, diagnosis, and guiding management of these potential complications. Ultrasound monitoring protocols vary between different types of twin pregnancies.
Zygosity, Chorionicity and Amniosity
Zygosity: Describes genetic origin of twins
Dizygotic twins: Both twins originate from a separate oocyte and each oocyte is fertilized by its own spermatocyte
Will always be dichorionic and diamniotic
Monozygotic twins: Both twins develop from a single zygote which then cleaves to form two embryos
The timing of cleavage will determine chorionicity and amniosity of monozygotic twins
Approximately 2/3 monochorionic/diamniotic | 1/3 dichorionic/diamniotic | 1to 2% monochorionic/monoamniotic
Chorionicity determines follow-up based on risks for adverse events
Image by Kevin Dufendach, MD (2008). Used by permission. CC BY 3.0
Dating (Ultrasound)
Ideal timing: Between 11w0d and 13w6d (45 and 84 mm)
Use CRL of the larger twin in spontaneously conceived twins
Use oocyte retrieval date or embryonic age from fertilization for twins conceived via IVF
Note: If a woman presents beyond 14 weeks gestational age then use head circumference of the larger twin (ISUOG)
Chorionicity Determination (Ultrasound)
Optimal timing to determine chorionicity by ultrasound is in the first or 2nd trimester
ACOG/SMFM recommend that chorionicity should be identified as early as possible
Ultrasound <13w6d may identify chorionicity in approximately 95% of cases based on membrane thickness and insertion
Dichorionic
Lambda (aka delta or twin peak) sign: Indicates dichorionic twins with thickening at membrane insertion site
2 distinct placental masses
Discordant sex signifies dichorionic, diamniotic (and dizygotic) twins
Monochorionic
T sign: Indicates monochorionic twins, with thin membrane and absence of thickening at membrane insertion site
Note: A single placental mass does not rule out dichorionic twins
Lambda or Delta Sign Indicating Dichorionic Twins
T Sign Indicating Monochorionic Twins
Monitoring
Uncomplicated monochorionic twin pregnancy (see SMFM checklist in ‘Learn More – Primary Sources’ below)
10 to 13 weeks:
NT | Size concordance
16 weeks
AFV and bladder filling q2 weeks
Fetal growth q2 to 4 weeks
18 to 22 weeks (earlier if possible)
Detailed anatomy and fetal echocardiogram
Antepartum surveillance (NST and/or BPP)
Monochorionic dichorionic: If fetal growth, AFV and bladder filling are all normal “there is no specific national recommendation regarding the need for, type of, or timing of surveillance”
Monochorionic monoamniotic: Initiation of surveillance typically at 32w0d | Clinicians may offer inpatient care starting at 24 to 28 weeks with daily surveillance but “optimal management remains uncertain” (ACOG)
Note: ISUOG guidelines do include umbilical artery Doppler monitoring as part of routine surveillance | ACOG/ SMFM considers evidence to be unclear for uncomplicate monochorionic twins
Uncomplicated dichorionic twin pregnancy
First trimester: Dating and chorionicity (see above)
18 to 22 weeks: Detailed anatomy | Biometry | Amniotic fluid volume (AFV) | Cervical length
20 weeks: q4 weeks until delivery: Fetal growth | AFV
36w0d: consider weekly antenatal fetal surveillance
SYNOPSIS:
Most twin pregnancies will have good outcomes. However, diligence is required, especially in the case of monochorionic twins due to risk for twin-twin transfusion syndrome (TTTS) and twin anemia polycythemia sequence (TAPS). Monochorionic twins may have potentially significant vascular anastomoses such that the twins share a common vasculature. Significant risks for dichorionic twins include preterm labor, medical complications due to increased placental mass (e.g., preeclampsia and GDM) and selective growth restriction. Different centers will have different protocols for labeling twin A vs twin B. The important point is to be consistent with labeling.
KEY POINTS:
TTTS
10 to 15% of monochorionic twins | 90% fetal demise if untreated
Diagnosis; AFV fluid imbalance noted on ultrasound
‘Donor’ has oligohydramnios (DVP of < 2 cm) | ‘Recipient’ has polyhydramnios (DVP > 8 cm)
TAPS
Can occur spontaneously in approximately 5% of monochorionic diamniotic twins
Result of small AV anastomoses that leads to transfusion of blood from donor to recipient twin
At birth, anemia in donor and polycythemia in the recipient
Prenatal diagnosis based on MCA Doppler
Donor MCA‐PSV > 1.5 MoM | Recipient MCA‐PSV < 1.0 MoM
When to Deliver (ACOG/SMFM)
Multiple gestation – uncomplicated
Di-di twins: 38w0d – 38w6d
Mono-di twins: 34w0d – 37w6d
Mono-mono twins: 32w0d – 34w0d
Note: Triplets and higher: Individualize
Multiple gestation – complicated by isolated FGR
Di-di twins: 36w0d-37w6d
Mono-di twins: 32w0d-34w6d
Note: If concurrent condition: Individualize
When to Refer
Monochorionic/ Monoamniotic twins
Growth discordance: Defined as EFW discordance is ≥ 20% (ACOG)
Calculation: Difference in the estimated fetal weight between the two fetuses/ divided by the weight of the larger fetus
ISUOG uses a 25% cut-off
Any findings on ultrasound that are of concern
Primary Sources – Learn More:
ACOG/ SMFM Practice Bulletin 231: Multifetal Gestations: Twin, Triplet, and Higher-Order Multifetal Pregnancies
SMFM Special Statement: Updated checklists for management of monochorionic twin pregnancy
ISUOG Practice Guidelines: role of ultrasound in twin pregnancy
ACOG SMFM Committee Opinion 831: Medically Indicated Late-Preterm and Early-Term Deliveries
SMFM Consult Series #72: Twin-twin transfusion syndrome and twin anemia-polycythemia sequence
Locate a Maternal Fetal Medicine Specialist
Maternal Fetal Medicine Specialist Locator-SMFM
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Do Twin-Specific Nomograms Really Make a Difference?
The MONOMONO Study: Inpatient or Outpatient Surveillance for Monochorionic/Monoamniotic Twins?
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Parabola, ellipse, and hyperbola are part of the topic called conic sections. A conic section is a shape made when a cone is cut in different ways. These shapes are formed by a point that moves in such a way that the distance from a fixed point and a fixed line stays in a constant ratio. This fixed point is called the focus, and the fixed line is called the directrix. Depending on the value of this ratio, we get different shapes: a parabola, ellipse, or hyperbola. All these figures lie on the same flat surface or plane.
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What are Parabola, Ellipse and Hyperbola?
Parabola: A parabola is defined as the locus of a point that is equidistant from a fixed point named focus and from a fixed straight line named the directrix.
Ellipse: An ellipse is defined as the locus of a point that travels in a plane such that the ratio of its distance from an established point (focus) to a fixed straight position (directrix) is constant and less than unity i.e. eccentricity e < 1.
Hyperbola: A hyperbola is defined as the locus of a point that travels in a plane such that the proportion of its distance from a fixed position (focus) to a fixed straight line (directrix) is constant and larger than unity i.e. eccentricity e > 1.
Focus: The fixed point is termed as the focus of a conic section.
Directrix: The fixed straight line is designated as the directrix of a conic section.
Eccentricity: The fixed ratio of the distance of point lying on the conic from the focus to its perpendicular distance from the directrix is termed the eccentricity of a conic section and is indicated by e.
The value of eccentricity is as follows;
For an ellipse: e < 1
For a parabola: e = 1
For a hyperbola: e > 1
For a circle: e = 0
For a pair of straight lines: e = ∞
Axis: The straight line passing through the focus and perpendicular to the directrix is designated as the axis of the conic section.
Vertex: The point of intersection of a conic section and its axis is called the vertex of the conic section.
Latus Rectum: The chord passing through the focus and perpendicular to the axis is known as the latus rectum of a conic section.
Principal Axis: It is the Line joining the two focal points/foci of ellipse/ hyperbola. Its midpoint is termed as the center of the curve.
Major axis: Major axis is defined as the line joining the two vertices of an ellipse, starting from one side of the ellipse passing through the center, and ends on the other side. The Major Axis is also called the longest diameter.
Minor axis: It is defined as the shortest chord of an ellipse or the shortest diameter.
The is one more term regarding the axis i.e. Semi-major Axis which is half of the Major Axis, and the Semi-minor Axis which is defined as half of the Minor Axis.
Fact: A Circle is an Ellipse, with a condition where both foci/focus are at the same point (i.e. the center). In other words, a circle can be called a “special case” of an ellipse.
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Standard Forms of Parabola
Check the standard forms of Equation of Parabola below:
Form (y^2 = 4ax):
In this form, the focus of the parabola lies on the positive side of the X-axis.
Form (y^2 = – 4ax):
In this form, the focus of the parabola lies on the negative side of the X-axis.
Form (x^2 = 4ay):
In this form, the focus of the parabola lies on the positive side of the Y-axis.
Form (x^2 = – 4ay):
In this form, the focus of the parabola lies on the negative side of the Y-axis.
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Standard Forms of Ellipse
Form: (\frac{x^2}{a^2}+\frac{y^2}{b^2}=1)
In this form both the foci rest on the X-axis.
Form: (\frac{x^2}{b^2}+\frac{y^2}{a^2}=1)
In this form both the foci rest on the Y-axis.
Learn about Equation of Hyperbola
Standard Form of Hyperbola
Form: (\frac{x^2}{a^2}-\frac{y^2}{b^2}=1)
In this form of hyperbola, the center is located at the origin and foci are on the X-axis.
Form: (\frac{y^2}{a^2}-\frac{x^2}{b^2}=1)
In this form of hyperbola, the center is located at the origin and foci are on the Y-axis.
Important Formulas Table for Parabola
This table helps you understand all the important formulas of a parabola in one place. It includes the standard equations, focus, directrix, axis, and latus rectum for easy learning and quick revision.
| | | | | |
--- ---
| Terms | (y^2 = 4ax) | (y^2 = – 4ax) | (x^2 = 4ay) | (x^2 = – 4ay) |
| Eccentricity | e = 1 | e = 1 | e = 1 | e = 1 |
| Coordinates of Vertex | (0, 0) | (0, 0) | (0, 0) | (0, 0) |
| Coordinates of focus | (a, 0) | (-a, 0) | (0, a) | (0, -a) |
| Equation of directrix | x = – a | x = a | y = – a | y = a |
| Equation of axis | y = 0 | y = 0 | x = 0 | x = 0 |
| Length of Latus Rectum | 4a | 4a | 4a | 4a |
| Parametric Equation | (x = at^2), y = 2at | (x = – at^2), y = 2at | x = 2at, (y = at^2) | x = 2at, (y = – at^2) |
Learn about Mensuration 2D
Parabola with Vertex other than (0, 0)
If the vertex of a parabola is at some point say A (h, k) and the length of the latus rectum is equal to 4a then:
((y – k)^2 = 4a (x – h)) is the parabola that opens towards the right side.((y – k)^2 = – 4a (x – h)) is the parabola that opens towards the left side.((x – h)^2 = 4a (y – k)) is the parabola that opens upwards.((x – h)^2 = – 4a (y – k)) is the parabola which opens downwards.
Equation of Tangents and Normals to the Parabola
Equation of a tangent to the parabola having equation (y^2 = 4ax) are as follows:
at ((x_1, y_1)) is given by: (y ⋅ y_1 = 2a ⋅ (x + x_1))
at ((at^2, 2at)) is given by: ( y ⋅ t = x + a ⋅ t^2)
If m is the slope of the tangent to the parabola (y^2 = 4ax) then its equation is (y=mx+\frac{a}{m}) and the point of contact is (\left(\frac{a}{m^2},\ \frac{2a}{m}\right))
Equation of normal to the parabola having equation (y^2 = 4ax) are as follows:
at (x1, y1) is given by (y-y_1=-\frac{y_1}{2a}\left(x-x_1\right))
at ((at^2, 2at)) is given by (y = t ⋅ x+ 2at + at^3)
If m is the slope of normal to the parabola (y^2 = 4ax), then its equation is (y = mx – 2am – m^3)
Important Formulas Table for Ellipse
This table gives you all the key formulas of an ellipse in a simple format. It shows the standard equations, focus points, major and minor axes, and latus rectum to help you revise quickly and clearly.
| | | |
---
| Terms | (\frac{x^2}{a^2}+\frac{y^2}{b^2}=1) | (\frac{x^2}{b^2}+\frac{y^2}{a^2}=1) |
| Coordinates of the center | (0, 0) | (0, 0) |
| Coordinates of the Vertices | (a, 0) and (-a, 0) | (0, a) and (0, – a) |
| Coordinates of the foci | (ae, 0) and (-ae, 0) | (0, ae) and (0, -ae) |
| Length of major axis | 2a | 2a |
| Length of minor axis | 2b | 2b |
| Eccentricity | (e=\sqrt{1-\frac{b^2}{a^2}}) | e=(\sqrt{1-\frac{b^2}{a^2}}) |
| Length of Latus Rectum | (\frac{2b^2}{a}) | (\frac{2b^2}{a}) |
Equation of Ellipse in Parametric Form
The parametric equation of an ellipse (\frac{x^2}{a^2}+\frac{y^2}{b^2}=1) is given by x = a cos θ, y = b sin θ, and the parametric coordinates of the points lying on it are furnished by (a cos θ, b sin θ).
Equation of Tangents and Normals to Ellipse
Equation of a tangent to the ellipse:
(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1) at the point (x1, y1) is presented by (\frac{x.x_1}{a^2}+\frac{y.y_1}{b^2}=1)
Having (y=m.x\ \pm\sqrt{a^2m^2+b^2}) slope m is and coordinates of the point of contacts are (\left(\pm\frac{a^2m}{\sqrt{a^2m^2+b^2}},\ \pm\frac{b^2}{\sqrt{a^2m^2+b^2}}\right))
Equation of normal to the ellipse :
(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1) at the point (x1, y1) is presented by (\frac{a^2x}{x_1}-\frac{b^2y}{y_1}=a^2-b^2)
Having (y=mx\pm\frac{m\left(a^2-b^2\right)}{\sqrt{a^2+b^2m^2}})
Important Formulas Table for Hyperbola
This table covers the main formulas of a hyperbola in a clear and simple way. It includes standard equations, focus, transverse and conjugate axes, and latus rectum to help you revise easily.
| | | |
---
| Terms | (\frac{x^2}{a^2}-\frac{y^2}{b^2}=1) | (\frac{x^2}{a^2}-\frac{y^2}{b^2}=1) |
| Coordinates of the center | (0, 0) | (0, 0) |
| Coordinates of the Vertices | (a, 0) and (-a, 0) | (0, a) and (0, – a) |
| Coordinates of the foci | (ae, 0) and (-ae, 0) | (0, ae) and (0, -ae) |
| Length of transverse axis | 2a | 2a |
| Length of conjugate axis | 2b | 2b |
| Eccentricity | (e=\sqrt{1+\frac{b^2}{a^2}}) | (e=\sqrt{1+\frac{b^2}{a^2}}) |
| Length of Latus Rectum | (\frac{2b^2}{a}) | (\frac{2b^2}{a}) |
Equation of Hyperbola in Parametric Form
The parametric equation of hyperbola is (\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1) where x = a sec θ, y = b tan θ and parametric coordinates of the point resting on it is presented by (a sec θ, b tan θ).
Equation of Tangents and Normals to Hyperbola
Equation of a tangent to the hyperbola: (\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1) at the point (x1, y1) is given by (\frac{x.x_1}{a^2}-\frac{y.y_1}{b^2}=1)
Having (y=m.x\ \pm\sqrt{a^2m^2-b^2})
Equation of normal to the hyperbola: (\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1) at the point (x1, y1) is given by (\frac{a^2x}{x_1}+\frac{b^2y}{y_1}=a^2+b^2)
Having (y=mx\pm\frac{m\left(a^2+b^2\right)}{\sqrt{a^2-b^2m^2}})
Circle Conic Section
A circle is formed when a flat surface cuts a cone parallel to its base.In a circle, every point on the curve is at the same distance from a fixed point called the center.This fixed distance is known as the radius.
The eccentricity (e) of a circle is 0, which means it is perfectly round.
It does not have a directrix (a guiding line found in other conic sections).
Standard Equation of a Circle:
(x − h)² + (y − k)² = r²(h, k) is the center, and r is the radius.
Parabola – U-Shaped Curve
A parabola is made when a flat surface cuts a cone at an angle, but not parallel to the base.It looks like a U-shaped curve, and it has one focus and one directrix.
The eccentricity (e) of a parabola is 1.
The curve is symmetric and can open upward or downward.
Real-life example: the path of a ball thrown in the air follows a parabolic shape.
Key fact:The graph of a quadratic equation like y = x² or y = −x² is a parabola.
Ellipse – Stretched Circle
An ellipse forms when a flat surface cuts the cone at a slant, but not steep enough to go through both sides.It looks like a flattened or stretched circle.
An ellipse has two foci (focus points) and two directrices.
It has a major axis (the longer line) and a minor axis (the shorter one).
The eccentricity (e) is less than 1 but more than 0.
Standard Equation of an Ellipse:
(x − h)² / a² + (y − k)² / b² = 1(h, k) is the center, a is the major radius, b is the minor radius)
Note: If the ellipse is taller (vertical), swap a² and b² in the formula.
Hyperbola – Opposite Curves
A hyperbola is created when the flat surface cuts through both sides of the cone.It looks like two open curves facing away from each other.
It has two branches, and both are mirror images of each other.
The eccentricity (e) is greater than 1.
A hyperbola has two foci and two directrices.
Standard Equation of a Hyperbola:
(x − h)² / a² − (y − k)² / b² = 1(h, k) is the center of the hyperbola)
The two curves get closer and closer to straight lines but never touch them. These lines are called asymptotes.
General Equation of Conic for Second Degree
The general equation of conics of a second degree is given by:
(a ⋅x^2 + 2hxy + b ⋅ y^2 + 2gx + 2fy + c = 0) and discriminant (Δ = abc + 2fgh – af^2 – bg^2 – ch^2)
The above-given equation depicts a non-degenerate conics whose nature is given below in the table:
| | | |
---
| S.No | Condition | Nature of Conic |
| 1 | Δ ≠ 0, h = 0, a = b, e = 0 | Circle |
| 2 | Δ ≠ 0, (h^2 – ab = 0), e = 1 | Parabola |
| 3 | Δ ≠ 0, (h^2 – ab) < 0, e < 1 | Ellipse |
| 4 | Δ ≠ 0, (h^2 – ab) > 0, e > 1 | Hyperbola |
| 5 | Δ ≠ 0, (h^2 – ab) > 0, a + b = 0, e = 1/2 | Rectangular Hyperbola |
Real-life Applications of Parabola Ellipse and Hyperbola
Planets revolve around the sun in elliptical paths at a single focus.
Mirrors employed to focus light rays at a point are parabolic.
The route traversed by an object launched into the air and stretched arc of a rocket launch is parabolic.
Telescopes use parabolic mirrors.
Satellite systems, Radio systems apply hyperbolic functions.
Lens, optical glasses, and monitors are of hyperbola shape.
Parabolic mirrors are used in solar ovens to focus light beams for heating.
Sound waves are focused on parabolic microphones.
Car headlights, spotlights, and Automobile headlights are designed based on the parabola’s principles.
Electrons in atoms travel about the nucleus in an elliptical path of orbit.
Hyperbolas are employed in long-range navigation systems named LORAN.
In lighthouses, parabolic bulbs are equipped to provide a good focus of beam to be observed from distance by mariners.
The satellite dish used in satellites is a parabolic structure that provides focus and reflection of radio waves.
Properties of Parabola, Ellipse & Hyperbola
Parabola, Ellipse, and Hyperbola are curved shapes called conic sections, formed when a cone is sliced in different ways. Each has unique features—parabola has one focus and directrix, ellipse has two foci with a constant total distance, and hyperbola has two foci with a constant difference in distance. These curves appear in nature, physics, and everyday technology.
Properties of Parabola
A parabola is a curved shape formed when a plane cuts a cone parallel to one of its slant sides.
It has one focus (a fixed point) and one directrix (a fixed line).
The distance from any point on the parabola to the focus is equal to its distance from the directrix.
It is symmetric around a line called the axis of symmetry.
The point where the curve turns is called the vertex.
A parabola can open up, down, left, or right depending on its equation.
Properties of Ellipse
An ellipse looks like a stretched circle.
It has two foci (plural of focus). The sum of distances from any point on the ellipse to both foci is always the same.
It has a major axis (the longest diameter) and a minor axis (the shortest diameter).
The center is the midpoint of both axes.
When both axes are equal, the ellipse becomes a circle.
Ellipses appear in real life in planetary orbits and lenses.
Properties of Hyperbola
A hyperbola is formed when a cone is cut in such a way that the angle is steeper than the side of the cone.
It has two separate curves that open in opposite directions.
It has two foci and two branches.
For any point on a hyperbola, the difference of distances to the two foci is constant.
It has asymptotes – invisible lines that the branches approach but never touch.
Hyperbolas are used in satellite signals, navigation systems, and radio antennas.
| |
| If you are checking Parabola Ellipse and Hyperbola article, also check related maths articles: |
| Centroid of a Triangle | Parabola Graph |
| Equation of a Circle | Difference Between Parabola and Hyperbola |
| Chord of a Circle | Equation of Hyperbola |
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More Articles for Maths
Hyperbola
Latus Rectum of Hyperbola
Pair of Linear Equation
Lines of Regression
Polyhedron
Equation of Parabola
Equation of Ellipse
Conic Section
Eccentricity
Parabola
FAQs For Parabola Ellipse and Hyperbola
Classify Parabola Ellipse and Hyperbola based on eccentricity.
The value of eccentricity for Parabola Ellipse and Hyperbola is as follows:For an ellipse: e < 1For a parabola: e = 1For a hyperbola: e > 1
Define the vertex in a conic section.
The point of intersection of a conic section and its axis is called the vertex of the conic section.
State the standard forms of the parabola.
The standard forms of the parabola are as follows:Form y2 = 4ax:In this form, the focus of the parabola lies on the positive side of the X-axis.Form y2 = - 4ax:In this form, the focus of the parabola lies on the negative side of the X-axis.Form x2 = 4ay:In this form, the focus of the parabola lies on the positive side of the Y-axis.Form x2 = - 4ay:In this form, the focus of the parabola lies on the negative side of the Y-axis.
How to identify the major and minor axis of an ellipse?
The major axis is defined as the line joining the two vertices of an ellipse, starting from one side of the ellipse passing through the center, and ending to the other side. The Major Axis is also called the longest diameter. whereas the minor axis is defined as the shortest chord of an ellipse or the shortest diameter.
Is a circle an ellipse?
A Circle is an Ellipse, with a condition where both foci/focus are at the same point (i.e. the center). In other words, a circle can be called a "special case" of an ellipse.
State some application of the conic section in real life.
Some of the application of the conic section is as follows:Planets revolve around the sun in elliptical paths at a single focus.Car headlights, spotlights, and Automobile headlights are designed based on the parabola’s principles. Lens, optical glasses, and monitors are of hyperbola shape.
What are foci in a hyperbola?
Like an ellipse, the hyperbola has two foci, but here, the difference of distances to the foci is constant.
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189663 | https://www.youtube.com/watch?v=krHqynVe6-g | How to Perform the Catalase Test - Staphylococcus vs Streptococcus
Hardy Diagnostics
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Posted: 22 Mar 2022
Catalase tests can be used to determine if a gram-positive cocci is staphylococcus or streptococcus bacteria. To learn more about Hardy Diagnostics visit our new website.
Hardy Diagnostics is your complete Microbiology supplier.
View our complete list of catalogs in the link below.
We are 100% employee owned and have been serving microbiologists for over 40 years.
To learn more about Hardy Diagnostics and the products we offer, visit us at
Contact us with any questions:
hardydiagnostics.com/contact-us
00:00 History of catalase test
00:53 What you will need
01:08 Start of catalase test
01:15 Applying the organism
01:40 Tips
01:48 Adding 3% hydrogen peroxide
01:57 Reaction/Results
02:25 Closing info
Filmed and Edited by Brian Tom
Catalase # Staphylococcus # Streptococcus
24 comments
Transcript:
History of catalase test Catalase tests can be used to
determine if a gram-positive cocci is Staphylococcus or Streptococcus bacteria. These
organisms will appear dark blue in the Gram stain. Staphylococci and Streptococci are both
round in shape, known as cocci. Streptococci form a chain of round cells because their
division occurs in one linear direction, whereas staphylococci divide in various directions
forming grape-like clusters. The easiest way to differentiate between Staphylococcus
and Streptococcus is the catalase test. Staphylococci are catalase positive
whereas Streptococci are catalase negative. Catalase is an enzyme used by bacteria to induce
the reduction of hydrogen peroxide into water and oxygen. A positive reaction will produce bubbles
of oxygen gas. In order to perform a catalase test, What you will need you will need: 3% hydrogen peroxide, a
pipet, glass slides, permanent marker, Staphylococcus bacteria, Streptococcus bacteria, and
inoculating loops. Start by labeling your slides. Applying the organism Using your sterile inoculating loop
touch an isolated Staphylococcus colony, then smear the organism on a clean
glass slide in one even layer. Next, using a new sterile loop touch a
Streptococcus colony and smear it on the clean glass slide in one even layer. Avoid touching the
that contain red blood cells. Red blood cells Tips contain catalase and may cause a false positive
result. Using a dropper or pipette release two to Adding 3% hydrogen peroxide three drops of 3% hydrogen peroxide
onto the Streptococcus slide, without mixing. Reaction/Results Note the reaction because it is catalase
negative there will be no bubbling effect. Release two to three drops of hydrogen peroxide
onto the Staphylococcus slide without mixing. The bubbling effect indicates that
your sample is catalase positive as the catalase enzyme is breaking down the
hydrogen peroxide into water and oxygen which you can see in the bubbles. Note that the microbial
culture should be 18 to 24 hours old. Thanks Closing info Thanks for watching this catalase demonstration. Hardy
Diagnostics is your complete microbiology supplier. To learn more about Hardy Diagnostics and the
products we offer visit us at HardyDiagnostics.com |
189664 | http://logicatorino.altervista.org/dstTurin17/slides/Schlicht_dst.pdf | Combinatorial Variants of Lebesgue’s Density Theorem Philipp Schlicht joint with David Schrittesser, Sandra Uhlenbrock and Thilo Weinert September 6, 2017 Philipp Schlicht Variants of Lebesgue’s Density Theorem 1/19 Lebesgue’s Density Theorem Definition Suppose that (X, d, µ) is a Polish metric space with a Borel measure µ.
An element x of X is a µ-density point of a subset A of X if lim inf ϵ>0 µ(Bϵ(x) ∩A)) µ(Bϵ(x)) = 1.
Theorem (1) (Lebesgue) Suppose that A is a Lebesgue measurable subset of Rn with the Lebesgue measure and DL(A) is the set of Lebesgue density points of A. Then µ(A△DL(A)) = 0.
(2) (Miller) Suppose that (X, d, µ) is an ultrametric Polish space with a finite Borel measure µ and A ⊆X is µ-measurable. Let DL,µ(A) be the set of µ-density points of A. Then µ(A△DL,µ(A)) = 0.
Philipp Schlicht Variants of Lebesgue’s Density Theorem 2/19 Lebesgue’s Density Theorem Theorem (Vitali’s Covering Theorem) Given a collection of open balls centered at the points of a set A ⊆Rn that contains arbitrary small balls at each point in A, there is a disjoint subcollection that covers A except for a null set.
Proof of Lebesgue’s Density Theorem.
We claim that Aϵ = {x ∈Rn | lim supr→0 µ(Br(x)\A) µ(Br(x)) > ϵ} is a null set for all ϵ > 0.
For any δ > 0, let Uδ be an open set with Aϵ ⊆Uδ and µ(Uδ \ Aϵ) < δ.
We obtain a collection C from Vitali’s Covering Theorem for the collection of all open balls B ⊆Uδ with µ(B\A) µ(B) > ϵ at elements of Aϵ. Then ϵµ(Aϵ) ≤ϵ X B∈C µ(B) < X B∈C µ(B \ A) ≤µ(Uδ \ A) < δ.
Since this holds for all δ > 0, we have µ(Aϵ) = 0.
Philipp Schlicht Variants of Lebesgue’s Density Theorem 3/19 Counterexamples Definition If (X, d) is a metric space, d is called doubling if for some n ∈N, any open ball B2r(x) can be covered by n balls of radius r.
Theorem (K¨ aenm¨ aki-Rajala-Suomala) There is a finite Borel measure ν and a complete doubling metric δ on the Cantor space, compatible with the standard topology, such that some closed set C of positive measure has no ν-density points.
Theorem (Andretta-Costantini-Camerlo) For any Polish measure space (X, d, µ) there is a compatible metric δ such that (X, δ, µ) does not satisfy Lebesgue’s density theorem.
Philipp Schlicht Variants of Lebesgue’s Density Theorem 4/19 Question Can the Lebesgue density theorem be generalized to other ideals instead of the ideal of null sets, in particular the σ-ideals defined by tree forcings?
Philipp Schlicht Variants of Lebesgue’s Density Theorem 5/19 Tree forcings and their ideals ⋆= 2 or ⋆= ω.
Definition We say P is a tree forcing iffthe conditions in P are perfect subtrees of <ω⋆ordered by inclusion such that for all T ∈P and all s ∈T we have that {t ∈T | s ⊆t or t ⊆s} ∈P.
Definition (Ikegami) Suppose that P is a tree forcing and A is a subset of ω⋆.
(i) A ∈NP if for every T ∈P, there is some S ∈P with S ⊆T and [S] ∩A = ∅. A set A in NP is also called P-null.
(ii) IP is the σ-ideal generated by NP.
(iii) A ∈I∗ P if for every T ∈P, there is some S ∈P with S ⊆T and [S] ∩A ∈IP.
Philipp Schlicht Variants of Lebesgue’s Density Theorem 6/19 Example: Random forcing Definition Let µ denote the uniform measure on ω2. Random forcing B is the tree forcing consisting of perfect trees T ⊆2<ω such that µ([T]) > 0 and for all s ∈T, µ([{t ∈T | s ⊆t or t ⊆s}]) > 0.
Definition A subset A of ω2 is B-measurable ifffor every T ∈B there is some S ∈B with S ⊆T such that either [S] ∩A ∈IB or [S] ∩Ac ∈IB.
What is a B-density point?
Philipp Schlicht Variants of Lebesgue’s Density Theorem 7/19 Density points for Random forcing Definition (i) Suppose that A is a B-measurable subset of ω2. Suppose that x ∈ω2. Then x is a B-translation density point of A if for every T ∈B and s = stemT , there is some n0 such that for all n ≥n0, fx↾n ◦f −1 s [T] ∩A / ∈I∗ B.
(ii) Let DB tr(A) denote the set of translation density points of A.
(iii) We say that B has the translation density property if for every B-measurable subset A of ω2, A△DB tr(A) ∈I∗ B.
Here fs(x) = s⌢x and f −1 s [T] = [T/s] = {t | s⌢t ∈[T]}.
Philipp Schlicht Variants of Lebesgue’s Density Theorem 8/19 Density points for Random forcing Lemma Suppose that A is a B-measurable subset of ω2.
(a) If lim infn µn(x, A) = 1, then x is a B-translation density point of A.
(b) If lim infn µn(x, A) = 0, then x is not a B-translation density point of A.
(c) If lim infn µn(x, A) ∈(0, 1), then x can be but does not have to be a B-translation density point of A.
Corollary For every B-measurable set A, DL(A) =I∗ B DB tr(A).
In particular B has the translation density property.
Philipp Schlicht Variants of Lebesgue’s Density Theorem 9/19 Density points for ideals Let I always denote a σ-ideal on the Borel subsets of ω⋆.
Definition (a) A map g: A →B between Borel sets A, B is I-invariant if for every Borel set X ⊆B, we have X ∈I if and only if g−1[X] ∈I.
(b) Let Bor(I) denote the set of all I-invariant Borel isomorphisms g: ω⋆→ω⋆.
(c) We say B is I-positive iffB / ∈I. Let I+ denote the I-positive sets.
Philipp Schlicht Variants of Lebesgue’s Density Theorem 10/19 Density points for ideals Definition Suppose that A is a subset of ω⋆and Γ is a subgroup of Bor(I).
(i) An element x of ω⋆is an I-density point of A w.r.t. Γ if for every I-positive Borel set B, there is some s ∈⋆<ω and some nB such that for all n ≥nB and all g ∈Γ, (fx↾n ◦g ◦f −1 s )[B] ∩A / ∈I.
Let DI,Γ(A) denote the set of I-density points of A w.r.t. Γ.
(ii) An element x of ω⋆is a strong I-density point of A if there is some n0 such that for all n ≥n0, we have f −1 x↾n[Ac ∩Nx↾n] ∈I.
Let DI,strong(A) denote the set of strong I-density points of A.
Note that DI,strong(A) ⊆DI,Bor(I)(A) ⊆DI,Γ(A) ⊆DI,{id}(A).
Philipp Schlicht Variants of Lebesgue’s Density Theorem 11/19 Density points Definition We say that I has the density property w.r.t. Γ if for all Borel subsets A of ω⋆, A△DI,Γ(A) ∈I.
Philipp Schlicht Variants of Lebesgue’s Density Theorem 12/19 Density points Definition (i) P is homogeneous if for all S, T ∈P, there is some U ≤T and f : [S] →[U] in Bor(I∗ P).
(ii) P is nondegenerate if it is not equivalent to Cohen forcing and ∀s∃S ∈P s ⊆stemS.
(iii) (Friedman-Khomskii-Kulikov) A tree forcing P is topological if for all S, T ∈P with [S] ∩[T] ̸= ∅, there is U ∈P with [U] ⊆[S] ∩[T].
For a topological tree forcing P, we let τP be the topology on ω⋆ with basis {[T] | T ∈P}.
Lemma Assume that P is a homogeneous, nondegenerate, topological tree forcing and let I = I∗ P. Then for all I-measurable A, DI,strong(A) = DI,Bor(I)(A).
Philipp Schlicht Variants of Lebesgue’s Density Theorem 13/19 Density property Definition Suppose that P is a topological tree forcing and let A be a I∗ P-measurable subset of ω⋆which has the property of Baire in τP. An x ∈ω⋆is a P-topological density point of A if x ∈U = DP top(A), where U is the unique open subset in τP such that A△U ∈I∗ P.
Theorem Suppose that P is a homogeneous, nondegenerate, topological tree forcing with the ccc w.r.t. I = I∗ P. Suppose that for every T ∈P there is an S ≤T such that every x ∈[S] is an I-density point of [T] w.r.t.
Bor(I). Then for every I-measurable A, DI,Bor(I)(A) = DI,strong(A) =I DP top(A).
Therefore I has the density property w.r.t. Bor(I).
Philipp Schlicht Variants of Lebesgue’s Density Theorem 14/19 Stem-linked forcings Definition Suppose that P is a tree forcing on <ω⋆. Then P is stem-linked if for all S, T ∈P, if stemS ⊆stemT and stemT ∈S, then S and T are compatible.
Stem-linked implies σ-linked, ccc w.r.t. I∗ P, and topological.
Lemma Let P be a stem-linked tree forcing on <ω⋆. Then for every T ∈P we have that every x ∈[T] is an I∗ P-density point of [T] w.r.t. Bor(I∗ P).
Corollary Suppose P is a stem-linked, nondegenerate, homogeneous tree forcing on <ω⋆. Then I∗ P has the density property w.r.t. Bor(I∗ P).
Philipp Schlicht Variants of Lebesgue’s Density Theorem 15/19 Examples The I-density property w.r.t Bor(I) holds for the σ-ideals I defined by the following tree forcings, since they are stem-linked: Cohen forcing C, Hechler forcing H, F-Laver forcing LF for a filter F, and F-Mathias forcing RF for a filter F.
However, random forcing B does not have a dense stem-linked subset.
Philipp Schlicht Variants of Lebesgue’s Density Theorem 16/19 Counterexamples The translation density property fails for the following tree forcings.
Sacks forcing S, Mathias forcing R, Laver forcing L, Miller forcing M, and Silver forcing V.
Philipp Schlicht Variants of Lebesgue’s Density Theorem 17/19 From ideals to forcings Theorem (Ikegami) Suppose that P is a proper tree forcing. Then the map ι: P →B/IP∗ that sends T ∈P to the IP∗-equivalence class represented by [T] is a dense embedding, where B denotes the class of Borel subsets of ω⋆and B/IP∗denotes the quotient Boolean algebra.
Definition A σ-ideal I on the Borel subsets of ω⋆is homogeneous if there are I-invariant Borel isomorphisms between any two I-positive Borel sets.
Philipp Schlicht Variants of Lebesgue’s Density Theorem 18/19 Open questions Question Does the density property fail for some homogeneous ccc σ-ideal?
Question Does the density property hold for some homogeneous non-ccc σ-ideal?
Question Is it consistent that there is no definable selector for the equivalence relation equal modulo countable on the class of Borel sets?
Philipp Schlicht Variants of Lebesgue’s Density Theorem 19/19 |
189665 | https://math.stackexchange.com/questions/4741217/help-with-finding-the-number-of-terms-in-a-geometric-sum | Stack Exchange Network
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Help with finding the number of terms in a geometric sum
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I'm currently stuck on a problem involving a geometric sum, and I was hoping to get some assistance with it. Here's the problem:
A geometric sum is equal to 215. The first term is 5, and the last term is 320. I need to find the number of terms in the sum.
Here's what I have so far:
[215 = 5 \cdot (r^n - 1) / (r - 1)] [320 = 5 \cdot r^{n-1}]
I'm having trouble finding the value of the common ratio (r) and the number of terms (n) in the sequence. I'm not sure where to begin or how to proceed.
One user suggested using the fact that the first term is 5 and the last term is 320 to find the ratio (r) in terms of the number of terms (n) and vice versa. However, I'm not sure how to do that.
I tried multiplying r on both sides of the second equation (320 = 5 r^(n-1)), but I'm not sure how that helps me find the ratio (r) or the number of terms (n).
I would greatly appreciate any guidance or insights on how to approach this problem and find the number of terms in the geometric sum. If you could provide a step-by-step explanation or walk me through the solution, that would be incredibly helpful.
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asked Jul 23, 2023 at 18:20
Bishop_1Bishop_1
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Since $r^{n-1}=\frac{320}5=64$,$$43=\frac{215}5=\frac{r^n-1}{r-1}=\frac{64r-1}{r-1},$$and therefore $r=-2$. And, since $(-2)^{n-1}=64$, $n=7$.
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answered Jul 23, 2023 at 18:30
José Carlos SantosJosé Carlos Santos
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$320=5\times r^{n-1}$
$64=r^{n-1}$ and $64r=r^n$
$215=\frac{5(r^n - 1)}{r-1}$
$215=\frac{5(64r - 1)}{r-1}$
$43=\frac{64r - 1}{r-1}$
$r=-2$
then
$320=5\times (-2)^{n-1}$
$64=(-2)^6=(-2)^{n-1}$
$n=7$
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answered Jul 23, 2023 at 18:36
Lion HeartLion Heart
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189666 | https://www.savemyexams.com/dp/physics/ib/23/hl/revision-notes/space-time-and-motion/kinematics/speed-and-velocity/ | Speed and Velocity - IB Physics Revision Notes
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Revision Notes
Space, Time & Motion
5 Topics · 57 Revision Notes
1.
Kinematics
1. ##### Distance & Displacement
2. ##### Speed & Velocity
3. ##### Acceleration
4. ##### Kinematic Equations
5. ##### Motion Graphs
6. ##### Projectile Motion
7. ##### Fluid Resistance
8. ##### Terminal Speed
2.
Forces & Momentum
1. ##### Free-Body Diagrams
2. ##### Newton’s First Law
3. ##### Newton’s Second Law
4. ##### Newton’s Third Law
5. ##### Contact Forces
6. ##### Non-Contact Forces
7. ##### Frictional Forces
8. ##### Hooke's Law
9. ##### Stoke's Law
10. ##### Buoyancy
11. ##### Conservation of Linear Momentum
12. ##### Impulse & Momentum
13. ##### Force & Momentum
14. ##### Collisions & Explosions in One-Dimension
15. ##### Collisions & Explosions in Two-Dimensions
16. ##### Angular Velocity
17. ##### Centripetal Force
18. ##### Centripetal Acceleration
19. ##### Non-Uniform Circular Motion
3.
Work, Energy & Power
1. ##### Principle of Conservation of Energy
2. ##### Sankey Diagrams
3. ##### Work Done
4. ##### Kinetic Energy
5. ##### Gravitational Potential Energy
6. ##### Elastic Potential Energy
7. ##### Conservation of Mechanical Energy
8. ##### Energy & Power
9. ##### Efficiency Formula
10. ##### Energy Density
4.
Rigid Body Mechanics
1. ##### Torque & Couples
2. ##### Rotational Equilibrium
3. ##### Angular Displacement, Velocity & Acceleration
4. ##### Angular Acceleration Formula
5. ##### Moment of Inertia
6. ##### Newton’s Second Law for Rotation
7. ##### Angular Momentum
8. ##### Angular Impulse
9. ##### Rotational Kinetic Energy
5.
Galilean & Special Relativity
1. ##### Reference Frames
2. ##### Galilean Relativity
3. ##### Postulates of Special Relativity
4. ##### Lorentz Transformations
5. ##### Velocity Addition Transformations
6. ##### Space-Time Interval
7. ##### Time Dilation
8. ##### Length Contraction
9. ##### Simultaneity in Special Relativity
10. ##### Space-Time Diagrams
11. ##### Muon Lifetime Experiment
The Particulate Nature of Matter
5 Topics · 47 Revision Notes
1.
Thermal Energy Transfers
1. ##### Solids, Liquids & Gases
2. ##### Density
3. ##### Temperature Scales
4. ##### Temperature & Kinetic Energy
5. ##### Internal Energy
6. ##### Thermal Equilibrium
7. ##### Changes of State
8. ##### Specific Heat Capacity
9. ##### Specific Latent Heat
10. ##### Thermal Conduction
11. ##### Thermal Convection
12. ##### Thermal Radiation
13. ##### Apparent Brightness & Luminosity
14. ##### Stefan-Boltzmann Law
15. ##### Wien’s Displacement Law
2.
Greenhouse Effect
1. ##### Albedo & Emissivity
2. ##### The Solar Constant
3. ##### Greenhouse Gases
4. ##### The Greenhouse Effect
5. ##### Energy Balance Problems
3.
Gas Laws
1. ##### Gas Pressure
2. ##### Amount of Substance
3. ##### Gas Laws
4. ##### Ideal Gas Equation
5. ##### Kinetic Theory of Gases
6. ##### Derivation of the Kinetic Theory of Gases Equation
7. ##### Average Kinetic Energy of a Molecule
4.
Thermodynamics
1. ##### Thermodynamic Systems
2. ##### First Law of Thermodynamics
3. ##### Entropy
4. ##### Calculating Changes in Entropy
5. ##### Second Law of Thermodynamics
6. ##### Thermodynamic Processes
7. ##### Heat Engines
8. ##### The Carnot Cycle
5.
Current & Circuits
1. ##### Circuit Diagrams
2. ##### Electric Current
3. ##### Electric Potential Difference
4. ##### Electrical Conductors & Insulators
5. ##### Electric Resistance
6. ##### Electrical Resistivity
7. ##### I-V Characteristics
8. ##### Series & Parallel Circuits
9. ##### Electrical Power
10. ##### Sources of Electrical Energy
11. ##### Electromotive Force & Internal Resistance
12. ##### Variable Resistance
Wave Behaviour
5 Topics · 31 Revision Notes
1.
Simple Harmonic Motion
1. ##### Describing Oscillations
2. ##### Simple Harmonic Motion (SHM)
3. ##### Time Period of a Mass–Spring System
4. ##### Time Period of a Simple Pendulum
5. ##### Energy Changes in Simple Harmonic Motion (SHM)
6. ##### Equations for Simple Harmonic Motion (SHM)
7. ##### Calculating Energy Changes in SHM
8. ##### Phase Angles in Simple Harmonic Motion (SHM)
2.
Wave Model
1. ##### Properties of Waves
2. ##### Transverse & Longitudinal Waves
3. ##### Sound Waves
4. ##### Electromagnetic Waves
3.
Wave Phenomena
1. ##### Wavefronts & Rays
2. ##### Reflection, Refraction & Transmission
3. ##### Diffraction of Waves
4. ##### Refraction of Waves
5. ##### Superposition of Waves
6. ##### Interference of Waves
7. ##### Young’s Double-Slit Experiment
8. ##### Single-Slit Diffraction
9. ##### Diffraction Gratings
4.
Standing Waves & Resonance
1. ##### Standing Waves
2. ##### Nodes & Antinodes
3. ##### Boundary Conditions for Standing Waves
4. ##### Harmonics in Strings & Pipes
5. ##### The Nature of Resonance
6. ##### The Effect of Damping
5.
Doppler Effect
1. ##### The Doppler Effect
2. ##### The Doppler Effect of Light
3. ##### Galactic Redshift
4. ##### Equations for the Doppler Effect of Sound
Fields
4 Topics · 34 Revision Notes
1.
Gravitational Fields
1. ##### Newton's Law of Gravitation
2. ##### Gravitational Field Strength
3. ##### Gravitational Field Lines
4. ##### Gravitational Potential
5. ##### Gravitational Potential Energy in a Non-Uniform Field
6. ##### Gravitational Potential Energy Equation
7. ##### Gravitational Potential Gradient
8. ##### Gravitational Equipotential Surfaces
9. ##### Kepler's Laws of Planetary Motion
10. ##### Escape Speed
11. ##### Orbital Motion, Speed & Energy
12. ##### Effects of Drag on Orbital Motion
2.
Electric & Magnetic Fields
1. ##### Electric Charge
2. ##### Millikan's Oil Drop Experiment
3. ##### Static Electricity
4. ##### Coulomb's Law
5. ##### Electric Field Strength
6. ##### Electric Field Lines
7. ##### Electric Potential
8. ##### Electric Potential Energy
9. ##### Electric Potential Gradient
10. ##### Electric Equipotential Surfaces
11. ##### Magnetic Fields
3.
Motion in Electromagnetic Fields
1. ##### Magnetic Force on a Current-Carrying Conductor
2. ##### Magnetic Force between Two Parallel Conductors
3. ##### Magnetic Force on a Charge
4. ##### Charged Particles in Magnetic Fields
5. ##### Charged Particles in Electric Fields
6. ##### Charged Particles in Electric & Magnetic Fields
4.
Induction
1. ##### Induced Emf
2. ##### Magnetic Flux
3. ##### Faraday’s Law of Induction
4. ##### Lenz's Law
5. ##### AC Generators
Nuclear & Quantum Physics
5 Topics · 39 Revision Notes
1.
Structure of the Atom
1. ##### Rutherford's Gold Foil Experiment
2. ##### Nuclear Notation
3. ##### Emission & Absorption Spectrum
4. ##### Photon Energy
5. ##### Rutherford Scattering & Nuclear Radius
6. ##### Deviations from Rutherford Scattering
7. ##### The Bohr Model of Hydrogen
2.
Quantum Physics
1. ##### The Photoelectric Effect
2. ##### The Photoelectric Equation
3. ##### The Particle Nature of Light
4. ##### The de Broglie Wavelength
5. ##### Wave-Particle Duality
6. ##### Compton Scattering
3.
Radioactive Decay
1. ##### Isotopes & Radioactive Decay
2. ##### Background Radiation
3. ##### Alpha, Beta & Gamma Particles
4. ##### Radioactive Decay Equations
5. ##### Activity & Half-Life
6. ##### Decay Constant & Half-Life
7. ##### The Law of Radioactive Decay
8. ##### Applications of Radioactivity
9. ##### Mass Defect & Nuclear Binding Energy
10. ##### Binding Energy per Nucleon Curve
11. ##### Nuclear Stability
12. ##### Nuclear Energy Levels
13. ##### Evidence for the Neutrino
4.
Fission
1. ##### Spontaneous & Induced Fission
2. ##### Energy Released in Fission Reactions
3. ##### Chain Reactions from Fission
4. ##### Operation of a Nuclear Reactor
5. ##### Radioactive Waste Management
5.
Fusion & Stars
1. ##### Fusion Reactions in Stars
2. ##### Energy Released in Fusion Reactions
3. ##### Star Formation
4. ##### Life Cycle of a Star
5. ##### The Hertzsprung–Russell (HR) Diagram
6. ##### Emission & Absorption Spectra in Stars
7. ##### Stellar Parallax
8. ##### Determination of Stellar Radii
Tools
3 Topics · 10 Revision Notes
1.
Measurements in Physics
1. ##### Fundamental & Derived Units in IB Physics
2. ##### Using Scientific Notation in Physics
3. ##### Using Dimensional Analysis
4. ##### Measurement Techniques in IB Physics
2.
Processing Uncertainties
1. ##### Random & Systematic Errors
2. ##### Calculating Uncertainties
3. ##### Determining Uncertainties from Graphs
3.
Scalars & Vectors
1. ##### Scalar & Vector Quantities
2. ##### Combining & Resolving Vectors
3. ##### Scale Diagrams
IBPhysicsDPHLRevision NotesSpace, Time & Motion Kinematics Speed & Velocity
Speed & Velocity(DP IB Physics):Revision Note
Download PDF
Author
Ashika
Last updated
1 September 2025
Exam board:
DP
DP Physics: HLDP Physics: SL
Speed & Velocity
Speed
The speed of an object is the distance it travels every second
Speed is a scalar quantity
This is because it only contains a magnitude (without a direction)
The average speed of an object is given by the equation:
The SI units for speed are meters per second(m s−1)
Sometimes speed is measured in alternative units, such as km h−1 or mph
Velocity
The velocity of a moving object is similar to its speed and also describes the direction of the velocity
Velocity is defined as:
The rate of change of displacement
Velocity is, therefore, a vector quantity because it describes both magnitude and direction
The difference between speed and velocity
Speed is ascalar quantity whilst velocity isvector
Velocity is thespeed in a givendirection
The cars in the diagram above have the same speed (a scalar quantity) but different velocities (a vector quantity). Fear not, they are in different lanes!
This means velocity can also have anegative value
E.g. a ball thrown upwards at a velocity of 3 m s–1 comes down at a velocity –5 m s–1, if upwards is considered positive
However, theirspeeds are still 3 m s–1 and 5 m s–1 respectively
Instantaneous Speed & Velocity
The instantaneous speed (or velocity) is the speed (or velocity) of an object at any given point in time
This could be for an object moving at a constant velocity or accelerating
An object at constant velocity is shown by astraight line on a displacement – time graph
An object accelerating is shown by a curved line on a displacement – time graph
An accelerating object will have a changingvelocity
To find the instantaneous velocity on a displacement-time graph:
Draw a tangent at the required time
Calculate the gradient of that tangent
The instantaneous velocity is found by drawing a tangent on the displacement time graph
In the graph above, at t = 9 s, the velocity is:
Average Speed & Velocity
The average velocity of an object can be calculated using
Where:
= total displacement, or change in position (m)
= total time taken (s)
If the acceleration is constant, and the initial velocity and final velocity are known, the average velocity can also be calculated from
To find the average velocity on a displacement-time graph, divide the total displacement (on the y-axis) by the total time (on the x-axis)
This method can be used for both a curved and a straight line on a displacement-time graph
Worked Example
Florence Griffith Joyner set the women’s 100 m world record in 1988, with a time of 10.49 s.
Calculate her average speed during the race.
Answer:
Sprinters typically speed up from rest to a maximum speed
Because Florence’s speed changes over the course of the race, we can calculate her average speed using the equation:
average speed = total distance ÷ time taken
Where:
Total distance, s = 100 m
Time taken, t = 10.49 s
average speed = 100 ÷ 10.49 = 9.5328 = 9.53 m s−1
Worked Example
The variation of displacement of a box sliding across a rough surface with time t is shown on the graph below.
The magnitudes of the instantaneous velocities of the trolley at time t 1 and t 2 are v 1 and v 2 respectively.
List the following velocities in order from fastest to slowest:
v 1 v 2 average velocity
Answer:
Step 1: Sketch the velocities from the graph
The instantaneous velocity is the gradient of a tangent at a certain time
The average velocity is the total displacement over the total time
Step 2: Compare the gradients of each velocity
The fastest velocity will have the steepestgradient and the slowest velocity the shallowestgradient
In order from fastest to slowest:
v 1> average velocity >v 2
Examiner Tips and Tricks
When you draw a tangent to a curve, make sure itjust touchesthe point at which you wish to calculate the gradient. The angle between the curve and the tangent line should be roughly equal on both sides of the point.
If you are asked to find the instantaneous velocity from a graph, you will be told thetime at which they want this velocity for.
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189667 | https://flexbooks.ck12.org/cbook/ck-12-basic-geometry-concepts/section/5.2/primary/lesson/perpendicular-bisectors-bsc-geom/ | Skip to content
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5.2
Perpendicular Bisectors
Written by:Dan Greenberg | Lori Jordan |
Fact-checked by:The CK-12 Editorial Team
Last Modified: Aug 01, 2025
Perpendicular Bisector Theorem
A perpendicular bisector is a line that intersects a line segment at its midpoint and is perpendicular to that line segment, as shown in the construction below.
One important property related to perpendicular bisectors is that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. This is called the Perpendicular Bisector Theorem.
If @$\begin{align}\overleftrightarrow{CD} \perp \overline{AB}\end{align}@$ and @$\begin{align}AD = DB\end{align}@$, then @$\begin{align}AC = CB\end{align}@$.
In addition to the Perpendicular Bisector Theorem, the converse is also true.
Perpendicular Bisector Theorem Converse: If a point is equidistant from the endpoints of a segment, then the point is on the perpendicular bisector of the segment.
Using the picture above: If @$\begin{align}AC = CB\end{align}@$, then @$\begin{align}\overleftrightarrow{CD} \perp \overline{AB}\end{align}@$ and @$\begin{align}AD = DB\end{align}@$.
When we construct perpendicular bisectors for the sides of a triangle, they meet in one point. This point is called the circumcenter of the triangle.
What if you were given @$\begin{align}\triangle FGH \end{align}@$ and told that @$\begin{align} \overleftrightarrow{GJ}\end{align}@$ was the perpendicular bisector of @$\begin{align}\overline{FH}\end{align}@$? How could you find the length of @$\begin{align}FG\end{align}@$ given the length of @$\begin{align}GH\end{align}@$?
Examples
Example 1
@$\begin{align}\overleftrightarrow{OQ}\end{align}@$ is the perpendicular bisector of @$\begin{align}\overline{MP}\end{align}@$.
Which line segments are equal? Find @$\begin{align}x\end{align}@$. Is @$\begin{align}L\end{align}@$ on @$\begin{align}\overleftrightarrow{OQ}\end{align}@$? How do you know?
@$\begin{align}ML = LP, \ MO = OP\end{align}@$, and @$\begin{align}MQ = QP\end{align}@$.
@$$\begin{align}4x + 3 & = 11\
4x & = 8\
x & = 2\end{align}@$$
Yes, @$\begin{align}L\end{align}@$ is on @$\begin{align}\overleftrightarrow{OQ}\end{align}@$ because @$\begin{align}ML = LP\end{align}@$ (the Perpendicular Bisector Theorem Converse).
Example 2
Determine if @$\begin{align}\overleftrightarrow{S T}\end{align}@$ is the perpendicular bisector of @$\begin{align}\overline{XY}\end{align}@$. Explain why or why not.
@$\begin{align}\overleftrightarrow{S T}\end{align}@$ is not necessarily the perpendicular bisector of @$\begin{align}\overline{XY}\end{align}@$ because not enough information is given in the diagram. There is no way to know from the diagram if @$\begin{align}\overleftrightarrow{S T}\end{align}@$ will extend to make a right angle with @$\begin{align}\overline{XY}\end{align}@$.
Example 3
If @$\begin{align}\overleftrightarrow{MO}\end{align}@$ is the perpendicular bisector of @$\begin{align}\overline{LN}\end{align}@$ and @$\begin{align}LO = 8\end{align}@$, what is @$\begin{align}ON\end{align}@$?
By the Perpendicular Bisector Theorem, @$\begin{align}LO = ON\end{align}@$. So, @$\begin{align}ON = 8\end{align}@$.
Example 4
Find @$\begin{align}x\end{align}@$ and the length of each segment.
@$\begin{align}\overleftrightarrow{WX}\end{align}@$ is the perpendicular bisector of @$\begin{align}\overline{XZ}\end{align}@$ and from the Perpendicular Bisector Theorem @$\begin{align}WZ = WY\end{align}@$.
@$$\begin{align}2x + 11 &= 4x - 5\
16 &= 2x\
8 &= x\end{align}@$$
@$\begin{align}WZ = WY = 2(8) + 11 = 16 + 11 = 27\end{align}@$.
Example 5
Find the value of @$\begin{align}x\end{align}@$. @$\begin{align}m\end{align}@$ is the perpendicular bisector of @$\begin{align}AB\end{align}@$.
By the Perpendicular Bisector Theorem, both segments are equal. Set up and solve an equation.
@$$\begin{align}3x-8 &=2x\
x &=8\end{align}@$$
Review
For questions 1-4, find the value of @$\begin{align}x\end{align}@$. @$\begin{align}m\end{align}@$ is the perpendicular bisector of @$\begin{align}AB\end{align}@$.
@$\begin{align}m\end{align}@$ is the perpendicular bisector of @$\begin{align}\overline{AB}\end{align}@$. Also imagine that point @$\begin{align}M\end{align}@$ is the intersection of line @$\begin{align}m\end{align}@$ and @$\begin{align}\overline{AB.}\end{align}@$
List all the congruent segments.
Is @$\begin{align}C\end{align}@$ on @$\begin{align}m\end{align}@$? Why or why not?
Is @$\begin{align}D\end{align}@$ on @$\begin{align}m\end{align}@$? Why or why not?
For Question 8, determine if @$\begin{align}\overleftrightarrow{S T}\end{align}@$ is the perpendicular bisector of @$\begin{align}\overline{XY}\end{align}@$. Explain why or why not.
In what type of triangle will all perpendicular bisectors pass through vertices of the triangle?
Fill in the blanks of the proof of the Perpendicular Bisector Theorem.
Given: @$\begin{align}\overleftrightarrow{C D}\end{align}@$ is the perpendicular bisector of @$\begin{align}\overline{AB}\end{align}@$
Prove: @$\begin{align}\overline{AC} \cong \overline{CB}\end{align}@$
| Statement | Reason |
--- |
| 1. | 1. |
| 2. @$\begin{align}D\end{align}@$ is the midpoint of @$\begin{align}\overline{AB}\end{align}@$ | 2. |
| 3. | 3. Definition of a midpoint |
| 4. @$\begin{align}\angle CDA\end{align}@$ and @$\begin{align}\angle CDB\end{align}@$ are right angles | 4. |
| 5. @$\begin{align}\angle CDA \cong \angle CDB\end{align}@$ | 5. |
| 6. | 6. Reflexive PoC |
| 7. @$\begin{align}\triangle CDA \cong \triangle CDB\end{align}@$ | 7. |
| 8. @$\begin{align}\overline{AC} \cong \overline{CB}\end{align}@$ | 8. |
Review (Answers)
Click HERE to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
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189668 | https://www.cs.cmu.edu/afs/cs/academic/class/16741-s07/www/lectures/Lecture13.pdf | Lecture 13 Foundations of Statics Foundations of statics Preview of statics Foundations Equivalence theorems Line of action Poinsot’s theorem Wrenches Lecture 13 Foundations of Statics Matthew T. Mason Mechanics of Manipulation Lecture 13 Foundations of Statics Foundations of statics Preview of statics Foundations Equivalence theorems Line of action Poinsot’s theorem Wrenches Today’s outline Foundations of statics Preview of statics Foundations Equivalence theorems Line of action Poinsot’s theorem Wrenches Lecture 13 Foundations of Statics Foundations of statics Preview of statics Foundations Equivalence theorems Line of action Poinsot’s theorem Wrenches Preview of statics ▶We will adopt Newton’s hypothesis that particles interact through forces.
▶We can then show that rigid bodies interact through wrenches.
▶Screw theory applies to wrenches.
▶Wrenches and twists are dual.
▶We also get: ▶Line of force; ▶Screw coordinates applied to statics; ▶Reciprocal product of twist and wrench; ▶Zero Moment Point (ZMP), and its generalization.
Lecture 13 Foundations of Statics Foundations of statics Preview of statics Foundations Equivalence theorems Line of action Poinsot’s theorem Wrenches What is force?
▶You cannot measure force, only its effects: deformation of structures, acceleration.
▶We could start from Newton’s laws, but instead we hypothesize: ▶A force applied to a particle is a vector.
▶The motion of a particle is determined by the vector sum of all applied forces.
▶A particle remains at rest only if that vector sum is zero.
Lecture 13 Foundations of Statics Foundations of statics Preview of statics Foundations Equivalence theorems Line of action Poinsot’s theorem Wrenches Moment of force about a line Definition ▶Let l be line through origin with direction ˆ l, ▶Let f act at x.
▶Then the moment of force (or the torque) of f about l is given by: nl = ˆ l · (x × f) Lecture 13 Foundations of Statics Foundations of statics Preview of statics Foundations Equivalence theorems Line of action Poinsot’s theorem Wrenches Moment of force about a point Definition ▶Let l be line through origin with direction ˆ l, ▶Let f act at x.
▶Then the moment of force (or the torque) of f about O is given by: nO = (x −O) × f ▶If the origin is O this reduces to n = x × f.
▶If n is moment about the origin, and nl is moment about l, and l passes through the origin, nl = ˆ l · n Lecture 13 Foundations of Statics Foundations of statics Preview of statics Foundations Equivalence theorems Line of action Poinsot’s theorem Wrenches Total force and moment ▶Consider a rigid body, and a system of forces {fi} acting at {xi} resp.
Definition The total force F is the sum of all external forces.
F = X fi Definition The total moment N is the sum of all corresponding moments.
N = X xi × fi Lecture 13 Foundations of Statics Foundations of statics Preview of statics Foundations Equivalence theorems Line of action Poinsot’s theorem Wrenches Equivalent systems of forces ▶We now develop some equivalence theorems, comparable to (or dual to) our earlier results in kinematics.
Definition Two systems of forces are equivalent if they have equal total force F and total moment N.
▶Equivalent, specifically, because they would have the same effect on a rigid body, according to Newton.
Lecture 13 Foundations of Statics Foundations of statics Preview of statics Foundations Equivalence theorems Line of action Poinsot’s theorem Wrenches Resultant Definition The resultant of a system of forces is a system comprising a single force, equivalent to the given system.
▶A question: does every system of forces have a resultant?
Lecture 13 Foundations of Statics Foundations of statics Preview of statics Foundations Equivalence theorems Line of action Poinsot’s theorem Wrenches Line of action ▶Consider a force f applied at some point x1.
▶Total force: F = f ▶Total moment: N = x1 × f.
N F x1 x2 f f line of action ▶Consider line parallel to f through x1, and a second point x2 on the line.
▶Force f through x2 is equivalent to force f through x1.
▶So point of application is more than you need to know . . .
Definition The line of action of a force is a line through the point of application, parallel to the force.
Lecture 13 Foundations of Statics Foundations of statics Preview of statics Foundations Equivalence theorems Line of action Poinsot’s theorem Wrenches Bound and free vectors ▶When you first learned about vectors (in high school?) you learned they aren’t attached anywhere.
We refer to those as free vectors.
▶We can also define bound vectors, specifically a vector bound to a point, called a point vector, and a vector bound to a line, called a line vector.
▶So a force is a line vector.
Lecture 13 Foundations of Statics Foundations of statics Preview of statics Foundations Equivalence theorems Line of action Poinsot’s theorem Wrenches Resultant of two forces ▶Let f1 and f2 act along L1 and L2 respectively.
▶Slide f1 and f2 along their respective lines of action to the intersection (if any) ▶Resultant: the vector sum f1 + f2, acting at the intersection.
L1 L2 f1 f2 f1 + f2 ▶So almost every system of forces in the plane has a resultant. Sort of like how almost every motion is a rotation. Can it be extended? Does every system of forces have a resultant?
Lecture 13 Foundations of Statics Foundations of statics Preview of statics Foundations Equivalence theorems Line of action Poinsot’s theorem Wrenches Change of reference Using reference Q or R, a system is described by FQ = X fi NQ = X (xi −Q) × fi FR = X fi NR = X (xi −R) × fi From which it follows FR =FQ NR −NQ = X (Q −R) × fi which gives NR =NQ + (Q −R) × F Lecture 13 Foundations of Statics Foundations of statics Preview of statics Foundations Equivalence theorems Line of action Poinsot’s theorem Wrenches Couple ▶Is a moment like a force? Can you apply a moment?
Does it have a line of action?
Definition A couple is a system of forces whose total force F = P fi is zero.
▶So a couple is a pure moment.
▶Notice that the moment N of a couple is independent of reference point. N is a free vector.
▶Does a couple have a resultant? No! This answers the previous question: Not every system of forces has a resultant.
▶For an arbitrary couple, can you construct an equivalent system of just two forces?
Lecture 13 Foundations of Statics Foundations of statics Preview of statics Foundations Equivalence theorems Line of action Poinsot’s theorem Wrenches Equivalence theorems ▶Our goal: to define a wrench, and show that every system of forces is equivalent to a wrench.
▶Analogous to the earlier notes on kinematics, resulting in definition of twist.
Theorem For any reference point Q, any system of forces is equivalent to a single force through Q, plus a couple.
Proof.
▶Let F be the total force; ▶let NQ be the total moment about Q.
▶Let new system be F at Q, plus a couple with moment NQ.
Lecture 13 Foundations of Statics Foundations of statics Preview of statics Foundations Equivalence theorems Line of action Poinsot’s theorem Wrenches Two forces are sufficient Theorem Every system of forces is equivalent to a system of just two forces.
Proof.
▶Given arbitrary F and N, construct equivalent force and couple, comprising three forces in total.
▶Move couple so that one of its forces acts at same point as F.
▶Replace those two forces with their resultant.
Lecture 13 Foundations of Statics Foundations of statics Preview of statics Foundations Equivalence theorems Line of action Poinsot’s theorem Wrenches Planar system with nonzero F has a resultant Theorem A system consisting of a single non-zero force plus a couple in the same plane, i.e. a torque vector perpendicular to the force, has a resultant.
Proof.
▶Let F be the force, acting at P.
▶Let N be the moment of the couple.
▶Construct an equivalent couple as in the figure.
▶Translate the couple so −F is applied at P.
F é F N/F Lecture 13 Foundations of Statics Foundations of statics Preview of statics Foundations Equivalence theorems Line of action Poinsot’s theorem Wrenches Poinsot’s theorem Theorem (Poinsot) Every system of forces is equivalent to a single force, plus a couple with moment parallel to the force.
Proof.
▶Let F and N be the given force and moment. We can assume nonzero F, else the theorem is trivially true.
▶Decompose the moment: N∥parallel to F, and N⊥ perpendicular to F.
▶Since planar system with nonzero force has a resultant, replace F and N⊥by a single force F′ parallel to F.
▶The desired system is F′ plus a couple with moment N∥.
Lecture 13 Foundations of Statics Foundations of statics Preview of statics Foundations Equivalence theorems Line of action Poinsot’s theorem Wrenches Wrench Definition A wrench is a screw plus a scalar magnitude, giving a force along the screw axis plus a moment about the screw axis.
▶The force magnitude is the wrench magnitude, and the moment is the twist magnitude times the pitch.
▶Thus the pitch is the ratio of moment to force.
▶Poinsot’s theorem is succinctly stated: every system forces is equivalent to a wrench along some screw.
Lecture 13 Foundations of Statics Foundations of statics Preview of statics Foundations Equivalence theorems Line of action Poinsot’s theorem Wrenches Screw coordinates for wrenches ▶Let f be the magnitude of the force acting along a line l, ▶Let n be the magnitude of the moment about l.
▶The magnitude of the wrench is f.
▶Recall definition in terms of Plücker coordinates: w = fq w0 = fq0 + fpq where (q, q0) are the normalized Plücker coordinates of the wrench axis l, and p is the pitch, which is defined to be p = n/f Lecture 13 Foundations of Statics Foundations of statics Preview of statics Foundations Equivalence theorems Line of action Poinsot’s theorem Wrenches Screw coordinates for wrenches demystified ▶Let r be some point on the wrench axis q0 = r × q ▶With some substitutions . . .
w = f w0 = r × f + n ▶which can be written: w = f w0 = n0 where n0 is just the moment of force at the origin.
▶Screw coordinates of a wrench are actually a familiar representation (f, n0).
▶Wrenches form a vector space. You can scale and add them, just as with differential twists.
Lecture 13 Foundations of Statics Foundations of statics Preview of statics Foundations Equivalence theorems Line of action Poinsot’s theorem Wrenches Reciprocal product of twist and wrench Reciprocal product: (ω, v0) ∗(f, n0) = f · v0 + n0 · ω The power produced by the wrench (f, n0) and differential twist (ω, v0).
A differential twist is reciprocal to a wrench if and only if no power would be produced.
Repelling if and only if positive power.
Contrary if and only if negative power.
Lecture 13 Foundations of Statics Foundations of statics Preview of statics Foundations Equivalence theorems Line of action Poinsot’s theorem Wrenches Force versus motion ▶Wrench coordinates and twist coordinates seem to use different conventions: ▶For twists, rotation is first. For wrenches, the opposite.
▶For twists, pitch is translation over rotation, the opposite.
▶But these seeming inconsistencies are not a peculiar convention. They reflect deep differences between kinematics and statics. For example, consider the meaning of screw axis—the line—in kinematics and in statics. In kinematics, it is a rotation axis. In statics, it is a line of force.
Lecture 13 Foundations of Statics Foundations of statics Preview of statics Foundations Equivalence theorems Line of action Poinsot’s theorem Wrenches Comparing motion and force Motion Force A zero-pitch twist is a pure rotation.
A zero-pitch wrench is a pure force.
For a pure translation, the direction of the axis is de-termined, but the location is not.
For a pure moment, the direction of the axis is de-termined, but the location is not.
A differential translation is equivalent to a rotation about an axis at infinity.
A couple is equivalent to a force along a line at infinity.
In the plane, any motion can be described as a ro-tation about some point, possibly at infinity.
In the plane, any system of forces reduces to a sin-gle force, possibly at infin-ity.
Lecture 13 Foundations of Statics Foundations of statics Preview of statics Foundations Equivalence theorems Line of action Poinsot’s theorem Wrenches Zero Moment Point The Zero Moment Point (ZMP) is a concept used in legged locomotion. For the simplest cases of a horizontal support surface, and a humanoid standing at rest, the ZMP coincides with the Center of Pressure, where the resultant of contact forces intersects the ground plane, inside the support polygon. |
189669 | https://pmc.ncbi.nlm.nih.gov/articles/PMC8409399/ | The nonsmokers’ and smokers’ pathways in lung adenocarcinoma: Histological progression and molecular bases - PMC
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Cancer Sci
. 2021 Jul 11;112(9):3411–3418. doi: 10.1111/cas.15031
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The nonsmokers’ and smokers’ pathways in lung adenocarcinoma: Histological progression and molecular bases
Koji Okudela
Koji Okudela
1 Department of Pathology, Graduate School of Medicine, Yokohama City University, Yokohama, China
Find articles by Koji Okudela
1,✉, Mai Matsumura
Mai Matsumura
1 Department of Pathology, Graduate School of Medicine, Yokohama City University, Yokohama, China
Find articles by Mai Matsumura
1, Hiromasa Arai
Hiromasa Arai
2 Devision of General Thoracic Surgery, Kanagawa Cardiovascular and Respiratory Center Hospital, Yokohama, China
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2, Tetsukan Woo
Tetsukan Woo
3 Devision of Thoracic Surgery, Yokohama City University Medical Center Hospital, Yokohama, China
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3
Author information
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Copyright and License information
1 Department of Pathology, Graduate School of Medicine, Yokohama City University, Yokohama, China
2 Devision of General Thoracic Surgery, Kanagawa Cardiovascular and Respiratory Center Hospital, Yokohama, China
3 Devision of Thoracic Surgery, Yokohama City University Medical Center Hospital, Yokohama, China
Correspondence, Koji Okudela, Department of Pathology, Yokohama City University, Graduate School of Medicine, 3‐9 Fukuura, Kanazawa‐ku, Yokohama, 236‐0004, Japan. Email: kojixok@yokohama-cu.ac.jp
✉
Corresponding author.
Revised 2021 Jun 12; Received 2021 May 18; Accepted 2021 Jun 13; Issue date 2021 Sep.
© 2021 The Authors. Cancer Science published by John Wiley & Sons Australia, Ltd on behalf of Japanese Cancer Association.
This is an open access article under the terms of the License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non‐commercial and no modifications or adaptations are made.
PMC Copyright notice
PMCID: PMC8409399 PMID: 34143937
Abstract
There could be two carcinogenetic pathways for lung adenocarcinoma (LADC): the nonsmokers’ pathway and the smokers’ pathway. This review article describes the two pathways with special reference to potential relationships between histological subtypes, malignant grades, and driver mutations. The lung is composed of two different tissue units, the terminal respiratory unit (TRU) and the central airway compartment (CAC). In the nonsmokers’ pathway, LADCs develop from the TRU, and their histological appearances change from lepidic to micropapillary during the progression process. In the smokers’ pathway, LADCs develop from either the TRU or the CAC, and their histological appearances vary among cases in the middle of the progression process, but they are likely converged to acinar/solid at the end. On a molecular genetic level, the nonsmokers’ pathway is mostly driven by EGFR mutations, whereas in the smokers’ pathway, approximately one‐quarter of LADCs have KRAS mutations, but the other three‐quarters have no known driver mutations. p53 mutations are an important factor triggering the progression of both pathways, with unique molecular alterations associated with each, such as MUC21 expression and chromosome 12p13‐21 amplification in the nonsmokers’ pathway, and HNF4α expression and TTF1 mutations in the smokers’ pathway. However, investigation into the relationship between histological progression and genetic alterations is in its infancy. Tight cooperation between traditional histopathological examinations and recent molecular genetics can provide valuable insight to better understand the nature of LADCs.
Keywords: lung adenocarcinoma, micropapillary, solid/acinar, progression, smoking
It has been supposed there could be two carcinogenetic pathways for lung adenocarcinoma (LADC): the nonsmokers’ pathway and the smokers’ pathway. This review article describes the two pathways with special reference to potential relationships between histological subtypes, malignant grades, and driver mutations
1. INTRODUCTION
Lung adenocarcinoma (LADC) shows considerable heterogeneity in patients’ characteristics, clinical courses, histological appearances, and molecular alternations. It is needed to clearly describe their biological nature for precision medicine.
Recent efforts in the field of molecular genetics have uncovered essential driver oncogenes, including EGFR, KRAS, BRAF, ALK, ROS1, RET, and NRG1, that can be targets for newly developed therapeutic agents.1, 2, 3, 4, 5, 6, 7 Subtyping of LADC based on the driver mutations is beneficial in a clinical setting and is becoming increasingly common. However, the driver mutations themselves do not seem to be direct determinants for malignant grades, 7, 8 as subtyping solely based on the driver mutations may not be enough to support a prognosis. On the other hand, traditional histological subtyping is informative in terms of identifying histogenesis and malignant grades.7
It has been supposed there could be two carcinogenetic pathways for LADC: the nonsmokers’ pathway and the smokers’ pathway. This review article describes the two pathways with special reference to potential relationships between histological subtypes, malignant grades, and driver mutations.
2. THE TWO PUTATIVE CARCINOGENETIC PATHWAYS
Current research suggests that there are two distinct pathways involved in the development of LADC in smokers and nonsmokers.7 Recently, Yatabe et al proposed a theory that the lung is composed of two different tissue units, the terminal respiratory unit (TRU) and the central airway compartment (CAC).7, 9, 10 The TRU includes the distal/terminal bronchiole to the alveoli and mainly participates in gas exchange, whereas non‐TRU/CAC includes the trachea, bronchus, and the proximal/lobular bronchioles, which are responsible for directing gas into the alveoli. Most LADCs are developed from the TRU, which constantly expresses thyroid transcription factor 1 (TTF1).7 TRU‐type LADCs predominantly occur in nonsmokers. The predisposition to nonsmokers is particularly interesting, as it is quite different from the other histological types, such as squamous cell, small cell, and large cell carcinomas.7 In contrast, TTF1‐negative, non‐TRU/CAC–type LADCs preferentially occur in smokers.7 Thus, this TRU/non‐TRU concept is a concise theory to better understand the histogenesis of the nonsmokers’ and smokers’ pathways.
3. A PROPOSAL OF FIVE ESSENTIAL GROUPS FOR LADCS
The TRU/non‐TRU concept is a theory based on histogenesis. On the other hand, the nonsmokers’/smokers’ concept is a theory to describe the potential effects of carcinogenetic stimuli on the development/progression of cancers. Actually, TRU‐type LADCs can develop in both smokers and nonsmokers and can differentially progress each other. Thus, we have been considering that the TRU/non‐TRU classification is not enough to better understand the tumor progression. To improve this, we here propose five groups based on histological appearances, which are modified from our previous publications,11, 12 and describe them while linking together the nonsmokers’/smokers’ pathways, the TRU/non‐TRU concept, patients’ baseline characteristics, clinical courses, and driver mutations (Table1).
TABLE 1.
Essential clinicopathological features in the five groups (A‐E) proposed
| | Group A (296) | Group B (18) | Group C (97) | Group D (65) | Group E (230) |
:--- :--- :--- |
| Histological | Lepidic/papillary | With mucinous cribriform | With micropapillary | Mucinous/enteric | Acinar/solid |
| Cytological | TRU | TRU | TRU | Non‐TRU | TRU/non‐TRU |
| Immunohistochemical | TTF1+/HNF4α‐ | TTF1+/HNF4α‐ | TTF1+/HNF4α‐ | TTF1‐/HNF4α+ | TTF1+‐/HNF4α+‐ |
| Cell growth (Ki‐67 LI, mean±SD) | Weak (0.08±0.11) | Moderate (0.14±0.09) | Moderate (0.15±0.12) | Moderate (0.23±0.22) | Strong (0.35±0.18) |
| Frequency sW (s≤I/s≥II) | 42.0% (54.3%/8.9%) | 2.5% (2.1%/3.6%) | 13.8% (11.5%/20.1%) | 9.3% (9.5%/8.3%) | 32.4% (22.5%/59.5%) |
| Age median (range) | 68 (28‐86) | 61 (29‐79) | 73 (31‐82) | 68 (43‐84) | 69 (36‐87) |
| Gender M/F | 0.7 | 1.3 | 0.42 | 1.8 | 3.5 |
| Smoking S/NS | 0.6 | 0.3 | 0.3 | 1.5 | 7.3 |
| Prognosis (5 y‐DFS sW/s≤I) | Favorable (92.6%/94.3%) | Worse (79.8%/100%) | Worst (49.0%/61.3%) | Worse (54.5%/70.0%) | Worst (46.6%/63.2%) |
| Main drivers | EGFR | ALK/ROS1 | EGFR | KRAS/NRG1 | KRAS |
| Potential progressors | | | p53 loss27; CXCL14 gain;32 E‐cadherin loss, axin1 gain, wnt signal gain;34 MUC21 gain;16 DYRK2 gain;31 c‐met gain33 | TTF1 loss;46, 47 pulmonary surfactant system loss46 | p53 loss;12, 41 DUSP6 loss;43 S100A11 gain;37 FXYF3 loss;42 HDAC9 loss;39 miR31 loss;40 CTSL1 loss;44 TPM1 loss:45 CLIC4 loss38 |
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Lung adenocarcinoma patients who underwent surgical operation in Kanagawa prefectural cardiovascular center hospital from 1994 to 2013 (706 cases in total, 514 pathological stage 0/I and 192 II/III) were subjected. Number of cases examined in each of the groups is shown parentheses after the alphabets. Pathological stages were determined according to the AJCC Cancer Staging Manual (8th edition).50 Superscript numbers indicate the reference numbers.
Abbreviations: 5y‐DFS, 5‐y disease‐free survival; F, female; LI, labeling index; M, male; NS, nonsmoker; S, smoker; sW, whole pathological stage; s≤I, pathological stage 0 and I; S≥II, pathological stage II and III; TRU, terminal respiratory unit.
Briefly, group A is defined as lepidic or papillary dominant LADC without any mucin‐producing element or micropapillary element (according to the WHO classification system,7 histological elements less than 5% were ignored [judged as none]); group B as LADC with acinar element of mucinous cribriform pattern; group C as LADC with micropapillary elements; group D as mucinous adenocarcinoma (both invasive and in situ) and/or enteric adenocarcinoma; and group E as conventional acinar (not mucinous cribriform pattern) and/or solid dominant LADC. Representative histological appearances are shown with references to the nonsmokers’/smokers’ pathways, essential molecular alterations, and the potential between‐group crosstalk in Figure1. Specific features in detail for each of the five groups are as follows:
FIGURE 1.
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A scheme of histological progression of lung adenocarcinomas (LADCs) in the nonsmokers’ (left panels, blue arrows) and smokers’ (right panels, red arrows) pathway is shown. In the smokers’ pathway, group A (lepidic histology) develops from the terminal respiratory unit (TRU) with EGFR mutations, and some of them can progress to group C (micropapillary) through accumulations of second molecular alterations. Group B (acinar/cribriform with mucin) may directly develop from the TRU with ALK mutations. In the smokers’ pathway, group D (mucinous subtype) develops from the non‐TRU/central airway compartment (CAC), where one major driver in the smoker's pathway is KRAS. Some can progress to group E (conventional acinar/solid) through second alterations. Alternatively, there are putative extra‐bypassing pathways. Under exposing to smoking stimuli, group A can progress to group E (orange arrow). Also, through acquired thyroid transcription factor 1 (TTF1) inactivation, group A can progress to group D (dashed orange arrow). Scale bars, 50 µm
3.1. Group A
Group A includes TRU‐type LADCs that typically affect female nonsmokers (Table1), mostly show lepidic‐dominant histology including adenocarcinoma in situ and minimally invasive adenocarcinomas, and occasionally show papillary‐dominant histology. LADCs of this group are generally slow growing (Table1) and not aggressive; hence, they are surgically operable in most cases. Thus, pathologists see this type of LADCs in surgical specimens frequently, where they comprise 42% (Table1). Surgical removal is enough to completely control this group in most cases, and it ultimately results in favorable outcomes (Figure2). Although majority of this group of LADCs have EGFR mutations (Table2 and Figure3), EGFR tyrosine kinase inhibitors (TKIs) are usually not needed because of the favorable postoperative outcomes.13
FIGURE 2.
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Kaplan‐Meier's disease‐free survival curves from whole (A) and pathological stage 0/I (pStage 0/I) lung adenocarcinomas (LADCs) (B) are shown. A total of 706 cases who underwent surgical resection in Kanagawa Prefectural Cardiovascular and Respiratory Center Hospital from 1994 to 2013 were examined: 514 stage 0/I (279 group A, 11 group B, 59 group C, 49 group D, and 116 group E), 192 stage II/III (17 group A, 7 group B, 38 group C, 16 group D, and 114 group E). Pathological stages were determined according to the AJCC Cancer Staging Manual 8th edition50
TABLE 2.
Frequencies (%) of driver mutations in the five groups (A‐E) proposed
| | A (184) | B (15) | C (79) | D (46) | E (166) |
:--- :--- :--- |
| EGFR | 72.3 | 0.0 | 74.7 | 0.0 | 11.5 |
| ERBB2 | 4.9 | 0.0 | 1.3 | 0.0 | 1.8 |
| MET | 2.7 | 0.0 | 5.1 | 0.0 | 1.2 |
| ALK | 1.1 | 60.0 | 2.5 | 0.0 | 1.2 |
| ROS1 | 1.1 | 20.0 | 0.0 | 0.0 | 0.0 |
| RET | 0.0 | 6.7 | 0.0 | 0.0 | 0.0 |
| BRAF | 0.5 | 0.0 | 1.3 | 0.0 | 3.6 |
| KRAS | 2.2 | 0.0 | 0.0 | 55.4 | 18.1 |
| NRG1 | 0.0 | 0.0 | 0.0 | 10.9 | 0.0 |
| NONE | 13.6 | 13.3 | 16.5 | 34.8 | 63.3 |
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Lung adenocarcinomas surgically resected in Kanagawa prefectural cardiovascular center hospital were examined. Number in each of the groups is shown in parentheses after the alphabets.
FIGURE 3.
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Frequencies of driver mutations are shown in each of the groups. A difference in the driver mutations is remarkable between the groups. EGFR mutations are mostly seen in groups A and C, ALK and ROS1 mutations are seen in group B, and KRAS mutations are more commonly seen in group D, followed by group E
3.2. Group B
This group includes TRU‐type LADCs that entirely or partially show cribriform and solid elements with mucin production. This group affects relatively young nonsmokers (Table1) and shows relatively favorable prognosis (Figure2). Gender predisposition seems relatively weak (Table1). This group is rare and comprises 2.5% of all surgically removed LADCs (Table1). A particular feature is frequent fusion gene mutations, such as ALK and ROS1 (Table2 and Figure3). This type can be described as “solid LADC with mucin production,” “acinar LADC with cribriform structure with mucin production,” or sometimes as “signet ring cell carcinoma,” in pathological diagnosis reports.
3.3. Group C
As group A, group C includes TRU‐type LADCs that predominantly affect female nonsmokers. This type has a micropapillary element in lepidic or papillary backgrounds, where proportions of the micropapillary element vary among cases, but generally are not so large (typically 5 to 25%) in surgically removed LADCs.13, 14 LADCs of this group are usually described as “lepidic or papillary‐dominant LADC with micropapillary element” or simply as “lepidic or papillary‐dominant LADC” or “minimally invasive adenocarcinoma” in pathological diagnosis reports, and they comprise 13.8% of surgically removed LADCs (Table1). Proliferating activities are generally not as strong (Table1), but they often show strong lymphatic canal and vascular involvements and aggressive clinical courses 13, 15 (Figure2). Most inoperable cases from nonsmokers belong to this group.13, 16 Fortunately, this group generally has EGFR mutations (Table2 and Figure3) and can respond well to EGFR‐TKI treatments.13, 15, 17, 18
3.4. Group D
This group exclusively comprises specific histological subtypes of mucinous LADC (invasive or in situ) and enteric LADC. They consist of tall columnar neoplastic cells that are usually mucin producing. This group is negative for TTF1 and positive for hepatocyte nuclear factor 4α (HNF4α), an important transcription factor in the upper digestive tract epithelia, implying their gastric/intestinal differentiation; hence they are categorized as non‐TRU–type.19 This group is infrequent and comprises 9.3% of surgically removed LADCs (Table1). LADCs of this group preferentially develop in male smokers, but gender difference and smoker predisposition seems to be not so significant. This group shows relatively poor clinical courses (Figure2). LADCs of this group are frequently affected by KRAS mutations but almost never by EGFR mutations (Table2 and Figure3).7, 10, 19, 20 Interestingly, NRG1 mutations are specific to group D.21 Another particular feature is a strong relationship to pulmonary fibrosis.20 Most of pulmonary fibrosis patients are smokers.20 Smoking‐related carcinogens, chronic cellular damage, and tissue remodeling might promote this group of LADC in cooperation. LADCs of this group can be described as “mucinous LADC,” “enteric LADC,” or maybe sometimes “acinar LADCs” in pathological diagnosis reports.
3.5. Group E
The fifth group is typically observed in male heavy smokers. This group comprises 32.4% of all surgically removed LADCs (Table1). LADCs of this group histologically show acinar or solid architecture, where neoplastic cells tend to be larger and show more remarkable nuclear atypism and polymorphism than the other groups.12 Noteworthily, 12.3% of LADCs in this group are negative for both TTF1 and HNF4α (our original data), suggesting their poor degree of differentiation. Proliferating activity is generally high, with a Ki‐67 labeling index of more than 0.3 (Table1). This group shows significantly worse clinical courses (Figure2). Genetically, 18.1% of LADCs have KRAS mutations, and also small proportions have EGFR or ALK mutations (Table2, Figure3). However, more than 60% of LADCs in this group have no known driver mutations (Table2, Figure3). Thus, due to its heterogeneity, group E might be the terminal of the different pathways. LADCs of this group can be described as “acinar dominant LADC,” “solid dominant LADC,” or “poorly differentiated LADC” in pathological diagnosis reports.
4. TUMOR PROGRESSION IN THE NONSMOKERS’ PATHWAY
A micropapillary element is an essential determinant for the malignant activity in TRU‐type LADCs.16, 17, 22, 23 As mentioned previously, group C has EGFR mutations as frequently as group A; both are TRU‐type LADCs and commonly share a lepidic (or papillary) element. Thus, it is suggested that a micropapillary element could generate from lepidic (or papillary) elements. So far, pathologists have investigated morphological features of micropapillary elements and suggested that a micropapillary element is a structure resulting from tumor cells’ focal stacking to form pseudopapillary projections without fibrovascular stalks.17, 24, 25 To form such structures, neoplastic cells are inevitably anchorage independent, detach from basement membranes, can grow, and simultaneously have to retain epithelial polarity and an intercellular adhesion system partially.13, 23, 24, 25, 26 It is essential to question how lepidic (or papillary) elements acquire the micropapillary phenotype in terms of their molecular basis.14, 23, 24, 25, 27 p53 mutations can be an important factor to trigger this process,28, 29, 30 but there also seem to be additional unique events. Our recent study demonstrated differentially expressed genes in micropapillary elements compared with lepidic elements.31 The results showed some alterations in adhesion molecules, basement membrane materials, and kinases.31 In particular, overexpression of oligo‐glycosylated MUC21 protein 22 and amplification of chromosome 12q13‐21 locus covering CDK4, MDM2, and DYRK2 genes 31 were suggested to participate in producing micropapillary elements. Although there are no other studies that comprehensively compare molecular profiles between micropapillary and background lepidic (or papillary) elements in individual tumors, several studies have shown differences in molecular alterations (genetic mutations) between high‐grade and low‐grade components of LADCs (that were not specified as micropapillary).28 They also demonstrated molecular alterations likely to be involved in producing micropapillary morphology, such as gain of CXCL14, MET, AXIN1, and WNT family proteins 18, 26, 32, 33, 34 (Table1). The mechanisms behind the molecular alterations and how these alterations produce micropapillary elements are still largely unclear. Uncovering these, as well as carcinogens which promote this process, could lead to the establishment of novel therapeutic and prevention strategies.
5. TUMOR PROGRESSION IN THE SMOKERS’ PATHWAY
The smokers’ pathway appears to be more complex. Poorly differentiated LADCs (group E) can arise from other groups mentioned, not only non‐TRU/CAC–type LADCs (group D) but also TRU‐type LADCs (group A), as group E includes both TTF1‐negative (non‐TRU) and positive (TRU) LADCs (Table1). Interestingly, in group E, even in TTF1‐positive LADCs, EGFR mutations are rather rare (Table2 and Figure3). The frequency of KRAS mutations, that are the most common driver mutations in the smokers’ pathway, is also not high (Table2 and Figure3),12, 35 suggesting that there could be another alternative tumor‐driving system.7, 28 We propose a hypothesis that there may be no single strong leading mutation in LADCs in the smoker's pathway. Several tiny mutations each could participate in small quantities, the sum of which could be equivalent to one driver mutation to promote tumor development. In fact, smokers’ LADCs have been shown to accumulate more genetic mutations than nonsmokers’.28, 36 It is of great interest to uncover how such small mutations collectively drive the driver mutation–negative smokers’ LADCs. Concentrating efforts in molecular genetics and bioinformatics will solve this molecular puzzle in the near future.
Apart from driver mutations, regarding tumor progression, p53 mutations are an important trigger factor,29, 30 and disruptions of oncogenic KRAS‐induced negative feedback systems, such as downregulation of DUSP6, miR‐31, and upregulation of S100A11, are common events in the smokers’ pathway.37, 38, 39, 40, 41, 42, 43, 44, 45 Moreover, TTF1 mutations and surfactant protein gene mutations are also reported to be unique to the smokers’ pathway.46, 47
6. EXTRA‐BYPASSING PATHWAYS
Alternatively, there could be extra‐bypassing pathways. Actually, LADCs having both TTF1‐positive lepidic and HNF4α‐positive mucinous components are occasionally seen. Interestingly, Matsubara D et al demonstrated that mucinous LADCs with TTF1‐positive lepidic component more often had TTF1 gene mutations and methylations than pure mucinous LADCs.47 The findings suggest that there could be a bypass from A to D (Figure1). Also, as mentioned afore, group E might be the terminal of the different pathways. Under exposing to smoking stimuli, different groups might progress to group E (Figure1).
7. ISSUES IN RECENT LUNG CANCER RESEARCH
Large‐scale genetic analyses have provided us with a large volume of information and are helping to uncover a fuller picture of the molecular basis of LADC. However, more care should be taken regarding the processing of analytical results. For example, it is important to take into consideration if the tumor is definitely negative for driver mutations. Analytical results may be false negatives due to extremely small neoplastic cell contents. In general, LADCs, particularly, poorly differentiated ones, have many leukocytes and fibroblasts, and hence this “noise” can easily result in false negatives. Purification of neoplastic cells from tumor tissues is an important process to improve accuracy of mutational analyses. At present, histological (or cytological) appearance is the most reliable biological marker that detects neoplastic cells. However, using artificial intelligence to detect neoplastic cells and the automatic operation of microdissection systems can improve accuracy.
8. FUTURE PERSPECTIVE
Again, the recent advance in molecular genetics has uncovered a lot of molecular targets for therapeutic agents. However, this progress seems to have been slowing down in recent years. Going forward, we should focus on molecular alterations responsible for tumor progression, which would be targets for next‐generation therapies. For such alterations, we here suggest a term “progressor.” We know intratumor subclonal heterogeneity and passenger mutations (nonfunctional noise) are critical obstacles against successful detection of essential molecular alterations to promote tumor progression.48, 49 Thus, simple large‐scale analyses on bulky tumor samples are not sufficient for the success. As is shown in Figure4, if we comparatively analyze high‐grade components and background low‐grade components from identical tumors, it alleviates the issue of noise. Microdissection systems can be the most dependable way to reach such targets.
FIGURE 4.
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A scheme for progression of lung adenocarcinoma (LADC). During the progression process, one LADC can produce genetically heterogenous subpopulations. At first, driver mutations transform normal counterpart cells (N) to low‐grade neoplastic cells (L). While the neoplastic cells are proliferating, many additional mutations can occur, most of which might be nonfunctional passenger mutations, and some of which can be true progressors to produce high‐grade elements (H)
9. SUMMARY AND CONCLUSION
There are the two major pathways in LADC carcinogenesis. In the nonsmokers’ and smokers’ pathways, the terminals are micropapillary and acinar/solid histology, respectively. LADCs are highly heterogenous even in an identical tumor. Different genetic alterations can participate in each pathway, and identifying essential molecular alterations promoting tumor progression is a critical task. To meet the next goal, focusing on high‐grade elements based on careful histological examinations is necessary.
CONFLICT OF INTEREST STATEMENT
The authors have no conflict of interest.
ACKNOWLEDGEMENTS
We thank Hideaki Mitsui and Takeshisa Suzuki (Department of Pathology, Yokohama City University) and Motoki Sekiya, Misaki Sugiyama, and Emi Honda (Division of Pathology, Kanagawa Prefectural Cardiovascular and Respiratory Center Hospital) for their technical assistance.
Okudela K, Matsumura M, Arai H, Woo T. The nonsmokers’ and smokers’ pathways in lung adenocarcinoma: Histological progression and molecular bases. Cancer Sci. 2021;112:3411–3418. 10.1111/cas.15031
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Abstract
1. INTRODUCTION
2. THE TWO PUTATIVE CARCINOGENETIC PATHWAYS
3. A PROPOSAL OF FIVE ESSENTIAL GROUPS FOR LADCS
4. TUMOR PROGRESSION IN THE NONSMOKERS’ PATHWAY
5. TUMOR PROGRESSION IN THE SMOKERS’ PATHWAY
6. EXTRA‐BYPASSING PATHWAYS
7. ISSUES IN RECENT LUNG CANCER RESEARCH
8. FUTURE PERSPECTIVE
9. SUMMARY AND CONCLUSION
CONFLICT OF INTEREST STATEMENT
ACKNOWLEDGEMENTS
REFERENCES
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189670 | https://creativealgebra.quora.com/How-to-expand-x-y-2 | How to expand (x-y) ^2 - Creative Algebra - Quora
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How do you expand (x-y) ^2?
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MyMathYourMath
Former Lead Instructor at Mathnasium (2018–2019)
·3y
Use the FOIL (firsts, outers, inners, lasts) method:
(x−y)2=(x−y)(x−y)=x 2−x y−x y+y 2=x 2−2 x y+y 2(x−y)2=(x−y)(x−y)=x 2−x y−x y+y 2=x 2−2 x y+y 2
as desired.
Edward M Young
Dermatologist at Veteran's Administration Hospital (2015–present)
·3y
Q = (x - y)^2 = (x - y)(x -y) = x^2 - 2xy + y^2
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3rd grade math (TX TEKS)
Course: 3rd grade math (TX TEKS)>Unit 2
Lesson 9: Money
Counting American coins
Counting dollars
Identify the value of US coins and dollars
Count money (U.S.)
Counting money with US coins and dollars
Count money with US coins and dollars
Math>
3rd grade math (TX TEKS)>
Addition and subtraction>
Money
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Count money with US coins and dollars
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(Choice D) $8.46 D $8.46
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189672 | https://www.mathsisfun.com/geometry/circle.html | Circle
| | |
--- |
| | A circle is easy to make: Draw a curve that is "radius" away from a central point. And so: All points are the same distance from the center. |
You Can Draw It Yourself
Put a pin in a board, put a loop of string around it, and insert a pencil into the loop. Keep the string stretched and draw the circle!
Play With It
Try dragging the point to see how the radius and circumference change.
(See if you can keep a constant radius!)
Radius, Diameter and Circumference
The Radius is the distance from the center to the edge.
The Diameter goes straight across the circle, through the center.
The Circumference is the distance once around the circle.
And here is the really cool thing:
When we divide the circumference by the diameter we get 3.14159265...which is the number π (Pi)
So when the diameter is 1, the circumference is 3.14159265
We can say:
Circumference = π × Diameter
Example: You walk around a circle which has a diameter of 100m, how far have you walked?
Distance walked = Circumference = π × 100m
= 314m (to the nearest m)
Also note that the Diameter is twice the Radius:
Diameter = 2 × Radius
And so this is also true:
Circumference = 2 × π × Radius
In Summary:
| | |
--- |
| × 2 | × π |
|
| | | |
---
| Radius | Diameter | Circumference |
Remembering
The length of the words may help you remember:
Radius is the shortest word and shortest measure
Diameter is longer
Circumference is the longest
Definition
| | |
--- |
| | The circle is a plane shape (two dimensional), so: |
Circle: the set of all points on a plane that are at a fixed distance from a center.
Area
The area of a circle is π times the radius squared, which is written:
A = π r2
Where
A is the Area
r is the radius
To help you remember think "Pie Are Squared" (even though pies are usually round):
Example: What is the area of a circle with radius of 1.2 m ?
Area= πr2 = π × 1.22 = 3.14159... × (1.2 × 1.2) = 4.52 (to 2 decimals)
Example: The Area of a Circular Garden
Imagine we have a circular garden with a radius of 5 meters:
Area= πr2 = π × (5 m)2 = 78.5 m2 (to 1 decimal)
Or, using the Diameter:
A = (π/4) × D2
Area Compared to a Square
A circle has about 80% of the area of a similar-width square. The actual value is (π/4) = 0.785398... = 78.5398...%
And something interesting for you to try: Circle Area by Lines
Names
Because people have studied circles for thousands of years special names have come about.
Nobody wants to say "that line that starts at one side of the circle, goes through the center and ends on the other side" when they can just say "Diameter".
So here are the most common special names:
Lines
A line that "just touches" the circle as it passes by is called a Tangent.
A line that cuts the circle at two points is called a Secant.
A line segment that goes from one point to another on the circle's circumference is called a Chord.
If it passes through the center it is called a Diameter.
And a part of the circumference is called an Arc.
Slices
There are two main slices of a circle.
The "pizza" slice is called a Sector
And the slice made by a chord is called a Segment
Quadrant
The Quadrant is a special sector with a right angle. It has a quarter of the circle's area.
Semicircle
Half a circle is called a Semicircle.
Inside and Outside
A circle has an inside and an outside (of course!). But it also has an "on", because we could be right on the circle.
Example: "A" is outside the circle, "B" is inside the circle and "C" is on the circle.
Ellipse
A circle is a "special case" of an ellipse.
765, 766, 767, 768, 769, 1764, 3232, 3233, 3234, 3235
Activity: Approximate Value For Pi
Pi Plane Unit Circle Circle Sector and Segment Circle Equations Plane Geometry Geometry Index
Copyright © 2025 Rod Pierce |
189673 | https://www.youtube.com/watch?v=NrHT1cwWYAQ | Make a Tangent Line Approximation for a Square Root Function Value
Mathispower4u
330000 subscribers
17 likes
Description
12366 views
Posted: 23 Jun 2021
This video explains how to make a linear approximation for square root function value.
1 comments
Transcript:
we're asked to find the linear approximation of f of x equals the square root of x at x equals four which means we need to find the equation of the tangent line to the function at x equals four and then we're asked to use a linear approximation to estimate f of 4.1 to do this we will substitute x equals 4.1 into the linear equation to make the approximation in order to find the equation of the tangent line we need to find the point of tangency we know the x coordinate is 4 we need to find f 4 to determine the y coordinate and then we have to find the slope of the tangent line by finding the derivative function of f of x and then evaluating the derivative at x equals 4. let's begin by determining the point of tangency since f of four is equal to the square root of four which is equal to two we know the point of tangency has an x coordinate of four and a y coordinate of two and now let's find the slope of the tangent line by evaluating the derivative function at x equals four so first f of x is equal to the square root of x which we need to write using a rational exponent in order to find the derivative because the exponent on x is one and the index is two we know the square root of x is equal to x to the power of one half and therefore the derivative of f applying the power rule of differentiation is equal to one half times x to the power of one half minus one which is equal to one half times x to the power of negative one half which is equal to one divided by two x to the power of positive one half or if we want one divided by two square root x next the slope of the tangent line is equal to f prime of four which is equal to one divided by the product of two and the square root of four which is equal to one divided by the product of two and two which is equal to one fourth so now we know the point of tangency is four comma two and the slope of the tangent line is positive one fourth let's go ahead and find the equation of the tangent line in point slope form where the form y minus y one is equal to m times the quantity x minus x sub one or in our case x sub one is equal to four y sub one is equal to two and m is equal to one-fourth this gives us y minus two equals one-fourth times the quantity x minus four let's go ahead and write the equation in slope-intercept form by distributing on the right and then adding two to both sides this gives us y minus two is equal to distributing one fourth we have one fourth x and then one fourth times negative four is negative one giving us minus one last step is to add two to both sides adding two to negative one gives us positive one we have the linear equation y equals one fourth x plus one and finally to make our linear approximation for f of 4.1 we evaluate the linear function at x equals 4.1 which gives us y equals 1 4 times 4.1 plus one which gives us 2.025 and if we compare this to the exact value of the square root of 4.1 we will see the linear approximation is a very good approximation of the true function value so we have a linear approximation of y equals 2.025 which means the square root of 4.1 is approximately 2.025 which we found is a very good approximation for the true function value i hope you found this helpful |
189674 | https://en.wikibooks.org/wiki/Structural_Biochemistry/Proteins/Introduction | Structural Biochemistry/Proteins/Introduction - Wikibooks, open books for an open world
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The Wikibooks community is developing a policy on the use of generative AI. Please review the draft policy and provide feedback on its talk page.
Contents
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Beginning
1 Amino AcidToggle Amino Acid subsection
1.1 Optical Activity
1.2 Zwitterion
1.3 Amino Acid Subdivisions
1.4 List of 20 Amino Acids
2 Alanine - Ala/ A
3 Arginine - Arg/ R
4 Asparagine - Asn/ N
5 Aspartic acid - Asp/ D
6 Cysteine - Cys/ C
7 Glutamine - Gln/ Q
8 Glutamic acid - Glu/ E
9 Glycine - Gly/ G
10 Histidine - His/ H
11 Isoleucine - Ile/ I
12 Leucine - Leu/ L
13 Lysine - Lys/ K
14 Methionine - Met/ M
15 Phenylalanine - Phe/ F
16 Proline - Pro/ P
17 Serine - Ser/ S
18 Threonine - Thr/ T
19 Tryptophan - Trp/ W
20 Tyrosine - Tyr/ Y
21 Valine - Val/ V
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From Wikibooks, open books for an open world
<Structural Biochemistry | Proteins
This page may need to be reviewed for quality.
Proteins are one of the most important macromolecules in living organisms that have many functions for biochemical processes. They are consisting almost entirely of carbon, hydrogen, oxygen, and nitrogen. The protein is a polymer of multiple monomer units called amino acid, which have many different functional groups. The 20 major amino acids, along with hundreds of other minor amino aids, sustain our lives. Proteins can have interactions with other proteins and biomolecules to form more complex structures and have either rigid or flexible structures for different functions.
Amino Acid
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Optical Activity
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All proteins or polypeptides are α amino acids. A typical α amino acid consists of a central carbon (which is the alpha carbon in this case) that is attached to an amino group (-NH2), a carboxylic acid (-COOH), a hydrogen atom, and a distinctive R group. The R groups, usually referred to as the side chains, determine the properties of each amino acid and classify amino acids into different categories. A tetrahedral carbon atom with four distinct groups is called chiral. The ability of a molecule to rotate to the polarized plane to the left is called Levorotatory, and all amino acids exhibit the same configuration as L-isomers. Although D-amino acids (D for Dextrorotatory, meaning that they rotate the plane of polarized light to the right instead), exist naturally, they are not found in proteins. Note: Since the central carbon has four distinct attached groups attached, all of amino acids are chiral except for glycine in which R group is another hydrogen atom.
Zwitterion
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An amino acid is a zwitterion when it is both "acidic and basic" (amphoteric) as a result of the two functional groups. Zwitterion is the ability of an ion to be positively charged (+) and negatively charged (-). In solid state, the carboxylic acid group deprotonates the amine function protonates, forming a zwitterion (dipolar ion). The structure of an amino acid in aqueous solution depends on the environment pH. The major form in neutral solution is the zwitterion. In strong acid (pH < 1), the predominant form is the cationic ammonium carboxylic acid. In strongly basic solutions (pH > 13), the predominant form is the deprotonated 2-aminocarboxylate ion. These forms interconvert by acid-base equilibria. For pH of about 2 to 9, an amino acid is zwitterion, for which the amino group is protonated (-NH3+) and carboxyl group is deprotonated (-COO-).
Amino Acid Subdivisions
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Twenty different side chains of amino acids have different functional groups, size, form, charge, capacity for hydrogen bond, hydrophobic nature, and chemical reactivity of proteins. The amino acids can be broadly divided into two catageories, hydrophobic and hydrophilic, according to the chemical properties of the R group. In aqueous environment, the hydrophobic amino acids are unable to participate in hydrogen bonding. They associate with one another and reside mostly inside the protein. On the other hand, hydrophilic amino acids tend to interact in the aqueous environment due to polarity. These amino acids are normally found on the exterior surface of proteins.
Amino Acids Classification
Non-polar Amino Acids
Aliphatic: glycine, alanine, valine, isoleucine, leucineAromatic: phenylalanine, tryptophan.Cyclic: Proline
Polar Amino Acids
Sulfur-Containing: cysteine, methionineHydroxyl-Containing: serine, threonineAromatic: tyrosineAcidic Amide: asparagine, glutamineCyclic Imine: histidine (90%)
Charged Amino Acids (at physiological pH)
Negative (acidic): aspartic acid, glutamic acidPositive (basic): histidine (10%), lysine, arginine
List of 20 Amino Acids
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Main article: w:List of standard amino acids
| Amino Acid | 3-Letter Abbreviation | 1-Letter Abbreviation | Class of Amino Acid (Side Chain) | Hydrophobicity Index (100 being extremely hydrophobic, 0 being neutral, and -55 being hydrophilic) | Structure | pKa of COOH group | pKa of NH3+ group | pKa of R group | Molecular Weight [g/mol] | alpha helix | beta sheet | Reverse turn |
--- --- --- --- --- ---
| Glycine | Gly | G | Aliphatic, nonpolar | Neutral (0 at pH = 2; 0 at pH = 7) | | 2.4 | 9.8 75.07 | 0.43 | 0.58 | 1.77 |
| Alanine | Ala | A | Aliphatic, nonpolar | Hydrophobic (47 at pH = 2; 41 at pH = 7) | | 2.4 | 9.9 89.1 | 1.41 | 0.72 | 0.82 |
| Valine | Val | V | Aliphatic, nonpolar | Very Hydrophobic (79 at pH = 2; 76 at pH = 7) | | 2.3 | 9.7 117.15 | 0.90 | 1.87 | 0.41 |
| Leucine | Leu | L | Aliphatic, nonpolar | Very Hydrophobic (100 at pH = 2; 97 at pH = 7) | | 2.3 | 9.7 131.18 | 1.34 | 1.22 | 0.57 |
| Isoleucine | Ile | I | Aliphatic, nonpolar | Very Hydrophobic (100 at pH = 2; 99 at pH = 7) | | 2.3 | 9.8 131.18 | 1.09 | 1.67 | 0.47 |
| Methionine | Met | M | Hydroxyl or Sulfur-Containing, nonpolar | Very Hydrophobic (74 at pH = 2; 74 at pH = 7) | | 2.1 | 9.3 149.21 | 1.30 | 1.14 | 0.52 |
| Serine | Ser | S | Hydroxyl or Sulfur-Containing, polar | Neutral (-7 at pH = 2; -5 at pH = 7) | | 2.2 | 9.2 105.09 | 0.57 | 0.96 | 1.22 |
| Cysteine | Cys | C | Hydroxyl or Sulfur-Containing, polar | Hydrophobic (52 at pH = 2; 49 at pH = 7) | | 1.9 | 10.7 | 8.4 | 121.16 | 0.66 | 2.40 | 0.54 |
| Threonine | Thr | T | Hydroxyl or Sulfur-Containing, polar | Neutral (13 at pH = 2; 13 at pH = 7) | | 2.1 | 9.1 119.12 | 0.76 | 1.17 | 0.96 |
| Proline | Pro | P | Cyclic | Hydrophilic (-46 at pH = 2; -46 at pH = 7) | | 2.0 | 9.6 115.13 | 0.34 | 0.31 | 1.32 |
| Phenylalanine | Phe | F | Aromatic | Very Hydrophobic (92 at pH = 2; 100 at pH = 7) | | 2.2 | 9.3 165.19 | 1.16 | 1.33 | 0.59 |
| Tyrosine | Tyr | Y | Aromatic | Hydrophobic (49 at pH = 2; 63 at pH = 7) | | 2.2 | 9.2 | 10.5 | 181.19 | 0.74 | 1.45 | 0.76 |
| Tryptophan | Trp | W | Aromatic | Very Hydrophobic (84 at pH = 2; 97 at pH = 7) | | 2.5 | 9.4 204.25 | 1.02 | 1.35 | 0.65 |
| Histidine | His | H | Basic | Hydrophilic at pH=2 (-42), Neutral at pH=7 (8) | | 1.8 | 9.3 | 6.0 | 155.16 | 1.05 | 0.80 | 0.81 |
| Lysine | Lys | K | Basic | Hydrophilic (-37 at pH = 2; -23 at pH = 7) | | 2.2 | 9.1 | 10.5 | 146.188 | 1.23 | 0.69 | 1.07 |
| Arginine | Arg | R | Basic | Hydrophilic (-26 at pH = 2; -14 at pH = 7) | | 1.8 | 9.0 | 12.5 | 174.2 | 1.21 | 0.84 | 0.90 |
| Aspartate | Asp | D | Acidic | Neutral at pH=2 (-18), Hydrophilic at pH=7 (-55) | | 2.0 | 9.9 | 3.9 | 133.10 | 0.99 | 0.39 | 1.24 |
| Glutamate | Glu | E | Acidic | Neutral at ph=2 (8), Hydrophilic at pH=7 (-31) | | 2.1 | 9.5 | 4.1 | 147.13 | 1.59 | 0.52 | 1.01 |
| Asparagine | Asn | N | Acidic, polar | Hydrophilic (-41 at pH = 2; -28 at pH = 7) | | 2.1 | 8.7 132.118 | 0.76 | 0.48 | 1.34 |
| Glutamine | Gln | Q | Acidic, polar | Neutral (-18 at pH = 2; -10 at pH = 7) | | 2.2 | 9.1 146.15 | 1.27 | 0.98 | 0.84 |
Alanine - Ala/ A
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Structure
Alanine (abbreviated as Ala or A) is an α-amino acid with the chemical formula HO2CCH(NH2)CH3. The α-carbon atom of alanine is bound with a methyl group (-CH3), making it one of the simplest α-amino acids with respect to molecular structure and also resulting in alanine being classified as an aliphatic amino acid. The methyl group of alanine is non-reactive and is thus almost never directly involved in protein function.
Features
Alanine is a nonessential amino acid which meant that it can be manufactured by the human body and does not need to be obtained directly through the diet. Alanine is found in a wide variety of foods, but is particularly concentrated in meats.
Functions
Alanine is the primary amino acids for sugar metabolism. It boosts up the immune system by producing antibodies, and provide energy for muscles.
Chemical Synthesis
Alanine can be manufactured in the body from pyruvate and branched chain amino acids such as valine, leucine, and isoleucine. Alanine is most commonly produced by reductive amination of pyruvate. Because transamination reactions are readily reversible and pyruvate pervasive, alanine can be easily formed and thus has close links to metabolic pathways such as glycolysis, gluconeogenesis, and the citric acid cycle. It also arises together with lactate and generates glucose from protein via the alanine cycle. Racemic alanine can be prepared via the condensation of acetaldehyde with ammonium chloride in the presence of potassium cyanide by the Strecker reaction.
Arginine - Arg/ R
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Structure
Arginine contained of a four-carbon aliphatic straight chain with the end of which is capped by a guanidinium group. With a pKa of 12.48, the guanidinium group is positively charged in neutral, acidic and even most basic environments. Therefore, arginine has basic chemical properties. Because of the conjugation between the double bond and the nitrogen lone pairs, the positive charge is delocalized and enable the formation of multiple H-bonds.
Features
Arginine is an essential amino acid that plays important role in nitrogen metabolism.
Functions
Arginine assists in wound healing and help in burn treatment. It is necessary in normal immune system activity by enhancing the production of T-cells.
Biosynthesis
Arginine is synthesized from citrulline with the presence of cytosolic enzymes argininosuccinate synthetase and argininosuccinatelyase. This is energetically costly reaction. Therefore, the synthesis of each molecule of argininosuccinate will be coupling with hydrolysis of adenosine triphosphate (ATP) to adenosine monophosphate (AMP).
Synthesis of arginine in human body occurs principally via the intestinal–renal axis, wherein epithelial cells of the small intestine, which produce citrulline primarily from glutamine and glutamate, then join with the proximal tubule cells of the kidney, which extract citrulline from the circulation and convert it to arginine, which comes back to the circulation.
Asparagine - Asn/ N
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Structure
Asparagine is polar and uncharged derivative of acidic amino acid aspartic acid or aspartate; it has a carboxamide group, which is neutral at physiological pH and can be changed to carboxylic acid by hydrolysis to form aspartate amino acid. The carboxamide group of the amino acid can form hydrogen bonds.
Functions
Asparagine, along with glutamate, is an important neurotransmitter. Since Aspartic acid and Asparigine have high concentration in the hippocampus and hypothalamus of the brain, which is important in short-term memory and emotions, the two amino acids serves essential role between the brain and the rest of the body.
Aspartic acid - Asp/ D
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Structure
Also known as aspartate, Aspartic acid is an acidic and polar amino acid that has carboxylic acid group, which loses a proton to be carboxylate group for physiological pH and has a negative charge; the carboxylic acid group of the amino acid has a pKa value of 4.1, which is a little basic than the terminal α-carboxyl group.
Features
Aspartic acid is a non-essential amino acid.
Functions
Aspartic acids is involved in transamination in which oxaloacetate and aspartate is interconvertible. It is also involved in immune system activity by promoting immunoglobulin production and antibody production. Moreover, aspartic acid protects the liver and helps in detoxification of ammonia.
Cysteine - Cys/ C
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Structure
An amino acid that is of sulfhydryl or thiol group, which is more reactive than hydroxyl group, and two of them form stable disulfide bonds. Disulfide bonds linked in cross-way to form polypeptide chain of extracellular proteins by the oxidation of two cysteine residues; the unit of two bonded cysteines is known as cystine.
Functions
Cysteine promotes iron production in iron deficiency anemia. It also assists in lung diseases by increasing production of red blood cells and red blood cells. In addition, Cystein is protective against UV light, radiation, and free radicals production.
Glutamine - Gln/ Q
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Structure
Glutamine is a polar and uncharged derivative of acidic amino acid glutamic acid or glutamate; it has a carboxamide group, which is neutral at physiological pH and can be changed to carboxylic acid by hydrolysis to form glutamate amino acid. The carboxamide group of the amino acid can form hydrogen bonds.
Functions
Glutamine is a non-essential amino acid meaning it will natually occur in the human body, and it is one of the most abundant amino acid manufacture in the body. Glutamine circulates in the blood and able to cross the blood-brain barrier directly.
Glutamine is critical in gastrointestinal system by providing energy to small intestine function. Interesting, intestine is the only organ in the body that has glutamine as a primary energy source.
Usage
Wound Healing 2. Inflammatory Bowel Disease 3. HIV/AIDS 4. Obesity 5. Peritonitis 6. Athletes 7. Cancer 8. etc.
Glutamic acid - Glu/ E
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Structure
Also known as glutamate, Gluctamic acid is a polar amino acid that has carboxylic acid group, which loses a proton to be carboxylate group for physiological pH and has a negative charge; the carboxylic acid group of the amino acid has a pKa value of 4.3, which is a little basic than the terminal α-carboxyl group and that of aspartic acid.
Function
Glutamic acid is a non-essential amino acid. It plays an important role in DNA synthesis. It also assists in wound and ulcer healing. Glutamic acid take place in the excitatory neurotransmitter and the metabolism of sugars and fats. It aids potassium move through the blood-brain barrier. Glutamic acid are a source of fuel for the brain. Glutamic acid can attach to amine group to form glutamine. The process of forming glutamine will detoxifies ammonia that the body contains.
Glutamic acid is user in correcting personality disorders and treating childhood behavioral disorders. It also take places in treating epilepsy, metal retardation, muscular dystrophy, ulcers, and hypoglycemic coma.
Glycine - Gly/ G
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Structure
Glycine is the smallest amino acid out of all 20 amino acids For this reason, it has the ability to fit into tight spaces of molecules where no other amino acid could possibly fit therefore glycine is evolutionarily conserved. Most proteins contain small amount of glycine, however collagen is one of the exception that contains 35% glycine. Thus, if glycine were cleaved from an amino acid chain composing a whole protein, it would either alter the function of that protein, or denature it entirely. It is also the only achiral amino acid since its R group is simply a H atom. In particular it does not favor the helix formation.
Functions
Glycione is a non-essential amino acids meaning the human can manufacture it in their body. It serves an important role in maintaining central nervous and digestive systems. Glycine prevents the breakdown of muscle by increase creatine, which is compound that helps build muscle mass. Glycine also keeps the skin firm and flexible. Without glycine, the skin can be damage from the UV rays, oxidation and free radical.
Glycine regulate blood sugar levels and helps provide glucose for the body.
Glycine serve as an inhibitory neurotransmitter in the central nervous system, especially in the spinal cord. When glycine binds to receptors, it activated chloride ion channels to open. As chloride ions enter the channels, the membrane becomes hyperpolarized, causing an Inhibitory postsynaptic potential (IPSP).
Histidine - His/ H
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Structure
Histidine is a basic, polar amino acid with imidazole group, which is an aromatic ring that can be of positive charge and hydrophilic. The imidazole group of the amino acid has a pKa value of 6, which can be either uncharged or positively charged for about neutral pH. The amino acid is most of time present in active sites of enzymes for the imidazole group can act as acid or base for chemical reactions.
Functions
Histidine is found to be highly concentrated in hemoglobin; thus, it aids in treatment of anemia and maintain optimal blood PH. Also, histidine is the precursor of histamine, which is involved in local immune responses.
Histidine is an essential amino acid meaning the body cannot manufacture by itself. Histadine play important role in stimulating the inflammatory response of skin and mucous membranes. It also stimulates the secretion of the digestive enzymes gastrin and maintain the adequate histamine level.
Isoleucine - Ile/ I
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Structure
Isoleucine is a nonpolar, aliphatic or hydrophobic amino acid that has two chiral centers for α-carbon atom and the R group; the structure stabilizes water-soluble proteins by hydrophobic effect.
Functions
Isoleucine is an essential amino acid meaning the human body cannot manufacture itself. It is needed for the formation of hemoglobin and regulate blood sugar level and energy level. Isoleucine serves important role in muscle strength and endurance and is a source of energy for muscle tissues.
Leucine - Leu/ L
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Structure
Leucine has aliphatic R group. It is one of the three amino acids with branched hydrocarbon side chains (generally buried in folded proteins) and result as a nonpolar or hydrophobic amino acid. The hydrophobic effect counts for stabilization of water-soluble proteins.
Features
Leucine is an essential amino acid. It is essential in promoting growth in infant and regulating nitrogen concentration in adults.
Functions
Leucine has all functions of the amino acid Isoleucine as their similarity in branched hydrocarbon side chain. Leucine facilitates skin healing and bone healing by modulating the release of natural pain-reducers, Enkephalins. It is also a precursor of cholesterol and increases the synthesis of muscle tissues by slowing down their degradation process.
Deficiency and Excess
Deficiency of this particular amino acids can result in Hypoinsulinemia, Depression, Chronic fatigue syndrome, Kwashiorkor (or starvation), etc. Excess of Leucine leads to Ketosis.
Lysine - Lys/ K
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Structure
Lysine has a positively charged amine group chain. The ε-amino group has a significant high pKa value of about 10.8, which is more basic than the terminal α-amino group. This basic amino group is highly reactive and parcipates in the reactions at the active center of enzymes. Although the terminal ε-amino group is charged under physiological condition, the hydrocarbon side chain with three methylene group is still hydrophobic.
Features
Lysine is a naturally occurring essential amino acid in human body. It promotes optimal growth of infants and nitrogen equilibrium in adults.
Functions
Lysine can be a treatment of Herpes Simplex and virus-associated Chronic Fatigue Syndrome as it inhibits viral growth. It facilitates the formation of collagen, which is the main component of fascia, bone, ligament, tendons, cartilage and skin. It also helps in absorption of calcium, which is critical in bone growth of infants.
Deficiency and Excess
Deficiency of lysine is seen in Herpes, Chronic Fatigue Syndrome, AIDS, Anemia, hair loss, and weight loss, etc. Having excessive lysine can result in high concentration of ammonia in the blood.
Methionine - Met/ M
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Structure
Methionine is one of the two amino acids with side chain containing sulfur. Like Cysteine, the chemical linkage of the sulfur is a thiol ether. Unlike Cysteine, the sulfur do not participate in covenlent bonding to other chemicals. The high inclination of the sulfur oxidation in methionine is one of the causes of smoking-induced emphysema in the human lung tissue.
Features
Methionine is a naturally occurring essential amino acid, which plays critical role in supplying methyl group and sulfur in metabolism. It is also one of only two amino acids coded for by a single codon.
Functions
Methionine helps breakdown of fat and reduce blood cholesterol levels. It is an antioxidant that neutralizes free radicals and removes toxic waste in the liver. Synthesis of DNA and RNA requires the presence of Methionine. It is also precursors of several critical amino acids, hormones, and neurotransmittors in human body. Its AUG codon also serves as a "start" signal for ribosomal translation of messenger RNA; this means that every peptide chain began with an methionine residual at its N-terminal. It may however be removed later on by cleavage.
Deficiency and Excess
Methionine deficiency can be seen in chemical exposure and vegetarians. Severe liver disease can be result of having excessive methionine.
Phenylalanine - Phe/ F
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Structure
The side chain of Phenylalanine has a derivative of alanine and a phenyl group on the β carbon. Phenylalanine has a stronger hydrophobic characteristics compared to the other amino acids that contain aromatic side chain, tyrosine and tryptophan. Tyrosine and tryptophan are less hydrophobic than phenylalanine due to their hydroxyul and NH side groups. The property of hydrophobicity allows the structure of phenylalanine to be almost always buried in the protein. The electrons of the phenyl ring stabilizes the protein by stacking to other aromactic structures.
Features
Phenylalaine is a naturally occurring amino acid that promote growth in infants and regulate nitrogen concentration in adults.
Functions
Phenylalaine is the precursor of amino acid tyrosine, which give rise to neutrotransmiters, such as dopamine, norepinephrine and epinephrine. It can be used to manage certain types of depression as a powerful anti-depressant and is found to be able to enhance memory, thought, and mood. This amino acid also plays a role in increasing blood pressure in hypertension. All other amino acids are beneficial to human body in L form; the D form of Phenylalanine can be used to reduce pain in arthritis.
Deficiency and Excess
Deficiency of Phenylalanine can be seen in depression, AIDS, obesity, Parkison's Disease, etc. People with the genetic PKU cannot process phenylalanine resulting in a buildup of the amino acid which leads to mental retardation and other permanent damages.
Proline - Pro/ P
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Structure
Proline is one of the twenty DNA-encoded amino acids. It is unique among the 20 protein-forming amino acids because the α-amino group is secondary rather than primary as other amino acid. The distinctive cyclic structure of proline side chain locks its φ backbone dihedral angle at approximately -75°, giving proline an exceptional conformational rigidity compared to other amino acids. Hence, proline loses less conformational entropy upon folding, which may account for its higher prevalence in the proteins.
Functions
Proline behaves as a structural disruptor in the middle of regular secondary structure elements. However, proline is commonly found as the first residue of an alpha helix and in the edge strands of beta sheets. Proline is most commonly found in turns, which may account for the curious fact that proline is usually solvent-exposed although it has a completely aliphatic side chain. Because proline lacks a hydrogen on the amide group, it cannot act as a hydrogen bond donor, only as a hydrogen bond acceptor.
Serine - Ser/ S
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Structure
This amino acid's R group is a hydroxyl group attached to a CH 2 group. The hydroxyl group is polar giving serine polar/hydrophilic properties. It has a pH of 5.68. pK a = 2.21, 9.15 .Serine is a non-essential amino acid which means it can be synthesized by the human body. For instance, serine can be synthesized by glycine.
Function
Serine is found in phospholipids, active sites of trypsin and chymotrypsin. It can synthesize pyrimidines and proteins, cysteine and tryptophan. It is also involved in fat and fatty acid formation, muscle synthesis.
Threonine - Thr/ T
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Structure
Threonine is a polar and uncharged amino acid, which is of an aliphatic side chain bonded by a hydroxyl group; the amino acid is constructed as a valine amino acid of a hydroxyl group instead of a methyl group, which is more hydrophilic and reactive. The amino acid is also of two chiral centers for the α-carbon atom and the R group. One of the only 2 amino acids with 2 chiral centers is threonine, the other being isoleucine. This results in the formation of 4 stereoisomers because of 2 chiral centers.
Features
Threonine is an essential amino acd, which means it cannot be synthesized by the human body. Humans must ingest it in the form of threonine containing foods.
Functions
Threonine aids the formation of elastin and collagen. In the immune system, threonine helps in the formation of antibodies. It also promotes growth and function thymus glands and absorption of nutrients. In addition, threonine is the precursor to isoleucine.
Tryptophan - Trp/ W
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Structure
Tryptophan is an amino acid of aromatic group of an indole group bonded to a methylene group as the side chain, which is of two aromatic rings of nitrogen and hydrogen group and is hydrophilic. One of the side chains is 5 membered while the other is 6, and 2 carbons are shared by both aromatic rings.
Features
Tryptophan is an essential amino acid meaning it cannot be produced by the human body. It usually present in peptides, enzymes, and structural proteins.
Functions
Trytophan is the precursor for various proteins, serotonin and niacin. It also promotes the formation of peptides and proteins.
Tyrosine - Tyr/ Y
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Tyrosine
Tyrosine is a polar aromatic amino acid that contains a hydroxyl group attached to an aromatic ring. The hydroxyl group is particularly important because these residues are utilized in the phosphorylation of other proteins. Tyrosine is a non essential amino acid meaning it ca be synthesized in the body. It is synthesized using phenylalanine in the body.
Functions
Tyrosine plays crucial roles in the human body: It helps deal with stress by becoming an adaptanogen, which helps minimize effects of the stress syndrome; in drug detoxification such as for cocaine, coffee and nicotine addictions, it reduces withdrawal symptoms and abuse. It assists in treating Vitiligo, pigmentation of skin, and Phenylketonuria, the condition where phenylalanine is not metabolized. In addition, it is effective for depression treatment.
Tyrosine is also important in the production of epinephrine, norepinephrine, seratonin, dopamine, melanin, and enkephalins, which has pain-relieveing effects in the body. It also affects the function of hormones by regulating thyroid, pituatary and adrenal glands. Moreover, tyrosine disattaches molecules that may be harmful to the cells, therefore is an antioxidant.
Deficiency and Excess
Deficiency of tyrosine is seen in low blood pressure, depression, low body temperature.
Valine - Val/ V
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Structure
Valine is an amino acid with an aliphatic side chain, therefore a hydrophobic side chain. Valine differs from threonine in a way that the OH group of threonine is replaced by a CH 3 group. This is a non polar amino acid. It is essential and therefore cannot be produced by the human body. Being hydrophobic this amino acid is found in the interior of proteins.
Features
In animals, valine must be ingested. In plants, it is created by using pyruvic acid converting it to leucine followed by the reductive amination with glutamate. Valine is found in food: soy flour, fish, cheese, meat and vegetables.
Functions
Valine is essential in muscle growth and development, muscle metabolism, and maintenance of nitrogen balance in the human body. It can be used as energy source in glucose and treatment of damage caused by alcohol in the brain.
Deficiency and Excess
Deficiency of valine affects myelin sheets of nerves. Maple Syrup Urine Disease is caused because Leucine, valine and Isoleucine can't be metabolized.
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189675 | https://www.uab.edu/icac/images/4th_Grade_Lesson_Plans/Science/Transparent_Translucent_and_Opaque.pdf | Lesson Plan format is adapted from the Alabama Learning Exchange (ALEX). Lessons were developed by staff of the UAB NSF project “Integrating Computing Across the Curriculum: Incorporating Technology into STEM Education Using XO Laptops.” 1 Title: Transparent, Translucent, and Opaque Grade(s): 4th Subject(s): Science Author: Brenda Daniels, Angelia Groves, Tikki Hines, Valencia Eaton Jacobs Overview: Students will become familiar with transparent, translucent, and opaque objects. Students predict whether items are transparent, translucent, or opaque. Student groups will create a product that demonstrates these concepts. Content Standards: SC(4) 3. Recognize how light interacts with transparent, translucent, and opaque materials. TC (3-5) 12. Create a product using digital tools. Local/National Standards: Content Standard B Develop an understanding of light. Primary Learning Objectives: Students will be able to recognize transparent, translucent, and opaque objects. Additional Learning Objectives: Students will be able to produce a complete product based on RAFT (Role, Audience, Format, Topic) Approximate Duration of Lesson: Two days /90 minute lessons (2nd day may be needed to complete products) Materials and Equipment: For Teacher: Board & markers For Students: 1.) Transparent and Opaque by Angela Royston 2.) Light Prediction Sheet 3.) Assessment sheet 4.) Bag of materials per group of 2-4 students. Include examples of transparent, translucent, and opaque materials, e.g.: saran wrap wax paper sheer fabric white tissue paper construction paper astro turf wood plexi glass frosted glass Technology Resources Needed: Computer, Internet Access, LCD projector or Promethean Board, programs (see websites listed in “Attachments”) Background/ Preparation: Collect materials that represent each of these characteristics when they interact with light: • Transparent – Most light rays pass through the material • Translucent – Some light rays pass through the material • Opaque – No light passes through the material Procedures/Activities: Step 1 a) The teacher has placed one of 3 items (a piece of wrapping paper, a clear drinking glass or candle Lesson Plan format is adapted from the Alabama Learning Exchange (ALEX). Lessons were developed by staff of the UAB NSF project “Integrating Computing Across the Curriculum: Incorporating Technology into STEM Education Using XO Laptops.” 2 holder, and a fabric softener sheet) in small group. b) Have students observe the characteristics of each object and how it interacts with light. Students will examine how: The wrapping paper does not allow light to pass through; The glass or candle holder allows most light to pass through; The fabric softener sheet allows only some light to pass through. Step 2 a) The teacher will go over the three items (wrapping paper, candle holder, and fabric softener sheet) and how light interacts with each. b) The teacher will write the terms for the three types of materials on the board: Transparent- allows most light to shine through (glass candle holder), Translucent- allows some light to pass through (fabric softener sheet), Opaque- does not allow light to pass through (wrapping paper). Step 3 a) The teacher will show students the Translucent, Transparent, and Opaque video (link below). b) The teacher will ask the students what the definitions of transparent, translucent, and opaque are based on what they viewed and heard from the video. Step 4 a) Hold up the wrapping paper or other opaque object and ask students what happens to the light that shines on an opaque object? (Most of it is reflected back into the room and our eyes, but some of it is absorbed by the object.) Write the terms reflected and absorbed on the board. b) Hold up the fabric softener sheet or other translucent object and ask students what happens to the light that shines on a translucent object? (Most of the light is scattered by the object and then reflected back. Some of the light is absorbed, and some of it passes through the object.) Ask students to give evidence from their observations to support each of the explanations for what happens to light. c) Hold up the glass or other transparent object and ask students what happens to light that shines on a transparent object? (Most of it passes through the Lesson Plan format is adapted from the Alabama Learning Exchange (ALEX). Lessons were developed by staff of the UAB NSF project “Integrating Computing Across the Curriculum: Incorporating Technology into STEM Education Using XO Laptops.” 3 object, but some light is reflected back to our eyes, which is why we can see the glass.) Step 5 (If time is not available, this can be assigned for homework. Students can locate every day objects that illustrate each of the levels of transparency.) a) Take a brief in-school field trip. Walk the students down the hallway, into the cafeteria, and outside the school building. Ask students to look for the different types of objects and share as they find an item that is transparent, translucent, or opaque. b) After returning to the classroom, have students brainstorm items around the community or in their homes that are transparent, translucent, and opaque. Make a chart on the board of the different items that are transparent, translucent, and opaque. Step 6 a) Explain to students they will be looking at different materials, which can be classified as transparent, translucent, or opaque. b) Give a bag of materials to each group of students. c) Students will use the Prediction Chart to predict whether each item in the bag is transparent, translucent, or opaque. d) Students will test their predictions by holding each object up to the light. e) On their Prediction Chart students should place a check by their correct predictions and explain what happens to the light shining on each type of object. f) Students and teachers will discuss the results together, comparing and contrasting their results. Step 7 Group students into groups of four. Then, allow students time to create a product that demonstrates today’s topic. Use the attached RAFT topic question and table as a guide for student projects. Students should include the words transparent, translucent, and opaque in their projects. Attachments: Prediction Chart Prediction Chart Answers Websites: www.xtranormal.com (Movie Maker) www.edublogs.org (Blog) (Comic Strip Maker) www.glogster.com (Online Poster) Assessment Strategies: 1. Assess the group RAFT product for quality and accuracy. 2. Have students use a magazine to locate two real world items in each category and classify on the assessment sheet as transparent, Lesson Plan format is adapted from the Alabama Learning Exchange (ALEX). Lessons were developed by staff of the UAB NSF project “Integrating Computing Across the Curriculum: Incorporating Technology into STEM Education Using XO Laptops.” 4 translucent, or opaque. Extension: Students can create an online poster using Glogster (see website list above). Remediation: Students can be directed to the book Transparent and Opaque by Angela Royston. Students can read more information on the different types of objects as well as be informed of types of objects used and seen in everyday life. Students can read with the book on tape or can pair read. RAFT Table Topic Question: How do materials differ as they relate to absorbing light? Role Audience Format Topic Cartoonist Self Cartoon strip Transparent Videographer Peer group Video Translucent Rapper Music lovers Song/lyrics Opaque Blogger Bloggers Blog parents Lesson Plan format is adapted from the Alabama Learning Exchange (ALEX). Lessons were developed by staff of the UAB NSF project “Integrating Computing Across the Curriculum: Incorporating Technology into STEM Education Using XO Laptops.” 5 Name ___ Date _____ Transparent, Translucent, or Opaque Predictions Directions: 1. Observe the following items and predict whether each is transparent, translucent, or opaque. 2. Test your predictions and explain how each item affects the light that shines on it. ITEM PREDICTION transparent, translucent, or opaque Effect on Light (List main effect first) 1. Saran Wrap 2. Wax Paper 3. Astro Turf 4. Sheer Fabric 5. White Tissue Paper 6. Construction Paper 7. Frosted glass 8. Wood 9. Plexiglass Lesson Plan format is adapted from the Alabama Learning Exchange (ALEX). Lessons were developed by staff of the UAB NSF project “Integrating Computing Across the Curriculum: Incorporating Technology into STEM Education Using XO Laptops.” 6 Transparent, Translucent, or Opaque Prediction Answers ITEM Classification transparent, translucent, or opaque Effect on Light (List main effect first) 1. Saran Wrap Transparent Pass through, reflect a little 2. Wax Paper Translucent Scatter, reflect, absorb, pass through 3. Astro Turf Opaque Reflect, absorb 4. Sheer Fabric Translucent Scatter, reflect, absorb, pass through 5. White Tissue Paper Translucent Scatter, reflect, absorb, pass through 6. Construction Paper Opaque Reflect, absorb 7. Frosted glass Translucent Scatter, reflect, absorb, pass through 8. Wood Opaque Reflect, absorb 9. Plexiglass Transparent Pass through, reflect a little |
189676 | https://www.uptodate.com/contents/chemical-terrorism-rapid-recognition-and-initial-medical-management | Published Time: Mon, 04 Aug 2025 14:04:51 GMT
Chemical terrorism: Rapid recognition and initial medical management - UpToDate
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SUMMARY AND RECOMMENDATIONS
INTRODUCTION
BACKGROUND
CHEMICAL AGENT DEFINITIONS
RECOGNITION OF CHEMICAL EXPOSURE
Features of chemical exposures
Clinical syndromes
Rapid detection and ancillary studies
- Rapid detection
- Ancillary studies
FIELD INCIDENT RESPONSE
HOSPITAL INCIDENT RESPONSE
INITIAL MANAGEMENT OF CHEMICAL EXPOSURES
Protection of providers
Triage
- Special considerations for chemical events
Stabilization
Decontamination
- Local or spot decontamination
- Field decontamination
- Hospital decontamination
Initial management of specific exposures
- Nerve agents
Antidotal autoinjectors
Role of scopolamine
Liquid exposure to Novichok
- Cyanide
- BZ (3-quinuclidinyl benzilate)
- Crowd-control agents
ADDITIONAL RESOURCES
United States resources
Regional poison centers
Society guideline links
SUMMARY AND RECOMMENDATIONS
ACKNOWLEDGMENTS
REFERENCES
GRAPHICS
Algorithms
- Diagnosis of chemical weapons exposure algorithm
- SALT mass casualty triage algorithm
Tables
- Recognition and initial treatment of chemical weapons exposure
- Findings of chemical and biological terrorist agent exposure
Pictures
- Reactive skin decontamination lotion
RELATED TOPICS
Anticholinergic poisoning
Approach to diagnosis and initial treatment of eye injuries in the emergency department
Clinical manifestations, evaluation, and diagnosis of acute radiation exposure
Cyanide poisoning
Identifying and managing casualties of biological terrorism
Management of radiation injury
Organophosphate and carbamate poisoning
Society guideline links: Chemical terrorism
Society guideline links: Regional poison centers
Topical chemical burns: Initial evaluation and management
Chemical terrorism: Rapid recognition and initial medical management
Author:James M Madsen, MD, MPH, COL (ret), MC-FS, USASection Editors:Michele M Burns, MD, MPHAndrew Stolbach, MD, MPH, FAACT, FACMT, FACEPDeputy Editor:Michael Ganetsky, MD
Contributor Disclosures
All topics are updated as new evidence becomes available and our peer review process is complete.
Literature review current through:Jul 2025.
This topic last updated:Jul 09, 2025.
Please read the Disclaimerat the end of this page.
INTRODUCTION—
Potential actions by terrorist groups span the chemical, biological, radiological, nuclear, and high explosive (CBRNE) threat spectrum . This topic provides guidance for the rapid recognition and initial management of patients exposed to the chemical agents that are most likely to be used in warfare or by terrorists.
Bioterrorism and clinical features and treatment of radiation exposure, including exposure cause by acts of nuclear terrorism, are reviewed separately. (See "Identifying and managing casualties of biological terrorism" and "Clinical manifestations, evaluation, and diagnosis of acute radiation exposure" and "Management of radiation injury".)
Planning and preparation for field and medical response to weapons of mass destruction are beyond the scope of this topic but are reviewed elsewhere [2-11].
BACKGROUND—
The use of chemical weapons violates current international law and is governed by treaties administered by the United Nations (UN). Since 1997, the Convention on the Prohibition of the Development, Production, Stockpiling and Use of Chemical Weapons and on Their Destruction, or Chemical Weapons Convention (CWC), has been in force. The CWC is administered by the Organisation for the Prohibition of Chemical Weapons (OPCW), in The Hague, Netherlands .
Despite international prohibitions against the use of chemical weapons, large amounts of various agents remain available in national stockpiles in several countries, and their use against military and civilian populations has been reported as follows:
●Use of nerve and sulfur mustard [H] agents by Iraq against military targets in Iran and Kurdish villages (eg, Halabjah) in northern Iraq [13,14]
●Terrorist use of sarin (GB) and VX by members of the Japanese cult Aum Shinrikyo [15,16]
●Assassinations using the nerve agent VX by the group Aum Shinrikyo
●Improvised explosive devices rigged to release chlorine gas by Iraqi insurgents
●Use of chlorine in barrel bombs in Syria and Iraq [19,20]
●Use of sarin in Ghouta and Khan Shaykun, Syria [21-25]
●Assassination attempts using Novichok [26,27]
●Risk of chemical agent use in Ukraine
In addition, many chemicals that are commonly used for industrial or commercial purposes are not prohibited by the CWC and have the potential for causing mass casualties.
CHEMICAL AGENT DEFINITIONS—
Chemical agents capable of causing mass casualties are described by several categories as follows:
●Traditional chemical weapons – Traditional chemical weapons refer to known agents that have been stockpiled by nations for use during war and will be the focus of this topic.
The North Atlantic Treaty Organization (NATO) has assigned a one- to three-character designation (often called a NATO code) to each of the traditional agents; for agents such as VX (O-ethyl S-[2-(diisopropylamino) ethyl] methylphosphonothioate) and BZ (3-quinuclidinyl benzilate), this code may be more widely used than the chemical name of the compound.
Categories of chemical weapons include [29,30]:
•Pulmonary agents (eg, chlorine or phosgene [GG])
•"Blood" agents (eg, cyanide compounds [AC])
•Vesicants (blister agents such as sulfur mustard [H] compounds)
•Nerve agents (eg, tabun [GA], sarin [GB], soman [GD], VX, and Novichok, including A-series agents ):
In contrast with so-called first-generation chemical agents (used during World War I), nerve agents include:
-Second-generation agents (the G-series agents developed by Germany before and during World War II) – These are nonpersistent liquids that evaporate relatively quickly.
-Third-generation agents (V-series agents, developed by the United Kingdom and the United States shortly after the end of World War II) – These are persistent liquids and are more potent than the G agents.
-Fourth-generation agents (FGAs), developed by the former Soviet Union beginning in the 1970s as "Novichok" agents and including A-series agents – These are even more persistent than V-series agents.
The onset of the clinical effects of nerve agents depends on the dose, the state or states (mainly vapor versus liquid), and route(s) of exposure (mainly inhalation versus dermal exposure). Skin exposure to liquid Novichok agents is a special case because of the extremely long latent periods (up to two days), the difficulty of treating symptomatic patients , and the importance of actions taken during the latent period.
•Incapacitating agents (eg, the anticholinergic agent, BZ [3-quinuclidinyl benzilate, or QNB])
Some compounds, such as chlorine, phosgene, and cyanide, have been used in war and are also used in industry; these are sometimes termed dual-usechemicals.
Although arsenicals (eg, arsine, ethyldichloroarsine [ED], methyldichloroarsine [MD] and phenyldichloroarsine [PD]) have characteristics that would make them attractive as a chemical weapon, they are primarily of historic interest and have not been stockpiled to any great degree .
●Crowd-control agents – The Chemical Weapons Convention (CWC) also regards crowd-control agents, for example OC (ie, oleoresin capsicum) and CS (o-chlorobenzylidene malononitrile), as weaponized chemical agents. The lay term "tear gas" is sometimes used to refer to some or all of these agents but is not an official military term and, in addition, is a misnomer since these agents are all solids at ambient temperatures and are dispersed as aerosols (eg, smokes or sprays) rather than as gases.
●Binary chemical weapons – Binary chemical weapons are not separate compounds; instead the term refers to the practice of developing munitions that hold two immediate precursors to a chemical agent in separate compartments divided by a membrane that ruptures when the round is launched. The precursors mix in flight and generate the desired chemical agent.
The CWC prohibits several important precursors to chemical agents,but given their availability, synthesis of even complex nerve agents is not beyond the reach of those with graduate-level training in chemistry, as the Aum Shinrikyo cult demonstrated with their nerve agent attacks in the Tokyo subway [15,16].The simpler chemical agents can be synthesized even more easily or, in the case of dual-use agents, simply purchased or stolen.
●Toxic industrial chemicals – Toxic industrial chemicals, or TICs, include a variety of industrial chemicals that have the potential for causing mass casualties including hydrogen fluoride, ammonia, formaldehyde, hydrogen sulfide, phosphine, and sulfuric acid [29,33,34].
However, serious chemical exposure does not require an industrial source. For example, "detergent suicides," the intentional mixing of common household products to produce toxic compounds such as hydrogen cyanide and hydrogen sulfide, demonstrate how easily toxic chemicals can be made using commercially available substances .
In the United States, local resources to identify TICs or dangerous commercial chemicals primarily reside in fire departments. Decontamination procedures and medical management of TIC or dangerous commercial chemical exposure vary according to agent. Resources to assist the clinician are available online. (See 'United States resources' below.)
●Nontraditional agents – This term refers to newer chemical agents that have been synthesized and weaponized outside the United States . This category is redefined over time; certain A-series nerve agents, for example, used to be in this category but are now considered traditional agents.
●Mid-spectrum agents – Mid-spectrum agents are chemical poisons produced by biological organisms(eg, ricin, T-2 mycotoxins, and botulinum toxin) and are also considered chemical agents by the CWC [36,37]. These agents are discussed separately. (See "Identifying and managing casualties of biological terrorism", section on 'Toxins of concern'.)
RECOGNITION OF CHEMICAL EXPOSURE—
The algorithm provides a means of rapid recognition of chemical exposure based upon clinical findings (algorithm 1). The table provides suggested decontamination and management according to chemical agent (table 1).
Recognition of chemical exposure can come from features of the exposure, clinical syndromes, and laboratory testing.Of these, laboratory testing of body fluids or tissues takes too long to play more than a confirmatory role in a mass-casualty incident or to document noncompliance with the United Nations Chemical Weapons Convention Treaty . However, preservation of decontamination fluids and samples of blood, urine, hair, and any foreign material taken from patients is an important forensic consideration during care.
Less commonly, announcements by perpetrators may identify the chemical agent, although confirmation of the agent is often necessary to ensure that a chemical exposure has indeed occurred and to verify that the terrorist claims are true.
Features of chemical exposures—Many of the features of chemical exposures potentially overlap with those of exposures to toxins or weaponized biological agents. Presenting features suggesting a chemical exposure include the following (table 2) [39-41]:
●Timing – The sudden onset of symptoms within minutes among multiple exposed patients should suggest the use of chemical agents, especially nerve agents or cyanide .By contrast, biologic agents may take many hours to weeks to become apparent. (See "Identifying and managing casualties of biological terrorism".)
However, the latent period (the length of time between exposure and the appearance of signs or symptoms in casualties) may be more on the order of hours for type II pulmonary, sulfur mustard, or BZ agents. As a general rule, the higher the dose of a chemical agent, the shorter the latent period. Also, skin exposures to liquid nerve agents may require several minutes to several hours for the agent to undergo absorption and produce clinically observable effects.
●Unusual fogs or smokes – Most chemicals of interest (eg, VX, mustard vapor, phosgene, or chlorine) are heavier than air and stay low to the ground. They may be deployed by an explosive device that causes little or no structural damage. In some instances, the physical characteristics such as odor, taste, or color of the released chemical can help identify it as follows:
•Chlorine – Yellow-green gas with a characteristic chlorine odor
•Phosgene – Colorless gas or white cloud with odor of newly mown or musty hay, grass, or corn
•Cyanide – Odor of bitter almonds (less commonly, of burning rope or of acetylene) (only about 50 percent of people can detect this smell)
•Sulfur mustard – Yellow-brown vapor, yellow liquid, or solid that is odorless or smells like onions, garlic, mustard, or asphalt
•Tabun (nerve agent) – Colorless and tasteless with a slight fruity odor
•Sarin (nerve agent) – Colorless and tasteless, often with a faint fruity odor
•Soman (nerve agent) – Colorless and tasteless with an odor described as sweet, musty, fruity, nutty, or like camphor
•VX (nerve agent) – Amber color, possibly faintly fishy odor, and tasteless
•BZ – Colorless, odorless, and tasteless
•Crowd-control agents – Colorless, odorless, and tasteless in solid form; extremely irritating (bypassing most descriptions of odor) when inhaled in aerosolized form
●Common clinical findings among multiple patients within a short period of time (minutes to hours). (See 'Clinical syndromes' below.)
●Patients were located near or downwind from the release.
●Sentinel case (illness due to an uncommon agent) – For example, initial casualties with high exposure followed by those exposed to lesser doses or a liquid form of the chemical weapon.
●Failure to respond to usual therapy – As an example, patients with exposure to pulmonary agents may have unremitting respiratory failure despite advanced therapies.
●Unexplained human deaths – Mass casualties without evidence of trauma suggests a chemical or biological exposure.
●Unexplained deaths of animals, fish, or plants – A biological or liquid chemical release may be persistent, although a gas release tends to disperse .
Clinical syndromes—The clinical diagnosis of exposure to chemical agents is aided by familiarity with presenting clinical signs and symptoms of chemical weapons exposure and the signs and symptoms that suggest exposure to cholinergic and anticholinergic agents.An algorithm can assist in rapid diagnosis of a chemical weapons exposure (algorithm 1). The table provides suggested decontamination and management according to chemical agent (table 1).
First responders and clinicians must take precautions to protect themselves prior to approaching suspected victims of a chemical weapons exposure and rendering care. (See 'Protection of providers' below and 'Stabilization' below and 'Initial management of specific exposures' below.)
The main toxidromes, or constellations of signs and symptoms that suggest terrorist release of chemical weapons and potential compounds, include the following (algorithm 1) [3,40,41,44]:
•Coma or seizures – Cyanide, hydrogen sulfide, opioids, or, if cholinergic findings are present (eg, miosis, bronchorrhea, wheezing, tearing, vomiting, diarrhea, sweating, fasciculations, or paralysis), nerve agents
•Rapid onset of respiratory distress with eye, nose, or throat irritation – Chlorine or other combination pulmonary agents, type I pulmonary agents (eg, ammonia, other bases, or acids), crowd-control agents, or Lewisite
•Cholinergic findings (eg, miosis, bronchorrhea, wheezing, tearing, vomiting, diarrhea, sweating, fasciculations, or paralysis) – Nerve agents
•Delayed onset of chest tightness and pulmonary edema – Phosgene or other type II pulmonary agents
•Skin erythema, burns, or conjunctivitis – Sulfur mustard agents, phosgene (contact with liquid form), crowd-control agents, hydrogen fluoride, Lewisite
•Disorientation with anticholinergic findings (flushed dry skin, dilated pupils, tachycardia, or hypertension) – BZ
•Rotten-egg odor followed by olfactory paralysis; "knockdown" (sudden collapse); conjunctivitis ("gas eye"); and pulmonary edema – Hydrogen sulfide
By contrast, clinical features consisting of fever, rash, or gastrointestinal bleeding suggest exposure to a biologic agent or toxin (table 2). (See "Identifying and managing casualties of biological terrorism".)
Key questions to answer during a thorough secondary survey in mass-casualty incidents involving chemical agents can be recalled using the mnemonic ASBESTOS as follows:
●A: Agent – Is a clinical toxic syndrome (toxidrome) present? What are the results of rapid detection or other features of the release that can identify the exposure? (See 'Rapid detection and ancillary studies' below.)
●S: State – Is the chemical exposure caused by a vapor, liquid, aerosol, gas, or combination?
●B: Body site of exposure – Was the chemical inhaled, ingested, or dermally absorbed?
●E: Effects – What kind of effects are present; local (at or near the body site of exposure), systemic, or both?
●S: Severity – How severe is the exposure? What is the severity of the clinical effects?
●T: Time course – How long has it been between exposure and onset of symptoms? Is the patient getting worse or better over time?
●O: Other diagnoses – What comorbidities does the patient have (eg, asthma)? What is the differential diagnosis for the clinical findings?
●S: Synergism – Are there combined effects caused by multiple exposures?
Rapid detection and ancillary studies
Rapid detection—Clues to the identity of a released chemical agent may come from any of the following :
●Announcement by the perpetrators
●Intelligence sources
●Environmental detectors
•Large-area vapor monitors (eg, M21, Joint Services Lightweight Standoff Chemical Agent Detector)
•Personal-space vapor monitors (M256A2, ICAD)
•Liquid detectors (M8 paper, M9 paper)
●Biological sampling of fluid or tissues from those suspected of having been exposed
•Serum electrolytes, lactate, anion gap, CBC with differential
•Special tests for specific compounds (usually not fast enough for use in initial treatment; may be useful in later confirmation)
●Clinical suspicion and identification of toxidromes
There are problems inherent in each of these sources; eg, announcements may be deliberately misleading, intelligence may be faulty, false positives and false negatives may be significant with environmental detectors, a given detector may not detect the agent in the state in which it is present, results from laboratory tests may not be definitive or may take too long, and clinical findings may vary for patients with the same exposure.
In many situations, the most reliable initial detector may be clinical recognition of toxidromes. (See 'Clinical syndromes' above.)
Ancillary studies—Patients with significant respiratory distress, regardless of the cause, warrant the following studies:
●Blood gas measurement
●Complete blood count (CBC)
●Chest radiograph
Additional studies obtained in the course of patient care help to confirm the clinical impression and, in some instances, document exposure by a specific agent as follows:
●Cyanide (see "Cyanide poisoning", section on 'Laboratory evaluation'):
•Serum lactate – Elevated
•Serum electrolytes – Elevated anion gap
•Arterial and central venous blood gas – Metabolic acidosis, decreased arteriovenous oxygen gradient (usually from a higher-than-usual venous oxygen content)
•Blood or urine cyanide level – Confirms exposure (rarely if ever available in time to contribute to real-time patient care)
●Nerve agent (see "Organophosphate and carbamate poisoning", section on 'Measurement of cholinesterase activity')
•Decreased red blood cell acetylcholinesterase – Confirms nerve agent exposure and can help guide oxime therapy
•Decreased pseudocholinesterase – Assists in documenting nerve agent exposure
●Sulfur mustard
•Serial daily CBCs – Leukopenia (typically begins day three to five days after exposure) after an initial leukocytosis
•Urinary thiodiglycol (investigational) – Elevated
•DNA and protein adducts (investigational) – Elevated
●Lewisite
•CBC – Hemolytic anemia (large dose exposure)
•Urinary arsenic – Elevated
•Urinary 2-chlorovinylarsonous acid (CVAA) (investigational) – Elevated
FIELD INCIDENT RESPONSE—
The medical field actions necessary to respond to a chemical terrorism incident are provided in detail by the United States Department of Health and Human Services here. In many civilian jurisdictions, the fire department is in charge of the incident.
Key activities include :
●Notify local authorities
●Establish local on-site incident command
●Establish the following control zones and perimeter security:
•Hot zone – Contaminated area or site of release, entry granted only to properly attired rescuers (first responders)
•Warm zone – Located uphill and upwind of hot zone, this area is designated for decontamination of victims and rescuers (first responders). Personnel performing decontamination and early medical care (first receivers) must be properly attired
•Cold (support) zone – Clean area where victims who are free of external liquid contamination are received and transported to definitive care
●Ensure protection of first responders and receivers – Guidelines for personal protective equipment (PPE) to be worn by first responders and first receivers are provided by the United States Occupational Safety and Health Administration.
Personal protection for first receivers are discussed separately. (See 'Protection of providers' below.)
For a suspected chemical terrorism incident, first responders who are evacuating victims from the hot zone should wear level A personal protective equipment (PPE) consisting of the following :
•Positive pressure, full face-piece, self-contained breathing apparatus (SCBA)
•Fully encapsulating chemical protective suit with suit openings sealed with tape
•Two pairs of chemical resistant gloves
•Chemical resistant boots with a steel toe and shank
•Hard hat, as needed, based upon conditions
•Disposable protective suit, gloves and boots (may be worn over fully encapsulating suit)
●Identify chemical hazard (algorithm 1) (see 'Clinical syndromes' above)
●Determine extent of threat and affected population
●Begin patient triage – Field triage guidance for chemical casualties and the triage algorithms, Simple Triage and Rapid Treatment (START and JumpSTART) and Sort – Assess – Life Saving Interventions (SALT) are discussed in detail here. Additional considerations specific to triage of victims of chemical exposures are discussed below. (See 'Triage' below and 'Special considerations for chemical events' below.)
HOSPITAL INCIDENT RESPONSE—
Upon notification of a chemical weapons release, receiving facilities should secure all entrances and hospital grounds, establish a security perimeter, and set up a decontamination zone that is outside the clean parts of the facility. Disaster plans should be activated. Facility incident command and close communication with local emergency management authorities should be established.
Planning and preparation for field and medical response to weapons of mass destruction are beyond the scope of this topic and are provided elsewhere [2-11].
INITIAL MANAGEMENT OF CHEMICAL EXPOSURES
Protection of providers—Providers responding to release of an unknown chemical should wear personal protective equipment (PPE) designed to protect against the highest possible personal threat. The levels of PPE as designated by the Occupational Safety and Health Administration are available here.
Appropriate personal protective equipment for a chemical terrorism event by provider type and location of care include the following [51-53]:
●First responders – First responders who enter the site of an unknown chemical release (the "hot zone") to extract casualties and provide field decontamination adjacent to the site of release: Level A . (See 'Field incident response' above.)
●First receivers (hospital decontamination zone) – For receivers performing care in the hospital decontamination zone at facilities that meet best practices for emergency planning: Level C, which consists of the following PPE :
•Powered air-purifying respirator (PAPR) with protection factor of 1000, and fitted with a combination 99.97 percent high-efficiency particulate air (HEPA)/organic vapor/ acid respirator cartridges (both of these items should be approved by the National Institute of Occupational Safety and Health [NIOSH] or similar agency)
•Double layer protective gloves
•Chemical resistant suit with openings taped
•Head covering and eye and face protection (if not already part of the PAPR)
•Chemical-protective boots
●First receivers (hospital post-decontamination zone) – For receivers performing care in the hospital post-decontamination zone at facilities that meet best practices for emergency planning: normal work clothes and PPE as needed for infection control (eg, gowns, gloves, and/or surgical mask) .
Once the chemical agent is identified and proper monitoring of hazard levels is in place, additional guidelines may apply. First responders and medical providers should receive communication as defined in their regional emergency management plan from appropriate personnel in the regional incident command center to ensure ongoing compliance with PPE standards during the event.
Triage—In a mass-casualty incident involving chemical agents, casualties will need to be triaged, or sorted, for medical treatment, decontamination, and transport to medical care or evacuation from the site of release.
The paramount question in triage is, "Who can afford to wait?" Most triage categories were developed for trauma patients; however, the general categories of immediate, delayed, minimal, and, in austere conditions, expectant can be adapted to chemical casualties .
General triage approaches vary by jurisdiction and include START (simple triage and rapid treatment), SALT (Sort, Assess, Lifesaving Interventions Treatment/Transport), and SMART tag systems. However, these algorithms have primarily been developed for triage of traumatic injuries and focus on medical sorting. Of these, only SALT has suggestions for antidote administration in the event of a chemical exposure.
Special considerations for chemical events—Triage systems specific to chemical, biological, radiologic, nuclear, and explosive terrorist events have been developed [54-57]. Although beyond the scope of this topic, training in field triage for chemical terrorism is available through the Chemical Casualty Care Division, United States (US) Army Medical Research Institute of Chemical Defense. (See 'United States resources' below.)
Field triage guidance for chemical casualties and the triage algorithms, Simple Triage and Rapid Treatment (START and JumpSTART) and Sort – Assess – Life Saving Interventions (SALT) are also discussed here.
Proper field triage of patients exposed to chemical weapons has the following differences from traditional mass casualty field triage:
●Time demands are greater.
●Personal protective equipment is needed and makes verbal communication and tactile examination challenging. (See 'Protection of providers' above.)
●Proper assessment of the type and seriousness of the exposure is more difficult.
●Sorting needs to occur for decontamination and evacuation in addition to medical treatment.
Special aspects of triage of victims of chemical weapons exposure also include:
●Trauma is frequently not present.
●Assessment for chemical toxidromes and prompt administration of properly dosed antidotes optimizes outcomes. (See 'Clinical syndromes' above and 'Initial management of specific exposures' below.)
●Respiratory failure is a serious threat with many exposures and frequently needs to be addressed in the prehospital setting.
●For quick onset chemicals (eg, nerve agents or cyanide), latent periods before symptoms can be very short (seconds to minutes). Thus lives may be saved or lost in the prehospital setting.
●For other chemicals (eg, phosgene or sulfur mustard), latent periods may be very long and exposure may not be recognized.
Special considerations for triage designation of victims of chemical exposure include the following:
●Immediate – Immediate casualties are those who cannot afford to wait more than a couple of minutes and are likely to survive with local decontamination, initial medical stabilization, and antidote administration given available resources.
The agents most likely to result in immediate casualties are cyanide and nerve agents; fast-acting antidotes are available for these agents. (See 'Nerve agents' below and 'Cyanide' below.)
Impending airway compromise or respiratory distress also requires triage as immediate.
In addition, any person with suspicious liquid on the skin must also be considered immediate until prompt (local, spot) decontamination has occurred and the patient is reassessed. (See 'Local or spot decontamination' below.)
●Delayed – Delayed casualties can wait up to several hours for medical care although if they need rapid local decontamination and prompt field decontamination, they are immediate until local decontamination has been occurred. These patients can obey commands, are not in respiratory distress, have peripheral pulses and no major hemorrhage but do have injuries that are more than minor. Typically, these patients cannot walk without assistance.
In addition to these criteria, patients with exposure to peripherally acting pulmonary agents, vesicants, BZ, and crowd-control agents are typically classified as delayed with respect to medical treatment.
●Minimal – Patients who meet all criteria for delayed care AND have only minor injuries are considered minimal once appropriately decontaminated. These patients are typically able to walk and talk.
For example, patients who have been exposed to nerve agent vapor but then removed from exposure and whose symptoms are now resolving are considered minimal.
●Expectant/dead – Expectant patients are those who are not likely to survive given available resources. At the scene of a mass casualty chemical exposure, patients who are not breathing after control of major hemorrhage, opening of the airway, chest decompression, administration of autoinjector antidotes, and, in children, provision of two rescue breaths are classified as dead. Furthermore, patients who have experienced a respiratory or cardiac arrest or continued seizures despite antidote therapy warrant withholding of medical resources if minimal or scant resources are available and there are large numbers of casualties requiring care and transport .
Additional considerations for triage of patients with chemical agent exposure include the following:
●Casualties whose only exposure is to vapor assume a lower priority for thorough patient decontamination than those exposed to liquid.
●When the chemical agent has a long latent period, the sorting of patients for evacuation may be different than for medical treatment. As an example, a patient who develops shortness of breath after only four hours of exposure to phosgene may be delayed for medical stabilization but urgent for transport to a pulmonary intensive care unit.
●Respiratory symptoms occurring less than four hours after exposure to a peripherally acting pulmonary agent or to a vesicant imply a high dose and a guarded prognosis. Although these patients would typically be triaged as delayed, the onset of symptoms so soon after exposure indicates a high dose capable of causing death.
●Following a chemical incident, the ratio of casualties presenting with fears of exposure but without objective evidence of toxicity to casualties with objective evidence of poisoning may be as high as 4 to 1, and considerations must be taken to distinguish between these two groups and ensure timely care of the poisoned patients .
Stabilization—Medical assessment and life-saving treatment after a chemical weapons exposure frequently must occur during or prior to field or hospital decontamination to ensure patient survival.During this phase of care, key actions include the following:
●A: Airway – Maintain an open airway and, if the patient has traumatic injuries, perform cervical spine stabilization.
●B: Breathing – Give oxygen for respiratory distress and, if needed, support breathing with bag-mask ventilation followed by endotracheal intubation. Avoid succinylcholine when performing rapid sequence intubation in patients exposed to nerve gas. (See "Organophosphate and carbamate poisoning", section on 'All patients: Supportive care'.)
●C: Circulation – Establish intravenous access, obtain initial laboratory studies, and give intravenous antidotes.
●D: Immediate decontamination – Stop exposure to the chemical agent; actions include application of a gas mask in the field if assisted breathing is not needed, local or spot decontamination of any suspicious liquid on the skin or in wounds, and removing the patient from the source of exposure. (See 'Local or spot decontamination' below.)
●D: Drugs – Administer antidotes, including autoinjector administration of antidotes in the field prior to establishment of intravenous access; for chemical warfare agents, specific antidotes are only available against cyanide compounds, nerve agents, and BZ. (See 'Initial management of specific exposures' below.)
●E: Exposure – Remove clothing and perform definitive decontamination while avoiding hypothermia, especially in infants, children, and older adults.
These steps need not occur in a strictly chronological order (eg, effective ventilation of an apneic nerve-agent casualty may be impossible before administration of sufficient atropine to break nerve-agent-induced bronchospasm) but should be accomplished nearly simultaneously if possible.
Even in the absence of specific antidotes in the field, general stabilization measures as described may, in many cases, permit casualty survival until definitive treatment can be begun. However, maximum survival following exposures to cyanide and nerve agents requires that antidotes be available to appropriately trained first responders in the field as critical life -saving measures during triage of casualties (algorithm 2) [60-62]. (See 'Triage' above.)
Decontamination—Proper decontamination consists of local or spot decontamination of any liquids on the skin, removal of clothing, and copious irrigation of the skin with lukewarm water and, if available, mild soap. Although mass decontamination may be accomplished in the field, decontamination should also occur at receiving hospitals.
This section provides a basic approach to decontamination. However, proper decontamination requires specialized equipment, extensive training of personnel, and close collaboration between hospitals and regional incident command. Proper setup and performance of decontamination are discussed in detail elsewhere .
Local or spot decontamination—Local or spot immediate decontamination of skin should be performed during triage and stabilization (algorithm 2). (See 'Stabilization' above.)
The following agents may be used for spot decontamination [3,63,64]:
●Reactive Skin Decontamination Lotion (RSDL) – RSDL is specifically formulated to neutralize the toxicity of the liquid nerve agent VX and blister agents such as sulfur mustard and Lewisite. It acts within seconds of being applied to the skin and is the preferred spot decontamination method for victims of a chemical attack [63,65]. The lotion is packaged on a foam applicator inside a single use pouch. The lotion is applied within three minutes of contamination and rubbed gently on the skin for two minutes, and the nontoxic residue is washed away at a later time (picture 1). Although reasonable to perform, application of RSDL to wounds is considered off label use. Application of RSDL to the eyes is not recommended.
●Other topical absorbents – If RSDL is not available, porous material such as activated charcoal, Fuller's earth, clay, tissue paper, flour, or bread, although less effective, may be applied to areas of contaminated skin to adsorb agent followed by irrigation. If an adsorbent is not available, irrigation alone should be performed.
●Irrigation – If RSDL is not available, any available adsorbent material (towels, tissue paper, charcoal, bread, clay-rich soil, etc) should be applied, allowed to remain on the skin for 30 seconds to two minutes, and removed by wiping, flushing with water, or (preferably) gentle but thorough washing with soap and water. A dilute bleach solution (0.5 percent hypochlorite, made by mixing one part standard household bleach with nine parts water) may also be used followed by rinsing with plain water. The use of straight bleach (5 percent hypochlorite or greater) is to be discouraged because of potential damage to the skin that may cause increased absorption of the chemical agent. For oily agents, such as sulfur mustard and VX, water plus a mild soap may be more effective than water alone.
Because many chemical agents start damaging or penetrating skin within a couple of minutes of exposure, the importance of immediate decontamination cannot be overemphasized.However,delayed decontamination, even if too late to prevent skin effects such as blistering from vesicants, may prevent continued absorption of the substance and the accumulation of a lethal internal dose .
Field decontamination—Mass decontamination is an important aspect of field incident response and often consists of stations for disrobing followed by showering or assisted decontamination. However, in civilian settings, patients might bypass field decontamination stations and report directly to medical facilities for care. Thus, receiving facilities should still perform definitive decontamination of all exposed patients prior to bringing them into clean areas to avoid contamination. (See 'Field incident response' above.)
The proper setup and performance of field decontamination are discussed in detail elsewhere . Training is available to qualified providers in the US under the auspices of the Chemical Casualty Care Division of the US Army Medical Research Institute of Chemical Defense (USAMRICD), Army Chemical Defense. (See 'United States resources' below.)
Hospital decontamination—Chemical decontamination consists of removal of all clothing and thorough washing of the skin and hair with lukewarm water and soap before the patient is brought into the clean area of the emergency department or other parts of the hospital.
Important considerations include :
●Persons performing chemical decontamination at first receiving facilities should wear Level C personal protective equipment (PPE). (See 'Protection of providers' above.)
●Providers assisting with decontamination should ensure that cleansing of the skin does not cause open wounds.
●Water temperature should be controlled so that hypothermia is avoided, especially in infants, children, and older adults.
●Once chemical decontamination has occurred, the patient should be dried, dressed in clean hospital gowns, and escorted or transported into the clean zone of the emergency department.
During chemical decontamination, medical stabilization and treatment may be necessary, particularly for victims exposed to cyanide or nerve agents. Thus, decontamination areas should have supplies and medications necessary to provide initial stabilization while decontamination is performed and medical personnel are outfitted in Level C PPE.
Contaminated patients should not be brought into clean areas of receiving facilities (hospitals and emergency departments) because they can sicken staff and contaminate the facility, thereby reducing the capacity of the health care system to respond to the chemical incident . Such patients should be kept outside and undergo decontamination before being brought into the hospital. A security perimeter and lock down of the receiving facility are key actions to prevent inadvertent contamination by such patients.
However, some patients may require emergency medical stabilization before thorough decontamination (see 'Stabilization' above). A complete plan responds to this need by mandating the establishment of an emergency medical treatment station in the "dirty" area after triage but before thorough decontamination.
Each hospital should have a management plan that maximizes the efficiency and efficacy of decontamination. Proposed concept of operations for health care facilities is discussed in detail elsewhere .
Important aspects of such planning include :
●Establishment of a designated fixed or rapidly deployed decontamination facility
●Proper training of staff in the donning and removal of Level C PPE
●Triage plan for contaminated patients that separates them into medical and nonmedical decontamination
●Decontamination procedures that maintain privacy and avoid hypothermia
●Secondary triage after decontamination
●Assurance of adequate personnel and supplies to perform simultaneous medical stabilization and chemical decontamination
Initial management of specific exposures—The table provides the mechanism of action, clinical findings, recommended decontamination, and management for chemical weapons exposures (table 1).
Antidotes are available for chemical exposure to nerve agents, cyanide compounds, and BZ .
Nerve agents
Antidotal autoinjectors—The use of autoinjectors available for the rapid intramuscular (IM) administration of nerve agent antidotes and prehospital antidote administration is discussed here. Hospital-based management, including the intravenous (IV) administration of antidotes, is discussed separately. (See "Organophosphate and carbamate poisoning", section on 'Management'.)
●Antidote Treatment-Nerve Agent, Autoinjector (ATNAA)/Duodote– An atropine-pralidoxime autoinjector that administers atropine 2.1 mg and pralidoxime 600 mg simultaneously.
●Convulsive Antidote, Nerve Agent (CANA) – An autoinjector containing diazepam 10 mg.
●AtropineAutoinjector – An atropine autoinjector in 0.5 mg, 1 mg, and 2 mg doses is available only in the US Strategic National Stockpile under an Emergency Use Authorization, but is not approved by the US Food and Drug Administration (FDA) [70,71].
In addition, studies of a midazolam autoinjector to treat children and adults with seizures caused by nerve agents have been funded by the US Department of Health and Human Services , and midazolam was subsequently approved in 2018 by the US FDA for IM administration for status epilepticus . Midazolam is more rapidly absorbed after IM administration compared with diazepam. Given these benefits, the US military is replacing CANA with an autoinjector that contains midazolam 10 mg in a volume of 0.7 mL .
Based upon animal studies, all nerve agent antidotes appear to have bioavailability after intraosseous (IO) administration that is equivalent to IV administration . Thus, the IO route is an option for nerve agent antidote administration, although in a mass casualty situation, IM administration permits more rapid treatment of a greater number of casualties.
Personnel should be familiar with the contents and operation of the autoinjector that they will use. Many jurisdictions have stockpiles of nerve agent autoinjectors available for rapid deployment in the event of a nerve agent release. Availability of such stockpiles is essential to an effective response because just one patient with moderate or severe effects of nerve agent exposure can rapidly deplete typical hospital stocks of atropine and pralidoxime.
The correct administration of autoinjectors is described here .
Treat adults, including pregnant patients, and children and adolescents weighing >41 kg with atropine, pralidoxime, and benzodiazepines based upon clinical effects as follows :
●Mild effects – Only selected patients with mild clinical effects warrant treatment as follows:
•Miosis alone with no respiratory symptoms – No antidote.
•Miosis and severe rhinorrhea – Atropine in syringes can be administered 1 to 2 mg IV/IM/IO in adults and 0.02 to 0.05 mg/kg (maximum dose 2 mg) for children. The 2mg atropine IM autoinjector (green label) can be used if available from the US Strategic National Stockpile. (See "Organophosphate and carbamate poisoning", section on 'Atropine'.)
•Do not give benzodiazepines.
●Moderate to severe effects
•For patients with moderate respiratory distress, nausea, vomiting, weakness, and/or muscle fasciculations – One atropine-pralidoxime autoinjector (2.1 mg and 600 mg) IM, may repeat one to two more injections every 5 to 10 minutes until dyspnea and secretions are minimized.
•For patients with coma, seizures, severe respiratory distress/apnea, or paralysis, give the following - Three atropine-pralidoxime autoinjectors (2.1 mg and 600 mg) IM in rapid succession.
•Persistent or recurrent cholinergic signs or symptoms such as excessive secretions or bronchoconstriction-induced respiratory difficulty can be treated with atropine (from syringes) 2 mg IV/IM/IO in adults and 0.05 mg/kg (maximum dose 2 mg) for children every three to five minutes until signs and symptoms respond. The 2 mg atropine IM autoinjector (green label) can be used if available from the US Strategic National Stockpile.
•One diazepam or midazolam autoinjector (10 mg) IM (or 10 mg of either from a syringe), may repeat one to two more injections every 10 minutes for persistent seizure activity.
When possible, weight-based dosing should be given to children up to the adult maximum doses described above and according to clinical effects. However, for children with severe, life-threatening nerve agent toxicity who lack intravenous access and for whom more precise mg/kg IM dosing would be logistically impossible, suggested autoinjector dosing guidelines for atropine, pralidoxime, and valium by weight are as follows :
●≤25 kg – One atropine-pralidoxime autoinjector (2.1 mg and 600 mg) IM; diazepam 5 mg IM (do not use autoinjector)
●26 to 41 kg – Two atropine-pralidoxime autoinjectors (2.1 mg and 600 mg) IM; one diazepam autoinjector (10 mg) IM
Pediatric weight-based dosing of the atropine autoinjector, if available from the US Strategic National Stockpile, is as follows :
●7 to 18.4 kg – 0.5 mg atropine autoinjector IM (blue label)
●18.5 to 41 kg – 1 mg atropine autoinjector IM (red label)
Role of scopolamine—If available, scopolamine can be used for patients with severe effects, especially during a large chemical event to conserve atropine.
●Scopolamineadult dose: 1 mg IM, IV, or via inhalation as a single dose with the initial dose of atropine.
●Scopolaminepediatric dosing (based upon preoperative parenteral dosing):
•Children 6 months to 3 years: 0.15 mg IM, IV, or via inhalation as a single dose with the initial dose of atropine.
•Children over 3 to 6 years: 0.3 mg IM, IV, or via inhalation as a single dose with the initial dose of atropine.
•Children over 6 years of age to puberty: 0.6 mg IM, IV, or via inhalation as a single dose with the initial dose of atropine.
Scopolamine is a tropane alkaloid that penetrates the CNS at lower doses than atropine. Based upon animal models, when given early enough, it can prevent nerve-agent-associated seizures and may be synergistic with atropine for the treatment of muscarinic symptoms [78-80]. It does not replace atropine (which is still useful in treating muscarinic effects outside the CNS), but even a small dose of scopolamine can significantly reduce the total dose of atropine needed to treat a nerve-agent casualty.
Although optimal dosing of scopolamine after nerve agent exposure in humans is unknown, the suggested single adult dose of 1 mg is chosen to conserve atropine while avoiding delirium. This dose is conservative given that, in healthy unexposed adults, delirium may occur at parenteral scopolamine doses of ≥1.5 mg.
Parenteral scopolamine is not widely available in the US and is not approved by the FDA for nerve agent exposure, although when available it could be given off-label where a physician-patient relationship exists.
Liquid exposure to Novichok—Novichok is a newer class of organophosphate nerve agents used in assassination attempts. (See "Organophosphate and carbamate poisoning", section on 'Sources of exposure'.)
Individuals with skin exposure to liquid Novichok can be very difficult to treat once they become symptomatic [27,31], but the long latent periods (up to two days) following this kind of exposure present a unique opportunity for presymptomatic management. Those who may have been exposed in this manner need to be identified, sequestered, and decontaminated by showering and with reactive skin decontamination lotion (RSDL). (See 'Local or spot decontamination' above.)
Cholinesterase monitoring should begin, and the Chemical Casualty Care Division of the US Army Medical Research Institute of Chemical Defense (USAMRICD) should be contacted. Specialized consultative advice can be found at USAMRICD (1-833-238-7756).
Cyanide—Availability of treatment varies by region and hospital. Immediately below is a series of antidotal management recommendations, based upon treatment availability, for patients with probable cyanide exposure (see "Cyanide poisoning", section on 'Suspected cyanide intoxication'):
●For patients where hydroxocobalamin is available, it is administered as follows:
•Hydroxocobalamin 70 mg/kg IV over 15 minutes (15 mL/minute) (5 g is the standard and maximum adult dose). The Cyanokit contains 2.5 g (one reconstituted vial). In patients <40 kg, the initial dose may be repeated once, but total dose should not exceed 5 g (two vials).
●For patients without contraindication to nitrites (eg, carbon monoxide toxicity), and where hydroxocobalamin is not available, use combinations of amyl nitrite and sodium nitrite to induce methemoglobinemia, and sodium thiosulfate to act as a sulfur donor as follows:
•Amyl nitrite inhaled by the patient (held under the patient's nose or via the endotracheal tube) for 30 seconds of each minute, for three minutes
•Sodium nitrite 10 mg/kg IV AND
•Sodium thiosulfate (25 percent) 1.65 mL/kg IV (maximum dose 12.5 g)
●Where 4-dimethylaminophenol (4-DMAP) or dicobalt edetate is available, they are options only when other antidotes are not available but should only be given after consultation with local critical care, military and/or toxicology experts. They are only for parenteral, not intramuscular, administration.
BZ (3-quinuclidinyl benzilate)—Most patients with anticholinergic toxicity do well with supportive care alone, but some may benefit from antidotal therapy with physostigmine. One approach is as follows (see "Anticholinergic poisoning", section on 'Antidotal therapy with physostigmine for severe toxicity'):
●Consider treating mild to moderate agitation with benzodiazepines alone (eg, lorazepam), although physostigmine is more effective for this purpose than are benzodiazepines; do not use phenothiazines or butyrophenones (eg, haloperidol).
●Patients who manifest both peripheral(eg, dilated pupils, dry mouth, and/or flushing)AND moderate central (moderate to severe agitation/delirium or seizures) anticholinergic toxicity without contraindications to physostigmine (eg, widened QRS on electrocardiogram) should receive the following dose: 0.5 to 2 mg (0.02 mg/kg IV, up to a maximum of 0.5 mg per dose in pediatric patients); physostigmine should be given by slow IV infusion, generally over five minutes. Benzodiazepines (eg, lorazepam) may also be administered as needed for seizures.
Because physostigmine is uncommonly used and unfamiliar to many clinicians, it is best given after consultation with a medical toxicologist or regional poison center, if possible.In the US, call 1-800-222-1222 to be connected to the nearest poison center. Contact information for poison centers around the world is provided separately. (See 'Regional poison centers' below.)
Crowd-control agents—Most patients who have been exposed to crowd-control agents such as OC (oleoresin capsicum, pepper spray), CS (o-chlorobenzylidene malononitrile), and CN (mace) have mild effects and do well with removal from exposure and supportive care as needed. However, serious ocular and respiratory effects can occur [81-84]. Skin blisters from irritant or allergic contact dermatitis can result in 12 hours to a week after exposure if decontamination is delayed or incomplete . Allergic contact dermatitis and tracheobronchitis may also occur with repeated exposure to CS .
Risk factors for serious injury include exposure in an enclosed space, underlying pulmonary disease (eg, asthma or chronic obstructive pulmonary disease), and delivery by projectile mechanisms. Since these compounds are solids, and since one method of dispersion is their forceful ejection from canisters, ocular effects can include impaction of particles in the cornea. High doses (high concentrations and high durations of exposure) in confined spaces can lead to pulmonary edema and fatal acute lung injury.
There is no antidote for these agents. Treatment begins with removal from exposure. Contact lenses should be removed before eye irrigation. The clinician should perform copious irrigation of eyes and skin with water or normal saline. Inform the patient that transient worsening of pain with water or saline is normal. Hypochlorite (bleach) solutions, which can cause additional skin damage and, in the case of CS (o-chlorobenzylidene malononitrile), can generate toxic epoxides, are contraindicated.
Symptomatic management is as follows (table 1) [81,87]:
●Respiratory distress – If respiratory symptoms do not resolve with removal from exposure and fresh air, patients should receive supplemental oxygen (humidified, if available). Further care is determined by the presence of upper or lower airway findings:
•Upper airway (stridor, drooling, hoarseness, or laryngospasm):
-Inhaled racemic epinephrine for stridor or upper airway obstruction
-Pulmonary toilet (frequent suctioning)
-Bronchoscopy for severe upper airway obstruction
•Lower airway (wheezing):
-Inhaled short-acting beta-2 agonists (eg, albuterol)
-Systemic corticosteroids (eg, oral prednisolone or dexamethasone, or intravenous prednisolone)
●Eye exposure – Patients with significant eye pain, tearing, and blepharospasm warrant the following treatment:
•If no signs of penetrating or serious blunt eye injury, provide topical ophthalmic anesthetic (eg, proparacaine 0.5 percent, one drop to each eye)
•Perform irrigation for at least 20 minutes with fresh water or normal saline (see "Topical chemical burns: Initial evaluation and management", section on 'Patient with eye exposure')
•Perform a complete ocular examination, including fluorescein staining to identify corneal abrasions or other injuries to the eye (see "Approach to diagnosis and initial treatment of eye injuries in the emergency department")
ADDITIONAL RESOURCES
United States resources—The following resources provide a means of rapid notification of a chemical weapons attack within the United States (US) and access to specific medical guidance and consultation:
●Emergency Federal Hotline (US) – Federal chemical and biological hotline (US Government Response Center): 1-800-424-8802
●Chemical Hazards Emergency Medical Management (CHEMM) – An interactive online and downloadable clinical guide.
●Centers for Disease Control and Prevention – The physician's telephone line is (404) 639-3311. The CDC also provides a website that addresses all hazards preparedness and medical care, including both bioterrorism and chemical terrorism.
●Army Chemical Defense – The US Army Medical Research Institute of Chemical Defense (USAMRICD), at Aberdeen Proving Ground, Maryland is an important source of current research and clinical data and consultation concerning the medical response to chemical-warfare agents.
The Chemical Casualty Care Division (CCCD; 1-833-238-7756) is the USAMRICD division responsible for training, education, and clinical consultation. The CCCD provides comprehensive courses, a variety of training materials, and consultative services.
The US Army also has developed clinical practice guidelines for the initial response and medical management of chemical, biological, and radiological nuclear injury.
●US Food and Drug Administration (FDA) – The FDA has an excellent counterterrorism website that provides up-to-date information on antidotes for chemical agents, including pediatric dosing as it is validated. The main telephone number for the drug center at the FDA is (301) 594-5400, in Rockville Maryland. The Chemical and Bioterrorism Office at the FDA is located in CDER (Center for Drug Evaluation and Research). The telephone number for the FDA counterterrorism office is (301) 827-7777.
●Chemical biological incident response force – Following the 1995 Tokyo subway attack, the United States Marine Corps formed the Chemical Biological Incident Response Force (CBIRF) based near Washington, DC . The CBIRF will deploy anywhere in the United States and provide capabilities for agent detection and identification, casualty search and rescue, personnel decontamination, and emergency care and stabilization of contaminated personnel. They can decontaminate 200 casualties per hour, and they have been trained and equipped to identify 120,000 toxic industrial chemicals. The CBIRF can be requested by local, state, or federal agencies. Contact information is available here.
●American Academy of Pediatrics (AAP) – Pediatric considerations during a chemical terrorism event and for preparedness are discussed in reports from the AAP [89,90].
Regional poison centers—Regional poison centers in the US are available at all times for consultation on patients with known or suspected poisoning, and who may be critically ill, require admission, or have clinical pictures that are unclear (1-800-222-1222). In addition, some hospitals have medical toxicologists available for bedside consultation. Whenever available, these are invaluable resources to help in the diagnosis and management of ingestions or overdoses. Contact information for poison centers around the world is provided separately. (See "Society guideline links: Regional poison centers".)
Society guideline links—Links to society and government-sponsored guidelines from selected countries and regions around the world are provided separately. (See "Society guideline links: Chemical terrorism".)
SUMMARY AND RECOMMENDATIONS
●Chemical agent definitions – Chemical compounds capable of creating mass casualties include (see 'Chemical agent definitions' above):
•Traditional chemical agents (pulmonary agents, "blood" agents [cyanide compounds], vesicants [blister agents], nerve agents, and the anticholinergic agent BZ)
•Nontraditional agents
•Toxic industrial chemicals (TICs)
•Crowd-control agents
•Mid-spectrum agents (biological toxins) (see "Identifying and managing casualties of biological terrorism", section on 'Toxins of concern')
●Recognition of chemical exposure – Recognition of a chemical weapons release is based upon the following (see 'Recognition of chemical exposure' above):
•Incident features that suggest a chemical exposure (table 2)
•Clinical syndromes among casualties (algorithm 1)
•Confirmation using rapid detection methods and clinical laboratory studies
●Field incident response and decontamination – Key medical actions in the field include protection of first responders (Level A personal protection equipment [PPE] as defined by OSHA [ patient triage, spot decontamination, administration of antidotes to victims of suspected cyanide or nerve gas exposure (algorithm 2), and field decontamination. (See 'Field incident response' above and 'Local or spot decontamination' above and 'Field decontamination' above.)
●Hospital incident response – Upon identification or notification of a chemical weapons release, receiving facilities should secure all entrances and hospital grounds, establish a security perimeter, and set up a decontamination zone that is outside the clean parts of the facility. Disaster plans should be activated. Facility incident command and close communication with local emergency management authorities should be established. (See 'Hospital incident response' above.)
●Initial management – Initial hospital management of patients with chemical weapons exposure warrants the following actions:
•Protection of first receivers prior to decontamination (Level C PPE as defined by OSHA [ (see 'Protection of providers' above)
•Triage with immediate stabilization of airway, breathing, and circulation and, for victims of cyanide or nerve agent exposure, antidote administration (see 'Triage' above and 'Stabilization' above and 'Nerve agents' above and 'Cyanide' above)
•Spot decontamination (see 'Local or spot decontamination' above)
•Definitive decontamination based upon the specific exposure (table 1) (see 'Hospital decontamination' above)
•Agent-specific medical care and administration of antidotes (table 1) (see 'Initial management of specific exposures' above)
●Additional resources – Several online resources provide additional information on the response to a chemical weapons release including access to specific medical guidance and consultation. (See 'United States resources' above.)
ACKNOWLEDGMENTS—
The views expressed in this topic are those of the author(s) and do not reflect the official policy of the Department of Army, Department of Defense, or the US Government.
The author and editors acknowledge John Beary, III, MD, and Arkadi Chines, MD, both of whom contributed to earlier versions of this topic review.
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2-Hydroxypropanoic acid, is an organic acid with applications in beer production as well as the cosmetic, pharmaceutical, food and chemical industries.
2-Hydroxypropanoic acid is commonly used as a preservative and antioxidant.
2-Hydroxypropanoic acid also has uses as a fuel additive, chemical intermediate, acidity regulator, and disinfectant.
CAS Number: 50-21-5
EC Number: 200-018-0
Molecular Formula: C3H6O3
Molar Mass: 90.078 g·mol−1
Synonyms: lactic acid, 2-hydroxypropanoic acid, DL-Lactic acid, 50-21-5, 2-hydroxypropionic acid, Milk acid, lactate, Tonsillosan, Racemic lactic acid, Ordinary lactic acid, Ethylidenelactic acid, Lactovagan, Acidum lacticum, 26100-51-6, Milchsaeure, Lactic acid, dl-, Kyselina mlecna, Lacticum acidum, DL-Milchsaeure, Lactic acid USP, (+/-)-Lactic acid, Propanoic acid, 2-hydroxy-, Aethylidenmilchsaeure, 598-82-3, 1-Hydroxyethanecarboxylic acid, alpha-Hydroxypropionic acid, Lactic acid (natural), (RS)-2-Hydroxypropionsaeure, FEMA No. 2611, Milchsaure, Kyselina 2-hydroxypropanova, Lurex, Propionic acid, 2-hydroxy-, Purac FCC 80, Purac FCC 88, Cheongin samrakhan, FEMA Number 2611, CCRIS 2951, HSDB 800, Cheongin Haewoohwan, Cheongin Haejanghwan, SY-83, 2-Hydroxypropionicacid, (+-)-2-Hydroxypropanoic acid, Biolac, NSC 367919, Lactic acid, tech grade, Propanoic acid, hydroxy-, Chem-Cast, alpha-Hydroxypropanoic acid, AI3-03130, HIPURE 88, DL- lactic acid, EINECS 200-018-0, EINECS 209-954-4, EPA Pesticide Chemical Code 128929, Lactic acid,buffered, NSC-367919, UNII-3B8D35Y7S4, 2-Hydroxy-2-methylacetic acid, BRN 5238667, INS NO.270, DTXSID7023192, (+/-)-2-hydroxypropanoic acid, CHEBI:78320, INS-270, 3B8D35Y7S4, E 270, MFCD00004520, LACTIC ACID (+-), .alpha.-Hydroxypropanoic acid, .alpha.-Hydroxypropionic acid, DTXCID003192, E-270, EC 200-018-0, NCGC00090972-01, 2-hydroxy-propionic acid, (R)-2-Hydroxy-propionic acid;H-D-Lac-OH, C01432, Milchsaure [German], Lactic acid [JAN], Kyselina mlecna [Czech], D(-)-lactic acid, CAS-50-21-5, 2 Hydroxypropanoic Acid, 2 Hydroxypropionic Acid, Kyselina 2-hydroxypropanova [Czech], Lactic acid [USP:JAN], lactasol, 1-Hydroxyethane 1, carboxylic acid, acido lactico, DL-Milchsaure, (2RS)-2-Hydroxypropanoic acid, L- Lactic acid, Lactate (TN), 4b5w, Propanoic acid, (+-), DL-Lactic Acid, Racemic, LACTIC ACID (II), (.+/-.)-Lactic acid, Lactic acid (7CI,8CI), Lactic acid (JP17/USP), Lactic acid, 85%, FCC, Lactic Acid, Racemic, USP, NCIOpen2_000884, (+-)-LACTIC ACID, DL-LACTIC ACID [MI], LACTIC ACID [WHO-IP], (RS)-2-hydroxypropanoic acid, LACTIC ACID, DL-(II), LACTICUM ACIDUM [HPUS], 1-hydroxyethane carboxylic acid, 33X04XA5AT, DL-Lactic Acid (90per cent), CHEMBL1200559, Lactic acid, natural, >=85%, BDBM23233, L-lactic acid or dl-lactic acid, Lactic Acid, 85 Percent, FCC, LACTIC ACID, DL- [II], DL-Lactic acid, ~90% (T), DL-Lactic acid, AR, >=88%, DL-Lactic acid, LR, >=88%, DL- LACTIC ACID [WHO-DD], LACTIC ACID (EP MONOGRAPH), Lactic Acid, 10 Percent Solution, HY-B2227, LACTIC ACID (USP MONOGRAPH), Propanoic acid, 2-hydroxy- (9CI), Tox21_111049, Tox21_202455, Tox21_303616, BBL027466, NSC367919, STL282744, AKOS000118855, AKOS017278364, Tox21_111049_1, ACIDUM LACTICUM [WHO-IP LATIN], AM87208, DB04398, SB44647, SB44652, Propanoic acid,2-hydroxy-,(.+/-.)-, 2-Hydroxypropionic acid, DL-Lactic acid, NCGC00090972-02, NCGC00090972-03, NCGC00257515-01, NCGC00260004-01, 26811-96-1, Lactic Acid, 85 Percent, Reagent, ACS, CS-0021601, FT-0624390, FT-0625477, FT-0627927,, FT-0696525, FT-0774042, L0226, EN300-19542, Lactic acid, meets USP testing specifications, D00111, F71201, A877374, DL-Lactic acid, SAJ first grade, 85.0-92.0%, Q161249, DL-Lactic acid, JIS special grade, 85.0-92.0%, F2191-0200, Z104474158, BC10F553-5D5D-4388-BB74-378ED4E24908, Lactic acid, United States Pharmacopeia (USP) Reference Standard, Lactic acid, Pharmaceutical Secondary Standard; Certified Reference Material, DL-Lactic acid 90%, synthetic, meets the analytical specifications of Ph. Eur., 152-36-3
2-Hydroxypropanoic acid was discovered in 1780 by Swedish chemist, Carl Wilhelm Scheele, who isolated the 2-Hydroxypropanoic acid from sour milk as an impure brown syrup and gave 2-Hydroxypropanoic acid a name based on its origins: 'Mjölksyra'.
The French scientist Frémy produced 2-Hydroxypropanoic acid by fermentation and this gave rise to industrial production in 1881.
2-Hydroxypropanoic acid is produced by the fermentation of sugar and water or by chemical process and is commercially usually sold as a liquid.
Pure and anhydrous racemic 2-Hydroxypropanoic acid is a white crystalline solid with a low melting point.
2-Hydroxypropanoic acid has two optical forms, L(+) and D(-).
L(+)-2-Hydroxypropanoic acid is the biological isomer as 2-Hydroxypropanoic acid is naturally present in the human body.
2-Hydroxypropanoic acid can be produced naturally or synthetically.
Commercial 2-Hydroxypropanoic acid is produced naturally by fermentation of carbohydrates such as glucose, sucrose, or lactose.
Wih the addition of lime or chalk, the raw materials are fermented in a fermenter and crude calcium lactate is formed.
The gypsum is separated from the crude calcium lactate, which results in crude 2-Hydroxypropanoic acid.
The crude 2-Hydroxypropanoic acid is purified and concentrated and L(+) 2-Hydroxypropanoic acid is the result.
2-Hydroxypropanoic acid, is an organic acid with applications in beer production as well as the cosmetic, pharmaceutical, food and chemical industries.
2-Hydroxypropanoic acid is commonly used as a preservative and antioxidant.
2-Hydroxypropanoic acid also has uses as a fuel additive, chemical intermediate, acidity regulator, and disinfectant.
One specific use of 2-Hydroxypropanoic acid is in I.V solutions, where 2-Hydroxypropanoic acid is an electrolyte to help replenish the bodies fluids.
2-Hydroxypropanoic acid is also used in dialysis solutions, which results in a lower incidence of side effects compared to Sodium Acetate which can also be used.
2-Hydroxypropanoic acid comes in both R (D-) and S (L+) enantiomers which can be manufactured individually to near perfect optical purity.
This means 2-Hydroxypropanoic acid is great in the production of other products which require a specific stereochemistry.
2-Hydroxypropanoic acid is used frequently in the cosmetic industry due to the effect of promoting collagen production, helping to firm the skin against wrinkles and sagging.
2-Hydroxypropanoic acid can also cause micro peeling, which can help reduce various scars and age spots.
2-Hydroxypropanoic acid is a great solution for people with sensitive or dry skin where exfoliants don’t work.
2-Hydroxypropanoic acid is used as a food preservative, curing agent, and flavoring agent.
2-Hydroxypropanoic acid is an ingredient in processed foods and is used as a decontaminant during meat processing.
2-Hydroxypropanoic acid is produced commercially by fermentation of carbohydrates such as glucose, sucrose, or lactose, or by chemical synthesis.
2-Hydroxypropanoic acid, also named ‘milk acid’, is an organic acid with the following chemicalformula: CH3CH(OH)CO2H.
The official name given by the International Union ofPure and Applied Chemistry (IUPAC) is Lactic acid.
2-Hydroxypropanoic acid can be naturally produced, but 2-Hydroxypropanoic acid importanceis correlated with synthetic productions.
Pure 2-Hydroxypropanoic acid is a colourless andhydroscopic liquid; 2-Hydroxypropanoic acid can be defined a weak acid because of 2-Hydroxypropanoic acid partial dissociationin water and the correlated acid dissociation constant (Ka= 1.38 10−4).
2-Hydroxypropanoic acid is a chiral compound with a carbon chain composed of a central (chiral) atomand two terminal carbon atoms.
A hydroxyl group is attached to the chiral carbon atom while oneof the terminal carbon atoms is part of the carboxylic group and the other atom is part of the methylgroup.
Consequently, two optically active isomeric forms of 2-Hydroxypropanoic acid exist: L(+) form, alsonamed (S)-2-Hydroxypropanoic acid, and D(−) form, or (R)-2-Hydroxypropanoic acid.
L(+)-2-Hydroxypropanoic acid is the biological isomer.
Antibacterial mechanism of 2-Hydroxypropanoic acid on physiological and morphological properties of Salmonella Enteritidis, Escherichia coli and Listeria monocytogenes:
Pathogens could be completely inactivated after exposure to 2-Hydroxypropanoic acid.
2-Hydroxypropanoic acid resulted in great leakage of protein of three pathogens.
Bacterial protein bands of 2-Hydroxypropanoic acid-treated cells got fainter or disappeared.
Z-Average sizes of pathogens were changed to smaller after 2-Hydroxypropanoic acid treatment.
2-Hydroxypropanoic acid caused collapsed or even broken cells with obvious pits and gaps.
2-Hydroxypropanoic acid is widely used to inhibit the growth of important microbial pathogens, but 2-Hydroxypropanoic acid antibacterial mechanism is not yet fully understood.
The objective of this study was to investigate the antibacterial mechanism of 2-Hydroxypropanoic acid on Salmonella Enteritidis, Escherichia coli and Listeria monocytogenes by size measurement, TEM, and SDS-PAGE analysis.
The results indicated that 0.5% 2-Hydroxypropanoic acid could completely inhibit the growth of Salmonella Enteritidis, E. coli and L. monocytogenes cells.
Meanwhile, 2-Hydroxypropanoic acid resulted in leakage of proteins of Salmonella, E. coli and Listeria cells, and the amount of leakage after 6 h exposure were up to 11.36, 11.76 and 16.29 μg/mL, respectively.
Fifty strains each of Staphylococcus aureus, beta haemolytic Streptococci, Proteus species, Esch coli and Pseudomonas aeruginosa were subjected to 2%, 1 % and 0. 1 % 2-Hydroxypropanoic acid in peptorie water.
Minimum inhibitory concentration of 2-Hydroxypropanoic acid for all the strains of each of these organisms was 0.1% or 1%.
Depending upon 2-Hydroxypropanoic acids concentration, 2-Hydroxypropanoic acid added to peptone water brings down the PH to 2.5-4 which by itself has some inhibitory effect on the microorganisms.
2-Hydroxypropanoic acid however, retains 2-Hydroxypropanoic acid inhibitory effect even if the Ph of the peptone water is brought back to 7.3.
2-Hydroxypropanoic acid is a nontoxic and non-sensitizing agent because 2-Hydroxypropanoic acid is a normal metabolite of the body.
Thus, 2-Hydroxypropanoic acid can be used as a safe and effective antibacterial agent for local application.
2-Hydroxypropanoic acid is a normal intermediate in the fermentation (oxidation, metabolism) of sugar.
2-Hydroxypropanoic acid is concentrated form is used internally to prevent gastrointestinal fermentation.
2-Hydroxypropanoic acid is conversion to glucose via gluconeogenesis in the liver and release back into the circulation
2-Hydroxypropanoic acid is an organic acid occurring naturally in the human body and in fermented foods.
2-Hydroxypropanoic acid is used in a wide range of food, beverages, personal care, healthcare, cleaners, feed & pet food and chemical products as a mild acidity regulator with flavour enhancing and antibacterial properties.
The commercial production of 2-Hydroxypropanoic acid is typically done by fermentation.
Because the L(+) form is preferred for 2-Hydroxypropanoic acid better metabolisation, Jungbunzlauer has chosen to produce pure L(+)-2-Hydroxypropanoic acid by traditional fermentation of natural carbohydrates.
L(+)-2-Hydroxypropanoic acid is a colourless to yellowish, nearly odourless, syrupy liquid with a mild acid taste.
2-Hydroxypropanoic acid is commercially available as aqueous solutions of various concentrations.
These solutions are stable under normal storage conditions.
2-Hydroxypropanoic acid is non-toxic to humans and the environment, but concentrated solutions of 2-Hydroxypropanoic acid can cause skin irritation and eye damage.
2-Hydroxypropanoic acid is readily biodegradable.
Due to the high hygroscopicity of 2-Hydroxypropanoic acid, 2-Hydroxypropanoic acid concentrated aqueous solutions are usually used - syrupy, colorless, odorless liquids.
Oxidation of 2-Hydroxypropanoic acid is usually accompanied by decomposition.
Under the action of HNO 3 or O 2 of air in the presence of Cu or Fe, HCOOH, CH 3 COOH, (COOH) 2 , CH 3 CHO, CO 2 and pyruvic acid are formed.
Reduction of 2-Hydroxypropanoic acid HI leads to propionic acid, and reduction in the presence of Re-mobile leads to propylene glycol.
2-Hydroxypropanoic acid dehydrates to acrylic acid, when heated with HBr, forms 2-bromopropionic acid, when the Ca salt reacts with PCl 5 or SOCl 2 -2-chloropropionyl chloride.
In the presence of mineral acids, self-esterification of 2-Hydroxypropanoic acid occurs with the formation of lactone, as well as linear polyesters.
When 2-Hydroxypropanoic acid interacts with alcohols, hydroxy acids RCH 2 CH (OH) COOH are formed, and when 2-Hydroxypropanoic acid salts react with alcohol esters.
The salts and esters of 2-Hydroxypropanoic acid are called lactates.
2-Hydroxypropanoic acid is formed as a result of 2-Hydroxypropanoic acid fermentation (with sour milk, sauerkraut, pickling vegetables, ripening cheese, ensiling feed); D- 2-Hydroxypropanoic acid is found in tissues of animals, plants, and also in microorganisms.
In industry, 2-Hydroxypropanoic acid is obtained by hydrolysis of 2-chloropropionic acid and 2-Hydroxypropanoic acid salts (100 ° C) or lactonitrile CH 3 CH (OH) CN (100 ° C, H 2 SO 4 ), followed by the formation of esters, the isolation and hydrolysis of which leads to a high quality.
Other methods of producing 2-Hydroxypropanoic acid are known: the oxidation of propylene with nitrogen oxides (15-20 ° C) followed by treatment with H 2 SO 4 , the interaction of CH 3 CHO with CO (200 ° C, 20 MPa).
2-Hydroxypropanoic acid is used in the food industry, in mordant dyeing, in leather production, in fermentation shops as a bactericidal agent, for the production of medicines, plasticizers.
Ethyl and butyl lactates are used as solvents for cellulose ethers, drying oils, vegetable oils; butyl lactate - as well as a solvent for some synthetic polymers.
2-Hydroxypropanoic acid is an organic acid.
2-Hydroxypropanoic acid has a molecular formula CH3CH(OH)COOH.
2-Hydroxypropanoic acid is white in the solid state and 2-Hydroxypropanoic acid is miscible with water.
When in the dissolved state, 2-Hydroxypropanoic acid forms a colorless solution.
Production includes both artificial synthesis as well as natural sources.
2-Hydroxypropanoic acid is an alpha-hydroxy acid (AHA) due to the presence of a hydroxyl group adjacent to the carboxyl group.
2-Hydroxypropanoic acid is used as a synthetic intermediate in many organic synthesis industries and in various biochemical industries.
The conjugate base of 2-Hydroxypropanoic acid is called lactate.
In solution, 2-Hydroxypropanoic acid can ionize, producing the lactate ion CH3CH(OH)CO−2.
Compared to acetic acid, 2-Hydroxypropanoic acids pKa is 1 unit less, meaning 2-Hydroxypropanoic acid is ten times more acidic than acetic acid.
This higher acidity is the consequence of the intramolecular hydrogen bonding between the α-hydroxyl and the carboxylate group.
2-Hydroxypropanoic acid is chiral, consisting of two enantiomers.
One is known as l-(+)-2-Hydroxypropanoic acid or (S)-2-Hydroxypropanoic acid and the other, 2-Hydroxypropanoic acid mirror image, is d-(−)-2-Hydroxypropanoic acid or (R)-2-Hydroxypropanoic acid.
A mixture of the two in equal amounts is called dl-2-Hydroxypropanoic acid, or racemic 2-Hydroxypropanoic acid.
2-Hydroxypropanoic acid is hygroscopic.
dl-2-Hydroxypropanoic acid is miscible with water and with ethanol above 2-Hydroxypropanoic acid melting point, which is around 16, 17 or 18 °C.
d-2-Hydroxypropanoic acid and l-2-Hydroxypropanoic acid have a higher melting point.
2-Hydroxypropanoic acid produced by fermentation of milk is often racemic, although certain species of bacteria produce solely (R)-2-Hydroxypropanoic acid.
On the other hand, 2-Hydroxypropanoic acid produced by anaerobic respiration in animal muscles has the (S) configuration and is sometimes called "sarcolactic" acid, from the Greek "sarx" for flesh.
In animals, l-lactate is constantly produced from pyruvate via the enzyme lactate dehydrogenase (LDH) in a process of fermentation during normal metabolism and exercise.
2-Hydroxypropanoic acid does not increase in concentration until the rate of lactate production exceeds the rate of lactate removal, which is governed by a number of factors, including monocarboxylate transporters, concentration and isoform of LDH, and oxidative capacity of tissues.
The concentration of blood lactate is usually 1–2 mM at rest, but can rise to over 20 mM during intense exertion and as high as 25 mM afterward.
In addition to other biological roles, l-2-Hydroxypropanoic acid is the primary endogenous agonist of hydroxycarboxylic acid receptor 1 (HCA1), which is a Gi/o-coupled G protein-coupled receptor (GPCR).
In industry, 2-Hydroxypropanoic acid fermentation is performed by 2-Hydroxypropanoic acid bacteria, which convert simple carbohydrates such as glucose, sucrose, or galactose to 2-Hydroxypropanoic acid.
These bacteria can also grow in the mouth; the acid they produce is responsible for the tooth decay known as caries.
In medicine, lactate is one of the main components of lactated Ringer's solution and Hartmann's solution.
These intravenous fluids consist of sodium and potassium cations along with lactate and chloride anions in solution with distilled water, generally in concentrations isotonic with human blood.
2-Hydroxypropanoic acid is most commonly used for fluid resuscitation after blood loss due to trauma, surgery, or burns.
2-Hydroxypropanoic acid is a hydroxycarboxylic acid CH3CH(OH)COOH with two stereoisomers (D(-) and L(+)) and 2-Hydroxypropanoic acid has several applications in food, chemical, pharmaceutical and health care industries.
2-Hydroxypropanoic acid is primarily used for food and pharmaceutical applications, preferentially the L(+) isomer, since 2-Hydroxypropanoic acid is the only 2-Hydroxypropanoic acid isomer produced in the human body.
Around 20 to 30% of the 2-Hydroxypropanoic acid production is used to obtain biopolymers (poly2-Hydroxypropanoic acid).
Other uses of 2-Hydroxypropanoic acid include fibers and green solvents.
2-Hydroxypropanoic acid is fully commercially available and largely (90%) produced by bacteria through anaerobic fermentation of sugars.
2-Hydroxypropanoic acid can also be commercially produced by chemical synthesis.
The chemical production pathway gives an optical inactive racemic mixture (with the same quantity of L and D isomers), while the anaerobic fermentation pathway mostly yieldsone of the two stereoisomers, depending on the microorganism chosen.
The biotechnological option is widely available due to 2-Hydroxypropanoic acid renewable origin.
2-Hydroxypropanoic acid can be produced via fermentation of sugars from different biomass, such as: starch crops, sugar crops, lignocellulosic materials and also from whey (a residue from cheese production).
The bulk of world production is based on homoplastic fermentation of sugars (from starch or sugar crops) where 2-Hydroxypropanoic acid is produced as sole product.
Conventional production systems require the addition of calcium hydroxide to control the fermentation pH.
This procedure results in calcium lactate as final product.
Several steps are required to ultimately obtain and purify 2-Hydroxypropanoic acid: filtration, acidification, carbon adsorption, evaporation, esterification, hydrolysis and distillation.
The conventional process is associated with high costs (due to the complex purification procedure) and poor environmental performance due to the production of large amounts of chemical effluents (e.g. calcium sulphate).
New separation technologies are being developed, such as bipolar electrodialysis with promising results.
2-Hydroxypropanoic acid, the most fundamental natural ingredient in the dairy industry
In dairy products, 2-Hydroxypropanoic acid is one of the most common ingredients.
2-Hydroxypropanoic acids purpose is generally as an acid regulator and in terms of flavouring.
The slightly sour taste observed in yogurts, cheeses and other milk products is generally the result of fermentation from 2-Hydroxypropanoic acid.
The signature flavour of sourdough bread is also a result of 2-Hydroxypropanoic acid during the baking process.
With the addition of this versatile supplement, the product can be acidified with ease to reach proper pH levels, while leaving the natural flavours undisturbed.
2-Hydroxypropanoic acid, DL- is the racemic isomer of 2-Hydroxypropanoic acid, the biologically active isoform in humans.
2-Hydroxypropanoic acid or lactate is produced during fermentation from pyruvate by lactate dehydrogenase.
This reaction, in addition to producing 2-Hydroxypropanoic acid, also produces nicotinamide adenine dinucleotide (NAD) that is then used in glycolysis to produce energy source adenosine triphosphate (ATP).
2-Hydroxypropanoic acid appears as a colorless to yellow odorless syrupy liquid.
Corrosive to metals and tissue.
Used to make cultured dairy products, as a food preservative, and to make chemicals.
A normal intermediate in the fermentation (oxidation, metabolism) of sugar.
The concentrated form is used internally to prevent gastrointestinal fermentation.
Sodium lactate is the sodium salt of 2-Hydroxypropanoic acid, and has a mild saline taste.
2-Hydroxypropanoic acid is produced by fermentation of a sugar source, such as corn or beets, and then, by neutralizing the resulting 2-Hydroxypropanoic acid to create a compound having the formula NaC3H5O3.
2-Hydroxypropanoic acid was one of active ingredients in Phexxi, a non-hormonal contraceptive agent that was approved by the FDA on May 2020.
2-Hydroxypropanoic acid (chemically, alpha or 2-Hydroxypropionic acid) takes roles in metabolic processes in the body; in red blood and in skeletal muscle tissues as a product of glucose and glycogen metabolism.
2-Hydroxypropanoic acid is an "alpha hydroxy acid: which has a hydroxyl group on the carbon atom next to the acid group.
If the hydroxy group is on the second carbon next to the acid group, 2-Hydroxypropanoic acid is called beta-hydroxy acid.
2-Hydroxypropanoic acid is converted in vivo to pyruvic acid (an alpha keto acid) which occurs as an intermediate product in carbohydrate and protein metabolism in the body.
2-Hydroxypropanoic acid occurs as two optical isomers since the central carbon atom is bound to four different groups; a dextro and a levo form ( or an inactive racemic mixture of the two); only the levo form takes part in animal metabolism. 2-Hydroxypropanoic acid is present in sour milk and dairy products such as cheese, yogurt, and koumiss, leban, wines.
2-Hydroxypropanoic acid causes tooth decay since 2-Hydroxypropanoic acid bacteria operates in the mouth.
Although 2-Hydroxypropanoic acid can be prepared by chemical synthesis, production of 2-Hydroxypropanoic acid by fermentation of glucose and other sugar substances in the presence of alkaline such as lime or calcium carbonate is a less expensive method.
The six-carbon glucose molecule is broken down to two molecules of the three-carbon compounds (2-Hydroxypropanoic acid), during this anaerobic condition.
Synthetic 2-Hydroxypropanoic acid is used commercially in tanning leather and dyeing wool; as a flavouring agent and preservative in food processing and carbonated beverages; and as a raw material in making plastics, solvents, inks, and lacquers; as a catalyst in numerous chemical processes.
2-Hydroxypropanoic acid is available as aqueous solutions of various concentrations, usually 22 - 85 percent (pure 2-Hydroxypropanoic acid is a colourless, crystalline substance.)
Although 2-Hydroxypropanoic acid is usually associated with milk and dairy products, 2-Hydroxypropanoic acid can also be found in many other fermented food products, including confectionery products, jams, frozen desserts, and pickled vegetables.
2-Hydroxypropanoic acid bacteria (LAB) are heterogenous group of bacteria which plays a significant role in a variety of fermentation processes.
They ferment food carbohydrates and produce 2-Hydroxypropanoic acid as the main product of fermentation.
In addition, degradation of proteins and lipids and production of various alcohols, aldehydes, acids, esters and sulphur compounds contribute to the specific flavour development in different fermented food products.
The main application of LAB is as starter cultures, with an enormous variety of fermented dairy (ie. cheese, yoghurt, fermented milks), meat, fish, fruit, vegetable and cereal products.
Besides, they contribute to the flavour, texture and nutritional value of the fermented foods, and thus they are used as adjunct cultures.
Acceleration of cheese maturation, enhancement of yoghurt texture with the production of exo polysaccharides and control of secondary fermentations in the production of wine are some examples.
The production of bacteriocins and antifungal compounds has lead to the application of bio-protective cultures in certain foods.
Moreover, the well-documented health-promoting properties of certain LAB have lead to the addition of selected strains, in combination with bifidobacteria, as probiotic cultures with various applications in food industry.
2-Hydroxypropanoic acid is an organic acid generated by microbial fermentation.
Several studies have tested a 2% concentration of 2-Hydroxypropanoic acid as a sanitizer, either by itself or in combination with a surface-active agent.
2-Hydroxypropanoic acid–based sanitizers interfere with cell membrane permeability and cell functions such as nutrient transport.
These sanitizers are very promising and research is ongoing regarding their uses.
For example, in a recent study, ten commercially available sanitizers were tested for their effectiveness against Listeria monocytogenes on high-density polyethylene cutting boards.
Of all the products tested, which included QACs and sodium hypochlorite, a lactic-based sanitizer was the most effective against biofilm cells.
2-Hydroxypropanoic acid is used since 1990s as a fine chemical (production 60 000–80 000 tons yr−1).
A major share (25 000 tons yr−1) is used as additive in the food industry.
The second main application is as building block for green polymers, solvents, and plasticizers.
2-Hydroxypropanoic acid is chemically produced by hydrocyanation followed by hydrolysis of the cyanohydrin.
The main drawbacks are the manipulation of hydrogen cyanide (HCN), the production of (NH4)2SO4 (1 eq), and the complex purification steps to obtain food-grade 2-Hydroxypropanoic acid because the racemic acid is obtained.
To overcome these difficulties, the anaerobic fermentation from carbohydrates using Lactobacillus delbrueckii is a good alternative because only (S)-2-Hydroxypropanoic acid is obtained in only one step.
The fermentation is performed at 50 °C over 2–8 days with a yield of 85–95% and the product concentration is 100 g l−1.
2-Hydroxypropanoic acid bacteria (LAB) play an important role in food, agricultural, and clinical applications.
The general description of the bacteria included in the group is gram-positive, nonsporing, nonrespiring cocci or rods, which produce 2-Hydroxypropanoic acid as the major end product during the fermentation of carbohydrates.
The common agreement is that there is a core group consisting of four genera; Lactobacillus, Leuconostoc, Pediococcus and Streptococcus.
Recent taxonomic revisions have proposed several new genera and the remaining group now comprises the following: Aerococcus, Alloiococcus, Carnobacterium, Dolosigranulum, Enterococcus, Globicatella, Lactococcus, Oenococcus, Tetragenococcus, Vagococcus, and Weissella.
Their importance is associated mainly with their safe metabolic activity while growing in foods utilising available sugar for the production of organic acids and other metabolites.
Their common occurrence in foods along with their long-lived uses contributes to their natural acceptance as GRAS (Generally Recognised as Safe) for human consumption.
The three main pathways which are involved in the manufacture and development of flavour in fermented food products are as follows:
1) glycolysis (fermentation of sugars)
2) lipolysis (degradation of fat) and
3) proteolysis (degradation of proteins)
Lactate is the main product generated from the metabolism of carbohydrates and a fraction of the intermediate pyruvate can alternatively be converted to diacetyl, acetoin, acetaldehyde or acetic acid (some of which can be important for typical yogurt flavours).
The contribution of LAB to lipolysis is relatively little, but proteolysis is the key biochemical pathway for the development of flavour in fermented foods.
Degradation of such components can be further converted to various alcohols, aldehydes, acids, esters and sulphur compounds for specific flavour development in fermented food products.
The genetics of the LAB have been reviewed and complete genome sequences of a great number of LAB have been published since 2001, when the first genome of LAB was sequenced and published.
2-Hydroxypropanoic acid Adjunct cultures:
Secondary cultures, or adjunct cultures or adjuncts, are defined as any cultures that are deliberately added at some point of the manufacture of fermented foods, but whose primary role is not acid production.
Adjunct cultures are used in cheese manufacture to balance some of the biodiversity removed by pasteurisation, improved hygiene and the addition of defined-strain starter culture.
These are mainly non-starter LAB which have a significant impact on flavour and accelerate the maturation process.
Extracellular polysaccharides (EPSs) are produced by a variety of bacteria and are present as capsular polysaccharides bound to the cell surface, or are released into the growth medium.
These polymers play a major role in the production of yogurt, cheese, fermented cream and milk-based desserts where they contribute to texture, mouth-feel, taste perception and stability of the final products.
In addition, 2-Hydroxypropanoic acid has been suggested that these EPSs or fermented milks containing these EPSs are active as prebiotics, cholesterol-lowering and immunomodulants.
EPS-producing strains of Streptococcus thermophilus and Lactobacillus delbreuckii ssp. bulgaricus have been shown to enhance the texture and viscosity of yogurt and to reduce syneresis.
For the production of wine, LAB are involved in the malolactic fermentation, that is a secondary fermentation, which involves the conversion of L-malate to L-lactate and CO2 via malate decarboxylase, also known as the malolactic enzyme, resulting in a reduction of wine acidity, providing microbiological stabilization and modifications of wine aroma.
Antifungal activities of LAB have been reported.
In addition; LAB strains also have the ability to reduce fungal mycotoxins, either by producing anti-mycotoxinogenic metabolites, or by absorbing them.
For LAB to be used as bio-protective starter cultures, they must possess a range of physical and biochemical characteristics, and most importantly, the ability to achieve growth and sufficient production of antimicrobial metabolites, which must be demonstrated in the specific food environment.
Probiotic culture:
LAB are considered as a major group of probiotic bacteria; probiotic has been defined by Fuller as "a live microbial feed supplement which beneficially affects the host animal by improving 2-Hydroxypropanoic acid intestinal microbial balance".
Salminen et al. proposed that probiotics are microbial cell preparations or components of microbial cells that have a beneficial effect on the health and well-being of the host.
Commercial cultures used in food applications include mainly strains of Lactobacillus spp., Bifidobacterium spp. and Propionibacterium spp. Lactobacillus acidophilus, Lactobacillus casei, Lb. reuteri, Lactobacillus rhamnosus and Lb. plantarum are the most used LAB in functional foods containing probiotics.
Argentinean Fresco cheese, Cheddar and Gouda are some examples of applications of probiotic LAB, in combination with bifidobacteria, in cheeses.
Apparently, these effects are species and strain specific, and the big challenge is the use of probiotic cultures composed of multiple species.
In addition, LAB, as part of gut microbiota ferment various substrates such as biogenic amines and allergenic compounds into short-chain fatty acids and other organic acids and gases.
In recent years, the genomes of several probiotic species have been sequenced, thus paving the way to the application of ‘omics’ technologies to the investigation of probiotic activities.
Moreover, although recombinant probiotics have been constructed, the industrial application of genetically engineered bacteria is still hampered by legal issues and by a rather negative general public opinion in the food sector.
Conclusion:
LAB are the most commonly used microorganisms for the fermentation and preservation of foods.
Their importance is associated mainly with their safe metabolic activity while growing in foods utilising available sugar for the production of organic acids and other metabolites.
Advances in the genetics, molecular biology, physiology, and biochemistry of LAB have provided new insights and applications for these bacteria.
Bacterial cultures with specific traits have been developed during the last 17 years, since the discovery of the complete genome sequence of Lc. lactis ssp. lactis IL1403 and a variety of commercial starter, functional, bio-protective and probiotic cultures with desirable properties have marketed.
However, the great challenge for food industry is to produce multiple strain cultures with multiple functions for specific products from specific regions of the world.
Also 2-Hydroxypropanoic acid is a challenge to produce foods, which are similar in sensory characteristics and nutritional value to the traditional products, even with special health-promoting properties, in a standardized, safe and controlled process.
2-Hydroxypropanoic acid and Lactate:
2-Hydroxypropanoic acid is a weak acid, which means that 2-Hydroxypropanoic acid only partially dissociates in water.
2-Hydroxypropanoic acid dissociates in water resulting in ion lactate and H+.
This is a reversible reaction and the equilibrium is represented below.
CH3CH(OH)CO2H H+ + CH3CH(OH)CO2-Ka= 1.38 x 10-4
Depending on the environmental pH, weak acids such as 2-Hydroxypropanoic acid are either present as the acid in 2-Hydroxypropanoic acid undissociated form at low pH or as the ion salt at higher pH.
The pH at which 50% of the acid is dissociated is called the pKa, which for 2-Hydroxypropanoic acid is 3.86.
Under physiological circumstances the pH is generally higher than the pKa, so the majority of 2-Hydroxypropanoic acid in the body will be dissociated and present as lactate.
In the undissociated (unionized) form the substrates are able to pass through the lipid membranes, unlike the dissociated (ionized) form which cannot.
2-Hydroxypropanoic acid (2-hydroxypropionic acid) is one of the large-scale chemical that is produced via fermentation.
The commonly used feedstocks are carbohydrates obtained from different sources like corn starch, sugarcane, or tapioca starch – depending on local availability.
The carbohydrates are hydrolyzed into monosaccharides and then fermented under the absence of oxygen by microorganisms into 2-Hydroxypropanoic acid.
2-Hydroxypropanoic acid is the building block for poly2-Hydroxypropanoic acid, but 2-Hydroxypropanoic acid is also used in a broad variety of food and cosmetic applications.
Bio-based 2-Hydroxypropanoic acid is optically active, and the production of either l-(+)- or d-(–)-2-Hydroxypropanoic acid can be directed with bioengineered microorganisms.
2-Hydroxypropanoic acid (2-hydroxypropionic acid) ranks among the high-volume chemicals produced microbially, with an annual world production volume in the range of 370 000 MT.
2-Hydroxypropanoic acid fermentation is among the oldest industrial fermentations, with industrial production via fermentation starting in the 1880s.
Seventy-five percent of the current world 2-Hydroxypropanoic acid production occurs in the fermentation facilities of Galactic, PURAC Corporation, Cargill Incorporated, Archer Daniels Midland Company, and the joint ventures derived from these companies.
Historically, the primary use of 2-Hydroxypropanoic acid has been in food for acidulation and preservation, and 2-Hydroxypropanoic acid has been granted GRAS (generally recognized as safe) status by the FDA.
2-Hydroxypropanoic acid also finds uses in leather tanning, cosmetics, pharmaceutical applications, as well as various other niches.
World 2-Hydroxypropanoic acid production has expanded 10-fold in the last decade due, in large part, to increased demand for green products derived from 2-Hydroxypropanoic acid, including ethyl lactate and poly2-Hydroxypropanoic acid (PLA).
Ethyl lactate can be utilized in a variety of green solvents, and although 2-Hydroxypropanoic acid low human toxicity relative to hydrocarbon alternatives is attractive, price is cited as the primary reason for 2-Hydroxypropanoic acid limited market use.
PLA is a polymer that is considered a green alternative to petroleum-derived plastics due to 2-Hydroxypropanoic acid biodegradability and reduced carbon footprint.
PLA products are on the market in a wide range of applications including packaging, fibers, and foams.
The world’s major producer of PLA is NatureWorks LLC, currently wholly owned by Cargill Incorporated.
The primary cost in the production of PLA and ethyl lactate is the cost of raw material, that is, 2-Hydroxypropanoic acid.
The key parameters that determine the cost of 2-Hydroxypropanoic acid are rate, titer, and yield, in both fermentation and downstream product recovery unit operations.
Furthermore, 2-Hydroxypropanoic acid production accounts for a large fraction of the energy input and greenhouse gas (GHG) emissions in 2-Hydroxypropanoic acid-derived products.
These carbon costs can be of great concern in the marketing and viability of a green product.
As discussed previously, 2-Hydroxypropanoic acid production has occurred for over 100 years, with only modest changes to conditions or host organisms.
2-Hydroxypropanoic acid is produced via fermentation, traditionally carried out by bacteria belonging to the genera Lactobacillus, Lactococcus, Streptococcus, Bacillus, and Enterococcus.
For the recent applications of 2-Hydroxypropanoic acid as a green chemical intermediate, for example, for PLA, the cost of production via traditional process is too high.
As a result, a production strain for industrial 2-Hydroxypropanoic acid must fit the following criteria: production of > 100 g l−1 2-Hydroxypropanoic acid at yields near theoretical (0.9 g 2-Hydroxypropanoic acid per gram of dextrose), high chiral purity of 2-Hydroxypropanoic acid produced (> 99%) with rates, media, and recovery costs able to meet the above cost targets.
Lowering this production cost holds the potential to expand the market for both 2-Hydroxypropanoic acid and 2-Hydroxypropanoic acid green derivatives.
The primary costs associated with fermentation are the nutrients and sugars required for cell growth and 2-Hydroxypropanoic acid production along with the downstream recovery and purification process.
In addition to a sugar source, traditional bacterial lactic fermentations typically require an organic nitrogen source (such as yeast extract or corn steep liquor) along with B vitamin supplementation.
Furthermore, these fermentations require that the pH be maintained in the range of 5–7, well above the pKa of 2-Hydroxypropanoic acid.
Maintaining the pH in this range requires neutralization of the 2-Hydroxypropanoic acid during fermentation, followed by costly downstream steps or acidulation to regenerate free 2-Hydroxypropanoic acid.
This greatly increases the cost of fermentation.
In 2008, Cargill implemented a new-to-the-world fermentation technology involving genetically modified yeast capable of producing 2-Hydroxypropanoic acid at industrially relevant rates, titers, and yields at pH values ≤ 3.0, which is well below the pKa of 2-Hydroxypropanoic acid.
The low-pH fermentation process results in improved product quality and downstream processing, reduced chemical usage and nutrient costs, and a 35% reduction in the GHG emissions associated with 2-Hydroxypropanoic acid production by fermentation.
Additionally, the potential for product loss due to bacteriophage attacks and microbial contamination that can occur in the traditional bacterial process are eliminated or greatly reduced with the low-pH yeast process.
This increased process robustness contributes to reduction in the overall cost of 2-Hydroxypropanoic acid production and subsequently has helped to grow the market for 2-Hydroxypropanoic acid and 2-Hydroxypropanoic acid derivatives.
Future advances in the low-pH yeast process are expected to lower the cost of 2-Hydroxypropanoic acid production even more by reducing the cost of the carbon source fermented to 2-Hydroxypropanoic acid.
To achieve this, low-pH yeasts need to be further developed to efficiently ferment low-cost carbon sources to free 2-Hydroxypropanoic acid.
2-Hydroxypropanoic acid was estimated by life cycle analysis that through the use of cellulosic feedstocks derived from biomass and the use of wind power to produce 2-Hydroxypropanoic acid and PLA, the overall GHG emissions could be calculated as a net negative
Applications of 2-Hydroxypropanoic acid:
Pharmaceutical and cosmetic applications:
2-Hydroxypropanoic acid is also employed in pharmaceutical technology to produce water-soluble lactates from otherwise-insoluble active ingredients.
2-Hydroxypropanoic acid finds further use in topical preparations and cosmetics to adjust acidity and for 2-Hydroxypropanoic acid disinfectant and keratolytic properties.
Foods:
2-Hydroxypropanoic acid is found primarily in sour milk products, such as koumiss, laban, yogurt, kefir, and some cottage cheeses.
The casein in fermented milk is coagulated (curdled) by 2-Hydroxypropanoic acid.
2-Hydroxypropanoic acid is also responsible for the sour flavor of sourdough bread.
In lists of nutritional information 2-Hydroxypropanoic acid might be included under the term "carbohydrate" (or "carbohydrate by difference") because this often includes everything other than water, protein, fat, ash, and ethanol.
If this is the case then the calculated food energy may use the standard 4 kilocalories (17 kJ) per gram that is often used for all carbohydrates.
But in some cases 2-Hydroxypropanoic acid is ignored in the calculation.
The energy density of 2-Hydroxypropanoic acid is 362 kilocalories (1,510 kJ) per 100 g.
Some beers (sour beer) purposely contain 2-Hydroxypropanoic acid, one such type being Belgian lambics.
Most commonly, this is produced naturally by various strains of bacteria.
These bacteria ferment sugars into acids, unlike the yeast that ferment sugar into ethanol.
After cooling the wort, yeast and bacteria are allowed to “fall” into the open fermenters.
Brewers of more common beer styles would ensure that no such bacteria are allowed to enter the fermenter.
Other sour styles of beer include Berliner weisse, Flanders red and American wild ale.
In winemaking, a bacterial process, natural or controlled, is often used to convert the naturally present malic acid to 2-Hydroxypropanoic acid, to reduce the sharpness and for other flavor-related reasons.
This malolactic fermentation is undertaken by 2-Hydroxypropanoic acid bacteria.
While not normally found in significant quantities in fruit, 2-Hydroxypropanoic acid is the primary organic acid in akebia fruit, making up 2.12% of the juice.
As a food additive 2-Hydroxypropanoic acid is approved for use in the EU, USA and Australia and New Zealand; 2-Hydroxypropanoic acid is listed by 2-Hydroxypropanoic acid INS number 270 or as E number E270.
2-Hydroxypropanoic acid is used as a food preservative, curing agent, and flavoring agent.
2-Hydroxypropanoic acid is an ingredient in processed foods and is used as a decontaminant during meat processing.
2-Hydroxypropanoic acid is produced commercially by fermentation of carbohydrates such as glucose, sucrose, or lactose, or by chemical synthesis.
Carbohydrate sources include corn, beets, and cane sugar.
Forgery:
2-Hydroxypropanoic acid has historically been used to assist with the erasure of inks from official papers to be modified during forgery.
Cleaning products:
2-Hydroxypropanoic acid is used in some liquid cleaners as a descaling agent for removing hard water deposits such as calcium carbonate, forming the lactate, Calcium lactate.
Owing to 2-Hydroxypropanoic acids high acidity, such deposits are eliminated very quickly, especially where boiling water is used, as in kettles.
2-Hydroxypropanoic acid also is gaining popularity in antibacterial dish detergents and hand soaps replacing Triclosan.
Uses of 2-Hydroxypropanoic acid:
2-Hydroxypropanoic acid is used as a solvent and acidulant in the production of foods, drugs, and dyes.
2-Hydroxypropanoic acid is also used as a mordant in woolen goods printing, a soldering flux, a dehairing agent, and a catalyst for phenolic resins.
2-Hydroxypropanoic acid is also used in leather tanning, oil well acidizing, and as a plant growth regulator.
The fastest growing use for 2-Hydroxypropanoic acid is 2-Hydroxypropanoic acid use as a monomer for the production of poly2-Hydroxypropanoic acid or polylactide (PLA).
Applications for PLA include containers for the food and beverage industries, films and rigid containers for packaging, and serviceware (cups, plates, utensils).
The PLA polymer can also be spun into fibers and used in apparel, fiberfill (pillows, comforters), carpet, and nonwoven applications such as wipes.
2-Hydroxypropanoic acid is used in metal plating, cosmetics, and the textile and leather industry.
2-Hydroxypropanoic acid is used in dyeing baths, as mordant in printing woolen goods, solvent for water-insoluble dyes (alcohol-soluble induline, nigrosine, spirit-blue).
2-Hydroxypropanoic acid is used in reducing chromates in mordanting wool.
2-Hydroxypropanoic acid is used in manufacturing cheese, confectionery.
2-Hydroxypropanoic acid is used in component of babies' milk formulas; acidulant in beverages; for acidulating worts in brewing.
2-Hydroxypropanoic acid is used in in preparation of sodium lactate injections.
2-Hydroxypropanoic acid is used in ingredient of cosmetics.
2-Hydroxypropanoic acid is used in component of spermatocidal jellies.
2-Hydroxypropanoic acid is used in for removing Clostridium butyricum in manufacturing of yeast; dehairing, plumping, and decalcifying hides.
2-Hydroxypropanoic acid is used in solvent for cellulose formate.
2-Hydroxypropanoic acid is used in flux for soft solder.
2-Hydroxypropanoic acid is used in manufacturing lactates which are used in food products, in medicine, and as solvents.
2-Hydroxypropanoic acid is used in plasticizer, catalyst in the casting of phenolaldehyde resins.
2-Hydroxypropanoic acid in Food:
2-Hydroxypropanoic acid is naturally present in many foodstuffs.
2-Hydroxypropanoic acid is formed by natural fermentation in products such as cheese, yogurt, soy sauce, sourdough, meat products and pickled vegetables.
2-Hydroxypropanoic acid is also used in a wide range of food applications such as bakery products, beverages, meat products, confectionery, dairy products, salads, dressings, ready meals, etc.
2-Hydroxypropanoic acid in food products usually serves as either as a pH regulator or as a preservative.
2-Hydroxypropanoic acid is also used as a flavoring agent.
Meat, Poultry & Fish:
2-Hydroxypropanoic acid can be used in meat, poultry and fish in the form of sodium or potassium lactate to extend shelf life, control pathogenic bacteria (improve food safety), enhance and protect meat flavor, improve water binding capacity and reduce sodium.
Beverages:
Because of 2-Hydroxypropanoic acid mild taste, 2-Hydroxypropanoic acid is used as an acidity regulator in beverages such as soft drinks and fruit juices.
Pickled vegetables:
2-Hydroxypropanoic acid is effective in preventing the spoilage of olives, gherkins, pearl onions and other vegetables preserved in brine.
Salads & dressings:
2-Hydroxypropanoic acid may be also used as a preservative in salads and dressings, resulting in products with a milder flavor while maintaining microbial stability and safety.
Confectionery:
Formulating hard-boiled candy, fruit gums and other confectionery products with 2-Hydroxypropanoic acid results in a mild acid taste, improved quality, reduced stickiness and longer shelf life.
Dairy:
The natural presence of 2-Hydroxypropanoic acid in dairy products, combined with the dairy flavor and good antimicrobial action of 2-Hydroxypropanoic acid, makes 2-Hydroxypropanoic acid an excellent acidification agent for many dairy products.
Baked Goods:
2-Hydroxypropanoic acid is a natural sourdough acid, which gives the bread 2-Hydroxypropanoic acid characteristic flavor, and therefore 2-Hydroxypropanoic acid can be used for direct acidification in the production of sourdough.
Savory Flavors:
2-Hydroxypropanoic acid is used to enhance a broad range of savory flavors.
2-Hydroxypropanoic acids natural occurrence in meat and dairy products makes 2-Hydroxypropanoic acid an attractive way to enhance savory flavors.
Pharmaceutical:
The primary functions for the pharmaceutical applications are: pH-regulation, metal sequestration, chiral intermediate and as a natural body constituent in pharmaceutical products.
Biomaterials:
2-Hydroxypropanoic acid is a valuable component in biomaterials such as resorbable screws, sutures and medical devices.
Detergents:
2-Hydroxypropanoic acid well known for 2-Hydroxypropanoic acid descaling properties and is widely applied in household cleaning products.
Also, 2-Hydroxypropanoic acid is used as a natural anti-bacterial agent in disinfecting products.
Technical:
2-Hydroxypropanoic acid is used in a wide variety of industrial processes where acidity is required and where 2-Hydroxypropanoic acid properties offer specific benefits.
Examples are the manufacture of leather and textile products and computer disks, as well as car coating.
Animal Feed:
2-Hydroxypropanoic acid is a commonly used additive in animal nutrition.
2-Hydroxypropanoic acid has health promoting properties, thus enhancing the performance of farm animals.
2-Hydroxypropanoic acid can be used as an additive in food and/or drinking water.
2-Hydroxypropanoic acid in biodegradable plastics
2-Hydroxypropanoic acid is the principal building block for Poly 2-Hydroxypropanoic acid (PLA).
PLA is a biobased and bio-degradable polymer that can be used for producing renewable and compostable plastics.
Industry Uses:
Agricultural chemicals (non-pesticidal)
Intermediate
Not Known or Reasonably Ascertainable
Plating agents and surface treating agents
Process regulators
Processing aids, not otherwise listed
Consumer Uses:
Agricultural chemicals (non-pesticidal)
Intermediate
Preservative
Processing aids, not otherwise listed
Industrial Processes with risk of exposure:
Petroleum Production and Refining
Soldering
Farming (Pesticides)
Leather Tanning and Processing
Fur Dressing and Dyeing
Textiles (Printing, Dyeing, or Finishing)
Biology of 2-Hydroxypropanoic acid:
l-2-Hydroxypropanoic acid is the primary endogenous agonist of hydroxycarboxylic acid receptor 1 (HCA1), a Gi/o-coupled G protein-coupled receptor (GPCR).
Exercise and lactate:
During power exercises such as sprinting, when the rate of demand for energy is high, glucose is broken down and oxidized to pyruvate, and lactate is then produced from the pyruvate faster than the body can process it, causing lactate concentrations to rise.
The production of lactate is beneficial for NAD+ regeneration (pyruvate is reduced to lactate while NADH is oxidized to NAD+), which is used up in oxidation of glyceraldehyde 3-phosphate during production of pyruvate from glucose, and this ensures that energy production is maintained and exercise can continue.
During intense exercise, the respiratory chain cannot keep up with the amount of hydrogen ions that join to form NADH, and cannot regenerate NAD+ quickly enough.
The resulting lactate can be used in two ways:
Oxidation back to pyruvate by well-oxygenated muscle cells, heart cells, and brain cells
Pyruvate is then directly used to fuel the Krebs cycle
Conversion to glucose via gluconeogenesis in the liver and release back into circulation; see Cori cycle
If blood glucose concentrations are high, the glucose can be used to build up the liver's glycogen stores.
However, lactate is continually formed even at rest and during moderate exercise.
Some causes of this are metabolism in red blood cells that lack mitochondria, and limitations resulting from the enzyme activity that occurs in muscle fibers having high glycolytic capacity.
In 2004, Robergs et al. maintained that 2-Hydroxypropanoic acidosis during exercise is a "construct" or myth, pointing out that part of the H+ comes from ATP hydrolysis (ATP4− + H2O → ADP3− + HPO2− 4 + H+), and that reducing pyruvate to lactate (pyruvate− + NADH + H+ → lactate− + NAD+) actually consumes H+.
Lindinger et al. countered that they had ignored the causative factors of the increase in [H+].
After all, the production of lactate− from a neutral molecule must increase [H+] to maintain electroneutrality.
The point of Robergs's paper, however, was that lactate− is produced from pyruvate−, which has the same charge.
2-Hydroxypropanoic acid is pyruvate− production from neutral glucose that generates H+:
C6H12O6 + 2 NAD+ + 2 ADP3− + 2 HPO2−4 → 2 CH3COCO−2 + 2 H+ + 2 NADH + 2 ATP4− + 2 H2O
Subsequent lactate− production absorbs these protons:
2 CH3COCO−2 + 2 H+ + 2 NADH → 2 CH3CH(OH)CO−2 + 2 NAD+
Overall:
C6H12O6 + 2 NAD+ + 2 ADP3− + 2 HPO2−4 → 2 CH3COCO−2 + 2 H+ + 2 NADH + 2 ATP4− + 2 H2O→ 2 CH3CH(OH)CO−2 + 2 NAD+ + 2 ATP4− + 2 H2O
Although the reaction glucose → 2 lactate− + 2 H+ releases two H+ when viewed on 2-Hydroxypropanoic acid own, the H+ are absorbed in the production of ATP.
On the other hand, the absorbed acidity is released during subsequent hydrolysis of ATP: ATP4− + H2O → ADP3− + HPO2−4 + H+.
So once the use of ATP is included, the overall reaction is C6H12O6 → 2 CH3COCO−2 + 2 H+.
The generation of CO2 during respiration also causes an increase in [H+].
Metabolism of 2-Hydroxypropanoic acid:
Although glucose is usually assumed to be the main energy source for living tissues, there are some indications that 2-Hydroxypropanoic acid is lactate, and not glucose, that is preferentially metabolized by neurons in the brain of several mammalian species (the notable ones being mice, rats, and humans).
According to the lactate-shuttle hypothesis, glial cells are responsible for transforming glucose into lactate, and for providing lactate to the neurons.
Because of this local metabolic activity of glial cells, the extracellular fluid immediately surrounding neurons strongly differs in composition from the blood or cerebrospinal fluid, being much richer with lactate, as was found in microdialysis studies.
Some evidence suggests that lactate is important at early stages of development for brain metabolism in prenatal and early postnatal subjects, with lactate at these stages having higher concentrations in body liquids, and being utilized by the brain preferentially over glucose.
2-Hydroxypropanoic acid was also hypothesized that lactate may exert a strong action over GABAergic networks in the developing brain, making them more inhibitory than 2-Hydroxypropanoic acid was previously assumed,acting either through better support of metabolites, or alterations in base intracellular pH levels, or both.
Studies of brain slices of mice show that β-hydroxybutyrate, lactate, and pyruvate act as oxidative energy substrates, causing an increase in the NAD(P)H oxidation phase, that glucose was insufficient as an energy carrier during intense synaptic activity and, finally, that lactate can be an efficient energy substrate capable of sustaining and enhancing brain aerobic energy metabolism in vitro.
The study "provides novel data on biphasic NAD(P)H fluorescence transients, an important physiological response to neural activation that has been reproduced in many studies and that is believed to originate predominately from activity-induced concentration changes to the cellular NADH pools."
Lactate can also serve as an important source of energy for other organs, including the heart and liver.
During physical activity, up to 60% of the heart muscle's energy turnover rate derives from lactate oxidation.
Blood testing:
Blood tests for lactate are performed to determine the status of the acid base homeostasis in the body.
Blood sampling for this purpose is often arterial (even if 2-Hydroxypropanoic acid is more difficult than venipuncture), because lactate levels differ substantially between arterial and venous, and the arterial level is more representative for this purpose.
Polymer precursor:
Two molecules of 2-Hydroxypropanoic acid can be dehydrated to the lactone lactide.
In the presence of catalysts lactide polymerize to either atactic or syndiotactic polylactide (PLA), which are biodegradable polyesters.
PLA is an example of a plastic that is not derived from petrochemicals.
Production of 2-Hydroxypropanoic acid:
2-Hydroxypropanoic acid is produced industrially by bacterial fermentation of carbohydrates, or by chemical synthesis from acetaldehyde.
In 2009, 2-Hydroxypropanoic acid was produced predominantly (70–90%) by fermentation.
Production of racemic 2-Hydroxypropanoic acid consisting of a 1:1 mixture of d and l stereoisomers, or of mixtures with up to 99.9% l-2-Hydroxypropanoic acid, is possible by microbial fermentation.
Industrial scale production of d-2-Hydroxypropanoic acid by fermentation is possible, but much more challenging.
As a starting material for industrial production of 2-Hydroxypropanoic acid, almost any carbohydrate source containing C5 and C6 sugars can be used.
Pure sucrose, glucose from starch, raw sugar, and beet juice are frequently used.
2-Hydroxypropanoic acid producing bacteria can be divided in two classes: homofermentative bacteria like Lactobacillus casei and Lactococcus lactis, producing two moles of lactate from one mole of glucose, and heterofermentative species producing one mole of lactate from one mole of glucose as well as carbon dioxide and acetic acid/ethanol.
2-Hydroxypropanoic acid was the first organic acid produced with microbes, carried out in 1880.
In the twenty-first century, synthetic processes for the production of 2-Hydroxypropanoic acid (e.g., from lactonitrile) are competitive at the same costs as biological processes; 2-Hydroxypropanoic acid production is divided about equally between the two processes.
The major supply of 2-Hydroxypropanoic acid in Europe is produced by fermentation using strains of L. bulgaricus when whey is used as the substrate, and other lactobacilli when different substrates are used.
According to the U.S. Food and Drug Administrating (FDA), 2-Hydroxypropanoic acid is a generally recognized as safe (GRAS) additive for miscellaneous or general purpose uses.
2-Hydroxypropanoic acid was one of the earliest organic acids used in foods.
2-Hydroxypropanoic acid is used by the food industry in a number of ways:
2-Hydroxypropanoic acid is used in packing Spanish olives, where 2-Hydroxypropanoic acid inhibits spoilage and further fermentation.
2-Hydroxypropanoic acid aids in the stabilization of dried-egg powder.
2-Hydroxypropanoic acid improves the taste of certain pickles when added to vinegar.
2-Hydroxypropanoic acid is used to acidify the grape juice (must) in winemaking.
In frozen confections, 2-Hydroxypropanoic acid imparts a milky tart taste and does not mask other natural flavors.
2-Hydroxypropanoic acid is also used in the production of the emulsifiers calcium and sodium stearoyl lactylates, which function as dough conditioners.
The sodium and potassium salts of 2-Hydroxypropanoic acid have significant antimicrobial properties, including in meat products against toxin production by Clostridium botulinum, and against Listeria monocytogenes in chicken, beef, and smoked salmon
2-Hydroxypropanoic acid is present in many foods both naturally and as a product of in situ fermentation, as in sauerkraut, yogurt, and many other fermented foods.
2-Hydroxypropanoic acid is also a principal metabolic intermediate in most living organisms.
Sodium and potassium lactates are produced commercially by neutralization of natural or synthetic 2-Hydroxypropanoic acid (FDA 184.1768, 1639).
2-Hydroxypropanoic acid to be used as a food additive can be obtained either by fermentation of carbohydrates or by a chemical procedure involving formation of lactonitrile from acetaldehyde and hydrogen cyanide and subsequent hydrolysis (FDA 184.1061).
The microbiological and chemical procedures to obtain 2-Hydroxypropanoic acid are very competitive, with similar production costs.
One method of biosynthesis in common use starts with glucose and produces pyruvate, which can be converted to both the l(+) and d(−) isomers using a stereospecific lactate dehydrogenase; however, only the l(+) form is produced commercially.
The racemic mixture is always obtained by chemical synthesis.
Synthetic 2-Hydroxypropanoic acid is free of the contaminants normally found in the product obtained by fermentation, and so 2-Hydroxypropanoic acid is completely colorless and probably more stable.
2-Hydroxypropanoic acid and its salts are highly hygroscopic, and therefore are usually handled in concentrated solutions (60–80% by weight) rather than in solid form.
These solutions are colorless and odorless, and have a mild saline taste
Chemical production:
Racemic 2-Hydroxypropanoic acid is synthesized industrially by reacting acetaldehyde with hydrogen cyanide and hydrolysing the resultant lactonitrile.
When hydrolysis is performed by hydrochloric acid, ammonium chloride forms as a by-product; the Japanese company Musashino is one of the last big manufacturers of 2-Hydroxypropanoic acid by this route.
Synthesis of both racemic and enantiopure 2-Hydroxypropanoic acids is also possible from other starting materials (vinyl acetate, glycerol, etc.) by application of catalytic procedures.
General Manufacturing Information of 2-Hydroxypropanoic acid:
Industry Processing Sectors:
Agriculture, Forestry, Fishing and Hunting
All Other Basic Organic Chemical Manufacturing
All Other Chemical Product and Preparation Manufacturing
Food, beverage, and tobacco product manufacturing
Oil and Gas Drilling, Extraction, and Support activities
Paint and Coating Manufacturing
Pesticide, Fertilizer, and Other Agricultural Chemical Manufacturing
Plastics Material and Resin Manufacturing
Plastics Product Manufacturing
History of 2-Hydroxypropanoic acid:
Swedish chemist Carl Wilhelm Scheele was the first person to isolate 2-Hydroxypropanoic acid in 1780 from sour milk.
The name reflects the lact- combining form derived from the Latin word lac, which means milk.
In 1808, Jöns Jacob Berzelius discovered that 2-Hydroxypropanoic acid (actually l-lactate) also is produced in muscles during exertion.
2-Hydroxypropanoic acids structure was established by Johannes Wislicenus in 1873.
In 1856, the role of Lactobacillus in the synthesis of 2-Hydroxypropanoic acid was discovered by Louis Pasteur.
This pathway was used commercially by the German pharmacy Boehringer Ingelheim in 1895.
In 2006, global production of 2-Hydroxypropanoic acid reached 275,000 tonnes with an average annual growth of 10%.
Identifiers of 2-Hydroxypropanoic acid:
CAS Number:
50-21-5
79-33-4 (l)
10326-41-7 (d)
3DMet: B01180
Beilstein Reference: 1720251
ChEBI: CHEBI:422
ChEMBL: ChEMBL330546
ChemSpider: 96860
ECHA InfoCard: 100.000.017
EC Number: 200-018-0
E number: E270 (preservatives)
Gmelin Reference: 362717
IUPHAR/BPS: 2932
KEGG: C00186
PubChem CID: 612
RTECS number: OD2800000
UNII:
3B8D35Y7S4
F9S9FFU82N (l)
3Q6M5SET7W (d)
UN number: 3265
CompTox Dashboard (EPA): DTXSID7023192
InChI: InChI=1S/C3H6O3/c1-2(4)3(5)6/h2,4H,1H3,(H,5,6)/t2-/m0/s1
Key: JVTAAEKCZFNVCJ-REOHCLBHSA-N
SMILES: CC(O)C(=O)O
Properties of 2-Hydroxypropanoic acid:
Chemical formula: C3H6O3
Molar mass: 90.078 g·mol−1
Melting point: 18 °C (64 °F; 291 K)
Boiling point: 122 °C (252 °F; 395 K) at 15 mmHg
Solubility in water: Miscible
Acidity (pKa): 3.86, 15.1
Boiling point: 122 °C (20 hPa)
Density: 1.21 g/cm3 (20 °C)
Melting Point: 18 °C
pH value: 2.8 (10 g/l, H₂O, 20 °C)
Vapor pressure: 0.1 hPa (25 °C)
Molecular Weight: 90.08 g/mol
XLogP3: -0.7
Hydrogen Bond Donor Count: 2
Hydrogen Bond Acceptor Count: 3
Rotatable Bond Count: 1
Exact Mass: 90.031694049 g/mol
Monoisotopic Mass: 90.031694049 g/mol
Topological Polar Surface Area: 57.5Ų
Heavy Atom Count: 6
Complexity: 59.1
Isotope Atom Count: 0
Defined Atom Stereocenter Count: 0
Undefined Atom Stereocenter Count: 1
Defined Bond Stereocenter Count: 0
Undefined Bond Stereocenter Count: 0
Covalently-Bonded Unit Count: 1
Compound Is Canonicalized: Yes
Specifications of 2-Hydroxypropanoic acid:
Assay (alkalimetric): 88.0 - 92.0 %
Assay (stereochemical purity of (S)-lactic acid): ≥ 95.0 %
Identity (IR-spectrum): passes test
Identity (pH): passes test
Identity (Density): passes test
Identity (Lactat): passes test
Identity (assay): passes test
Appearance: clear, oily liquid, not more intense in color than reference solution Y₆
Ether-insoluble substances: passes test
Citric, oxalic and Phosphoric acids: passes test
Density (d 20/20): 1.20 - 1.21
Chloride (Cl): ≤ 0.2 %
Sulfate (SO₄): ≤ 200 ppm
As (Arsenic): ≤ 3 ppm
Ca (Calcium): ≤ 200 ppm
Fe (Iron): ≤ 10 ppm
Hg (Mercury): ≤ 1 ppm
Pb (Lead): ≤ 2 ppm
Ethanol: ≤ 5000 ppm
Acetic acid: ≤ 5000 ppm
Methanol: ≤ 50 ppm
Other residual solvents (ICH Q3C): excluded by manufacturing process
Sugars and other reducing substances: passes test
Sulfated ash (600 °C): ≤ 0.10 %
Total aerobic microbial count (TAMC): ≤ 10²
Total combined yeasts/moulds count (TYMC): ≤ 10²
Bacterial endotoxins: ≤ 5 I.U./g
Thermochemistry of 2-Hydroxypropanoic acid:
Std enthalpy of combustion (ΔcH⦵298): 1361.9 kJ/mol, 325.5 kcal/mol, 15.1 kJ/g, 3.61 kcal/g
Pharmacology of 2-Hydroxypropanoic acid:
ATC code: G01AD01 (WHO) QP53AG02 (WHO)
Related compounds of 2-Hydroxypropanoic acid:
1-Propanol
2-Propanol
Propionaldehyde
Acrolein
Sodium lactate
Ethyl lactate
Other anions:
Lactate
Related carboxylic acids:
Acetic acid
Glycolic acid
Propionic acid
3-Hydroxypropanoic acid
Malonic acid
Butyric acid
Hydroxybutyric acid
Some examples of lactates (salts or esters of lactic acid) are:
Ammonium Lactate (NH4C3H5O3, CAS RN: 515-98-0): clear to yellow, syrupy liquid used in in electroplating, in finishing leather and as humectant for food, pharmaceutical, and cosmetics.
Butyl Lactate (CH3CHOHCOOC4H9, CAS RN:138-22-7): a clear liquid: nontoxic, miscible with many solvents; used as a solvent for varnish, lacquers, resins and gums, used in making paints, inks, dry cleaning fluid, flavoring and as a chemical intermediate.
Calcium Lactate Pentahydrate [Ca(C3H5O3)2·5H2O, CAS RN: 814-80-2] : white crystals; soluble in water; used as a calcium source; administered orally in the treatment of calcium deficiency; as a blood coagulant.
Ethyl Lactate(CH3CHOHCOOC2H5, CAS RN: 97-64-3): clear liquid with mild odur; boiling point 154 C; miscible with alcohols, ketones, esters, and hydrocarbons as well as with water; used in pharmaceutical preparations, feed additive, as a flavoring ( odor description: sweet butter, coconut, fruity, creamy dairy, butterscotch) and as a solvent for cellulose compounds such as nitrocellulose, cellulose acetate, and cellulose ethers.
Magnesium Lactate Trihydrate [Mg(C3H5O3)2·3H2O, CAS RN: 18917-93-6 ]: white crystals with bitter taste; soluble in water, slightly soluble in alcohol; used in medicine and as an electrolyte replenisher.
Manganese Lactate Trihydrate [Mn(C3H5O3)2·3H2O]: pale red crystals; insoluble in water and alcohol; used in medicine.
Mercuric Lactate [Hg(C3H5O3)2]: poisonous white powder that decomposes when heated; soluble in water; used in medicine.
Methyl Lactate (CH3CHCHCOOCH3): clear liquid with mild odur; boiling point 145 C; miscible with alcohols, ketones, esters, and hydrocarbons as well as with water; used in pharmaceutical preparations, feed additive, as a flavoring and as a solvent for cellulose compounds such as nitrocellulose, cellulose acetate, and cellulose ethers.
Sodium Lactate (CH3CHOHCOONa, CAS RN: 72-17-3) clear to yellow, hygroscopic syrupy liquid; soluble in water; melting point 17 C; used in medicine, in antifreeze, and hygroscopic agent and as a corrosion inhibitor.
Zinc Lactate (Zn(C3H5O3)2·2H2O, CAS RN: 16039-53-5): white crystals; used as an additive in toothpaste and food; preparation of drugs.
Names of 2-Hydroxypropanoic acid:
Preferred IUPAC name:
2-Hydroxypropanoic acid
Other names:
Lactic acid
Milk acid
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189679 | https://www.ncbi.nlm.nih.gov/books/NBK560700/ | Lichen Planus Erosive Form - StatPearls - NCBI Bookshelf
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StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing; 2025 Jan-.
StatPearls [Internet].
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Treasure Island (FL): StatPearls Publishing; 2025 Jan-.
Search term
Lichen Planus Erosive Form
Ryan Gall; Inigo N. Navarro-Fernandez.
Author Information and Affiliations
Authors
Ryan Gall 1; Inigo N. Navarro-Fernandez 2.
Affiliations
1 NCC
2 Hospital Universitario Marques de Valdecilla
Last Update: July 24, 2023.
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Continuing Education Activity
Erosive lichen planus (ELP) is a variant of lichen planus which involves chronic and painful ulceration of the skin and mucosal surfaces. ELP is thought to be the result of autoimmune damage of the basal cell layer, which is mediated by activated CD8 T lymphocytes. This activity describes the evaluation and management of erosive lichen planus and reviews the role of the interprofessional team in managing patients with this condition.
Objectives:
Identify the etiology of lichen planus erosive form.
Describe the common history/physical exam findings of lichen planus erosive form.
List the management options available for lichen planus erosive form.
Discuss interprofessional team strategies for improving care coordination and communication to advance lichen planus erosive form and improve outcomes.
Access free multiple choice questions on this topic.
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Introduction
Erosive lichen planus (ELP) is a variant of lichen planus which involves chronic and painful ulceration of the skin and mucosal surfaces. ELP is thought to be the result of autoimmune damage of the basal cell layer, which is mediated by activated CD8 T lymphocytes.Occasionally, ELP may present in conjunction with other clinical forms of lichen planus or may be induced by drug exposure. Clinical findings include painful, persistent ulcers, primarily of the mouth and genitals.Complications of ELP include secondary infection, development of squamous cell carcinoma, and scarring.
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Etiology
Lichen planus (LP) is thought to be a T-cell mediated auto-immune inflammatory disorder, which destroys basal epithelial cells.CD8 T cells are considered primary offending cells based on biopsy specimens. It is believed that the presentation of exogenous antigens, such as viruses, metals, or drugs, may lead to CD8 activation and destruction of keratinocytes.LP has also been associated with other auto-immune diseases, including vitiligo, auto-immune thyroid disease, and alopecia areata.
Hepatitis C is well known to be associated with LP, although the link between HCV and erosive LP has not been established. Odds ratios of up to 5.4 for HCV positivity were found among patients with LP. However, this association was not significant statistically among all geographic groups in further analysis.Like other forms of LP, erosive LP may be drug-induced and often resolves with the removal of the offending agent.
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Epidemiology
Overall, lichen planus (LP) is thought to afflict between 0.5% and 2% of the world’s population.Oral LP is reported as the most common form of LP. Onset is most common in middle age, with the average age of onset being 50 to 60 and rarely presents in children.Cutaneous LP appears to occur equally among the sexes, while oral LP is three times more common in women than in men.
Erosive lichen planus is one of the many clinical presentations of lichen planus. The incidence of erosive LP has not been determined. Similar to other presentations of LP, erosive LP occurs most commonly between the 5th and 8th decades of life.Women develop erosive LP at about twice the rate of men.Erosive LP most commonly presents as painful ulcerations of either the oral or genital mucosa. Patients may present with ulcerations at multiple sites; in one study, 57% of patients with oral LP were also found to have vulvar LP.In another study, 17.6% of patients with vulvar LP were identified to have the erosive subtype of LP.
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Histopathology
The diagnosis of erosive lichen planus (ELP) is typically made by history and clinical exam. However, biopsy helps to confirm the diagnosis and rule out the potential for malignancy. On histopathology, typical findings include hyperkeratosis without parakeratosis, liquefaction of the basal layer, saw-toothed rete ridges, Civatte bodies (eosinophilic masses representing apoptotic keratinocytes), and a band-like lymphohistiocytic infiltrate near the dermal-epidermal border.Unfortunately, the presence of ulceration, leading to the absence of the epidermis, often prevents many of these features from being observed. In such cases, biopsy specimens often appear very non-specific.Direct immune-fluorescence is also helpful in ruling out immune-bullous disorders.
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History and Physical
Erosive lichen planus (ELP) most typically affects the oral mucosa or genitals. However, it may rarely involve the eyelids, esophagus, larynx, anus, bladder, or external auditory canal.Patients develop painful, erythematous erosions and ulcerations, which may be present for several months or longer.
Vulvar and vaginal erosive lichen planus typically presents with complaints of pain, dysuria, a burning sensation, and dyspareunia, often with post-coital bleeding.Patients may also notice blood-tinged vaginal discharge. Lesions are characterized by glazed appearing, erythematous erosions, and patches with well-demarcated borders. White, serpiginous striae, known as Wickham striae, are often seen around the border.Lesions tend to be symmetrical and bilateral. Lesions tend to heal slowly, and recurrent exacerbations are very common. Architectural change, including scarring, loss of the labia minora, and narrowing or obliteration of the vagina may occur, especially if erosive LP is left untreated.
In oral erosive LP, lesions may occur on the buccal mucosa, labial mucosa, tongue, or vermillion border. Often, the lesions are bilateral and symmetrical.The often severe pain associated with these ulcers may lead to anorexia, weight loss, nutritional deficiencies, and depression.Mucosal bleeding may occur with minimal trauma, such as with tooth brushing. The development of new erosions at sites of minimal trauma, known as the Koebner phenomenon, is also common.Compared to aphthous ulcers, lesions of erosive LP are typically larger, have irregular shapes, and usually do not resolve for at least several weeks. Desquamative gingivitis, which is the development of widespread gingival erosions, may also result from erosive LP.After the eventual resolution of erosive lesions, scarring and post-inflammatory hyperpigmentation are very common.
Vulvovaginal-gingival (VVG) syndrome is a specific variant of erosive lichen planus, which involves the vulva, vagina, vestibule, and oral mucosa, as well as potential additional sites, such as the skin and esophagus.The involvement of all three areas is common; however, lesions typically do not occur concurrently. VVG is often particularly refractory to treatment.
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Evaluation
Diagnosis of erosive lichen planus is most often made based on a presentation with a typical history and clinical appearance. The biopsy of the lesion is usually performed when the diagnosis is in question or to rule out malignancy. As mentioned above, ulceration of the lesion may result in the absence of the characteristic lichenoid features on histology.
Regardless of the location of the patient’s symptoms, full evaluation of the cutaneous and mucosal surfaces should be performed when lichen planus is suspected. Patients with lichen planus frequently present with manifestations in more than one location. A thorough review of other systems should also be obtained to identify any symptoms suggestive of mucosal involvement, such as esophagus, conjunctiva, urethra, anus, or larynx. Untreated erosive lichen planus frequently progresses to scarring and functional impairment, especially when undiagnosed and untreated. Screening for an unknown diagnosis of hepatitis C should also be considered.
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Treatment / Management
Management of erosive lichen planus is often challenging for both the patient and the provider. Treatment response is often poor, and relapses are common. Topical corticosteroids have been shown in a randomized control trial to be effective for oral lichen planus and are the mainstay of treatment for both genital and oral erosive lichen planus.
Topical steroids are generally applied for courses of 4 to 6 weeks in the acute setting, with maintenance therapy often being necessary for the long term. For genital erosions, ultra-potent steroid ointment or cream should be applied to the lesion daily. A stepwise lowering of application frequency should be performed after remission has been achieved to minimize the risk of side effects while still preventing relapse. For oral disease, ultra or high potency topical steroids are recommended. The application should occur 3 to 4 times per day in the acute setting and should be performed after the site has been dried.
The gingival disease may be treated by either rinsing with oral elixirs or with the aid of a gingival tray.For second-line therapy, topical calcineurin inhibitors such as tacrolimus and pimecrolimus are effective in both oral and vulvar LP.For patients with severe erosive LP, initiating a four to six-week course of oral prednisone, tapered down from 40-60mg daily, may prove beneficial.For refractory disease, many systemic treatments such as methotrexate, mycophenolate, minocycline, cyclosporine, trimethoprim-sulfamethoxazole, hydroxychloroquine, and acitretin have been utilized, but overall data regarding their efficacy is lacking.
Pain is often a significant symptom in erosive LP. Topical anesthetics such as viscous lidocaine frequently prove useful, especially in patients who have decreased oral intake due to painful oral LP. For vulvar and vaginal erosive LP, dilators and surgery can often help correct anatomic distortions due to adhesions and scarring.
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Differential Diagnosis
The differential diagnosis for erosive lichen planus may vary based on the affected location.
Crohn disease may present with erosions of the oral cavity, vulva or perineum, or anus, and may present years before any bowel findings.
Autoimmune bullous diseases may present clinically identical to erosive LP and can be differentiated by immunofluorescence studies.
Behcet syndrome, erythema multiforme, and Stevens-Johnson syndrome all may present in ways clinically similar to erosive LP.
When affecting the female genitalia, erosive LP may be confused with lichen sclerosus. However, unlike erosive LP, lichen sclerosus rarely affects the vagina or oral mucosa.
Other disorders of the genitalia that should be considered include plasma cell vulvitis, vulvar intraepithelial neoplasm, and atrophic vaginitis.
When occurring in the oral cavity, the differential for erosive LP should consist of oropharyngeal candidiasis, leukoplakia, squamous cell carcinoma, leukoedema, and allergic contact mucositis.
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Prognosis
The lesions of erosive lichen planus are often persistent and tend to respond poorly to therapy.Bouts of the disease usually last for years, and relapses are frequent even when maintenance therapy is appropriately utilized.
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Complications
Patients with erosive lichen planus are at significant risk of developing secondary infections. This risk is especially high for the development of candidiasis, staphylococcus aureus cellulitis, and herpes simplex.Oral lichen planus has been shown in a systemic review to carry an approximate rate of transformation to squamous cell carcinoma of 1%, which is thought to be the result of chronic mucosal inflammation.
A similar risk of development of squamous cell carcinoma has also been found in penile and vulvar lichen planus, although the rates of transformation have been less clearly identified.Scarring is also a frequent complication of erosive lichen planus, which may lead to interference with intercourse, urination, and eating.
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Deterrence and Patient Education
Patients should be educated on the clinical course and potential complications of erosive lichen planus. Smoking cessation and HPV vaccination should be advised to minimize the risk of transformation to squamous cell carcinoma.
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Enhancing Healthcare Team Outcomes
Erosive lichen planus is a chronic, often debilitating disease that can affect many organ systems. Specialists such as dermatologists, dentists, and gynecologists may be needed to work together to coordinate the delivery of optimal patient care. A multi-disciplinary approach should be taken in accordance with the patient’s symptoms and goals of treatment.
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Review Questions
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Comment on this article.
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Simpson RC, Littlewood SM, Cooper SM, Cruickshank ME, Green CM, Derrick E, Yell J, Chiang N, Bell H, Owen C, Javed A, Wilson CL, McLelland J, Murphy R. Real-life experience of managing vulval erosive lichen planus: a case-based review and U.K. multicentre case note audit. Br J Dermatol. 2012 Jul;167(1):85-91. [PubMed: 22384934]
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Martin J, Holdstock G. Isolated vulval oedema as a feature of Crohn's disease. J Obstet Gynaecol. 1997 Jan;17(1):92-3. [PubMed: 15511783]
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Murphy GM, Cronin E. Lichen planus pemphigoides. Clin Exp Dermatol. 1989 Jul;14(4):322-4. [PubMed: 2686875]
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Kirtschig G, Becker K, Günthert A, Jasaitiene D, Cooper S, Chi CC, Kreuter A, Rall KK, Aberer W, Riechardt S, Casabona F, Powell J, Brackenbury F, Erdmann R, Lazzeri M, Barbagli G, Wojnarowska F. Evidence-based (S3) Guideline on (anogenital) Lichen sclerosus. J Eur Acad Dermatol Venereol. 2015 Oct;29(10):e1-43. [PubMed: 26202852]
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Lewis FM, Shah M, Harrington CI. Vulval involvement in lichen planus: a study of 37 women. Br J Dermatol. 1996 Jul;135(1):89-91. [PubMed: 8776366]
39.
Edwards L. Vulvar lichen planus. Arch Dermatol. 1989 Dec;125(12):1677-80. [PubMed: 2589863]
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Fitzpatrick SG, Hirsch SA, Gordon SC. The malignant transformation of oral lichen planus and oral lichenoid lesions: a systematic review. J Am Dent Assoc. 2014 Jan;145(1):45-56. [PubMed: 24379329]
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Lewis FM, Harrington CI. Squamous cell carcinoma arising in vulval lichen planus. Br J Dermatol. 1994 Nov;131(5):703-5. [PubMed: 7999604]
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Kennedy CM, Peterson LB, Galask RP. Erosive vulvar lichen planus: a cohort at risk for cancer? J Reprod Med. 2008 Oct;53(10):781-4. [PubMed: 19004404]
Disclosure:Ryan Gall declares no relevant financial relationships with ineligible companies.
Disclosure:Inigo Navarro-Fernandez declares no relevant financial relationships with ineligible companies.
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189680 | https://math.libretexts.org/Courses/Hawaii_Community_College/Hawaii_Community_College_MA82X_Textbook/08%3A_Rational_Expressions_and_Equations/8.01%3A_Simplifying_Rational_Expressions | Skip to main content
8.1: Simplifying Rational Expressions
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8: Rational Expressions and Equations
8.2: Multiplying and Dividing Rational Expressions
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( \newcommand{\kernel}{\mathrm{null}\,})
Learning Objectives
Determine the restrictions to the domain of a rational expression.
Simplify rational expressions.
Simplify expressions with opposite binomial factors.
Simplify and evaluate rational functions.
Rational Expressions, Evaluation, and Restrictions
A rational number, or fraction , is a real number defined as a quotient of two integers a and b, where . Similarly, we define a rational expression, or algebraic fraction , as the quotient of two polynomials P and Q, where . Some examples of rational expressions follow:
The example consists of linear expressions in both the numerator and denominator. Because the denominator contains a variable, this expression is not defined for all values of x.
Example
Evaluate for the set of x-values .
Solution:
Substitute the values in for x.
Answer:
When , the value of the rational expression is ; when , the value of the rational expression is ; and when , the value of the rational expression is undefined.
This example illustrates that variables are restricted to values that do not make the denominator equal to 0. The domain of a rational expression is the set of real numbers for which it is defined, and restrictions are the real numbers for which the expression is not defined. We often express the domain of a rational expression in terms of its restrictions.
Example
Find the domain of the following:
Solution:
In this example, the numerator is a linear expression and the denominator is a quadratic expression. If we factor the denominator, then we will obtain an equivalent expression.
Because rational expressions are undefined when the denominator is 0, we wish to find the values for x that make it 0. To do this, apply the zero product property. Set each factor in the denominator equal to 0 and solve.
We conclude that the original expression is defined for any real number except and . These two values are the restrictions to the domain. It is important to note that is not a restriction to the domain because the expression is defined as 0 when the numerator is 0.
Answer:
The domain consists of any real number x, where and .
We can express the domain of the previous example using notation as follows:
The restrictions to the domain of a rational expression are determined by the denominator. Ignore the numerator when finding those restrictions.
Example
Determine the domain:
Solution:
To find the restrictions to the domain, set the denominator equal to 0 and solve:
These two values cause the denominator to be 0. Hence they are restricted from the domain.
Answer:
The domain consists of any real number x, where .
Example
Determine the domain:
Solution:
There is no variable in the denominator and thus no restriction to the domain.
Answer:
The domain consists of all real numbers, R.
Simplifying Rational Expressions
When simplifying fractions, look for common factors that cancel. For example,
We say that the fraction is equivalent to . Fractions are in simplest form if the numerator and denominator share no common factor other than . Similarly, when working with rational expressions, look for factors to cancel. For example,
The resulting rational expression is equivalent if it shares the same domain. Therefore, we must make note of the restrictions and write
In words, is equivalent to, if and . We can verify this by choosing a few values with which to evaluate both expressions to see if the results are the same. Here we choose and evaluate as follows:
It is important to state the restrictions before simplifying rational expressions because the simplified expression may be defined for restrictions of the original. In this case, the expressions are not equivalent. Here −4 is defined for the simplified equivalent but not for the original, as illustrated below:
Example
Simplify and state the restriction:
Solution:
In this example, the expression is undefined when x is 0.
Therefore, the domain consists of all real numbers x, where . With this understanding, we can cancel common factors.
Answer:
, where
Example
State the restrictions and simplify:
Solution:
To determine the restrictions, set the denominator equal to 0 and solve.
The domain consists of all real numbers except for and . Next, we find an equivalent expression by canceling common factors.
Answer:
, where and
Typically, rational expressions are not given in factored form. If this is the case, factor first and then cancel. The steps are outlined in the following example.
Example
State the restrictions and simplify:
Solution:
Step 1: Completely factor the numerator and denominator.
Step 2: Determine the restrictions to the domain. To do this, set the denominator equal to 0 and solve.
The domain consists of all real numbers except and .
Step 3: Cancel common factors, if any.
Answer:
, where and
Example
State the restrictions and simplify:
Solution:
First, factor the numerator and denominator.
Any value of x that results in a value of in the denominator is a restriction. By inspection, we determine that the domain consists of all real numbers except and . Next, cancel common factors.
Answer:
, where and
It is important to remember that we can only cancel factors of a product. A common mistake is to cancel terms. For example,
Exercise
State the restrictions and simplify:
Answer
: , where and
In some examples, we will make a broad assumption that the denominator is nonzero. When we make that assumption, we do not need to determine the restrictions.
Example
Simplify:
(Assume all denominators are nonzero.)
Solution:
Factor the numerator by grouping. Factor the denominator using the formula for a difference of squares.
Next, cancel common factors.
Answer:
Opposite Binomial Factors
Recall that the opposite of the real number a is −a. Similarly, we can define the opposite of a polynomial P to be −P. We first consider the opposite of the binomial :
This leads us to the opposite binomial property:
This is equivalent to factoring out a .
If , then we can divide both sides by and obtain the following:
Example
State the restrictions and simplify:
Solution:
By inspection, we can see that the denominator is if . Therefore, is the restriction to the domain. Apply the opposite binomial property to the numerator and then cancel.
Answer:
, where
Since addition is commutative, we have
or
Take care not to confuse this with the opposite binomial property. Also, it is important to recall that
In other words, show a negative fraction by placing the negative sign in the numerator, in front of the fraction bar, or in the denominator. Generally, negative denominators are avoided.
Example
Simplify and state the restrictions:
Solution:
Begin by factoring the numerator and denominator.
Answer:
, where and
Exercise
Simplify and state the restrictions:
Answer
: , where
Rational Functions
Rational functions have the form
,
where p(x) and q(x) are polynomials and q(x)≠0. The domain of a rational function consists of all real numbers x such that the denominator q(x)≠0.
Example
Simplify: .
State the domain.
Calculate .
Solution:
a. To simplify the rational function, first factor and then cancel.
b. To determine the restrictions, set the denominator of the original function equal to 0 and solve.
The domain consists of all real numbers x, where and .
c. Since is not a restriction, substitute it for the variable x using the simplified form.
Answer:
a. b. The domain is all real numbers except and . c.
If a cost function represents the cost of producing x units, then the average cost is the cost divided by the number of units produced.
Example
The cost in dollars of producing t-shirts with a company logo is given by , where x represents the number of shirts produced. Determine the average cost of producing
40 t-shirts
250 t-shirts
1,000 t-shirts
Solution:
Set up a function representing the average cost.
Next, calculate c(40), c(250), and c(1000).
Answer:
If 40 t-shirts are produced, then the average cost per t-shirt is $12.00.
If 250 t-shirts are produced, then the average cost per t-shirt is $7.80.
If 1,000 t-shirts are produced, then the average cost per t-shirt is $7.20.
Key Takeaways
Rational expressions usually are not defined for all real numbers. The real numbers that give a value of 0 in the denominator are not part of the domain. These values are called restrictions.
Simplifying rational expressions is similar to simplifying fractions. First, factor the numerator and denominator and then cancel the common factors. Rational expressions are simplified if there are no common factors other than 1 in the numerator and the denominator.
Simplified rational expressions are equivalent for values in the domain of the original expression. Be sure to state the restrictions if the denominators are not assumed to be nonzero.
Use the opposite binomial property to cancel binomial factors that involve subtraction. Use to replace factors that will then cancel. Do not confuse this with factors that involve addition, such as .
Exercise Rational Expressions
Evaluate for the given set of x-values.
Fill in the following chart:
Figure
10. Fill in the following chart:
Figure
Fill in the following chart:
Figure
12. Fill in the following chart:
Figure
Answer
: 1. , undefined,
3. , undefined,
5. , undefined,
7. Undefined, , undefined
9.
11.
Exercise Rational Expressions
An object’s weight depends on its height above the surface of earth. If an object weighs 120 pounds on the surface of earth, then its weight in pounds, W, x miles above the surface is approximated by the formula
For each problem below, approximate the weight of a 120-pound object at the given height above the surface of earth. (1 mile = 5,280 feet)
100 miles
1,000 miles
44,350 feet
90,000 feet
Answer
: 1. 114 pounds
3. 119.5 pounds
Exercise Rational Expressions
The price to earnings ratio (P/E) is a metric used to compare the valuations of similar publicly traded companies. The P/E ratio is calculated using the stock price and the earnings per share (EPS) over the previous 12-month period as follows:
P/E=price per share earnings per share
If each share of a company stock is priced at $22.40, then calculate the P/E ratio given the following values for the earnings per share.
$1.40
$1.21
What happens to the P/E ratio when earnings decrease?
What happens to the P/E ratio when earnings increase?
Answer
: 1. 16
3. The P/E ratio increases.
Exercise Rational Expressions
State the restrictions to the domain.
Answer
: 1.
3.
5.
7. and
9.
11. , , and
13. and
Exercise Simplifying Rational Expressions
State the restrictions and then simplify.
Answer
: 1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
Exercise Simplifying Rational Expressions with Opposite Binomial Factors
State the restrictions and then simplify.
Answer
: 1.
3.
5.
7.
9.
11.
13.
15. ; none
17.
Exercise Simplifying Rational Expressions with Opposite Binomial Factors
Simplify. (Assume all denominators are nonzero.)
Answer
: 1.
3.
5.
7.
9.
11.
Exercise Rational Functions
Calculate the following.
Answer
: 1. f(0)=0, f(2)=−10, f(4)=20
3. g(0)=0, g(2) undefined, g(−2)=−
5. g(−1)=−, g(0)=0, g(1)=
Exercise Rational Functions
State the restrictions to the domain and then simplify.
The cost in dollars of producing coffee mugs with a company logo is given by , where x represents the number of mugs produced. Calculate the average cost of producing 100 mugs and the average cost of producing 500 mugs.
The cost in dollars of renting a moving truck for the day is given by , where x represents the number of miles driven. Calculate the average cost per mile if the truck is driven 250 miles in one day.
The cost in dollars of producing sweat shirts with a custom design on the back is given by , where x represents the number of sweat shirts produced. Calculate the average cost of producing 150 custom sweat shirts.
The cost in dollars of producing a custom injected molded part is given by , where x represents the number of parts produced. Calculate the average cost of producing 1,000 custom parts.
Answer
: 1.
3.
5.
7. The average cost of producing 100 mugs is 1.08 per mug.
9. $12.50
Exercise Discussion Board
Explain why and illustrate this fact by substituting some numbers for the variables.
Explain why and illustrate this fact by substituting some numbers for the variables.
Explain why we cannot cancel x in the expression .
Answer
: 1. Answers may vary
3. Answers may vary
8: Rational Expressions and Equations
8.2: Multiplying and Dividing Rational Expressions |
189681 | https://mathworld.wolfram.com/Little-ONotation.html | Little-O Notation -- from Wolfram MathWorld
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MathWorld Contributors
Stover
Little-O Notation
The symbol , pronounced "little-O of ," is one of the Landau symbols and is used to symbolically express the asymptotic behavior of a given function.
In particular, if is an integervariable which tends to infinity and is a continuous variable tending to some limit, if and are positive functions, and if and are arbitrary functions, then it is said that provided that . Thus, or grows much faster than or .
Note that little-O notation is the inverse of little-omega notation, i.e., that
Additionally, little-O notation is related to big-O notation in that is stronger than and implies .
See also
Asymptotic, Asymptotic Notation, Big-O Notation, Big-Omega Notation, Big-Theta Notation, Landau Symbols, Little-Omega Notation
This entry contributed by Christopher Stover
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References
Hardy, G.H. and Wright, E.M. "Some Notations." §1.6 in An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, pp.7-8, 1979.
Referenced on Wolfram|Alpha
Little-O Notation
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Stover, Christopher. "Little-O Notation." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein.
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189682 | https://mathoverflow.net/questions/11964/strong-induction-without-a-base-case | Skip to main content
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Strong induction proves a sequence of statements P(0), P(1), … by proving the implication
"If P(m) is true for all nonnegative integers m less than n, then P(n) is true."
for every nonnegative integer n. There is no need for a separate base case, because the n=0 instance of the implication is the base case, vacuously. But most strong induction proofs nevertheless seem to involve a separate argument to handle the base case (i.e., to prove the implication for n=0).
Can you think of a natural example of a strong induction proof that does not treat the base case separately? Ideally it should be a statement at the undergraduate level or below, and it should be a statement for which strong induction works better than ordinary induction or any direct proof.
co.combinatorics
examples
mathematics-education
lo.logic
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edited Jul 3, 2010 at 11:49
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Bjorn Poonen 100%
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Interesting question. (I confess that, in the introduction to proofs class I taught twice in the last year, I didn't want to address the logical superfluity of the base case in strong induction for fear it would confuse my students. But I guess MIT students are not so easily confused.) Why is it tagged combinatorics?
– Pete L. Clark
Commented
Jan 16, 2010 at 6:47
3
This comment is too facetious to be an answer, but you could let P(n) be the statement "P(t) is true for all 0<=t<n" ;-)
– Kevin Buzzard
Commented
Jan 16, 2010 at 8:35
4
Bjorn, this phenomenon is not limited to induction on the natural numbers, but arises naturally in transfinite recursion also. Indeed, it is usually considered a feature of a properly performed transfinite recursion if it has the property you state. Perhaps you want to generalize your question?
– Joel David Hamkins
Commented
Jan 16, 2010 at 23:03
2
Yes, I'm aware of transfinite induction, but since the thrust of my question is the same in that setting as in the natural number setting, I phrased my question in the most elementary terms.
– Bjorn Poonen
Commented
Jan 16, 2010 at 23:33
1
@Pete: As for the combinatorics tag: I couldn't find a better one. I was thinking that "discrete math" might be appropriate, and combinatorics seemed to be closest to this. Feel free to re-tag the question.
– Bjorn Poonen
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Jan 16, 2010 at 23:49
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My example is the classical proof that sqrt(2) is irrational.
More generally, many proofs that proceed by showing that there are no minimal counterexamples exemplify your phenomenon. The method of no-minimal-counterexamples is exactly the same as strong induction, but where one proves the required implication by contradiction. In many applications of this method, it is often clear that the smallest numbers are not counterexamples, and this would not ordinarily regarded as a separate base "case".
In the classical proof that sqrt(2) is irrational, for example, we suppose sqrt(2) = p/q, where p is minimal. Now, square both sides and proceed with the usual argument, to arrive at a smaller counterexample. Contradiction! This amounts to a proof by strong induction that no rational number squares to 2, and there seems to be no separate base case here.
People often carry out the classical argument by assuming p/q is in lowest terms, but the argument I just described does not need this extra complication. Also, in any case, the proof that every rational number can be put into lowest terms is itself another instance of the phenomenon. Namely, if p/q is a counterexample with p minimal, then divide by any common factor and apply induction. There seems to be no separate base case here where it is already in lowest terms, since we were considering a minimal counterexample. Perhaps someone objects that there is no induction here at all, since one can just divide by the gcd(p,q). But the usual proof that any two numbers have a gcd is, of course, also inductive: considering the least linear combination xq+yp amounts to strong induction, again with no separate base case.
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Thanks for the vote of confidence. With three tries, I think I've got it now...
– Joel David Hamkins
Commented
Jan 17, 2010 at 3:56
1
Why, any proof that uses Fermat's method of infinite descent invariably uses the strong induction. Or am I committing a blunder here?
– Abhishek Parab
Commented
Jan 17, 2010 at 4:01
2
It doesn't work since verifying descent requires proving p/2 < p so requires proof that p isn't 0, i.e. disproving the base case P(0). Even if you start at 1 vs. 0 there are still analogous objections.
– Bill Dubuque
Commented
Jul 7, 2010 at 21:10
2
Bill, I'm not sure it would be considered a separate "case" to observe that if p/q=2–√ then p/2<p. I had mentioned that in this argument and other instances of no-minimal-counterexamples, it is often clear that the smallest numbers are not counterexamples; we typically understand those smallest cases very thoroughly and know very well that any supposed counterexample will be large. But I agree that such observations could be considered a logical base case, even when they would not be presented as part of the argument. In this event, we would need Bjorn to supply a precise definition.
– Joel David Hamkins
Commented
Jul 8, 2010 at 1:04
2
@Joel Yes, without a rigorous definition of what it means to "not treat the base case separately" the question cannot be answered. I've seen many dozens of similar questions in various forums and a consensus is never reached due to the lack of such precision.
– Bill Dubuque
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Jul 22, 2010 at 22:13
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I hope the following will satisfy Bjorn. It is a proof by induction which naturally skips over the base case and is at the undergraduate level. I saw the argument for the first time today in the paper containing 10 proofs in Russian of the Fundamental Theorem of Algebra which Ilya Nikokoshev made a link to in his answer to a question asking for lots of different proofs of that theorem. Here we go:
Claim: A nonzero polynomial (over a field) has no more roots than its degree.
Proof:
We prove this by induction on the degree n of the polynomial. Assume that the polynomial
p(X)=anXn+⋯+a1X+a0
of degree n has at least n+1 different roots r1,…,rn+1. Consider the polynomial
q(X)=an(X−r1)⋯(X−rn).
We have p(X)≠q(X) since p(rn+1)=0 and q(rn+1)≠0. The difference d(X)=p(X)−q(X) is a nonzero polynomial of degree less than n having at least n roots r1,…,rn. This contradicts the inductive hypothesis. QED
[EDIT: IGNORE what follows in the next paragraph, which was in the original post, since I confused myself about strong vs. ordinary induction. The above proof is by strong induction since the degree of d(X) is merely less than n and not necessarily n-1 itself.]
One aspect of this which does not fit Bjorn's request is that this argument uses ordinary induction, not strong induction. But really, is that such a big deal? I suspect his main interest is seeing an inductive argument at all where the base case is naturally not mentioned, rather than specifically one using strong induction.
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You're ok, this does use strong induction.
– François G. Dorais
Commented
Jan 17, 2010 at 2:10
Really? Although one could run through the argument as a strong induction type statement, it only involves two adjacent cases. I tend to think of true strong inductive arguments as those (like factorization into primes) where you prove one case by appealing to some earlier case, but it in practice is not going to be the immediately preceding case.
– KConrad
Commented
Jan 17, 2010 at 2:29
2
It's not the immediately preceding case: d(X) has degree less than n, not necessarily n−1. (The n+1 is misleading, it's just the smallest integer bigger than n.)
– François G. Dorais
Commented
Jan 17, 2010 at 2:32
3
Good example! One comment: The claim is stronger, and the inductive step clearer, if in the claim you change "polynomial of nonzero degree" to "nonzero polynomial".
– Bjorn Poonen
Commented
Jan 18, 2010 at 6:07
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Not only is it not an example, it is not a correct proof. The difference d(X) has not been shown to have nonzero degree, so the induction hypothesis does not apply. If you replace "of nonzero degree" by "nonzero" in the statement, then the argument becomes correct. The smallest case n=0 then constructs to a nonzero polynomial of negative degree which ...(vacuous); this is a contradiction in itself. Since no appeal is made to the induction hypothesis for n=0, one might say the case is handled differently though. In any case it falls under the "minimal counterexample cannot exist" label.
– Marc van Leeuwen
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I think the best example of this will be the fundamental theorem of arithmetic: the assertion that every natural number greater than 1 is either prime or the product of primes (and uniquely so).
Proof of existence is by strong induction. Assume true below n. If n is prime, we're done. Otherwise, n = ab for some a,b < n, and by induction these are products of primes, so n is also. QED (and no need for special anchor case).
Proof of uniqueness does not use induction.
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edited Feb 11, 2018 at 7:25
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3 revs, 2 users 90%Joel David Hamkins
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Nitpick: Perhaps replace positive by ≥2 in the statement, otherwise the base case is different, though clearly not an "anchor case."
– François G. Dorais
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Jan 16, 2010 at 23:18
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@Joel: That is a nice example of strong induction, but I am really hoping for an argument that does not need a separate case to get started (here the separate case is the case where n is prime). Sorry if my question is vague; I'm not sure I can formalize what I want.
– Bjorn Poonen
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Jan 16, 2010 at 23:26
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Bjorn is correct. Primes are the base case in the divisibility ordering - that is what this induction is really on, the standard ordering is just a rank function.
– François G. Dorais
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Jan 17, 2010 at 0:08
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OK, I'm beginning to understand what you want. So I posted another example, on the cumulative hierarchy (see below....or above?)
– Joel David Hamkins
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Jan 17, 2010 at 0:24
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@PeterHeinig You are right.
– Maxis Jaisi
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Feb 11, 2018 at 14:35
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The cumulative hierarchy in set theory is the hierarchy Vα that is often defined by the transfinite recursion:
V0 = emptyset
Vα+1 = P(Vα), taking the power set at successor stages
Vλ = U{ Vα | α<λ }, taking unions at limits.
And if one wants to consider only the class HF of hereditarily finite sets, one restricts to the natural number induction α=n, leading to HF = Vω = U Vn. These definitions, however, split into separate cases for zero, successor and limit.
An equivalent definition, however, completely avoids this split. Namely:
For any ordinal α, let Vα = U { P(Vβ) | β < α }.
This is easily seen to be equivalent to the previous definition.
Similarly, one can define the hereditary finite sets HF as the union of Vn, where Vn = U { P(Vm | m < n }. This definition needs no base case, and does not split into cases.
One can now prove all the basic facts about the Vα hierarchy, also without splitting into zero, successor and limit cases. For example, every Vα is transitive, since by induction it is the union of transitive sets. Similarly, the hierarchy is increasing, etc.
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It seems to me that, when you use the improved (non-case-splitting) definition of the hierarchy, the particular facts you mention at the end --- transitivity and monotonicity --- can be proved without any induction at all (provided you know that the < relation on ordinals is transitive). But I agree that other facts about the hierarchy become provable by non-case-splitting inductions.
– Andreas Blass
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Dec 25, 2010 at 0:11
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One context in which one does inductive proofs without a base case is that of Conway's games/numbers, which are defined inductively without a base case.
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answered Jul 7, 2010 at 21:23
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Mariano Suárez-Álvarez
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Any constructively valid proof by well-founded induction, specialized to the natural numbers as a particular well-founded set, will be an example. Recall that a set A with a relation < is well-founded if for any S⊆A, if (∀y<x)(y∈S)⇒x∈S, then S=A. A proof by well-founded induction proceeds by proving that the set S of "all x∈A such that blah" satisfies that condition, i.e. that if blah is true for all y<x, then it is also true for x. In classical logic, one can separate out such a proof into "case 1: there are no y<x" and "case 2: there are some y<x", but in constructive logic this is not generally possible. (It is still possible in the particular case of strong induction on the naturals, since equality of naturals is decidable.) However, interesting proofs by well-founded induction do still exist constructively.
For example, if A is well-founded, and B is equipped with a function t:PB→B, then one can prove by well-founded induction on A that there is a unique function f:A→B defined by well-founded recursion, i.e. such that for all x∈A we have f(x)=t({f(y)∣y∈A∧y<x}). Define an attempt to be a partial function A⇀B whose domain is down-closed for < and which satisfies the desired condition insofar as it is defined. We can then prove by well-founded induction that any two attempts are equal on the intersection of their domains, and that for all x there exists an attempt whose domain contains x, hence the union of all attempts is the desired function.
In classical logic, where emptiness of a set is decidable, we could separate out the empty set as a special case in this argument (or any other), but it wouldn't gain us anything; it would be just as "non-genuine" as Tran Chieu Minh's construction in the other direction.
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Mike Shulman 83%
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There is another of this same fact called noetherian induction by applying the descending chain condition on the spectrum of a noetherian ring.
– Harry Gindi
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Jan 17, 2010 at 1:06
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One may transform any strong induction proof into one which (legalistically speaking!) doesn't explicitly treat the base case.
Proving P(n) by induction, one assumes ∀k<n P(k) which weakens to ∀k<n P(0)⟹P(k).` Now one may adapt whatever proof one had for the induction step to establish from this that P(0)⟹P(n). Now one proves P(0) and concludes P(n) by modus ponens.
Yes, I know, morally the base case still got special treatment, but formally now that happens in the induction step. Thus finding a formal distinction between theorems that require special treatment for the base case and those that don't seems impossible.
In any case, if you can prove ∀n≥0 P(n) by strong induction, you can prove ∀n>0 P(0)⟹P(n) by strong induction with no special treatment for the base case, morally or formally. So examples abound.
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This is perhaps a rather strange example. There is a paper of Andreas Blass An induction principle and pigeonhole principle for K-finite sets (J. Symbolic Logic 59, 1995, 1186-1193) where the goal is to give an intuitionistic proof of that there is no surjection from X onto X+1 when X is finite (Theorem 2). Before proving this result, Blass proves a strong induction principle for finite sets (Theorem 1). The proof of Theorem 1 uses ordinary induction with a base case, but the proof of Theorem 2 uses the strong induction principle of Theorem 1 instead. Blass' proof of Theorem 2 very straightforward, but I think that a direct proof of Theorem 2 (along the same lines) would be unbearably long.
I guess it's hard to understand this one without seeing the proofs. So I'll give a similar proof (without the intuitionistic fuss, for clarity). The strong induction on finite sets I will use is the following.
(SI) If K is a family of sets such that if all proper subsets of A are in K then A is in K too, then K contains all finite sets.
Let K be the family of all sets A such that if A is a proper subset of B and f:A→B then the image f[A] is not all of B. I claim that K satisfies the hypothesis of (SI).
Suppose all proper subsets of A are in K. Let B be a proper superset of A. Given f:A→B, we consider two cases.
If f−1[A]=A, then f[A]⊆A and so f[A] is certainly not all of B.
If A′=f−1[A] is a proper subset of A. Then A′∈K and hence f[A′] is not all of A. But then A∖f[A′]=A∖f[A]⊆B∖f[A], which shows that f[A] is not all of B.
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Here's another possible example. Let S(0), S(1), S(2), ..., be the sequence of numbers defined by the formula S(n)=1+∑n−1k=0S(k) for every nonnegative integer n. Then we can show that S(n)=2n by strong induction on n.
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answered Jan 19, 2010 at 3:04
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Ravi Boppana
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This doesn't seem to be the kind of example that was requested. First, the argument here seems more naturally carried out with (weak) induction, rather than strong induction, since the induction appeals to the immediately preceding case. Secondly, the nature of the argument at n=0, even if you do it with strong induction, is not the same as for other n, so it treats what amounts to the base case differently.
– Joel David Hamkins
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Jan 21, 2010 at 13:19
Here is the proof by strong induction I had in mind. Suppose by strong induction that S(k)=2k for all k<n. Then S(n)=1+∑n−1k=0S(k)=1+∑n−1k=02k=1+(2n−1)=2n. (The third equation is using the usual formula for geometric series.) The proof seems to be using strong induction, not weak induction. I don't think I needed to handle n = 0 separately. If you'd rather avoid the appeal to the formula for geometric series, then the examples in my other answer might be better.
– Ravi Boppana
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Jan 21, 2010 at 13:59
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@Ravi: Yes, I thought that is what you had had in mind. My point was that your defining recurrence formula simplifies in one step to S(n+1)=S(n)+S(n), which avoids the series and seems naturally treated with weak induction.
– Joel David Hamkins
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Jan 21, 2010 at 19:10
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@steve: I'm not sure I understand your objection, but how about this modification. Let A be defined by A(n)=∑n−1k=0A(k) for every nonnegative integer n. Then by strong induction we can show that A(n) = 0. That's a trivial example, but if we wanted to, we could make it less trivial: B(n)=1−n+∑n−1k=0B(k), which has solution B(n)=1.
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answered Jan 21, 2010 at 12:38
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Ravi Boppana
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This may qualify, though there is a special case hidden inside the argument.
Consider a simplified game of nim in which there are n>0 matchsticks, a player may remove 1, 2, or 3 matchsticks each turn, and the player who takes the last matchstick wins.
Theorem. The first player has a winning strategy if n≢0(mod4); the second player has a winning strategy if n≡0(mod4).
Proof. Strong induction on n. Assume the result holds for all k<n. If n≡0(mod4), then after player 1's turn there will be k<n matchsticks left, with k≢0(mod4). By the induction hypothesis, the first person to play at this point has a winning strategy, this being player 2; thus, player 2 has a winning strategy.
If n≢0(mod4), then write n=4ℓ+t with 1≤t≤3. Have player 1 take t matchsticks, leaving 4ℓ matchsticks. If ℓ=0, player 1 just won. If ℓ>0, then there are k<n matchsticks left, with k≡0(mod4). By the induction hypothesis, the player who moves second has a winning strategy, this being the original player 1. So player 1 has a winning strategy in this case.
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answered Jul 3, 2010 at 19:02
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Arturo Magidin
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It's difficult to answer such questions without a rigorous definition of what it means for a proof to 'treat the base case separately'. What if the base case is proved as the first step in a lemma that is invoked? Or explicitly somewhere way down the line in some long chains of lemmas. Does that count or not? It's really a subtle proof-theoretical question. @Born: did any reply satisfy you? If so, I'd be very interested to know which one(s).
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answered Jul 7, 2010 at 21:14
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Bill Dubuque
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I posted an answer on sci.math.research recently where I used induction with a base case, and then thought I could use strong induction instead. Later another poster came up with a nice argument that hid or did away with the induction. Perhaps you can frame it to fit your needs.
The problem: Given an ascending sequence b_i and descending sequence a_i, both
containing n positive numbers, show that for every permutation p on n letters
that max (a_ib_i, 1 <=i <= n) <= max (a_ib_p(i), 1 <= i <= n) .
Proof sketch (by strong induction?): Assume the result is true for all m < n.
If p fixes n, we're done. Otherwise, swap b_n and b_p(n) and note that the
maximum will not increase. Done.
The above may not be the most natural example nor the best proof of the result.
It may suggest something that will help. Although it could be argued that
this is a "strong inductive" example of a different proof, I think it could
also be argued that the different proof is one that hides the inductive
principle at work. Now let the community judge.
Gerhard "Ask Me About System Design" Paseman, 2010.01.15
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answered Jan 16, 2010 at 7:34
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Gerhard Paseman
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@RaviB: You still got the "base case" issue, namely, 2^0 =1;
@poonen: structurally speaking, we will always be in need of a base case regardless of whether strong or ordinary reduction is used.
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answered Jan 21, 2010 at 9:53
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steve
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@RaviB: how on earth did your comment get minused ? I understand where trying to get. The problem that I am referring to is one of systemic level. The way we build up definitions for various systems necessitates base cases.
– steve
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Jan 22, 2010 at 6:22
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I'm confused a little about not proving base case in strong induction. Can someone point out the error in following proof( I'm using strong induction)?
Theorem: Prove that for all n∈N, 1.30+3.31+5.32+..+(2n+1)3n=n3n+1
Proof:
Let n be arbitrary natural number. Suppose, for all natural numbers k smaller than n,
1.30+3.31+5.32+..+(2k+1)3k=k3k+1
Since (n-1) < n, Then it follows from our assumption that
1.30+3.31+5.32+..(2n−1)3n−1=(n−1)3n
So, 1.30+3.31+5.32+..+(2n+1)3n
= 1.30+3.31+5.32+..(2n−1)3n−1+(2n+1)3n
= (1.30+3.31+5.32+..(2n−1)3n−1)+(2n+1)3n
= (n−1)3n+(2n+1)3n
= 3n.3n
= n3n+1
Hence, by the assumptions of strong induction, 1.30+3.31+5.32+..+(2n+1)3n=n3n+1
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answered Jul 3, 2010 at 4:25
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189683 | https://math.wvu.edu/~kciesiel/teach/Fall03Spr04/451NadlerText/451Nadler101-120.pdf | Intermediate Value Property for Derivatives When we sketched graphs of speciÞc functions, we determined the sign of a derivative or a second derivative on an interval (complementary to the critical points) using the following procedure: We checked the sign at one point in the interval and then appealed to the Intermediate Value Theorem (Theorem 5.2) to conclude that the sign was the same throughout the interval. This works Þne as long as the derivatives are continuous. Can a derivative fail to be continuous?
If so, is there a systematic way to check signs for such a derivative in order to apply various tests easily? (I am referring to the tests in Theorem 10.19 and Corollary 10.31.) The answer to the Þrst question is yes, a derivative can fail to be continuous.
The answer to the second question is that the answer to the Þrst question is irrelevant: We can determine the sign of a derivative on an interval the way as we always did — by checking the sign at only one point of the interval — whether the derivative is continuous or not! In other words, derivatives do not change sign on an interval on which they are deÞned without having value zero at some point of the interval.
We give an example that veriÞes our answer to the Þrst question, and we give a theorem that explains our answer to the second question.
Example 10.48: We give an example of a differentiable function f : R1 → R1 such that its derivative is not continuous. DeÞne f by f(x) = ½ x2 sin( 1 x) , if x 6= 0 0 , if x = 0.
Using various results in Chapter VII and Theorem 8.20, we see that f is differentiable at every point x 6= 0 and that f0(x) = x2cos( 1 x) + 2x sin( 1 x) = 2x sin( 1 x) −cos( 1 x), x 6= 0.
furthermore, we see that f is differentiable at x = 0 as follows: For x 6= 0, 0 ≤ ¯ ¯ ¯ f(x)−f(0) x−0 ¯ ¯ ¯ = ¯ ¯x sin( 1 x) ¯ ¯ ≤|x|; thus, since limx→0 |x| = 0, the Squeeze Theorem (Theorem 4.34) applies to give us that limx→0 ¯ ¯ ¯ f(x)−f(0) x−0 ¯ ¯ ¯ = 0.
This proves that f0(0) = 0 (recall Exercise 6.10).
Finally, we show that f0 is not continuous at 0 by showing that limx→0 f0(x) does not exist. Recall that f0(x) = x2cos( 1 x) + 2x sin( 1 x) = 2x sin( 1 x) −cos( 1 x), x 6= 0.
Note that 101 0 ≤ ¯ ¯2x sin( 1 x) ¯ ¯ ≤|2x|, x 6= 0; thus, since limx→0 |2x| = 0, we have by the Squeeze Theorem (Theorem 4.34) that limx→0 2x sin( 1 x) = 0.
Hence, if limx→0 f0(x) existed, then we would have limx→0 cos( 1 x) 4.2 = limx→0 2x sin( 1 x) −limx→0 f0(x), which is impossible (since, as is clear, limx→0 cos( 1 x) does not exist).
Next, we show why, even though derivatives may not be continuous, we can determine the sign of a derivative on an interval complementary to the critical points by checking the sign at only one point of the interval. The reason is simple enough — derivatives, continuous or not, satisfy the conclusion to the Intermediate Value Theorem (Theorem 5.2). We prove this in Theorem 10.50.
First, we introduce relevant terminology and discuss the notion we deÞne. (The terminology carries the name of the French mathematician G. Darboux (1842 -1917) who proved the theorem we will prove.) DeÞnition: Let I be an interval, and let f : I →R1 be a function. We say that f is a Darboux function provided that for any two points p, q ∈I and any point y between f(p) and f(q), there is a point x between p and q such that f(x) = y (i.e., for any subinterval J of I, f(J) is an interval).
There are fairly simple functions that are Darboux but not continuous: For example, let f(x) = ½ sin( 1 x) , if x 6= 0 0 , if x = 0.
Actually, the derivative f0 of the function in Example 10.48 is another ex-ample of a discontinuous Darboux function. This fact about the function in Example 10.48 illustrates the content of the theorem we will prove: Any deriva-tive on an interval is a Darboux function.
We use the following lemma in the proof of our theorem.
Lemma 10.49: Let f be a continuous function on an interval I, and let C denote the set of all slopes of chords joining any two points on the graph of f; that is, C = { f(s)−f(r) s−r : s, r ∈I and s 6= r}.
Then C is an interval.
Proof: Fix p ∈C, say p = f(a)−f(b) a−b , a < b.
102 We show that there is an interval in C joining p to any other point of C. To this end, let z ∈C, say z = f(u)−f(v) u−v , u < v.
Note that since a −b < 0 and u −v < 0, 1 −t + t(u −v) 6= 0 for all t ∈[0, 1]; in anticipation of what comes next, we write this as follows: [1 −t]a + tu −[1 −t]b −tv 6= 0 for all t ∈[0, 1].
Hence, the following formula deÞnes a function σ : [0, 1] →C such that σ(0) = p and σ(1) = z as follows: σ(t) = f([1−t]a+tu)−f([1−t]b+tv) [1−t]a+tu−[1−t]b−tv , all t ∈[0, 1].
By the continuity of f and by various theorems about continuity in Chapter IV (notably, 4.4, 4.21 and 4.28), we see that σ is continuous. Thus, by the Intermediate Value Theorem (Theorem 5.2), σ([0, 1]) is an interval. Therefore, since σ(0) = p and σ(1) = z, we have proved that p and any other point z of C lie in an interval in C. It now follows easily that C is an interval. ¥ Theorem 10.50: If f is a differentiable function on an interval I, then f0 is a Darboux function.
Proof: Let D be the set of all values of the Þrst derivative of f on I, D = {f0(x) : x ∈I}.
We prove that D is an interval, which is simply another way of stating the theorem we are proving.
Let C be as in Lemma 10.49. Since f is continuous by Theorem 6.14, C is an interval by Lemma 10.49. Let E denote the set of end points of C (E may be empty).
The Mean Value Theorem (Theorem 10.2) says that C ⊂D. The deÞnition of the derivative says that every value of the Þrst derivative of f is a limit of slopes of chords; hence, D ⊂C ∪E (since C ∪E = C∼, where C∼is the set of all points arbitrarily close to C, as deÞned in sections 1 and 2 of Chapter II).
We have proved that C is an interval and C ⊂D ⊂C ∪E.
Therefore, it follows at once that D is an interval. ¥ In Exercise 10.16 you were asked if a certain function with a simple discon-tinuity was a derivative of some function. You probably worked the exercise in a fairly computational way. Theorem 10.50 yields the solution to Exercise 10.16 immediately and furnishes a completely different perspective on the exercise.
We brießy discuss the situation in general.
103 Let f be a function deÞned on an open interval I. Then f is said to have a simple discontinuity at a point p ∈I, sometimes called a discontinuity of the Þrst kind, provided that f is not continuous at p and limx→p−f(x) and limx→p+ f(x) exist. The function f is said to have a discontinuity of the second kind at p provided that f is not continuous at p and f does not have a simple discontinuity at p.
There are exactly two ways a function can have a simple discontinuity at p : Either limx→p−f(x) 6= limx→p+ f(x) or limx→p−f(x) = limx→p+ f(x) 6= f(p).
Corollary 10.51: If f is a differentiable function on an open interval I, then f0 has no simple discontinuities.
Proof: Left as the Þrst exercise below. ¥ Exercise 10.52: Prove Corollary 10.51. In fact, prove that the corollary ex-tends to all Darboux functions; that is, any discontinuity of a Darboux function on an open interval is a discontinuity of the second kind.
Exercise 10.53: A differentiable function on R1 can have derivative equal to zero at a point and yet not have a local extremum at the point (e.g., f(x) = x3).
Similarly, a differentiable function on R1 can have a positive derivative at a point without being strictly increasing in any neighborhood of the point (compare with Theorem 10.17): Modify the function in Example 10.48 to give an example.
(Hint: Think geometrically: modify the graph of the function in Example 10.48.) Exercise 10.54: DeÞne f : [ 9 10, 21 10] →R1 by f(x) = x4 −6x3 + 12x2. Find D = {f0(x) : x ∈[ 9 10, 21 10]}, C = { f(s)−f(r) s−r : s, r ∈[ 9 10, 21 10] and s 6= r}; D and C are the sets in the proof of Theorem 10.50.
Exercise 10.55: Let f : R1 →R1 be a polynomial of odd degree. Theorem 10.50 implies that the set D of all values of the Þrst derivative of f is an interval.
What types of intervals can D be? What types of intervals can the set C in Lemma 10.49 be?
Exercise 10.56: Repeat Exercise 10.55 for the case when f is a polynomial of even degree.
Exercise 10.57: Prove that at most one of the functions f and g below can be a derivative of a function: f(x) = sin(1 x) , if x 6= 0 0 , if x = 0 g(x) = sin(1 x) , if x 6= 0 1 , if x = 0.
104 Chapter XI: Area The chapter is a bridge between previous chapters and the topic of sub-sequent chapters (the integral). We simply present an informal, nonrigorous discussion of an aspect of area for the purpose of motivating the integral. Our discussion connects derivatives with area!
Consider the continuous function f whose graph we have drawn in Figure 1 below. We want to Þnd the area between the graph of f and the interval [a, b] on x - axis.
Figure 1 There is an obvious question here: What do we mean by area (referring to the area between the graph of f and the interval [a, b])? We will answer the question in a precise way in Chapter XIV. Here we answer the question somewhat intuitively, and then we describe how to compute the area.
We start by dividing the interval [a, b] into n intervals whose end points are x0 = a < x1 < x2 < · · · < xn = b.
We think of each of the intervals [xi−1, xi] as being small, and we consider the rectangles Ri of height f(xi) and width xi −xi−1, as in Figure 2 (we use f(xi) as a matter of convenience; we could use f(ti) for any ti ∈[xi−1, xi]).
105 Figure 2 We know from elementary geometry that the area of each rectangle Ri is f(xi)(xi −xi−1). Thus, the sum S = Σn i=1f(xi)(xi −xi−1) represents the area of the region covered by all the rectangles. Observe that if xi−1 and xi are very close to one another for each i, then the sum S is very close to what we would call the area between the graph of f and the interval [a, b]. Consider dividing the interval [a, b] into more and more subintervals in such a way that the end points xi−1 and xi of the intervals get closer and closer together: If we can compute the “limit” of the sums S associated with the subdivisions, then we will have computed what we would call the area between the graph of f and the interval [a, b].6 Now, having indicated what we mean by the area between the graph of f and the interval [a, b], we give a procedure for computing the area. The method is so ingenious that it stands as a monument to human thought.
We make use of the area function A : [a, b] →R1, deÞned as follows: For each x ∈[a, b], A(x) is the area between the graph of f|[a, x] and the interval [a, x]. (We will see in section 2 of Chapter XIV that A(x) is the integral of f over the interval [a, x].) If we knew a formula for A, computing the area between the graph of f and the interval [a, b] would be easy — we would simply plug b into the formula.
Thus, we want to Þnd a formula for A, or at least enough information about A to Þnd A(b).
6Note that the “limit” mentioned here is not a limit as we deÞned the term in Chapter III since each sum S depends on many points xi. In other words, S is not a function of a single real variable. We have used the term “limit” in an intuitive way — to conjure up a picture in the reader’s mind. We give a rigorous deÞnition in section 2 of Chapter XIV.
106 We “show” that the area function A is differentiable by “computing” its derivative (the quotes mean we show and compute as best as we can without a mathematically precise deÞnition of area). Then we discover what the derivative of A has to do with Þnding the area we want.
Fix x ∈[a, b]. In order to Þnd A0(x) = limh→0 A(x+h)−A(x) h , it is clear that we must write the numerator with a factor of h.
We Þrst examine the numerator A(x + h) −A(x) for some given h > 0; we assume h to be near enough to 0 so that x + h < b (if x = b, we only consider the case when h < 0, which we will consider later for any x).
We see from Figure 3 that A(x + h) −A(x) is the area between the graph of f|[x, x + h] and the interval [x, x + h].
Figure 3 The continuous function f has a maximum value M and a minimum value m on [x, x +h] (by Theorem 5.13). Consider the function ϕ : [m, M] →R1 that assigns to a point t ∈[m, M] the area of the rectangle [x, x + h] × [0, t] (see Figure 4); since the height of the rectangle is t and its width is h, ϕ(t) = th for each t ∈[m, M].
107 Figure 4 We know that the function ϕ is continuous (see Example 2.23); furthermore, since A(x + h) −A(x) is the area between the graph of f|[x, x + h] and the interval [x, x + h], we know that ϕ(m) ≤A(x + h) −A(x) ≤ϕ(M).
Hence, there is a point th ∈[m, M] such that ϕ(th) = A(x + h) −A(x); in other words, thh = A(x + h) −A(x).
Now, note that f is continuous on [x, x + h] (by Exercise 5.3); thus, since th ∈[m, M] and since m and M are values of f on [x, x + h], there is a point xh ∈[x, x + h] such that f(xh) = th (by Theorem 5.2).
Therefore, by the previous displayed item, we have () f(xh)h = A(x + h) −A(x).
The equality in () also holds when h < 0 (and near enough to 0 so that x + h > a): For then the area between the graph of f|[x + h, x] and the interval [x + h, x] is A(x) −A(x + h), and the rectangle [x + h, x] × [0, t] has width −h for any t ∈[m, M]; hence, by the analogue of the argument above (in this case, ϕ(t) = t(−h)), there is a point th ∈[m, M] such that th(−h) = A(x) −A(x + h), and there is a point xh ∈[x + h, h] such that f(xh) = th, thus 108 f(xh)(−h) = A(x) −A(x + h), which is the same as ().
We are ready to compute the derivative of A at x : Using that () holds whether h is positive or negative, we have that A(x+h)−A(x) h = f(xh)h h = f(xh), where xh lies between x and x + h.
Hence, A0(x) = limh→0 A(x+h)−A(x) h = limh→0 f(xh); furthermore, since limh→0 xh = x by the Squeeze Theorem (Theorem 4.34) and since f is continuous at x, we see that limh→0 f(xh) = f(x) (by Theorem 4.29 by considering the function h 7→xh). Therefore, A0(x) = f(x).
So, the derivative of the area function is f; but what does that have to do with computing the area between the graph of f and the interval [a, b]? Think about it before reading further. Here is a hint: The area we want to compute is A(b), and A(b) = A(b) −A(a).
We show the way to compute A(b). The method is theoretical, but after we discuss the method we will illustrate that it works quite well in practice.
Let g be any function whose derivative on [a, b] is f. Then, since g0 = A0, g and A differ by a constant (by Theorem 10.8), say A −g = C. Thus, A(b) −A(a) = ³ g(b) + C ´ − ³ g(a) + C ´ = g(b) −g(a).
Therefore, since A(b) = A(b) −A(a), we can now conclude the following: (#) To Þnd the area between the graph of f and the interval [a, b], we need only Þnd a function g whose derivative on [a, b] is f; then the area between the graph of f and [a, b] is g(b) −g(a).
We give two examples to illustrate how easy it is to apply the procedure we have found.
Example 11.1: We Þnd the area between the graph of f(x) = x2 and the interval [1, 3]. The function g(x) = x3 3 has derivative f (by Lemma 7.11); therefore, by (#), the area between the graph of f and the interval [1, 3] is g(3) −g(1) = 9 −1 3 = 26 3 .
Example 11.2: We Þnd the area between the graph of f(x) = x 2 5 + 3x3 and the interval [1, 3]. The function g(x) = 5 7x 7 5 + 3 4x4 has derivative f (by Theorem 7.1 and Theorem 8.16); hence, by (#), the area between the graph of f and the interval [1, 3] is 109 g(3) −g(1) = 5 73 7 5 + 243 4 −41 28.
How do we know that the procedure in (#) really does give the area? The most reasonable way to check this is to see if the procedure gives various areas that are known from geometry. We offer the following exercise as a start: Exercise 11.3: Show that the procedure in (#) gives the formulas from geometry for the areas of rectangles, triangles and circles.
(Hint: In the case of a circle of radius r about the origin, consider the function g(x) = x 2 √ r2 −x2 + r2 2 sin−1( x 2).) When more complicated Þgures (than those in Exercise 11.3) whose areas are known from geometry are analyzed using the procedure in (#), the answer is always the same: Applying (#) results in arriving at the known areas. In the end, therefore, we will be jusiÞed in deÞning area in terms of the integral and using the procedure in (#) to Þnd the area — see section 2 of Chapter XIV.
We conclude with a few exercises.
Exercise 11.4: Find the area between the graph of f(x) = sin(x) and the interval [0, π].
Exercise 11.5: Find the area between the graph of f(x) = 1 √ 1−x2 and the interval [0, 1 2].
Exercise 11.6: Find formulas for the area functions for Examples 11.1 and 11.2.
Exercise 11.7: Using the intuitive observation that the area of two nonover-lapping regions is the sum of the areas of the two regions, Þnd the area above the interval [0, 1] between the graphs of the two functions f1(x) = x4 and f2(x) = x5.
110 Chapter XII: The Integral In the Þrst part of preceding chapter, we intuitively discussed a way of deÞn-ing area in order to provide a tangible picture to keep in mind when studying the integral. In this chapter, we begin a rigorous treatment of the integral. This is the Þrst of four chapters concerned directly with the theory of the integral.
(There are many types of integrals; we will only study one type — the Riemann integral — which we simply refer to as the integral.) After presenting preliminary notions and results, we deÞne the integral in section 3. In section 4, we prove an existence theorem that gives a necessary and sufficient condition for a function to be integrable (Theorem 12.15); we also prove a theorem that provides a way (albeit limited) to evaluate the integral (Theorem 12.17). In section 5, we use the existence theorem in section 4 to prove that all continuous functions are integrable.
Partitions In this section (and the next) we present a rigorous and systematic treatment of some of the ideas that we introduced informally in the preceding chapter.
Thus, we consider the preceding chapter as motivation for what follows.
DeÞnition. A partition of [a, b] when a < b is a Þnite subset P of [a, b] that can be indexed so that P = {x0, x1, ..., xn}, where x0 = a < x1 < x2 < · · · < xn = b, some n ≥1.
It is also to be understood that the interval [a, a] has a (unique) partition, namely, {a}.
For example, {0, 1} and {0, 1 3, 1 2, 1} are partitions of [0, 1]. Obviously, every interval [a, b] has a partition.
Whenever P is a partition and we write P = {x0, x1, ..., xn}, we assume (without explicitly saying so) that the points xi satisfy the condition in the def-inition above. We prove all results that involve partitions, directly or indirectly (as in the case of integrals), assuming that a < b. It will be evident that the results hold when a = b.
DeÞnition.
Let P1 and P2 be partitions of [a, b].
We say that P2 is a reÞnement of P1, written P2 ¹ P1, provided that P2 ⊃P1.
We can think of a reÞnement of a partition P as being obtained from P by adding points to P (although, of course, a partition is a reÞnement of itself).
Obviously, every partition of [a, b] is a reÞnement of {a, b}.
Exercise 12.1: Give an example of two partitions of [a, b] such that neither one is a reÞnement of the other.
A relation ¿ between elements of a set S is a partial order on S provided that the relation is reßexive (s ¿ s for all s ∈S), antisymmetric (if s1 ¿ s2 and s2 ¿ s1, then s1 = s2), and transitive (if s1 ¿ s2 and s2 ¿ s3, then s1 ¿ s3).
111 For example, ≤is a partial order on R1 by axioms O1 and O2 in section 1 of Chapter I.
Note the following simple fact: Exercise 12.2: The relation ¹ of reÞnement on the collection P of all partitions of a given interval [a, b] is a partial order.
DeÞnition. Let P1 and P2 be reÞnements of [a, b]. A common reÞnement of P1 and P2 is a partition P of [a, b] such that P ¹ P1 and P ¹ P2.
Exercise 12.3: For any two partitions P1 and P2 of [a, b], there is a smallest common reÞnement of P1 and P2; that is, there is a common reÞnement, P, of P1 and P2 such that every common reÞnement of P1 and P2 contains P.
Upper and Lower Sums We continue with our presentation of the background necessary for deÞning the integral and understanding the deÞnition.
We adopt the following notation: Let f : [a, b] →R1 be a bounded function, and let P = {x0, x1, ..., xn} be a partition of [a, b]. For each i = 1, 2, ..., n, ∆xi = xi −xi−1, Mi(f) = lub f([xi−1, xi]), mi(f) = glb f([xi−1, xi]).
DeÞnition.
Let f : [a, b] →R1 be a bounded function, and let P = {x0, x1, ..., xn} be a partition of [a, b].
• The upper sum of f with respect to P, denoted by UP (f), is deÞned by UP (f) = Σn i=1Mi(f)∆xi.
• The lower sum of f with respect to P, denoted by LP(f), is deÞned by LP (f) = Σn i=1mi(f)∆xi.
Exercise 12.4: DeÞne f : [−4, 4] →R1 by f(x) = x3 −12x. Evaluate UP (f) and LP (f) for the partition P = {−4, 1, 4}.
Exercise 12.5: DeÞne f : [0, 4] →R1 by f(x) = x3 −9x2 + 26x −24.
Evaluate UP(f) and LP (f) for the partition P = {0, 1, 3, 4}.
Lemma 12.6: Let f : [a, b] →R1 be a bounded function. For any partition P = {x0, x1, ..., xn} of [a, b], LP (f) ≤UP(f).
Proof: For each i, mi(f) ≤Mi(f) and ∆xi > 0, hence mi(f)∆xi ≤ Mi(f)∆xi. Therefore, the lemma follows immediately by summing over i. ¥ Lemma 12.7: Let f : [a, b] →R1 be a bounded function. Let P be a partition of [a, b], and let q be a point of [a, b] such that q / ∈P. Let Q = P ∪{q} (considered as a partition of [a, b]). Then UQ(f) ≤UP (f) and LQ(f) ≥LP(f).
112 Proof: Assume that P = {x0, x1, ..., xn}. Let k be such that xk < q < xk+1.
Then, letting α = ³ lub f([xk, q]) ´ (q −xk) + ³ lub f([q, xk+1]) ´ (xk+1 −q), we have that UQ(f) = Σi6=k+1Mi(f)∆xi + α. Also, since lub(A) ≤lub(B) when A ⊂B, α = ³ lub f([xk, q]) ´ (q −xk) + ³ lub f([q, xk+1]) ´ (xk+1 −q) ≤ ³ lub f([xk, xk+1]) ´ (q −xk) + ³ lub f([xk, xk+1]) ´ (xk+1 −q) = ³ lub f([xk, xk+1]) ´ (xk+1 −xk).
Therefore, UQ(f) = Σi6=k+1Mi(f)∆xi + α ≤Σn i=1Mi(f)∆xi = UP (f).
Similarly, LQ(f) ≥LP(f). ¥ Lemma 12.8: Let f : [a, b] →R1 be a bounded function, and let P1 and P2 be partitions of [a, b] such that P2 ¹ P1. Then UP2(f) ≤UP1(f) and LP2(f) ≥LP1(f).
Proof: Let y1, y2, ..., ym be the points in P2 −P1 (we assume that P1 6= P2 since, otherwise, the lemma is obvious). We successively deÞne partitions Qj, j = 1, ..., m, of [a, b] as follows: Q1 = P1, Q2 = Q1 ∪{y1}, Q3 = Q2 ∪{y2}, ... , Qm = P2.
Since Qj+1 has exactly one more point than Qj for each j, each successive inequality below follows at once from Lemma 12.7: UP2(f) = UQm(f) ≤UQm−1(f) ≤· · · ≤UQ2(f) ≤UQ1(f) = UP1(f) and LP2(f) = LQm(f) ≥LQm−1(f) ≥· · · ≥LQ2(f) ≥LQ1(f) = LP1(f). ¥ Lemma 12.9: Let f : [a, b] →R1 be a bounded function, and let P1 and P2 be partitions of [a, b]. Then LP1(f) ≤UP2(f).
Proof: Let P be a common reÞnement of P1 and P2 (see Exercise 12.3).
Then LP1(f) 12.8 ≤LP(f) 12.6 ≤UP (f) 12.8 ≤UP2(f). ¥ 113 The numbers lubP∈PLP(f) and glbP∈PUP (f) in the next lemma are the basis for our deÞnition of the integral in the next section.
Lemma 12.10: Let f : [a, b] →R1 be a bounded function, and let P denote the collection of all partitions of [a, b]. Then lubP ∈PLP(f) and glbP∈PUP (f) exist and lubP ∈PLP(f) ≤glbP∈PUP (f).
Proof: There is a partition P1 of [a, b]. By Lemma 12.9, LP1(f) is a lower bound for the set of all upper sums of f with respect to all partitions of [a, b]. Hence, by the Greatest Lower Bound Axiom (section 8 of Chapter I), glbP ∈PUP(f) exists, and () LP1(f) ≤glbP∈PUP (f).
Note that we have proved () for any partition P1 of [a, b]. Hence, glbP∈PUP (f) is an upper bound for the set of all lower sums of f with respect to all partitions of [a, b]. Therefore, by the Least Upper Bound Axiom (Completeness Axiom), lubP ∈PLP(f) exists, and it is clear that lubP∈PLP(f) ≤glbP∈PUP(f). ¥ Except for very simple functions, it is difficult to directly compute the num-bers lubP ∈PLP(f) and glbP∈PUP(f) in Lemma 12.10. For example, the reader might try to compute the numbers in Lemma 12.10 for the case when f is the function on [0, 1] deÞned by f(x) = x. In fact, computing the numbers lubP ∈PLP(f) and glbP∈PUP (f) is actually evaluating integrals or showing inte-grals do not exist, as we will see from the deÞnition of the integral (in the next section). Nevertheless, we can at this time compute the numbers in Lemma 12.10 for a few functions. We illustrate how to do this in the two examples be-low. In the Þrst example, lubP∈PLP(f) = glbP∈PUP (f); in the second example, lubP ∈PLP(f) 6= glbP∈PUP (f).
Example 12.11: DeÞne f : [0, 2] →R1 by f(x) = ½ 1 , if x 6= 1 2 , if x = 1.
Let P denote the collection of all partitions of [0, 2]. We show that lubP∈PLP(f) = glbP∈PUP (f) = 2.
Let P = {x0, x1, ..., xn} be a partition of [0, 2]. Note that each of the intervals [xi−1, xi] contains a point different from 1; hence, mi(f) = 1 for each i. Thus, LP(f) = Σn i=1∆xi = xn −x0 = 2 −0 = 2.
Therefore, lubP∈PLP(f) = 2.
We now show that glbP ∈PUP (f) = 2. Let ² > 0 such that ² < 1. Consider the following very simple partition Q of [0, 2] : 114 Q = {0, 1 −², 1 + ², 2}.
We compute UQ(f) : UQ(f) = 1([1 −²] −0) + 2([1 + ²] −[1 −²]) + 1(2 −[1 + ²]) = 2 + 2².
Thus, since ² can be as close to zero as we like, we have proved that glbP ∈PUP(f) ≤2.
Also, having proved above that lubP ∈PLP(f) = 2, we know from Lemma 12.10 that 2 ≤glbP ∈PUP(f). Therefore, glbP ∈PUP(f) = 2 = lubP∈PLP (f).
Example 12.12: DeÞne f : [0, 1] →R1 by f(x) = ½ 0 , if x is rational 1 , if x is irrational.
Let P denote the collection of all partitions of [0, 1]. We show that lubP∈PLP(f) = 0 and glbP∈PUP(f) = 1.
Let P = {x0, x1, ..., xn} be a partition of [0, 1]. By Theorem 1.26 (and its analogue for irrational numbers), there is a rational number and an irrational number in each of the intervals [xi−1, xi]. Hence, LP (f) = Σn i=1(0)∆xi = 0 and UP (f) = Σn i=1(1)∆xi = (x1 −x0) + (x2 −x1) + · · · + (xn −xn−1) = xn −x0 = 1 −0 = 1.
Therefore, lubP∈PLP(f) = 0 and glbP∈PUP (f) = 1.
The cancellation that gave Σn i=1∆xi = xn−x0 in Example 12.12 is trivial but has far - reaching generalizations in multi - dimensional calculus (for example, in the proof of Green’s Theorem).
Exercise 12.13: Let f be a constant function on an interval [a, b], say f(x) = c for all x ∈[a, b]. Compute lubP∈PLP(f) and glbP∈PUP(f).
Exercise 12.14: DeÞne f : [0, 2] →R1 by f(x) = ½ 1 , if 0 ≤x < 1 3 , if 1 ≤x ≤2.
Compute lubP∈PLP (f) and glbP∈PUP (f).
115 3. DeÞnition of the Integral We are ready to deÞne the integral.
DeÞnition. Let f : [a, b] →R1 be a bounded function, and let P denote the collection of all partitions of [a, b]. Recall that we showed in Lemma 12.10 that the numbers glbP∈PUP(f) and lubP∈PLP (f) exist.
• The upper integral of f over [a, b] is glbP∈PUP (f), which we denote from now on by R b af.
• The lower integral of f over [a, b] is lubP∈PLP(f), which we denote from now on by R b af.
• We say that f is integrable over [a, b] provided that R b af = R b af, in which case we call the common value R b af = R b af the integral of f over [a, b] (or the integral of f from a to b). We denote the integral of f over [a, b] by R b a f or by R b a f(x)dx. The notation R b a f(x)dx is read integral of f over [a, b] with respect to the variable x.7 In the expressions R b af, R b af and R b a f, the numbers a and b are referred to as the limits of integration (a being the lower limit of integration and b being the upper limit of integration) The function f is called the integrand.
From what we showed in Example 12.11, we can now say that the function f in the example is integrable and R 2 0 f = 2. On the other hand, from what we showed in Example 12.12, the function f in Example 12.12 is not integrable.
We prove results about integrals over [a, b] as though a < b without saying so. The reader can easily check that the results are true when a = b (R a a f = 0 since {a} is the only partition of the interval [a, a]).
Two Theorems about Integrability We prove two theorems about integrability and show how the theorems can be applied.
Our Þrst theorem is useful for proving that a function is integrable; we illustrate this for a speciÞc function after we prove the theorem. We use the theorem in the next section to prove that all continuous functions are integrable, and we use the theorem in many other places as well.
7Regarding the notation R b a f(x)dx, the symbol dx has absolutely no mathematical content other than to indicate the variable with respect to which the integration is being performed.
Thus, the symbol dx can be used to clarify situations when the expression being integrated contains two or more letters as symbols; for example, simply writing R b a t2x3 puts in doubt whether we are integrating with respect to t or with respect to x, whereas writing R b a t2x3dx and R b a t2x3dt makes it clear what the variable of integration is in each case.
116 Theorem 12.15: Let f : [a, b] →R1 be a bounded function. Then f is integrable over [a, b] if and only if for each ² > 0, there is a partition P of [a, b] such that UP(f) −LP (f) < ².
Proof: Assume that f is integrable over [a, b]. Let ² > 0. Since R b a f = R b af = glbP∈PUP(f) and R b a f = R b af = lubP∈PLP (f), there are a partitions P1 and P2 of [a, b] such that (1) UP1(f) < R b a f + ² 2 and LP2(f) > R b a f −² 2.
Let P be a common reÞnement of P1 and P2 (see Exercise 12.3). Then, by Lemma 12.6 and Lemma 12.8 , we have (2) LP2(f) ≤LP (f) ≤UP (f) ≤UP1(f).
Now, UP(f) −LP (f) (2) ≤UP1(f) −LP2(f) (1) < R b a f + ² 2 −(R b a f −² 2) = ².
This proves that P is as required in the theorem.
Conversely, assume that for each ² > 0, there is a partition P² of [a, b] such that UP²(f) −LP²(f) < ².
Then, since R b af = glbP∈PUP(f) and R b af = lubP∈PLP (f), 0 12.10 ≤R b af −R b af ≤UP²(f) −LP²(f) < ² for all ² > 0.
Hence, R b af −R b af = 0 (it follows from the axioms in section 1 of Chapter I that if 0 ≤x < ² for all ² > 0, then x = 0). Therefore, R b af = R b af, which proves that f is integrable. ¥ Lest it escape us without notice, we point out that Theorem 12.15 says that we need only Þnd one appropriate partition for each ² > 0 in order to show a function is integrable. This feature of Theorem 12.15 makes it signiÞcantly easier to show a function is integrable than it would be to show the function is integrable using the deÞnition of integrability directly. We illustrate this with the following example: Example 12.16: DeÞne f : [0, 2] →R1 by f(x) = x2. We show that f is integrable over [0, 2] by applying Theorem 12.15.
Let ² > 0. Let n be a natural number such that 4 n < ² (the number n exists by the Archimedean Property (Theorem 1.22)). Let P be the partition of [0, 2] given by 117 P = {x0 = 0, x1 = 1 n, ..., xi = i n, ..., x2n = 2}.
Note that f is strictly increasing (by Theorem 10.17 since f0(x) = 2x > 0 for all x ∈[0, 2]). Hence, Mi(f) = x2 i , mi(f) = x2 i−1, each i = 1, 2, ..., 2n.
Thus, since ∆xi = 1 n for each i, UP(f) −LP (f) = Σ2n i=1x2 i 1 n −Σ2n i=1x2 i−1 1 n = 1 n(Σ2n i=1x2 i −Σ2n i=1x2 i−1) = 1 n(x2 2n −x2 0) = 1 n(4 −0) < ².
Therefore, by Theorem 12.15, f is integrable over [0, 2].
Note that we did not evaluate the integral in Example 12.16 — Theorem 12.15 is not set up to evaluate integrals. Our next theorem gives a condition that can be used to evaluate integrals (in practice, however, the theorem has very limited use for this purpose). After we prove the theorem, we apply the theorem to evaluate the integral in the example above.
We note that the limits in the following theorem are limits of sequences, which we discussed in section 8 of Chapter IV.
Theorem 12.17: Let f : [a, b] →R1 be a bounded function. Assume that P1, P2, ..., Pn, ... are partitions of [a, b] such that limn→∞UPn(f) = limn→∞LPn(f) = c.
Then f is integrable over [a, b] and R b a f = c.
Proof: By deÞnition, R b af = lubP∈PLP(f) and R b af = glbP∈PUP (f); hence, LPn(f) ≤R b af 12.10 ≤R b af ≤UPn(f), all n = 1, 2, ... .
Thus, by the Squeeze Theorem (Theorem 4.34), which holds for sequences by Theorem 4.38, we have that R b af = c and R b af = c.
Therefore, f is integrable and R b a f = c. ¥ Example 12.18: We use Theorem 12.17 to evaluate the integral of the function in Example 12.16; we show that R 2 0 x2 = 8 3.
We use following formula; the formula can be veriÞed by induction (we leave the veriÞcation for the reader in Exercise 12.19): () Σn i=1i2 = n(n+1)(2n+1) 6 for each n = 1, 2, ... .
For each n = 1, 2, ..., let Pn be the partition of [0, 2] given by 118 Pn = {x0 = 0, x1 = 1 n, ..., xi = i n, ..., x2n = 2}.
Then, since Mi(f) = x2 i and mi(f) = x2 i−1 for each i (as in Example 12.16), UPn(f) = Σ2n i=1x2 i 1 n and LPn(f) = Σ2n i=1x2 i−1 1 n for each n.
Hence, for each n, UPn(f) = 1 nΣ2n i=1( i n)2 = 1 n3 Σ2n i=1i2 () = 1 n3 2n(2n+1)(4n+1) 6 = (2n+1)(4n+1) 3n2 = 8 3 + 2 n + 1 3n2 and LPn(f) = Σ2n i=1( i−1 n )2 1 n = 1 n3 Σ2n i=1(i −1)2 = 1 n3 Σ2n−1 i=1 i2 () = 1 n3 (2n−1)(2n)(4n−1) 6 = (2n−1)(4n−1) 3n2 = 8 3 −2 n + 1 3n2 .
Thus, limn→∞UPn(f) = 8 3 and limn→∞LPn(f) = 8 3. Therefore, by Theorem 12.17, R 2 0 x2 = 8 3.
Exercise 12.19: Verify that Σn i=1i2 = n(n+1)(2n+1) 6 for each n = 1, 2, ... by using induction (Theorem 1.20). (We used the formula in Example 12.18.) In Examples 12.16 and 12.18, we used partitions that divide the interval of integration into intervals of equal length. These types of partitions are useful because we can factor ∆xi out of summations when computing upper and lower sums. We call a partition of an interval [a, b] that divides [a, b] into intervals of equal length ∆xi a regular partition.
Exercise 12.20: Evaluate R b a x for any a ≤b.
(Hint: First prove that Σn i=1i = n(n+1) 2 for each n = 1, 2, ... .) Exercise 12.21: Determine if f is integrable, where f : [0, 1] →R1 is deÞned as follows (Q denotes the set of all rational numbers; for integers m and n, m n in lowest terms means m and n have no common divisor other than ±1): f(x) = 0 , if x is irrational 1 , if x = 0 1 n , if x ∈Q −{0} and x = m n in lowest terms.
Exercise 12.22: Assume that f(x) ≤g(x) ≤h(x) for all x ∈[a, b] and that f and h are integrable over [a, b]. If R b a f = R b a h, then g is integrable and R b a g is equal to R b a f = R b a h.
Exercise 12.23: If f is increasing on [a, b] or decreasing on [a, b], then f is integrable over [a, b].
Exercise 12.24: In connection with Exercise 12.23, is every one - to - one bounded function on an interval [a, b] integrable over [a, b] ?
119 Exercise 12.25: If f : [a, b] →R1 is a nonnegative function that is inte-grable over [a, b], then R b a f ≥0.
Exercise 12.26: Let f : [a, b] →R1 be a nonnegative function that is integrable over [a, b]. Then R b a f = 0 if and only if glbf(I) = 0 for each open interval I in [a, b].
Exercise 12.27: Let f : [a, b] →R1 be a function that is integrable over [a, b], and let g : [a, b] →R1 be a function that agrees with f except at Þnitely many points. Is g integrable over [a, b] ?
Continuous Functions Are Integrable We prove that any continuous function deÞned on a closed and bounded interval is integrable. This is an existence theorem — it does not show how to evaluate the integral. We will be able to evaluate integrals of many simple con-tinuous functions using the Fundamental Theorem of Calculus, which we prove in Chapter XIV. However, evaluating integrals of most continuous functions is difficult, usually impossible; ad hoc methods can sometimes be employed, but most often one has to settle for approximate evaluations by numerical methods.
The following notion is of general importance and is the key idea that we use to prove our theorem: DeÞnition: Let X ⊂R1, and let f : X →R1 be a function. We say that f is uniformly continuous on X provided that for any ² > 0, there is a δ > 0 such that if x1, x2 ∈X and |x1 −x2| < δ, then |f(x1) −f(x2)| < ².
Exercise 12.28: Let X ⊂R1. If f : X →R1 is uniformly continuous, then f is continuous.
Exercise 12.29: The converse of the result in Exercise 12.28 is false: The function f : R1 →R1 given by f(x) = x2 is continuous but not uniformly continuous.
Exercise 12.30: Any linear function f (i.e., f(x) = mx + b) is uniformly continuous on R1. More generally, if f is differentiable on an interval I and the derivative f0 is bounded on I, then f is uniformly continuous on I.
The following theorem is not concerned with integrals, but it is the basis of our proof that continuous functions are integrable. The theorem is so important in all of mathematics that even though it plays the role of a lemma here, we can not bring ourselves to call the theorem a lemma. The theorem shows that the converse of the result in Exercise 12.28 is true when X is a closed and bounded interval.
Theorem 12.31: If f : [a, b] →R1 is continuous, then f is uniformly continuous.
Proof: Suppose by way of contradiction that f is not uniformly continuous.
Then, for some ² > 0, there are points xn, yn ∈[a, b] for each n ∈N such that 120 |
189684 | https://journals.biologists.com/jcs/article/134/23/jcs259110/273634/Cargo-sorting-at-the-trans-Golgi-network-at-a | Published Time: 2021-12-06
Cargo sorting at the trans-Golgi network at a glance | Journal of Cell Science | The Company of Biologists
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Volume 134, Issue 23
December 2021
Previous Article
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Article contents
ABSTRACT
Introduction
Lysosomal hydrolase sorting in clathrin-coated vesicles
Retrograde sorting of Golgi residents
Trafficking in epithelial cells
Perspective
Acknowledgements
Footnotes
Cell science at a glance
References
Supplementary information
Article Navigation
CELL SCIENCE AT A GLANCE|06 December 2021
Cargo sorting at the trans-Golgi network at a glance Free
In collection:Lipid biology,Membrane trafficking
Charlotte Ford,
Charlotte Ford
Department of Cell Biology
,
Yale School of Medicine
,
Yale University
,
New Haven, CT 06520
,
USA
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Anup Parchure,
Anup Parchure
Department of Cell Biology
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Yale School of Medicine
,
Yale University
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New Haven, CT 06520
,
USA
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Julia von Blume Corresponding Author,
Julia von Blume
Department of Cell Biology
,
Yale School of Medicine
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Yale University
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New Haven, CT 06520
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USA
Authors for correspondence (christopher.burd@yale.edu; julia.vonblume@yale.edu)
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Christopher G. Burd Corresponding Author
0000-0003-1831-8706
Christopher G. Burd
Department of Cell Biology
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Yale School of Medicine
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Yale University
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New Haven, CT 06520
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USA
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Author and article information
Charlotte Ford
Department of Cell Biology
,
Yale School of Medicine
,
Yale University
,
New Haven, CT 06520
,
USA
Anup Parchure
Department of Cell Biology
,
Yale School of Medicine
,
Yale University
,
New Haven, CT 06520
,
USA
Julia von Blume
Department of Cell Biology
,
Yale School of Medicine
,
Yale University
,
New Haven, CT 06520
,
USA
Christopher G. Burd
Department of Cell Biology
,
Yale School of Medicine
,
Yale University
,
New Haven, CT 06520
,
USA
Authors for correspondence (christopher.burd@yale.edu; julia.vonblume@yale.edu)
Competing interests
The authors declare no competing or financial interests.
Online ISSN: 1477-9137
Print ISSN: 0021-9533
Funding
Funding Group:
Award Group:
Funder(s):National Institutes of Health
Award Id(s):GM060221 , GM134083 , GM95766
© 2021. Published by The Company of Biologists Ltd
2021
J Cell Sci (2021) 134 (23): jcs259110.
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Charlotte Ford, Anup Parchure, Julia von Blume, Christopher G. Burd; Cargo sorting at the trans-Golgi network at a glance. _J Cell Sci_ 1 December 2021; 134 (23): jcs259110. doi:
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ABSTRACT
The Golgi functions principally in the biogenesis and trafficking of glycoproteins and lipids. It is compartmentalized into multiple flattened adherent membrane sacs termed cisternae, which each contain a distinct repertoire of resident proteins, principally enzymes that modify newly synthesized proteins and lipids sequentially as they traffic through the stack of Golgi cisternae. Upon reaching the final compartments of the Golgi, the trans cisterna and trans-Golgi network (TGN), processed glycoproteins and lipids are packaged into coated and non-coated transport carriers derived from the trans Golgi and TGN. The cargoes of clathrin-coated vesicles are chiefly residents of endo-lysosomal organelles, while uncoated carriers ferry cargo to the cell surface. There are outstanding questions regarding the mechanisms of protein and lipid sorting within the Golgi for export to different organelles. Nonetheless, conceptual advances have begun to define the key molecular features of cargo clients and the mechanisms underlying their sorting into distinct export pathways, which we have collated in this Cell Science at a Glance article and the accompanying poster.
Keywords:
Golgi,Secretion,Clathrin,Glycoprotein,Calcium,Epithelial cells,Lipids
Subjects:
Membrane trafficking
Introduction
The Golgi is an organelle of the eukaryotic endomembrane system that functions principally in the biogenesis and intracellular sorting of newly synthesized glycoproteins and lipids, herein termed ‘biosynthetic cargo’. It is composed of three or more flattened membrane sacs termed the cis, medial and trans cisternae, which adhere to each other in a polarized orientation to form the Golgi stack (Klumperman, 2011). The terminal Golgi compartment is a network of convoluted membranes termed the trans-Golgi network (TGN). Newly synthesized proteins and lipids produced in the endoplasmic reticulum (ER) are directed to the cis Golgi, where they enter the Golgi stack and are trafficked in the anterograde direction to the medial and trans cisternae and the TGN (Li et al., 2019). Within the Golgi stack, cargo-processing enzymes, primarily glycosyltransferases that attach carbohydrate moieties to biosynthetic cargo, reside in one or two cisternae. This arrangement establishes a processing pathway whereby sequentially acting Golgi-resident enzymes appropriately modify cargo proteins, via reactions that include elaboration of glycan chains on proteins and lipids, sulfation of proteins and proteolysis (Stanley, 2011; Stone et al., 2009; Tan and Gleeson, 2019; Thomas, 2002) (see Box 1).
Box 1. How is secretory cargo transported through the Golgi?
The mechanism(s) by which secretory cargo is transported through the stack of Golgi cisternae has been a contentious topic of debate for decades. Two models currently dominate the debate: the cisterna maturation model and the stable compartments model (Lujan and Campelo, 2021; Rabouille and Klumperman, 2005). A key feature of the cisterna maturation model is that secretory cargo remains within a single Golgi cisterna that matures from an early compartment (for example the cis cisterna) into a later compartment (the medial and trans cisternae) by the removal of existing cisterna-resident proteins and their replacement with residents of the subsequent cisterna. Transport vesicles are posited to mediate trafficking of Golgi residents (such as glycosyltransferases) in the retrograde direction, that is, from late to early cisternae. In the stable compartments model, secretory cargo is trafficked via transport vesicles that bud from an early cisterna and fuse with the subsequent cisterna.
COPI-coated vesicles are derived from Golgi cisternae, and the cargo that they contain – Golgi residents or secreted cargo proteins – has been used to distinguish between the two models. Whereas the cisterna maturation model posits that Golgi residents are the major cargo of COPI-coated vesicles, the stable compartments model posits that secretory cargo is the major component. It is now firmly established that ER and Golgi residents are abundant integral membrane proteins of COPI-coated vesicles (Adolf et al., 2019; Gommel et al., 1999; Martínez-Menárguez et al., 2001), although some studies have reported that such vesicles also contain anterograde secretory cargo (Malsam et al., 2005; Orci et al., 1997). Some secretory cargoes (such as algal scales of algae and some collagens) are too large to be accommodated by COPI-coated vesicles (which are 40–80 nm in diameter), and they are observed to transit the Golgi stack while remaining within cisternae (Bonfanti et al., 1998; Melkonian et al., 1991). Cisterna maturation has been observed to occur in yeast cells, suggesting that cisterna maturation is the major if not sole mechanism of anterograde transport through the Golgi of this organism (Losev et al., 2006; Matsuura-Tokita et al., 2006). In favor of the stable compartments model, normal rates of secretion have been observed for mammalian cell lines in which transfer of secretory cargo could transit successive cisternae via vesicles (Dunlop et al., 2017; Lavieu et al., 2013). Ultimately, elucidation of the mode of intra-Golgi transport may require observation of both anterograde and retrograde protein trafficking in living cells.
Once biosynthetic cargo processing is complete, cargo is exported from the Golgi by coated vesicles and pleiomorphic uncoated vesicles, and subsequently transported to the plasma membrane, endosome or other Golgi compartments (De Matteis and Luini, 2008). Cargo sorting and processing in the Golgi is essential for the generation of bioactive proteins (such as hormones and cell surface receptors), organelle biogenesis, cell polarization and lipid homeostasis. Organismal physiology depends critically on these Golgi-mediated cargo-sorting processes as their disruption can contribute to a wide range of disorders, including neurodegenerative diseases, diabetes and cancer (Liu et al., 2021). This Cell Science at a Glance article and the accompanying poster summarize the conceptual advances made toward understanding mechanisms of cargo sorting and export from the trans Golgi and TGN (referred to hereafter as the trans/TGN) during secretion. While most of the cargo-sorting mechanisms presented here apply generally to all eukaryotic cells, the poster focuses on research of mammalian cell types.
Lysosomal hydrolase sorting in clathrin-coated vesicles
Clathrin-coated vesicles (CCVs) traffic integral membrane proteins, predominantly precursors of lysosomal resident enzymes and proteins required for lysosome biogenesis, from the trans/TGN to organelles of the endo-lysosome system (see poster). The CCV coat is composed of two protein shells that are associated with the cytoplasmic leaflet of the vesicle membrane; the inner layer comprises a network of integral membrane proteins and peripheral cargo adaptor proteins that provide a platform for the assembly of clathrin triskelia into the second, outer layer (Wood and Smith, 2021). The best-characterized CCV cargo adaptors are those of the heterotetrameric clathrin adaptor protein family: AP-1, AP-2 and AP-3. These adaptors are comprised of four subunits: two large (one of α, γ, δ or ε and one β) subunits, a medium (μ) subunit and a small (σ) subunit (Sanger et al., 2019). For example, the AP-1 adaptor complex (which consists of β1 γ, μ1 and σ1 subunits) responsible for sorting at the trans/TGN has two γ (γ1 and γ2), two μ1 (μ1A and μ1B, also known in mammals as AP1M1 and AP1M2, respectively) and three σ1 (σ1A, σ1B and σ1C) isoforms, which are implicated in cell type-specific sorting functions of AP-1 (discussed below; Mattera et al., 2011). AP-1 binds two core trans/TGN membrane components, activated Arf1 GTPase (i.e. the GTP-bound form) and the signaling lipid phosphatidylinositol 4-phosphate (PI4P) (Kirchhausen et al., 2014). Additional CCV-associated proteins complement AP-1-mediated sorting by recognizing overlapping but distinct cargo clients. Of these, the Golgi-localized γ-ear-containing ADP-ribosylation factor-binding (GGA) proteins GGA1, GGA2 and GGA3 have prominent roles in lysosome biogenesis through the trafficking of mannose 6-phosphate (mannose 6-P) receptors (discussed below), with a principal role for GGA2 (Uemura and Waguri, 2020). Like AP-1, GGA proteins recognize sorting signals in the cytoplasmic segments of cargo proteins that conform to the sequence motif YXXΦ or [DE]XXXL[LI] (where X is any amino acid and Φ is a bulky hydrophobic amino acid) (Doray et al., 2007; Ohno et al., 1998, 1995; Puertollano et al., 2001; Zhu et al., 2001). Whereas AP-1 is present in two types of Golgi-derived CCVs, those containing only AP-1 and those containing both AP-1 and GGA proteins, GGA2 is specific to only AP-1-containing CCVs (Hirst et al., 2012).
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Retrograde sorting of Golgi residents
The vesicle coat protein complex coatomer I (COPI) is the core component of Golgi retrograde pathways. COPI localizes to the rims of Golgi cisternae, whose edges are surrounded by vesicles, suggesting that these represent dynamic sites of protein sorting and export (Orci et al., 1997). Retrograde sorting of some trans/TGN-resident Golgi proteins is initiated by recruitment of COPI from the cytosol to Golgi membranes by Arf1-GTP and GOLPH3, to which COPI binds (Donaldson et al., 1992; Orci et al., 1993; Palmer et al., 1993; Serafini et al., 1991; Tu et al., 2012) (see poster). On Golgi membranes, COPI assembles into a polymeric membrane coat that contains binding sites for retrograde sorting signals present in the cytoplasmic segments of integral membrane client cargo proteins (Cosson and Letourneur, 1994; Letourneur et al., 1994). Cargo is captured by this nascent vesicle coat during the budding process, and once budded from the cisterna, the COPI coat dissociates and the vesicle fuses with an earlier, maturing cisterna, thus maintaining Golgi cisterna composition (Popoff et al., 2011).
In addition to direct capture of cargo by the COPI coat, the peripheral membrane protein GOLPH3 associates with COPI on Golgi membranes, and these interactions are necessary for retention of many residents of the early Golgi cisternae (Eckert et al., 2014; Tu et al., 2012, 2008). Loss of GOLPH3 increases the rate at which these Golgi residents are degraded in the lysosome, resulting in decreased levels of these proteins in the Golgi, perturbations to protein glycosylation and complex sphingolipid homeostasis (Chang et al., 2013; Rizzo et al., 2021; Wood et al., 2012), and ultimately secretion (Dippold et al., 2009; Rahajeng et al., 2019; Xing et al., 2016). GOLPH3 contains an evolutionarily conserved pattern of arginine residues (two or three within the first 12 amino acids of the N termini) that confers binding to coatomer (COPI) and is required for retention of Golgi residents (Eckert et al., 2014; Tu et al., 2012). Based on these observations, GOLPH3 has been proposed to be a cargo-selective adaptor for the COPI vesicle coat via coincident recognition of PI4P, COPI and sequence motifs – LXX[RK] and [FL][LIV]XX[RK] – present in many residents of early Golgi compartments (such as the cis or medial cisternae) (Chang et al., 2013; Dippold et al., 2009; Eckert et al., 2014; Rizzo et al., 2021; Tu et al., 2012; Welch et al., 2021; Wood et al., 2009). Alternatively, GOLPH3 and COPI might prevent packaging of Golgi residents into anterograde intra-Golgi transport vesicles to maintain Golgi residence. GOLPH3 expression is increased in cells derived from a wide variety of human tumors, reportedly contributing to cellular transformation through enhanced mitogenic signaling caused by altered sphingolipid metabolism (Farber-Katz et al., 2014; Rizzo et al., 2021; Scott et al., 2009).
Ca 2+-dependent constitutive and regulated pathways
The mechanisms for sorting of constitutively secreted soluble proteins and those destined for regulated secretion remain poorly understood, mostly because of a lack of an identified sorting receptor. Nevertheless, Ca 2+ has emerged as a critical regulator in these processes (see poster).
In the constitutive secretion pathway, Ca 2+ is pumped into the trans/TGN lumen, resulting in Ca 2+-dependent protein aggregation that facilitates cargo sorting via SPCA1 (also known as ATP2C1), a trans/TGN-localized Ca 2+ ATPase (von Blume et al., 2011). Conversely, knockdown of SPCA1 reduces Ca 2+ levels in the TGN lumen and results in decreased secretion of soluble cargoes (Deng et al., 2018; von Blume et al., 2011). The Golgi-resident protein Cab45 (also known as SDF4) couples Ca 2+ concentration to secretory activity as it oligomerizes in the presence of Ca 2+ (Crevenna et al., 2016; von Blume et al., 2012) and binds to soluble secretory proteins (including lysozyme C and cartilage oligomeric matrix protein) (von Blume et al., 2012). Thus, sorting of constitutively secreted soluble cargo is regulated by Ca 2+, although further studies are necessary to understand how Cab45 oligomers drive sorting.
In the regulated secretory pathway, secretory cargo is retained within cytoplasmic vesicles, including dense-core vesicles (DCVs), which fuse with the plasma membrane upon stimulation (see poster). Regulated secretion is crucial for the physiology of specialized secretory cells, such as pancreatic β-cells, cells of the neuroendocrine system and the immune system. Members of the granin family of proteins, including chromogranin A (CHGA or CgA), chromogranin B (CHGB or CgB) and secretogranin II (SCG2 or SgII), are thought to play a role in DCV biogenesis via Ca 2+-dependent aggregation (Beuret et al., 2004; Colomer et al., 1996; Gerdes et al., 1989; Huh et al., 2003; Kim et al., 2001; Yoo, 1995). Biochemical studies of crude extracts derived from pituitary or adrenal glands and purified proteins have demonstrated that chromogranins can aggregate at acidic pH and high (millimolar) Ca 2+ concentrations (Colomer et al., 1996; Gerdes et al., 1989; Yoo, 1995). This has led to the ‘sorting for entry’ (also termed ‘sorting by aggregation’) hypothesis, whereby chromogranins aggregate within the TGN milieu and, in the process, co-aggregate other secretory granule-destined cargoes, resulting in active sorting (Tooze, 1998).
Trafficking in epithelial cells
The plasma membrane of polarized cells is itself polarized. In the case of epithelial cells, the apical plasma membrane faces the external environment, and the basolateral domain faces neighboring cells and the growth substratum, with intercellular tight junctions preventing diffusion of proteins and lipids between the two domains (see poster) (Cao et al., 2012; Stoops and Caplan, 2014). A longstanding goal regarding trafficking in polarized cells is to elucidate the mechanisms by which newly synthesized lipids and proteins are targeted to the correct plasma membrane domains and to understand the physiology of polarized cells in these terms.
At least four distinct Golgi-to-plasma membrane trafficking pathways have been described for polarized epithelial cells based on distinct sorting requirements for different cargo proteins (see poster) (Weisz and Fölsch, 2020). For basolateral trafficking, the most straightforward sorting mechanisms involve the recognition of tyrosine- or dileucine-based sorting motifs by AP-1, which mediates polarized sorting at the trans/TGN into CCVs (see above) (Caceres et al., 2019; Deborde et al., 2008; Gravotta et al., 2012). Some types of epithelial cells, including Madin–Darby canine kidney (MDCK)-derived cell lines that are commonly used for polarized cell sorting studies, express two forms of AP-1, AP-1A and AP-1B (Fölsch et al., 1999; Ohno et al., 1999), which differ solely in their distinct medium subunits (μ1A and μ1B). Curiously, AP-1A and AP-1B recognize tyrosine- or dileucine-based motifs (see above) with partly overlapping cargo-recognition preferences and so cooperate and compensate to accomplish basolateral sorting (Gravotta et al., 2012; Guo et al., 2013). Despite functional overlap, AP-1A localizes prominently to the trans/TGN and AP-1B to the recycling endosome (Fölsch, 2015). The role of AP-1 exclusively in basolateral trafficking has been challenged by recent reports showing that loss of AP-1 broadly effects both basolateral and apical protein targeting, highlighting the requirement for enhanced scrutiny when limited cargoes or cell types are employed (Caceres et al., 2019; Gravotta et al., 2019). One further heterotetrameric adaptor complex, AP-4, functions as a cargo adaptor for non-clathrin-coated vesicles at the trans/TGN, with a role in basolateral sorting that is apparently redundant to AP-1 (Simmen et al., 2002). Although little is known about the role of AP-4 in basolateral sorting at the trans/TGN, only AP-4 mediates sorting of the autophagy factor ATG9A from the trans/TGN to the nascent autophagosome (Davies et al., 2018; De Pace et al., 2018; Mattera et al., 2017). Additionally, several integral membrane proteins, notably the amyloid precursor (APP) and related proteins (likely APLP1 and APLP2), along with ATG9A, accumulate in the trans/TGN in AP-4-deficient cell lines (Burgos et al., 2010; Mattera et al., 2020), suggesting that they are AP-4 clients. Mutations in the genes encoding each of the AP-4 subunits cause a hereditary spastic paraplegia referred to as AP-4-deficiency syndrome, likely due to perturbed autophagy in neurons (Moreno-De-Luca et al., 2011; Tüysüz et al., 2014; Verkerk et al., 2009).
The apical plasma membrane of many types of epithelial cells is enriched in cholesterol and glycosphingolipids, such as galactosylceramide sulfate (also known as sulfatide) and Forssman glycolipid (Hansson et al., 1986; Koichi et al., 1974; Nichols et al., 1987), that are synthesized in the Golgi. Pioneering studies of lipid trafficking in MDCK cells employed synthetic fluorescent sphingolipid analogs that could be tracked and visualized in cells (van 't Hof and van Meer, 1990; van der Bijl et al., 1996; van Genderen and van Meer, 1995; van IJzendoorn and Hoekstra, 1998; van IJzendoorn et al., 1997), revealing that vesicles containing these fluorescent lipids are trafficked directly to the apical plasma membrane (van IJzendoorn et al., 2020).
In all cell types, sphingolipids reside exclusively in the exofacial and lumenal membrane leaflets of cellular membranes (Lorent et al., 2020; Verkleij et al., 1973), so it is not obvious how their identities and organization in the lumenal leaflet could be coupled to budding of secretory vesicles, which typically requires cytoplasmic factors. The ‘raft’ hypothesis postulates that phase condensation of cholesterol and sphingolipids within membrane bilayers forms a patch and/or domain of locally ordered lipids [the liquid-ordered (L o) domain], termed a ‘lipid raft’ (Simons and Van Meer, 1988). Proteins bearing a glycosylphosphatidylinositol anchor (GPI-APs) and some palmitoylated integral membrane proteins co-segregate with ‘raft’ lipids in model membranes (Friedrichson and Kurzchalia, 1998; Levental et al., 2010; Varma and Mayor, 1998), and structural features of the membrane-spanning segments of model and native proteins have been identified whose segregation correlates with lipid rafts, with efficient targeting to the plasma membrane (Lorent et al., 2017; Sharpe et al., 2010; Yurtsever and Lorent, 2020). In addition, glycosylation of proteins has been shown to contribute to their clustering within these domains and export from the Golgi within apically targeted transport vesicles (see below) (Lebreton et al., 2019). Though it is obvious that the physicochemical properties of Golgi membranes are harnessed for the concentration and export of secretory products, it is now appreciated that vesicle-sized sphingolipid–cholesterol condensates are not present in biological membranes due to their molecular complexity (Anderson and Jacobson, 2002; Veatch and Keller, 2005). Nevertheless, lipid-based protein sorting mechanisms represent an active area of debate (Levental et al., 2020).
Role of glycans in cargo sorting
Glycosylation of cargo proteins plays a role in sorting at the trans/TGN. Two distinct glycosylation patterns exist on proteins: N-linked and O-linked. N-linked glycosylation is initiated in the ER and involves the covalent attachment of glycosidic linkages to the amide side chain of asparagine residues (Vagin et al., 2009). In contrast, O-linked glycosylation takes place in the Golgi by linkage of glycosyl chains to serine or threonine residues (Potter et al., 2006).
One of the best-characterized TGN sorting mechanisms, the sorting of lysosomal hydrolases by mannose 6-P receptors, relies on glycosylation (see poster). The N-linked glycosyl chains on lysosomal hydrolases are sequentially modified by two Golgi-resident enzymes, N-acetylglucosamine 1-phosphotransferase and N-acetylglucosamine-1-phosphodiester α-N-acetylglucosaminidase, to generate the mannose 6-P moiety (Kornfeld and Mellman, 1989). Mannose 6-P-tagged lysosomal hydrolases are then recognized by the mannose 6-P receptor and sorted into CCVs (Brown and Farquhar, 1984; Friend and Farquhar, 1967; Geuze et al., 1985; Hoflack and Kornfeld, 1985a,b; Lemansky et al., 1987). These vesicles deliver cargo–mannose 6-P complexes to the late endosome and/or lysosome, where the acidic lumenal pH drives dissociation of the enzymes from mannose 6-P receptors, allowing for their recycling back to the trans/TGN (Griffiths et al., 1988). Deficiency of N-acetylglucosamine 1-phosphotransferase leads to the lysosomal storage disorder mucolipidosis type 2 (Kornfeld and Mellman, 1989), causes secretion of lysosomal hydrolases (Gelfman et al., 2007; Vogel et al., 2009) and results in the formation of lysosomes filled with undigested substrates (Otomo et al., 2011).
N- and O-linked glycosylation have also been shown to contribute to apical sorting of both membrane-anchored and soluble proteins in polarized cells (see poster). Treatment of cells with inhibitors of early steps in glycan addition, expression of glycosylation-deficient mutant proteins and studies of glycosylation gain-of-function mutations have revealed a strong correlation between N-glycosylation and apical sorting of secreted proteins (Hendriks et al., 2004; Scheiffele et al., 1995; Urban et al., 1987; Vagin et al., 2009). There is limited data to delineate the role of O-linked glycosylation in protein sorting (Lebreton et al., 2019; Potter et al., 2006), although it has been shown to promote efficient exit of cargoes from the Golgi of HeLa cells (Sun et al., 2020). How these glycosylation signals promote sorting and exit at the trans/TGN remains unclear. Lectins, including VIP36 (also known as LMAN2) and galectin-3, have been implicated as putative glycan-sorting receptors (Delacour et al., 2006; Hara-Kuge et al., 2002); however, it is not clear to what extent endogenous levels of these proteins can contribute to sorting (Fullekrug et al., 1999).
Regulation of cargo export
Intracellular signaling pathways control numerous aspects of trans/TGN functions, including protein sorting, transport carrier formation and lipid homeostasis (Farhan and Rabouille, 2011) (see poster).
GTPase-mediated TGN export
G proteins such as small GTPases act as molecular switches that facilitate the formation and transport of trans/TGN-derived carriers. Effectors generally interact with the GTP-bound form of the respective GTPase to induce a specific downstream signaling cascade that modulates cargo recognition, vesicular budding, membrane curvature, fission and transport of the vesicle to the cell surface on cytoskeletal tracks (Hutagalung and Novick, 2011).
The best-described GTPases regulating membrane trafficking are the Arf, Rab and Rho subfamily members of the Ras superfamily, which serve as membrane-associated platforms that recruit specific effectors to the trans/TGN, facilitating vesicle formation (Anitei and Hoflack, 2012; Bankaitis et al., 2012). These effectors include clathrin adaptor-associated proteins and F-actin, as well as microtubule-associated proteins that modulate membrane bending for budding and fission, and motors that transport the vesicles to their final destination (Anitei et al., 2010). Specifically, members of the Rab GTPase family are involved in TGN carrier budding, fission and movements of vesicles via cytoskeletal networks (both F-actin and microtubules). Rab6 connects myosin and kinesin motors to promote vesicular movement from the TGN to the cell periphery or focal adhesions (Eisler et al., 2018; Fourriere et al., 2019; Grigoriev et al., 2007, 2011; Hutagalung and Novick, 2011; Jasmin et al., 1992).
A role for heterotrimeric G proteins in trans/TGN carrier formation has also been described (Jamora et al., 1999; Pimplikar and Simons, 1994) but remains poorly understood. Heterotrimeric G proteins are associated with G-protein-coupled receptors (GPCRs), and it has been speculated that cargo exit from the Golgi is regulated by yet-to-be-identified GPCRs (Di Martino et al., 2019).
Protein kinase signaling and cargo export
Protein kinases and phosphatases have been associated with secretory carrier formation at the trans/TGN (Mayinger, 2011). AP-1 recruitment to the membrane is coupled with protein phosphatase 2A-mediated dephosphorylation of the µ1 subunit of AP-1, promoting clathrin assembly. Once on the membrane, the AP-1 µ1 subunit is phosphorylated, which induces a conformational change and increases the binding to sorting signals in the cytosolic tails of cargo proteins (see poster). This process is a well-established example of how cyclical phosphorylation and dephosphorylation of AP-1 regulate its function from membrane recruitment until release into the cytosol (Ghosh and Kornfeld, 2003).
Protein kinase D (PKD, of which there are three mammalian isoforms with a similar modular structure, known as PRKD1, PRKD2 and PRKD3) is a key regulator of TGN lipid homeostasis (von Blume and Hausser, 2019) and TGN carrier fission (Bard and Malhotra, 2006). The C1a domain of PKD binds to diacylglycerol (DAG) (Baron and Malhotra, 2002), whereas the C1b domain binds to Arf1 (Pusapati et al., 2010) to tightly associate PKD with the TGN membrane (see poster). Fission of some secretory carriers from the TGN requires catalytic activation of PKD by protein kinase C (PKC)-mediated phosphorylation (Añel and Malhotra, 2005). Although several models describing how PKD could promote carrier fission have been proposed, the mechanism is still unknown (Campelo and Malhotra, 2012). Moreover, relevant substrates that influence fission have not yet been identified (Wakana and Campelo, 2021). Involvement of PKA–cyclic AMP signaling in export from the TGN has also been described, but the relevant substrates are also unknown (Pimplikar and Simons, 1994).
Lipid-based signaling and cargo export
Rapid changes in particular lipids at the trans/TGN membranes play a significant role in cargo sorting, budding and fission (von Blume and Hausser, 2019). Lipid effectors are proteins that recognize these lipids and are recruited from the cytosol to the TGN membrane. Such lipids include phosphatidylserine (PS), phosphatidic acid (PA) and, in particular, PI4P. PI4P generated by phosphatidylinositol 4-kinase-IIIβ (encoded by PI4KB) recruits sorting factors such as AP-1, GGAs and GOLPH3 to TGN membranes (Bankaitis et al., 2012). It is also critical for determining TGN membrane composition by regulating non-vesicular lipid transfer of sphingolipids and cholesterol via ER–TGN contact sites by CERT (also known as CERT1) and OSBP, respectively (Hanada et al., 2003; Mesmin et al., 2013). CERT and OSBP activities are regulated by PKD phosphorylation, facilitating the crosstalk between lipid metabolism and protein signaling at the trans/TGN (Wang et al., 2003) (see poster).
Perspective
A great deal is known about the features of cargo proteins that confer their sorting and trafficking from the Golgi to other organelles, yet much remains to be learned about the mechanisms that produce Golgi-derived specific transport carriers (see Box 2 for outstanding key questions). A large body of work suggests that in contrast to canonical, coat protein-driven budding mechanisms that are induced by cytoplasmic coat proteins, secretory carrier formation may be directed partially by the cargo itself. Aggregation of lumenal cargo proteins is controlled in part by the surrounding milieu, including pH and Ca 2+ concentration, and can account for cargo sorting. Such aggregates could themselves provide a substrate around which membrane is wrapped to form a secretory carrier. In this scenario, association of cargo aggregates with the lumenal membrane leaflet could involve the lipid-binding activity of cargo proteins or, alternatively, integral membrane receptors that would capture cargo aggregates. Similarly, condensation of sphingolipids and cholesterol in the membrane, along with proteins with affinity for these condensates, likely explains sorting of membrane components such as ‘raft’ lipids and proteins, yet here too the mechanism(s) underlying carrier formation is unknown. Future insights into carrier formation may come from efforts to understand how the actin- and microtubule-based cytoskeletons influence Golgi membrane dynamics, which may initiate carrier budding and/or contribute to carrier fission.
Box 2. Open questions
How are the activities of Arf and Rab GTPase family members orchestrated to confer cargo sorting, carrier formation and transport?
In general, Arf GTPases control the recruitment to Golgi membranes of cytosolic factors that aid in cargo sorting and formation of a subset of Golgi-derived transport carriers. Rab and Rho family GTPases, in general, link vesicle formation and transport to the cytoskeleton (Mizuno-Yamasaki et al., 2012). How the activities of all these GTPases and crosstalk between their signaling pathways are coordinated is key for understanding the role of the Golgi in secretion.
What are the mechanisms of vesicle fission from the TGN?
The mechanisms that mediate fission of transport carriers from Golgi compartments are largely unknown. Prominent roles for the actin and microtubule-based cytoskeleton (Chakrabarti et al., 2021; Efimov et al., 2007), Arf1 (Beck et al., 2011), dynamin (Cao et al., 2005), PKD (Liljedahl et al., 2001) and CtBP3 (also known as BARS and CTBP1; Bonazzi et al., 2005) have been proposed to regulate and/or mediate fission, but the underlying mechanisms are yet to be elucidated.
How do carriers acquire the appropriate SNARE molecules to mediate vesicle fusion with the appropriate target membrane?
Unique combinations of SNARE molecules on the carrier and target membrane mediate fusion of the transport carrier with a particular target organelle; it is unknown how the appropriate SNAREs are loaded into transport carriers (Südhof and Rothman, 2009).
How do changes in lipid composition of the TGN influence cargo sorting and trafficking?
It is likely that transfer of sterol and sphingolipid precursors from the ER to the trans/TGN, as well as processing and/or synthesis of these lipids and others (for example, PI4P) within the TGN, is tightly coordinated with carrier formation, functioning not only to provide a reservoir of membrane for the nascent vesicle but also for spatiotemporal control of cargo sorting and membrane budding required for TGN export (Wakana and Campelo, 2021).
What are the mechanisms that underpin cargo sorting and budding of non-coated vesicles?
In the paradigm of coated vesicle biogenesis, the vesicle is formed by coat and accessory proteins that capture cargo and shape the membrane (Tan and Gleeson, 2019). It is largely unclear how any of these processes occur for non-coated carriers.
Acknowledgements
We are grateful to colleagues for discussions and critical reading of the manuscript. The authors would like to thank Edward Felder (University of Ulm, Germany) for the collaboration to produce the electron micrograph shown in the poster.
Footnotes
Funding
Our work in this area is supported by funds from the National Institute of General Medical Sciences of the National Institutes of Health under award numbers GM060221 and GM95766 (to C.G.B.), and GM134083 (to J.v.B.). Deposited in PMC for release after 12 months.
Cell science at a glance
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Competing interests
The authors declare no competing or financial interests.
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Supplementary information
Poster- jpeg file
Poster Panel 1. TGN-derived transport carriers- jpeg file
Poster Panel 2. Glycans confer protein sorting- jpeg file
Poster Panel 3. Protein and lipid sorting in epithelial cells- jpeg file
Poster Panel 4. Control of export from the Golgi by intracellular signaling- jpeg file
Poster Panel 5. Clathrin-coated vesicles in lysosomal hydrolase sorting- jpeg file
Poster Panel 6. Ca 2+-dependent sorting- jpeg file
Poster Panel 7. COPI- and GOLPH3-mediated retrograde transport of Golgi residents- jpeg file
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189685 | https://mathematica.stackexchange.com/questions/251067/maximization-of-piecewise-function | mathematical optimization - Maximization of piecewise function - Mathematica Stack Exchange
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Maximization of piecewise function
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I'm trying to maximize piecewise functions with parameters but haven't been able to do so. Here is a minimum example:
mathematica
f[x_, a_] = -(x - 10a)^2 + 50a;
w[x_, a_] = \[Piecewise] {
{f[x, a], 1/2 < a < 8/x && 0 < x < 20},
{-10, True}
};
I want to maximize w w over x x (a a is a parameter). Any ideas on how to solve this symbolically (or even numerically with a a in a grid)?
mathematical-optimization
piecewise
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asked Jul 16, 2021 at 0:30
AraratArarat
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Use the approach by @Bob Hanlon
mathematica
f[x_, a_] = -(x - 10a)^2 + 50a;
w[x_, a_] = Piecewise[{{f[x, a], 1/2 < a < 8/x && 0 < x < 20}}, -10];
max1[a_] = Maximize[{w[x, a], a > 0}, x]
max2[a_] = Maximize[{w[x, a], a <= 0}, x]
Plot3D[w[x, a], {a, -2, 2}, {x, -20, 20}, PlotPoints -> 80,
MaxRecursion -> 4, ViewPoint -> Front,
ViewProjection -> "Orthographic"]
Plot[{max1[a], max2[a]}, {a, -2, 2}, PlotPoints -> 100]
When a>0 a>0, ⎧⎩⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪−10 50 a−2(50 a 4−25 a 3−80 a 2+32)a 2−∞a≥Root[50#1 4−25#1 3−85#1 2+32&,2]∨0<a≤1 2 a=2 5√∨1 2<a<2 5√2 5√<a<Root[50#1 4−25#1 3−85#1 2+32&,2]True{−10 a≥Root[50#1 4−25#1 3−85#1 2+32&,2]∨0<a≤1 2 50 a a=2 5∨1 2<a<2 5−2(50 a 4−25 a 3−80 a 2+32)a 2 2 5<a<Root[50#1 4−25#1 3−85#1 2+32&,2]−∞True
When a≤0 a≤0
{−10−∞a≤0 True{−10 a≤0−∞True
Original
Maybe this?
mathematica
f[x_, a_] = -(x - 10a)^2 + 50a;
w[x_, a_] = Piecewise[{{f[x, a], 1/2 < a < 8/x && 0 < x < 20}}, -10];
max[a_] := NMaximize[w[x, a], x];
Plot3D[w[x, a], {a, -2, 2}, {x, -20, 20}, PlotPoints -> 200,
ViewPoint -> Front, ViewProjection -> "Orthographic"]
Plot[max[a], {a, -2, 2}, PlotPoints -> 100]
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edited Jul 16, 2021 at 4:01
answered Jul 16, 2021 at 1:35
cvgmtcvgmt
90.7k 6 6 gold badges 112 112 silver badges 193 193 bronze badges
3
1 max[a_] := MaxValue[{w[x, a], a > 0, x > 0}, x, Reals] gives a smoother and more accurate plot. ({wmax, arg} = Maximize[{w[x, a], x > 0, a > 0}, {a, x}, Reals]) // N // Quiet evaluates to {46.4011, {a -> 0.964128, x -> 8.29765}}Bob Hanlon –Bob Hanlon 2021-07-16 02:05:14 +00:00 Commented Jul 16, 2021 at 2:05
@BobHanlon Thanks, updated.cvgmt –cvgmt 2021-07-16 02:31:09 +00:00 Commented Jul 16, 2021 at 2:31
Beautiful approach! In going beyond the minimum example (more than two pieces functions), I wonder if there are any heuristics on how to partition the parameter set. Are there more or less general guidelines for choosing the number of intervals and for selecting the cutoff points?Ararat –Ararat 2021-07-16 11:17:49 +00:00 Commented Jul 16, 2021 at 11:17
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Fractions & Decimals | Freebies | Grades 3-5 | Number Sense | Operations
Reasoning about Decimal Operations
The Common Core State Standards (CCSS) now have 5th graders computing with decimals. CCSS 5.NBT.7 reads:
Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
Well, that’s certainly a mouthful! This post is going to focus on place value strategies, or what I call number sense.
This post contains affiliate links, which simply means that when you use my link and purchase a product, I receive a small commission. There is no additional cost to you, and I only link to books and products that I personally use and recommend.
First, computing with decimals is essentially the same as computing with whole numbers. Don’t believe me? Multiply 12.1 x 34, 121 x 34, and 121 x .34 What do you get? All three products contain exactly the same digits-4114. The only difference is place value, or in other words, the placement of the decimal point. We traditionally teach students to count the places after the decimal point in the factors and move that many places from the right of the product and insert the decimal point. That certainly works, but it’s just a “trick”, and tricks can lead to unreasonable answers.
John Van de Walle suggests that instruction on computation with decimals must start with estimating. If students can accurately estimate products and quotients, they are more likely to correctly place the decimal point. Look at the card shown below. The digits in the product of the two numbers are shown below the multiplication problem. Without multiplying, decide where the decimal point should go.
Did you place the decimal after the 28? Why? How would you justify your answer?
With this next problem, you are placing the decimal points in the factors. It’s trickier because there could be more than one right answer (don’t you just love that!).
What solution or solutions did you come up with? 18 x 14.5 would work, but so would 1.8 x 145. Could you explain your reasoning on both those answers?
Not surprisingly, the same process works with division. Look at the card below. Where would you place the decimal in the quotient? Why?
So, I hope that helps some. Remember, you always want your kiddos to understand the math they’re doing. I think this little activity is very powerful and really encourages deep understanding.
Click here to download a set of cards like the ones above that you can use in your classroom. And, please, if you teach math, don’t start the year without a copy of the Van de Walle book for your grade level.
Post Tags: #Division#Multiplication
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18 Comments
Diane Hubaczsays: July 6, 2012 at 6:02 pm I am so addicted to your blog! I especially love that you are from Texas ( I teach in The Woodlands!). Check out my post today about Math Analogies!
I have nominated your blog for the Leibster Award! Come by my blog to grab it and pass it on!
Diane
Teaching with Moxie Reply
1. Donna Bouchersays: July 6, 2012 at 8:40 pm The Woodlands? Well, howdy neighbor. Ha ha. I’m following your blog now, too! Reply
Vivsays: July 6, 2012 at 6:29 pm Thank you so much for the great cards! I love Van de Walle’s work. Reply
Donna Bouchersays: July 6, 2012 at 8:41 pm Van de Walle is the man! Reply
Karen Greenbergsays: July 6, 2012 at 7:52 pm This is great. Thank you! I, too, love anything where the students have to explain why they are doing something. I can’t wait to use these in my classroom. Reply
Donna Bouchersays: July 6, 2012 at 8:41 pm You’re very welcome, Karen. Thanks for stopping by! Reply
Fontenot's Firebreatherssays: July 20, 2012 at 1:48 pm I just found this blog by a link in Pintrest! I love it! I am always working on growing my math skills. I move to 4th grade from 5th this next school year! I am always looking for new ideas! Thanks for the great site! Reply
Donna Bouchersays: July 20, 2012 at 2:03 pm Gotta love Pinterest! Good luck in your new assignment. Reply
Anonymoussays: January 16, 2013 at 11:00 am Just found this via Pinterest – I’m a UK teacher and I think this will be a great extension task for some of my Year 4s. Thanks ever so! Reply
Donna Bouchersays: January 17, 2013 at 1:31 am Wow, kinda cool! Love international sharing! Reply
Anonymoussays: November 16, 2013 at 9:37 pm Thank you. I really like your ideas and it is refreshing to know others math teachers out there truly get the math. Van De Walle is a valuable resource! Reply
Nancysays: November 22, 2015 at 5:50 pm When I first read about this in Van de Walle’s book, I was so excited! It’s so much easier and makes more sense than counting and moving the decimal. But once you move to both numbers less than 1, it’s a little more difficult. Any suggestions on how this applies to decimals that are in the hundredths? Like 0.03 x 0.12 Reply
Donna Bouchersays: November 22, 2015 at 7:12 pm Nancy, check out this post on multiplying decimals! Reply
Nancysays: November 24, 2015 at 8:20 am Thanks – I think using those models for decimals is great. Reply
Tiffanysays: December 20, 2016 at 1:59 pm I hate this math. I can’t help my 5th grader because you don’t make this easy for parents to explain to kids. I’m really good at math, and I now have to google things in order to help him with his homework. This is horrible Reply
Donna Bouchersays: December 20, 2016 at 8:59 pm I agree that it is very different from the way we learned math. I can see why you find it frustrating. Reply
Krystal L. Smithsays: January 9, 2017 at 10:02 pm Such a great post! I remember reading Van de Walle’s book in graduate school, and being upset at how my instructor expected us to learn and then teach math. I am glad I have a growth mindset mentality now because I am much more open to what I have read over a decade ago, and how and why I need to teach math differently than the way I was taught. Reply
Sylvia Parkersays: November 26, 2017 at 8:35 pm Thank you! I loved how you used reasoning to show why this works. While knowing a trick can be helpful, in the long term, it does not help with mathematical understanding. I’m off to rethink my lessons; in a good way. Reply
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189687 | https://www.cv.nrao.edu/~sransom/web/Ch6.html | Essential Radio Astronomy5 Synchrotron Radiation7 Spectral Lines
Chapter 6 Pulsars
6.1 Pulsar Properties
Pulsars are magnetized neutron stars that appear to emit periodic short pulses of radio radiation with periods between 1.4 ms and 8.5 s. The radical proposal that neutron stars even exist was made with trepidation by Baade & Zwicky in 1934 : “With all reserve we advance the view that a supernova represents the transition of an ordinary star into a new form of star, the neutron star, which would be the endpoint of stellar evolution. Such a star may possess a very small radius and an extremely high density. As neutrons can be packed much more closely than ordinary nuclei and electrons, the ‘gravitational packing’ energy in a cold neutron star may become very large, and, under certain circumstances, may far exceed the ordinary nuclear packing fractions.”
The name pulsar blends “pulse” and “star,” but pulsars are not pulsating stars. Like lighthouses, they continuously emit rotating beams of radiation and appear to flash each time the beam sweeps across the observer’s line of sight. The pulse periods are quite stable because they equal the rotation periods of massive neutron stars. Even though their radio emission mechanism is not well understood, pulsars have become uniquely valuable astrophysical tools:
1.
Neutron stars are physics laboratories sampling extreme conditions—deep gravitational potentials , densities exceeding those in atomic nuclei, and magnetic field strengths as high as or even gauss—not reproducible on Earth.
2. 2.
Pulse periods can be timed with fractional errors as small as . Accurate pulsar timing permits exquisitely sensitive measurements of quantities such as the power of gravitational radiation emitted by a pulsar in a binary system, neutron-star masses, general relativistic effects in strong gravitational fields, orbital perturbations from binary companions as light as planets, accurate pulsar positions and proper motions, and potentially the distortions of interstellar space produced by long-wavelength gravitational radiation from the mergers of supermassive black holes throughout the universe.
Lorimer and Kramer and Lyne and Graham-Smith have written excellent reference books about pulsars and their astrophysical applications.
6.1.1 Discovery
Pulsars were discovered serendipitously in 1967 on chart recordings (Figure 6.1) obtained during a low-frequency ( MHz) search for compact extragalactic radio sources that scintillate in the interplanetary plasma, just as stars twinkle in the Earth’s atmosphere.
This history of this important discovery is a warning against overprocessing data before looking at them, ignoring unexpected signals, and failing to explore the observational “parameter space” covered by the data—here the relevant parameter being time. The strong pulsar PSR B0329+54 was clearly visible in 1954 survey data from the Jodrell Bank 250-foot radio telescope , but nobody paid any attention to it at the time. The X-ray pulsar in the Crab Nebula (Figure 8.10) was present in data taken several months before the discovery of radio pulsars, but only after the radio pulsar in the Crab Nebula was announced were the X-ray pulses extracted . As radio instrumentation and data-processing software become more sophisticated, more data are “cleaned up” automatically before they reach the astronomer. Matched filtering that brings out the expected signal usually suppresses the unexpected. Thus, clipping circuits or software remove the strong impulses that are usually caused by terrestrial interference, and integrators smooth out fluctuations shorter than the integration time. Most pulses seen by radio astronomers are just artificial interference from radar, electric cattle fences, etc., and short pulses from sources at interstellar distances imply unexpectedly high brightness temperatures , which is much higher than the K upper limit for incoherent electron-synchrotron radiation imposed by synchrotron self-Compton cooling (Section 5.5.3).
Cambridge University graduate student Jocelyn Bell recognized that pulsars are astronomical sources where others had failed because she noticed that some “scruffy” pulses in her chart-recorder data (Figure 6.1) didn’t look like other forms of interference and they reappeared exactly once per sidereal day, indicating an origin outside the Solar System. Fortunately, she and her supervisor, Antony Hewish, “decided initially not to computerize the output because until we were familiar with the behavior of our telescope and receivers we thought it better to inspect the data visually, and because a human can recognize signals of different character whereas it is difficult to program a computer to do so.” Read for the full discovery story in her own words.
6.1.2 Neutron Star Masses and Densities
The sources of the pulses were originally unknown, and even intelligent transmissions by “LGM” (Little Green Men) were seriously suggested as explanations for pulsars. Their short periods imply very compact sources such as white dwarf stars, black holes, and neutron stars; their stable periods rule out black holes. Astronomers were familiar with slowly varying or pulsating emission from stars, but the natural period of a radially pulsating star depends on its mean density and is typically days, not seconds. There is a comparable lower limit to the rotation period of a gravitationally bound star, set by the requirement that the centrifugal acceleration at its equator not exceed the gravitational acceleration. If a nearly spherical star of mass and radius rotates with angular velocity ,
| | |
--- |
| | (6.1) |
| | |
--- |
| | (6.2) |
In terms of the mean density
| | |
--- |
| | (6.3) |
| | (6.4) |
| | |
--- |
| | (6.5) |
Equation 6.5 gives a conservative lower limit to the mean density because a rapidly spinning star is oblate, which increases the centrifugal acceleration and decreases the gravitational acceleration at its equator.
The first pulsar discovered has a period s, so its mean density is at least
| |
| |
This limit is just consistent with the known densities of white dwarf stars. But soon the faster ( s) pulsar in the Crab Nebula was discovered, and its period implies a density much higher than any stable white-dwarf star supported by electron-degeneracy pressure. Also, the Crab Nebula (Figure 8.10) is the remnant of a supernova recorded by Chinese astronomers as a “guest star” in 1054 AD, so the discovery of this pulsar confirmed the suggestion by Baade and Zwicky that neutron stars are the compact remnants of supernovae. The fastest known pulsar has s implying g cm, the density of atomic nuclei.
A star whose mass is greater than the Chandrasekhar mass
| | |
--- |
| | (6.6) |
cannot be supported by electron degeneracy pressure and will collapse to become a neutron star. Equation 6.2 implies the maximum radius
| | |
--- |
| | (6.7) |
of a s pulsar with mass is
| | |
--- |
| | |
| | (6.8) |
These numbers motivate the definition of the canonical neutron star as being a uniform density sphere with mass , radius km, and moment of inertia . “Canonical” is perhaps too strong a term for what is really no more than a convention for the typical properties of neutron stars; individual neutron stars can have different masses and radii. The extreme density and pressure turn most of the star into a neutron superfluid that is a superconductor at temperatures up to K. The masses of individual pulsars have been measured with varying degrees of accuracy, and many are close to the canonical . The highest accurately measured pulsar masses are , and they rule out all currently proposed hyperon or boson condensate equations of state and “free” quarks . Any neutron star of significantly higher mass ( in standard models) must collapse and become a black hole.
6.1.3 Magnetic Fields
The Sun and many other stars are known to possess approximately dipolar magnetic fields. Stellar interiors are fully ionized and hence good electrical conductors. Charged particles are constrained to move along magnetic field lines, and magnetic field lines are tied to the charged particles. When a star collapses from a radius km to km, its cross-sectional area is divided by , its magnetic flux (where is the unit vector normal to each infinitesimal surface area ) is conserved, and the magnetic field strength is multiplied by . An initial magnetic field strength G becomes G after collapse, so young neutron stars should have very strong dipolar fields. The best models of the core-collapse process show that a dynamo effect can generate even stronger magnetic fields. Such dynamos may be able to produce the – G fields observed in magnetars, which are neutron stars having such strong magnetic fields that their radiation is powered by magnetic field decay. Conservation of angular momentum during collapse increases the rotation rate by about the same factor, , yielding initial rotation periods in the millisecond range. Thus young neutron stars should contain rapidly rotating magnetic dipoles (Figure 6.2).
6.1.4 Magnetic Dipole Radiation
If a rotating magnetic dipole is inclined by some inclination angle from the rotation axis, it emits electromagnetic radiation at the rotation frequency. Rewriting the Larmor formula (Equation 2.143) in terms of power radiated by a rotating electric dipole gives
| | |
--- |
| | (6.9) |
where is the electric dipole moment and is its component perpendicular to the rotation axis. J. J. Thomson’s derivation of the Larmor formula in terms of electric field lines (Section 2.7) is also valid for magnetic field lines. The Gaussian CGS units for magnetic and electric field are the same, so the power of magnetic dipole radiation is
| | |
--- |
| | (6.10) |
where is the perpendicular component of the magnetic dipole moment. For a uniformly magnetized sphere with radius and surface magnetic field strength , the magnitude of the magnetic dipole moment is
| | |
--- |
| | (6.11) |
If the inclined magnetic dipole rotates with angular velocity , then
| | |
--- |
| | (6.12) |
where is the pulsar period. This electromagnetic radiation will appear at the very low radio frequency kHz, so low that it cannot propagate through the surrounding ionized nebula or ISM. Magnetic dipole radiation extracts rotational kinetic energy from the neutron star and causes the pulsar period to increase with time. The absorbed radiation deposits energy in the surrounding nebula, the Crab Nebula (Figure 8.10) being a prime example.
6.1.5 Spin-Down Luminosity
The rotational kinetic energy of a spinning object is related to its moment of inertia by
| | |
--- |
| | (6.13) |
The moment of inertia of a small mass element about any rotation axis is its mass multiplied by the square of its radial distance from the rotation axis. The moment of inertia of a sphere with radius , mass , and uniform density spinning about its -axis is obtained by summing over its mass elements:
| | |
--- |
| | (6.14) |
where is the distance from the rotation axis and is the height in cylindrical coordinates centered on the sphere. Then
| | |
--- |
| | (6.15) |
The moment of inertia of a canonical neutron star is
| | |
--- |
| | (6.16) |
The rotational kinetic energy of a canonical neutron star with the rotation period s of the Crab pulsar is
| |
| |
As magnetic dipole radiation extracts rotational energy, it slowly increases the period of a pulsar:
| | |
--- |
| | (6.17) |
Note that the period derivative is a dimensionless (seconds per second) pure number. Combining the observed period and period derivative yields an estimate of the rate at which the rotational energy is changing. The quantity
| | |
--- |
| | (6.18) |
is called the spin-down luminosity. It is not a measured luminosity; it is the measured loss rate of rotational energy, which is presumed to equal the luminosity of magnetic dipole radiation. The spin-down luminosity is usually expressed in terms of the pulse period :
| | |
--- |
| | (6.19) |
and Equation 6.18 becomes
| | |
--- |
| | (6.20) |
The Crab pulsar has s and . If (Equation 6.16), its spin-down luminosity is
| |
| |
If , the luminosity of the low-frequency () magnetic dipole radiation from the Crab pulsar is comparable with the entire radio output of our Galaxy! It even exceeds the Eddington luminosity limit (Section 5.4.2) of the neutron star, which is possible because the energy source is not accretion. It greatly exceeds the average radio pulse luminosity of the Crab pulsar, . The long wavelength ( m) magnetic-dipole radiation is absorbed by and heats up the surrounding Crab Nebula (Figure 8.10), making it the “megawave oven” counterpart of a kitchen microwave oven. The observed bolometric luminosity of the Crab Nebula is comparable with the spin-down luminosity, supporting the model that rotational kinetic energy is converted to magnetic dipole radiation that is absorbed by the surrounding ionized nebula and later reradiated at radio through X-ray wavelengths.
6.1.6 Minimum Magnetic Field Strength
If , Equations 6.12 and 6.20 can be combined to yield a lower limit to the magnetic field strength at the neutron star surface, where is the unknown inclination angle between the rotation and magnetic axes:
| | |
--- |
| | (6.21) |
| | (6.22) |
| | (6.23) |
| | (6.24) |
Inserting the constants for the canonical pulsar in CGS units yields for the first factor
| | |
--- |
| | (6.25) |
so the minimum magnetic field strength at the surface of a canonical pulsar is
| | |
--- |
| | (6.26) |
It is sometimes called the characteristic magnetic field of a pulsar.
The minimum magnetic field strength of the Crab pulsar ( s, ) is
| |
| |
This is an amazingly strong magnetic field. Its energy density is
| | |
--- |
| | (6.27) |
Just of this magnetic field contains over of energy, the annual output of a large nuclear power station.
6.1.7 Characteristic Age
If the spin-down luminosity equals the magnetic dipole radiation luminosity and doesn’t change significantly with time, a pulsar’s age can be estimated from on the further assumption that the pulsar’s initial period was much shorter than its current period. Solving Equation 6.23 for shows that
| | |
--- |
| | (6.28) |
also doesn’t change with time. Rewriting the identity as and integrating over the pulsar’s age gives
| | |
--- |
| | (6.29) |
because is constant. Integrating Equation 6.29 gives
| | |
--- |
| | (6.30) |
In the limit , the characteristic age of a pulsar defined by
| | |
--- |
| | (6.31) |
should be close to the actual age of the pulsar. The characteristic age depends only on the observables and ; it does not depend on the unknown radius , moment of inertia , or perpendicular magnetic field . However, a newly formed neutron star with small may be quite oblate and will initially be slowed down by emitting quadrupole gravitational radiation. This can cause the characteristic age to be somewhat larger than the true age for young pulsars.
For example, the characteristic age of the Crab pulsar ( s, ) is
| |
| |
It is slightly larger than the actual age of the Crab pulsar, which is known to be just under because the Crab supernova was observed in 1054 AD.
6.1.8 Braking Index
If magnetic dipole radiation is solely responsible for pulsar spin down, then and Equations 6.12 and 6.18 together imply
| | |
--- |
| | (6.32) |
The pulsar braking index is defined by
| | |
--- |
| | (6.33) |
where is the constant of proportionality. The braking index is completely determined by the observables , , and , so comparing its observed value with the expected provides a useful check on pulsar spin-down models. The time derivative of Equation 6.33 is
| | |
--- |
| | (6.34) |
so
| | |
--- |
| | (6.35) |
Converting from angular velocities to periods with
| |
| |
| |
| yields |
| | (6.36) |
| | |
--- |
| | (6.37) |
the braking index in terms of the observables , , and .
Braking indices in the range have been observed and used to investigate alternative spin-down mechanisms and to make more sophisticated estimates of pulsar ages and initial spin periods .
6.1.9 The Lives of Pulsars
Pulsars are born in supernovae and appear in the upper left corner of the pulsar diagram (Figure 6.3). If is conserved and they age as described above, they gradually move to the right and down, along lines of constant and crossing lines of constant characteristic age. Pulsars with characteristic ages yr are often found in or near recognizable supernova remnants (SNRs). Older pulsars are not, either because their SNRs have faded to invisibility or because the supernova explosions expelled the pulsars with enough speed that they have since escaped from their parent SNRs. The bulk of the pulsar population is older than yr but much younger than the Galaxy ( yr). The observed distribution of pulsars in the diagram indicates that something changes as pulsars age. One controversial possibility is that the magnetic fields of old pulsars must decay on timescales yr, causing old pulsars to move almost straight down in the diagram until either their magnetic field is too weak or their spin rate is too slow to produce radio emission via the normal, and as yet still highly uncertain, emission mechanism. Rotating Radio Transients (RRATs) are pulsars that emit so sporadically that they are more easily detected in searches for single pulses rather than for periodic pulse trains. RRATs with measurable periods usually have (Figure 6.3). Some RRATs may be old pulsars on the verge of becoming radio quiet.
Almost all short period ( s) pulsars having fairly weak magnetic field strengths ( G) are in binary systems, as evidenced by periodic orbital variations in their observed pulse periods (Figure 6.4). These recycled pulsars have been spun up by accreting mass and angular momentum from their stellar companions, to the point that they emit radio pulses despite their relatively low magnetic field strengths G. (Apparently, currents in the accreting plasma “bury” the magnetic field of the neutron star itself.) The magnetic fields of neutron stars funnel the ionized accreting material onto the magnetic polar caps, which become so hot that they, as well as the hot accretion disk, emit X-rays. We observe these systems as the Low Mass X-ray Binaries (LMXBs). As the neutron stars rotate, their inclined magnetic polar caps can appear and disappear from view, causing periodic fluctuations in X-ray flux, and making some of these systems detectable as X-ray pulsars.
|
| |
Figure 6.4: Examples of Doppler variations observed in binary systems containing pulsars. Top: The Doppler variations of the globular cluster MSP J17482446N in Terzan 5. This pulsar is in a nearly circular orbit (eccentricity ) with a companion of minimum mass 0.47 M. The difference between the semimajor and semiminor axes for this orbit is only 514 cm! The thick lines show the periods as measured during GBT observations. Bottom: Similar Doppler variations from the highly eccentric binary MSP J05144002A in the globular cluster NGC 1851. This pulsar has one of the most eccentric orbits known () and a massive white-dwarf or neutron-star companion.
Millisecond pulsars (MSPs) with low mass (–) white-dwarf companions typically have orbits with small eccentricities owing to strong tidal dissipation during the accretion phase which spins up the pulsars. The eccentricity of an elliptical orbit is defined as the ratio of the separation of the foci to the length of the major axis. It ranges between for a circular orbit and for a parabolic orbit. Pulsars with extremely eccentric orbits usually have neutron-star companions, indicating that these companions exploded as asymmetric supernovae and nearly disrupted the binary system. Stellar interactions in globular clusters cause a much higher fraction of recycled pulsars per unit mass than in the Galactic disk. These interactions can result in very strange systems such as pulsar–main-sequence-star binaries and MSPs in highly eccentric orbits. In both cases, the original low-mass companion star that recycled the pulsar was ejected in an interaction and replaced by another star.
About 15% of millisecond pulsars are isolated. They were probably recycled via the standard scenario in binary systems, but the energetic MSPs eventually ablated their companions away. Recently, many new “black widow” and “redback” systems have been detected which seem to be doing exactly this. They exhibit eclipses of their radio MSP emission, likely owing to free–free absorption by the ionized gas in the systems being blown off the companion stars.
6.1.10 Emission Mechanisms
The radio pulses originate in the pulsar magnetosphere. Because the neutron star is a spinning magnetic dipole, it acts as a unipolar generator. The total Lorentz force acting on a charged particle is
| | |
--- |
| | (6.38) |
Charges in the magnetic equatorial region redistribute themselves by moving along closed magnetic field lines until they build up an electrostatic field large enough to cancel the magnetic force and give . The induced voltage is about in MKS units. However, the corotating field lines emerging from the polar caps cross the light cylinder (Figure 6.2), an imaginary cylinder centered on the pulsar and aligned with the rotation axis at whose radius the corotating speed equals the speed of light, so these field lines cannot close. Electrons in the polar cap are magnetically accelerated to very high energies along the open but curved field lines, where the acceleration resulting from the curvature causes them to emit curvature radiation that is strongly polarized in the plane of curvature. As the radio beam sweeps across the line of sight, the plane of polarization is observed to rotate by up to 180 degrees, a purely geometrical effect. Normal “slow” pulsars usually have quite large amounts of typically linear polarization. There are several relativistic effects in the rapidly rotating magnetospheres of millisecond pulsars that complicate this emission-geometry-based polarization, yet millisecond pulsars are typically highly polarized as well. High-energy photons produced by curvature radiation interact with the magnetic field and lower-energy photons to produce electron–positron pairs that radiate additional high-energy photons. The final results of this cascade process are bunches of charged particles that emit at radio wavelengths. Pulsars “die” in the lower right corner of the diagram (Figure 6.3) when they have sufficiently low and high that the curvature radiation near the polar surface is no longer capable of generating particle cascades.
The extremely high brightness temperatures of pulsars are explained by coherent radiation. The electrons do not radiate as independent charges ; instead bunches of electrons in volumes whose dimensions are less than a wavelength emit in phase as charges . Larmor’s formula indicates that the power radiated by a charge is proportional to , so the radiation intensity can be times brighter than incoherent radiation from the same total number of electrons. Because the coherent volume is smaller at shorter wavelengths, most pulsars have extremely steep radio spectra. Typical pulsar spectral indices (defined using the positive convention, see Equation 4.55) are (i.e., ), although some can be much steeper (), and a handful are almost flat ().
6.2 Pulsars and the Interstellar Medium
With their sharp and short-duration pulse profiles allowing continuous “on–off” differential measurements, small sizes, and high brightness temperatures, pulsars are unique probes of the interstellar medium (ISM). This section closely follows the discussion in Lorimer and Kramer , and Equations 6.39 through 6.42 are derived in Appendix D.
The electrons in the ISM make up a cold plasma whose refractive index is
| | |
--- |
| | (6.39) |
where is the frequency of the radio waves, is the plasma frequency
| | |
--- |
| | (6.40) |
and is the electron number density. For a typical ISM value , kHz. If then is imaginary and radio waves cannot propagate through the plasma.
For propagating radio waves, and the group velocity
| | |
--- |
| | (6.41) |
of pulses is less than the vacuum speed of light. For most radio observations , so
| | |
--- |
| | (6.42) |
A broadband pulse moves through a plasma more slowly at lower frequencies than at higher frequencies. If the distance to the source is , the dispersion delay at frequency is
| | | |
---
| | | (6.43) |
| | (6.44) |
In astronomically convenient units the dispersion delay is
| | |
--- |
| | (6.45) |
| where |
| | (6.46) |
in units of pc cm is called the dispersion measure and represents the integrated column density of electrons between the observer and the pulsar.
Because pulsar observations almost always cover a wide bandwidth, uncorrected differential delays across the band cause dispersive smearing of the pulsed signal when integrated across the band. If uncorrected, the delays would smear out the integrated pulse in time and make most pulsars undetectable (see Figure 6.5). For pulsar searches, the DM is unknown a priori and is a search parameter much like the pulsar spin frequency. This extra search dimension is one of the primary reasons that pulsar searches are computationally intensive. For high-precision timing observations of pulsars with known DMs, if Nyquist-sampled voltage data (often called “baseband” data) are available, the dispersion may be completely removed from the data by a technique known as coherent dedispersion. The dispersed data are de-convolved using the complex conjugate of the complex transfer function of the ISM that caused the dispersion in the first place.
Dispersion measures can be used to provide distance estimates to pulsars. Crude distances can be calculated for pulsars near the Galactic plane by assuming that . However, several sophisticated models of the Galactic electron-density distribution now exist (e.g., NE2001; Cordes and Lazio ) that provide much better ( or less) distance estimates.
The ionized ISM affects pulsar signals in several other ways besides dispersion. Inhomogeneities in the turbulent ISM result in both diffractive and refractive scintillation, or time- and frequency-dependent flux-density variations of the pulsar signal much like the “twinkling” of starlight by Earth’s turbulent atmosphere. Diffractive scintillations occur over typical timescales of minutes to hours and radio bandwidths of kHz to hundreds of MHz, and they can cause more than order-of-magnitude flux-density fluctuations. Refractive scintillations tend to be less than a factor of 2 in amplitude and occur on timescales of weeks.
A phenomenon related to scintillation is pulse broadening caused by scattering of radio waves. ISM inhomogeneities cause multipath propagation of a pulsar signal, whereby some rays travel longer physical distances because they do not follow straight lines to the observer. Such rays are delayed in time relative to those traveling more direct paths, and so cause a strongly frequency-dependent (typically ) exponential-like scattering tail of the pulse (see Figure 6.6). This scatter broadening can greatly decrease both the observed pulsed flux density from a pulsar and its timing precision.
Finally, pulsars have broadband continuum spectra, so if there are gas clouds along our line of sight, pulsars can be used to probe the ISM via absorption by spectral lines of Hi or molecules. Such absorption spectra can be used to estimate pulsar distances.
6.3 Pulsar Timing
Pulsars are intrinsically interesting and exotic objects, but much of the best science based on pulsar observations has come from their use as tools via pulsar timing. Pulsar timing is the regular monitoring of the rotation of the neutron star by tracking (nearly exactly) the arrival times of the radio pulses. The key point to remember is that pulsar timing unambiguously accounts for every single rotation of the neutron star over long periods (years to decades) of time. This unambiguous and very precise tracking of rotation phase allows pulsar astronomers to probe the interior physics of neutron stars, make extremely accurate astrometric measurements, uniquely test gravitational theories in the strong-field regime, and possibly within the next few years, directly detect gravitational waves (GWs) (GWs are propagating distortions of space–time) from supermassive black hole binaries.
For pulsar timing, astronomers “fold” (average) the data from many pulses modulo the instantaneous pulse period . The instantaneous pulse frequency is , and the instantaneous pulse phase is defined by . Pulse phase is usually measured in turns of radians, so .
Averaging over many pulses yields an average pulse profile. Although the shapes of individual pulses vary considerably because pulsar emission is intrinsically a noise process, the shape of the average profile is quite stable.
For timing, the average pulse profile is correlated with a template or model profile so that its phase offset can be determined. When multiplied by the instantaneous pulse period, that phase yields a time offset that can be added to a high-precision reference point on the profile (for example, the left edge of the profile based on the recorded time of the first sample of the observation) to create the time of arrival (TOA).
The precision with which a TOA can be determined is approximately equal to the duration of a sharp pulse feature (e.g., the leading edge) divided by the signal-to-noise ratio of the average profile. It is usually expressed in terms of the width of the pulse features in units of the pulse period , and the signal-to-noise ratio such that . Strong, fast pulsars with narrow pulse profiles provide the most accurate arrival times.
In the nearly inertial frame of the Solar System barycenter (center of mass), the rotation period of a pulsar is nearly constant, so the time-dependent phase of a pulsar can be approximated by the Taylor expansion
| | |
--- |
| | (6.47) |
where and are arbitrary reference phases and times for each pulsar. The critical constraint for pulsar timing is that the observed rotational phase difference between each of the TOAs must contain an integer number of rotations. Each TOA corresponds to a different time , so the correct fitting parameters (e.g., and ) must result in a phase change between each pair of TOAs and that is an integer number of turns, or turns. Because all measurements are made with regard to the integrated pulse phase rather than the instantaneous pulse period, the precision with which astronomers can make long-term timing measurements can be quite extraordinary.
With what precision can timing determine the spin frequency of a pulsar? Because when is measured in turns, the precision is based on how precisely a change in phase can be measured over some time interval . Typically, is the length of time (up to several tens of years for many pulsars now) over which a pulsar’s phase has been tracked through regular monitoring. is determined principally by the individual TOA precisions, although for some types of measurements a statistical component is important as well because precision improves as the number of measurements if the random errors are larger than the systematic errors. For example, the original millisecond pulsar B193721 has pulse period s and the TOA precision is s, which corresponds to a phase error of turns. This pulsar has been timed for years, so
| | |
--- |
| | (6.48) |
That pulsar’s spin frequency is 642 Hz, so the absolute frequency error implies that the spin rate is known to 15 significant figures!
Many corrections have to be applied to the observed TOAs before can be expressed as a Taylor series (Equation 6.47). The arrival of a pulse at an observatory on Earth at topocentric (topocentric means measured from a fixed point on the Earth’s surface) time can be corrected to the time in the nearly inertial Solar System barycentric frame, which we assume to be nearly the same as the time in the frame comoving with the pulsar. Note that the measured pulse rates will differ from the actual pulse rates in the pulsar frame by the Doppler factor resulting from the unknown line-of-sight pulsar velocity as well as unknown relativistic corrections from within the pulsar system itself.
The principal terms in the timing equation are
| | |
--- |
| | (6.49) |
As before, is a reference epoch, represents a clock correction that accounts for differences between the observatory clocks and terrestrial time standards, and is the frequency-dependent dispersion delay caused by the ISM. The other terms are delays from within the Solar System and, if the pulsar is in a binary, from within its orbit. The Roemer delay is the classical light travel time across the Earth’s orbit. Its magnitude is s, where is the ecliptic latitude of the pulsar (the angle between the pulsar and the ecliptic plane containing the Earth’s orbit around the Sun), and is the corresponding delay across the orbit of a pulsar in a binary or multiple system. The Einstein delay accounts for the time dilation from the moving pulsar (and observatory) and the gravitational redshift caused by the Sun and planets or the pulsar and any companion stars. The Shapiro delay is the extra time required by the pulses to travel through the curved space–time containing the Sun, planets, and pulsar companions. Errors in any of these parameters, as well as other parameters such as , , and proper motion, give very specific systematic signatures in plots of timing residuals (see Figure 6.7), which are simply the differences between the observed TOAs and the predicted TOAs based on the current timing model parameters.
A good example showing how pulsar timing can be extremely useful is timing-based pulsar astrometry. Pulsar positions on the sky are determined by timing a pulsar over the course of a year as the Earth orbits the Sun and tracking the changing Roemer delay.
The Roemer delay of a pulsar at ecliptic coordinates (ecliptic longitude) and (ecliptic latitude) is
| | |
--- |
| | (6.50) |
where is the orbital phase of the Earth with respect to the vernal equinox (the intersection of the ecliptic plane and the celestial equator). Equation 6.50 is only approximate because the Earth’s orbit is not quite circular.
If there is an error in our position estimate, the individual position error components and cause a differential time delay to be present in the timing residuals with respect to the correct Roemer delay:
| | |
--- |
| | (6.51) |
If the position errors are small enough that , , and , we can use trigonometric angle-sum identities and then simplify to get
| | |
--- |
| | (6.52) |
Applying the trig identity to the equation for , we see that
| | |
--- |
| | (6.53) |
| | (6.54) |
and therefore
| | |
--- |
| | (6.55) |
| | (6.56) |
where and are the amplitude (in time units because it corresponds to light-travel time delay) and phase of an error sinusoid that we would observe in the timing residuals from the pulsar (see the middle panel in Figure 6.7).
If the pulsar is located near the ecliptic plane (), then and there is maximum timing leverage, and therefore minimum error, in the determination of . However, and so the errors on are huge. A similar problem occurs near the ecliptic pole for . VLBI positions give better astrometric accuracy for pulsars near the ecliptic plane or ecliptic pole.
In a timing fit for position, the amplitude of the error sinusoid in the timing residuals as described above will be determined to an absolute precision approximately equal to the TOA uncertainty divided by the square-root of the number of observations made of the pulsar (so long as there is at least one year of timing data).
Example. How precisely can we measure the position of a millisecond pulsar at an ecliptic latitude of , with typical TOA errors of 2 s, and where there have been 16 observations over a year? With 2 s TOAs and 16 independent observations, we should be able to constrain the amplitude of the sinusoidal position error amplitude to be within about s. Because both , our errors on both and should be similar: There are 206,265 arcseconds (as) per radian, so those errors correspond to errors in both directions of only 290 as! Even normal pulsars with slow spin periods typically provide astrometric precisions of 0.1 as or better.
For binary pulsars, the time delays across the neutron-star orbit allow for similar high-precision measurements of the pulsar orbital parameters. The binary pulsar Roemer delays comprise up to five Keplerian parameters describing elliptical orbits: the projected semimajor axis , the longitude of periastron , the time of periastron passage , the orbital period , and the orbital eccentricity .
Relativistic binaries, particularly those with compact and elliptical orbits, may allow the measurement of up to five post-Keplerian (PK) parameters: the rate of periastron advance (elliptical orbits do not close in relativistic theories), the orbital period decay caused by the emission of gravitational radiation, the relativistic term describing time dilation and gravitational redshift, and the Shapiro delay terms (range) and (shape). An example of a full “timing solution,” listing high-precision spin, astrometric, binary, and two post-Keplerian parameters , is shown in Figure 6.8.
In any theory of gravity, the five PK parameters are functions only of the pulsar mass , the companion mass , and the standard five Keplerian orbital parameters. For general relativity, the formulas are
| | | |
---
| | | (6.57) |
| | | (6.58) |
| | | (6.59) |
| | | (6.60) |
| | | (6.61) |
In these equations, s is the solar mass in time units (which is known much more precisely than either or individually), , , and are in solar masses, and (where is the orbital inclination). If any two of these PK parameters are measured, the masses of the pulsar and its companion can be determined. If more than two are measured, each additional PK parameter yields a different test of a gravitational theory.
For the famous case of the Hulse–Taylor binary pulsar B191316, high-precision measurements of and were first made to determine the masses of the two neutron stars accurately. The Nobel-prize-winning measurement came with the eventual detection of , which implied that the orbit was decaying in accordance with general relativity’s predictions for the the emission of gravitational radiation.
More recently, the double-pulsar system J07373039 was discovered, which contains two pulsar clocks in a more compact orbit (2.4 hrs compared to 7.7 hrs for PSR B1913+16), allowing the measurement of all five PK parameters as well as the pulsar mass ratio and relativistic spin precession, giving a total of five tests of general relativity. Kramer et al. showed that general relativity is correct at the 0.05% level and measured the masses of the two neutron stars to within 1 part in , and the measurements continue to improve (see Figure 6.9).
The double neutron-star systems have indirectly confirmed the existence of gravitational waves by matching the predicted orbital decays as orbital energy is carried away by gravitational radiation. But over the last decade, one of the driving efforts in pulsar astronomy has become the direct detection of GWs using pulsar timing arrays (PTAs). A PTA is an array of MSPs spread over the sky rather than an array of telescopes, and the goal is to use that pulsar array to detect correlated signals in the timing residuals of dozens of MSPs caused by the distortions of interstellar space from nanohertz (i.e., periods of years) GWs passing through our Galaxy.
Because GW emission and propagation is a quadrupolar process in general relativity, in contrast to the dipolar emission of electromagnetic waves from an accelerating electron, GWs cause specific angular correlations in the timing residuals between pairs of pulsars on the sky. Pulsars close together on the sky will be similarly affected by a passing GW, whereas those much farther apart on the sky will be uncorrelated or even negatively correlated by the same GW. That angular pattern is known as the Hellings and Downs curve , and detecting it would be the key to confirming that correlated signals in timing residuals are caused by GWs and not by other effects such as clock or planetary ephemeris errors.
The most likely sources of detectable nanohertz GWs are supermassive black hole binaries (with total masses of – M) and years-long orbital periods after their parent galaxies have merged. A single massive nearby system, or an ensemble of more distant, less massive systems (making a “stochastic background” of GWs), will cause tens-of-nanosecond spatially and temporally correlated systematics in PTA timing residuals. This level of long-term timing precision for the best MSPs is now being achieved.
Three PTA experiments have been working on this endeavor: NANOGrav in North America and the Parkes and European PTAs in Australia and Europe, respectively. Together, they are collaborating in the International Pulsar Timing Array (IPTA), and huge progress toward a detection has been made recently. Current PTA limits, based on upper limits for appropriately correlated low-frequency timing residuals, are beginning to constrain models of galaxy mergers throughout the universe. And given continued improvements in pulsar timing capability and many new high-precision MSPs from recent surveys, a direct detection of GWs seems possible or even likely within the next five years. |
189688 | https://study.com/learn/lesson/pentagonal-prism-faces-shape.html | Pentagonal Prism | Properties, Faces & Shape - Lesson | Study.com
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Pentagonal Prism | Properties, Faces & Shape
Contributors: Rachel Mcconnell, Joseph Vigil
Author
Author:
Rachel Mcconnell
Rachel is a certified math teacher for grades 6-8. She graduated from the University of Kansas with a bachelors in Middle Math Education. She has taught middle school math for four years throughout Connecticut, Georgia and Italy. She has passed Praxis tests in math, curriculum, and special education.
Instructor
Instructor:
Joseph Vigil
Joseph has a master's degree in literature as well as alternative teaching and ESL educator certifications. He has worked with middle school, high school, and college students in writing and language arts.
Learn what a pentagonal prism is and its connection to polygonal prisms. Understand prism properties and see diagrams of pentagonal prism faces, sides, and vertices. Updated: 11/21/2023
Table of Contents
Prism Properties
Polygonal Prisms
What is a Pentagonal Prism?
Pentagonal Prism Structure
Lesson Summary
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FAQ
What is the meaning of pentagonal prism?
A pentagonal prism is a prism with the base of a pentagon. It is made up of seven faces, two hexagon bases and five parallelogram faces.
What are the properties of a pentagonal prism?
A pentagonal prism has seven faces, fifteen edges, and ten vertices. Of the seven faces, the two bases are pentagons and the other five are parallelograms that connect the pentagon bases.
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Prism Properties ----------------
A prism is a three-dimensional shape with two identical polygon bases connected by parallelogram sides. When looking at a prism, it looks as if the base was stretched out and the parallelograms are created from the distance between the two bases. A prism, like all three-dimensional shapes, are made up of faces, edges, and vertices. Faces are the two-dimensional polygons that create three-dimensional shapes. Edges are the line segments where two faces meet. Vertices, or vertex if singular, are the corners of the shape. This is where two or more line segments meet. Together, the faces, edges, and vertices help describe all three-dimensional shapes, along with prisms.
The faces, edges, and vertices are highlighted on this rectangular prism.
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Polygonal Prisms ----------------
A prism is named by the polygon of the base. These polygons could be regular or irregular. A regular polygon is a shape with straight sides that have equal side lengths and equal angle measurements. If it does not fit the criteria of a regular polygon then is it categorized as an irregular polygon. This is the same with prisms. If the base has a regular polygon as its base then the prism is called a regular prism.
A regular pentagon has equal sides and angles. An irregular pentagon still has five sides but they can have different measurements and angles.
Another way to describe prisms are right prisms and oblique prisms. A right prism has parallel bases and its base is also perpendicular faces to the base. Parallel bases means that if the bases continued forever they will never intersect. Perpendicular meaning to be at a 90 degree angle. For a right prism, each face is at a 90 degree angle to the base. An oblique prism is at an angle. The bases and faces are not at a 90 degree angle therefore giving a slanted appearance. For an oblique prism, the bases are not directly on top of each other because the faces and bases are not at a 90 degree angle.
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What is a Pentagonal Prism? ---------------------------
As listed above, a prism is named for its base. A pentagonal prism is a prism with the base of a pentagon. A pentagon has five sides, therefore, a pentagonal prism as a total of 7 faces, two bases which are pentagons and five parallelograms which connect the bases. For a regular pentagonal prism, the pentagons are directly above each other because the pentagons are at a 90 degree angle with the parallelogram faces. A real world example of a pentagonal prism is the US government building, The Pentagon. This building has five rectangular faces going around the building and two bases, the top and bottom of the building. Another example of pentagonal prisms are old fortresses. These forts would use the shape of a pentagon in order to have more observation towers and opportunities to utilize their cannons against enemy forces. They could have five look outs instead of four if using a rectangular prism.
A pentagonal prism is a prism with the base of a hexagon.
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Pentagonal Prism Structure --------------------------
The structure of a pentagonal prism, no matter if it is regular, irregular, right or oblique, remains the same. Every pentagonal prism has a total of 7 faces, 15 edges, and 10 vertices. These can be counted on the prism. Remember that a face is the two-dimensional polygon that creates the three-dimensional shape. The edges are the line segments that connect the faces. Lastly, vertices are the corners, or points, where the line segments come together.
There are seven faces on a pentagonal prism; two pentagons and five parallelograms.
There are fifteen edges on a pentagonal prism, five along each pentagon giving ten and five more around the height of the parallelogram.
There are 10 vertices on a pentagonal prism, five on the top pentagon, five on the bottom pentagon.
Another important part of the pentagonal prism structure is the net. A net in geometry is the arrangement of unfolded polygons that create the three-dimensional shape. For most three-dimensional shapes there are more than one way to draw a net. As long as the net shows the correct amount of faces and can fold together to make the three-dimensional shape then it is good! Nets can be incorrect if they put the wrong shape next to each other, like connecting the bases together for a prism which would not create a prism because a base is always connected to a parallelogram! Below is one example of a net of a pentagonal prism. Try to draw more combinations! A good way to check if a net works is by cutting it out and folding it into its three-dimensional shape!
This net can fold up into the three-dimensional shape of a pentagonal prism.
Pentagonal prisms, along with all other three-dimensional shapes, can also be described by the surface area and volume of the shape. The surface area of a shape is the sum of the areas of each face. The surface area for a pentagonal prism is calculated by adding the area of both pentagons and the five parallelograms. There is a simplified formula for pentagonal prisms which is {eq}Surface Area = (5ah+5ab) {/eq} where a is the apothem length of the pentagon, h is the height of the prism, and b is the base length of the pentagon. The volume of a shape is the space a shape takes up. The formula for the volume of a pentagonal prism is {eq}Volume = (\frac{5}{2} + abh) {/eq} where a is the apothem length of the pentagon, h is the height of the prism, and b is the base length of the pentagon. These calculations can help compare different pentagonal prisms.
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Lesson Summary --------------
Prisms are a very common shape in the real world, most businesses actually work in a prism! A prism is a three-dimensional shape with two identical polygon bases connected by parallelogram sides. Each prism, along with each three-dimensional shape, is defined by faces, edges, and vertices. Faces are the two-dimensional polygons that create three-dimensional shapes. Edges are the line segments where two faces meet. Vertices, or vertex if singular, are the corners of the shape. A regular polygon is used to create a regular prism, which is a prism whose base has equal side lengths and equal angle measurements. There are also right prisms and oblique prisms. A right prism has a right angle, 90 degrees, between its faces and base. An oblique prism is at a slant therefore does not have a 90 degree angle between its faces and base. Additionally, the surface area and volume can be calculated in order to compare different three-dimensional shapes.
With a thorough overview of prisms, understand what is important about pentagonal prisms. A pentagonal prism is a prism with the base of a pentagon. They can be regular, irregular, right or oblique but they each contain 7 faces, 15 edges, and 10 vertices. Look for pentagonal prisms in your real world!
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Video Transcript
Prisms
Prisms are a certain kind of shape, but what makes them stand out? A prism consists of two two-dimensional shapes joined together to form an enclosed three-dimensional shape. For example, a drum is a prism because it has two circles joined together to make the enclosed three-dimensional shape we see here:
In fact, the two-dimensional shape (in this case, a circle) makes the top and bottom, or faces, of a prism.
Cans of food, soda cans, and trash cans are all prisms because they're three-dimensional shapes with circular faces. Likewise, boxes are prisms because they're three-dimensional shapes with square or rectangular faces.
Types
Since there are many different shapes that can serve as faces, there are many types of prisms we can make. In fact, prisms are named for the shape of their faces. So a pentagonal prism is simply a prism that has pentagons as its faces. Similar to the drum or box, it's an enclosed three-dimensional shape based on two pentagons.
It's very similar to the snare drum, except its bottom and top are pentagons rather than circles.
This image is also a pentagonal prism:
Even though the sides are slanted, it's still a three-dimensional shape based on two pentagons.
Properties
Since all pentagonal prisms have the same basic qualities, they all share certain properties:
First, all pentagonal prisms have seven sides.
As we can see in this illustration, the five sides of the prism connect the five sides of the pentagons. The top and bottom make sides six and seven.
Additionally, all pentagonal prisms have fifteen edges.
In this illustration, the first five edges (or numbers 1-5 in black) form the top pentagonal face, while edges 6-10 (shown in white) form the bottom face. Meanwhile, edges 11-15 (shown in silver) are the 5 edges connecting the pentagonal faces.
Finally, all pentagonal prisms have ten vertices, or corners.
There are five corners on both top and bottom where the sides and faces meet, making a total of ten vertices.
Lesson Summary
Pentagonal prisms are simply two pentagons joined together to form an enclosed three-dimensional shape. Because this is true for all pentagonal prisms, they all have:
7 sides
15 edges
10 vertices
The seven sides of a pentagonal prism include the top and bottom, which are known as faces.
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CAHSEE Math Exam: Test Prep & Study Guide
22 chapters
218 lessons
Chapter 1
Number Theory & Basic Arithmetic
Types of Numbers & Its Classifications 6:56 minNumber Line Definition, Use & Examples 5:16 minGraphing Rational Numbers on a Number Line | Chart & Examples 5:02 minNotation for Rational Numbers, Fractions & Decimals 6:16 minThe Order of Real Numbers: Inequalities 4:36 minFinding the Absolute Value of a Real Number 3:11 minBinary and Non-Binary Operations 5:34 minArithmetic Calculations with Signed Numbers 5:21 minCommutative Property | Definition, Examples & Applications 3:53 minAssociative Property | Definition & Examples 4:28 minThe Zero Property of Multiplication | Definition & Examples 2:40 minWhat is the Greatest Common Factor? | GCF Examples 4:56 minLeast Common Multiple | Definition, Formula & Examples 5:37 minParentheses in Math | Definition & Examples 4:01 minAlgebra Terms & Vocabulary 3:48 minOrder of Operations in Math | Steps & Examples 5:50 min
Chapter 2
Problems with Decimals and Fractions
Arithmetic with Decimal Numbers 10:40 minHow to Estimate with Decimals to Solve Math Problems 8:51 minHow to Build and Reduce Fractions 3:55 minFinding the Least Common Denominator | Overview & Examples 4:30 minComparing & Ordering Fractions | Method & Examples 7:33 minImproper Fractions & Mixed Numbers | Conversion & Examples 4:55 minAdding & Subtracting Fractions | Rules & Examples 4:14 minHow to Add and Subtract Unlike Fractions and Mixed Numbers 6:46 minMultiplying Mixed Numbers | Steps & Examples 7:23 minDividing Fractions & Mixed Numbers | Overview & Examples 7:12 minPractice with Fraction and Mixed Number Arithmetic 7:50 minEstimation Problems using Fractions 7:37 minSolving Problems using Fractions and Mixed Numbers 7:08 minHow to Solve Complex Fractions 5:20 minUsing the Number Line to Compare Decimals, Fractions, and Whole Numbers 6:46 minHow to Simplify Word Problems with Fractions Using Whole Numbers 3:38 min
Chapter 3
Problems with Percents
Percentage | Definition & Calculation 4:20 minChanging Between Decimals and Percents 4:53 minDecimal to Fraction | Conversion & Examples 7:32 minConverting Fractions to Percents 3:43 min
Chapter 4
Problems with Radical Expressions & Equations
Estimating Square Roots | Overview & Examples 5:10 minEvaluating Square Roots of Perfect Squares 5:12 minSimplifying Square Roots When not a Perfect Square 4:45 minSimplifying Square Root Expressions | Steps & Examples 7:03 minSimplifying Square Roots | Overview & Examples 4:49 minRationalizing the Denominator | Overview & Examples 7:01 minAddition and Subtraction Using Radical Notation 3:08 minHow to Multiply Radical Expressions 6:35 minSolving Radical Equations | Overview & Examples 6:48 minSolving Radical Equations with Two Radical Terms 6:00 min
Chapter 5
Problems with Algebraic Expressions and Equations
Algebraic Expression | Definition, Operations & Examples 5:12 minEvaluating Algebraic Expressions | Rules & Examples 7:27 minCombining Like Terms in Algebraic Expressions 7:04 minPractice Simplifying Algebraic Expressions 8:27 minNegative Signs and Simplifying Algebraic Expressions 9:38 minWriting Equations with Inequalities: Open Sentences and True/False Statements 4:22 minAlgebra Equations | Formula, Types & Examples 7:28 minDefining, Translating, & Solving One-Step Equations 6:15 minSolving Equations Using the Addition Principle 5:20 minMultiplication Principle | Definition, Equations & Examples 4:03 minSolving Equations Using Both Addition and Multiplication Principles 6:21 minCollecting Like Terms On One Side of an Equation 6:28 minSolving Equations Containing Parentheses 6:50 minTranslating Words into Algebraic Expressions | Phrases & Examples 6:31 minHow to Solve One-Step Algebra Equations in Word Problems 5:05 minSolving Multiple Step Equations | Explanation, Steps & Examples 5:44 minSolving Algebra Word Problems | Multi-Step Equations & Examples 6:16 min
Chapter 6
Algebraic Linear Equations & Inequalities
Linear Equations | Definition, Formula & Solution 7:28 minLinear Equation | Parts, Writing & Examples 8:58 minSolving Linear Equations: Practice Problems 5:49 minSolving Linear Equations with Literal Coefficients 5:40 minProblem-Solving using Linear Equations 6:40 minSystem of Equations in Algebra | Overview, Methods & Examples 8:39 minHow Do I Use a System of Equations? 9:47 minSolving a System of Equations with Two Unknowns 6:15 minSolving Problems Involving Systems of Equations 8:07 minInequality Signs in Math | Symbols, Examples & Variation 7:09 minSolving Linear Inequalities: Practice Problems 6:37 minLinear Transformation Definition, Formula & Examples
Chapter 7
Problems with Exponents
Scientific Notation | Definition, Conversion & Examples 6:49 minProperties of Exponents | Formula & Examples 5:26 minHow to Define a Zero and Negative Exponent 3:13 minSimplifying Expressions with Exponents | Overview & Examples 4:52 minRational Exponents | Definition, Calculation & Examples 3:22 minSimplifying Algebraic Expressions with Rational Exponent 7:41 minPower of Powers: Simplifying Exponential Expressions 3:33 min
Chapter 8
Overview of Functions
Function in Math | Definition & Examples 7:57 minTransformations: How to Shift Graphs on a Plane 7:12 minHow to Add, Subtract, Multiply and Divide Functions 6:43 minDomain & Range of a Function | Definition, Equation & Examples 8:32 minHow to Compose Functions 6:52 minInverse Functions | Definition, Methods & Calculation 6:05 minApplying Function Operations Practice Problems 5:17 min
Chapter 9
Rational Expressions & Practice
Adding & Subtracting Rational Expressions | Overview & Examples 8:02 minPractice Adding and Subtracting Rational Expressions 9:12 minHow to Multiply and Divide Rational Expressions 8:07 minMultiplying and Dividing Rational Expressions: Practice Problems 4:40 minDivision and Reciprocals of Rational Expressions 5:09 minSimplifying Complex Rational Expressions | Steps & Examples 4:37 minRational Equations | Definition, Formula & Examples 7:58 minRational Equations: Practice Problems 13:15 min
Chapter 10
Calculations with Ratios, Percent & Proportions
Ratios & Rates | Differences & Examples 6:37 minHow to Solve Problems with Money 8:29 minProportion | Definition, Formula & Types 6:05 minCalculations with Ratios and Proportions 5:35 minPercents: Definition, Application & Examples 6:20 minHow to Solve Word Problems That Use Percents 6:30 minSimple Interest Problems | Definition, Formula & Examples 6:05 minCompounding Interest | Formula, Types & Examples 7:45 minTaxes & Discounts: Calculations & Examples 8:07 minHow to Solve Problems with Time 6:18 minDistance Equations | Formula, Calculation & Examples 6:31 min
Chapter 11
Understanding Matrices & Absolute Value
Matrix in Math | Definition, Properties & Rules 5:39 minFinding the Determinant of a Matrix | Properties, Rules & Formula 7:02 minAbsolute Value | Explanation & Examples 4:42 minAbsolute Value Expression | Evaluation, Simplification & Examples 5:28 minSolving Absolute Value Functions & Equations | Rules & Examples 5:26 minAbsolute Value | Overview & Practice Problems 7:09 minAbsolute Value | Graph & Transformations 8:14 minGraphing Absolute Value Functions | Definition & Translation 6:08 min
Chapter 12
Quadratics & Polynomials
Solving Quadratics: Assigning the Greatest Common Factor and Multiplication Property of Zero 5:24 minQuadratic Function | Formula, Equations & Examples 9:20 minHow to Solve Quadratics That Are Not in Standard Form 6:14 minSolving Quadratic Inequalities Using Two Binomials 5:36 minMultiplying Binomials | Overview, Methods & Examples 5:46 minFactoring Quadratic Equations Using Reverse Foil Method 8:50 minFactoring Quadratic Equations | Solution & Examples 7:35 minQuadratic Trinomial | Definition, Factorization & Examples 7:53 minHow to Complete the Square | Method & Examples 8:43 minCompleting the Square Practice Problems 7:31 minHow to Solve a Quadratic Equation by Factoring 7:53 minPolynomial Long Division | Overview & Examples 8:05 minSynthetic Division of Polynomials | Method & Examples 6:51 minDividing Polynomials with Long and Synthetic Division: Practice Problems 10:11 minOperations with Polynomials in Several Variables 6:09 min
Chapter 13
Geometry: Graphing Basics
Parts of a Graph | Labels & Examples 6:21 minPlotting Points on the Coordinate Plane 5:23 minReflection Rules in Math | Graph, Formula & Examples 6:07 minPlotting Simple Figures on Coordinate Graphs 4:27 min
Chapter 14
Graphing on the Coordinate Plane
Find the Slope of a Line | Formula & Examples 9:27 minHow to Find and Apply the Intercepts of a Line 4:22 minUndefined & Zero Slope Graph | Definition & Examples 4:23 minParallel vs Perpendicular vs Transverse Lines Overview & Examples 6:06 minDistance Formula | Overview & Examples 5:27 minMidpoint | Formula & Examples 3:33 minGraphing and Analyzing Quantitative Relationships 2:58 minGraphing Quantity Values With Constant Ratios 5:53 minInterpreting Systems of Linear Equations Graphically 4:50 minParabola | Definition & Parabolic Shape Equation 4:36 minTypes of Parabolas | Overview, Graphs & Examples 6:15 minCubic, Quartic & Quintic Equations | Graphs & Examples 11:14 min
Chapter 15
Measurement in Math
Standard Units of Measurement | Overview & Examples 4:02 minHow to Convert Standard Units of Measure 7:19 minHow to Perform Basic Operations with Measurements 8:45 minMetric System | Definition, Lists & Examples 5:31 minHow to Convert Units in the Metric System 6:06 minHow to Take Measurements with Scales, Meters & Gauges 4:33 min
Chapter 16
Properties of Shapes
Quadrilaterals | Properties, Formula & Differences 5:46 minQuadrilateral Shape | Properties & Types 6:42 minProperties of Triangles | Sides, Angles & Types 5:09 minCircle in Geometry | Definition, Parts & Examples 4:45 min
Chapter 17
Triangles, the Pythagorean Theorem & Congruency
Pythagorean Theorem | Overview, Formula & Examples 7:33 minSimilar Triangles | Theorems, Formula & Examples 7:23 minSimilar Triangles | Definition, Application Problems & Examples 6:23 minHow to Classify Triangles | Overview & Examples 5:44 minAngles and Triangles: Practice Problems 7:43 minCongruent in Geometry | Definition & Examples 2:13 minASA, SSS & SAS Triangle Postulates | Properties & Examples 6:15 minProving Congruent Isosceles Triangles 4:51 minRight Triangle Congruence Theorems | Definition & Examples 7:00 min
Chapter 18
Perimeter, Area & Volume in Geometry
Three-Dimensional Shapes | Definition, Types & Characteristics 3:28 minPerimeter of Triangles and Rectangles 8:54 minArea of Triangles & Rectangles | Formula, Calculation & Examples 5:43 minFinding the Area & Circumference of a Circle 7:24 minVolume of Cylinders, Cones & Spheres | Formula & Examples 7:50 minVolume of Prisms & Pyramid | Types, Formula & Calculation 6:15 minSurface Area of a Cube & Rectangular Prism | Definition & Formula 4:08 minSurface Area of a Cylinder | Formula, Calculation & Examples 4:26 minSurface Area of a Pyramid | Formula, Calculation & Examples 5:11 minArea of Complex & Irregular 2D & 3D Shapes 4:54 minLinear Scale Factor | Shapes, Area & Volume 7:33 minArea in Geometry | Overview, Formula & Examples 4:52 minPerimeter: Real-World Geometry Problems 6:15 minVolume in Real Life | Formula, Calculation & Examples 7:48 min
Chapter 19
Statistics, Probability & Working with Data
Conditional Probability | Overview, Calculation & Examples 5:10 minProbability of at Least One Event | Overview & Calculation 5:27 minProbability of an Event | Simple, Compound & Complementary 6:55 minIndependent & Dependent Events | Overview, Probability & Examples 12:06 minPie Chart vs. Bar Graph | Overview, Uses & Examples 9:36 minMeasures of Central Tendency | Definition, Formula & Examples 8:30 minCumulative & Relative Frequency | Formula, Table & Calculations 5:47 minProbability of A or B | Overlapping & Non-Overlapping Events 7:05 minStatistical Analysis with Categorical Data 5:20 minSummarizing Categorical Data using Tables 4:57 minMake Estimates and Predictions from Categorical Data 3:13 minQuantitative Data Overview, Types & Examples 4:11 minReading and Interpreting Line Graphs 6:09 minMaking Estimates and Predictions using Quantitative Data 4:07 minCreating & Interpreting Scatterplots: Process & Examples 6:14 minThe Relationship Between Variables: Correlation Coefficient & Scatterplots 5:03 minStatistics, Data Analysis & Probability in Real Life 6:36 minTables & Graphs in the Real World | Uses & Examples 5:50 min
Chapter 20
Mathematical Reasoning
Recognizing & Generalizing Patterns in Math 5:37 minIdentifying & Organizing Relevant Information in Math 4:27 minInductive vs. Deductive Reasoning in Geometry | Definition & Uses 4:59 minGeneralizing Mathematical Results & Strategies 4:31 minVerifying Calculated Results with Estimation 4:59 min
Chapter 21
Basic Mathematical Logic
Critical Thinking and Logic in Mathematics 4:27 minTruth Value | Definition, Propositions & Tables 9:49 minConjunction vs. Disjunction in Math | Overview & Characteristics 3:39 minConditional Statement | Definition & Examples 4:54 minConditional Statements | Converse, Inverse & Contrapositive 7:09 min
Chapter 22
CAHSEE Math Exam Flashcards
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189689 | https://pmc.ncbi.nlm.nih.gov/articles/PMC3280198/ | Deconstructing the skin: cytoarchitectural determinants of epidermal morphogenesis - PMC
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Nat Rev Mol Cell Biol
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Published in final edited form as: Nat Rev Mol Cell Biol. 2011 Aug 23;12(9):565–580. doi: 10.1038/nrm3175
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Deconstructing the skin: cytoarchitectural determinants of epidermal morphogenesis
Cory L Simpson
Cory L Simpson
Department of Pathology, Northwestern University, Feinberg School of Medicine.
Find articles by Cory L Simpson
, Dipal M Patel
Dipal M Patel
Department of Pathology, Northwestern University, Feinberg School of Medicine.
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, Kathleen J Green
Kathleen J Green
Department of Pathology, Northwestern University, Feinberg School of Medicine.
‡Department of Dermatology, Northwestern University, Feinberg School of Medicine.
§Robert H. Lurie, Comprehensive Cancer Center, Northwestern University, Feinberg School of Medicine, Chicago, Illinois 60611, USA.
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,‡,§
Author information
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Department of Pathology, Northwestern University, Feinberg School of Medicine.
‡Department of Dermatology, Northwestern University, Feinberg School of Medicine.
§Robert H. Lurie, Comprehensive Cancer Center, Northwestern University, Feinberg School of Medicine, Chicago, Illinois 60611, USA.
✉
Correspondence to K.J.G., kgreen@northwestern.edu
© 2011 Macmillan Publishers Limited. All rights reserved
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PMCID: PMC3280198 NIHMSID: NIHMS354842 PMID: 21860392
The publisher's version of this article is available at Nat Rev Mol Cell Biol
Abstract
To provide a stable environmental barrier, the epidermis requires an integrated network of cytoskeletal elements and cellular junctions. Nevertheless, the epidermis ranks among the body’s most dynamic tissues, continually regenerating itself and responding to cutaneous insults. As keratinocytes journey from the basal compartment towards the cornified layers, they completely reorganize their adhesive junctions and cytoskeleton. These architectural components are more than just rivets and scaffolds — they are active participants in epidermal morphogenesis that regulate epidermal polarization, signalling and barrier formation.
The epidermis is a highly specialized epithelium that has evolved to perform multiple essential protective functions: it prevents water loss, excludes toxins, resists mechanical stress and participates in immune responses. To establish a barrier between the organism and its environment, keratinocytes, the main cells of the epidermis, form an adhesive network organized into multiple layers, or ‘strata’ (REFS 1,2) (FIG. 1). This presents us with a paradox: although the tissue exhibits incredible stability that shields underlying organs from external insults, its cellular components must remain dynamic to allow tissue regeneration and response to cutaneous insults.
Figure 1. Epidermal architecture.
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The epidermis is composed of stratified cell layers, which undergo programmed differentiation to allow for constant renewal of the skin. Four main layers are illustrated by a hematoxylin- and eosin-stained human skin sample and an accompanying schematic of the stratum basale, stratum spinosum, stratum granulosum and stratum corneum. The basal, proliferating cell layer of the epidermis remains in contact with the dermis through hemidesmosomes and integrin-based adhesions, both of which provide connections to the underlying extracellular matrix (ECM). During keratinocyte differentiation, a unique cytoarchitecture is elaborated in each of the four layers that comprises specific cytoskeleton and cell junction types, including adherens junctions, tight junctions, desmosomes and gap junctions. The differentiation-dependent changes in the composition and organization of epidermal cytoarchitecture help to drive tissue morphogenesis while supporting the specific functions of each layer, from the regenerative capacity of the stratum basale to the assembly of the cornified envelope and the sloughing of terminally differentiated cells from the stratum corneum. The graded distribution of specific cytoskeletal and junction components, including specific keratins (Ks), desmogleins (DSGs) and cadherins, is crucial for driving morphogenesis. Image in top left courtesy of R. Lavker, Northwestern University, USA. DP, desmoplakin; DSC, desmocollin; E-cadherin, epithelial cadherin; P-cadherin, placental cadherin; PG, plakoglobin; PKP1, plakophilin 1.
Keratinocytes undergo a dramatic transformation as they differentiate and migrate outwards to replace cells that are shed from the body surface1. While basal cells of the ‘stratum basale’ remain attached to an underlying matrix and proliferate, some of their daughter keratinocytes enter the spinous layer (or ‘stratum spinosum’) through asymmetric mitoses, where they exit the cell cycle, grow larger and establish robust intercellular connections. Cells in the granular layer (the ‘stratum granulosum’) flatten and assemble a water-impermeable cornified envelope underlying the plasma membrane. Finally, corneal layer (or ‘stratum corneum’) keratinocytes release lysosomal enzymes to degrade major organelles, become completely squamous and are tightly crosslinked together to complete the cutaneous barrier2. Thus, the mature epidermis exhibits tissue-level polarization with asymmetric distribution of signalling activity, protein expression and cytoarchitectural organization that reflects the unique functions of its multiple layers.
The embryonic epidermis begins as a single layer of ectodermal cells that then undergo stratification to construct a multilayered epithelium in response to specific transcription factors3. Once constructed, the epidermis is maintained by continual stratification and differentiation of keratinocytes throughout adult life. A number of outstanding articles have reviewed the factors that mediate epidermal development and homeostasis1,4. These factors include cytoskeletal building blocks and their associated intercellular junctions, which have classically been thought to serve as the scaffold and rivets that impart structural integrity to the epidermis. However, these elements of cell architecture are themselves increasingly being viewed as active participants in epidermal morphogenesis.
Various junctional and cytoskeletal proteins control the regenerative capacity of the epidermis by affecting maintenance of the stem cell population that resides primarily in the hair follicles and the stratum basale (reviewed in REF. 5). In this Review, we chronicle the journey of the interfollicular keratinocyte through the epidermal layers. Along the way, we highlight how the cytoplasmic and cortical cytoskeleton and associated adhesion molecules provide instructions for epidermal morphogenesis. We review their contributions to the establishment of polarity and to the alterations in cell signalling, morphology and protein expression that drive the keratinocyte from the basal compartment to the cornified layers. Finally, we discuss how these advances at the cellular and molecular level have improved our understanding of human disease.
Adhesion at the basement membrane
The boundary between the epidermis and the underlying dermis is established by deposition of a specialized layer of extracellular matrix (ECM) called the basement membrane6. Keratinocytes of the basal layer are inherently polarized as their lower surface is anchored to the basement membrane by integrins (FIG. 2). These heterodimeric transmembrane receptors, consisting of α- and β-integrin subunits, bind specific ECM components via their extracellular domains7. At least 11 integrin dimers have been described in epidermal keratinocytes8. On the intracellular side, most integrin tails associate with actin via adaptor proteins. However, α6β4 integrin has a unique role in organizing large integrin complexes called hemidesmosomes, which are tethered to intermediate filaments by the cytolinker proteins plectin and bullous pemphigoid antigen 1e (BPAG1e; also known as BP230 and dystonin)6. A range of human disorders result from integrin-based adhesion being compromised by mutation or by autoantibodies that target specific integrins, integrin-associated proteins or matrix components; such disorders are characterized by varying degrees of epidermal fragility and blistering (TABLE 1 and Supplementary information S1 (table)).
Figure 2. Integrins crosstalk with growth factor receptors to regulate proliferation in the basal layer.
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The stratum basale has a high density of hemidesmosomes and integrin-based adhesions that maintain cell attachment to the underlying basement membrane, which is composed of the lamina lucida and lamina densa. Hemidesmosomes connect to the basement membrane through α6β4 integrins and the transmembrane protein bullous pemphigoid antigen 2 (BPAG2; also known as collagen XVII), and are tethered to intermediate filaments by the plakin family members plectin and BPAG1e6. α3β1 integrins provide transmembrane connections to the intracellular actin network through recruitment of several factors to their cytoplasmic tails. Integrins are thought to crosstalk with receptors such as EGFR (epidermal growth factor receptor) to induce proliferation of cells in the stratum basale via mitogen-activated protein kinase (MAPK) signalling. As cells stratify, decreased integrin density allows cell cycle exit and differentiation.
Table 1.
Human diseases of the epidermis
| Molecular target‡ | Disease | Phenotype |
:---
| Gap junctions | | |
| CX26 | Keratitis ichthyosis deafness syndrome and hystrix-like ichthyosis deafness syndrome | Vascularizing keratitis; progressive erythrokeratoderma; sensorineural hearing loss |
| Vohwinkel’s syndrome (keratoderma hereditaria mutilans) | Keratoderma of palmoplantar surfaces; circumferential hyperkeratosis of digits leading to autoamputation; moderate sensorineural hearing loss |
| Bart–Pumphrey syndrome | Hyperkeratosis of knuckle pads; sensorineural hearing loss |
| CX30 | Clouston syndrome (hidrotic ectodermal dysplasia) | Palmoplantar hyperkeratosis; hair defects (partial to total alopecia); nail deformities |
| CX30.3, CX31 | Erythrokeratodermia variabilis | Local or diffuse hyperkeratosis; migratory erythematous patches |
| Adherens junctions | | |
| P-cadherin (encoded by CDH3) | Hypotrichosis with juvenile macular dystrophy | Hair loss; progressive macular degeneration and early blindness |
| Ectodermal dysplasia, ectrodactyly, macular degeneration syndrome | Hypotrichosis with partial adontia; absence deformities and syndactyly; atrophy of retinal pigment epithelium |
| Keratin intermediate filaments | |
| K4, K13 | White sponge nevus | Spongy white plaques, often on buccal mucosa |
| K9 | Epidermolytic palmoplantar keratoderma | Epidermolysis and hyperkeratosis of palms and soles |
| K6, K16, K17 | Pachyonychia congenita | Painful blisters on hands and feet; thickened nails; hyperkeratosis of hair follicles; leukokeratosis of oral mucosa |
| K2e | Ichthyosis bullosa of Siemens | Bullous ichthyosis without erythroderma; epidermolysis limited to upper suprabasal layers |
| K1, K10 | Bullous congenital ichthyosis erythroderma (epidermolytic hyperkeratosis) | Generalized erythema; erosions and blisters owing to fragility of suprabasal keratinocytes |
| K5, K14 | Epidermolysis bullosa simplex | Skin blistering from fragility of basal keratinocytes |
| Desmosomes | | |
| DSG1 | Bullous impetigo | Epidermal blisters at the granular layer caused by a bacterial protease |
| Staphylococcal scalded skin syndrome |
| Pemphigus foliaceus | Epidermal blisters at the granular layer caused by autoantibodies |
| DSG3 | Pemphigus vulgaris | Epidermal blisters at the basal–suprabasal cell interface caused by autoantibodies |
| DSG4 | Hypotrichosis | Sparse, fragile hair with abnormal hair follicles; epidermal hyperproliferation |
| DSC3 | Hypotrichosis with skin vesicles | Sparse, fragile hair with normal hair follicles; recurrent skin vesicles |
| DSC2 | Arrhythmogenic right ventricular cardiomyopathy with mild palmoplantar keratoderma and woolly hair | Ventricular arrhythmias with fibro-fatty replacement of heart tissue; thickening of palms and soles; tightly coiled hair |
| DP, DSG1 | Striate palmoplantar keratoderma | Linear and focal hyperkeratosis of palms and soles |
| DP | Carvajal syndrome | Epidermolytic palmoplantar keratoderma with woolly hair and dilated cardiomyopathy |
| Lethal acantholytic epidermolysis bullosa | Acantholysis and shedding of skin at birth, leading to early death |
| PKP1 | Ectodermal dysplasia-skin fragility syndrome | Skin fragility; plantar keratoderma; nail dystrophy; alopecia |
| PG | Naxos disease | Woolly hair; palmoplantar keratoderma; arrhythmogenic right ventricular cardiomyopathy |
| Lethal congenital epidermolysis bullosa | Lethal epidermal blistering at birth |
| Hemidesmosomes | | |
| Laminins, integrins, BPAG2 | Junctional epidermolysis bullosa | Generalized blistering at dermal–epidermal junction due to either congenital mutation or acquired autoantibodies |
| BPAG1e | Epidermolysis bullosa simplex | Trauma-induced epidermal blisters and episodic limb numbness |
| BPAG2 | Bullous pemphigoid | Fluid-filled subepidermal blisters with deroofing of epidermis caused by autoantibodies |
| Stratum corneum | | |
| ABCA12 (lipid transport) | Harlequin ichthyosis | Hard, thickened skin with fissures |
| Filaggrin | Ichthyosis vulgaris | Dry skin; mild hyperkeratosis |
| CDSN | Hypotrichosis simplex of scalp | Childhood-onset loss of hair |
| Generalized peeling skin syndrome | Peeling of the skin and itching |
| SPINK5 (also known as LEKT1; serine protease inhibitor) | Netherton syndrome | Exfoliative erythroderma; hair abnormalities; atopic manifestations |
| TGase 1 | Lamellar ichthyosis | Newborns covered with colloid membrane that is later shed; erythema with white scales; hyperkeratosis of palms and soles |
| Loricrin | Vohwinkel’s syndrome (keratoderma hereditaria mutilans) | Keratoderma of palmoplantar surfaces; circumferential hyperkeratosis of digits leading to autoamputation; moderate sensorineural hearing loss |
| Progressive symmetric erythrokeratodermia | Hyperpigmented, hyperkeratotic plaques with symmetrical growth |
| Other | | |
| ATP2C1 (calcium pump) | Hailey–Hailey disease | Outbreaks of rashes and blisters, usually in skin folds |
| ATP2A2 (calcium pump) | Darier’s disease | Acantholysis; abnormal keratinization; greasy, hyperkeratotic papules |
| Collagen VII | Dystrophic epidermolysis bullosa | Severe blistering with atrophic scarring |
| Kindlin 1 | Kindler syndrome | Skin atrophy with blistering at dermal–epidermal junction |
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ABCA12, ATP-binding cassette, sub-family A, member 12; ATP2A2, sarcoplasmic/endoplasmic reticulum calcium ATPase 2; ATP2C1, calcium-transporting ATPase type 2C member 1; BPAG, bullous pemphigoid antigen; CDH3, cadherin 3; CDSN, corneodesmosin; CX, connexin; DP, desmoplakin; DSC, desmocollin; DSG, desmoglein; K, keratin; PG, plakoglobin; PKP1, plakophilin 1; TGase 1, transglutaminase 1.
A version of this table including references is available in Supplementary information S1 (table).
‡
Listed molecular targets are affected by gene mutation in these diseases unless otherwise specified.
Intriguingly, integrin complexes also contain signalling proteins and are well positioned to transduce external cues into intracellular signals. Studies are beginning to suggest a broader role for integrins and their associated proteins in regulating epidermal homeostasis and basement membrane organization. However, the extent to which the functions of integrins in tissue integrity can truly be separated from their roles in morphogenesis and homeostasis remains controversial8.
Integrins in epidermal homeostasis
Homeostasis of the epidermis requires precise regulation of basal cell proliferation to offset keratinocyte loss through sloughing of the cornified layer4. Early in vitro experiments indicated that releasing keratinocytes from an underlying matrix induced cell cycle withdrawal and expression of differentiation markers9,10. In intact epidermis, keratinocytes cease proliferating as they leave the basal layer, which coincides with loss of contact with the basement membrane and suppression of integrin expression. Thus, it has been hypothesized that stratification-associated downregulation of integrins dampens proliferation in the suprabasal epidermal layers7,8. Under normal circumstances, mitogenic signalling from epidermal growth factor receptor (EGFR) via the mitogen-activated protein kinase (MAPK) pathway is limited to basal keratinocytes, which express abundant integrins11,12 (FIG. 2). Integrins can crosstalk with receptor tyrosine kinases, including EGFR, providing a possible mechanism for how they may regulate proliferation8,13,14. In fact, integrin ligation by certain ECM molecules leads to MAPK activation in vitro12,15.
In mice, deletion of β4 integrin prohibits formation of hemidesmosomes, resulting in severe blistering16,17. Loss of β4 integrin also appeared to induce apoptosis of basal cells16, whereas deleting the cytoplasmic tail of β4 impairs proliferation18, together suggesting that hemidesmosomes regulate tissue homeostasis. Conversely, tamoxifen-induced deletion of α6 integrin, the partner of β4 in hemidesmosomes, increases proliferation and skin inflammation19. Nevertheless, all of these effects could simply be secondary to defective basement membrane adhesion. Consistent with this, mice lacking α6 and α3 integrin in the skin show normal morphogenesis and differentiation in all non-blistered epidermis20. Similarly, mosaic epidermal deletion of β4 integrin disrupted proliferation only in areas of basement membrane detachment21.
Integrin expression is seen beyond the basal layer in hyperproliferative skin in humans, such as in psoriasis and carcinomas14,22,23. Accordingly, ectopic integrin expression in mice increases proliferation and impairs differentiation. For example, ectopic expression of β1 integrin in suprabasal cells leads to a phenotype resembling psoriasis24, and expression of α6β4 or α5β1 integrin in the suprabasal compartment increases susceptibility to epidermal carcinogenesis25,26. Conversely, deletion of β1 integrin in skin produces a hypoproliferative epidermis with more differentiating keratinocytes than in normal epidermis27,28, although it also results in extensive epidermal blistering. Inducible deletion of β1 integrin in adult epidermis results in hyperproliferation in targeted areas of the skin29. So although integrin deletion or mis-expression may alter proliferation, it remains difficult to dissect the potential homeostatic function of integrins from their role in maintaining skin integrity.
Forming the basement membrane
Keratinocytes can secrete ECM components, including collagen IV and laminin 5, to help establish and organize the matrix, an ability that depends on integrins themselves6,30. Total loss of α3 integrin results in neonatal lethality and subepidermal blistering owing to a discontinuous basement membrane between hemidesmosomes31. Epidermal-specific deletion of α3 integrin results in duplicated areas of the basement membrane and microblisters between the stratum basale and the dermis (the dermal– epidermal junction)32. Although these animals differentiate and proliferate normally, loss of α3 integrin actually accelerated wound sealing, suggesting that defective basement membrane adhesion may allow more efficient migration of keratinocytes into wound beds. In addition to causing thinning of the epidermis and blistering, deletion of β1 integrin in mice results in a defective basement membrane, with large areas of the skin lacking a subepidermal matrix27. Mice deficient in integrin-linked kinase (ILK), a cytoplasmic pseudokinase associated with integrins, have similar abnormalities33. In addition to epidermal hyperplasia and impaired differentiation, ILK-deficient mice display a discontinuous basement membrane. Thus, integrin complexes are crucial for proper morphogenesis of the basement membrane.
Kindlin 1 regulates epidermal integrity and homeostasis
A novel epidermal function has been uncovered for kindlins, which are β-integrin-binding proteins that are thought to cooperate with talin to regulate integrin-based adhesion34 (FIG. 2). Kindlin 1 (also known as FERMT1), which is highly expressed in the epidermis35, is targeted in Kindler syndrome, an autosomal recessive disease characterized by transient perinatal blistering at the dermal–epidermal junction followed by longer term skin atrophy36. In patients with Kindler syndrome, the basement membrane is grossly disorganized with both aberrant thickening and substantial gaps in the matrix (or lamina densa) between the basal keratinocytes and the dermis37. Thus, kindlin 1 seems to be essential for organizing the epidermal ECM. Although it has no intrinsic enzymatic activity, kindlin 1 probably functions as a scaffold in integrin complexes and may reorganize microfilaments through its association with α-actinin and migfilin, two actin-binding proteins38,39.
Genetic ablation of kindlin 1 in mice results in skin atrophy with reduced epidermal proliferation and thickness40. Keratinocytes isolated from patients with Kindler syndrome have cell autonomous defects in proliferation and apoptosis, suggesting that kindlin 1 may directly affect signalling41. Patients with Kindler syndrome are also more prone to epidermal carcinogenesis later in life, implying that kindlin 1 may affect long-term skin homeostasis34. Surprisingly, mice lacking kindlin 1 do not develop epidermal blisters, although keratinocytes from these mice show reduced substrate adhesion in vitro40. Instead, the animals die from sloughing of the intestinal epithelium owing to faulty substratum adhesion; thus, kindlin 1 may have an additional role in maintaining the integrity of the gut, another highly regenerative organ. Interestingly, kindlin 2 (also known as FERMT2), which is also expressed in the epidermis, colocalizes with epithelial cadherin (E-cadherin; also known as cadherin 1) at intercellular contacts35 and is required for motility and intercellular adhesion in keratinocytes42. The potential function of kindlin 2 in epidermal integrity and morphogenesis remains unexplored.
Serum response factor promotes differentiation
During stratification, basal keratinocytes produce suprabasal cells that no longer have cell–matrix adhesions, a process that completely alters cell polarity and cytoskeletal architecture7,43. In isolated keratinocytes, actin associates with integrin-based adhesions, but then assembles into a robust cortical actin ring during stratification in vitro44–46. Moreover, manipulating the area or shape of keratinocyte adhesion on micropatterned substrates coated with ECM molecules affects their differentiation47, and this effect is not altered by the ECM component used.
Serum response factor (SRF) signalling has been proposed to provide a potential mechanotransduction mechanism that may explain this shape-dependent effect47. SRF drives transcription with its cofactor MAL (also known as MRTF), which can be bound and sequestered by globular actin (G-actin)48. When substratum area is restricted, G-actin levels decrease, allowing SRF–MAL to activate transcription and initiate differentiation47. This provides a key example of the inverse relationship between substrate adhesion and differentiation, and should spark further investigation of how mechanical signalling and stratification-associated cell shape changes directly regulate differentiation.
In vivo, targeted ablation of SRF causes epidermal hyperproliferation accompanied by defects in actin organization, reduced adhesion through desmosomes and hemidesmosomes, and disrupted compaction of the epidermal layers49. Others have found that deletion of SRF in epidermis correlates with transcriptional downregulation of both actin and its regulators and blocks cortical enrichment of actin and myosin IIA during keratinocyte mitosis50. These cortical cytoskeletal defects disrupt the apical polarity complex in basal cells, causing aberrant orientation of mitotic spindles and disorganized epidermal architecture. Together, these studies suggest an intriguing model in which substratum adhesion and actin can directly influence SRF signalling to regulate epidermal morphogenesis. This signalling network may offer a new treatment avenue for cutaneous diseases characterized by aberrant morphology and differentiation. For example, levels of SRF and its target gene, JUNB, are reduced in psoriasis51,52, and this pathway may be a relevant therapeutic target.
Adherens junctions, actin and polarity
Moving upwards from the basement membrane, cad-herin-based junctions, including adherens junctions and desmosomes, are first assembled in the lateral region between basal keratinocytes (FIG. 1). Gap junctions in the epidermis allow direct cytoplasmic communication between keratinocytes and are implicated in epidermal morphogenesis and disease (BOX 1, TABLE 1 and Supplementary information S1 (table); for excellent review articles, see REFS 53,54). Differences in the type or levels of cadherins are crucial for epithelial morphogenesis because they allow cells to be sorted into discrete epithelial layers55,56. Epidermal adherens junctions are composed of the classic cadherins — E-cadherin and placental cadherin (P-cadherin; also known as cadherin 3) — both of which are important for skin morphogenesis: targeted ablation of E-cadherin causes hyperproliferation, defective differentiation and impaired barrier formation with loosening of tight junctions57–59, whereas depletion of both E- and P-cadherin results in lethal blistering60. E-cadherin loss can disrupt morphogenesis without overt loss of integrity, suggesting additional roles beyond adhesion. In fact, the cytoplasmic domains of classic cadherins interact with various signalling-competent partners, including p120 catenin and β-catenin, the latter of which associates with α-catenin (also known as αE-catenin), an actin-binding protein61 (BOX 1). However, adherens junction components affect not only adhesion but also epidermal polarity, stratification and inflammatory signalling.
Intercellular junctions of the epidermis.
Tight junctions form a belt at the apical side of keratinocytes of the stratum granulosum, providing an additional barrier beneath the stratum corneum that controls fluid loss and protects against pathogens. They consist of the transmembrane proteins claudins, occludins and junctional adhesion molecules and are scaffolded by the cytoplasmic zonula occludens (ZO) proteins ZO1, ZO2 and ZO3. These ZO proteins also link these junctions with the actin cytoskeleton134.
Adherens junctions are intercellular connections that coordinate the assembly and organization of the cortical actin cytoskeleton throughout the epidermis. Classic cadherins (such as epithelial (E)-cadherin and placental (P)-cadherin) make up the adhesive core of the junctions through homophilic interactions mediated by characteristic extracellular homology domains, the conformation of which is regulated by calcium. Their cytoplasmic tails recruit p120 catenin and β-catenin (β-cat), which bind directly to cadherins via armadillo repeat domains, and α-catenin, which is linked to the cadherin complex by β-catenin. α-catenin (α-cat) associates with actin and coordinates the activity of actin nucleating proteins at the cell cortex to regulate assembly of the adherens junction plaque61. The plaque is reinforced by additional actin binding partners such as vinculin and α-actinin.
Desmosomes are a third class of intercellular adhesions; in contrast to adherens junctions, desmosomes link to the intracellular network of keratin intermediate filaments. In a similar way to adherens junctions, desmosomes from neighbouring cells are connected by members of the cadherin family, called desmogleins (DSGs) and desmocollins (DSCs). In contrast to the classic cadherins of adherens junctions, DSGs have unique extended cytoplasmic tails, the functions of which are yet to be fully elucidated. Plakoglobin (PG) and plakophilins (PKPs) are homologous to β-catenin and p120 catenin, respectively, and bind to desmosomal cadherins via armadillo repeat domains and amino-terminal head domains, respectively. PG and PKPs also bind desmoplakin (DP), a plakin family protein that tethers keratin intermediate filaments to the desmosomal plaque. The exact nature of DSG and DSC complexes has yet to be defined in situ; however, both homophilic and heterophilic interactions have been reported188–190.
Gap junctions are unique in their ability to provide a direct connection between neighbouring cells. Gap junctions are formed by connexons, which are composed of oligomers of six connexins (CXs); in the skin, these include CX26, CX43, CX30, CX30.3 and CX31 (also known as GJB2, GJA1, GJB6, GJB4 and GJB3, respectively)53. These connexons can join heterotypically or homotypically to form an open channel, allowing for the transport of ions and other small molecules that aid in signal transmission between cells.
Cell adhesion is essential for keratinocyte polarity
Although the embryonic epidermis begins as a single layer, around embryonic day 12.5 keratinocytes undergo stratification to establish the multiple layers needed for an environmental barrier3,62. This vertical expansion has been suggested to occur through reorientation of mitotic spindles in the basal layer63. While a horizontal axis of division (parallel to the basement membrane) produces two basal cells, vertical mitotic spindles allow stratification by production of one daughter cell that occupies the suprabasal compartment (FIG. 3a). A complex of the polarity protein partitioning defective 3 (PAR3), mouse inscuteable (MINSC) and LGN is recruited to the apical region of basal cells undergoing mitosis63 (FIG. 3b). The PAR3–MINSC–LGN complex also associates with nuclear mitotic apparatus protein 1 (NUMA1), a regulator of the mitotic spindle, and dynactin, a microtubule motor-associated protein, suggesting a mechanism by which this polarity complex could directly facilitate spindle reorientation to promote asymmetric division64,65. In fact, LGN, NUMA1 and dynactin are all essential for proper spindle positioning and asymmetric cell division during epidermal stratification64. Moreover, compromising these apical polarity complex components disrupts Notch signalling, which is a critical driver of differentiation in the suprabasal compartment64.
Figure 3. Mitotic spindle orientation directs stratification.
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Keratinocytes of the stratum basale provide the regenerative capacity of the epidermis. a | Basal cells use symmetric cell division to promote lateral expansion of the epidermis and undergo asymmetric cell division to enable vertical expansion through the production of differentiated keratinocytes. The direction of expansion is thought to depend on the orientation of the mitotic spindle: spindles that lie parallel to the basement membrane favour symmetric division, whereas spindles perpendicular to the basement membrane promote asymmetric division. b | Asymmetric cell division depends on apical polarity factors, including the partitioning defective 3 (PAR3)–mouse inscuteable (MINSC)–LGN complex, which interacts with nuclear mitotic apparatus protein 1 (NUMA1) and dynactin to regulate spindle orientation63,65. The adherens junction component α-catenin is thought to recruit this complex via merlin, which links α-catenin and PAR3 (REF. 75). Through knockout studies, p120 catenin and β1 integrin have also been shown to have a role in mitotic spindle orientation63,70. The roles of these factors in regulating mitotic spindle pole orientation and subsequent division, including the precise location of complexes within basal cells, are yet to be fully elucidated.
Cellular junctions have a polarized organization in basal keratinocytes and contribute to mitotic spindle orientation during stratification66 (FIG. 3b). Mice lacking β1 integrin fail to recruit the polarity complex to the apex of dividing keratinocytes and have randomized mitotic axes63. Likewise, in epidermis lacking α-catenin, spindle poles are randomly aligned, and this correlates with loss of polarity, the presence of suprabasal mitoses and a propensity to develop carcinomas67,68. Surprisingly, epidermal deletion of another adherens junction component, p120 catenin, does not affect adhesion69. However, loss of p120 catenin impairs cytokinesis and produces binucleate cells in the suprabasal layers, probably owing to impaired mitosis70. p120 catenin regulates RHO signalling, which directly affects actin organization44,71,72, and this may explain how p120 catenin might mechanically orient mitotic spindles.
How do epithelial cells integrate the formation of adhesive junctions and the establishment of cellular polarity? Depletion of the adherens junction component E-cadherin disrupts localization of atypical protein kinase C (aPKC), which is a crucial regulator of cell polarity73, in the upper epidermis59; this suggests that E-cadherin might recruit aPKC to adhesive complexes in the suprabasal layers. Although asymmetric divisions in the basal layer depend on α-catenin63, exactly how adherens junctions associate with the PAR3–MINSC–LGN polarity complex had been unclear. The FERM (4.1 protein, ezrin, radixin, moesin) domain protein merlin, which localizes to adherens junctions and promotes their formation74, may have such a role75. In mitotic basal keratinocytes, merlin binds both PAR3 and α-catenin and is required for their association75. Accordingly, epidermal loss of merlin results in impaired basal cell polarity, randomized mitotic spindle orientation and a disrupted epidermal barrier owing to faulty tight junctions. Thus, through its association with adherens junctions, merlin promotes assembly of the apical polarity complex to orientate cell division during epidermal morphogenesis.
Although apical–basal polarity is essential for stratification of the interfollicular epidermis, keratinocytes also exhibit planar cell polarity, which allows coordinated movement of cells within an epithelial sheet76. Signalling proteins in the planar cell polarity pathway, including the frizzled 6 (FZD6) receptor and its effectors VANGL2 and CELSR1 are required for cell patterning across the surface of the skin, which drives the orientation of hair follicles and allows the repair of epidermal wounds in mice77,78. Whether junctional or cytoskeletal components in basal cells affect signalling via planar cell polarity proteins to regulate epidermal wound healing or morphogenesis remains to be determined.
Actin dynamics during keratinocyte stratification
Whereas actin filaments are highly associated with cell–matrix junctions in undifferentiated keratinocytes, actin in differentiating keratinocytes becomes coupled to intercellular junctions44,46,79. During keratinocyte stratification in vitro, cadherin–catenin complexes at adherens junctions are linked into a cortical ring of bundled microfilaments, which effectively couples the actin cytoskeletons of neighbouring cells80. Through association with motor proteins such as myosin, these actin-linked adhesions are thought to generate the tension required for a keratinocyte to move over a neighbouring cell44,46. Other in vitro studies have revealed that the RHO actin modulators and their effectors, RHO-associated protein kinase 1 (ROCK1) and ROCK2, are required for keratinocyte stratification and differentiation46,81. RHOE, in particular, directly promotes keratinocyte stratification82. Moreover, ROCK1 and ROCK2 have opposing roles in balancing the trade-off between matrix adhesion and differentiation83. Given the identification of SRF as an actin-regulated transcription factor that is crucial for skin morphogenesis47,49,50, it will be important to identify how these actin regulatory proteins might couple the mechanical signalling pathways driving acto-myosin contraction during stratification to the nuclear transcriptional events that initiate differentiation.
Catenin control of epidermal inflammation
In addition to their traditional roles in adhesion, adherens junction components regulate inflammatory signalling in the epidermis84. Epidermal deletion of α-catenin produces hyperproliferation in mouse skin grafts, and this depends on elevated mitogenic MAPK signalling68,85. Moreover, α-catenin deficiency also disrupts keratinocyte polarity and promotes epidermal tumour formation through p53-mediated apoptotic signalling68,86. Although impaired adhesion might have been assumed to be a primary trigger for carcinogenesis, nuclear factor-κB (NF-κB) signalling is markedly dysregulated in α-catenin-null tumours. Elevated NF-κB activity is also observed in keratinocytes lacking α-catenin that are cultured in low calcium (without robust intercellular adhesion), suggesting that loss of α-catenin causes an intrinsic signalling defect that not secondary to tissue infiltration by immune cells or loss of adhesion. p120 catenin similarly affects inflammatory signalling in the epidermis69. Epidermal deletion of p120 catenin results in increased RHOA activity, but also aberrantly upregulates NF-κB signalling. As a result, p120 catenin loss in the skin results in hyperproliferation and increased MAPK signalling with prominent dermal inflammation. p120 catenin loss also leads to increased epidermal tumour formation70. Interestingly, the ability of p120 catenin to regulate NF-κB signalling is independent of its ability to bind and stabilize E-cadherin, again implying a supra-adhesive function. Together, these studies show that rather than simply ensuring epidermal integrity, α-catenin and p120 catenin have unappreciated roles in suppressing an inflammatory cascade that promotes tumorigenesis.
Diverse roles for desmosomes and keratins
Although desmosomes are present in basal keratinocytes, stratification induces a marked increase in the concentration of these adhesive structures87 and also reorganizes their associated cytoskeletal elements88. Desmosomes are built from clustered transmembrane cadherins called desmogleins (DSGs) and desmocollins (DSCs). These bind to plakoglobin (PG) and plakophilins (PKPs), which are members of the intracellular armadillo protein family. In turn, this binding recruits the cytolinker desmoplakin (DP), which binds keratin intermediate filaments89 (BOX 1). Through this chain of interactions, desmosomal components directly link intercellular junctions and the intermediate filament cytoskeleton that fills the cytoplasm and surrounds the nucleus. Epidermal differentiation induces dramatic changes in desmosomal cadherin expression and the partitioning of PKPs between the nucleus and cell junctions. Suprabasal keratinocytes also change their complement of keratins88, which have roles in the regulation of cellular growth and metabolism addition to supporting the cytoarchitecture of the epidermis90,91. Desmosomal proteins also have supra-adhesive effects in the epidermis, including effects on microtubule reorganization during differentiation.
Desmosomal cadherins regulate differentiation
Desmosomes in vivo are tightly adherent and exhibit property called hyperadhesion, reflecting an insensitivity to extracellular calcium92. However, these intercellular rivets can also revert to a more plastic state during wound healing through PKC activity93. In fact, PKC may govern desmosome stability by regulating interactions with keratin, as mutation of a PKC consensus site in DP increases affinity for intermediate filaments and promotes hyperadhesion in vitro191. The complement of desmosomal components is extensively modified as keratinocytes their dynamic nature89,94 (FIG. 1). For example, DSG2 is normally restricted to low expression in the proliferative basal layer, but becomes upregulated in epidermal carcinomas95,96. Increased PG, PKP1 and DP in the suprabasal layers is accompanied by upregulation of specific cadherins, beginning with DSG1 expressed as cells emerge from the basal layer, along with DSC1 in the spinous layers and DSG4 in the granular layers96–98.
In addition to maintaining epidermal integrity, the regulated expression of these desmosomal components is crucial for altering keratinocyte morphology and signalling to drive epidermal morphogenesis89,99,100. In particular, desmosomal cadherins modulate intracellular signalling and control differentiation101–105. Ectopic expression of DSG2 in the mouse suprabasal epidermis augments various signalling pathways downstream of EGFR, resulting in suppressed differentiation, impaired apoptosis and pre-malignant papillomas106. In contrast to DSG2, DSG1 expression increases as EGFR activity is downregulated (FIG. 1). DSG1 is essential for suppressing EGFR signalling to MAPKs to allow differentiation in organotypic epidermis107. DSG1 can promote differentiation independently of a functional adhesive ectodomain, implying an adhesion-independent effect. Together, these data suggest that desmosomal cadherins might exert opposing roles in keratinocyte signalling, perhaps promoting the switch from proliferation to differentiation upon stratification. This is further supported by other in vivo models that show altered epidermal morphogenesis and homeostasis upon deletion or aberrant expression of desmosomal cadherins89,99.
The expanding role of epidermal keratins
The epidermis provides an excellent demonstration of the diverse functions of various keratin isoforms, the expression of which is highly regulated in this tissue. Although keratins are crucial in hair follicles108, here we focus on their importance in the interfollicular epidermis, which has been underscored by mutations that result in diseases ranging from hyperthickened palms and soles (mutations in keratin 1 (K1), K2e, K6, K9 or K10) to lethal blistering (K5 or K14 mutation)109,110. Other epidermal roles of keratins include regulation of signalling, growth and apoptosis90,91.
In epidermal keratinocytes, intermediate filaments fill the cytoplasm and mechanically connect hemidesmosomes at the basement membrane and desmosomes at the lateral membrane to the cell nucleus. The intermediate-filament-associated protein plectin binds α6β4 integrin at hemidesmosomes but also associates with nesprin 3, a protein embedded in the outer nuclear membrane111 (FIG. 2). Nesprin 2 regulates tissue thickness and nuclear morphology in the epidermis112. Thus, a desmosome–nesprin connection could provide a unique mechanosensory apparatus in keratinocytes, allowing mechanical forces perceived at the periphery to directly influence nuclear activity during epidermal morphogenesis. It has also been hypothesized that the regulation of cytoplasmic viscosity by specific keratin expression might regulate keratinocyte mobility, for example during stratification or wound healing90,113. Supporting this model, K6 and K16 are upregulated in basal cells as they seal cutaneous wounds, and they probably contribute to the migration of these cells114.
Keratinocytes flatten as they move upwards in the epithelium, and keratins are thought to contribute to the morphological transformation of these cells through their intrinsic bundling properties, their association with filaggrin and their crosslinking to desmosomes and cornified envelopes2,115. In the suprabasal compartment, expression of K5 and K14 is replaced by expression of K1 and K10, along with K9 in the palms and soles88,110. Mice lacking K10 exhibit larger-than-normal suprabasal keratinocytes and defective flattening116. Loss of K10 in the epidermis also triggers hyperproliferation with aberrant activation of MAPKs and the signalling scaffold protein 14-3-3σ117.
Keratins may directly control cell size through the regulation of metabolic signalling. Deletion of K17, which is normally expressed only in activated epidermis (for example, during wounding or in psoriasis), reduces keratinocyte size118. Loss of K17 also diminishes total protein synthesis through AKT and mammalian target of rapamycin (mTOR) signalling; this function of K17 depends on its association with cytosolic 14-3-3σ to inhibit its nuclear translocation. Keratins can also interact with the protein translation apparatus, including ribosomes, which suggests that the regulated expression of keratins may modulate global protein synthesis to allow proper evolution of cell morphology in complex tissues such as the epidermis90. Further support for keratins regulating cellular metabolism is found in mice lacking all keratin genes, in which lethal growth defects are associated with mislocalization of glucose transporters, resulting in AMP kinase activation and downregulation of mTOR targets119. In addition, drug treatment that mimics oxidative stress modulates expression of K16 and K17, suggesting that keratin expression can be dynamically regulated in response to environmental stimuli120.
An immunomodulatory role for specific keratins is supported by the recent demonstration of increased recruitment of Langerhans cells to the epidermis of mice and human patients harbouring mutations in K5 but not K14 (REF. 121). K17-null cells also show increased sensitivity to tumour necrosis factor (TNF; also known as TNFα) in vitro, suggesting that it affects susceptibility to apoptosis122. Moreover, K17 potentiates chronic proinflammatory signalling in the epidermis, which leads to basal cell carcinoma formation and may also contribute to psoriasis123. Furthermore, the keratin cytoskeleton collapses in epidermal blistering diseases such as pemphigus, which is induced by auto-antibodies against desmosomal cadherins124. One intriguing possibility is that this collapse contributes to the aberrant signalling that occurs in response to pathogenic antibodies in pemphigus125, but this effect might also arise from altered mechanics of the cytoplasm, allowing increased nuclear import. Moreover, the phenotypic manifestations of skin diseases targeting desmosome components and keratins, which can be limited to areas of high stress, such as palms and soles126, could perhaps be explained by altered mechanotransduction between desmosomes, keratin and the nucleus. Accordingly, the mutations in K5 and K14 that cause severe skin blistering also downregulate transcription of cell junction components both in cells from patients and in normal keratinocytes transfected with mutant keratins127.
Desmosomal crosstalk with microtubules and actin
During epidermal differentiation, microtubules are substantially restructured128. Although there is a normal astral array of tubulin filaments emanating from a perinuclear centrosome in basal cells, microtubules concentrate at the cortical region of suprabasal cells and colocalize with intercellular junctions (FIG. 4). A connection between adherens junctions and microtubule dynamics has been demonstrated129. More recently, the desmosome protein DP has been found to be required for microtubule reorganization in suprabasal mouse keratinocytes128. Here, DP colocalizes at intercellular junctions with ninein (a microtubule-anchoring protein that is normally found in the centrosome130), which may recruit and/or anchor microtubules to desmosomes. Interestingly, microtubule organization by DP does not require its interaction with intermediate filaments128.
Figure 4. Desmoplakin regulates microtubule reorganization in the stratified epidermis.
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Whereas keratinocytes of the stratum basale have an astral array of microtubules emanating from perinuclear centrosomes, microtubules in suprabasal keratinocytes reorganize to lie parallel with cell borders. This reorganization depends on ninein, a protein that localizes to centrosomes but is recruited to desmosomes in suprabasal keratinocytes through association with desmoplakin128.
Desmosomal components are also functionally linked to the actin cytoskeleton. In fact, the p120-related desmosomal protein PKP1 associates with actin and can induce filopodia formation131. In addition, PKP2 regulates RHO activity and actin organization during intercellular junction assembly in keratinocytes132. Actin reorganization and reduced activity of RHOA have been suggested to underlie the pathogenesis of pemphigus133, which may imply that links between desmosomal adhesion and the actin cytoskeleton are essential for supporting epidermal integrity in vivo.
These studies have revealed that although desmosomes have been traditionally associated with intermediate filaments, they more broadly regulate actin and microtubules in epidermal keratinocytes.
Tight junctions in the epidermis
As keratinocytes move into the granular layers, tight junctions help to promote an environmental barrier134. Tight junctions seal multicellular sheets by forming belt-like adhesion between cells, allowing the passage of only small molecules and ions135. Several families of transmembrane proteins contribute to tight junctions, including claudins, junctional adhesion molecules, occludins and tricellulin, an occludin-like protein found at tricellular intersections134 (BOX 1). Intracellular tight junction components include scaffolding proteins of the zonula occludens (ZO) family, which cluster transmembrane proteins and allow coupling to actin. In simple epithelial layers, tight junctions reside at the apical region of polarized cells. However, in the epidermis, although claudins are expressed in lower cell layers, functional tight junctions only form in the granular layers. This appears to be driven by differentiation-dependent expression of ZO proteins136 and relies on E-cadherin, which is needed for the localization of claudins and ZO1 in the granular layers59. Here, we discuss how tight junctions allow the simultaneous functioning of the epidermis as both an environmental shield and as a site where external antigens are ‘sampled’ by immune cells.
Tight junctions provide an epidermal barrier
In the epidermis, the regulated expression of multiple claudin genes is thought to ‘tailor’ barrier selectivity134,137. The first in vivo evidence demonstrating that tight junctions are essential for epidermal barrier function came from mice lacking claudin 1 (REF. 138), which die shortly after birth owing to profound trans-epidermal water loss (TEWL). A human gastrointestinal syndrome associated with epidermal scaling (ichthyosis) was subsequently linked to mutations in claudin 1 (REF. 139). In other animal models, ectopic expression of claudin 6 in the suprabasal compartment results in a dose-dependent defect in epidermal barrier function, suggesting that perturbing the ratio claudins in the epidermis can disrupt epidermal morphogenesis140. It has been suggested that the unique roles different claudins (for example, in intracellular signalling) may result from their divergent cytoplasmic tails. support of this, ectopic expression of claudin 6 mutants lacking a full cytoplasmic tail resulted in epidermal hyperproliferation and lethal skin barrier dysfunction age-related dermatitis and increased TEWL, depending on the extent of the deletion141,142.
Dynamic tight junctions permit immune sampling
The epidermis is also a site of active immune surveillance abundant antigen-presenting cells143. Langerhans cells, particular, reside within the lower epidermis, but their cytoplasmic projections form an extensive network that permeates the upper layers despite the presence of tight junctions (FIG. 5).
Figure 5. Tight junction dynamics during antigen sampling.
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Tight junctions contribute to the barrier between the superficial epidermis and underlying stratum spinosum but must also be dynamic to allow antigen sampling. In the resting state, Langerhans cells reside among keratinocytes in the stratum spinosum and extend dendrites through suprabasal layers. When activated, for instance by disruption of the stratum corneum or by infiltration of antigens, the dendrites of Langerhans cells dock with tight junctions and gain the ability to extend into the stratum corneum. The transmembrane protein tricellulin localizes to these tricellular tight junctions formed between keratinocytes and Langerhans cells. This dynamic adjustment of tight junctions allows Langerhans cells to internalize antigens, which can then be presented to the host immune system144.
Advances in three-dimensional imaging have revealed the mechanism by which the epidermis allows antigen sampling but preserves the cutaneous barrier144: Langerhans cells form tight junctions with keratinocytes in the epidermis, and tight junctions undergo an intricate reorganization to permit epidermal antigen surveillance. This local rearrangement allows dendritic processes Langerhans cells to sample for antigens beyond the interkeratinocyte tight junction, but the overall epidermal barrier is maintained by unique tricellular tight junctions between two adjacent keratinocytes and a penetrating Langerhans cell. Indeed, Langerhans cells express claudin 1 and ZO1 at their cell membranes, which permits the formation of tight junctions between their dendrites and granular layer keratinocytes.
The upper tips of the Langerhans cell projections also act as endocytic sites for antigen uptake into Birbeck granules, which allows the processing and presentation of external antigens to the host immune system144. Thus, this study has revealed the dynamic nature of tight junctions and the essential role that their reorganization has in immune surveillance. The signalling pathways that drive this reorganization remain unknown but might underlie cutaneous pathologies, such as atopic dermatitis, that are caused by impaired barrier function and enhanced antigen uptake145. Intriguingly, tight junction organization is altered early in the development of psoriatic epidermal lesions146. Further investigation is likely to improve our understanding of the role that tight junctions have in other skin diseases caused by, or resulting in, defective barrier function and chronic inflammation.
Filaggrin in barrier function
In addition to tight junctions, another key morphological feature of the granular layer is the keratohyalin granule, a multiprotein complex that is mostly composed of profilaggrin147. Profilaggrin consists of 10 to 12 repeated units and is cleaved to generate mature filaggrin, which binds to and promotes the aggregation of intermediate filaments in the upper layers. Thus, filaggrin helps to stabilize the keratin network, which serves as a crucial scaffold for other components of the cornified envelope2. In vitro studies suggest that filaggrin may also promote collapse of the intermediate filament cytoskeleton during later stages of differentiation, which might facilitate cell compaction in the upper epidermis148. This structural protein also helps to maintain the cutaneous barrier. Genetic studies have confirmed that mutation of the filaggrin gene underlies the scaly skin phenotype seen in ichthyosis vulgaris and is a major risk factor for atopic dermatitis (eczema), a prevalent condition characterized by cutaneous inflammation149–151. Mice harbouring a mutation in the filaggrin gene have increased immunological response to topical antigens, indicating a defective cutaneous barrier152. Furthermore, filaggrin processing affects skin hydration: mice lacking a protease that cleaves profilaggrin have a dehydrated stratum corneum153. Moreover, mutations in this protease are found in certain patients with atopic dermatitis, which may explain the chronic dry skin typical of this disease. These studies have provided crucial advances in our understanding of the pathogenesis of atopic dermatitis and may have further implications for the treatment of common related diseases such as asthma, hay fever and even food allergies147,154,155.
Cornified envelopes and corneodesmosomes
As keratinocytes progress towards their ultimate destination in the upper epidermis, they undergo a unique process of cell death termed cornification, which is distinct from apoptosis2. Cornification involves biochemical crosslinking of various keratinocyte proteins such as loricrin and involucrin by transglutaminases (TGases), but it eventually terminates with nuclei and organelles being broken down by intracellular and secreted proteases, including a specialized caspase156,157. However, before dying, these keratinocytes produce specialized proteins and lipids to construct the cornified envelope, which is a heavily crosslinked submembranous sheath that provides structure to the upper epidermis and acts as a water-impermeable barrier2. In this barrier, desmosomal components are crosslinked to the cornified envelope to form corneodesmosomes, which bind cornified cells together and are essential for barrier formation158. However, these linkages must be reversed to allow shedding of cornified cells (desquamation) during normal epidermal turnover159,160.
The cornified envelope promotes barrier function
Crosslinking of involucrin and loricrin by TGase 1 promotes their incorporation into a submembranous matrix of tightly knit proteins formed by keratin filaments and filaggrin in the granular layer2. TGase 1 is upregulated in the upper layers and is essential for epidermal barrier function in vivo161,162. In addition to these components, specialized plakin proteins, called envoplakin and periplakin, and the secreted desmosomal protein corneodesmosin (CDSN) are incorporated into the cornified envelope2,163,164. Envoplakin and periplakin are intermediate- filament-binding proteins that localize to desmosomes in the upper layers, where they are thought to integrate the keratin cytoskeletons of the stratum corneum165,166.
Surprisingly, deletion of individual components of the cornified envelope, such as loricrin, involucrin, periplakin and envoplakin, produce minor phenotypes, suggesting that these constituents can compensate for one another in barrier function167–170. In a more aggressive approach, a triple-knockout mouse lacking periplakin, envoplakin and involucrin shows barrier dysfunction and impaired desquamation of the cornified layers, probably owing to the faulty processing and aberrant retention of corneodesmosomes in addition to defective degradation of DSG1 during desquamation171. Mutations in cornified envelope components may contribute to genetic susceptibility to chronic barrier defects, as in atopic dermatitis172,173.
Corneodesmosomes in barrier formation and desquamation
Corneodesmosomes contain the cadherins DSG1 and DSC1, which must be cleaved by serine proteases to allow proper shedding of the outer epidermis160. In fact, deficiency of SPINK5 (also known as LEKT1), a serine protease inhibitor, results in weakened adhesion in the cornified layers, premature desquamation and defective barrier function in mice160. SPINK5 mutations have also been linked to Netherton syndrome, a human disease of similar phenotype174.
CDSN is an essential component of corneodesmosomes that is secreted in the upper granular layers during the final stages of differentiation164. It is thought to function as intercellular ‘glue’ that helps to solidify the linkage of desmosomal cadherin ectodomains between keratinocytes in the stratum corneum, but it may have inherent adhesive properties175. CDSN is also thought to be essential for desquamation176. Its targeted ablation in the epidermis results in death shortly after birth owing to sloughing of the outer epidermal layers, accompanied the appearance of split corneodesmosomes177. In humans, mutations in CDSN cause chronic skin inflammation and peeling owing to defective epidermal desquamation and cutaneous barrier dysfunction178 and can also associated with congenital hair loss179.
Thus, the structural linkages that form in cornified keratinocytes are dynamic and must undergo a finely tuned cycle of aggregation and desquamation in precise balance with basal cell proliferation to simultaneously preserve epidermal homeostasis and provide environmental barrier.
Conclusions
In this Review we have traced the journey of the keratinocyte as it progresses outwards through the epidermal layers, a process that is paralleled by key alterations adhesive junctions and their associated cytoskeletal elements. These cytoarchitectural elements are far from passive scaffolds — they actively cooperate with transcriptional and translational pathways to establish cell and tissue polarity, guide differentiation and regulate cutaneous responses to environmental insults and pathogens. For instance, stratification-associated alterations integrin- and cadherin-based adhesions are important for balancing proliferation and differentiation. Although tight junctions are crucial for preventing water loss, their remodelling also has an active role in antigen sampling. The proper construction of corneodesmosomes makes essential contribution to the skin barrier, but their timely breakdown is necessary for normal epidermal turnover. Our increased understanding of these processes has turn provided insights into the dysfunction of adhesive and cytoskeletal proteins that leads to epidermal pathology in humans and has suggested potential therapeutic avenues for cutaneous disease.
However, many questions remain about the detailed mechanisms by which cytoskeletal and adhesive proteins directly contribute to epidermal morphogenesis and disease. These mechanisms are likely to hinge on interconnections between keratinocytes and the cytoskeletal scaffolding that connects the cell surface with the nucleus. This scaffold could contribute to various functions ranging from mechanosensing to regulation of the diffusion or nuclear import of signalling proteins180. Differentiation-dependent remodelling of this scaffold could coordinate changes in morphology with altered signalling and transcription. Moreover, the ability of adhesive junctions to interconnect the cells of the epidermis may regulate communication among layers and allow coordinated responses to pathogenic insults or mechanical strain. It has been suggested that the meshwork of interlaced cytoskeletons that fill the cytoplasm may globally regulate cell plasticity and signalling during dynamic processes such as tissue stratification or cell migration90,113,181. However, we still have much to learn about the specific contributions of epidermal cytoskeletal elements. For instance, the significance of microtubule redistribution during stratification128 is completely unknown. In addition, junction proteins themselves, including catenins, PKPs and even cadherin fragments, can enter the nucleus and affect transcription182,183. This dual localization at junctions and in transcriptional complexes places these versatile proteins in a prime position to orchestrate alterations in adhesion with changes in signalling during epidermal morphogenesis. In fact, PKP1 can control cell size and proliferation through the regulation of protein translation184.
How are the mechanical cues borne by epidermal cytoskeletal scaffolds translated into chemical information? One can envision that signal transmission occurs through a series of molecular sensors and actuators present in cell junctions and cortical cytoskeletal attachments, and that information is communicated through alterations in protein conformation and protein–protein interactions. To illuminate exactly how these cell elements translate environmental cues, strategies will be needed that directly couple the delivery and measurement of mechanical forces with molecular probes that report how information is perceived and processed. The development of molecular fluorescent sensors is still in its infancy, but one example is a biosensor that assesses tension in the actin-binding protein vinculin, which is found in both focal contacts and adherens junctions185. This sensor has provided insights into the relationship between force transmission and junction assembly and size. Combining the use of these probes with super-resolution microscopy, intravital imaging techniques and physiologically relevant models of epidermal morphogenesis will be needed to directly assess how endogenous contractile forces or environmentally applied stress is transmitted through the epidermal cell architecture. Applications of these strategies could be used, for instance, to understand how genetic deficiencies impair the coupling of contractile forces with the differentiation programme that normally directs stratification.
Although cell biologists have for years promoted the idea that cytoarchitecture governs cell fate186,187, we still have a lot to learn about how this occurs at a molecular level. The next decade holds much promise for grappling with these complex questions. We are now in a new era of interdisciplinary cooperation, with teams bringing to bear their combined expertise in bioengineering and materials science, quantitative biology, optical imaging, cell and molecular biology. Advances resulting from these interdisciplinary teams promise to illuminate how the hard-wiring of cells transforms their behaviour and fate.
Supplementary Material
Supplemental Table
NIHMS354842-supplement-Supplemental_Table.pdf (167.6KB, pdf)
Acknowledgements
The authors would like to thank M. Amagai, J. Jones, T. Lechler and T. Magin for critical reading of the manuscript and/or advice on figures. We also apologize to our colleagues whose work we were unable to include owing to space limitations. The authors are supported by US National Institutes of Health grants AR043380, AR041836 and CA122151, the Leducq Foundation and the J.L. Mayberry Endowment to K.J.G.
Glossary
Organotypic
An in vitro reconstituted model of a tissue grown from cultured cellular elements
Filopodia
Thin, transient actin protrusions that extend out from the cell surface and are formed by the elongation of bundled actin filaments in their cores
Endocytic sites
Sites of endocytosis, which is the internalization and transport of extracellular material and plasma membrane proteins from the cell surface to intracellular organelles known as endosomes
Transglutaminases
(TGases). A family of enzymes that can catalyse covalent bond formation between a glutamine on a peptide and a free amine group
Footnotes
Competing interests statement
The authors declare no competing financial interests.
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Abstract
Adhesion at the basement membrane
Adherens junctions, actin and polarity
Diverse roles for desmosomes and keratins
Tight junctions in the epidermis
Cornified envelopes and corneodesmosomes
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Sum and sum of cubes are both perfect cubes
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I am interested in integer tuples (a 1,a 2,…,a n) with n>3, satisfying the following conditions:
Each a i∈Z∖{0};
The a i are pairwise distinct and no two are negatives of each other (i.e., a i≠−a j for i≠j);
gcd(a 1,a 2,…,a n)=1;
The sum ∑n i=1 a i is a perfect cube;
The sum of cubes ∑n i=1 a 3 i is also a perfect cube.
Is there a known structural characterization or parametrization of such tuples?
nt.number-theory
diophantine-equations
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edited May 3 at 15:36
Ali Taghavi
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asked May 3 at 12:31
Tien DinhTien Dinh
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3 (t+1)3+(−t)3+(−t)3+(t−1)3=6 t, so taking t=36 z 3 the four nonzero integers t+1,−t,−t,t−1 sum to the perfect cube zero, and their cubes sum to the perfect cube 216 z 3. But this fails to meet the condition that the a i be pairwise distinct.Gerry Myerson –Gerry Myerson 2025-05-04 01:02:51 +00:00 Commented May 4 at 1:02
2 Some brute force results: (−7,1,5,9), (−8,−7,5,9), (−3,7,11,12), (−7,−5,−1,13), (−6,2,3,4,5), (−6,−3,−2,−1,5,7), (−8,−4,−2,−1,3,6,7), (−7,−5,−4,−2,1,3,6,8), (−10,−9,−5,−4,1,3,6,7,11), ...მამუკა ჯიბლაძე –მამუკა ჯიბლაძე 2025-05-04 03:31:27 +00:00 Commented May 4 at 3:31
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We need for (n=6) terms:
(p+q+r+s+t+u)=m 3 ----------------(1)
(p 3+q 3+r 3+s 3+t 3+u 3)=n 3 -------(2)
Below is the parametric solution for (1) & (2):
p=(3 x 6+3 x 3 y 3−y 6)
q=(3 x 6−3 x 3 y 3+y 6)
r=−(3 x 6−3 x 3 y 3−y 6)
s=(6 x 3 y 3)
t=−(3 x 6+3 x 3 y 3+y 6)
u=(2 x 3 y 3)
m=(2 x y)3
n=(2 x 3 y 3)
For, (x,y)=(3,2), we get:
(p,q,r,s,t,u)=(2771,1603,−1475,1296,−2899,432)
And,
(m,n)=(12,432)
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edited May 11 at 13:36
answered May 10 at 21:25
DavidDavid
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@Tien Dieh. I have added solutions for terms, n=7 & 9 in my below answer.David –David 2025-05-15 19:55:47 +00:00 Commented May 15 at 19:55
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I don't know whether one can get a parametrization that captures all solutions, but here's a formula that gives infinitely many; take n=4, and the numbers t−4, 3−t, 1−t, and t. The numbers sum to the cube zero, and their cubes sum to 18 t−36. If t=12 z 3+2, then 18 t−36=216 z 3 is a cube.
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answered May 4 at 1:21
Gerry MyersonGerry Myerson
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1 We can generalise this to understand solutions when x,y,−z,−w with x+y=z+w is a solution: we have x 3+y 3−z 3−w 3=(x+y)(z−x)(y−z) and parametrizing when the product of 3 numbers is a cube is easy.Random –Random 2025-05-04 05:27:51 +00:00 Commented May 4 at 5:27
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There is a full description for n=6, see On some cubic equations. The main idea is the following. The system x 1+x 2+x 3=y 1+y 2+y 3,x 3 1+x 3 2+x 3 3=y 3 1+y 3 2+y 3 3. in terms of a j=x j−y j,b j=x j+y j, (j=1,2,3) can be rewritten in the form a 1+a 2+a 3=0,a 1 b 2 1+a 2 b 2 2+a 3 b 2 3+a 1 a 2 a 3=0, or a 1+a 2+a 3=0,|a 1 b 3−b 2−b 3 a 2 b 1 b 2−b 1 a 3|=0. To each nontrivial solution a 1,a 2,a 3,b 1,b 2,b 3 corresponds an eigenvector (d 1,d 2,d 3) such that −d 1 a 1+d 2 b 3−d 3 b 2=0,−d 1 b 3+d 2 a 2+d 3 b 1=0,−d 1 b 2−d 2 b 1+d 3 a 3=0. Solving this system with respect to a 1,a 2,a 3,b 1,b 2,b 3, we obtain the full parametrization in terms of d 1,d 2,d 3 (α,β∈Q): a 1=β(d 2 3−d 2 2),b 1=α d 1+β d 2 d 3,a 2=β(d 2 1−d 2 3),b 2=α d 2+β d 1 d 3,a 3=β(d 2 2−d 2 1),b 3=α d 3+β d 1 d 2.
Also there is a nice collection of similar problems in Dickson's Introduction To The Theory Of Numbers, see §§ 32-36 (Sets of integers having equal sums of like powers).
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answered May 4 at 10:47
Alexey UstinovAlexey Ustinov
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The case of n=5:
(t+a)+(t+b)+(−t+c)+(−t+d)+1(t+a)3+(t+b)3+(−t+c)3+(−t+d)3+1 3
Taking (a,b,c,d)=(−1,−4,2,3). Then equation (1) becomes to 1. The equation (2) becomes to 12 t−29. Taking t=144 m 3+252 m 2+147 m+31. Then equation (2) becomes to (12 m+7)3.
(144 m 3+252 m 2+147 m+30)3+(144 m 3+252 m 2+147 m+27)3+(−144 m 3−252 m 2−147 m−29)3+(−144 m 3−252 m 2−147 m−28)3+1 3=(12 m+7)3 where m is any integer.
The case of n=6:
Let (a 1,a 2,a 3,a 4,a 5,a 6)=(t+p 1,t+p 2,t+p 3,−t+p 4,−t+p 5,−t+p 6).
Taking (p 1,p 2,p 3,p 4,p 5,p 6)=(5,4,2,−1,−3,−7).
As in the case n=5, we have that the sum of a i=0 and sum of a 3 i=216(7 m+3)3.
The case of n=7:
Let (a 1,a 2,a 3,a 4,a 5,a 6,a 7)=(t+p 1,t+p 2,t+p 3,−t+p 4,−t+p 5,−t+p 6,−1).
Taking (p 1,p 2,p 3,p 4,p 5,p 6)=(5,4,2,−1,−3,−7).
As in the case n=6, we have that the sum of a i=−1 and sum of a 3 i=343(6 m+5)3.
The case of n=8:
Let (a 1,a 2,a 3,a 4,a 5,a 6,a 7,a 8)=(t+p 1,t+p 2,t+p 3,t+p 4,−t+p 5,−t+p 6,−t+p 7,−t+p 8). Taking (p 1,p 2,p 3,p 4,p 5,p 6,p 7,p 8)=(8,4,2,1,0,−3,−5,−7).
We have that the sum of a i=0 and sum of a 3 i=216 m 3.
This method would be applicable for n>8.
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edited May 5 at 7:08
answered May 4 at 4:11
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1 Thank you for your solution; it is correct. I would like to offer a suggestion: in most of your approach, you used parametric formulas to transform the sum of (a_i) into a fixed cube, such as (0), (1), etc. Is there any formula that transforms the sum (\sum a_i) into a cubic expression instead of just a fixed number? I would appreciate your insight on this.Tien Dinh –Tien Dinh 2025-05-05 02:45:40 +00:00 Commented May 5 at 2:45
1 @Tien, What is the meaning of the cubic expression? For the case of n=5,(12 m+7)3 is a polynomial expression where m is any integer.Tomita –Tomita 2025-05-05 03:21:05 +00:00 Commented May 5 at 3:21
1 Thank you for your solution; it is correct. I have a question regarding your approach. Is it possible to construct a parametrization in which both the sum and the sum of cubes can be expressed as explicit cubic expressions, such as: [ \sum a_i = (f(k))^3 \quad \text{and} \quad \sum a_i^3 = (g(k))^3, ] where ( f(k) ) and ( g(k) ) are polynomial or rational functions of a parameter (k)?Tien Dinh –Tien Dinh 2025-05-05 04:40:58 +00:00 Commented May 5 at 4:40
1 ＠Tien, I added an explicit parametric solution for n=5. Is this okay?Tomita –Tomita 2025-05-05 07:06:43 +00:00 Commented May 5 at 7:06
1 Thank you for your solution. For n=5, according to your formula, sum=1 that is a fixed cube. Is it possible to construct a parametrization in the sum=(g(k))^3 where g(k) are polynomial or rational functions of a parameter (k)?Tien Dinh –Tien Dinh 2025-05-05 12:29:03 +00:00 Commented May 5 at 12:29
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I was disappointed by all the work based on the sum being 0, so I wrote a program to try all n=4,a i>0,a i≤1000. There are a lot.
The first is 23, 19, 13, 9; sum 64 (4 3) sum of cubes 21952 (28 3).
I believe my tests show that the g c d rule, while somewhat desirable, isn't thought out enough. I believe the purpose is to eliminate tuples that are multiple of other tuples. Such a multiple only occurs when the g c d has a factor that is a cube greater than 1 (which in the range I'm trying means 8 or 27). The first tuple that isn't a multiple but has a non-one gcd is 60, 35, 25, 5; sum 125 (5 3) sum of cubes 274625 (65 3). While the sum of cubes of 12, 7, 5, 1 is 13 3, the sum is 25, which is not a cube.
I also find that the density of tuples relative to the maximum number in the tuples seems to be increasing. Further, with n=6, it quickly (a 1≤100) goes well above 1 (which is to say there are many tuples with any largest value > 51 (there might be more gaps, but I haven't seen any yet)).
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answered May 6 at 22:51
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1 Thank for your idea. I have provided general solution above, how do you think about it ?Tien Dinh –Tien Dinh 2025-05-07 11:58:43 +00:00 Commented May 7 at 11:58
2 The number of tuples with maximum value ≤X is expected (say, by Manin's conjecture) to be proportional X n−2−2/3 with the −2/3 coming from the condition that the sum is a cube and the −2 coming from the condition that the sum of cubes is a cube. So the number of tuples with maximum value =X should be roughly proportional to X−3−2/3. So indeed for n=4 it should be increasing and for n=6 it should be rapidly increasing.Will Sawin –Will Sawin 2025-05-11 18:23:34 +00:00 Commented May 11 at 18:23
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Solution
Step 1: Define auxiliary variables
Let a+b=x, then from the given identity:
a b=k(a+b)+c
we have:
a 3+b 3=x 3−3 k x 2−3 c x
which can be rewritten as:
(x−k)3=a 3+b 3+(−k)3+3(k 2+c)x
Define:
k 2+c=m 1 p and x=m 2 p 2
Then:
3 m 1 m 2=b 3 4+⋯+b 3 t
So:
(x−k)3=a 3+b 3+(−k)3+(b 4 p)3+⋯+(b t p)3
Step 2: Express a and b
From equation (1), we have:
(a−k)(b−k)=k 2+c=m 1 p
Let:
a−k=n⇒b−k=m 1 p n
Then:
a+b=2 k+n+m 1 p n=m 2 p 2
So:
k=m 2 2 p 2−m 1 2 n p−n 2
Step 3: Compute the sum S
Define:
S=(a+b)+(−k)+p(b 4+⋯+b t)
Substitute values:
S=m 2 2 p 2+(m 1 2 n+b 4+⋯+b t)p+n 2
Step 4: Define new variables
Let:
n 2=q 3
and:
m 1 2 n+b 4+⋯+b t=3 q 2
Then:
S=m 2 2 p 2+3 p q 2+q 3=(p+q)3−p 3+(m 2 2−3 q)p 2
Step 5: Condition for S to be a perfect cube
Set:
−p 3+(m 2 2−3 q)p 2=0⇒p=m 2 2−3 q
Step 6: Solve for m 1 and m 2
From (2):
m 1=[3 q 2−(b 4+⋯+b t)]2 n=[3 q 2−(b 4+⋯+b t)]4 q 3
m 2=b 3 4+⋯+b 3 t 3 m 1=b 3 4+⋯+b 3 t 12 q 3[3 q 2−(b 4+⋯+b t)]
So:
p=b 3 4+⋯+b 3 t 24 q 3[3 q 2−(b 4+⋯+b t)]−3 q
Step 7: Expression for p
Let:
b 5=c 5 b 4,…,b t=c t b 4
Then:
p=b 3 4(1+c 3 5+⋯+c 3 t)24 q 3[3 q 2−b 4(1+c 5+⋯+c t)]−3 q
Step 8: Express p in terms of d
Let:
b 4=6 d q 2
Then:
p=3 d 3 q(1+c 3 5+⋯+c 3 t)1−2 d(1+c 5+⋯+c t)−3 q
Assume:
1−2 d(1+c 5+⋯+c t)=3 q
Then:
p=d 3(1+c 3 5+⋯+c 3 t)−3 q
So:
d(1+c 5+⋯+c t)=1−3 q 2
with q odd, and choose d,c 5,…,c t such that this is satisfied.
Step 9: Compute values a 1,a 2,…,a t
From equation (), we get:
k=(p+3 q)p 2−9 q 3 p−q 3
Then:
a 1=k+n=k+2 q 3
a 2=k+m 1 p n=k+18 q 3 p
a 3=−k
b 4=6 d q 2
a 4=b 4 p, ...
a t=b t p=c t b 4 p
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answered May 5 at 12:36
Tien DinhTien Dinh
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6 I don't understand this answer (probably because it has very few words, mostly symbols). What have you achieved here?Sam Hopkins –Sam Hopkins♦ 2025-05-05 14:56:43 +00:00 Commented May 5 at 14:56
1 Is this supposed to be a generalized generating formula? If so, please demonstrate. If not, please say what it is.David G. –David G. 2025-05-07 12:59:23 +00:00 Commented May 7 at 12:59
1 I note the last sentence in step 8 appears to be: use something very similar to: use a solution to the original problem....David G. –David G. 2025-05-07 12:59:48 +00:00 Commented May 7 at 12:59
1 @DavidG. Thank for your opinions, I checked the solution and I don’t find any mistakes. If you find mistakes, I can correct and appreciate about that Tien Dinh –Tien Dinh 2025-05-07 14:43:58 +00:00 Commented May 7 at 14:43
1 What is this "solution"? It looks like it might be a generating formula for arbitrary n, but beyond that, I can't tell (please demonstrate). From the looks of it, I suspect it does not produce all possible tuples.David G. –David G. 2025-05-08 19:31:31 +00:00 Commented May 8 at 19:31
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We need to solve the simultaneous equation shown below, for five terms on the (LHS):
(a+b+c+d+e)=x 3 ------------ (1)
(a 3+b 3+c 3+d 3+e 3)=y 3 -----(2)
In his comment "OP" requested a parametric form for (a,b,c,d,e) & also for (x,y)
So we take:
a=108 p 6+30 p 4−5 p 2
b=144 p 6−24 p 4+6 p 2
c=180 p 6−30 p 4−3 p 2
d=−(216 p 6−24 p 4+4 p 2)
e=6 p 2
And,
x=(6 p 2)
y=(6 p 2)
For, p=1 we get:
(133+126+147−196+6)=(x)3=(6)3
(133,126,147,−196,6)3=(y)3=(6)3
Previously I gave solutions for terms, n=(5 & 6). Below I have shown solutions for terms, n=(7 & 9)
Seven terms:
(p,q,r,s,t,u,v)3=(m)3
(p,q,r,s,t,u,v)=(n)3
The above can be written as:
[(a+b−c),(a+c),(b+c)(−a−b−c),(c−a),(c−b),d]3=(m)3
[(a+b−c),(a+c),(b+c)(−a−b−c),(c−a),(c−b),d]=(n)3
a=12(6 x 3−1)2
b=18(4 x 3−1)2
c=36(6 x 3−1)(4 x 3−1)
d=72(10 x 3−1)
For, (x=1) we get:
(p,q,r,s,t,u,v)=(−78,840,702,−1002,240,378,648)
(m,n)=(648,12)
Nine Terms:
(a,b,c,d,e,f,g,h,w)3=(p)3
(a,b,c,d,e,f,g,h,w)=(q)3
a=(m u+n v+1)
b=(m v+n u−1)
c=−(n u−m v−1)
d=−(m v−n u−1)
e=(n v−m u−1)
f=−(m v+n u+1)
g=−(m u+n v−1)
h=(m u−n v−1)
w=(m n+u v+1)3
For, (m,n,u,v)=(5,2,4,3), we get:
(a,b,c,d,e,f,g,h,w)=(27,22,8,6,−15,−25,−24,13,12167)
(p,q)=(12167,23)
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edited May 15 at 19:54
answered May 6 at 14:23
DavidDavid
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1 Thank for your solution with n=5. Is there a general solution for any n>3?Tien Dinh –Tien Dinh 2025-05-07 08:41:36 +00:00 Commented May 7 at 8:41
@Tien Dinh. I am glad you liked my answer. Finding general solutions to Diophantine equations is a hard problem in number theory. But, there is a numerical solution for seven terms on the (LHS) of the equation. The solution is: (a,b,c,d,e,f,g)=(24150,9134,2033,-19425,-8084,-6233,-1575). And, the sum of their cubes equals, (18900)^3 & the integer sum, sums upto zero. Anyway, I wish you the best in your research.David –David 2025-05-07 18:24:44 +00:00 Commented May 7 at 18:24
@Tien Dinh. Previously, I had provided a solution for five terms. if you look below, I have provided a solution for six terms. The solution also has small integer coeficents.David –David 2025-05-10 21:30:41 +00:00 Commented May 10 at 21:30
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Is there a difference between "treble" and "triple"?
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I've been reading The Economist lately and noticed that the magazine uses both trebled and tripled. According to my dictionary, "treble" means "threefold; triple". Is there a subtle difference, not captured by the dictionary entry?
Some examples, "trebled":
The Economist’s index of non-oil commodity prices has trebled in the past decade.
The number of companies from Brazil, India, China or Russia on the Financial Times 500 list trebled in 2006-08 from 20 to 62.
That number has more than trebled since 1999.
"Tripled":
In the ten years to 2010, internet users in the developed economies just about tripled.
Intercepts of Chinese planes almost tripled last year, to 96 (see chart).
Many of the 20 leading economic performers in the OECD doubled or tripled their education spending in real terms between 1970 and 1994, yet outcomes in many countries stagnated—or went backwards.
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edited Aug 27, 2014 at 10:43
Mari-Lou A
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According to the Cambridge Corpus of American English, Americans strongly prefer triple as an adjective, noun and verb. British and Australian writers, on the other hand, seem to use both triple and treble, but with treble more frequent as a verb and triple as a noun and adjective.
Fowler distinguished between treble meaning that something had become three times as large in size, and triple meaning consisting of three parts, but that no longer seems a reliable guide, if it ever was.
(Adapted from ‘The Cambridge Guide to English Usage’)
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answered Oct 4, 2011 at 13:00
Barrie EnglandBarrie England
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Fowler is correct. And why not refer to usage in India, the world's largest English speaking country?user50736 –user50736 2013-08-28 20:28:27 +00:00 Commented Aug 28, 2013 at 20:28
As an American, the frequency of treble seems counter to what I hear. Usually, I hear treble as a noun, especially in the sporting world to mean three of something. As a verb, it would sound so foreign to me, I would insist that the speaker misspoke or the writer misspelt.demongolem –demongolem 2017-02-21 19:30:37 +00:00 Commented Feb 21, 2017 at 19:30
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I'm a British English speaker, and I think I agree with Russell: triple suggests three different things and treble suggests three the same. A triathlon would be a triple event (never a treble), but three successive wins would be a treble (rarely a triple). Analogously, a double of something would always be two the same; duple (though its rarely used outside technical contexts such as music and biology) would indicate two different things.
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answered Jan 7, 2014 at 14:11
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1 Welcome to EL&U. To agree with an existing answer, it is not necessary to add a new answer; you can upvote Russell's answer using the up icon to the left. When you have sufficient experience on the site, you will be able to leave comments.choster –choster 2014-01-07 15:01:15 +00:00 Commented Jan 7, 2014 at 15:01
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In British English usage I think Fowler is right. For example you'd talk about a 'triple sundae' (three different components) or 'triple therapy' (therapy comprising three different drugs), whereas you might say 'treble nine' for 999. Personally I wouldn't use the other word in any of those cases. To me, 'treble' is three times the same thing and 'triple' is three of different things.
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answered Jan 13, 2013 at 14:49
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If "treble" means "three times as large," I'd expect "treble 9" to mean "27."herisson –herisson 2016-09-06 19:29:40 +00:00 Commented Sep 6, 2016 at 19:29
e.g. A treble 20 in darts Ben Kane –Ben Kane 2018-01-10 17:01:21 +00:00 Commented Jan 10, 2018 at 17:01
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Well I'm not so sure about treble being used more as a verb in the UK because whenever you hear a British sports commentator, they say: "This team/player did the treble last year" meaning he won three competitions and also when people call out their phone number, they will say "Oh treble five seven two ..." but treble is definitely used more than triple in the sense of to grow three-fold just as double means to grow two-fold.
And I'm not too happy about the rules for responding here. It says, Don't make statements based on opinion- back them up with references. What are references but others' opinions? Even official facts are opinions about a set of data, are they not? :) With less strict rules, there might be triple the number of responses.
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edited Aug 27, 2014 at 18:58
Mari-Lou A
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One other use of treble I have heard is as an alternative to the word soprano. In this case, triple is never used.
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answered Jan 6, 2014 at 2:29
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3 That's quite clearly not what the question is about. Nobody would ever speak of triple and bass in music either; that much is obvious. Only the ‘threefold’ word is being discussed here.Janus Bahs Jacquet –Janus Bahs Jacquet 2014-01-06 02:36:15 +00:00 Commented Jan 6, 2014 at 2:36
1 We appreciate your input. This is more of a "comment" than an answer, but once you have earned enough reputation, you will be able to comment, which can include opinions and additional information. In the meantime, we ask that you include links to support your answers.anongoodnurse –anongoodnurse 2014-01-06 04:25:13 +00:00 Commented Jan 6, 2014 at 4:25
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189692 | https://alexanderrem.weebly.com/uploads/7/2/5/6/72566533/miscellaneousproblems.pdf | IMO Training 2010 Russian-style Problems Alexander Remorov Russian-style Problems Alexander Remorov alexanderrem@gmail.com Today we will be doing Russian-style problems related to combinatorics. A lot of these have very non-standard solutions and are rather difficult.
The following tricks apply to pretty much all problems. If you feel that you are not getting far on a combinatorics-related problem, it is always good to try these.
• Induction: ”Induction is awesome and should be used to its full potential” - Jacob Tsimer-man, winter camp 2010. Seriously, it is awesome. For hard combinatorics problems, don’t expect it to be easy application of induction. Think about how you can reduce your problem to a case for a smaller n in ”a powerful way”. For example, if you have n + 1 vertices in a graph, and you want to use the result on n vertices, take out a vertex with very specific properties and not just any vertex.
• Extremal Principle: Define some function f whose domain is ”the configuration in your problem” (i.e. configuration of points, sequence of numbers, a graph, etc.) and the range is (usually) the positive integers. Usually it is a rather simple function, i.e. the minimum distance between two points, the largest prime dividing a number, etc. Sometimes you have to be clever and come up with a more complicated function (i.e. the sum of pairwise dis-tances between points). Then consider a configuration for which f achieves its minimum or maximum.
• Notice Interesting Things: This idea applies to all olympiad problems, however more so for combinatorics problems. After playing around with the problem for some time you will hopefully come up with useful properties of ”things” in the problem (e.g. points, edges in a graph, numbers in a sequence, differences between numbers, etc.) You can often tell if the property you found is useful or not. Sometimes it is enough to find one thing with a specific property. Sometimes you can remove it and use induction.
• Reduce the Problem: After noticing some properties in the problem, you can often reduce or transform the problem to one that is more approachable. Important: When you reduce the problem, you are often losing some information from the original problem. It can happen that the results in the reduced problem may not hold because you left out some conditions in the original problem. Check if the result in your reduced problem is even true.
• Try Small Numbers and See a Pattern: Self-explanatory.
• Pigeon-Hole Principle: Again, usually you have to be clever.
• Try Lots of Things: For combinatorics problems there is a lot of freedom and a lot of different approaches you can try. It is possible that you think your current approach is the 1 IMO Training 2010 Russian-style Problems Alexander Remorov right one, you feel stubborn and keep trying to go further with this approach. If you are using it for 2 hours and having absolutely no new ideas on how to proceed, it is probably a good idea to try another approach. Keep an open mind, since many combinatorics problems have unexpected solutions.
Combinatorial Geometry Some tricks relevant specifically to combinatorial geometry: • Consider the convex hull made up of the points • Consider the point with the smallest x−or y−coordinate • Find the triangle (quadrilateral, pentagon, etc.) with the vertices being the points from your set S, so that the area of the triangle is minimal/maximal • Helly’s Theorem: If X1, X2, ..., Xn are convex subsets of Rk so that the intersection of any k + 1 of them is non-empty, then the intersection of all the sets is non-empty.
1. The two legs of a compass are located at two distinct lattice points in the coordinate plane drawn on an infinite sheet of paper. The distance between the two legs cannot be changed. It is allowed to fix one of the legs, and move the other leg to any other lattice point. Is it possible to switch the positions of the two legs after a finite number of steps?
2. A is a convex set in the plane (so that for any two points in A, the line segment joining the two points lies completely in A). Prove that there exists a point O in A, such that for any points X, X′ on the boundary of A, such that O lies on line segment XX′, 1 2 ≤OX OX′ ≤2 3. Find all sets S of finitely many points in the plane, no three of which are collinear and such that for any three points A, B, C in S, there is another point D in S such that A, B, C, D (in some order) are the vertices of a parallelogram.
4. A strip of width w is the set of all points which lie on or between two parallel lines that are a distance w apart. Let S be a set of n (n ≥3) points on the plane such that any three different points of S can be covered by a strip of width 1. Prove that S can be covered by a strip of width 2.
5. There are two circles, each with circumference length 1000 cm. 1000 points are marked on the first circle, and on the other circle - several arcs are marked, so that the sum of the lengths of the arcs is less than 1 cm. Prove that it is possible to lay the first circle on the second so that no marked point lies on a marked arc.
6. Find all positive integers n such that in the coordinate plane, there exists a convex n-sided polygon with all vertices having integer coordinates, and whose side-lengths are odd integers, no two of which are equal.
7. In the plane there are finitely many red and blue lines, no two of which are parallel. For every point of intersection of two lines of the same color, there exists a line of the other color passing through that point. Prove that all the lines are concurrent.
2 IMO Training 2010 Russian-style Problems Alexander Remorov 8. A convex polygon is given. Prove that there is at most one way to draw several of its diagonals in such a way, that no two diagonals intersect each other and as a result the polygon is partitioned into acute triangles.
9. There are n lines in the plane, all passing through a point O. For any two lines, there is a third line which bisects one of the pairs of vertical angles formed by the two lines. Prove that the n lines divide the 360◦angle at O into equal angles.
10. A finite collection of squares has total area 4. Show that they can be arranged to cover a square of side 1.
11. Several identical paper squares of n different colors are lying on a rectangular table, with sides of the squares parallel to the sides of the table. Among any n squares of pairwise distinct colors it is possible to find 2 which can be pinned to the table using one pin. Prove that all squares of a certain color can be pinned to the table using 2n −2 pins.
12. There are N ≥3 points in the plane. Among the pairwise distances between these points there are at most n different distances. Prove that N ≤(n + 1)2.
3 IMO Training 2010 Russian-style Problems Alexander Remorov Processes Some tricks relevant specifically to processes: • Find an invariant - a quantity that does not change; or a half-invariant - a quantity that does not increase/decrease.
• Use discrete continuity - if a quantity changes by -1, 0, or 1 each time; and it is equal to a and b at two different times, then for any integer between a and b, the quantity will be equal to that integer at some point • Group things (i.e. moves made, part of the configuration, etc.) 1. A number is written in each of the squares of an m × n grid. It is allowed to switch the sign of all numbers from one row or one column. Prove that eventually it is possible to get a grid, in which the sums of the numbers in every column and every row are non-negative.
2. Ivan has a 52-card deck. He draws the cards from the deck one by one, without putting them back in the deck. Every time before drawing a card he guesses the suit of the card he will draw.
He decides to always guess the suit that occurs most frequently in the remaining deck (if there are several such suits, he chooses any one of them). Prove that he will guess the right suit at least 13 times.
3. Two distinct positive integers a, b are written on the board. The smaller of them is erased and instead of it the number ab |a−b| is written. This process is repeated as long as the two numbers are not equal. Prove that eventually the two numbers on the board will be equal.
4. A checker is placed in each of the unit squares of a n × n square, which is part of an infinite chessboard. A move is the process of selecting two checkers located in unit squares sharing a side, and using one of the checkers to jump over the other checker into an empty square adjacent by a side to the square in which the other checker is located. The checker that has been jumped over is removed from the board. After several moves it will be impossible to make a move. Prove that this will happen after at least ⌊n2 3 ⌋moves.
5. There are 2000 distinct points, every two of which are connected by a line segment. Danny and Cynthia take turns erasing line segments, so that Danny is allowed to erase only one line segment per turn, and Cynthia is allowed to erase two or three line segments per turn. The person after whose move there is a point not connected to any other points loses. Who will win in this game?
6. A n × n grid is given, n −1 squares of which contain a one, and the rest of the squares contain a zero. It is allowed to select a square, subtract 1 from the number in that square, and add 1 to all numbers in the same row and column as this square. Is it possible to get a grid where all numbers in the squares are equal?
7. An infinite strip of paper is given, divided into unit squares, numbered by the integers from left to right (like a number line). Several stones lie in some of the squares, and a square can have more than 1 stone in it. It is allowed to make the following moves: (a) Remove a stone from each of the squares n and n + 1 and place one stone into square n + 2.
(b) Remove two stones from square n and place one stone into each of the squares n + 1, n −2.
Prove that eventually it is impossible to make any more moves. Also, prove that the final configu-ration of the stones is always the same regardless of the order in which the moves were made.
4 IMO Training 2010 Russian-style Problems Alexander Remorov 8. In a mathematical competition some competitors are friends. Friendship is always mutual. Call a group of competitors a clique if each two of them are friends. (In particular, any group of fewer than two competitiors is a clique.) The number of members of a clique is called its size. Given that, in this competition, the largest size of a clique is even, prove that the competitors can be arranged into two rooms such that the largest size of a clique contained in one room is the same as the largest size of a clique contained in the other room.
Graphs Some results relevant specifically to graphs: • The sum of the degrees of the vertices in a graph is even (a degree is the number of edges exiting the graph).
• If a graph with n vertices has no cycles, but there is a path connecting any two vertices, the graph has n −1 edges.
• The set of vertices in a graph can be partitioned into two sets A and B such that no two vertices in A are connected by an edge, and no two vertices in B are connected by an edge iffthere are no odd cycles in this graph.
Some useful tricks: • Take a vertex A and consider the disjoint sets A1, A2, ..., An so that all vertices in A1 are connected by an edge to A; all vertices in Ai+1 are connected by an edge to some vertex in Ai, and not connected by an edge to any of the vertices in {A}, A1, A2, ..., or Ai−1.
• Look at specific parts of the graph satisfying various properties • Color vertices or edges in the graph • Define your graph, vertices, and edges in a non-standard way • Create an algorithm which will produce the desired configuration 1. In a country there are several cities and several roads. Every road connects exactly 2 cities. Out of every city exit at least 3 roads. Prove that there is a cycle, the number of cities in which is not divisible by 3.
2. The inhabitants of a village start getting sick with the flu. One day in the morning some of them ate too much ice cream and got sick; and after that day the only way a healthy person would get sick is if they visited a sick friend. Every person in the village is sick for exactly 1 day, and the next day he is immune to the flu virus - he cannot get sick that day. Despite the pandemic every day a healthy person visits all his sick friends. After the pandemic started, nobody got vaccines.
Prove that: (a) If some people got a vaccine before the first day when the pandemic started, and were immune to the flu on the first day, the pandemic can last forever.
(b) If nobody was immune to the flu on the first day, eventually the pandemic will end.
5 IMO Training 2010 Russian-style Problems Alexander Remorov 3. In a certain group of 12 people, among any 9 people, there are 5 who know each other. Show that in this group there are 6 people who know each other.
4. In a country with 2010 cities, there are several two-way roads. Every road connects exactly 2 cities. It is possible to travel from any city to any city along the roads. Furthermore, it is possible to do this even if any one of the roads is closed. Two construction companies A and B are playing a game. On every turn a construction company selects, if possible, one of the roads and enforces one-way traffic on that road (if there is already one-way traffic traffic on the road, this road is not allowed to be selected). A company loses its license if after its move it is impossible to travel from some city to some other city. Company A goes first. Can one of the companies guarantee that the other company will lose its license?
5. In a country with 2010 cities, there are several roads. Every road connects exactly 2 cities.
Through every city there are at most n different non-self-intersecting cycles of odd length. Prove that the cities can be divided into n + 2 groups, so that any two cities from two different groups are not connected by a road.
6.
There are 100 representatives from 25 countries seating at a round table, 4 representatives from each country. Prove that it is possible to divide the representatives into 4 groups with one representative from each group so that no two representatives from the same group are sitting side by side at the table.
7. An m × n rectangular board is given where m, n are odd integers. The board is covered with 2 × 1 dominoes, so that no two dominoes overlap and only the bottom left square of the board is empty (i.e. not covered by any dominoes). At any point in time it is allowed to slide a domino so that it covers an empty square and still stays on the board, and none of the other dominoes are moved during this process. As a result, a new square becomes empty. Prove that after several such moves it is possible to make any corner square on the board empty.
8. 2n+3 players participate in a chess tournament. Every two play exactly one game. The schedule is set so that no two games are played at the same time, and each player, after playing game, is free for at least n next (consecutive) games. Prove that one of the players who plays in the first game will also play in the last game.
6 |
189693 | https://uomustansiriyah.edu.iq/media/lectures/5/5_2020_03_15!07_19_18_PM.pdf | CHAPTER THREE ONE-DIMENSIONALHEAT CONDUCTION EQUATION Dr. Haider Ali Hussein 1 CHAPTER THREE 3.1 INTRODUCTION Heat transfer problems are also classified as being one-dimensional, two dimensional, or three-dimensional, depending on the relative magnitudes of heat transfer rates in different directions and the level of accuracy desired. For example, the steady temperature distribution in a long bar of rectangular cross section can be expressed as T(x, y) if the temperature variation in the z-direction (along the bar) is negligible and there is no change with time (Fig 3.1) FIGURE 3.1 Two-dimensional heat transfer in a long rectangular bar. 3.2 ONE-DIMENSIONAL HEAT CONDUCTION EQUATION Consider heat conduction through a large plane wall such as the wall of a house, the glass of a single pane window, the metal plate at the bottom of a pressing iron, a cast iron steam pipe, a cylindrical nuclear fuel element, an electrical resistance wire, the wall of a spherical container, or a spherical metal ball that is being quenched or tempered. Heat conduction in these and many other geometries can be approximated as being one-dimensional since heat conduction through these CHAPTER THREE ONE-DIMENSIONALHEAT CONDUCTION EQUATION Dr. Haider Ali Hussein 2 geometries will be dominant in one direction and negligible in other directions. Below we will develop the onedimensional heat conduction equation in rectangular, cylindrical, and spherical coordinates. 3.2.1Heat Conduction Equation in a Large Plane Wall Consider a thin element of thickness Δx in a large plane wall, as shown in Figure 3.2 . Assume the density of the wall is , the specific heat is C, and the area of the wall normal to the direction of heat transfer is A. An energy balance on this thin element during a small time interval Δt can be expressed as FIGURE 3.3 One-dimensional heat conduction through a volume element in a large plane wall. Rate of heat conduction at x 𝑄𝑄̇=E =𝑞𝑞𝑥𝑥= KA ԁT ԁX Rate of heat conduction at x+ Δx 𝑄𝑄̇=E= 𝑞𝑞𝑥𝑥+𝛥𝛥𝛥𝛥= 𝑞𝑞𝑥𝑥+ ԁ𝑞𝑞𝑥𝑥 ԁ𝑥𝑥ԁ𝑥𝑥 Rate of heat generation (energy source) inside the element CHAPTER THREE ONE-DIMENSIONALHEAT CONDUCTION EQUATION Dr. Haider Ali Hussein 3 𝑄𝑄̇=E==𝐺𝐺̇= 𝑞𝑞̇ԁxԁyԁz Rate of change of the energy content (energy storage) of the element 𝑄𝑄̇=E=ρ C ԁ𝑇𝑇 ԁ𝑡𝑡 ԁxԁyԁz where the property α= k/ρC is the thermal diffusivity of the material and represents how fast heat propagates through a material. It reduces to the following forms under specified conditions. 3.2.2.Heat Conduction Equation in a Long Cylinder CHAPTER THREE ONE-DIMENSIONALHEAT CONDUCTION EQUATION Dr. Haider Ali Hussein 4 3.2.3 Heat Conduction Equation in a Sphere CHAPTER THREE ONE-DIMENSIONALHEAT CONDUCTION EQUATION Dr. Haider Ali Hussein 5 3.3 SOLUTION OF STEADY ONE-DIMENSIONAL HEAT CONDUCTION PROBLEMS Boundary conditions CHAPTER THREE ONE-DIMENSIONALHEAT CONDUCTION EQUATION Dr. Haider Ali Hussein 6 Case 1 PlaneWall with Heat Sources CHAPTER THREE ONE-DIMENSIONALHEAT CONDUCTION EQUATION Dr. Haider Ali Hussein 7 Case 2 PlaneWall with Heat Sources and one side insulation CHAPTER THREE ONE-DIMENSIONALHEAT CONDUCTION EQUATION Dr. Haider Ali Hussein 8 EXAMPLE 3.1 CHAPTER THREE ONE-DIMENSIONALHEAT CONDUCTION EQUATION Dr. Haider Ali Hussein 9 EXAMPLE3.2 EXAMPLE 3.4 EXAMPLE 3.3 CHAPTER THREE ONE-DIMENSIONALHEAT CONDUCTION EQUATION Dr. Haider Ali Hussein 10 CHAPTER THREE ONE-DIMENSIONALHEAT CONDUCTION EQUATION Dr. Haider Ali Hussein 11 EXAMPLE 3.5 Consider a large plane wall of thickness L _ 0.2 m, thermal conductivity k 1.2 W/m · °C, and surface area A 15 m2. The two sides of the wall are maintained at constant temperatures of T1 120°C and T2 50°C, respectively, as shown in Figure . Determine (a) the variation of temperature within the wall and the value of temperature at x 0.1 m and (b) the rate of heat conduction through the wall under steady conditions. Sol CHAPTER THREE ONE-DIMENSIONALHEAT CONDUCTION EQUATION Dr. Haider Ali Hussein 12 EXAMPLE 3.6 Consider a steam pipe of length L 20 m, inner radius r1 6 cm, outer radius r2 8 cm, and thermal conductivity k 20 W/m · °C. The inner and outer surfaces of the pipe are maintained at average temperatures of T1 150°C and T2 60°C, respectively. Obtain a general relation for the temperature distribution inside the pipe under steady conditions, and determine the rate of heat loss from the steam through the pipe. Sol q q CHAPTER THREE ONE-DIMENSIONALHEAT CONDUCTION EQUATION Dr. Haider Ali Hussein 13 T(r) = 𝐶𝐶1 ln r + 𝐶𝐶2 We now apply both boundary conditions by replacing all occurrences of r and T (r ) q q CHAPTER THREE ONE-DIMENSIONALHEAT CONDUCTION EQUATION Dr. Haider Ali Hussein 14 HW sheet 3 1. Consider a large plane wall of thickness L _ 0.4 m, thermal conductivity k _ 2.3 W/m · °C, and surface area A _ 20 m2. The left side of the wall is maintained at a constant temperature of T1 _ 80°C while the right side loses heat by convection to the surrounding air at T _ 15°C with a heat transfer coefficient of h _ 24 W/m2 · °C. Assuming constant thermal conductivity and no heat generation in the wall, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall, (b) obtain a relation for the variation of temperature in the wall by solving the differential equation, and (c) evaluate the rate of heat transfer through the wall. Answer: (c) 6030 W 2. Consider the base plate of a 800-W household iron with a thickness of L _ 0.6 cm, base area of A _ 160 cm2, and thermal conductivity of k _ 20 W/m · °C. The inner surface of the base plate is subjected to uniform heat flux generated by the resistance heaters inside. When steady operating conditions are reached, the outer surface temperature of the plate is measured to be 85°C. Disregarding any heat loss through the upper part of the iron, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the plate, (b) obtain a relation for the variation of temperature in the base plate by solving the differential equation, and (c) evaluate the inner surface temperature. Answer: (c) 100°C 3. Consider a large plane wall of thickness L _ 0.3 m, thermal conductivity k _ 2.5 W/m · °C, and surface area A _ 12 m2. The left side of the wall at x _ 0 is subjected to a net heat flux of q· 0 _ 700 W/m2 while the temperature at that surface is measured to be T1 _ 80°C. Assuming constant thermal conductivity and no heat generation in the wall, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall, (b) obtain a relation for the variation of temperature in the wall by solving the differential equation, and (c) evaluate the temperature of the right surface of the wall at x _ L. Answer: (c) _4°C CHAPTER THREE ONE-DIMENSIONALHEAT CONDUCTION EQUATION Dr. Haider Ali Hussein 15 4. Aspherical container of inner radius r1 _ 2 m, outer radius r2 _ 2.1 m, and thermal conductivity k _ 30 W/m · °C is filled with iced water at 0°C. The container is gaining heat by convection from the surrounding air at T _ 25°C with a heat transfer coefficient of h _ 18 W/m2 · °C. Assuming the inner surface temperature of the container to be 0°C, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the container, (b) obtain a relation for the variation of temperature in the container by solving the differential equation, and (c) evaluate the rate of heat gain to the iced water. 5. Consider a homogeneous spherical piece of radioactive material of radius r0 _ 0.04 m that is generating heat at a constant rate of g· _ 4 _ 107 W/m3. The heat generated is dissipated to the environment steadily. The outer surface of the sphere is maintained at a uniform temperature of 80°C and the thermal conductivity of the sphere is k _ 15 W/m · °C. Assuming steady one-dimensional heat transfer, (a) express the differential equation and the boundary conditions for heat conduction through the sphere, (b) obtain a relation for the variation of temperature in the sphere by solving the differential equation, and (c) determine the temperature at the center of the sphere. 6. A long homogeneous resistance wire of radius r0 _ 5 mm is being used to heat the air in a room by the passage of electric current. Heat is generated in the wire uniformly at a rate of g· _ 5 _ 107 W/m3 as a result of resistance heating. If the temperature of the outer surface of the wire remains at 180°C, determine the temperature at r _ 2 mm after steady operation conditions are reached. Take the thermal conductivity of the wire to be k _ 8 W/m · °C. Answer: 212.8°C |
189694 | https://www.spanishdict.com/answers/112674/the-personal-a- | The personal "a"
I am a little confused about when to use the personal "a", which has no equivalent structure in English.
I believe one would use it when you have the subject of the sentence is a person, and they direct object is also a person. But I am not sure, and also I don't know if it is used in other ways.
If someone could help me or point me to some grammar (I looked here and didn't find it), I would be most grateful.
Thank you,
Rolest
7 Answers
Escucho a Paco - I am listening to
Paco
Escucho a él - I am listening to him.
Escucho a mi hermano - I am listening
to my brother
Escucho a mi perro - I am listening to
my dog
This is correct, except for the fact that "Escucho a él" must be "Lo escucho (a él)", with the "a él" being optional.
The rule is this:
Whenever a tonic pronoun is used (yo, tú, él, ella, Ud., nosotros, vosotros, Uds.) as the direct/indirect object, the corresponding atonic pronoun (me, te, lo, la, nos, os, los, las OR me, te, le, nos, vos, les) must also be used.
Escucho a Paco - I am listening to
Paco
Escucho a él - I am listening to him.
In the first example, there is no tonic pronoun used, so it is fine the way it is. In the second, the tonic pronoun "él" is used, so the corresponding direct object pronoun "lo" must be used.
As I said, this also works with indirect object pronouns. To simply say, "I gave the book to her" you would say "Le di el libro (a ella)." Because the indirect object is a tonic pronoun, the corresponding indirect object pronoun "le" must be used, and the "a ella" is purely optional. Of course, in this case, it would probably be needed to clarify who the "le" is referring to, as "le" can mean "to him/her/you (formal)".
Anyway, to say something like "I gave the book to Rosa", it is completely and grammatically correct to simply say "Di el libro a Rosa", without even using the indirect object pronoun, since "Rosa" is not a tonic pronoun. It is more common to say "Le di el libro a Rosa", with "le" acting as an anticipatory pronoun to alert the reader to the fact that an indirect object is coming later in the sentence. Both options are equally correct, but the second provides a certain nuance.
I know all of this kind of strays from the original question, but I saw it as a great teaching moment. I'm sorry for the length.
The personal "a" is used any time before a person's name.
Just to avoid any confusion, this statement is true but incomplete. The personal a precedes any direct object that is a person whether named or not (and is also used when the direct object is a beloved pet). For example:
Escucho a Paco - I am listening to Paco
Escucho a él - I am listening to him.
Escucho a mi hermano - I am listening to my brother
Escucho a mi perro - I am listening to my dog
Hi Rolest,
You got it half right. The personal a is used to introduce a direct object that is a person but it is not necessary that the subject of the sentence be a person, too. I hope this helped.
Try looking under prepositions in the reference section Spanishdict reference section: Prepositions You could also try this link: Personal a
Yes, you are correct that a personal a is used before a direct object that refers to a person. The subject of the sentence may or may not be a person, but if the d.o. is a person, you need the personal a.
(I'm trying to think of an example in which the subject would not be a living thing...Nothing is coming to mind, other than personification of an inanimate object, such as in a children's story...maybe it's time to go to sleep!)
Anyway, some examples are: I know the boy - Conozco al chico. She sees her friends. Ella ve a sus amigas. They love their little brother. Ellos quieren a su hermanito. I take your dog in the car. Llevo a tu perro en el coche. (pets also take the personal a).
I'm sorry I can't point you to the proper spot on this site; I'm sure there is one, and someone will come along and help you in that regard. Hopefully I have at least temporarily answered your question.
Perhaps this free ebook with help. It covers many uses of the Spanish 'a', including the so-called 'personal a'.
(I'm trying to think of an example in which the subject would not be a living thing...Nothing is coming to mind, other than personification of an inanimate object, such as in a children's story...maybe it's time to go to sleep!)
Las aguas del río los llevaron a todos.
The personal "a" is used any time before a person's name.
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189695 | https://personalpages.manchester.ac.uk/staff/richard.baker/BasicAcoustics/5_addition_of_sound_intensities.html | Addition of sound intensities | Basic Acoustics
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Basic Acoustics
1. Basic Logarithms
2. The bel and decibel scale
3. Sound Intensity and Pressure
4. Inverse Square Law
5. Addition of sound intensities
6. Spectrum Level
7. Combining sound energy over time
8. Definitions
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5. Addition of sound intensities
Objectives
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Understanding the principles of adding two sounds together
Understand how to convert dB SPL or dB IL values to intensities prior to adding
Understand how to how to combine octave or 1/3rd octave measures
Understand what is meant by spectrum level.
Understand how to combine sound exposures over time.
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5.1 Conversion from dB intensity level (dB IL) to sound intensity
Because the decibel scale is a logarithmic scale, if we have two different sound sources combining together we can't simply add the sound pressure levels - what we have to do is to add the intensities. That means we have to convert our decibel values into intensities (with units of W/m 2).
Remember that if we have an sound intensity (I) an wish to express it in dB intensity level we need to use:
What we need is an expression for intensity (I). So let us now rearrange the equations to get an I on its own.
To do this we first divide by 10 on both sides:
Then take the inverse log (antilog) of both sides:
then we multiply both sides by the reference intensity to get I on its own: (5.1)
Reflection
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Example 1. Using equation 5.1, if a sound is 80 dB IL, what is the sound intensity?
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5.2 Adding two equal sound intensities
So, for example suppose we have two independent sound sources producing white-noise and the sound pressure level of each one measured on it's own is 80 dB SPL - our question is, what is the resulting sound pressure level when they are both turned on together?
If we assume that the value in dB SPL is the same as it would be if we measured it in dB IL (i.e. assumptions of a plane wave) then the first thing we need to do is convert our dB SPLs into intensities as in 5.1. (see Example 1). If we refer to the two sound intensities as I 1 and I 2 which are both equal, then as we have already seen: I 1 = I 2 = 10-4 W/m 2
If we now add I 1 and I 2 to give I total we have:
I total = I 1 + I 2 = 10-4 + 10-4=2 x 10-4 W/m 2
So we now have the sound intensity of our combined signal and we can now convert this back to a dB value:
Now since we are talking about plane waves, our total sould pressure level = 83.01 dB SPL.
This example gives us a simple rule:
If we add two unrelated sounds of the same intensity together, it is equivalent to a 3 dB increase in the total sound pressure level.
Reflection
Hide
Example 2. Given the above example, what do you think the total sound pressure level would be if 4 unrelated white-noise sound sources each of 80 dB SPL were combined?
Feedback
One way of thinking about this is that the combined sound intensity is four times that of one of the single exposures. Thus,I total=I x 4. But remember that the decibel scale is a logarithmic scale so that we could refer back to what we have learned about logarithms earlier and get an expression for dB total
As in the description above 80 dB SPL corresponds to an intensity of 10-4 W/m 2, but this time we have 4 such signals to add together. So the total intensity = 10-4 W/m 2 x 4
The first part of this is our original 80 dB SPL (but remember we have to deal with it as though it was a sound intensity measure).
Thus dB SPL total = 80dB SPL + 10 log 10(4) = 80+6.02 = 86.02 dB SPL
(An alternative way of thinking about this particular example is that we have doubled the sound intensity twice i.e. it has increased by 2 x 3 dB)
Hide
5.3 Adding two unequal sound intensities
Suppose we have two unrelated sound sources of unequal SPLs (e.g. 80 and 74 dB SPL. Using the above procedure we can show that the two intensities are 10-4 and 2.5x10-5 W/m 2 respectively. If we add these together we get 1.25x10-4 W/m 2 which if we convert back to decibels gives us approximately 81 dB SPL. The lower level sound only makes a relatively small additional contribution to the total sound pressure level.
We can extend this process further if we want to add more than two unrelated sound levels and this would lead to the general equation for a set of sound levels L 1, L 2, ... L n:
(5.2)
But this can be simplified since the reference intensities cancel out to give:
(5.3)
Hide
5.4 Nomogram for adding sound levels
Various people have come up with simple ways of short-cutting these procedures - figure 5.1 shows one way of doing this for two sound levels.
Figure 5.1: Nomogram for the addition of two decibel levels. (1) Calculate the difference between the two sound levels and select this value on the upper scale (2) read off the value on the lower scale and add this to the higher of the two sound levels.
Figure 5.2: Nomogram for addition of decibels
So for our previous example, we take the difference between the two sound levels (80 - 74 = 6 dB) and read the lower scale to find the correction (approx. 1 dB) this is then added to the higher sound level (i.e. 80+1 = 81 dB SPL).
At the left hand side of the nomogram, if the two sound levels are equal (difference = zero) then we should add 3 dB (i.e. doubling the sound intensity). At the right hand of the scales, if the two sound levels differ by as much as 20dB then the lower sound level makes very little difference to the total sound level.
If we have more than two sound levels to add we can simply break them down into a series of pairs. For example if we have 3 measurements of 80.8, 83 and 84 dB SPL. We can add the 80.8 and 83 first to give approx. 85 dB SPL and then add this to the 84 dB SPL which would give us a total of approximately 87.5 dB SPL. If we were to calculate this using equation (5.3) we would get 87.6 dB SPL - try this for yourself.
Hide
5.4 Why Unrelated Sounds?
In the above descriptions it is emphasized that we are concerned with adding unrelated sounds - the reason for this is that if two sound waveforms are related (e.g. two sinusoids of the same frequency) then we have to take into account the actual phases as well as the amplitudes.
For example if we have two speakers producing a sinusoid of the same amplitude and frequency the actual amplitude of the combines signal will depend on the relative phases. If they are 180 degrees out of phase they will cancel out (destructive interference) and the resulting sound level will be zero. If they are in phase with each other then their amplitudes (sound pressures) will add (constructive interference). In this case the sound pressure will double so the sound level will increase by 6 dB (i.e. 20 log 10(2)).
So if we are adding two sound from the same source or sounds with waveforms that are similar then we have to think carefully before adding them together.
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Nine-point circle
Triangle ABC with the nine-point circle in light orange
The nine-point circle (also known as Euler's circle or Feuerbach's circle) of a given triangle is a circle which passes through 9 "significant" points:
The three feet of the altitudes of the triangle.
The three midpoints of the edges of the triangle.
The three midpoints of the segments joining the vertices of the triangle to its orthocenter. (These points are sometimes known as the Euler points of the triangle.)
"The nine-point circle is tangent to the incircle, has a radius equal to half the circumradius, and its center is the midpoint of the segment connecting the orthocenter and the circumcenter." -hankinjg
That such a circle exists is a non-trivial theorem of Euclidean geometry.
The center of the nine-point circle is the nine-point center and is usually denoted .
The nine-point circle is tangent to the incircle, has a radius equal to half the circumradius, and its center is the midpoint of the segment connecting the orthocenter and the circumcenter, upon which the centroid also falls.
It's also denoted Kimberling center .
Contents
[hide]
1 First Proof of Existence
2 Second Proof of Existence
3 Common Euler circle
4 See also
First Proof of Existence
Since is the midpoint of and is the midpoint of , is parallel to . Using similar logic, we see that is also parallel to . Since is the midpoint of and is the midpoint of , is parallel to , which is perpendicular to . Similar logic gives us that is perpendicular to as well. Therefore is a rectangle, which is a cyclic figure. The diagonals and are diagonals of the circumcircle. Similar logic to the above gives us that is a rectangle with a common diagonal to . Therefore the circumcircles of the two rectangles are identical. We can also gain that rectangle is also on the circle.
We now have a circle with the points , , , , , and on it, with diameters , , and . We now note that . Therefore , , and are also on the circle. We now have a circle with the midpoints of the sides on it, the three midpoints of the segments joining the vertices of the triangle to its orthocenter on it, and the three feet of the altitudes of the triangle on it. Therefore, the nine points are on the circle, and the nine-point circle exists.
Second Proof of Existence
We know that the reflections of the orthocenter about the sides and about the midpoints of the triangle's sides lie on the circumcircle (side proof, midpoint proof), as do the vertices of the triangle. So, consider the homothety centered at with ratio . It maps the circumcircle of (and those 9 points) to a circle, including mapping the vertices of the triangle to its Euler points (by definition). This is the nine-point circle.
Common Euler circle
Let an acute-angled triangle with orthocenter be given.
be the point on opposite
Points and such that is a parallelogram. The line intersects at the points and
Prove that triangles and has common Euler (nine-point) circle.
Proof Denote is midpoint
Let’s consider Circumcenter of point is the midpoint point is the midpoint
Denote the centroid of
is the centroid of
Denote the midpoint of is the midpoint of
is the centroid of
Point is the circumcenter of is the orthocenter of
The triangles and has common circumcircle and common center of Euler circle (the midpoint of ) therefore these triangles has the common Euler circle.
vladimir.shelomovskii@gmail.com, vvsss
See also
Kimberling center
Center line
Evans point
Euler line
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Gastrointestinal Complications in the Postoperative Period
PERFORATION
The clinical presentation of a perforated peptic ulcer is with the sudden onset of severe abdominal pain that quickly generalizes to the entire abdomen and is followed by hypotension and fever. Acute peritonitis typically is accompanied by a rigid, boardlike abdomen, absent bowel sounds, and leukocytosis. Free air under the diaphragm may be seen on an erect chest radiograph.
Treatment of a perforated ulcer is usually surgical and consists of closure of the perforation, possibly combined with a proximal gastric vagotomy. Rarely, a nonoperative approach may be considered if an upper gastrointestinal contrast series with meglumine diatrizoate (Gastrografin) shows no free leakage into the peritoneal cavity.
Ulcers may also penetrate posteriorly into the pancreas, resulting in acute pancreatitis with severe back pain and hyperamylasemia. Posterior penetration may respond to medical therapy with nasogastric decompression and gastric acid suppression with a proton pump inhibitor.
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Chapter
Acid Peptic Disease
Perforation
Perforation may manifest as an acute event, whereby gastric contents spill into the peritoneal cavity, or more insidiously as the ulcer slowly penetrates into surrounding tissues. Acute free perforation typically causes abrupt and severe abdominal pain associated with abdominal muscular spasm that produces board-like rigidity of the abdomen and other manifestations of peritoneal irritation. Secondary hemodynamic shock is common. The clinical diagnosis can be confirmed in approximately 80% of patients by a plain chest radiograph with the patient standing (Fig. 141-5); a CT scan can be obtained if doubt persists. Leukocytosis and elevated C-reactive protein levels develop rapidly, and mild hyperamylasemia may occur. Treatment begins by correcting hemodynamic, fluid, and electrolyte imbalances. Nasogastric suction is helpful, and prophylactic antibiotics (e.g., amoxicillin-clavulanic acid 1 g every 8 hours intravenously) are usually administered. Unless a specific contraindication exists, emergency surgery is usually indicated, although more conservative approaches are sometimes appropriate. Given the success in achieving the long-term cure of ulcer disease through the eradication of H. pylori and the withdrawal of NSAIDs, suturing of the perforated ulcer may be adequate, permitting the patient to avoid a more radical vagotomy with or without gastric resection.
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Chapter
Vomiting and Regurgitation
Gastrointestinal Perforation and Peritonitis
Gastrointestinal perforation is often the end stage of obstructing, inflammatory, or ischemic disorders. Perforation is heralded by sudden abdominal pain, with subsequent signs of peritonitis. Perforated peptic ulcer pain may track to the right lower quadrant and mimic appendicitis, but the onset is more sudden, and the child is sicker than with appendicitis. Shock, metabolic acidosis, sepsis, and disseminated intravascular coagulopathy may ensue. Vomiting is not prominent.
When luminal obstruction leads to perforation and peritonitis, the abdominal findings change in characteristic ways. Vague, crampy, periumbilical pain becomes sharp, continuous, and localized. Rushes of increased, high-pitched bowel sounds disappear, leaving the abdomen silent. The active, sometimes writhing child becomes still. Vomiting previously associated with cramping pain is no longer present. The physical examination discloses point tenderness, abdominal rigidity, involuntary guarding, and rebound tenderness.
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Surgery of the Bovine Digestive System
Adult Cattle and Feedlot Steers.
After exposure of the abomasum, the site of ulceration should be identified. The perforation is generally located at the site of the most well-established adhesions. Once the site has been identified, it should be isolated from as many surrounding adhesions as possible and elevated toward the incision if it is mobile. Before beginning adhesion lysis, the abomasal wall in the vicinity of the perforation should be clamped with atraumatic intestinal forceps or, if this is not possible, isolated manually and the surrounding tissues packed off to help control accidental leakage. Peripheral thin fibrinous adhesions may be gently separated manually, whereas thicker fibrous adhesions may require sharp incision. If the ulcer is in a location that cannot be safely isolated, the adhesions should be left in place and the cow recovered. At this time, a decision to treat medically, perform a second surgery through another approach, or elect slaughter/euthanasia will be needed.
Once the site has been isolated, the area of ulceration should be resected and oversewn with an inverting pattern with an absorbable suture material such as polyglycolic acid, polyglactin 910, or polydioxanone. Chromic gut has been used for this purpose but is not recommended because of the potential for premature absorption in the presence of abomasal acid and the enzyme activity of bacteria and white blood cells. Some authors have described successful management of perforated ulcers by inverting the ulcer site without resecting the ulcer and oversewing the site with an inverting pattern. Care should be taken to avoid spreading debris or contaminated fluid beyond the local site of contamination. The incision should be closed routinely, taking care to lavage each layer of the incision thoroughly before closure. Antibiotic therapy should be continued to treat the peritonitis as indicated based on the level and stage of infection.
If ulceration has produced a localized abscess adjacent to the ventral body wall or within the omental bursa, it may be possible to marsupialize the abscess and treat it by drainage and lavage. Once drainage has stopped, it may be necessary to surgically close the artificial tract.
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Book2017, Farm Animal Surgery (Second Edition)Norm G. Ducharme, ... Ava M. Trent
Chapter
Diseases of the Cornea and Sclera
2008, Handbook of Small Animal Practice (Fifth Edition)Ruth Marrion
Corneal Ulceration
Definition
I.
: Superficial erosion is a loss of the corneal epithelium only.
II.
: Stromal ulceration involves loss of both the epithelium and some portion of stroma.
III.
: With a descemetocele, stroma is lost down to Descemet's membrane.
IV.
: Perforation is a wound in Descemet's membrane, with leakage of aqueous humor and/or iris prolapse.
Causes
I.
: Trauma
A.
: External sources: cat scratch, foreign body, others
B.
: Eyelid disease: distichiasis, ectopic cilia, entropion
II.
: Tear film disease
A.
: Keratoconjunctivitis sicca (KCS)
B.
: Goblet cell deficiency
C.
: Lipid tear film abnormality from meibomian gland pathology (Moore, 1999)
III.
: Lagophthalmos
A.
: Macropalpebral fissure
B.
: Exophthalmos: pathologic or conformational
C.
: Buphthalmos
D.
: Decreased blink frequency
1.
: It may occur from corneal denervation after trigeminal nerve injury.
2.
: Brachycephalic dogs have relatively few corneal nerves and often an incomplete blink.
E.
: Palpebral nerve palsy
IV.
: Infections
A.
: Bacterial (Tolar et al., 2006; see previous discussion)
B.
: Fungal: aspergillosis (Marlar et al., 1994; see previous discussion)
C.
: Viral: FHV (see previous discussion)
1.
: Infection may be primary or may be a recurrence of latent infection.
2.
: Infection may be more common in immunosuppressed or stressed cats.
V.
: Thermal or chemical burns
A.
: Detergent agents
B.
: Acids
C.
: Alkaline agents
VI.
: Immune-mediated disease: marginal keratitis (Parshall and Kellum, 1987)
VII.
: Secondary to other corneal disease
A.
: Calcium infiltrates
B.
: Edema (especially bullous keratopathy)
C.
: Corneal epithelial basement membrane disorder
Pathophysiology
I.
: One of the causative events results in damage to the corneal epithelium, with focal or widespread loss.
II.
: In some cases, corneal stroma is lost as well.
III.
: Epithelial cell mitosis and migration occur, covering the wound in several days.
IV.
: Continued presence of an inciting cause (e.g., trauma, lagophthalmos) or a secondary factor (e.g., basement membrane disease, secondary bacterial infection, FHV infection) may prevent healing.
Clinical Signs
I.
: Superficial erosions
A.
: Blepharospasm
B.
: Epiphora
C.
: Congestion of conjunctival vessels
D.
: Miosis in some cases
II.
: Stromal ulcers
A.
: All of the signs of superficial erosions
B.
: Visible defect in the stroma
C.
: Mucopurulent discharge
D.
: Aqueous flare, with or without hypopyon
E.
: Perilimbal vascularization (brush border)
III.
: Descemetoceles
A.
: All the signs of stromal ulcers are usually present.
B.
: Exposed Descemet's membrane is smooth and clear, not edematous like stroma, does not retain fluorescein stain.
IV.
: Perforated corneal ulcers
A.
: All the signs of descemetoceles, plus intense blepharospasm
B.
: Fibrin or pigmented mass (iris prolapse) in the ulcer bed
C.
: Possibly fluid leaking from the wound
V.
: Herpesvirus keratitis
A.
: Young kittens
1.
: Signs of upper respiratory infection
2.
: Ocular discharge associated with corneal ulceration
B.
: Adult cats
1.
: Signs of upper respiratory infection are rarely seen.
2.
: Very small epithelial linear or dendritic lesions, or erosions and ulcers of any size and shape may be found.
3.
: Secondary KCS may be present.
Diagnosis
I.
: Stain the cornea with fluorescein to determine the pres-ence of an ulcer (Descemet's membrane will not stain).
II.
: Test palpebral nerve function and ability to blink completely.
III.
: Perform a Schirmer tear test (STT) unless obvious epiphora is present.
IV.
: Carefully examine the adnexa to determine whether the ulcer is from an endogenous or exogenous irritant.
Differential Diagnosis
I.
: Anterior uveitis may also cause pain, epiphora, miosis, and congestion of episcleral vessels; however, a fluorescein dye test is negative.
II.
: Glaucoma may cause pain, epiphora, and episcleral vessel congestion; however, the pupil is usually dilated, unresponsive.
A.
: Lack of normal menace reflex occurs.
B.
: The fluorescein dye test is negative.
III.
: Entropion, distichiasis, and ectopic cilia may cause pain, epiphora, and conjunctival hyperemia, with or without a concurrent corneal erosion or ulcer.
IV.
: KCS or conjunctivitis may cause pain and conjunctival hyperemia.
A.
: Epiphora is not present in cases of KCS, and the STT is abnormally low.
B.
: Fluorescein dye test is negative.
Treatment
I.
: Topical antibiotics
A.
: Apply TID to QID for superficial erosions, 4 to 12 times a day for stromal ulcers.
B.
: Stromal ulcers are treated with antibiotics that are bactericidal and broad spectrum.
C.
: Neomycin is used with caution in cats because of the potential for anaphylactic reactions (Plunkett, 2000).
D.
: Fluoroquinolones and tobramycin should not be used prophylactically but are reserved for rapidly progressive ulcers, as discussed previously.
II.
: Topical atropine
A.
: Give to effect.
B.
: Usually SID to QID is sufficient, but some cases require a higher frequency.
C.
: Also indicated for anterior uveal inflammation as manifested by miosis, aqueous flare, and hypopyon.
III.
: Systemic nonsteroidal antiinflammatory agents in dogs
A.
: Indicated if uveitis is present
B.
: Aspirin 10 mg/kg PO BID
C.
: Carprofen 2 mg/kg PO BID
IV.
: Systemic antibiotic medications
A.
: Indicated for corneal perforations
B.
: Amoxicillin 22 mg/kg PO BID
V.
: Contact lenses
A.
: Soft contact lenses are indicated for superficial nonhealing erosions and are contraindicated in infected corneal ulcers.
B.
: Collagen contact lenses can be rehydrated in topical antibiotic solution and used in infected corneal ulcers (last 24 to 72 hours).
VI.
: Surgical therapy (Table 98-4)
A.
: Third eyelid flaps
1.
: Useful to protect ulcers secondary to lagophthalmos, decreased blink frequency, poor lid conformation, and KCS
2.
: Contraindicated in rapidly progressive ulcers because they prevent monitoring of the condition
B.
: Conjunctival flaps
1.
: They are indicated for descemetoceles or for deep stromal ulcers.
2.
: They act as a graft with an intact blood supply rather than a bandaging effect.
3.
: The graft is cut at the base 6 to 8 weeks after surgery to interrupt blood supply and reduce scarring.
C.
: Primary closure
1.
: It is used for descemetoceles and for ruptured corneal ulcers <2 to 3 mm in diameter.
2.
: If performed in larger wounds, it may distort the cornea excessively.
D.
: Corneoscleral transposition and lamellar grafts (Brightman et al., 1989)
1.
: Used for closure of descemetoceles and perforated corneal ulcers too large to close primarily
2.
: Require adjacent healthy cornea to transpose
E.
: Swine intestinal submucosa (SIS) (Bussieres et al., 2004)
1.
: Has been used for perforated ulcers, deep stromal ulcers, and corneal abscesses
2.
: Requires adjacent healthy cornea to which to suture
VII.
: Therapy of FHV (see previous discussion)
VIII.
: Therapy of bacterial fungal ulcers (see previous discussion)
IX.
: Therapy of persistent erosions (see following section)
Monitoring of Animal
I.
: Recheck visits are important.
A.
: Superficial erosions: in 5 to 7 days
B.
: Stromal ulcers: every 2 to 3 days until reepithelialized or until no purulent discharge is seen
II.
: Watch for signs of infection (change from epiphora to purulent discharge, increased depth of the lesion).
A.
: Culture the wound.
B.
: Increase antibiotic frequency and/or change antibiotics.
C.
: Consider surgical intervention.
III.
: If not healed in 1 to 2 weeks, then a thorough ocular examination is repeated to rule out any previously undiagnosed cause.
IV.
: Postoperative rechecks are scheduled every 2 to 3 days for a week, then every 1 to 2 weeks until the cornea is healed.
V.
: Herpesvirus keratitis is controllable but not curable; periodic flare-ups are common.
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Chapter
Cocaine
2006, Meyler's Side Effects of Drugs: The International Encyclopedia of Adverse Drug Reactions and Interactions (Fifteenth Edition)
Peptic ulceration
There is a higher incidence of gastric ulcers in cocaine users, both perforated ulcers and giant gastroduodenal ulcers, thought to be due to localized ischemia secondary to vasoconstriction (146,147). Two reports have afforded data on gastrointestinal ulcers and cocaine. In one study the authors observed that since the advent of crack cocaine they had seen more than 70 cases of crack-related perforated ulcers (146). They suggested that an ischemic process rather than an acid-producing mechanism was to blame. They described three patients, all of whom had laparoscopic omental patches for ulcers, with good results. In a longitudinal assessment of patients with endoscopically diagnosed gastric ulcers (n = 98) or duodenal ulcers (n = 116) users of cocaine or metamfetamine were nearly 10 times more likely to have giant gastric or duodenal ulcers (over 2.5 cm) compared with non-users (147). The authors speculated that cocaine and amfetamine-induced catecholamine stimulation of α-adrenoceptors may cause intense vasoconstriction and thus a reduced blood supply to an ulcer, resulting in a giant ulcer.
Five cases of gastric perforation (rather than the more common duodenal perforation) have been reported in young male smokers of crack, all of whom had only brief histories of prodromal symptoms and none of whom had long-standing peptic ulcer disease (148).
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Reference work2006, Meyler's Side Effects of Drugs: The International Encyclopedia of Adverse Drug Reactions and Interactions (Fifteenth Edition)
Chapter
Gastrointestinal Disease in Systemic Lupus Erythematosus
2007, Systemic Lupus ErythematosusChi Chiu Mok MD, FRCP
CLINICAL MANIFESTATIONS
Oral Cavity
Oral ulceration is a common feature of SLE, occurring in 6 to 52% of patients.1 Oral ulcers is one of the 11 American College of Rheumatology (ACR) revised criteria for the classification of SLE, and is a marker for disease activity. Typically, these ulcers are superficial, painless, and mostly found on the hard palate, buccal cavity, and vermiform border. Less commonly, ulcers may also develop in the nasal cavity and the pharyngeal wall. Histology is usually nonspecific.
Chronic discoid lupus erythematosus (DLE) may develop in the oral mucosa. Up to 24% of patients with chronic cutaneous LE had concomitant mucous membrane lesions.2 Mucosal DLE usually starts as a painless erythematosus patch that slowly matures into a chronic plaque-like lesion. It is frequently found in the buccal mucosa, but the palate and tongue may also be involved. DLE lesions can be severely painful, and their morphology may be confused with lichen planus or leukoplakia. Tissue biopsy may show lupus-specific histopathology similar to that of the skin.
Oral ulceration may also be caused by infection and therapy of SLE. Viral infection such as herpes simplex and fungal infections such as candidiasis may lead to painful oral ulcers and plaque-like lesions. Immunosuppressive agents such as cyclophosphamide and methotrexate may induce mucositis and mucosal ulceration.
Sicca symptoms such as dry mouth and dry eyes are fairly common in SLE patients. Manoussakis and colleagues3 reported a 9.2% prevalence of secondary Sjögren's syndrome in 283 unselected SLE patients using the American-European classification criteria. The clinical presentation of Sjögren's syndrome in SLE was no different from that of primary Sjögren's syndrome, but older age, Raynaud's phenomenon, anti-Ro, anti-La, and rheumatoid factor were more frequent in SLE patients, whereas renal disease, lymphadenopathy, and thrombocytopenia were less common.
SLE patients are prone to poor dental health. This is a result of multiple factors, including disease activity, reduced salivary flow, bleeding diathesis, and the use of medications such as corticosteroids (risk of gingival infection), aspirin, and nonsteroidal anti-inflammatory drugs (NSAIDs) (platelet dysfunction), cyclosporin A (gingivitis, gingival hypertrophy), methotrexate (stomatitis and mucositis), antiepileptic agents (gum hypertrophy), and tricyclic antidepressants (which worsen sicca).
Meyer and colleagues4 studied the frequency of oral, dental, and periodontal findings in 46 patients with SLE. Compared with healthy matched controls, oral mucosal lesions such as aphthous ulcers, erythema, gingival overgrowth, and hemorrhage were more frequently found in SLE patients (48% vs. 25%). The extent of periodontal disease was related to the severity and duration of SLE. In addition to disease and treatment-related factors, chronic periodontitis in SLE has also been linked to genetic factors such as the FcgammaRIIa polymorphisms5 and the antineutrophil cytoplasmic antibodies.6 Periodontal disease may pose a potentially serious health risk in SLE patients because a recent systematic review suggested a modest association between periodontitis and cardiovascular diseases.7
Esophagus
Dysphagia occurs in 1 to 13% and heartburn in 11 to 50% of patients with SLE.1 These may be attributed to dry mouth, esophageal hypomotility, esophagitis, or esophageal ulceration because of acid reflux and infection. Manometry studies reveal functional abnormalities of the esophagus in 10 to 32% of SLE patients.8,9 Aperistalsis or hypoperistalsis is most frequently found in the upper one-third of the esophagus,9 and is associated with Raynaud's phenomenon in some studies.8 The reasons for esophageal hypomotility in SLE remain elusive. Skeletal muscle fiber atrophy, inflammatory reaction in the esophageal muscles, and ischemic or vasculitic damage of the Auerbach plexus have been postulated.
Esophagitis with ulceration was reported in 3 to 5% of patients with SLE.1 This may be caused by gastroesophageal reflux or infections such as Candida, herpes simplex, and cytomegalovirus (CMV). Endoscopic examination with biopsy is necessary to establish the diagnosis. A true vasculitis leading to esophageal ulceration is probably rare.10 In addition, medications such as NSAIDs and the bisphosphonates are occasionally associated with esophagitis and bleeding esophageal ulcers.
Stomach
Gastritis, gastric erosion, and ulceration in SLE patients may result from treatment with high-dose corticosteroids and NSAIDs. In two studies of acute abdomen in SLE patients, perforated peptic ulcer was diagnosed in 6 to 8% of cases.11,12 While the exact incidence of peptic ulcer disease in SLE patients is unknown, adverse effects of medications are the most common causes. Vasculitis of the gastric mucosa related to active SLE causing ulceration and bleeding is exceedingly rare.
Although pernicious anemia has been reported in patients with SLE, its prevalence is low. A study of 30 SLE patients reported that only one patient (3%) suffered from pernicious anemia characterized by low serum cobalamin level, macrocytic anemia, and the presence of antibody against intrinsic factor.13 Another study indicated that 19% of female SLE patients had low serum cobalamin levels, but none developed overt anemia.14
Gastric antral vascular ectasia (GAVE) is a rare vascular malformation in the GI tract that may cause acute or chronic bleeding. The characteristic endoscopic appearance is a collection of red spots of ectatic vessels arranged in stripes along the antral rugal folds. GAVE is mostly found in patients with systemic sclerosis, but has been reported in SLE.15
Although the stomach is relatively resistant to infection, CMV gastritis has been reported in heavily immunocompromised patients. Renal transplant recipients who receive mycophenolate mofetil (MMF)-based immunosuppressive protocols are prone to disseminated CMV infections. As MMF is increasingly used in patients with SLE, CMV infection of the GI tract should not be overlooked.
Small Intestine
Mesenteric/Intestinal Vasculitis
The prevalence of intestinal vasculitis in patients with SLE ranged from 0.2 to 1.1%.15 In SLE patients presenting with acute abdominal pain, intestinal vasculitis was diagnosed in 5 to 60% of patients.11,16–18 Most patients with mesenteric vasculitis present with cramping or persistent abdominal pain, a variable degree of nausea and vomiting, fever, diarrhea, and bloody stools. Abdominal distension, tenderness, and rebound tenderness are usually present, and bowel sound may be diminished or absent. In severe cases, mucosal ulceration with bleeding, bowel edema with paralytic ileus, hemorrhagic ileitis, intussusception, and even bowel gangrene and perforation may develop.19,20 Active SLE in other organs is usually evident.
Abdominal radiographs in patients with lupus mesenteric vasculitis may reveal changes such as pseudo-obstruction of the gastric outlet, duodenal hypomotility, bowel loop distension, effacement of the mucosal folds, and thumb-printing appearance (submucosal edema as a result of bowel ischemia). Intra-abdominal free gas may appear after intestinal perforation, or because of pneumatosis cystoids intestinalis. Ultrasound and computed tomography (CT) scan of the abdomen are important in excluding intra-abdominal abscesses, pancreatitis, and other intra-abdominal pathologies. In addition, a contrast CT scan may reveal bowel wall changes, mesenteric vascular and fat changes, fluid collection, retroperitoneal lymphadenopathy, peritoneal enhancement, and hepatomegaly. Conspicuous prominence of mesenteric vessels with a palisade pattern or comb-like appearance supplying focal or diffuse dilated bowel loops, ascites with slightly increased peritoneal enhancement, and bowel wall thickening with double halo or target sign (enhancing outer and inner rim with hypoattenuation in the center) are characteristic early CT findings of lupus mesenteric vasculitis.21
The typical histopathologic findings of lupus mesenteric vasculitis usually occur in the arterioles and venules of the submucosa of the small bowel wall rather in the medium-sized mesenteric arteries.20,22,23 Vasculitic lesions tend to be segmental and focal.19 Immunohistochemical staining of the tunica adventitia and media may reveal immune complex, C3 complement, and fibrinogen deposition. Fibrinoid necrosis, intraluminal thrombosis of affected vessels, acute or chronic inflammatory infiltrates consisting of lymphocytes, plasma cells, histiocytes, and neutrophils may also be demonstrated.23
Mesenteric Insufficiency
Patients with SLE are prone to premature atherosclerosis. Chronic mesenteric insufficiency, or “intestinal angina,” should be considered in patients who present with chronic intermittent abdominal pain. Symptoms usually start in the postprandial state and persist for several hours. Abdominal pain may be mild at onset and progress in severity over weeks or months. Fear of eating often leads to weight loss. Concomitant atherosclerotic disease in the coronary and carotid vessels is usually present. SLE patients at risk are those with long-standing disease, renal insufficiency, persistent proteinuria, antiphospholipid positivity, chronic corticosteroid therapy, and traditional risk factors for atherosclerosis.
The diagnosis of chronic mesenteric insufficiency relies on a high index of suspicion. Conventional angiography is the gold-standard imaging procedure. Digital subtraction angiography, Doppler ultrasonography, and magnetic resonance imaging with angiography are adjunctive diagnostic modalities.24
Acute mesenteric ischemia can result from impaired blood flow within the mesenteric arterial or venous systems. Classically, abdominal pain is persistent and disproportionately severe relative to physical signs. Patients may also present with acute abdomen with distention, rigidity, fever, bloody diarrhea, melena, and hypotension. SLE patients with underlying chronic mesenteric insufficiency due to atherosclerosis or secondary antiphospholipid syndrome are particularly prone to acute intestinal ischemia, which may be precipitated by hypoperfusion states. Acute mesenteric thrombosis may result in bowel infarction, perforation, and peritonitis.
Intestinal Pseudo-Obstruction
Intestinal pseudo-obstruction (IPO) is a clinical syndrome characterized by impaired intestinal motility as a result of dysfunction of the visceral smooth muscle or the enteric nervous system. IPO may be the initial presentation of SLE and usually occurs in the setting of active lupus.25 The small bowel is more commonly involved than the large bowel.
Common presenting symptoms of IPO are a subacute onset of abdominal pain, nausea, vomiting, abdominal distention, and constipation. Physical examination often reveals a diffusely tender abdomen with sluggish or absent bowel sound. Rebound tenderness is usually absent. Radiologic examinations may demonstrate dilated, fluid-filled bowel loops, with thickened bowel wall and multiple fluid levels (Fig. 34.1). Organic causes for intestinal obstruction should be sought, preferably by nonsurgical assessment but laparotomy may be necessary in some patients.
Manometry motility studies in patients with IPO may demonstrate esophageal aperistalsis and intestinal hypomotility.26 Interestingly, 63% of the reported cases of SLE-related IPO had concomitant ureterohydronephrosis and contracted urinary bladder, and around one-third of these patients had documented histologic features of interstitial cystitis.25 Lupus interstitial cystitis may lead to bladder wall thickening and reduced bladder capacity. This may in turn induce ureterohydronephrosis because of detrusor muscle spasm and secondary vesiculo-ureteric reflux.
The pathogenesis of IPO in SLE is unclear. The association with autoimmune cystitis and the demonstration of antibodies against proliferating cell–nuclear antigen in some patients27 suggests that vasculitis of the visceral smooth muscles is a mechanism which may lead to muscular damage and hypomotility. The simultaneous presence of ureterohydronephrosis in many patients with SLE-related IPO and the association of hypomotility of other parts of the GI tract indicate that the basic pathology may be dysmotility of the intestinal musculature. Whether this is caused by a primary myopathy, neuropathy, vasculitis, or antibodies directed against the smooth muscle of the gut wall requires further study.
Malabsorption
Intestinal malabsorption in SLE may result in protein losing enteropathy, hypoalbuminemia, and ascites. Mader and colleagues28 screened 21 SLE patients for malabsorption by the D-xylose absorption test (DXT), microscopic examination of the stool for fat droplets, and biopsy from the second part of the duodenum. Two patients (10%) were found to have an abnormal DXT and excessive fecal fat excretion. In one of these patients, histologic examination revealed flattened and deformed villi with an inflammatory infiltrate. Immunoperoxidase staining did not reveal excessive deposition of immunoglobulins and light chains within the intestinal mucosa in these patients.
Up to 23% of patients with SLE may be tested positive for either the IgA or IgM antigliadin antibodies,29 but biopsy-proven celiac disease (gluten-sensitive enteropathy) is exceedingly uncommon.
Protein-Losing Gastroenteropathy
Protein-losing gastroenteropathy (PLGE) is characterized by hypoalbuminemia secondary to loss of protein from the GI tract. It is usually identified by an elevated clearance of stool α1-antitrypsin or the technetium99m-labeled human serum albumin scan (Fig. 34.2). Significant loss of protein from the kidneys should be ruled out. A variety of pathologies from the stomach down to the colon may be responsible for protein loss. Investigations into the causes of PLGE such as gastrointestinal lymphoma, malabsorption state, bacterial overgrowth, chronic infection, polyposis, and lymphatic obstruction are essential. Endoscopic examination with mucosal biopsies, barium studies, radiologic examinations, and absorption tests may be required.
PLGE is a rare manifestation of SLE, and fewer than 50 cases have been described. We recently reported 16 cases of SLE-related PLGE and reviewed 32 other patients in the literature.30 PLGE was the presenting feature in three-quarters of our patients and most patients had active SLE in other organs. The most common presentation was generalized or dependent edema, and abdominal symptoms, such as pain, nonbloody diarrhea, nausea, vomiting, and anorexia. Protein leakage occurred more frequently from the small bowel (69%) than the large bowel (31%). Specific endoscopic, imaging, and histologic findings were often absent. The most common endoscopic appearance was mucosal edema.31 The biopsy was either normal or revealed nonspecific findings such as villous atrophy, submucosal edema, dilated lacteals, and inflammatory infiltrates. Definite lymphangiectasia, vasculitis, or C3 deposition in the capillary walls of the lamina propriae of villi was uncommon.
The exact pathogenesis of PLGE remains elusive. Mucosal disruption and increase in mucosal capillary permeability as a result of complement- or cytokine-mediated damage, mesenteric venulitis, and dilated/ruptured mucosal lacteals have been postulated.30
Infective Enteritis
Infective enteritis should be considered in SLE patients presenting with abdominal symptoms. Bacterial enteritis is the most common, with nontyphoidal Salmonella infection being most frequently reported.32 Campylobacter jejuni infection and CMV enteritis may lead to ileal perforation.
Ascites and Peritonitis
Ascites in SLE may be inflammatory or noninflammatory in nature. Acute peritonitis with and without ascites can be caused by mesenteric vasculitis or serositis as a result of active SLE, infection, bowel infarction, perforated viscera, and pancreatitis. On the other hand, subacute or chronic peritoneal effusion can be the result of lupus peritonitis, hypoalbuminemia (nephrotic syndrome, protein-losing enteropathy, and liver cirrhosis), right heart failure, constrictive pericarditis, hepatic venous thrombosis, malignancy, and more indolent infections such as tuberculosis.
Inflammatory peritonitis in SLE is generally painful, but clinical signs may be masked by corticosteroid and immunosuppressive treatment. Conversely, lupus peritonitis may present with severe abdominal pain mimicking acute surgical abdomen. In a recent cross-sectional study of 310 patients with SLE, 69 episodes of SLE-related serositis were reported in 37 patients (12%).33 Thirty percent of these episodes were peritonitis/ascites. All patients presented with abdominal pain, but physical signs (abdominal distension, voluntary guarding, rebound tenderness and ascites) were present in less than 20% of patients. One patient presented with acute abdomen, but laparotomy did not reveal any significant pathologies. On follow-up, recurrence of peritonitis was more common than pericarditis and pleuritis.
The exact pathogenesis of SLE-related peritonitis remains obscure. Inflammatory infiltrates, immunoglobulin, and complement deposits may be demonstrated in peritoneal tissues and the peritoneal vessels.34 Imaging studies such as contrast CT scan may reveal ascites and asymmetric thickening of the small bowel wall.
Large Intestine
Lupus Colitis
Although lupus enteritis mainly involves the small bowel, the large bowel may also be affected. In the series by Zizic and colleagues35 and Medina and colleagues,11 colonic involvement by SLE with perforation was described. Most patients had active SLE in other organs, and mortality was high. In addition, vasculitic ulcers of the rectal mucosa that may perforate and lead to septicemia have been described in patients with SLE.36
Inflammatory Bowel Disease
Crohn's disease and ulcerative colitis (UC) are rarely associated with SLE. Whether there is a true association between SLE and inflammatory bowel disease is unclear. Clinically and pathologically, lupus colitis may be indistinguishable from UC. Symptoms include lower abdominal discomfort, perirectal bleeding, and persistent diarrhea that may be bloody. The prevalence of UC in SLE patients is around 0.4%.15 Alarcon-Segovia and colleagues37 reported SLE in 3% of patients with UC. However, this prevalence figure might have been overestimated because cases of sulfasalazine-induced lupus were likely to be included in this early series.
Collagenous Colitis
Collagenous colitis is a disorder characterized by colonic intraepithelial lymphocytosis, expansion of the lamina propria with acute and chronic inflammatory cells, and a thickened subepithelial collagen band. Patients usually present with chronic watery diarrhea despite normal radiologic and endoscopic findings. Collagenous colitis has been reported in association with DLE and SLE.15
Infective Colitis
Colonic infections should be considered in SLE patients presenting with lower GI symptoms. CMV and amoebic colitis has been reported in patients with SLE.10 Lymphopenia, cytotoxic treatment, presence of renal disease, and a travel history to endemic areas are predisposing factors.
Diverticular Disease
The incidence of diverticular disease does not appear to be higher in SLE patients than in the general population. Diverticular disease is expected to occur in older individuals with SLE, and is an important differential diagnosis in patients who present with fever, abdominal pain, and tenderness.
Liver
Liver Function Abnormalities
Liver function abnormalities are common but usually mild in patients with SLE. Multiple factors may contribute, such as the use of aspirin, NSAIDs, azathioprine, and methotrexate; fatty infiltration of liver as a result of corticosteroid treatment; diabetes mellitus; obesity; viral hepatitis; and alcoholism. In around one-quarter of cases, no causes other than active SLE itself are responsible. Persistent and severe liver function abnormalities are uncommon, but require further investigations such as ultrasonography and liver biopsy to delineate the underlying causes.
In a series of 206 SLE patients, Runyon and colleagues38 reported that 124 (60%) patients had abnormal liver function test results. However, significant liver disease was diagnosed in 43 (21%) patients only. Liver biopsy in 33 patients revealed steatotic hepatitis (36%), cirrhosis (12%), chronic active hepatitis (9%), chronic granulomatous hepatitis (9%), centrilobular necrosis (9%), chronic persistent hepatitis (6%), and microabscesses (6%). Eight patients improved with corticosteroid treatment, but three patients died of liver failure. Gibson and Myers39 studied 81 patients with SLE, and reported that 45 (55%) of them had abnormal liver function results at some point. The majority of these patients had mild liver function derangement. No causes other than SLE itself for the liver dysfunction were present in 19 (23%) patients. Of the patients with liver biopsy performed, seven showed normal histology, five had portal inflammatory infiltrates, one had fatty liver, and one had chronic active hepatitis. In a prospective study, Miller and colleagues40 reported liver function abnormalities in 23% of their SLE patients. One-third of them did not have identifiable causes. In 80% of these patients with persistent “unexplained” transaminase elevations during follow-up visits, changes in SGPT levels were concordant with SLE activity.
Lupus Hepatitis
Autoimmune hepatitis (AIH) is characterized histologically by interface hepatitis and portal plasma cell infiltration, hypergammaglobulinemia, and the presence of a variety of autoantibodies that direct against hepatic antigens or liver–kidney microsomal proteins such as ANA, antismooth muscle antibodies (SMA), and anti-LKM antibodies. AIH may be classified into three types based on their immunoserologic markers. Type I AIH (the classical “lupoid hepatitis” described in the 1950s) is the most common form worldwide and is associated with ANA and/or SMA. Type II AIH is associated with the anti-LKM1 antibody, while type III AIH is associated with anti-SLA/LP antibodies.
Patients with AIH usually present with insidious onset of nonspecific symptoms such as fatigue, malaise, and anorexia. Liver enlargement, jaundice, and ascites may be present in severe cases. AIH is also associated with lupus-like features such as positive ANA, hypergammaglobulinemia, and joint symptoms. However, only around 10% of patients with AIH fulfill the ACR criteria for SLE.41 The term “lupus hepatitis” should be reserved for patients fulfilling the ACR criteria for SLE who have chronic active hepatitis, with documented lymphocytic infiltration of periportal areas on histology (Fig. 34.3). Other causes of liver function derangement such as viral infection, alcoholism, metabolic or genetic liver diseases, and effects of drugs have to be excluded.
The incidence of AIH in SLE patients is unclear because not all patients will have the diagnosis confirmed by liver biopsy. In one study, evidence for chronic active hepatitis was present in 4.7% of patients who fulfilled the ACR criteria for SLE.42 Arnett and Reichlin43 reported that 4 (3%) of their 131 SLE patients had a clinical picture of chronic active hepatitis. Evidence for chronic viral infection was absent, and only 1 patient had low-titer SMA. Compared with non-SLE patients, SLE patients with AIH are more likely to have autoantibodies against dsDNA, Sm, and antiribosomal P.
Chronic Viral Hepatitis
The prevalence of chronic hepatitis-B virus (HBV) infection does not seem to be higher in patients with SLE when compared to the general population, even in endemic areas. In a study from Taiwan, the prevalence of HBV infection was reported to be significantly lower than that in the general population (3.5% vs. 14.7%).44 Patients with coexistent SLE and chronic HBV infection had less lupus activity, including less proteinuria and a lower serum titer of anti-dsDNA than HBsAg-negative lupus patients. Another study from the Middle East did not find HBV infection in 96 SLE patients, compared to prevalence of 2% in the general population.45
Perlemuter and colleagues46 reported that 19 (3%) of their 700 SLE patients had chronic hepatitis C (HCV) infection. Compared with age- and gender-matched control patients, SLE patients with HCV infection had a higher prevalence of asymptomatic cryoglobulinemia. Ramos-Casals and colleagues47 reported an increased prevalence of HCV infection in their SLE patients compared to healthy blood donors (13% vs. 1%). SLE patients with HCV infection were less likely to have cutaneous disease and anti-dsDNA, but more likely to have hepatic dysfunction, low complement levels, and cryoglobulinemia than those without SLE.
Drug-Induced Hepatotoxicity
Aspirin, NSAIDs, methotrexate, and leflunomide may cause elevation of parenchymal liver enzymes. Corticosteroids may induce fatty liver disease (steatotic hepatitis). Azathioprine and hydroxychloroquine occasionally cause hepatitis. Of interest is minocycline, a drug used in the treatment of rheumatoid arthritis and acne, which may induce a syndrome of drug-induced lupus and autoimmune hepatitis. The statins are increasingly used in patients with SLE. Isolated case reports of statin-induced lupus-like syndrome and hepatitis should be noted.
Other Liver Diseases
Thromboembolic disorders of the liver may occur in patients with SLE, especially in the presence of the antiphospholipid antibodies. Budd-Chiari syndrome, a disease caused by occlusion of the hepatic veins, hepatic veno-occlusive disease, and hepatic infarction have been reported in patients with SLE and secondary antiphospholipid syndrome.48
Nodular regenerative hyperplasia (NRH) is characterized by diffuse nodularity of the liver with little or no fibrosis. It is a cause of noncirrhotic portal hypertension and may lead to ascites and variceal bleeding. NRH has been described in patients with SLE and primary antiphospholipid syndrome.49,50 The association with the antiphospholipid antibodies suggests that NRH may result from liver regeneration to maintain its functional capacity after ischemia-induced injury.50
In an autopsy study of 160 livers, Matsumoto and colleagues51 described 7 cases of NRH, 5 of which were found in patients with SLE. NRH should be suspected in SLE patients with unexplained portal hypertension, and confirmed by liver biopsy. Hepatic nodules may be better visualized with magnetic resonance imaging (MRI) of the liver.49 Many patients with NRH of the liver are asymptomatic with normal liver function. Treatment should target at control of portal hypertension and its related complications.
Biliary Tract Disease
Gallbladder disease appears to be no more frequent in SLE patients than in the general population. Cholecystitis in SLE may be confused with serositis. Acute acalculous cholecystitis has been described in patients with SLE.52 Patients usually present with acute abdomen, and cholecystectomy specimens may reveal vasculitis of the gall bladder. Although successful conservative treatment with corticosteroids has been reported,52 most patients were diagnosed after surgical treatment, especially if there was evidence of septicemia.
On the other hand, primary biliary cirrhosis (PBC), autoimmune cholangiopathy (antimitochondrial antibody-negative PBC), and primary sclerosing cholangitis, a rare disorder associated with the inflammatory bowel diseases, have also been reported in patients with SLE.15
Pancreas
Pancreatitis is an uncommon manifestation of SLE. The prevalence of pancreatitis in SLE patients ranges from 0 to 4%.15,53 Medications such as corticosteroids, azathioprine, and thiazide diuretics have been attributed to cause pancreatitis in some cases.
Pascual-Ramos and colleagues53 analyzed 49 episodes of acute pancreatitis in 35 SLE patients. Seventeen episodes were considered idiopathic, and disease activity scores were significantly higher than those with identified causes of pancreatitis. Compared with non-SLE controls, “idiopathic” pancreatitis was more frequent in SLE patients. Medication use did not seem to be associated with the development of pancreatitis. Saab and colleagues54 reported eight SLE patients with pancreatitis. All responded to corticosteroid treatment. Derk and De Horatius55 studied 25 SLE patients diagnosed to have acute pancreatitis in a 20-year period. Three-quarters of the patients had active SLE in other systems. Pancreatitis improved in most patients with systemic corticosteroids. These studies suggest that lupus pancreatitis is likely to be a distinct entity that occurs in patients with active disease and responds to immunosuppressive treatment. In fact, in the pre-steroid era, cases of pancreatic vasculitis were documented histopathologically.15 Autopsy studies have also demonstrated vascular damage consisting of severe intimal proliferation in the pancreatic vessels in patients with lupus pancreatitis.56
Hasselbacher and colleagues57 studied 25 patients with SLE, and demonstrated that 20% of patients had elevated amylase level and 25% had macroamylase activity. None of the patients had clinical pancreatitis. Eberhard and colleagues58 measured serum immunoreactive cationic trypsinogen (IRT) in 35 asymptomatic patients with SLE. Fifteen patients (43%) had elevated IRT levels on at least one occasion. There was no apparent association with the use of drugs such as prednisone and azathioprine. This suggested that subclinical pancreatic dysfunction might be present in some patients with SLE.
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Book2007, Systemic Lupus ErythematosusChi Chiu Mok MD, FRCP
Chapter
Surgery of the Bovine Digestive System
2017, Farm Animal Surgery (Second Edition)Norm G. Ducharme, ... Ava M. Trent
Abomasal Erosions and Ulcers
Definition
Abomasal ulcers are lesions that penetrate the basement membrane of the abomasal mucosa. Erosion of the mucosa presumably precedes the development of an ulcer. Once the basement membrane has been invaded, the clinical presentation is based on the depth of penetration and the structures involved. Four different types of abomasal ulcerations have been described: Type 1) nonpenetrating ulcers; Type 2) ulcers with profuse intraluminal hemorrhage; Type 3) perforations with localized peritonitis (Figure 14-112); and Type 4) perforations with diffuse peritonitis. The Type 1 category of ulcers has been used to describe both erosions and true ulcers that have penetrated the basement membrane but have not fully broken through the abomasal wall (nonpenetrating ulcers). Perforation on the visceral surface of the abomasum can lead to the syndrome known as omental bursitis (see Intraabdominal and Retroperitoneal Abscesses, considered in this text as a subset of Type 3 ulcers). An individual cow may have multiple ulcers that fall into more than one category.
Predisposing Factors
Abomasal ulcers have been recognized in cattle of all ages and breeds but are more common in cattle in intensive-management settings. Specific groups recognized to be at risk for ulcers in general include high-production dairy cows, feedlot cattle, veal calves, and beef calves. Abomasal ulceration in calves is of sufficient concern in Europe to receive attention in the recommendations of the Council of the European Community's minimum standards for protection of calves. Some reports indicate that the incidence of clinically significant abomasal ulcers is increasing.
Diffuse nonperforating erosions/ulcers are commonly recognized in some groups of cattle, including veal calves, 2- to 8-week-old calves, weanling calves, and fattening cattle, primarily at the time of slaughter. Stress from a variety of sources including changes in housing or feed, straw ingestion, exposure to infectious agents, and high milk production have been implicated as predisposing factors. The overall prevalence of Type 1 ulcers in veal calves in one study that compared the effects of different types of housing was 86.8%. However, because most cases of Type 1 ulcers are believed to be subclinical, the incidence in groups of cattle that are not routinely seen at slaughter or necropsy is difficult to estimate.
Type 2 (bleeding) ulcers may be multiple or single, but the category is generally reserved for ulcers that cause severe intraluminal blood loss. Cows with bleeding ulcers represented 26 (0.41%) of 6385 cattle admitted to one referral center over a 14-year period. Bleeding abomasal ulcers can be divided into two groups based on etiology: those associated with lymphosarcoma and those that are not. Cows with lymphosarcoma-associated bleeding ulcers are generally over 5 years of age and are diagnosed throughout the lactation period. Cows with ulcers unassociated with lymphosarcoma generally are less than 4 years of age, present in the first few weeks after parturition, and typically have one or more concurrent postparturient diseases (LDA, metritis, mastitis, and ketosis).
The occurrence of perforating ulcers in adult cattle appears to be more sporadic and associated with episodes of metabolic stress, including recent parturition, peak milk production, and one or more concurrent diseases (abomasal displacement, metritis, mastitis, and ketosis). Diets high in concentrate and corn silage have also been implicated. In a review of cases over a 14-year period in one referral hospital, 43 cases of perforating ulcers were admitted and represented 0.63% of cases admitted during this period. One early study reported that 85% of perforating ulcers resulted in localized peritonitis in the omental bursa, although a more recent study showed an equal or greater percentage of perforating ulcers resulting in diffuse peritonitis.
Diagnosis and Prognosis.
The clinical signs produced by abomasal ulcers depend largely on the category of ulcer and range from vague signs of digestive disturbance to signs consistent with peritonitis or anemia.
Type 1 Ulcers
Type 1 ulcers often lack any detectable clinical signs. However, the presence of Type 1 erosions/ulcers may be suspected in cattle known to be at risk and that show signs of poor appetite, decreased weight gain, and decreased ruminal motility. Concurrent disease is common. Affected animals may be positive for fecal occult blood, but a negative test does not rule out the diagnosis. Erosions do not penetrate the mucosal basement membrane and can heal without contraction or scarring (Figure 14-113). They produce little detectable change when viewed from the serosal surface of the abomasum and can only be diagnosed with certainty at necropsy or during abomasotomy. However, when erosions progress to ulcers, they produce a local inflammatory response with peripheral thickening and occasional serositis that can be detected by palpation of the abomasal wall during abdominal exploration. The contraction and scarring that occurs as a part of healing is also detectable by palpation during exploratory surgery. Nonperforating ulcers are also commonly associated with concurrent diseases, but up to 50% of affected animals may have clinical signs associated with ulceration, including abdominal pain, melena, or pale mucous membranes.
Type II Ulcers
The hallmark signs of bleeding abomasal ulcers are melena caused by blood digested in the abomasum and a positive fecal occult blood test (Figure 14-114). This test is very sensitive, and fresh feces should be collected for examination before performing abdominal palpation per rectum to avoid false-positive results. Other sources of gastrointestinal hemorrhage must be considered as differentials.
Cows with bleeding ulcers unrelated to lymphosarcoma are initially identified by the acute drop in milk production and the appearance of dark loose feces. Pale mucous membranes are common. Cows with non–tumor-associated ulcers are usually anemic (packed cell volume <25%) and are likely to have severe anemia (packed cell volume <15%) with signs of regeneration (nucleated red blood cells and/or increased reticulocyte counts). Signs of abdominal pain may also be present. Ulceration over large submucosal arteries or veins can produce acute severe blood loss that leads to death before external signs are detectable in either adults or calves.
The initial signs in cows with lymphosarcoma are more variable and depend on the effect of the tumor on abomasal function, the amount of bleeding, and the involvement of other viscera. Cows with tumors isolated to the abomasum are typically recognized based on signs associated with altered abomasal motility (abomasal displacement, anorexia, or hemorrhage, depression, dark loose stool, pale mucous membranes, and tachycardia). Only 50% of cows with lymphosarcoma-associated abomasal ulcers were found to be anemic in one study, and only 25% had severe anemia (packed cell volume <15%). Other signs of lymphosarcoma—including lymphadenopathy, lymphocytosis, and abnormal lymphocytes in peritoneal fluid—may also be present in some cases.
Type III and IV Ulcers
The outlook for cattle that present with perforating ulcers depends on the perforation depth, ulcer location, the animal's age, and the presence and nature of concurrent diseases. Ulcers that penetrate slowly in areas covered by omentum are more likely to produce localized peritonitis or omental bursitis (Type III ulcers) with less noticeable clinical signs. Cases of perforation associated with LDA also fall into this category, even though they may occur on the uncovered serosal surfaces of the abomasum. It has been hypothesized that the distended abomasum enhances the contact between the perforation site and the body wall, thus allowing better localization of the contamination. Ulcers that occur rapidly in areas that are not covered by omentum are more likely to produce generalized peritonitis (Type IV ulcers) with severe acute clinical signs (see Figure 14-113).
In adult cattle, Type III ulcers may lack any clinical signs specific to the perforation, with identification occurring during investigation of concurrent diseases. Signs, when present, include intermittent anorexia, ruminal stasis and/or distention, abdominal distention, abdominal pain, melena, and anorexia. Perforation on the visceral surface of the abomasum can lead to the syndrome known as omental bursitis, with partial confinement of contaminants between the two layers of the greater omentum. In these cases clinical signs tend to progress gradually and include anorexia, decreased milk production, bilateral ventral abdominal distention, decreased rumen contractions, loose or scant feces, and loss of body condition.
Physical examination with manual pressure on the ventral abdomen may localize abdominal pain to the right cranioventral body wall. This can help distinguish the localized peritonitis caused by Type III ulcers from that caused by traumatic reticuloperitonitis, which is more commonly associated with left cranioventral pain. Localization is not always possible and overlap in location does occur; therefore results should be considered as supportive rather than diagnostic.
Laboratory results are also seldom diagnostic but may provide supportive information. Feces will be positive for occult blood in some but not all cases. Nonspecific systemic signs of inflammation (pyrexia, neutrophilia, hyperfibrinogenemia) may be present in the acute stages of perforation and intermittently afterward. Peritoneocentesis can indicate peritonitis, but the adult cow's ability to localize peritoneal contaminants results in many false negatives in the face of established infection. Elevated peritoneal white blood cell counts and normal to increased peritoneal protein in the face of a systemic hypoproteinemia suggest peritonitis. Cows with Type III localized perforating ulcers in one study were observed to have a mild hypochloremic, hypokalemic metabolic alkalosis. However, 83% of the cows in this group also had LDAs, and the metabolic and electrolyte changes may reflect the abomasal displacement rather than the ulcer. In cows with a diagnosis of LDA or RDA/RVA, the presence of pneumoperitoneum, signs of abdominal pain (arched back, pain on abdominal pressure), and pyrexia that is not explained by other concurrent disease suggests the presence of perforating ulcers. Ultrasonography can be used to help identify or confirm cranial right abdominal peritonitis. Ultrasonography can also help identify fibrin accumulation and/or abscess formation along the cranioventral abdomen. In some cases the fibrin accumulation is sufficiently localized to the abomasal body to suggest abomasal ulcers. However, it is often difficult to differentiate between traumatic reticulitis and abomasal ulcers by ultrasound alone.
Cows with Type IV abomasal ulcers present with acute signs of depression, anorexia, agalactia, and systemic shock. Tachycardia, tachypnea, pyrexia, and abdominal pain are common clinical signs. Other gastrointestinal disturbances, including LDA and ruminal tympany, are less common than in cows with Type III ulcers but still present in about half of cases. A normal or low serum total protein in the face of hemoconcentration that results from loss of protein into the peritoneal cavity is often present in cows with diffuse peritonitis. Ultrasonography can confirm a diffuse peritonitis. Leukocytosis, neutrophilia, and left shift are also common in affected cattle. Elevated white cell counts and protein concentrations in peritoneal fluid can be expected in some—but not all—cases. Cows with Type IV ulcers may show a metabolic acidosis with hypokalemia and hypocalcemia.
Cows that survive an acute episode of either Type III or Type IV abomasal ulcers may develop chronic recurrent signs associated with adhesions or chronic abscessation.
Treatment.
Treatment of individual animals with Type I or multiple Type II ulcers should focus on medical management, with tools directed at reduction of metabolic stress, resolution of concurrent diseases, and supportive care for systemic disturbances. Management changes to reduce stress should be considered for the herd in general. Treatment is not recommended for cows with Type II ulcers associated with lymphosarcoma because of the poor prognosis for lymphosarcoma in general. Medical management tools are also important as the sole means of management or as an adjunct to surgical therapy for isolated Type II, III, or IV ulcers.
Surgical therapy is rarely the first choice for managing ulcers of any type, even when an isolated ulcer is suspected. By the time of diagnosis, cattle with isolated bleeding ulcers are often in poor condition and may not tolerate the recumbent approach necessary for access to the abomasum. The extensive omentum and propensity for fibrin deposition in adults provide a reasonably effective initial seal for ulcers that perforate gradually. Surgical intervention can disrupt tentatively localized infection, which leads to more diffuse distribution and increases the risk of septicemia and systemic shock. In most cases the cow's own defense mechanisms are better capable of safely localizing and sealing a perforating abomasal ulcer than is the surgeon. However, surgery is commonly involved in treating concurrent abomasal displacements and diagnostic evaluation of cases with nonspecific signs of forestomach motility disturbances, and ulcers may be encountered incidentally. The goals for surgical therapy are to control hemorrhage, eliminate further peritoneal contamination, eliminate any outflow obstruction produced by ulcers or their sequelae, and ensure a functional abomasal position. The primary surgical procedures performed are submucosal vessel ligation, ulcer resection, or ulcer inversion and oversew.
Surgical access to the abomasum for therapy is limited. The standing left-flank approach will allow separation of adhesions from some Type III ulcers with concurrent LDA and restoration of normal abomasal position but does not provide adequate access for any other procedure, with or without abomasal displacement. The preferred approaches in adult cattle are low right paracostal or right-paramedian incisions with the animal positioned in left lateral or dorsal (right-paramedian only) recumbency. Surgical antibiotic prophylaxis is indicated when planning surgery in which ulcers may be encountered.
Type II Ulcers
Surgical intervention is not generally recommended as the primary approach for treatment of bleeding ulcers. However, when bleeding ulcers are encountered during surgery (thickened and discolored area) for treatment of abomasal displacement or diagnostic exploratory, it is possible in some cases to identify the site of hemorrhage and decrease or eliminate bleeding. This requires identification of the site or sites of hemorrhage and ligation or compression of the involved submucosal vessels. The quantity of hemorrhage seems to decrease once the abomasum is returned to its normal position.
After the abomasum is exposed, the site of hemorrhage should be identified by palpating focal abomasal wall thickening. Whenever possible, the involved area should be exteriorized, packed off from the adjacent tissues, and isolated with intestinal forceps before full-thickness excision of the ulcerated area. Stay sutures (No. 1 monofilament) should be placed at either end of the exposed site to support the intestinal forceps and maintain control of the site, should it be necessary to release the forceps to identify and ligate submucosal vessels. The abomasal serosa should be lavaged to remove debris if the lavage fluid can be directed out of the peritoneal cavity. The abomasal defect should be closed in one or two layers.
If the ulcer is located in the lesser curvature or near the omasal orifice, gaining direct access to the serosal surface over the lesion may be impossible. In a few of these cases, it may be possible to oversew the lesion and compress the involved vessels without entering the abomasal lumen. Large-gauge (No. 1 or No. 2) synthetic absorbable suture material should be used to place large overlapping horizontal mattress pattern sutures across the course of the involved vessels. Alternatively, exposing the luminal surface of the lesion on the lesser curvature may be possible by suturing the parietal surface of the abomasum to the skin as described previously for treatment of abomasal impactions. This technique will allow ligation of bleeding ulcers and will potentially allow the site to be oversewn, although it carries an increased risk of peritoneal contamination and peritonitis.
Type III and IV Ulcers
The majority of Type III ulcers that are identified ante mortem are found during exploratory surgery for LDA. Type IV ulcers that perforate rapidly on the parietal surface are often impossible for the peritoneal cavity to contain and lead to rapid deterioration and death. However, no reports suggest that surgical intervention can improve the outcome. Acute perforation of a partial-thickness or fibrin-sealed ulcer during exploratory surgery is an exception to the rule. If the ulcer can be quickly isolated and oversewn, a combination of debridement, extensive abdominal lavage, antibiotics, and supportive care can be successful (see Figure 14-114 and Figure 14-115A and B).
Adult Cattle and Feedlot Steers.
After exposure of the abomasum, the site of ulceration should be identified. The perforation is generally located at the site of the most well-established adhesions. Once the site has been identified, it should be isolated from as many surrounding adhesions as possible and elevated toward the incision if it is mobile. Before beginning adhesion lysis, the abomasal wall in the vicinity of the perforation should be clamped with atraumatic intestinal forceps or, if this is not possible, isolated manually and the surrounding tissues packed off to help control accidental leakage. Peripheral thin fibrinous adhesions may be gently separated manually, whereas thicker fibrous adhesions may require sharp incision. If the ulcer is in a location that cannot be safely isolated, the adhesions should be left in place and the cow recovered. At this time, a decision to treat medically, perform a second surgery through another approach, or elect slaughter/euthanasia will be needed.
Once the site has been isolated, the area of ulceration should be resected and oversewn with an inverting pattern with an absorbable suture material such as polyglycolic acid, polyglactin 910, or polydioxanone. Chromic gut has been used for this purpose but is not recommended because of the potential for premature absorption in the presence of abomasal acid and the enzyme activity of bacteria and white blood cells. Some authors have described successful management of perforated ulcers by inverting the ulcer site without resecting the ulcer and oversewing the site with an inverting pattern. Care should be taken to avoid spreading debris or contaminated fluid beyond the local site of contamination. The incision should be closed routinely, taking care to lavage each layer of the incision thoroughly before closure. Antibiotic therapy should be continued to treat the peritonitis as indicated based on the level and stage of infection.
If ulceration has produced a localized abscess adjacent to the ventral body wall or within the omental bursa, it may be possible to marsupialize the abscess and treat it by drainage and lavage. Once drainage has stopped, it may be necessary to surgically close the artificial tract.
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Book2017, Farm Animal Surgery (Second Edition)Norm G. Ducharme, ... Ava M. Trent
Chapter
Disorders of the Digestive System
2014, Llama and Alpaca CareChristopher Cebra
Ulcerative Gastritis
First Compartment Ulcers
First compartment ulcers are a poorly recognized entity, in part because they are near-impossible to recognize before death. Ulcers may be focal, multifocal, or diffuse. They usually occur along the transverse pillar or other raised areas of the squamous mucosa (see Figure 40-28). The etiology is unclear. Previous bouts of forestomach acidosis, ingestion of caustic or abrasive feeds and substances, presence of sand, hair balls, or fiber balls, tumors, or infection by membrane-damaging agents may initiate the lesions, which are then perpetuated by superinfection with fungi such as Aspergillus or bacteria such as Fusobacterium.
Signs are vague and include poor growth or body condition, anemia, weight loss, or intermittent diarrhea. Blood abnormalities include hypoproteinemia, mild to moderate anemia, toxic changes in the neutrophils, and alterations in the WBC profile, reflective of blood loss, toxemia, or microbial invasion. Ultrasonography of the forestomach may reveal areas of decreased mucosal thickness, but they are often focal and obscured by feed or gas. Radiography may reveal radiodense contents such as sand. Further diagnostics may reveal metastasis of infection to other organs, particularly the liver and lungs. On rare occasions, catastrophic change occurs with gastric rupture. More commonly, a slow decline is followed by a rapid terminal bout of bacteremia and shock. Treatment is usually based on a surmise, as the lesions are not identified before death. If sand is recognized or suspected, psyllium-based feed supplements may be of some value, and serial radiography may be used to assess sand removal. Antibiotic or antifungal agents may have some value in treating all forestomach ulcerative lesions.
Third Compartment and Duodenal Peptic Ulcers
GI peptic ulceration has long been considered one of the main health concerns in llamas and alpacas, but we actually know little about the incidence or importance of this disorder.69 In fact, referring to these as “peptic” ulcers is entirely an extrapolation but is useful in differentiating these lesions from GI ulcers thought to be caused by microbes, parasites, or external agents. Various sources estimate the prevalence of GI ulcers in necropsied North American camelids to be approximately 6%, but this includes primary, secondary, and incidental lesions. Interestingly, the occurrence of peptic ulcers appears to be diminishing, possibly because of the “maturation” of the industry and an increased knowledge of feeding and management practices among veterinarians and owners.
In spite of the frequency of diagnosis of ulcers, relatively few scientific reports exist. Most case reports describe camelids with chronic diseases, and it is impossible to determine when in the course of the illness the ulcer developed, and what role it played in disease signs.70–72 The pathogenesis likewise remains a speculation. The third gastric compartment is long and tubular, running craniocaudal in the right ventral abdomen. Within the first two thirds to 80% of its length, fermentative digestion takes place, and the pH is approximately 6.4. At its caudal extreme, where the organ abruptly turns dorsal and cranial, a small region of hydrochloric acid secretion exists. Peptic ulcers typically occur at this caudal flexure or near the pylorus and into the cranial duodenum, areas where the luminal contents are most acidic or subsequently neutralized (Figure 40-29). Most ulcers occur along the greater curvature. The usual suspects—stress, high grain diets, NSAIDs, and concurrent diseases—have been suggested as possible causes, but most camelids known to have ulcers do not have good evidence of any of these. Through retrospective study of case records, we have identified seven historical factors associated with perforating GI ulcers; it is likely that others exist and that some factors vary in importance with geographic location. These specific factors are (1) frequent harassment by a dominant camelid, (2) recent transport, (3) recent delivery of a cria (this may relate to transport, as this was most frequently seen in camelids that delivered on one property and were subsequently moved to another), (4) grazing lush spring pasture, (5) enteritis or septicemia, (6) GI foreign body, and (7) bowel ischemia. The last three factors were associated with focal ulceration and perforation at any point along the gastrointestinal tract while the first three were associated with third compartment or proximal duodenal ulceration. In addition to these factors, forestomach acidosis may cause nonperforating, but severe, ulceration in the forestomach and mild ulceration in the third gastric compartment. GI tumors are associated with focal nonperforating ulceration at any point in the GI tract, and copper poisoning may cause massive, diffuse gastric ulceration. Factors associated with nonfatal, nonperforating ulcers are unknown, but it should be noted that chronic disease conditions, hospital stays, and long-term and short-term treatment with NSAIDs were not identified as risk factors for perforating ulcers.
One study suggested that the specific mechanism leading to ulcers is lack of progressive gastric or duodenal motility.73 Motility in that area is peristaltic. In normal camelids, fermented ingesta frequently move into the fundic region, diluting the hydrochloric acid, and the mixture is regularly expelled into the pyloric region and duodenum, where the acids should be neutralized. With poor progressive motility, the acid contents remain unneutralized and possibly damage the mucosa. Most of the identified risk factors such as anorexia or intermittent eating (as may occur with sick, transported, or bullied camelids), dehydration, electrolyte or acid-base abnormalities, and gastric hyperacidity (feeding too much grain, or even overindulgence on lush spring grass) could plausibly be linked to poor gastric emptying. Reflux of bile from the duodenum could exacerbate acid injury or may simply provide a marker for lack of progressive outflow.
Low mucosal blood flow may contribute by adversely affecting mucosal health and healing. Camelids are very good at masking and tolerating dehydration, so these abnormalities may not be detected during the period of ulcer formation. Many of the same risk factors that are suggested to be inhibitors of gastric emptying are also likely to decrease blood flow.
Ulcers may be single or multiple, pinprick or extensive, superficial or deep, and possibly perforating (Figure 40-30). Approximately half the total cases of dead camelids had a perforation, but the prevalence of nonperforating ulcers is probably larger in the live population. Clinical presentation relates to the nature of the lesion. Nonperforating ulcers are usually blamed for causing anemia, depression, inappetence, colic, sensitivity to right cranioventral abdominal palpation, recumbency, and death in camelids of all ages, as in the clinical disorders associated with these lesions in horses, cattle, and humans. However, the reality is that most nonperforating ulcers are clinically silent, even when extensive. Camelids show those particular signs with a multitude of disorders (or in complete health in the case of resenting palpation) and rarely show any signs, except perhaps mild anemia, with ulceration. Chronic ulceration, sometimes with replacement of the entire acid-secreting mucosa by granulation tissue, is an exception, often leading to weeks or months of progressive ill-thrift. Fecal occult blood tests are not a reliable method of diagnosing nonperforating gastric ulcers, and melena is more common with gastric masses or massive ulceration caused by copper toxicosis. Thus, it is difficult to identify nonperforating ulcers, and their frequency is unknown.
Although we are uncertain of the significance of superficial ulcers, the importance of perforations cannot be doubted. Peritonitis and ulcers as separate diagnoses accounted for a total of between 9% and one third of camelid deaths according to two surveys conducted by the International Lama Association. Rupture of gastric, duodenal, or colonic ulcers in camelids confers a grave prognosis, with most camelids showing anorexia, severe depression, increased recumbency, and signs of septic shock. Fecal production and gastric motility are greatly reduced. Owners rarely report having seen active colic in the days preceding this acute decline, but colic signs are occasionally seen after the perforation has occurred. In a small minority of cases, affected camelids are chronic poor-doers for months before perforation, but most are outwardly completely healthy until perforation. Blood and peritoneal fluid may provide evidence of septic inflammation, but these changes often normalize with time, particularly with localized peritonitis. Clinical changes may also largely normalize and cause more of a chronic ill-thrift syndrome, although appetite rarely returns to normal.
Diagnosis of nonperforating ulcers remains speculative. To date, the affected regions are not accessible by endoscopy, ultrasonography is rarely sensitive enough, and blood work changes are nonspecific. Anemia and hypoproteinemia may be seen but are common findings in many sick camelids (a substantial number of which have unfortunately died over the years and been confirmed not to have had ulcers). Various fecal occult blood methods have been evaluated anecdotally, with none providing consistent, helpful results. The same is true for serum pepsinogen determination. Abdominal fluid is usually unremarkable. Feces are usually normal, albeit possibly scant. Melena is extremely uncommon and more often linked to a tumor or copper poisoning than simple ulceration, with or without a perforation.
All of these findings may also be true for perforating ulcers, especially if abdominal contamination is confined to the omental bursa. Clinical disease is more apparent, but the diagnostic tests may be frustratingly unhelpful. Complete blood cell count (CBC) may reveal toxic changes and immature forms of neutrophils. Abdominal fluid may reveal bacteria or fungi, high or low cell counts, high protein content, and toxic changes. Ultrasonography may reveal thickening of the omentum, flocculation of fluid and pockets of fluid; the caveat is that fluid accumulations are often fairly normal fluid around the lesion, rather than abnormal fluid from the actual lesion. Exploratory surgery or postmortem examination may reveal overt contamination and the hole in the GI tract. Except for surgery, however, all of these tests may also yield normal or equivocal results.
Treatment of nonperforating ulcers is controversial, particularly because the diagnosis is usually speculative. Camelids showing the signs popularly ascribed to ulcers may, in fact, have other diseases, many of the putative risk factors for ulcers have not been substantiated by broad clinical experiences, and many of the camelids with ulcers show no outward signs of illness, calling into question which population to treat. Several common medications have been shown to be ineffective at reducing gastric acidity at conventional dosages. These include cimetidine (up to 25 mg/kg, intramuscularly [IM]), ranitidine (1.5 mg/kg, IV), oral omeprazole (up to 12 mg/kg), and intravenous omeprazole at 0.2 mg/kg.69,74–77 Effective treatments have included high doses of intravenous omeprazole (4 to 8 mg/kg) and pantoprazole (1 mg/kg, IV or up to 2 mg/kg, SC).75,77 It is speculated that H2-blockers are effective at extremely high intravenous doses, but this has not been substantiated scientifically, and oral forms of these agents are likely to face severe impediments to systemic absorption. Misoprostol is also effective but has a high rate of unacceptable adverse reactions and therefore cannot be recommended.75 Oral sucralfate, whose efficacy is difficult to establish because it is not absorbed systemically and does not affect gastric acidity, has also been used (20 to 40 mg/kg, PO, q6-8h). In spite of these data and the problems with diagnosis, anecdotal reports of improvement after use of the “ineffective” agents are common.
Although specific pharmaceutical treatment of nonperforating ulcers has been fairly unrewarding—it is difficult to identify which camelids to treat and most antiulcer medications are poorly efficacious in camelids—overall good medical treatment may substantially contribute to ulcer prophylaxis. On the basis of the identified risk factors and putative pathogenesis, correction of underlying diseases, maintenance of good mucosal blood flow and gastric emptying, and avoiding causes of stress or anorexia are probably the best way to avoid and treat nonperforating gastric ulcers. Palatable, forage-based rations may be prokinetic, epitheliotropic, and nonacidogenic. Fluids should support mucosal health and good GI function. Analgesic medications may increase appetite and decrease pain-mediated ileus. Effective management, with readily available food and water and a noncompetitive environment, is the cornerstone. Philosophically, the practitioner needs to decide whether all sick or at-risk (bullied, new introductions, transported, competing breeding males) camelids need preemptive intervention or if the lack of effective treatments or infrequency of clinical progression (most perforations occur in outwardly healthy camelids, not poor-doers) precludes the use of specific antiulcer treatments. Following the principles of promoting healthy gastric emptying suitably addresses both circumstances. Prophylactic and therapeutic goals of restoring or maintaining perfusion; acid–base, mineral, and electrolyte homeostasis; and physical stimulation of progressive gastric motility through the regular provision of good-quality roughage that the camelid can eat comfortably and throughout the day appear to minimize the chance of perforation and perhaps the prevalence of nonperforating ulceration.
Treatment after perforation is usually ineffective. Camelids do not always die acutely; many are able to surround the lesion with omentum, fibrin, and adhered loops of bowel, but these camelids do not do well in the long term. Partial gastrectomy and local resection of contaminated tissue may be of benefit, if the damage is narrowly contained. Medical treatments include fluids, antibiotics, antiinflammatory or analgesic medications, and appetite stimulants. The use of specific antiulcer medications is probably no longer pertinent, although inhibition of acid production may allow small lesions to heal. Overall, the prognosis for camelids with perforated ulcers is grave. As ulcers have been seen occasionally in small outbreaks, if one camelid in a herd develops a perforation, the others should be scrutinized for risk and treated accordingly.
Neoplasia
Squamous cell carcinoma is the most commonly reported primary neoplasm affecting the gastrointestinal tract of camelids, while multicentric lymphoma is the most commonly reported neoplasm in camelids overall.78–80 Internal squamous cell carcinoma usually affects the first compartment (Figure 40-31), and most affected camelids are adults, many older than 10 years. Lymphoma more commonly affects the caudal end of the third compartment (Figure 40-32) but may also affect the first or second compartment and appears to be common in all ages of camelid. Other neoplasms, particularly carcinomas of glandular tissue and sarcomas of smooth muscle origin, occur sporadically and also tend to occur in older adults. In general, neoplastic disorders cause gradual weight loss with progressive anemia, hypoproteinemia, lethargy, and anorexia. Melena is occasionally seen when gastric ulceration is severe. Diarrhea might be noted early in the course of the disease or terminally. Lymphoma may cause palpable masses on other body parts; it is covered more extensively in Chapter 36. Often, the early clinical signs are missed, and the llama is either found dead or extremely debilitated. Antemortem diagnosis and successful treatment of malignant internal neoplasms are rare but could be improved by earlier identification of the sick animal, greater awareness of the tumors, and a diagnostic workup directed toward neoplastic disorders.
Clostridial Gastroenteritis or Enterotoxemia
Clostridium perfringens infection has been associated with fatal third compartment gastritis and enteritis in neonatal and adult camelids. As with some other clostridial diseases, the question remains whether Clostridia are primary pathogens or secondary invaders that cause easily recognizable and usually lethal disease. Clostridial organisms are gram-positive, motile, spore-forming, facultatively anaerobic rods. They may be present in low numbers in the gut contents of healthy animals and proliferate under certain conditions. High fermentable carbohydrate in gastric contents and slow gut transit are generally thought to promote clostridial overgrowth. Clostridial organisms are also toxin producers, and slowed transit or organism overgrowth may allow these toxins to reach pathogenic concentrations. Other diseases may facilitate clostridial disease by slowing gut transit, changing the gut microbial population, or damaging the mucosa to allow for clostridial invasion and greater systemic absorption of the toxins. Specifically, peptic ulcers or gastric nematodes are thought to facilitate gastric disease, and nematodes, coronavirus, Giardia, and coccidia are thought to facilitate intestinal disease.81,82
In both North America and South America, clostridial gastroenteritis has been associated with herd outbreaks of death. These tend to be associated with damp weather, which also tends to be most conducive to the proliferation of nematode and protozoal pathogens. Crias are generally considered to be more susceptible compared with adults, and outbreaks in South America are associated with a death rate of up to 70% of newborn crias in bad years, but adults are also occasionally affected.83,84
Several types of C. perfringens exist. These were traditionally defined by the toxins secreted but now are typically defined by the toxin genes present. Type A is best known for its α-toxin, whereas type C additionally secretes β-toxin. ε-toxin is the main effector of type D. Type A is usually blamed for neonatal enteritis. This is supported by one Peruvian study, in which all C. perfringens isolates from crias suspected of dying from enterotoxemia had the α-toxin gene and extremely few had the genes for toxins typical of types B, C, D, or E.85 In Oregon, type C also appears to play a role.
Types C and D cause diseases resembling enterotoxemia in young ruminants. β-toxin is inactivated by trypsin and thus usually has a narrow window in which to affect the neonate. Type D typically affects animals older than 3 days. Newer research has also shown that some toxins important for disease may not be included among those used to classify the types, such as the β-2 toxin.85,86 In contrast, enterotoxin appears not to play much of a role.
Clostridial toxins cause local necrosis, which may become generalized with systemic absorption. The infection itself may also cause hemorrhage, necrosis, and gas gangrene of the gastric or intestinal wall. Clinical signs include severe depression, shock signs, colic, abdominal distension, possibly fever, and fetid or hemorrhagic diarrhea. Diarrhea is usually seen only if the camelid survives at least 12 hours after the onset of clinical signs. Signs are often peracute and severe, but with clostridial disease superimposed on some other preceding digestive disorder such as forestomach acidosis, coronavirus infection, and GI parasitism, signs of that other disease may have been present for days to weeks before the rapid worsening. Some camelids die suddenly, others within hours of the onset of severe signs, and still others within days. Survivors are the minority in spite of aggressive treatment.
Premortem diagnosis is usually presumptive. Fecal toxin assays developed for use in other species are not always accurate, and rapid assays do not exist for many of the important toxins. Fecal culture followed by toxin or genetic analysis is possible but usually too time consuming to have any impact on treatment, except in herd outbreaks. Radiography of the abdomen may reveal gas-distended loops of bowel. Ultrasonography may reveal gas-distended viscera and possibly thickening and gas shadowing of the gastric or intestinal wall.
Hematologic abnormalities include neutrophilia in most cases and neutropenia in some. Lymphopenia, anemia, toxic changes, and immature neutrophils are often present. Hyperfibrinonemia may develop if the camelid survives more than a day. Biochemical abnormalities include hyperglycemia, metabolic acidosis with hyperlactemia, often hypoproteinemia, and potentially other indicators of shock. Anemia, hypoproteinemia, and electrolyte changes may be present because of the preceding disease.
Postmortem examination tends to yield impressive lesions. The mucosa of the third compartment is thickened, necrotic, hemorrhagic, edematous, and emphysematous. Small intestine might also be affected, and ingesta may be hemorrhagic. Body cavity fluids tend to be blood tinged. Differentiating premortem changes from terminal or postmortem changes may be difficult. Clostridia tend to overgrow with lack of GI motility, particularly after death. Significant hemorrhage is usually good evidence that changes occurred after death. Culturing C. perfringens from lesions and demonstrating the presence of toxin support the diagnosis.
Identifying the disease in the individual camelid is less important than recognizing the need for aggressive treatment. IV fluids, antiinflammatory drugs (flunixin meglumine; 0.5 to 1 mg/kg, IV, q12h), and antibiotics are essential. Although Clostridia themselves are best treated with agents such as penicillin, ampicillin, or ceftiofur, the uncertainty of the diagnosis and the likelihood of gut damage dictates broad-spectrum antimicrobial coverage. Penicillin (44,000 units/kg with q6h IV, or q12h SQ or IM) and ceftiofur (4 to 8 mg/kg IV, SQ, or IM, q8-12h) are typically used at high doses, twice the usual amount. Oral penicillin (22,000 units/kg, PO, once or q12h) may have some value as an adjunct to decrease gastric overgrowth. Affected camelids may also require plasma transfusion. Antisera against clostridial toxins may have some value, if type C is involved but may not counteract other important toxins. Use of commercial toxoid vaccines is likewise only partially effective unless the vaccines contain specific alpha toxoid.87 Autogenous vaccines made during outbreaks may be more effective, although they also might not protect against all causative toxins.
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Book2014, Llama and Alpaca CareChristopher Cebra
Review article
Treatment of gastric ulcer, traditional Chinese medicine may be a better choice
2024, Journal of EthnopharmacologyHaiying Gong, ... Sen Liu
1 Introduction
Gastric ulcer (GU) refers to a deep mucosal tissue defect of the gastric mucosa stimulated by gastric acid and pepsin, which penetrates the muscularis mucosa (Lanas and Chan, 2017). Deep damage or long-term healing failure may affect the intrinsic muscle layer or deeper layers and is sometimes associated with a duodenal ulcer (DU), which is collectively referred to as a peptic ulcer (PU) (Lanas and Chan, 2017). The primary factor contributing to greater PU death rates is the significant likelihood that PU may result in acute and severe complications such as perforation, hemorrhage, and malignancy (Hernandez-Diaz et al., 2013). A systematic review of PU-related research found that between 19 and 57 people out of 100,000 experienced upper gastrointestinal bleeding, with concurrent perforation being extremely rare. Nonetheless, approximately 8.6 % of patients with PU-accompanied bleeding and 23.5 % of patients with PU perforation died within 30 days (Lau et al., 2011). Cancer is more common in GUs than in DUs; within two years of a diagnosis of GUs, there is a 10-fold increased risk of stomach cancer compared to the general population (Tamaddonfard et al., 2019), where 1 %–7 % of people have cancer (Graham, 2014).
GU is a complex and multifactor process, and current research generally shows that the imbalance between mucous invasive forces and protective factors results in the loss of the mucosal protective barrier and the formation of ulcers and is key to the occurrence of GU (Zhou et al., 2020). Clinical investigations have demonstrated that inhibiting gastric acid secretion as a primary drug therapy or eradicating Helicobacter pylori (Hp)-based treatments can be effective, but they are also accompanied by a variety of unfavorable adverse effects and increased drug resistance. Unsatisfactory, ulcers are very likely to recur after discontinuation of the drugs that inhibit the secretion of gastric acid, with a recurrence rate of up to 60–80 % (de Oliveira et al., 2022). Not only must damaged mucosa be repaired during ulcer healing, but the submucous tissue structure must also be repaired and rebuilt in good condition, which could improve the quality of ulcer healing (QOUH) and strengthen the gastric mucosal barrier defense; therefore, single-target drugs may have difficulty in healing GUs efficiently.
GU can be treated by several classical Chinese medicine decoctions, clinical experience formulas, or chemical components made from naturally occurring animal and plant sources (Fu et al., 2022; Gong et al., 2023; Song et al., 2020). At the same time, numerous clinical and experimental studies on the targets and mechanisms of natural medications have been carried out, and Chinese medicine research has produced great outcomes in both cases (Gong et al., 2023; Song et al., 2020; Yang et al., 2017). This review provides a summary of recent developments in GU treatments using traditional Chinese medicine (TCM). The full names of the botanicals referred to in this study have been checked with on November 1, 2023.
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189698 | https://pmc.ncbi.nlm.nih.gov/articles/PMC3262949/ | Role of C3a Receptors, C5a Receptors, and Complement Protein C6 Deficiency in Collagen Antibody-Induced Arthritis in Mice - PMC
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. Author manuscript; available in PMC: 2013 Feb 1.
Published in final edited form as: J Immunol. 2011 Dec 28;188(3):1469–1478. doi: 10.4049/jimmunol.1102310
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Role of C3a Receptors, C5a Receptors, and Complement Protein C6 Deficiency in Collagen Antibody-Induced Arthritis in Mice
Nirmal K Banda
Nirmal K Banda
Division of Rheumatology, Departments of Medicine and Immunology, University of Colorado School of Medicine, Aurora, Colorado, USA
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Stephanie Hyatt
Division of Rheumatology, Departments of Medicine and Immunology, University of Colorado School of Medicine, Aurora, Colorado, USA
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Alexandra H Antonioli
Division of Rheumatology, Departments of Medicine and Immunology, University of Colorado School of Medicine, Aurora, Colorado, USA
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Jason T White
Division of Rheumatology, Departments of Medicine and Immunology, University of Colorado School of Medicine, Aurora, Colorado, USA
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, Magdalena Glogowska
Magdalena Glogowska
Division of Rheumatology, Departments of Medicine and Immunology, University of Colorado School of Medicine, Aurora, Colorado, USA
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, Kazue Takahashi
Kazue Takahashi
+Developmental Immunology, Massachusetts General Hospital for Children, Boston, Massachusetts, USA
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+, Tod J Merkel
Tod J Merkel
±Laboratory of Respiratory Pathogens, Division of Bacterial Products, CBER, FDA, USA
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Gregory L Stahl
§Center of Experimental Therapeutics and Reperfusion Injury, Brigham and Women’s Hospital, Boston, Massachusetts, USA
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Stacey Mueller-Ortiz
¶Institute of Molecular Medicine, University of Texas, Houston, USA
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¶Institute of Molecular Medicine, University of Texas, Houston, USA
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Division of Rheumatology, Departments of Medicine and Immunology, University of Colorado School of Medicine, Aurora, Colorado, USA
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Division of Rheumatology, Departments of Medicine and Immunology, University of Colorado School of Medicine, Aurora, Colorado, USA
+Developmental Immunology, Massachusetts General Hospital for Children, Boston, Massachusetts, USA
±Laboratory of Respiratory Pathogens, Division of Bacterial Products, CBER, FDA, USA
§Center of Experimental Therapeutics and Reperfusion Injury, Brigham and Women’s Hospital, Boston, Massachusetts, USA
¶Institute of Molecular Medicine, University of Texas, Houston, USA
✉
Address correspondence to: Dr. V. Michael Holers, Division of Rheumatology, Mail Stop B115, University of Colorado School of Medicine, 1775 Aurora Court, Aurora, Colorado 80045, USA. Phone (303) 724-7605. Fax: 303-724-7581. Michael.Holers@ucdenver.edu
Issue date 2012 Feb 1.
PMC Copyright notice
PMCID: PMC3262949 NIHMSID: NIHMS342564 PMID: 22205026
The publisher's version of this article is available at J Immunol
Abstract
The complement system, especially the alternative pathway (AP), plays essential roles in the induction of injury in collagen antibody-induced arthritis (CAIA) in mice. The goal of the current study was to directly compare the roles of receptors for C3a and C5a, as well as the membrane attack complex (MAC), as effector mechanisms in the pathogenesis of CAIA. Clinical disease activity (CDA) in C3aR−/−, C5aR−/−, and C6 deficient (C6-def) mice was decreased by 52%, 94%, and 65%, respectively, as compared with WT mice. Decreases in histopathologic injury as well as in IgG and C3 deposition paralleled the CDA. A decrease in the percentage of synovial neutrophils was observed in C3aR−/−, C5aR−/−, and C6-def mice, and a decrease in macrophages was observed in C3aR−/− and C5aR−/−, but not in C6-def, mice. Synovial mRNA obtained by laser capture microdissection exhibited a decrease in TNF-α in C5aR−/− mice and in IL-1β in both C5aR−/− and C6-def mice, while C3aR−/− mice demonstrated no change in either cytokine. Our findings show that absent C3aR-, C5aR- or MAC-initiated effector mechanisms each decreases susceptibility to CAIA, with clinical effects most pronounced in C5aR deficient mice. Although the absence of C3aR, C5aR, or C6 led to differential deficiencies in effector mechanisms, decreased proximal joint IgG and C3 deposition was common to all three genotypes in comparison to WT mice. These data suggest the existence of positive feedback amplification pathways downstream of all three effectors that promote additional IgG deposition and C3 activation in the joint.
Keywords: autoimmunity, complement, inflammation
Introduction
Rheumatoid arthritis (RA) is an inflammatory autoimmune arthritis whose pathogenesis is complex (1, 2). In order to better understand the pro-inflammatory pathways involved in this disease, mouse models of inflammatory arthritis such as collagen-induced arthritis (CIA), anti-GPI Ab-induced arthritis (anti-GPI Ab) and collagen Ab-induced arthritis (CAIA) have been devised and studied extensively. Our laboratory, along with others, has shown a significant and necessary role for the alternative pathway (AP) of complement in the pathogenesis of inflammatory arthritis in mice (3–9).
Complement is a potent effector pathway of innate immunity that accomplishes its biologic roles in inflammation by using several key pro-inflammatory and immunomodulatory mechanisms. C3 and C5 are central pillars of this system. For example, all three activation pathways of the complement system converge to form a C3 convertase, or activating enzyme, which cleaves C3 into the C3a and C3b fragments. The generation of C3b leads to the formation of another enzyme, the C5 convertase, which then cleaves C5 into the C5a and C5b fragments. C3a and C5a fragments are the most potent pro-inflammatory anaphylatoxins generated during complement pathway activation. These anaphylatoxins recruit and/or activate monocytes/macrophages and neutrophils, which themselves are involved in a myriad of pathologic states including those of autoimmune diseases, inflammatory reactions, allergic reactions, asthma, and cancer (10–14). In addition to anaphylatoxins, through the formation of the membrane attack complex (MAC) the complement system eliminates pathogens through lysis and causes local tissue injury by the initiation of pro-inflammatory signaling in cells.
C3a and C5a induce their biological actions through two specific receptors designated the C3aR and C5aR (CD88), respectively (15, 16). C5L2 (GPR77) is another non-signaling receptor for C5a (17–19), which likely acts as a decoy receptor and a negative modulator of C5a-induced responses (20). Both major receptors for C3a and C5a belong to a family of transmembrane G protein coupled receptors, but C5L2 is not coupled to the G proteins (17, 21). Many different cell types express receptors for C3a and C5a. These include cells of myeloid origin (22), non-myeloid origin (23), dendritic cells (24), monocyte/macrophages (25), and neutrophils (26). Resting mast cells express C5aR below threshold levels, but stimulation with phorbol myristate acetate (PMA) or ionomycin results in increases in C5aR expression as well as in slight increases in C3aR receptors (27).
Following C5b generation, C6 interacts with C5b on the cell surface to begin formation of the MAC (C5b, C6, C7, C8α, C8β, C8γ, and C9) that can insert into any cell membrane (28). Deficiency of any of the aforementioned proteins of the MAC would block the formation of the lytic complex in the membrane of cells. If present at high enough levels, the MAC causes lysis of cells; perhaps more importantly, when present in sublytic concentrations, the MAC also transduces pro-inflammatory cell activation signals (29). The MAC also plays a role in the cell cycle and apoptosis (30, 31) and has been shown to be present in RA tissue, suggesting a role in the pathogenesis of arthritis (32).
Serum-induced arthritis in K/BxN mice is mediated by anti-GPI-immunoglobulins (Igs) (33) and the development of disease requires both C5aR and FcγIII receptors (7). This study also showed that disease was dependent on the AP of complement. On the other hand, C6-deficient (C6-def) mice on a C3H/He background were fully susceptible to anti-GPI Ab-induced arthritis (7), suggesting a lack of role for the MAC. In contrast, there was a 60% decrease in monosodium urate monohydrate (MSU) crystal-induced arthritis in NZW rabbits deficient in C6 (34). This study reported infiltration of mononuclear leukocytes in the synovial tissue in all animals, but substantial infiltration of neutrophils was also seen in C6-def rabbits in response to MSU crystals. In addition, in a mouse model of choroidal neovascularization (CNV), i.e. laser-induced CNV which involves inflammation, anti-C6 mouse polyclonal Ab inhibited the formation of the MAC and resulted in amelioration of CNV (35). Anti-C6 Fab also reduced experimental autoimmune myasthenia gravis disease passively induced in rats (36), showing the dependency of this disease on MAC formation.
Despite this body of work on the role of individual effector pathways, no prior study has directly compared the relative roles of C3aR, C5aR, and the MAC in the development of tissue injury in any single disease model. The purpose of the current study was to explore the relative roles of these three major effector pathways in CAIA in C57BL/6 mice. Our hypothesis was that the interactions between C3a-C3aR and C5a-C5aR, and a deficiency of MAC formation, would result in differential effector function and thus lead to different disease phenotypes in C3aR−/−, C5aR−/−, and C6-def mice. Although we found that each effector demonstrated unique characteristics with regard to changes in downstream pro-inflammatory effects in their absence, there were similar ameliorative effects on the disease course itself. One unexpected feature shared by all effector deficient mice was decreases in the levels of local IgG and C3 deposition in the joint.
Materials and Methods
Mice
Ten to twelve week-old homozygous C3−/−, C3aR−/−, C5aR−/−, and C6-def C57BL/6 male and female mice were used for this study of CAIA. C3aR−/− and C5aR−/− mice were obtained from Dr. Rick Wetsel, University of Texas, Houston, and C6-def mice were obtained from Dr. Tod Merkel, CBER, FDA. Because C57BL/6 mice naturally lack complement protein C6 and are not gene-targeted mice, in the current studies these mice have been designated as C6 deficient (C6-def). These C6-def C57BL/6 mice have been derived from a C6-def C3H/He mouse strain, as narrated in detail below. Sera from C1q−/−, C3−/, C4−/−, Bf−/−, and Df−/− mice backcrossed to at least F10, as well as C5-deficient NOD (non-obese diabetic) mice, were used as negative controls in ELISA assays as described. Age- and sex-matched C57BL/6 mice (Jackson Labs, Bar Harbor, ME) were used as wild type (WT) controls. Genotypes of deficient strains were confirmed by deletion-specific DNA PCR analysis prior to use of the animals. The studies were performed in four different cohorts with the following total mice studied: WT n = 25, C3−/− n = 4, C3aR−/− n = 13, C5aR−/− n = 11, C6-def n = 8. All animals were kept in a barrier animal facility with a climate-controlled environment providing 12 h light/dark cycles. Filter top cages were used with three mice in each cage. During the course of this study, all experimental mice were fed breeder’s chow provided by the Center for Laboratory Animal Care, University of Colorado School of Medicine.
Derivation of C57BL/6 C6-def mice
C6-def C3H/He mice were derived from a Peru-Peacock strain of mice that lacked functional C6 (37). The molecular basis of the deficiency was determined to be due to the presence of several base-substitutions in the C6-deficient allele relative to the wild-type allele (38). These base-substitutions result in the presence of restriction enzyme site Bst NI in the wild-type allele that is absent in the C6-def allele and the presence of restriction enzyme site Alw NI in the C6-def allele that is absent in the wild-type allele. This allowed for unambiguous identification of heterozygous mice, mice homozygous for the C6-def allele, and mice homozygous for the wild-type allele. Genomic DNA was isolated from whole blood from individual mice using the MoBio UltraClean DNA BloodSpin Kit kit (MO BIO Laboratories Inc., Carlsbad, California) according to the manufacturer’s instructions. DNA amplification was performed using primers C6DE-F1 (5’GACCCTTGCCAGTGTGCTCCATGTCCCA-3’ and C6DE-R1 (5’-GGACCTGCGCTCACAGTTCTCA-3’) using Roche PCR Master Mix (Roche Applied Science, Indianapolis, Indiana) according to the manufacturer’s instructions. The resulting PCR product was gel purified and independently digested with restriction enzymes Bst NI and Alw NI. The restriction patterns for each digestion were analyzed to determine whether the wild-type allele or the C6-allele, or both alleles, were present. In order to transfer the C6-def allele to the C57BL/6 background, C6-def C3H/He mice were backcrossed 8 times to C57BL/6 mice. Following each backcross, offspring homozygous for the C6-deficient allele were identified using the PCR/restriction enzyme screen described above and crossed with wild-type C57BL/6 mice. Following the eighth backcross, offspring homozygous for the C6-deficient allele were selected and used to set up homozygous breeding pairs. The offspring of these breeding pairs were confirmed to be homozygous for the C6-deficient allele using the PCR/restriction enzyme screen described above and were determined to be deficient for complement-mediated lysis in a red blood cell assay and to lack C6 protein by Western blot (data not shown). A coagulation defect, characterized as decreased platelet aggregation, was described in the original C6-def C3H/He mice, corrected by adding purified rat C6 protein in vitro (38). It is not known if a similar coagulation defect is present in the C6-def C57BL/6 mice used in this study.
Induction of collagen antibody-induced arthritis
CAIA was induced in C3aR−/−, C5aR−/−, and C6-def, and WT mice by using a cocktail of five mAb to bovine CII (Arthrogen-CIA, Chondrex) suspended in sterile Dulbecco’s PBS. All five mAb (3 IgG2a and 2 IgG2b) in this cocktail recognize conserved epitopes within the CB11 fragment, whose recognition sequences are shared by CII in many species. All mice received i.p. injections of 8 mg/mouse of Arthrogen on day 0 and 50 µg/mouse of LPS from E. coli strain 0111B4 on day 3 to synchronize the development of arthritis. Mice started to develop arthritis at day 4 and were sacrificed at day 10. The studies were performed in four separate experiments. The first experiment consisted of C3aR−/− (n = 5), C5aR−/− (n = 5), and WT (n = 6) mice; the second consisted of C3aR−/− (n = 3), C5aR−/− (n = 2), C6-def (n = 3), and WT (n = 4) mice; the third consisted of C3aR−/− (n = 5), C5aR−/− (n = 4), and WT (n = 4) mice; and the fourth consisted of C6-def (n = 5) and WT (n =11) mice. For presentation of results, all genotype identical mice were grouped together from each of the four experiments and included in the final analyses.
Examination for clinical disease activity
The prevalence of disease and severity of clinical disease activity (CDA) in all C3aR−/−, C5aR−/−, C6-def, and WT mice were determined every day by a trained laboratory person blinded to the experimental treatment group according to our previously published studies (5). The CDA score is based on a 3 point scale per paw: 0 = normal joint; 1 = slight inflammation and redness; 2 = severe erythema and swelling affecting the entire paw with inhibition of use; and 3 = deformed paw or joint with ankylosis, joint rigidity and loss of function. The total CDA score was based on all 4 paws with a maximum total of 12 for each mouse.
Histopathology and immunohistochemistry for C3 and IgG
Knee joints from both fore limbs, and the right hind limb with knee joint, ankle and paw, from C3aR−/−, C5aR−/−, C6-def, and WT mice at day 10 following Arthrogen injection were fixed in 10% Neutral buffered formalin (NBF). Toluidine-blue stain was used to assess histopathology scores for inflammation, pannus formation, cartilage and bone damage, according to the published criteria (39, supplemental data). Histology sections were cut (7 µm) and processed for C3 and IgG immunohistochemistry staining. Non-specific binding was blocked using a protein block serum free solution (Dako). C3 was localized with a primary polyclonal goat anti-mouse C3 antiserum (dilution 1:10,000) (ICN Pharmaceuticals) and detected by goat HRP polymer kit (BioCare Medical) (5). IgG was localized with a primary polyclonal goat anti-mouse Ab (dilution 1:200) (Vector Laboratories, Burlington, CA) and detected by a goat HRP polymer kit, as mentioned above. Development of staining identifying the presence of tissue-fixed C3 and IgG was carried out using DAB plus solution substrate (Dako), which reacts with HRP and produces a brown color for positive staining. All slides for histopathology, C3 and IgG deposition were observed under light microscopy at a magnification of 20X in a blinded fashion and scored according to published criteria (39). IgG deposition on the surface of cartilage in the knee joints of WT, C3aR−/−, C5aR−/−, and C6-def mice with disease was determined by using the following scale: 0 = normal WT with no disease, i.e. background endogenous mouse IgG staining, 1 = minimum staining, 2 = moderate staining, and 3 = intense staining. The knee joints from RAG2−/− mice on C57BL/6 background with no disease were also used as negative controls.
Quantitative assessment of monocytes/macrophages and neutrophils in the knee joints
Histology sections from the knee joints of all C3aR−/−, C5aR−/−, C6-def, and WT mice with CAIA sacrificed at day 10 were also examined for the infiltration of monocytes/macrophages and neutrophils in the knee joints. To determine the percentages of monocytes/macrophages and neutrophils, sections were pre-treated with proteinase K (0.05 mol/L) (Dako) for 5 min for Ag retrieval, followed by blocking with a serum free protein block solution (no dilution) (Dako). Immunohistochemistry analysis for monocytes/macrophages was performed by staining sections with rat anti-mouse F4/80 (dilution 1:1000) (Serotec) and rabbit anti-rat (dilution 1:400) (Dako), as primary and secondary Ab, respectively. Rabbit Alkaline Phospatase Polymer (ALP) (no dilution) (BioCare Medical) was used as a tertiary Ab. Detection of monocytes/macrophages was performed using Vulcan Fast Red Chromogen (no dilution) (BioCare Medical). To determine the percentage of neutrophils, knee joint sections were stained with a primary rat anti-mouse neutrophil Ab (dilution 1:2000) (Serotec) and a secondary rabbit anti-rat Ab (dilution 1.400) (Dako), followed by Rabbit Envision Polymer (no dilution) (HRP conjugated) (Dako). Neutrophils were detected by using 3,3’-diaminobenzidine (DAB+) (no dilution) (Dako). The percentages of the monocytes/macrophages and neutrophils were calculated by marking the boundaries of synovium using Scan Scope XT (Aperio). The formula used to calculate such percentages was the total number of positively stained synovial area/total marked synovial area x100. Although the areas of synovium were heterogeneous due to inflammation, all stained areas were included in assessing percentages of monocytes/macrophages and neutrophils.
Measurement of C3 deposition and C5a generation in vitro using sera from mice
Complement activity in sera from C3−/−, C3aR−/−, C5aR−/−, C6-def, NOD, and WT mice was assayed in vitro by measuring C3 deposition and C5a generation. Blood for these studies was collected by retro-orbital bleeding and allowed to clot for 30 min at 4°C. After centrifugation at 3000 rpm for 15 min at 4°C, sera were separated from the clot on ice and were kept at −70°C immediately after collection until further analysis. To avoid complement activation, sera were used only one time without being subjected to repeated cycles of freezing and thawing. Sera were discarded that showed any discoloration due to hemolysis. Frozen serum samples were thawed at 4°C and the diluted sera were kept on ice prior to use. For analysis of all three pathways of complement activation, sera were serially diluted 2-fold from 1:10 in Ca++-sufficient buffer for C3b deposition and serially diluted 2-fold from 1:50 for C5a generation. To study specific activation of the AP only, the same sera were serially diluted 2-fold in Ca++-deficient buffer containing Mg++/EGTA. These sera were then added to 96-well Costar ELISA plates pre-coated with anti-CII mAb (Arthrogen, 2.5 ug/well) and incubated at 37° C for 1 h. C3 deposition adherent to the plate and C5a generation in the supernatant were measured by ELISA, as previously described (4, 39).
Levels of complement components in the sera from complement-deficient and WT mice
Serum levels of C1q, C4, C3, factor B and factor D proteins from C3aR−/−, C5aR−/−, C6-def, and WT mice were measured using standard ELISA protocols, according to our published methods (4, 39).
Cytokine mRNA levels from the synovium of knee joints using laser capture micro-dissection (LCM)
The left knee joint was surgically removed from mice with and without CAIA at day 10, the skin was removed, and the tissue was placed in liquid nitrogen. After removing extra muscle using a surgical blade, the knee joint was embedded for 5 min in Tissue-Tek® O.C.T.™ Compound (Sakura Finetek, The Netherlands). The histology sections were cut at 8 micron thickness (Leica Microsystems, Wetzlar, Germany) and mounted onto Histobond® slides (Statlab Medical Products, McKinney, TX). All slides were dehydrated for 30 sec sequentially in 70%, 95%, and 100% ethanol, and for 5 min in xylene (Arcturus® Histogene®, Carlsbad, CA). The slides were rehydrated in nuclease-free water (Arcturus® Histogene®) containing 50 µL of RNase inhibitor (Sigma-Aldrich, St. Louis, MO) for 30 sec to remove the O.C.T. compound. The slides were air-dried for 5 min. The knee joint was located at 2X magnification and the synovium was viewed at 10X. The capture Macro LCM Cap (Arcturus Histogene®) was placed on the area around the identified synovium. The histo-pencil from the drawing tools was used to mark the boundaries of the synovium to be placed on the cap, and an infrared laser was fired. The infrared laser melted the polymer onto the cap creating an adhesion of the cells to the polymer. The cap was moved to the quality control station to view the synovium. The cap with the synovium was placed in a tube with 50 µL of RNA extraction buffer (Arcturus® Histogene®) and incubated for 30 min at 42°C. RNA was isolated using the PicoPure RNA isolation kit (Arcturus® Histogene®), and then amplified (1.5–2.0 round amplification) using the RiboAmp Plus kit (Arcturus® Histogene®) by synthesizing cDNA strands from the isolated RNA with enhancers and transcribing it into amplified RNA (aRNA). The aRNA was purified using a column method supplied in the kit. RNA concentration was measured using a nanodrop. This aRNA was then used for quantitiative RT-PCR using specific primers for the mRNA levels of TNF-α, IFN-γ, IL-1β, and IL-10, as previously published (5, 39)
Statistical analyses
p-values were calculated using Student’s t test with the GraphPad Prism R 4 statistical program. The data in graphs, histograms and tables are shown as the mean ± SEM, with p< 0.05 considered significant using an unpaired two-tailed t-test. One-way analysis of variance (ANOVA) using Tukey's multiple comparison test was also performed to further confirm the significant differences between WT, C3aR−/−, C5aR−/−, and C6-def mice for CDA, histology, C3 deposition/C5a generation, and QRT-PCR data. Pearson correlation was used to determine the correlation between CDA, neutrophils, macrophages, histology, and absolute serum complements levels. Preliminary analyses using a null hypothesis for w-statistics indicated that the data were usually normally distributed. Where data were not normally distributed, the Mann-Whitney test was used.
Results
Clinical disease activity and prevalence of disease
CDA in all cohorts of mice was evaluated every day after the LPS injection on day 3. Mice injected with Arthrogen developed disease after day 3, and at day 10 the CDA in WT, C3aR−/−, and C5aR−/− mice were 10.8 ± 0.54, 5.2 ± 1.1, and 0.64 ± 0.20, respectively (Fig. 1A). These scores were significantly reduced by 52% and 94% in C3aR−/− and C5aR−/− mice, respectively, as compared to WT mice. The prevalence of disease at day 10 in WT, C3aR−/−, and C5aR−/− mice was 100%, 85%, and 55%, respectively (Fig. 1B). At day 10 the CDA in WT and C6-def mice was 9.3 ± 0.66 and 3.3 ± 0.41, respectively (Fig. 1C). The CDA in C6-def mice was significantly reduced by 65% as compared to WT mice. The prevalence of disease at day 10 both in WT and C6-def was 100% (Fig. 1D). C5aR−/− mice were more resistant to the development of CAIA as measured by CDA than C3aR−/− mice and C6-def mice (p< 0.01). No statistically significant (p = 0.18) difference was observed when comparing CDA between C3aR−/− and C6-def mice.
Figure 1.
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CDA and prevalence of CAIA among WT, C3aR−/−, C5aR−/−, and C6-def mice. Arthrogen was injected i.p. on day 0 followed by an injection of LPS on day 3. Mice were evaluated daily by an observer blinded to the genotype of each mouse. Data are expressed as the CDA score (A, C) and prevalence of arthritis (B, D) vs. days after the injection. A. CDA among WT, C3aR−/−, and C5aR−/− mice. B. The prevalence of disease in WT, C3aR−/−, and C5aR−/− mice. C. CDA in WT and C6-def mice. D. The prevalence of disease in WT and C6-def mice. Data shown in A represent the mean ± SEM based on WT, n = 14; C3aR−/−, n = 13; and C5aR−/−, n = 11. Data shown in B represent the mean ± SEM based on WT, n = 11 and C6-def, n = 8. p < 0.05 in C3aR−/−, C5aR−/−, and C6-def mice in comparison with CDA in WT from day 5 to day 10.
Differential patterns of disease development in C3aR−/− mice
We examined CDA in each mouse from day 3 to day 10 in all four cohorts of mice. There were only scattered individual variations of CDA in C5aR−/− and C6−/− mice (Figs. S1, panels C and D). However, there was substantial variation in the individual CDA in WT and C3aR−/− mice (Fig. S1, panels A and B). Four C3aR−/− mice developed severe disease similar to the WT mice, while five mice developed moderately high levels of disease and four mice developed minimal levels of disease. This variation in the CDA in C3aR−/− mice was found consistently in all three cohorts tested. The genotype of the mice was confirmed twice as C3aR−/− prior to the induction of CAIA by PCR using genomic DNA.
Histopathology, C3 and IgG deposition scores in forelimbs and hind limbs
All mice were sacrificed at day 10, after which both forelimbs and the right hind limb (knee, ankle and paw) were processed for histopathology studies (Figs. 2A and 2B), for measurement of local C3 deposition (Figs. 2C and 2D), and for IgG deposition (Fig 3). Five joints from WT, C3aR−/−, C5aR−/−, and C6-def mice used in this study were examined for inflammation, pannus formation, cartilage damage and bone damage (Figs. 2A and 2B). Individual scores for these parameters were all significantly (p< 0.05) decreased in C3aR−/− and C5aR−/− compared with WT mice (Fig. 2A). In addition, all joint mean (AJM) scores for histopathology were significantly (p< 0.001) reduced by 44% and 57% in C3aR−/− and C5aR−/− mice, respectively, compared with the WT mice (WT 14.07 ± 0.544, C3aR−/− 7.86 ± 0.66, and C5aR−/− 6.02 ± 0.17). Individual scores for inflammation, pannus formation, cartilage and bone damage were also significantly (p< 0.05) decreased in C6-def compared with WT mice (Fig. 2B). Similarly, there was a significant decrease by 39% in the AJM histopathology scores in C6-def mice compared with the WT mice (WT 12.07 ± 0.947 and C6-def 7.35 ± 0.73). C5aR−/− mice have significantly less inflammation vs. C3aR−/− mice (p< 0.0078) and vs. C6-def mice (p< 0.017), less pannus formation vs. C3aR−/− mice (p< 0.012) and vs. C6-def mice (p< 0.023), and less cartilage damage vs. C3aR−/− mice (p< 0.041) (Figs. 2A and 2B). All joint mean scores were also significantly reduced in C5aR−/− mice vs. C3aR−/− (p< 0.020) and vs. C6-def mice (p< 0.049). No significant reduction in cartilage and bone damage was observed between C5aR−/− and C6-def mice. Representative histopathologic examples of the knee joints from WT, C3aR−/−, C5aR−/−, and C6−/− mice are shown in Fig. 4 (A, B, C and D).
Figure 2.
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Histopathological scores and C3 deposition in the joints of all WT, C3aR−/−, C5aR−/−, and C6-def mice. At day 10 following Arthrogen injection, mice were sacrificed. Histopathologic scoring for inflammation, pannus formation, cartilage and bone damage from five joints, including fore limbs (right and left) and one hind limb (right knee, ankle and paw), was performed following tissue processing and Toluidine-blue staining of sections. A. Individual components of histopathologic scores from WT (n =14), C3aR−/−(n =13), and C5aR−/− (n =11) mice. B. Histopathologic scores from all five joints of WT (n = 11) and C6-def (n = 8) mice. Knee joints of mice with CAIA were used to examine for C3 deposition. C. C3 deposition in knee joints in the synovium, on the surface of cartilage, and total scores (synovium plus cartilage) from WT, C3aR−/−, and C5aR−/− mice. D. C3 deposition in the synovium and on the surface of cartilage from WT and C6-def mice. All data are represented as scores (mean ± SEM). p < 0.05 in comparison to WT mice of individual histopathologic and C3 deposition scores. p < 0.05 inter-group comparison of individual histopathologic and C3 deposition scores between C5aR−/− and C3aR−/− or C6-def mice
Figure 3.
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Immunohistochemical analysis of IgG deposition on the surface of cartilage from knee joints of WT, C3aR−/−, C5aR−/−, and C6-def mice with CAIA. A. Cartilage surface in the knee joints is marked as (C). IgG deposition (brown color stain) on the cartilage surface is shown by black arrows. Top panel left to right, cartilage surface from the knee joints of: 1. WT mice, and 2.C3aR−/− mice, both with CAIA. Central panel left to right: 3.C5aR−/− mice, and 4. C6-def mice, both with CAIA. Bottom panel left to right: 5. C57BL/6 mice, and 6.RAG2−/− mice, both without CAIA. Magnification in all pictures was 40X to show the surface of cartilage. B. Quantification of IgG deposition in the joints of all WT, C3aR−/−, C5aR−/−, and C6-def mice. At day 10 following Arthrogen injection, mice were sacrificed and IgG deposition was scored on a scale of 0–3. Endogenous IgG was considered as normal background levels and knee joints from RAG2−/− mice on a C57BL/6 background naturally lacking IgG were used as negative controls. All data represent the mean ± SEM based on n = 21 for WT, n = 13 for C3aR−/−, n = 11 for C5aR−/−, and n= 8 for C6-def mice. p < 0.001 in comparison with WT mice, by Tukey’s multiple comparison test.
Figure 4.
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Histopathology, C3 deposition, monocyte/macrophage infiltration, and neutrophil infiltration from WT, C3aR−/−, C5aR−/−, and C6-def mice with CAIA. Knee joints with maximum CDA scores from WT, C3aR−/−, C5aR−/−, and C6-def mice with CAIA were selected. Areas of synovium (S), cartilage (C), and meniscus (M) are identified. The black arrows all point to the synovium. From left to right, knee joints of WT, C3aR−/−, C5aR−/−, and C6-def mice stained with Toluidine-blue (blue color) are shown in A, B, C and D. Similarly, knee joints with C3 deposition (brown color) are shown in E, F, G and H; knee joints stained with F4/80 (red color) for monocytes/macrophages are shown in I, J, K and L; and knee joints stained with neutrophil (brown color) surface marker are shown in M, N, O and P. Magnification for all pictures was 10X (a magnification red scale bar at 10X of 10 µm (0.01mm) is included on the lower right hand corner in all frames).
Deposition of C3 and IgG was specifically examined in the knee joints of all WT, C3aR−/−, C5aR−/−, and C6-def mice. No C3 deposition was present in the knee joints of control WT and C3−/− mice without CAIA (Fig. S2). Similarly, no C3 deposition was present in the knee joints of control C5aR−/−, C3aR−/−, and C6-def mice without CAIA (data not shown). C3 deposition in the synovium and in the cartilage was significantly reduced in the knee joint of C3aR−/− and C5aR−/− mice compared with WT (Fig. 2C), and was also reduced significantly in the synovium and cartilage of C6-def mice compared with WT mice (Fig. 2D), all with CAIA. AJM scores (synovium and cartilage) for C3 deposition were reduced by 41%, 57% and 30% in C3aR−/−, C5aR−/−, and C6-def mice, respectively, compared with WT mice with CAIA. With regard to individual compartments, C3 deposition in the synovium of C3aR−/−, C5aR−/−, and C6-def mice compared with the WT mice was decreased by 37%, 55%, and 23%, respectively (Figs. 2C and 2D). C3 deposition on the cartilage surface of C3aR−/−, C5aR−/−, and C6-def mice compared with the WT mice was decreased to 45%, 60%, and 42%, respectively (Figs. 2C and 2D). The correlations (r) between AJM C3 deposition in the knee joints and CDA at 95% CI in WT, C3aR−/−, C5aR−/−, and C6-def were 0.57 (p< 0.0017), 0.90 (p< 0.001), 0.65 (p< 0.027), and 0.53 (p< 0.18), respectively. There was more decrease in C3 deposition (all joint mean score) in the synovium as well as on the cartilage surface in the knee joint of C5aR−/− mice than in C3aR−/− (p< 0.016) and C6-def (p< 0.0027) mice (Fig 2). Representative C3 deposition pictures of the knee joints from WT, C3aR−/−, C5aR−/−, and C6-def mice are shown in Fig. 4 (E, F, G and H).
IgG deposition was specifically examined in the knee joints of all WT, C3aR−/−, C5aR−/−, and C6-def mice. No IgG deposition was observed in the synovia of these mice. Representative IgG deposition pictures on the surface of cartilage from the knee joints of WT, C3aR−/−, C5aR−/−, and C6-def mice are shown in Fig. 3A (1, 2, 3 & 4). Representative IgG deposition pictures on the surface of cartilage from the knee joints of C57BL/6 WT mice without CAIA and RAG2−/− C57BL/6 mice without CAIA are shown in Fig. 3A (panels 5 and 6). IgG deposition on the surface of the cartilage was significantly (p< 0.001) reduced in the knee joints from C3aR−/− and C5aR−/− mice, but not in C6-def mice, in comparison with the WT mice with CAIA (Fig. 3B). Endogenous IgG present on the cartilage of knee joints from WT and RAG2−/− mice without CAIA was considered as the baseline background.
C3 deposition and C5a generation induced by anti-collagen antibodies in vitro
Sera from WT, C3aR−/−, C5aR−/−, and C6-def mice were used for in vitro studies on complement activation. To study activation by all three complement pathways, sera were serially diluted 2-fold from 1:10 for C3b generation, and from 1:50 for C5a generation, in buffer containing Ca++. To analyze activation by the AP only, sera were serially diluted 2-fold in buffer in the absence of Ca++ with Mg++/EGTA. Serial two-fold dilutions of sera were incubated on plates with adherent anti-CII mAb and C3 deposition on the ELISA plate and C5a generation in the supernatant were measured (Fig. 5). Negative controls included NOD sera naturally lacking C5 and sera from C3−/− mice. With Ca++-sufficient buffer, equivalent levels of C3 deposition were observed using all sera except for sera from C3−/− mice where no C3 deposition was observed, as expected (Fig. 5A). Levels of C5a generation in the presence of Ca++ were slightly lower using sera from C3aR−/−, C5aR−/−, and C6-def mice in comparison to WT, and were absent using sera from NOD mice (Fig. 5B). In the absence of Ca++, where only the AP was active, levels of C3b deposition and of C5a generation were slightly lower using sera from C6-def mice in comparison to WT (Figs. 5C and D).
Figure 5.
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Anti-collagen Ab-induced activation of the AP in vitro using sera from WT, C3aR−/−, C5aR−/−, and C6-def mice without CAIA. C3 deposition and C5a generation were measured by incubating sera from WT, C3aR−/−, C5aR−/−, and C6-def mice on ELISA plates pre-coated with four anti-collagen mAb specific for bovine type II collagen. The experiments were performed with the same sera serially diluted 2-fold in Ca++-sufficient buffer (panels A and B), where all three complement activation pathways were active, or with Ca++-deficient buffer (panels C and D), where only the AP was active. Sera from C3−/− and non-obese diabetic (NOD) mice were used as negative controls for C3 deposition and C5a generation, respectively. The X-axis shows various serum dilutions and the Y-axis shows mean OD values. A. C3 deposition on the ELISA plates using Ca++-sufficient buffer. B. C5a generation in the supernatant using Ca++-sufficient buffer. C. C3 deposition using Ca++-deficient buffer. D. C5a generation using Ca++-deficient buffer. All data are expressed in optical density units (OD). The baseline levels of C5a in the sera before incubation on the mAb to CII were subtracted from the total C5a measured at the end of each experiment. The data shown here represent the mean ± SEM based experiments with Ca++-sufficient buffer: n = 4 for WT, n = 4 for C3aR−/−, n = 4 for C5aR−/−, n = 3 for C6−/−, n = 4 for NOD, and n = 4 for C3−/− mice. The data for experiments using Ca++-deficient buffer represent the mean + SEM based on: n = 5 for WT, n = 5 for C3aR−/−, n = 5 for C5aR−/−, n = 5 for C6-def, n = 5 for NOD, and n = 5 for C3−/− mice. = p< 0.05: in panel B for.each of the complement-deficient sera vs. WT; in panel C for sera from C6-def vs. WT mice; and in panel D for sera from C6-def vs. WT mice.
Assessment of macrophage and neutrophil infiltration in the synovium of knee joints from mice with CAIA
The infiltration of macrophages and neutrophils in the knee joint synovium from WT, C3aR−/−, C5aR−/−, and C6-def mice was determined using immunohistochemical methods with specific cell surface markers, as outlined in the Methods. The percentages of macrophages and neutrophils were decreased significantly in the synovium of C3aR−/− and C5aR−/− mice with CAIA in comparison with the WT mice (Fig. 6). The decrease in synovial macrophages in C3aR−/− and C5aR−/− as compared with the WT mice with disease was 20% (p< 0.005) and 35% (p< 0.001), respectively. A more dramatic decrease in the percentages of synovial neutrophils was observed in C3aR−/−, C5aR−/−, and C6-def mice with disease as compared to WT mice with decreases of 56% (p< 0.014), 72% (p< 0.002), and 57% (p< 0.044), respectively. No statistically significant decrease was seen in the percentages of synovial macrophages in C6−/− mice with disease as compared with WT mice with disease (Fig. 6). Representative examples of neutrophil and macrophage infiltration are shown in Fig. 4 (panels I–L and M–P, respectively).
Figure 6.
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Percentages of macrophages and neutrophils in the synovium of knee joints from WT, C3aR−/−, C5aR−/−, and C6-def mice with CAIA. All mice were sacrificed at day 10 and knee joints were stained using methods specific for macrophages and neutrophils. The percentages of macrophages and neutrophils in the synovium were calculated by image analysis quantitating the stained marked areas of neutrophils and macrophages in comparison to the total marked area of the synovium. All data shown here represent the mean ± SEM based on n = 14 for WT, n = 13 for C3aR−/−, and n = 11 for C5aR−/−. WT n = 11 and n= 8 for C6-def mice. p < 0.05 in comparison with WT mice.
Cytokine mRNA from synovium obtained by LCM from the knee joints of mice with disease
mRNA levels were evaluated by quantitative RT-PCR using cDNA made from the amplified mRNA (aRNA) obtained using LCM from the synovium of the left hind limb of WT, C3aR−/−, C5aR−/−, and C6-def mice (Fig. 7). No significant differences were seen in the levels of TNF-α mRNA in the synovium of C3aR−/−, and C6-def mice with disease (Fig. 6A). In contrast, a significant decrease (p< 0.011) was observed in the levels of TNF-α mRNA in the synovium of C5aR−/− mice in comparison to WT mice (Fig. 7A). Significant decreases in levels of IL-1β mRNA were also seen in the synovium of C5aR−/− (p< 0.046) and C6-def (p< 0.005) mice, but not C3aR-/ mice, in comparison to WT mice (Fig. 7B).
Figure 7.
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mRNA levels of TNF-α and IL-1β in synovium obtained by LCM from the knee joints of WT, C3aR−/−, C5aR−/−, and C6-def mice with CAIA. The mRNA levels for synovial cytokines were measured by quantitative RT-PCR using cDNA made from aRNA, as described in Methods, with specific primers and probes for TNF-α (Fig. 7A) and IL-1β (Fig. 7B). The mRNA levels for each cytokine were expressed as specific mRNA (pg)/18s rRNA (pg). All data represent the mean ± SEM based on n = 5 for WT, n = 5 for C3aR−/−, n = 3 for C5aR−/−, and n = 6 for C6-def mice. p< 0.05 in comparison with WT mice.
Absolute levels of complement components in mice sera
The absolute levels of various complement components such as C1q, C4, C3, factor B and factor D were measured in sera from WT, C3aR−/−, C5aR−/−, and C6-def mice (Table 1). No major decreases in the levels of complement proteins were observed that might provide alternative explanations for differences in CDA and histologic changes in these strains. However, decreases of 35%, 32%, and 26% in the absolute levels of C4 were seen in the sera from C5aR−/− mice in comparison with sera from WT, C3aR−/−, and C6-def mice, respectively. The decrease in the levels of C4 in sera from C5aR−/− mice compared with WT mice was significant (p< 0.014).
Table 1.
Levels of complement components in sera from WT and complement component deficient miceA
| Mice (n) | C1q | C3 | C4 | factor B | factor D |
:--- :--- :--- |
| WT (23) B | 0.502 ± 0.04 | 1.730 ± 0.09 | 1.086 ± 0.09 | 0.608 ± 0.03 | 1.721 ± 0.05 |
| C3aR−/− (15) B | 0.696 ± 0.04 | 1.674 ± 0.08 | 1.137 ± 0.08 | 0.539 ± 0.01 | 1.777 ± 0.05 |
| p | 0.002 | 0.650 | 0.668 | 0.069 | 0.449 |
| C5aR−/− (14) B | 0.567 ± 0.03 | 1.661 ± 0.08 | 0.742 ± 0.10 | 0.500 ± 0.04 | 1.751 ± 0.14 |
| p | 0.227 | 0.571 | 0.014 | 0.0429 | 0.847 |
| C6-def (6) | 0.536 ± 0.06 | 1.873 ± 0.22 | 1.009 ± 0.14 | 0.567 ± 0.01 | 1.618 ± 0.06 |
| p | 0.654 | 0.563 | 0.786 | 0.249 | 0.197 |
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A
Data are expressed as optical density units with mean ± SEM based on the indicated number of sera (n).
B
WT mice used to measure factor B (n = 9); C3aR−/− (n=6); C5aR−/− (n = 6); B WT mice used to measure factor D (n=13).
All p-values for different complement components were compared with the corresponding values of WT mice. p < 0.05 were considered statistically significant.
Discussion
The primary goal in this study was to compare the roles of the C3aR, C5aR, and MAC (C5b-9) in the pathogenesis of inflammatory arthritis using an identical mouse model, (CAIA), in a single strain of C57BL/6 mice. We found that each of the three effector mechanisms initiated by the C3aR, C5aR, or the MAC was essential to the full development of arthritis; deficiency states in each of the three resulted in significant amelioration in both the primary clinical and histopathologic disease endpoints. The lack of C5aR showed the greatest decreases in CDA and parameters of histological change in these studies. Previous studies demonstrated no effect of a deficiency in the C3aR on CAIA on the Balb/c background (40), and a lack of effect of C6-def in anti-GPI-induced arthritis in the C3H/He background (7). Nevertheless, our current studies in C57BL/6 mice have demonstrated a substantial role for C3aR as well as a comparably important role of the MAC in CAIA, pointing out the importance of evaluating more than one strain of mice and model before concluding a lack of effect of a particular complement effector pathway.
We observed some key differences in the specific downstream effects of each mechanism of inflammation and tissue destruction. A significant decrease in the percentage of synovial neutrophils was observed in C3aR−/−, C5aR−/−, and C6-def mice, and a decrease in macrophages was observed in both C3aR−/− and C5aR−/−, but not in C6-def, mice. In addition, a significant decrease in TNF-α mRNA levels was observed in the synovium of C5aR−/− mice, and a decrease in IL-1β mRNA in both C5aR−/− and C6-def mice, while C3aR−/− mice demonstrated no changes in either cytokine. These results may reflect the effects of different expression of the two receptors or of alternate receptors for C3a and C5a, differences in signal transduction pathways that follow engagement of C3aR, C5aR, and the G-protein linked pathways that are subsequently activated, or differences in the numbers or types of infiltrating cells. However, the specific mechanisms involved in absent expression of mRNA for TNF-α and IL-1β in particular strains of gene-deficient mice remain unknown.
Neutrophil activation through C5aR in CAIA, possibly acting synergistically through enhancement in activating Fc receptors, likely plays an important role in the differential effects following chemotactic peptide engagement. This conclusion is supported by data from other experimental models of arthritis initiated by immune complexes where the absence of receptors for C5a on the surface of neutrophils in C5aR−/− mice likely resulted in the observed decrease in infiltration of neutrophils (39). In addition, mouse neutrophils and macrophages are known to express C5aR (41) and upon contact with human recombinant C5a mononuclear phagocytes release TNF-α and IL-1β (42). Thus, with a decrease in synovial neutrophils and the lack of a C5aR signal, the absence of detectable mRNAs for these cytokines in our studies is not unexpected.
Alternatively, in the absence of C5aR there may be counter-regulatory mechanisms available such as the existence of C5L2 receptors that would interact with the available C5a. It has been shown that C5aR−/− mice that also express C5L2 receptors alone do not respond with a pro-inflammatory phenotype to C5a (21). This receptor may thus serve to modulate C5a biological functions in vivo. In addition to the potential effects of C5L2, blockade of C5aR on alveolar macrophages in lung Arthus reactions led to an increased ratio of FcγRIIB (inhibitory) to FcγRIII (activating) receptors (43). Therefore, local inhibition of lung C5aR can abrogate inflammation by increasing the relative expression ratio of the inhibitory receptor FcγRIIB.
Despite the major role for C5a and C5aR, deficiencies in either C3aR or MAC function in our studies also led to substantial decreases in the CDA and joint histologic injury scores. Consistent with this outcome, receptors for C3a are also present on murine monocytes/macrophages and neutrophils. It was shown that C3a stimulation of non-adherent PBMCs suppressed LPS-induced mRNA levels of TNF-α and IL-1β whereas C3a stimulation of adherent PBMCs led to enhanced LPS-induced TNF-α and IL-1β mRNA levels (44). Thus, C3a causes cytokine release from many cell types in vitro including IL-1β and TNF-α (44). However, the absence of changes in the levels of these cytokines in C3aR−/− mice suggests that the C5a that is generated is able to provide a sufficient signal in the absence of C3aR. Alternatively, it has also been shown that C3a binds to the receptor for advanced glycation end products (RAGE) (45). In CIA, the expression of RAGE is increased and synovial tissue inflammation, cartilage and bone destruction are decreased by treatment with soluble RAGE (46). Therefore, the more modest decrease in disease in C3aR−/− mice might be due to the availability of alternate receptors for C3a, such as RAGE, on the surface of effector cells. In this instance, the high levels of TNF-α and IL-1β in the synovium from the knee joints of C3aR−/− with CAIA may be due in part to the binding of C3a to RAGE on macrophages.
Another unexpected result, based on prior studies of anti-GPI-induced arthritis, was our finding of protection from CAIA in the presence of C6 deficiency and the resulting absence of the MAC. One explanation may be that, despite the influx of macrophages and the presence of TNF-α in the knee joints of C6-def mice with CAIA that was similar to WT mice, the influx of neutrophils was reduced. Thus, partial protection of C6-def mice from CAIA may be dependent on decreased neutrophils and not on macrophages. Our studies are also consistent with the results of previous studies on experimental models of arthritis in rats or myasthenis gravis in rabbits where it was shown that C6 deficiency effectively reduced disease severity (34, 36). An important direct or bystander role for MAC in inflammatory arthritis may be the induction of cytokines. This is supported by the minimal levels of IL-1β mRNA in the joints in C6-def mice with CAIA.
It should be emphasized that C6 deficiency was originally described in the Peru-Coppock strain, which were then backcrossed for 10 generations into the C3H/He strain (37). Thus, the C6 deficiency is due to a spontaneously occurring mutation, not to a specific induced gene deletion. The mice used in this study were obtained by backcrossing C6-def C3H/He mice into the C57BL/6 strain for 8 generations. A defect in coagulation, characterized as impaired platelet aggregation, was described in C6-def C3H/He mice and was reversed in vitro by restoration with purified rat C6 protein (38). The coagulation and complement systems are known to exhibit interactions and the possibility exists that platelet aggregation in rodents is dependent on the terminal components of the complement system. To our knowledge, a similar defect in platelet aggregation has not been examined for in C6-def C57BL/6 mice and theoretically, if present, may have influenced our observations.
One striking finding common to mice with deficiencies in mice lacking C3aR or C5aR was a decrease in local IgG and C3 deposition in the joint in comparison to WT mice. Since each effector pathway is “downstream” of C3 activation, it would seem that joint IgG and C3 deposition levels would be comparable between WT and mice with complement deficiencies. Nevertheless, this was not the case, suggesting that WT mice hypothetically may possess mechanisms that enhance IgG deposition with subsequent binding of C3. Thus, WT mice may exhibit increased migration of IgG into the joints and/or greater deposition of the anti-CII mAb. In other studies, C5-deficient mice failed to develop CAIA, although deposition of anti-CII mAb and C3 on the cartilage surface was unchanged (47). This finding indicates that the dependency of CAIA on C5 may be due to increased chemotaxis of neutrophils and macrophages into the joint.
The increased deposition of IgG in the joints of WT mice in the present studies, in comparison to mice with the three complement deficiencies, suggests the possibility of degradation of collagen by enzymes from phagocytic cells. This breakdown could expose new epitopes to which further anti-CII mAb could bind (47–49), leading to additional C3 fixation with further amplification of local complement activation through the AP. The explanation seems less likely that the increased IgG and C3 deposition in WT mice was secondary merely to the enhanced inflammation since these conditions would lead to further enzymatic degradation of deposited IgG and C3. A possibility also exists that IgG is processed or cleared more rapidly in C3aR−/−, C5aR−/−, and C6-def mice in comparison to WT mice. A slower rate of IgG clearance in WT mice could hypothetically lead to more deposition in joints over time. Studies are in progress to study rates of IgG clearance in mice deficient in C3aR, C5aR, or C6 protein.
We observed that serum levels of C4 were decreased in C5aR−/− mice. Similar decreases in serum C4 levels were previously found in C1q−/−, C3−/−, MBL−/−, and Bf−/− mice, and the mechanisms remain unexplained (3). Nevertheless, the absence of changes in C3 deposition, and a slight decrease in generation of C5a, in vitro using sera from C5aR−/− mice suggests that the decrease in C4 levels should not have affected the in vivo results.
Lastly, mice genetically deficient in a single component of the complement system may develop associated changes in other proteins. Thus, an alternative explanation for our results could be that the decreases in CDA observed in mice deficient in C3aR (Fig. 1A) or in C6 (Fig. 1C) may be secondary to decreased C5a levels in these mice, as possibly suggested by the data expressed in Fig. 5. This possibility will be explored in future studies.
In summary, we have for the first time directly compared, in a single strain of mice that are comparably backcrossed, the effects of three of the major effector pathways of complement activation that have been proposed to cause tissue injury. Notably, we determined each effector to be important as deficiencies in each led to decreased clinical disease activity and protection from injury using histologic criteria. There may be important differences in the engagement of non-complement dependent downstream pathways of inflammation that occur in some strains of mice in the absence of C3aR, C5aR, or C6 protein. However, a shared final effect in these strains may be enhanced local IgG binding with secondary C3 deposition, the latter possibly occurring through amplification mediated by the AP.
Supplementary Material
1
NIHMS342564-supplement-1.tif (1.4MB, tif)
2
NIHMS342564-supplement-2.tif (1.7MB, tif)
Acknowledgements
The authors thank: Ms. Jessica Nicholas for assisting in various complement ELISA assays, determining clinical disease scores and breeding various gene knockout mice; Ms. Nicole Spoelstra, Laser Capture Microscopy Core, Cancer Center, University of Colorado Denver-AMC for technical advice; Ms. Umarani Pugazhenthi, PCR Core University of Colorado Denver-AMC for performing quantitative RT-PCR on samples used in this study and Mr. Gaurav Mehta for taking histology pictures and adding a magnification scale bar.
This work was supported by NIH grant AR051749 to V.M. Holers.
Abbreviations used in this paper
CP
classical pathway
AP
alternative pathway
LP
lectin pathway
MAC or C5b-9
membrane attack complex
C6-def mice
C6 deficient mice
CAIA
collagen antibody-induced arthritis
CIA
collagen-induced arthritis
CII
type II collagen
DAS
disease activity score
AJM
all joint mean
IC
immune complex
NBF
neutral buffered formalin
RA
rheumatoid arthritis
Footnotes
The online version of this article contains supplemental material.
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AI-数学-高中-3.斜率、倾斜角及他们之间的关系
zylhuo已于 2024-01-22 20:07:35 修改
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文章标签：算法斜率与倾斜角
于 2024-01-22 17:28:56 首次发布
版权声明：本文为博主原创文章，遵循CC 4.0 BY-SA版权协议，转载请附上原文出处链接和本声明。
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该篇文章通过小高老师的讲解，探讨了π在弧度制中的180度对应于直角三角形中斜角的概念，以及如何根据倾斜角的范围确定斜率的正负。还涉及了三角函数的基本概念如sin、cos、tan及其在斜率计算中的应用示例。
原作者视频：
1.倾斜角：
【小高老师】π为什么是180度·弧度制·三角函数_哔哩哔哩_bilibili
2.斜率：
当倾斜角θ ϵ （0，π/2）之间，锐角时，斜率是正的；
当倾斜角θ ϵ （π/2，π）之间，钝角时，斜率是负的。
3.斜率和倾斜角关系：
相关概念：数学 三角函数 sin 正弦、cos 余弦、tan 正切、cot 余切、sec 正割、csc 余割 简介_sec csc cot 的三角函数图像-CSDN博客
4.斜率、倾斜角示例：
已知tan求倾斜角度arctan√3等于多少怎么算的呢_百度知道
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【2025 算法 面试通关】【四 . 计算机视觉 - 传统图像处理】【29 . 计算机视觉面试必刷100题：霍夫变换 与 形态学操作核心考点解析】 最新发布
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答：霍夫变换是一种将图像空间中的曲线检测问题转换为参数空间投票的特征检测 算法，核心思想是通过投票机制在参数空间中寻找峰值，从而确定图像中是否存在特定形状（如直线、圆等）。
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题目中提到函数在x=0处的切线 倾斜角 是π/4，这意味着 斜率 是1，由此可解出x的值。 6 . 组合问题：志愿者的分配问题属于组合问题，涉及到排列组合的知识。题目要求每个小区至少分配一名志愿者，可以使用“隔板法”或 . . .
实用工具:常用 数学 公式
云，风扬起的地方
12-18 2332
实用工具:常用 数学 公式
三角函数知识随笔
qq_43016560的博客
04-20 1296
三角函数的基本知识的定义及常用公式和特殊值展示，以及numpy的实现方式。对于理解线性代数几何空间有很大帮助。
C/C++三角函数math . h库详解
ungu1314的博客
02-19 4694
在C和C++中，math . h库提供了一系列用于处理 数学 运算的函数，包括三角函数、反三角函数等。以下是常用的三角函数、反三角函数和一些常用的其他函数，以及它们的简要介绍和示例，希望对你有所帮助。
Matlab使用之三角函数中需要注意
weixin_42660638的博客
09-13 2019
在matlab中使用三角函数时需要注意角度制及弧度制
三角函数及其常用公式
mtc1170824134的博客
06-02 1万+
三角函数是 数学 中属于初等函数中的超越函数的一类函数。它们的本质是任何角的集合 与 一个比值的集合的变量 之间 的映射。通常的三角函数是在平面直角坐标系中定义的。其定义域为整个实数域。三角函数看似很多，很复杂，但只要掌握了三角函数的本质及内部规律就会发现三角函数各个公式 之间 有强大的联系。而掌握三角函数的内部规律及本质也是学好三角函数的关键所在。
AI 作画新时代：GPT - 3 与 DALL - E的创新突破
总结来说，GPT - 3 和DALL - E作为人工智能技术的前沿代表，不仅展示了 AI 在语言理解和图像生成方面的巨大潜力，同时也为艺术创作领域带来了新的可能性和挑战。随着 AI 技术的不断发展和成熟，未来在艺术、设计、娱乐等创意 . . .
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