content stringlengths 86 994k | meta stringlengths 288 619 |
|---|---|
Are schemes pushouts of neighbourhoods and formal neighbourhoods?
up vote 3 down vote favorite
I have two questions, the first less important.
Let $X$ be a scheme, $x \in X$ a schematic point.
What is an elegant way of defining/characterizing the map $\operatorname{Spec}(O_{X,x}) \to X$?
This map can be defined by choosing affine neighbourhood, building the map and then showing independence; maybe there is a better way? For example a characterization which will make sense for locally
ringed spaces (but existence perhaps will not be in that generality).
Now, suppose furthermore that $X$ is integral, $x \in X$ is a closed point, $U=X-\{x\}$. We denote by $K$ the field of rational functions on $X$, i.e. stalk at the generic point.
$$ \begin{matrix} \operatorname{Spec}(K) & \to & U \\\\ \downarrow & & \downarrow \\\\ \operatorname{Spec}(O_{X,x}) & \to & X \end{matrix} $$
Is it true that this diagram is cartesian and co-cartesian?
If one can require more to get the result then it is also interesting (say pushout is in the category of schemes of certain type, or $X$ is a non-singular curve over a field...).
Thanks, Sasha
schemes ag.algebraic-geometry locally-ringed-spaces universal-property
3 $\mathrm{Spec}(\mathcal O_{X,x})$ is the scheme-theoretic intersection of all open neighborhoods of $x$. This is not quite a description of the morphism $\mathrm{Spec}(\mathcal O_{X,x})\to X$, but
at least this description may be checked in a single open affine chart. – user2035 Nov 25 '11 at 17:00
So you claim that $\mathrm{Spec}(O_{X,x}) = \prod_{x \in U} U$ in the category of schemes over $X$? – Martin Brandenburg Nov 25 '11 at 17:06
Yes, that is correct. You may assume $X=\mathrm{Spec}(A)$ affine and restrict to the cofinal subsystems of neighborhoods of the form $\mathrm{Spec}(A_f)$, so $\prod_{x\in U}U=\prod_{f\notin x}\
mathrm{Spec}(A_f)=\mathrm{Spec}(\varinjlim A_f)=\mathrm{Spec}(\mathcal O_{X,x})$. – user2035 Nov 25 '11 at 17:22
Thanks! I was a bit puzzled because Jonathan Wise showed before (mathoverflow.net/questions/65506/…) that infinite products are very rare in the category of schemes; but apparently there are more
examples for relative schemes, i.e. infinite fiber products. – Martin Brandenburg Nov 25 '11 at 17:59
The title of this question is misleading, since "formal neighborhood" could either refer to the formal scheme which is the completion of a scheme at a closed subscheme, or to the map $\mathrm
{Spec}(\mathbb{C}[[t]]) \to \mathrm{Spec}(\mathbb{C}[t])$ (or its generalization when the target is a smooth curve). Though it would be interesting to record the answer to the question of whether
a scheme is glued, in the sense of being a colimit in the appropriate category, from an open set and a formal neighborhood (in this sense) of its closed complement. – Ryan Reich Nov 26 '11 at 6:32
show 1 more comment
3 Answers
active oldest votes
As for the first question: Let us define a pointed scheme be a pair $(X,x)$, consisting of a scheme together with some point $x \in X$. Morphisms of pointed schemes are defined in an
obvious way. Thus we get the category of pointed schemes. Also, we have the category of local rings with local ring homomorphisms. Then we have a functor
$\mathrm{Spec} : (\text{local rings})^{op} \longrightarrow (\text{pointed schemes})$
which maps a local ring $(A,\mathfrak{m})$ to the pointed scheme $(\mathrm{Spec}(A),\mathfrak{m})$. In the other direction, we have a functor
$\mathrm{Stalk} : (\text{pointed schemes}) \to (\text{local rings})^{op}$
which maps $(X,x) \mapsto \mathcal{O}_{X,x}$. Now Proposition 2.4.4. in EGA I may be reformulated as:
up vote 7
down vote Proposition: $\mathrm{Spec}$ is left adjoint to $\mathrm{Stalk}$.
The counit of this adjunction is the canonical morphism $i : \mathrm{Spec}(\mathcal{O}_{X,x}) \to X$ for a pointed scheme $(X,x)$ and the unit is the isomorphism $\mathcal{O}_{\mathrm{Spec}
(A),\mathfrak{m}} \cong A_{\mathfrak{m}} \cong A$ for a local ring $(A,\mathfrak{m})$. So in more down-to-earth terms: $i$ is the universal morphism from the spectrum of a local ring to $X$
which maps to the closed point to $x$.
I doubt that for a pointed locally ringed space we have a morphism at all $\mathrm{Spec}(\mathcal{O}_{X,x}) \to X$. The reason is that the stalks of the structure sheaf are not sufficiently
tied up together: There is no way of getting from prime ideals of the single local ring $\mathcal{O}_{X,x}$ to other points of $X$. You might try a topological (smooth) manifold with its
sheaf of continuous (smooth) functions $(X,\mathcal{O}_X)$; see also this recent MO discussion about prime ideals in $\mathcal{O}_{X,x}$ in this example.
add comment
For simplicity, put $X_x=\mathrm{Spec}(\mathcal{O}_{X,x})$ and $X'_x=X_x\setminus\{x\}$.
As was pointed out in name's answer, the diagram in the question is not cartesian in general. However, if we replace $\mathrm{Spec}(K)$ by the punctured spectrum $X'_x$, we get $$\begin
{array}{ccc} X'_x & \longrightarrow & U\\ \downarrow & & \downarrow\\ X_x & \longrightarrow & X \end{array}$$ which is trivially cartesian (no assumption on $X$ or $x$ here).
If, moreover, you assume that $\{x\}$ is defined by finitely many equations (in some affine neighborhood) then the natural map $X_x\coprod U\to X$ is (faithfully flat and) quasicompact,
which by flat descent implies that our diagram is also cocartesian. (This works in particular if $X$ is locally noetherian.)
up vote 3
down vote If it is cocartesian and $X$ is integral, and you work in the category of separated schemes, then your original diagram is also cocartesian, because if two morphisms from $X'_x$ to a
separated scheme $Z$ coincide on $\mathrm{Spec}(K)$, they must be equal by density.
Apart from these cases I don't have a general answer. An interesting special case is when $X=\mathrm{Spec} k[(x_n)_{n\in\mathbb{N}}]$ ($k$ a field), and $x$ is the origin. In this case,
the natural map $X'_x\coprod U\to X$ is not a topological quotient map! In other words, the above diagram is not cocartesian as a diagram of topological spaces. However, I could not prove
that it is not cocartesian as diagram of schemes.
add comment
How about this: $Spec (\mathcal{O}_{X,x})$ is the sub-locally ringed space of $X$ whose underlying topological space consists of all the points $y$ of $X$ such that $x$ is in the closure
of $y$.
up vote 1 The square is not cartesian unless $X$ has dimension one. Open immersions are preserved by pull-back and so the pullback would be the open subscheme of $Spec(\mathcal{O}_{X, x})$ which is
down vote the complement of $x$. If you replace $Spec(K)$ with the pull-back, the square is not cocartesian, due to the existance of non-separated phenomena, like the affine line with a double
2 For the first paragraph: This gives a description of the "local spectrum" as locally ringed space if $X$ is a scheme, but this is not true if $X$ is just a locally ringed space. So we
have to be careful here. I don't think that for a locally ringed space $X$ there is a natural map $\mathrm{Spec}(O_{X,x}) \to X$ at all. – Martin Brandenburg Nov 25 '11 at 16:38
add comment
Not the answer you're looking for? Browse other questions tagged schemes ag.algebraic-geometry locally-ringed-spaces universal-property or ask your own question. | {"url":"http://mathoverflow.net/questions/81892/are-schemes-pushouts-of-neighbourhoods-and-formal-neighbourhoods?answertab=votes","timestamp":"2014-04-17T13:04:32Z","content_type":null,"content_length":"70249","record_id":"<urn:uuid:717e0a75-bfaf-430c-8275-c0d24ca90830>","cc-path":"CC-MAIN-2014-15/segments/1397609530131.27/warc/CC-MAIN-20140416005210-00201-ip-10-147-4-33.ec2.internal.warc.gz"} |
Need help with spot light pixel shader [Archive] - OpenGL Discussion and Help Forums
01-18-2008, 09:18 AM
Obviously I am too dang stupid to figure something as simple as a spot light via pixel shader, so I am asking for help.
The light source can be anywhere in the view space, position and direction are given by lightPos and lightDir (lightDir is normalized).
I don't want to pass them via OpenGL's light stuff. Actually the shader can handle multiple spotlights, but I have simplified it here.
vEye is the view point.
aspect serves for making the headlight round.
cutOff is the opening angle, spotExp the rate of decay.
grAlpha is some global alpha (usually just 1.0)
The OpenGL transformation matrixes are all properly set up (or the renderer wouldn't work). Some scaling is involved, but that should be stuck in the model view matrix, or am I wrong?
Even if the viewer is the light source for the spotlight, the spotlight doesn't light the proper area right in front, but is off.
If I rotate the view, the spotlight wanders just somewhere, and I dunno what I am doing wrong.
//base texture and decal
uniform sampler2D btmTex, topTex;
varying vec3 vertPos;
uniform vec3 vEye, lightPos, lightDir;
uniform vec4 matColor;
uniform float grAlpha, aspect, cutOff, spotExp, brightness;
void main(void) {
vec4 btmColor = texture2D (btmTex, gl_TexCoord [0].xy);
vec4 topColor = texture2D (topTex, gl_TexCoord [1].xy);
vec3 lp, ld, lightVec, spotColor, v = vec3 (vertPos.x * aspect, vertPos.y, vertPos.z);
float spotEffect, lightDist, spotBrightness = 0.0;
lightPos -= vEye; //translate
//rotate the light dir by adding it to the light pos, rotating the result, rotating the light pos,
//then subtracting the rotated light pos from the rotated light dir (better way? Cannot figure)
lightDir = vec3 (gl_ModelViewMatrix * vec4 (lightPos + lightDir, 1.0));
lightPos = vec3 (gl_ModelViewMatrix * vec4 (lightPos, 1.0));
lightDir = normalize (lightDir - lightPos);
//this should be standard per pixel lighting fare ...
lightVec = v - lightPos;
lightDist = length (lightVec);
spotEffect = dot (lightDir, lightVec / lightDist);
if (spotEffect >= cutOff) {
float attenuation = min (brightness / lightDist, 1.0);
spotBrightness += pow (spotEffect * 1.1, spotExp) * attenuation;
//compute the final light (probably more noob stuff ...)
spotColor = vec3 (max (spotBrightness, gl_Color.r), max (spotBrightness, gl_Color.g), max (spotBrightness, gl_Color.b));
spotColor = vec3 (min (spotColor.r, matColor.r), min (spotColor.g, matColor.g), min (spotColor.b, matColor.b));
gl_FragColor = vec4 (vec3 (mix (btmColor, topColor, topColor.a)), (btmColor.a + topColor.a) * grAlpha) * vec4 (spotColor, gl_Color.a);
The vertex shader:
varying vec3 vertPos;
void main(void)
gl_TexCoord [0]=gl_MultiTexCoord0;
gl_TexCoord [1]=gl_MultiTexCoord1;
vertPos=vec3(gl_ModelViewMatrix * gl_Vertex);
gl_Position = ftransform();
Please be so kind and help me to get this going. | {"url":"http://www.opengl.org/discussion_boards/archive/index.php/t-163879.html","timestamp":"2014-04-16T10:44:19Z","content_type":null,"content_length":"13539","record_id":"<urn:uuid:4af27471-68f0-454c-8fd4-3b92a4593dd5>","cc-path":"CC-MAIN-2014-15/segments/1397609523265.25/warc/CC-MAIN-20140416005203-00183-ip-10-147-4-33.ec2.internal.warc.gz"} |
Higher category theory
Basic concepts
Basic theorems
Universal constructions
Extra properties and structure
1-categorical presentations
A $3$-category is any of several concepts that generalize $2$-categories one step in higher category theory. The original notion is that of a globular strict 3-category, but the one most often used
here is that of a tricategory. The concept generalizes to $n$-categories.
Fix a meaning of $\infty$-category, however weak or strict you wish. Then a $3$-category is an $\infty$-category such that every 4-morphism is an equivalence, and all parallel pairs of $j$-morphisms
are equivalent for $j \geq 4$. Thus, up to equivalence, there is no point in mentioning anything beyond $3$-morphisms, except whether two given parallel $3$-morphisms are equivalent. This definition
may give a concept more general than your preferred definition of $3$-category, but it will be equivalent; basically, you may have to rephrase equivalence of $3$-morphisms as equality.
Specific versions | {"url":"http://www.ncatlab.org/nlab/show/3-category","timestamp":"2014-04-20T14:11:05Z","content_type":null,"content_length":"30135","record_id":"<urn:uuid:4020fe32-8f23-4c95-b9f1-ea8d8087c9a1>","cc-path":"CC-MAIN-2014-15/segments/1397609538787.31/warc/CC-MAIN-20140416005218-00414-ip-10-147-4-33.ec2.internal.warc.gz"} |
Possible Answer
Explore This Topic: What are Roman Numerals? Roman Numerals are what Romans used to use for numbers. Different symbols have different numeral values. - read more
What does the roman numeral XXL mean? XXL is not a valid roman numeral. What are all the Roman numerals and what do they mean? The Roman numeral system works by having separate symbols to represent
Share your answer: what is what number is xxl in roman numerals?
Question Analizer
Social Tag: Linguistics
Elementary arithmetic
Mathematical notation
Numeral systems
Roman numerals
Roman numeral analysis
what is what number is xxl in roman numerals resources | {"url":"http://www.askives.com/what-is-what-number-is-xxl-in-roman-numerals.html","timestamp":"2014-04-17T19:29:28Z","content_type":null,"content_length":"31691","record_id":"<urn:uuid:87b64904-7a99-4e32-ae23-263efa8940c5>","cc-path":"CC-MAIN-2014-15/segments/1397609530895.48/warc/CC-MAIN-20140416005210-00291-ip-10-147-4-33.ec2.internal.warc.gz"} |
Estimating the mean using confidence levels
July 14th 2009, 09:55 PM #1
Oct 2008
Estimating the mean using confidence levels
A company is interested in estimating the mean number of sick days taken by its employees. The firm's statistician selects 100 files at random and ntoes the number of sick days taken by each
employee. The mean was 12.2 days and the standard deviation was 10 days. Estimate the mean with 90% confidence and interpret.
I got (11.662, 12.738) with an E of .538 after doing the formula for E
My professor wrote down the answer of (10.555,13.845), which corresponds with an E of 1.645 if you do the subtractions.
1.645 is also the Critical Value for a 90% confidence level, what in the world is going on here?
A company is interested in estimating the mean number of sick days taken by its employees. The firm's statistician selects 100 files at random and ntoes the number of sick days taken by each
employee. The mean was 12.2 days and the standard deviation was 10 days. Estimate the mean with 90% confidence and interpret.
I got (11.662, 12.738) with an E of .538 after doing the formula for E
My professor wrote down the answer of (10.555,13.845), which corresponds with an E of 1.645 if you do the subtractions.
1.645 is also the Critical Value for a 90% confidence level, what in the world is going on here?
Confidence intervals are 'two-sided' so you use the two-sided critical value of z when $\alpha = 0.1$.
Is this only when alpha = .1?
A company is interested in estimating the mean number of sick days taken by its employees. The firm's statistician selects 100 files at random and ntoes the number of sick days taken by each
employee. The mean was 12.2 days and the standard deviation was 10 days. Estimate the mean with 90% confidence and interpret.
I got (11.662, 12.738) with an E of .538 after doing the formula for E
My professor wrote down the answer of (10.555,13.845), which corresponds with an E of 1.645 if you do the subtractions.
1.645 is also the Critical Value for a 90% confidence level, what in the world is going on here?
The sample mean is $12.2$ the standard error of this mean is $10/\sqrt{100}=1$, and the sample mean has an approximatly normal distribution.
Hence the interval $[12.2-\lambda, 12.2+\lambda]$ contains the mean with probability $p$, where $\lambda=P^{-1}(p/2)$ where $P$ denotes the cumulative normal distribution.
Do this and you will get your professors answer.
(Note it is the interval which is the random variable not the population mean)
July 14th 2009, 10:18 PM #2
July 14th 2009, 10:21 PM #3
Oct 2008
July 14th 2009, 11:26 PM #4
Grand Panjandrum
Nov 2005 | {"url":"http://mathhelpforum.com/advanced-statistics/95173-estimating-mean-using-confidence-levels.html","timestamp":"2014-04-19T01:52:27Z","content_type":null,"content_length":"43328","record_id":"<urn:uuid:cc789f36-8ad4-4205-aed1-48dea4d98d19>","cc-path":"CC-MAIN-2014-15/segments/1397609535745.0/warc/CC-MAIN-20140416005215-00530-ip-10-147-4-33.ec2.internal.warc.gz"} |
Posts by
Posts by andy
Total # Posts: 803
explain the Eutectic and Eutectoid reaction in cast irons
Identify and discuss the main safety legislation applicable to the installation, commissioning operating and maintaining the tube swaging machine.
G(t)=5200/(1+12e^(-.52t)) Find G'(t) I keeo getting (-32448e^(-.52t))/(1+12e^(-.52t))^2 Is this correct?
In a shipping yard, a crane operator attaches a cable to a 1130-kg shipping container and then uses the crane to lift the container vertically at a constant velocity for a distance of 30 m. Determine
the amount of work done by each of the following. (a) the tension in the cabl...
what would happen to the impedance of a series circuit containing an inductor, capacitor and resistor if the supply frequency is varied from 0 to infinity Hz
D- Transverse
A mixture of NaCN and NaHSO4 consists of a total of 0.60 mol. When the mixture is dissolved in 1.0 L of water and comes to equilibrium the pH is found to be 9.7.
A rocket is launched into the sky on a windy day. The rocket has a vertical velocity of 15 m/s. There is a strong wind blowing east to west at 35 m/s. How far from the start point is the rocket after
60 seconds?
f(x)=6x^3+19x^2+8x-5 find all the zeros of the given function
For the reaction given, the value of the equilibrium of the constant at 400 K is 7.0. Br2(g)+ Cl2(g)=2BrCl(g) Does the: Reaction proceed to the left? Reaction proceed to the right? Partial pressure
represent a system in an equation?
Let lim f(x) =16 as x->4 and lim g(x) =8 as x->4 Use the limit rules to find lim [cos(pi*f(x)/g(x))] as x->4
Salmonella bacteria grows rapidly in a nice warm place. If just a few hundred were left on a cutting board when a chicken was cut up, and they get into the potato salad, the population begins
compounding. Suppose the number present in the potato salad after x hours is given by...
Congress represents the larger public interest by (Points : 1)
A car travels 3.0km due west and then 2.0km to the north. Find the magnitude and direction of the car s resultant displacement?
Two boys want to pull a car. One of them exerts a force of 200 N toward West. The other a force of 150 N toward south. What is the net force exerted on the car? (Assume friction to be negligible.)
if a 5-foot tall bush casts a 2-foot shadow how tall is a tree standing next to the bush that casts an 8-foot shadow at the same time?
How many CO2 molecules are formed when 10 methanol molecules react?
8.01xers Can anybody help with the falling ruler. I submission left(
A ruler stands vertically against a wall. It is given a tiny impulse at θ=0∘ such that it starts falling down under the influence of gravity. You can consider that the initial angular velocity is
very small so that ω(θ=0∘)=0. The ruler has mass m= 10...
physics I'M STUCK PZL HELP
A ruler stands vertically against a wall. It is given a tiny impulse at θ=0∘ such that it starts falling down under the influence of gravity. You can consider that the initial angular velocity is
very small so that ω(θ=0∘)=0. The ruler has mass m= 10...
physics Classical Mechanics
Consider a rocket in space that ejects burned fuel at a speed of vex= 1.5 km/s with respect to the rocket. The rocket burns 8 % of its mass in 280 s (assume the burn rate is constant). (a) What is
the speed v of the rocket after a burn time of 140.0 s? (suppose that the rocket...
physics Classical Mechanics
Hi, guys! What's about doppler shift? Can u tell me formulas?
Anonymous can u explain c onemore time?
Physics Classical Mechanics
@kumar can you explain a)
What is the lattice energy of NaI? Use the given information below. Heat of formation for NaI = -288.0 kJ/mol Heat of sublimation for Na = 107.3 kJ/mol Ionization energy for Na = 496.0 kJ/mol Bond
dissociation energy for I2 = 149 kJ/mol Electron affinity of I = -295.0 kJ/mol H...
Heisenberg's uncertainty principle can be expressed mathematically as Δx*Δp = h/4π, where Δx and Δp denote the uncertainty in position and momentum respectively and h is Planck's constant. What would
be the uncertaintry in the position of a ne...
What is the mass of a fly in grams if its de Broglie wavelength is 1.545e-31 m when it is traveling at a velocity of 3.605 m/s
Hydrogen exhibits several series of line spectra in different spectral regions. For example the Lyman series (nf = 1 in Balmer-Rydberg equation) occurs in the ultraviolet region while the Balmer (nf
= 2) series occurs in the visible range and the Paschen (nf = 3), Brackett (n...
Hydrogen exhibits several series of line spectra in different spectral regions. For example the Lyman series (nf = 1 in Balmer-Rydberg equation) occurs in the ultraviolet region while the Balmer (nf
= 2) series occurs in the visible range and the Paschen (nf = 3), Brackett (n...
elbow raises a 1200 N piano a distance of 5 meters using a set of pulleys. elbow pulls in 20.0 meter of rope while exerting a force of 340 N. a) what is the work output? b) what is work input c) what
is the mechanical advantage of this machine? d) what is the efficiency of thi...
mass of passenger is 90 kg and mass of scale is 40 kg what is scale reading inside an elevator moving at 7.8 m/s2 upward? does the mass of the scale affect the scale reading ?
prove the statement Angle ABD is a right angle and Angle CBE is a Right Angle and prove Angle ABC is Congruent to Angle DBE
The energy (in joules) of an electron energy level in the Bohr atom is given by the expression: En = -2.179 x 10-18/n2 J where n is the principal quantum number for the energy level. What is the
frequency in Hz of the electromagnetic radiation absorbed when an electron is rais...
What volume of a liquid having a density of 4.55 g/cm3 is needed to supply 10.47 grams of that liquid? Answer in cm3.
thank you :)
Don't know how to recognize it but i know what it means. It is something that is ironic or sarcastic. Right?
really need help on this question it is worth 5 marks. The question is: Explain how "A Thankless Experience" is a satire with support with direct reference to the essay. The short essay is called A
Thankless Experience by Stephen Lautens' it is on the internet j...
A Thankless Experience
I did study these but can't seem to start on a sentence. I dont know what sentences from the essay are satire. If i could get started on one i might be able to understand.
A Thankless Experience
I really need help on this question it is worth 5 marks. The question is: Explain how "A Thankless Experience" is a satire with support with direct reference to the essay. The short essay is called A
Thankless Experience by Stephen Lautens' Thank you :)
Story: A Thankless Experience Author: Stephen Lautens Question: Describe the diction that Lautens uses in "A Thankless Experience"? Describe Lautens tone in "A Thankless Experience"? Help will be
appreciated :)
english A Thankless Experience Questions
Abstract words present qualities or ideas that cannot be felt by the senses. They are often general words, as opposed to concrete words which express something more tangible. Truth, honor and
happiness are all abstract words, while aroma, stone and fire are concrete words. Exp...
Thank you please help me on my other posts please and thank you help will be appreciated
I could not please help pleaseeee :)
books "A Thankless Experience" Short Essay Help
This is the story: A Thankless Experience by Stephen Lautens. The story is on the internet. jiskha does not allow me to post the url The question is: Provide two examples of figurative language used
by Lautens in his essay and describe the effect of each example. Please help a...
books (A thankless experience)
Thank you Ms. Sue
books (A thankless experience)
Explain whether Lautens' essay is written formally or informally, referring to examples from the essay for support. The short essay is on the internet called A thankless experience by Stephen
Lautens. I can not post the url because jiskha does not allow it.
books(short essay)
Yes this is the short essay. Thanks so much
books(short essay)
Describe the sentence structure Stephen Lautens uses in "A Thankless Experience". Support your view with examples from the essay. This is the story: A Thankless experience by Stephen Lautens this
story is on the internet I was about to post the url but jiskha does no...
Thank you
It's from the Journey's text book.
Double Dutch 5th grade reading.
What was the order in which all the girls learned double dutch?
A sheet of aluminum (Al) foil has a total area of 2.119 ft2 and a mass of 2.714 g. What is the thickness of the foil in millimeters? (Density of Al = 2.699 g/cm3? I got 5.108*10^-4 cm but that is
wrong. (2.714g)/(2.699g/cm^3)/(2.119ft^2) * 1ft/30.48cm = 5.108*10^-4 cm
Thanks for your help.
How would I show my work for this answers?
how do you write 3.08 as a fraction?
Suppose the price of widgets rises from $7 to $9 and consumption of widgets falls from 25 widgets a month to 15 widgets. Calculate your price elasticity of demand of widgets. What can you say about
your price elasticity of demand of widgets? Is it Elastic, Inelastic, or Unitar...
How do you know if a steam and leaf display is uniform, unimodal or bimodal?
One advantage of a _____________ is that the actual data values are retained in the graphical display of the data. A) Pie chart B) Dot plot (This one?) C) Histogram D) boxplot If we want to discuss
any gaps and clusters in a data set, which of the following should not be chose...
The length of one side of an isosceles triangle is two times the base b. This length is equal to (8b - 12),in. What is the value of b?
A two-player game is played with two piles of stones, with sizes m,n. On a player's turn, that player can remove any positive integer number of stones from one pile, or the same positive integer
number of stones from each pile. A player loses when they are unable to take a...
Math (Combinatorics)
How many ways to rearrange 9 a's, 2 b's, and 2c's so that we never see bc and both b's always appear before both c's?
calculus (please help steve)
Evaluate ∬(x^2+y^2)^2/(x^2y^2) dx dy over the region common to the circles x^2+y^2=7x and x^2+y^2=11y.
calculus (please help steve)
ok, thanks!
calculus (please help steve)
But we are taking a double integral. This would be finding a volume.
calculus (please help steve)
Evaluate ∬(x^2+y^2)^2/(x^2y^2) dx dy over the region common to the circles x^2+y^2=7x and x^2+y^2=11y.
Evaluate ∬(x^2+y^2)^2/(x^2y^2) dx dy over the region common to the circles x^2+y^2=7x and x^2+y^2=11y.
wolfram alpha says (s^2+8)/(s^3+16s)
valuate ∬(x^2+y^2)^2/(x^2y^2) dx dy over the region common to the circles x^2+y62=7x and x^2+y^2=11y
Evaluate ∬R 1/sqrt(x^2+y^2) dx dy, where R is the region bounded by y≥0 and x^2−x+y^2≤0.
ok, thanks
could you give me a bit help on how to proceed if I were to use a volume integral?
Let V be the volume of the region bounded by x^2+y^2≥z^2, z≥0 and x^2+y^2+z^2≤1. What is the value of ⌊100V⌋?
What is the wind speed in m/s required to keep a great white shark suspended in midair during a summer day on the California beach? Details and assumptions Model the shark as a horizontal cylinder 6
m long and 1 m in diameter. The air is at a pressure of 1 atm and a temperatur...
Data Structures and Algorithms
Let S be the set of {(1,1), (1,−1), (−1,1), (1,0), (0,1)}-lattice paths which begin at (1,1), do not use the same vertex twice, and never touch either the x-axis or the y-axis. Let Sx,y be the set of
paths in S which end at (x,y).For how many ordered pairs (x,y) su...
A token is placed on the leftmost square in a strip of four squares. You are allowed to move the token left or right along the strip by sliding it a single square, provided that the token stays on
the strip. How many ways can the token be moved such that after 15 moves, it is ...
integral (1+cos 2T) dT = T + sinTcosT so (2/Pi)v integral (1+cos 2T) dT from 0 to pi/2 = 1 ?
so we would solve to get 66.51?
so how would we apply this 3v/2 into your original equation rho * 2 r L v^2 = 1000(9.8)(pi r^2)(L) ?
how did you get the volume of air that hits the shark per second?
physics (fluids)
If a object of radius 3 cm is attached to the ground in a 3 m deep sea, what is the vertical force in N with which the water (density = 1000 kg/m^3) presses on it?
calculus (hint?)
f(x) is a twice differentiable function such that f(2x)=f(x+5)+(x−5)^2 What is f''(x)?
If f(x)=∫ (from -x to x) cos(t)/(1+e^t) dt and x=asin(77/85), then the absolute value of f′(x)−f(x) can be expressed as a/b, where a and b are coprime positive integers. What is the value of a+b?
I would still like help as to how I would proceed. That is why I still ask for the answer.
However, I am still confused as to how I would proceed.
so what is the answer to the question?
If f(x)=∫ (from -x to x) cos(t)/(1+e^t) dt and x=asin(77/85), then the absolute value of f′(x)−f(x) can be expressed as a/b, where a and b are coprime positive integers. What is the value of a, and
what is the value of b?
f(x) and f′(x) are continuous, differentiable functions that satisfy f(x)=x^3+4x^2+∫ (from 0 to x)(x−t)f′(t) dt. What is f′(5)−f(5)?
calculus (point me in the right direction please?)
but how would you get f(5)?
calculus (point me in the right direction please?)
f(x) and f′(x) are continuous, differentiable functions that satisfy f(x)=x^3+4x^2+∫(from 0 to x)(x−t)f′(t) dt. What is f′(5)−f(5)?
calculus (point me in the right direction please?)
thank you steve!
calculus (point me in the right direction please?)
Let V be the volume of the three-dimensional structure bounded by the region 0≤z≤1−x^2−y^2. If V=a/bπ, where a and b are positive coprime integers, what is a+b?
114 mm Hg = 15198.75 pascals 16.0 cm^2 = 0.0016 m^2 P=F/A 15198.75=F/0.0016 F=24.318 newtons
he volume of the solid obtained by rotating the region bounded by x=(y−2)^2 and y=x about the x-axis has the form N/2π. What is the value of N?
oops! Thanks for the help
alright, so i got that f'(x)=4x^3-76x^2+4ax =4x(x^2-19x+4a) since this must never equal 0, it must have no solutions. Therefore, x must not be 0 and x^2-19x+4a must not be 0. For that to occur,
289-16a<0, so a > 18.0625. Can you please check me work? Sorry for bother...
How many positive integers a (<1000) are there such that the function f(x)=x^4−76/3x^3+2ax^2 has no local maxima?
Are you just going to assume that any problem I ask for help on is from "Brilliant"?
How do you know anyways?
Pages: 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Next>> | {"url":"http://www.jiskha.com/members/profile/posts.cgi?name=andy","timestamp":"2014-04-18T17:16:53Z","content_type":null,"content_length":"27679","record_id":"<urn:uuid:9ad26e98-5527-4964-bdd1-c4a185b59db3>","cc-path":"CC-MAIN-2014-15/segments/1397609533957.14/warc/CC-MAIN-20140416005213-00159-ip-10-147-4-33.ec2.internal.warc.gz"} |
Re: LALR parsing
Torben AEgidius Mogensen <torbenm@diku.dk>
Mon, 07 Dec 2009 11:43:20 +0100
From comp.compilers
Related articles
LALR parsing alinsoar@voila.fr (A. Soare) (2009-12-04)
Re: LALR parsing torbenm@diku.dk (Torben AEgidius Mogensen) (2009-12-07)
Re: LALR parsing alinsoar@voila.fr (A. Soare) (2009-12-09)
Re: LALR parsing Danny.Dube@ift.ulaval.ca (2009-12-09)
Re: LALR parsing torbenm@diku.dk (2009-12-10)
Re: LALR parsing rsc@swtch.com (Russ Cox) (2009-12-11)
Re: LALR parsing torbenm@diku.dk (2009-12-14)
Re: LALR parsing ott@mirix.org (Matthias-Christian ott) (2009-12-14)
[1 later articles]
| List of all articles for this month |
From: Torben AEgidius Mogensen <torbenm@diku.dk>
Newsgroups: comp.compilers
Date: Mon, 07 Dec 2009 11:43:20 +0100
Organization: Department of Computer Science, University of Copenhagen
References: 09-12-007
Keywords: LALR
Posted-Date: 08 Dec 2009 21:36:09 EST
"A. Soare" <alinsoar@voila.fr> writes:
> I want to implement a LALR parser for an arbitrary grammar (many
> common point to yacc, however different).
> However, I did read that these methods are not the most fast. The
> fastest methods use matrix multiplications, etc. In the book of Grune
> is it explained something about the equalence between parsing and
> matrix multiplication, but I see nothing useful apart of some vagues
> ideas.
> My question for you is: what are the most efficient methods of lalr parsing?
LALR(1) defined a class of grammars that can be parsed with a
deterministic LALR(1) parser. These can be parsed in something
approaching linear time. But LALR(1) can not deterministically parse
arbitrary grammars. You can add backtracking to allow parsing of
arbitrary grammars, but that can in the worst case give exponential
runtimes. GLR parsers (see http://en.wikipedia.org/wiki/GLR_parser)
handle the multiple parses in a breath-first manner instead of a
depth-first backtracking, so they can merge identical states. This
reduces the worst case to O(n^3).
While the matrix-multiplication methods you refer to have better
worst-case performance, GLR will outperform them in most cases. Matrix
multiplication can be done in O(n^2.376), but the algorithm for this has
a huge constant factor overhead that makes the traditional O(n^3) method
faster except for extremely large matrices. So I doubt the O(n^2.376)
algorithm is of any practical use for parsing.
Note, however, that while it has been proven that the complexity of
parsing is bounded by the complexity of matrix multiplication, the
converse is not true: There may well be general parsers that are faster
than matrix multiplication. IIRC, the lower bound for CF parsing is
still O(n).
Post a followup to this message
Return to the comp.compilers page.
Search the comp.compilers archives again. | {"url":"http://compilers.iecc.com/comparch/article/09-12-009","timestamp":"2014-04-18T13:14:19Z","content_type":null,"content_length":"6731","record_id":"<urn:uuid:947a1b1e-3117-43d3-a6d1-e28118dc07db>","cc-path":"CC-MAIN-2014-15/segments/1397609533689.29/warc/CC-MAIN-20140416005213-00259-ip-10-147-4-33.ec2.internal.warc.gz"} |
Mathematical SciencesDefining metabolically healthy obesity: role of dietary and lifestyle factorsAn investigation of post-primary students' images of mathematicsDifferential and numerical models of hysteretic systems with stochastic and deterministic inputsFinancial modelling with 2-EPT probability density functions
http://hdl.handle.net/10468/88 2014-04-18T10:57:11Z http://hdl.handle.net/10468/1474 Defining metabolically healthy obesity: role of dietary and lifestyle factors Phillips, Catherine M.; Dillon,
Christina; Harrington, Janas M.; McCarthy, Vera J. C.; Kearney, Patricia M.; Fitzgerald, Anthony P.; Perry, Ivan J. Background: There is a current lack of consensus on defining metabolically healthy
obesity (MHO). Limited data on dietary and lifestyle factors and MHO exist. The aim of this study is to compare the prevalence, dietary factors and lifestyle behaviours of metabolically healthy and
unhealthy obese and non-obese subjects according to different metabolic health criteria. Method: Cross-sectional sample of 1,008 men and 1,039 women aged 45-74 years participated in the study.
Participants were classified as obese (BMI ≥30kg/m2) and non-obese (BMI <30kg/m2). Metabolic health status was defined using five existing MH definitions based on a range of cardiometabolic
abnormalities. Dietary composition and quality, food pyramid servings, physical activity, alcohol and smoking behaviours were examined. Results: The prevalence of MHO varied considerably between
definitions (2.2% to 11.9%), was higher among females and generally increased with age. Agreement between MHO classifications was poor. Among the obese, prevalence of MH was 6.8% to 36.6%. Among the
non-obese, prevalence of metabolically unhealthy subjects was 21.8% to 87%. Calorie intake, dietary macronutrient composition, physical activity, alcohol and smoking behaviours were similar between
the metabolically healthy and unhealthy regardless of BMI. Greater compliance with food pyramid recommendations and higher dietary quality were positively associated with metabolic health in obese
(OR 1.45-1.53 unadjusted model) and non-obese subjects (OR 1.37-1.39 unadjusted model), respectively. Physical activity was associated with MHO defined by insulin resistance (OR 1.87, 95% CI
1.19-2.92, p = 0.006). 2013-10-17T00:00:00Z http://hdl.handle.net/10468/1096 An investigation of post-primary students' images of mathematics Lane, Ciara Mary Frances This research study investigates
the image of mathematics held by 5th-year post-primary students in Ireland. For this study, “image of mathematics” is conceptualized as a mental representation or view of mathematics, presumably
constructed as a result of past experiences, mediated through school, parents, peers or society. It is also understood to include attitudes, beliefs, emotions, self-concept and motivation in relation
to mathematics. This study explores the image of mathematics held by a sample of 356 5th-year students studying ordinary level mathematics. Students were aged between 15 and 18 years. In addition,
this study examines the factors influencing students‟ images of mathematics and the possible reasons for students choosing not to study higher level mathematics for the Leaving Certificate. The
design for this study is chiefly explorative. A questionnaire survey was created containing both quantitative and qualitative methods to investigate the research interest. The quantitative aspect
incorporated eight pre-established scales to examine students‟ attitudes, beliefs, emotions, self-concept and motivation regarding mathematics. The qualitative element explored students‟ past
experiences of mathematics, their causal attributions for success or failure in mathematics and their influences in mathematics. The quantitative and qualitative data was analysed for all students
and also for students grouped by gender, prior achievement, type of post-primary school attending, co-educational status of the post-primary school and the attendance of a Project Maths pilot school.
Students‟ images of mathematics were seen to be strongly indicated by their attitudes (enjoyment and value), beliefs, motivation, self-concept and anxiety, with each of these elements strongly
correlated with each other, particularly self-concept and anxiety. Students‟ current images of mathematics were found to be influenced by their past experiences of mathematics, by their mathematics
teachers, parents and peers, and by their prior mathematical achievement. Gender differences occur for students in their images of mathematics, with males having more positive images of mathematics
than females and this is most noticeable with regards to anxiety about mathematics. Mathematics anxiety was identified as a possible reason for the low number of students continuing with higher level
mathematics for the Leaving Certificate. Some students also expressed low mathematical self-concept with regards to higher level mathematics specifically. Students with low prior achievement in
mathematics tended to believe that mathematics requires a natural ability which they do not possess. Rote-learning was found to be common among many students in the sample. The most positive image of
mathematics held by students was the “problem-solving image”, with resulting implications for the new Project Maths syllabus in post-primary education. Findings from this research study provide
important insights into the image of mathematics held by the sample of Irish post-primary students and make an innovative contribution to mathematics education research. In particular, findings
contribute to the current national interest in Ireland in post-primary mathematics education, highlighting issues regarding the low uptake of higher level mathematics for the Leaving Certificate and
also making a preliminary comparison between students who took part in the piloting of Project Maths and students who were more recently introduced to the new syllabus. This research study also holds
implications for mathematics teachers, parents and the mathematics education community in Ireland, with some suggestions made on improving students‟ images of mathematics. 2013-01-01T00:00:00Z http:/
/hdl.handle.net/10468/1138 Differential and numerical models of hysteretic systems with stochastic and deterministic inputs McCarthy, Stephen Patrick Many deterministic models with hysteresis have
been developed in the areas of economics, finance, terrestrial hydrology and biology. These models lack any stochastic element which can often have a strong effect in these areas. In this work
stochastically driven closed loop systems with hysteresis type memory are studied. This type of system is presented as a possible stochastic counterpart to deterministic models in the areas of
economics, finance, terrestrial hydrology and biology. Some price dynamics models are presented as a motivation for the development of this type of model. Numerical schemes for solving this class of
stochastic differential equation are developed in order to examine the prototype models presented. As a means of further testing the developed numerical schemes, numerical examination is made of the
behaviour near equilibrium of coupled ordinary differential equations where the time derivative of the Preisach operator is included in one of the equations. A model of two phenotype bacteria is also
presented. This model is examined to explore memory effects and related hysteresis effects in the area of biology. The memory effects found in this model are similar to that found in the non-ideal
relay. This non-ideal relay type behaviour is used to model a colony of bacteria with multiple switching thresholds. This model contains a Preisach type memory with a variable Preisach weight
function. Shown numerically for this multi-threshold model is a pattern formation for the distribution of the phenotypes among the available thresholds. 2013-01-01T00:00:00Z http://hdl.handle.net/
10468/1430 Financial modelling with 2-EPT probability density functions Sexton, Hugh Conor The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the
Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of
which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b;
c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to
be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with
rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically
independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace
Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a
prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation
problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained
approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy
processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely
monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for
calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling. 2013-01-01T00:00:00Z | {"url":"http://cora.ucc.ie/feed/rss_1.0/10468/88","timestamp":"2014-04-18T10:57:11Z","content_type":null,"content_length":"12140","record_id":"<urn:uuid:c3105efd-193c-4ac5-9257-fa8c4c9b9179>","cc-path":"CC-MAIN-2014-15/segments/1397609533308.11/warc/CC-MAIN-20140416005213-00362-ip-10-147-4-33.ec2.internal.warc.gz"} |
Butztown, PA Math Tutor
Find a Butztown, PA Math Tutor
...Every student can be successful --- we, as educators, need to find the right learning style/method(s) to allow the student to experience success. I live in the Easton/Bethlehem area and will
travel to your home --- preferably in the early evening and/or on the weekends. I raised my son, as a si...
24 Subjects: including algebra 1, prealgebra, ACT Math, geometry
...Contact me if you have any questions at all and I will be more than happy to answer them!I have a Bachelor of Science degree in Physics with a minor in mathematics. I spent one year as a
one-on-one tutor for introductory physics courses at Kutztown University and have one semester of experience ...
16 Subjects: including algebra 1, algebra 2, calculus, chemistry
...I have worked with students from all backgrounds; I have also worked extensively with children with disabilities. I hold a BA in Anthropology from Florida Atlantic University and am currently
a graduate student in the Anthropology Department. As a lifelong student and educator, excellent study skills are essential to my daily responsibilities.
55 Subjects: including linear algebra, probability, SAT math, ACT Math
...I have privately tutored many students when it comes to the techniques involved in developing proper tone, embouchure, fingerings, marching steps, keeping time, etc. It is something that just
comes naturally to me. Before I became a sociology major, I was a physics-math major---quite the change, I know.
18 Subjects: including geometry, algebra 2, Spanish, English
...I already have admitted as a PhD student and am ready to continue my education. I have experience as a teaching assistant for Engineering Mechanics-Static and Strength of Materials course
while at Texas A&M University. In addition to being a practicing engineer in the industry, I am an expert in most design concepts too.
13 Subjects: including calculus, SAT math, discrete math, differential equations
Related Butztown, PA Tutors
Butztown, PA Accounting Tutors
Butztown, PA ACT Tutors
Butztown, PA Algebra Tutors
Butztown, PA Algebra 2 Tutors
Butztown, PA Calculus Tutors
Butztown, PA Geometry Tutors
Butztown, PA Math Tutors
Butztown, PA Prealgebra Tutors
Butztown, PA Precalculus Tutors
Butztown, PA SAT Tutors
Butztown, PA SAT Math Tutors
Butztown, PA Science Tutors
Butztown, PA Statistics Tutors
Butztown, PA Trigonometry Tutors
Nearby Cities With Math Tutor
Clayton, PA Math Tutors
College Hill, PA Math Tutors
Emerald, PA Math Tutors
Freemansburg, PA Math Tutors
Hancock, PA Math Tutors
Harlem, PA Math Tutors
Ironton, PA Math Tutors
Klines Corner, PA Math Tutors
Lehigh Valley Math Tutors
Longswamp, PA Math Tutors
Lower Longswamp, PA Math Tutors
Lynn, PA Math Tutors
Shamrock Station, PA Math Tutors
Wescosville, PA Math Tutors
Willow Grove, NJ Math Tutors | {"url":"http://www.purplemath.com/Butztown_PA_Math_tutors.php","timestamp":"2014-04-19T17:23:21Z","content_type":null,"content_length":"24064","record_id":"<urn:uuid:32562fc0-e3a5-49a1-980c-ff0769941eac>","cc-path":"CC-MAIN-2014-15/segments/1398223207046.13/warc/CC-MAIN-20140423032007-00148-ip-10-147-4-33.ec2.internal.warc.gz"} |
River Rouge Trigonometry Tutor
Find a River Rouge Trigonometry Tutor
...Such topics have included high school chemistry, college general/organic chemistry, college biology, college calculus, college trigonometry, medical school biochemistry, and medical school
anatomy/physiology. I am very patient when it comes to working with individuals who are having difficulty w...
9 Subjects: including trigonometry, chemistry, algebra 1, biology
...My credentials are a Major in Mathematics and Secondary Education, a Masters in Education Leadership, and I am a certified teacher for the State of Michigan. I have over seven years of teaching
experience in both public and private schools (from 6th grade to High School). I took time off to stay...
9 Subjects: including trigonometry, geometry, algebra 1, algebra 2
...I have tutored small children, teenagers and adults in a variety of subjects for over (30) years, starting while I was in college (University of Michigan, Ann-Arbor). Elementary students
(k-6th) will learn foundational academic facts, principles, rules, and strategies for learning (and more) for ...
30 Subjects: including trigonometry, reading, chemistry, writing
...I have taught online mathematics classes as well. My focus is on building the confidence of my students. It is then they can grow and develop to reach their maximum academically.
22 Subjects: including trigonometry, chemistry, calculus, physics
...I have taught high school Mathematics and have had great indicators of success with working with students. Individual instruction will greatly improve your abilities in math and create the
aptitudes that you have to improve in math. School will be more rewarding and that is a goal for me to help you attain.
6 Subjects: including trigonometry, geometry, algebra 1, algebra 2 | {"url":"http://www.purplemath.com/river_rouge_trigonometry_tutors.php","timestamp":"2014-04-19T17:13:19Z","content_type":null,"content_length":"24215","record_id":"<urn:uuid:ce9d30d2-36c4-40cc-8f8a-b49c56f8622c>","cc-path":"CC-MAIN-2014-15/segments/1397609537308.32/warc/CC-MAIN-20140416005217-00195-ip-10-147-4-33.ec2.internal.warc.gz"} |
North Attleboro Prealgebra Tutor
...I am a certified teacher with Masters' degrees in Clinical Social Work and special education. I hold Professional level certification in Elementary Education (Pre-K to 6) and and Moderate
Special Needs (K-8). This is my 14th year working as a special educator in Massachusetts. I am a certified teacher with Masters' degrees in Clinical Social Work and special education.
23 Subjects: including prealgebra, reading, English, geometry
...My best experience teaching guitar was the first time I formally began; while I was in high school, our music teacher (Penny - still there at Brockton High) sent a group of teen guitar students
to begin a program for Brockton elementary schools, creating an afterschool program for them. At my sc...
17 Subjects: including prealgebra, reading, writing, geometry
...I have ample experience tutoring math, both as a graduate instructor of basic math courses, and as a high school tutor. I have tutored a dozen students in SAT math specifically. I do well on
standardized tests and scored perfect on the Verbal and Quantitative sections of the GRE in 2013.
29 Subjects: including prealgebra, reading, calculus, English
...I would welcome the opportunity to let you uncover the beauty of physics. I enjoy helping students begin their study of higher level math courses like algebra and geometry by allowing them to
develop strong number skills with integers and fractions. With my students, I try to develop an adheren...
11 Subjects: including prealgebra, physics, calculus, geometry
...I am in my 10th year of teaching high school math, and have also taught one semester of college algebra as an adjunct professor. I taught AP Statistics last year and believe that I am qualified
to teach discrete math. I have been a high school math teacher for 10 years and have a master's degree in math education.
15 Subjects: including prealgebra, calculus, geometry, statistics | {"url":"http://www.purplemath.com/North_Attleboro_Prealgebra_tutors.php","timestamp":"2014-04-19T02:22:23Z","content_type":null,"content_length":"24475","record_id":"<urn:uuid:c1d66eff-39c5-4051-9bed-06728e017f5f>","cc-path":"CC-MAIN-2014-15/segments/1397609535745.0/warc/CC-MAIN-20140416005215-00564-ip-10-147-4-33.ec2.internal.warc.gz"} |
Model Keeps Running Forever (fails to terminate)
First, thanks for providing such a useful software package!
Second, I am having some trouble getting my model to finish running, and since I have to manually stop the script, I don't get any helpful output that would help me debug. Please find attached my
A brief description of what I'm trying to do, since some of the code is tricky (since I need many workarounds to deal with my data and model). I am feeding OpenMx a meta-analyzed correlation matrix
(O), with each observed correlation being a correlation between psychological constructs at 2 time points. The objective function to be minimized is a least-squares approach. Matrix B contains 2
parameters I'm trying to estimate (a and e). I then want to take a and e, plug them into EFF, and use that to iteratively calculate the parameters of my gamma matrices. The parameters from these
gamma matrices are then plugged into my PSI matrix. Both B and PSI go into the objective function to be minimized here.
I'm unsure what is causing my script to malfunction, but I wonder if the following have to do with it:
1) The circularity of my calculations. Using B to calculate PSI, and having both B and PSI go into the optimizer.
2) When I did some troubleshooting, sometimes it seemed as if the XI matrices were not being treated as matrices (but instead as some other type of object or data frame).
3) During troubleshooting, I also sometimes saw the error: Attempted to set improper value (1,3) to (3,2) matrix. What does this mean?
Thank you very much!
Best regards, | {"url":"http://openmx.psyc.virginia.edu/print/1276","timestamp":"2014-04-18T23:24:50Z","content_type":null,"content_length":"9658","record_id":"<urn:uuid:0eba601f-fd9a-44a8-bc30-50e77b1c7c57>","cc-path":"CC-MAIN-2014-15/segments/1397609535535.6/warc/CC-MAIN-20140416005215-00595-ip-10-147-4-33.ec2.internal.warc.gz"} |
During The First Stage Of Its Launch, A Space Shuttle ... | Chegg.com
During the first stage of its launch, a space shuttle goes from rest to 4961 km/h while rising a vertical distance of 45.0 km . Assume constant acceleration and no variation in g over this distance.
What is the acceleration of the shuttle?
a =21.1 m/s^2
If a 55.0 kg astronaut is standing on a scale inside the shuttle during this launch,How hard will the scale push on the astronaut in part (B)?
If this astronaut did not realize that the shuttle had left the launch pad, what would she think were her weight and mass?
She would think the scale reading is her weight, 1700 173
She would think the scale reading is her weight, 539 55.0
She would think the scale reading is her weight, 0 | {"url":"http://www.chegg.com/homework-help/questions-and-answers/first-stage-launch-space-shuttle-goes-rest-4961-km-h-rising-vertical-distance-450-km--assu-q1325277","timestamp":"2014-04-25T04:23:54Z","content_type":null,"content_length":"26453","record_id":"<urn:uuid:4820cb61-0ab4-4430-a76e-9a0eb230bc2e>","cc-path":"CC-MAIN-2014-15/segments/1398223207985.17/warc/CC-MAIN-20140423032007-00534-ip-10-147-4-33.ec2.internal.warc.gz"} |
Since 2002 Perimeter Institute has been recording seminars, conference talks, and public outreach events using video cameras installed in our lecture theatres. Perimeter now has 7 formal presentation
spaces for its many scientific conferences, seminars, workshops and educational outreach activities, all with advanced audio-visual technical capabilities. Recordings of events in these areas are all
available On-Demand from this Video Library and on Perimeter Institute Recorded Seminar Archive (PIRSA). PIRSA is a permanent, free, searchable, and citable archive of recorded seminars from relevant
bodies in physics. This resource has been partially modelled after Cornell University's arXiv.org.
Many authors have proposed what are known as "phase-space" or "classical" representations of quantum mechanics. A unifying framework is given which illustrates the relationship among these various
theories. Examples relevant to quantum computing will be given.
The one-way measurement model is a model of quantum computation which is intriguing for its' potential as a means of implementing quantum computers, but also for theoretical purposes for the
different way in which it allows quantum operations to be described. Instead of a sequence of unitary gates on an array of ``wires'', operations are described in terms of emph{patterns}, consisting
of a graph of entanglement relations on a set of qubits, together with a collection of measurement angles for these qubits (except possibly for a subset which will support a final quantum state).
In this presentation I will briefly explain the cluster state model of quantum computing. Then will talk about a scheme that uses polarization and time-bin degrees of freedom of photons in optical
fibres for the optical realization of this model. We are currently working on the implementation of this scheme in our lab.
Quantum coin tossing is a cryptographic task in which two parties, Alice and Bob, wish to generate a shared random bit but do not necessarily trust each other. This task is completely impossible to
realize with classical asynchronous communication but becomes at least partially feasible when quantum communication is also available. The best quantum protocol known so far, due to Ambainis, uses
qutrits and is near optimal in the sense that either party can bias the outcome with at most a 75% probability of success.
The notion of weak-degradability of quantum channels is introduced by generalizing the degradability definition given by Devetak and Shor. Exploiting the unitary equivalence with beam-splitter/
amplifier channels we then prove that a large class of one-mode Bosonic Gaussian channels are either weakly degradable or anti-degradable. In the latter case this implies that their quantum capacity
Q is null.
The essential insight of quantum error correction was that quantum information can be protected by suitably encoding this quantum information across multiple independently erred quantum systems.
Recently it was realized that, since the most general method for encoding quantum information is to encode it into a subsystem, there exists a novel form of quantum error correction beyond the
traditional quantum error correcting subspace codes.
In quantum information, one can prove that a secure quantum cryptography channel based on photon key distribution requires reliable single photon sources. If not, a potential eavesdropper may be able
to get information using the extra photons. Current sources are based on either attenuated laser beams, which may produce randomly 2 or even more photons at a time following a poissonian statistics,
or either based on two level-systems providing single photon sources often requiring cooling or complex set-ups. | {"url":"https://perimeterinstitute.ca/video-library?title=&page=610","timestamp":"2014-04-18T01:37:31Z","content_type":null,"content_length":"69299","record_id":"<urn:uuid:1506fe92-ac14-4697-a66d-0d62c1904c4d>","cc-path":"CC-MAIN-2014-15/segments/1398223203841.5/warc/CC-MAIN-20140423032003-00519-ip-10-147-4-33.ec2.internal.warc.gz"} |
CFI Forums | The two envelopes problem
The two envelopes problem
kkwan Posted: 04 November 2012 10:04 PM [ Ignore ] [ # 1546 ]
Sr. Member This is impossible. One person’s gain is the others loss in this set up.
Total Posts: 1822 From the respective perspectives of both players, there is potential gain/loss.
Joined 2007-10-28
kkwan Posted: 04 November 2012 10:08 PM [ Ignore ] [ # 1547 ]
Sr. Member The formula does recommend switching a second time, if you get the chance.
Total Posts: 1822 So the problem is it does and it doesn’t.
Joined 2007-10-28 However, we know switching twice or any even number of times is equivalent to not switching at all. So, we switch once or any odd number of times.
kkwan Posted: 04 November 2012 10:43 PM [ Ignore ] [ # 1548 ]
Sr. Member What we can do is stick with a pair of numbers.
Total Posts: 1822 We don’t have to consider more than 1 pair of numbers.
Joined 2007-10-28 You have no reasonable objection to doing that.
If you do that, it is a simplification and/or an incomplete description of the TEP because for any finite value of X, either (X, 2X) or (X, 1/2X) are in the two envelopes.
For example, if we consider the pair (10, 20), it is also possible (5, 10) are in the two envelopes.
So, both (10, 20) and (5, 10) must be considered in a complete description of the TEP.
StephenLawrence Posted: 04 November 2012 11:05 PM [ Ignore ] [ # 1549 ]
Sr. Member This is impossible. One person’s gain is the others loss in this set up.
Total Posts: 5939 From the respective perspectives of both players, there is potential gain/loss.
Joined 2006-12-20 And they must cancel each other out.
StephenLawrence Posted: 04 November 2012 11:08 PM [ Ignore ] [ # 1550 ]
Sr. Member The formula does recommend switching a second time, if you get the chance.
Total Posts: 5939 So the problem is it does and it doesn’t.
Joined 2006-12-20 However, we know switching twice or any even number of times is equivalent to not switching at all. So, we switch once or any odd number of times.
Kkwan the contradiction is there you can’t remove it as you are trying to do.
The reason is we also know that on the second go if you are asked if you want to switch the formula says you should switch too.
The same formula is saying you should and you shouldn’t
StephenLawrence Posted: 04 November 2012 11:18 PM [ Ignore ] [ # 1551 ]
Sr. Member For example, if we consider the pair (10, 20), it is also possible (5, 10) are in the two envelopes.
Total Posts: 5939 So, both (10, 20) and (5, 10) must be considered in a complete description of the TEP.
Joined 2006-12-20 What we know is we either have $10 and $20 or $5 and $10, or another pair of numbers.
Because whatever two numbers we have makes no difference we can simply imagine any pair we like and work with that.
We don’t have to compare two different situations that we might be in at all.
I’m sure the only interesting bit is what goes wrong when we do the T.E.P that way and how should we work out what to do when we open our envelope.
GdB Posted: 04 November 2012 11:39 PM [ Ignore ] [ # 1552 ]
Sr. Member kkwan,
Total Posts: Choosing different descriptions for two unknown but fixed amounts is of no relevance for any calculation. But you do as if it makes a difference.
Your argument is flawed because it is based on the premise that the total amount has changed which is not so.
2007-08-31 <snip>
Hence, either 3X or 3/X are the total amounts in the two envelopes.
This is a contradiction kkwan: you use 3X when you choose the envelope with smallest amount first, and you use (3/2)X when you pick the envelope with the biggest amount first. For the
same X these are different amounts.
Again: show me where you use that the total amount does not change. You haven’t done that yet.
StephenLawrence Posted: 04 November 2012 11:42 PM [ Ignore ] [ # 1553 ]
Sr. Member kkwan,
Total Posts: Choosing different descriptions for two unknown but fixed amounts is of no relevance for any calculation. But you do as if it makes a difference.
Your argument is flawed because it is based on the premise that the total amount has changed which is not so.
2006-12-20 <snip>
Hence, either 3X or 3/X are the total amounts in the two envelopes.
This is a contradiction kkwan: you use 3X when you choose the envelope with smallest amount first, and you use (3/2)X when you pick the envelope with the biggest amount first. For
the same X these are different amounts.
Again: show me where you use that the total amount does not change. You haven’t done that yet.
Kkwan only needs to say that he is comparing two different situations that he might be in, which he has agreed to many times.
So the total amount does not change.
GdB Posted: 05 November 2012 12:02 AM [ Ignore ] [ # 1554 ]
Sr. Member We are in only one situation, not two.
Total Posts: 4375 I dealt with that here.
Joined 2007-08-31 In reality, of course the ‘two situations’ are just one, only with different descriptions.
StephenLawrence Posted: 05 November 2012 12:26 AM [ Ignore ] [ # 1555 ]
Sr. Member We are in only one situation, not two.
Total Posts: 5939 Which is banal.
Joined 2006-12-20 In reality, of course the ‘two situations’ are just one, only with different descriptions.
In reality Kkwan is comparing two different situations. $5 and $10, $10 and $20, for instance.
He insists there is a need to do that and we agree there is no need .
But he can do that and the amounts don’t change half way through when he does it because he’s comparing what would be the case if he were in the two different situations in the
first place.
GdB Posted: 05 November 2012 01:13 AM [ Ignore ] [ # 1556 ]
Sr. Member In reality Kkwan is comparing two different situations. $5 and $10, $10 and $20, for instance.
Total Posts: He insists there is a need to do that and we agree there is no need .
There is not ‘no need’, it is just wrong.
2007-08-31 Imagine we have two amounts, $5 and $10. (Total $15). Imagine I pick $10 first. Oh, but then I look at $10 and $20. (Total $30). Sorry, this is wrong as wrong can be. Depending on what
is picked first, the amounts change.
Correct is: if I have $5 and $10 and I pick $5 then the other amount is $10. And if I pick the $10, then the other is $5. That is the fact kwann wipes under the carpet.
But he can do that and the amounts don’t change half way through when he does it because he’s comparing what would be the case if he were in the two different situations in the
first place.
One must compare the situations separately, as I did here.
[ Edited: 05 November 2012 04:21 AM by GdB ]
StephenLawrence Posted: 05 November 2012 01:21 AM [ Ignore ] [ # 1557 ]
Sr. Member There is not ‘no need’, it is just wrong.
Total Posts: 5939 That won’t do as a solution to the problem.
Joined 2006-12-20 Stephen
GdB Posted: 05 November 2012 02:51 AM [ Ignore ] [ # 1558 ]
Sr. Member There is not ‘no need’, it is just wrong.
Total Posts: 4375 That won’t do as a solution to the problem.
Joined 2007-08-31 The explanation follows after the sentence you quote.
StephenLawrence Posted: 05 November 2012 06:15 AM [ Ignore ] [ # 1559 ]
Sr. Member There is not ‘no need’, it is just wrong.
Total Posts: 5939 That won’t do as a solution to the problem.
Joined 2006-12-20 The explanation follows after the sentence you quote.
No, the amounts don’t change depending upon what is picked because Kkwan is comparing two different situations that he might be in.
The question is what is wrong with doing that.
Post 1535 contains my thoughts and why I’m still puzzled. Have a go at answering it if you like.
GdB Posted: 05 November 2012 09:21 AM [ Ignore ] [ # 1560 ]
Sr. Member No, the amounts don’t change depending upon what is picked because Kkwan is comparing two different situations that he might be in.
Total Posts: 4375 The question is what is wrong with doing that.
Joined 2007-08-31 Post 1535 contains my thoughts and why I’m still puzzled. Have a go at answering it if you like.
That calculation was already don by Mingy Jongo, a long, long time ago.
kkwan Posted: 04 November 2012 10:04 PM [ Ignore ] [ # 1546 ]
Sr. Member This is impossible. One person’s gain is the others loss in this set up.
Total Posts: 1822 From the respective perspectives of both players, there is potential gain/loss.
Joined 2007-10-28
Posted: 04 November 2012 10:04 PM [ Ignore ] [ # 1546 ]
This is impossible. One person’s gain is the others loss in this set up.
From the respective perspectives of both players, there is potential gain/loss.
kkwan Posted: 04 November 2012 10:08 PM [ Ignore ] [ # 1547 ]
Sr. Member The formula does recommend switching a second time, if you get the chance.
Total Posts: 1822 So the problem is it does and it doesn’t.
Joined 2007-10-28 However, we know switching twice or any even number of times is equivalent to not switching at all. So, we switch once or any odd number of times.
Posted: 04 November 2012 10:08 PM [ Ignore ] [ # 1547 ]
The formula does recommend switching a second time, if you get the chance. So the problem is it does and it doesn’t.
The formula does recommend switching a second time, if you get the chance.
However, we know switching twice or any even number of times is equivalent to not switching at all. So, we switch once or any odd number of times.
kkwan Posted: 04 November 2012 10:43 PM [ Ignore ] [ # 1548 ]
Sr. Member What we can do is stick with a pair of numbers.
Total Posts: 1822 We don’t have to consider more than 1 pair of numbers.
Joined 2007-10-28 You have no reasonable objection to doing that.
If you do that, it is a simplification and/or an incomplete description of the TEP because for any finite value of X, either (X, 2X) or (X, 1/2X) are in the two envelopes.
For example, if we consider the pair (10, 20), it is also possible (5, 10) are in the two envelopes.
So, both (10, 20) and (5, 10) must be considered in a complete description of the TEP.
Posted: 04 November 2012 10:43 PM [ Ignore ] [ # 1548 ]
What we can do is stick with a pair of numbers. We don’t have to consider more than 1 pair of numbers. You have no reasonable objection to doing that.
What we can do is stick with a pair of numbers.
We don’t have to consider more than 1 pair of numbers.
If you do that, it is a simplification and/or an incomplete description of the TEP because for any finite value of X, either (X, 2X) or (X, 1/2X) are in the two envelopes.
For example, if we consider the pair (10, 20), it is also possible (5, 10) are in the two envelopes.
So, both (10, 20) and (5, 10) must be considered in a complete description of the TEP.
StephenLawrence Posted: 04 November 2012 11:05 PM [ Ignore ] [ # 1549 ]
Sr. Member This is impossible. One person’s gain is the others loss in this set up.
Total Posts: 5939 From the respective perspectives of both players, there is potential gain/loss.
Joined 2006-12-20 And they must cancel each other out.
Posted: 04 November 2012 11:05 PM [ Ignore ] [ # 1549 ]
This is impossible. One person’s gain is the others loss in this set up. From the respective perspectives of both players, there is potential gain/loss.
StephenLawrence Posted: 04 November 2012 11:08 PM [ Ignore ] [ # 1550 ]
Sr. Member The formula does recommend switching a second time, if you get the chance.
Total Posts: 5939 So the problem is it does and it doesn’t.
Joined 2006-12-20 However, we know switching twice or any even number of times is equivalent to not switching at all. So, we switch once or any odd number of times.
Kkwan the contradiction is there you can’t remove it as you are trying to do.
The reason is we also know that on the second go if you are asked if you want to switch the formula says you should switch too.
The same formula is saying you should and you shouldn’t
Posted: 04 November 2012 11:08 PM [ Ignore ] [ # 1550 ]
The formula does recommend switching a second time, if you get the chance. So the problem is it does and it doesn’t. However, we know switching twice or any even number of times is equivalent to not
switching at all. So, we switch once or any odd number of times.
Kkwan the contradiction is there you can’t remove it as you are trying to do.
The reason is we also know that on the second go if you are asked if you want to switch the formula says you should switch too.
The same formula is saying you should and you shouldn’t
StephenLawrence Posted: 04 November 2012 11:18 PM [ Ignore ] [ # 1551 ]
Sr. Member For example, if we consider the pair (10, 20), it is also possible (5, 10) are in the two envelopes.
Total Posts: 5939 So, both (10, 20) and (5, 10) must be considered in a complete description of the TEP.
Joined 2006-12-20 What we know is we either have $10 and $20 or $5 and $10, or another pair of numbers.
Because whatever two numbers we have makes no difference we can simply imagine any pair we like and work with that.
We don’t have to compare two different situations that we might be in at all.
I’m sure the only interesting bit is what goes wrong when we do the T.E.P that way and how should we work out what to do when we open our envelope.
Posted: 04 November 2012 11:18 PM [ Ignore ] [ # 1551 ]
For example, if we consider the pair (10, 20), it is also possible (5, 10) are in the two envelopes. So, both (10, 20) and (5, 10) must be considered in a complete description of the TEP.
What we know is we either have $10 and $20 or $5 and $10, or another pair of numbers.
Because whatever two numbers we have makes no difference we can simply imagine any pair we like and work with that.
We don’t have to compare two different situations that we might be in at all.
I’m sure the only interesting bit is what goes wrong when we do the T.E.P that way and how should we work out what to do when we open our envelope.
GdB Posted: 04 November 2012 11:39 PM [ Ignore ] [ # 1552 ]
Sr. Member kkwan,
Total Posts: Choosing different descriptions for two unknown but fixed amounts is of no relevance for any calculation. But you do as if it makes a difference.
Your argument is flawed because it is based on the premise that the total amount has changed which is not so.
2007-08-31 <snip>
Hence, either 3X or 3/X are the total amounts in the two envelopes.
This is a contradiction kkwan: you use 3X when you choose the envelope with smallest amount first, and you use (3/2)X when you pick the envelope with the biggest amount first. For the
same X these are different amounts.
Again: show me where you use that the total amount does not change. You haven’t done that yet.
Posted: 04 November 2012 11:39 PM [ Ignore ] [ # 1552 ]
Choosing different descriptions for two unknown but fixed amounts is of no relevance for any calculation. But you do as if it makes a difference.
Your argument is flawed because it is based on the premise that the total amount has changed which is not so. <snip> Hence, either 3X or 3/X are the total amounts in the two envelopes.
Your argument is flawed because it is based on the premise that the total amount has changed which is not so.
Hence, either 3X or 3/X are the total amounts in the two envelopes.
This is a contradiction kkwan: you use 3X when you choose the envelope with smallest amount first, and you use (3/2)X when you pick the envelope with the biggest amount first. For the same X these
are different amounts.
Again: show me where you use that the total amount does not change. You haven’t done that yet.
StephenLawrence Posted: 04 November 2012 11:42 PM [ Ignore ] [ # 1553 ]
Sr. Member kkwan,
Total Posts: Choosing different descriptions for two unknown but fixed amounts is of no relevance for any calculation. But you do as if it makes a difference.
Your argument is flawed because it is based on the premise that the total amount has changed which is not so.
2006-12-20 <snip>
Hence, either 3X or 3/X are the total amounts in the two envelopes.
This is a contradiction kkwan: you use 3X when you choose the envelope with smallest amount first, and you use (3/2)X when you pick the envelope with the biggest amount first. For
the same X these are different amounts.
Again: show me where you use that the total amount does not change. You haven’t done that yet.
Kkwan only needs to say that he is comparing two different situations that he might be in, which he has agreed to many times.
So the total amount does not change.
Posted: 04 November 2012 11:42 PM [ Ignore ] [ # 1553 ]
kkwan, Choosing different descriptions for two unknown but fixed amounts is of no relevance for any calculation. But you do as if it makes a difference. Your argument is flawed because it is based on
the premise that the total amount has changed which is not so. <snip> Hence, either 3X or 3/X are the total amounts in the two envelopes. This is a contradiction kkwan: you use 3X when you choose the
envelope with smallest amount first, and you use (3/2)X when you pick the envelope with the biggest amount first. For the same X these are different amounts. Again: show me where you use that the
total amount does not change. You haven’t done that yet.
Kkwan only needs to say that he is comparing two different situations that he might be in, which he has agreed to many times.
GdB Posted: 05 November 2012 12:02 AM [ Ignore ] [ # 1554 ]
Sr. Member We are in only one situation, not two.
Total Posts: 4375 I dealt with that here.
Joined 2007-08-31 In reality, of course the ‘two situations’ are just one, only with different descriptions.
Posted: 05 November 2012 12:02 AM [ Ignore ] [ # 1554 ]
In reality, of course the ‘two situations’ are just one, only with different descriptions.
StephenLawrence Posted: 05 November 2012 12:26 AM [ Ignore ] [ # 1555 ]
Sr. Member We are in only one situation, not two.
Total Posts: 5939 Which is banal.
Joined 2006-12-20 In reality, of course the ‘two situations’ are just one, only with different descriptions.
In reality Kkwan is comparing two different situations. $5 and $10, $10 and $20, for instance.
He insists there is a need to do that and we agree there is no need .
But he can do that and the amounts don’t change half way through when he does it because he’s comparing what would be the case if he were in the two different situations in the
first place.
Posted: 05 November 2012 12:26 AM [ Ignore ] [ # 1555 ]
In reality Kkwan is comparing two different situations. $5 and $10, $10 and $20, for instance.
He insists there is a need to do that and we agree there is no need .
But he can do that and the amounts don’t change half way through when he does it because he’s comparing what would be the case if he were in the two different situations in the first place.
GdB Posted: 05 November 2012 01:13 AM [ Ignore ] [ # 1556 ]
Sr. Member In reality Kkwan is comparing two different situations. $5 and $10, $10 and $20, for instance.
Total Posts: He insists there is a need to do that and we agree there is no need .
There is not ‘no need’, it is just wrong.
2007-08-31 Imagine we have two amounts, $5 and $10. (Total $15). Imagine I pick $10 first. Oh, but then I look at $10 and $20. (Total $30). Sorry, this is wrong as wrong can be. Depending on what
is picked first, the amounts change.
Correct is: if I have $5 and $10 and I pick $5 then the other amount is $10. And if I pick the $10, then the other is $5. That is the fact kwann wipes under the carpet.
But he can do that and the amounts don’t change half way through when he does it because he’s comparing what would be the case if he were in the two different situations in the
first place.
One must compare the situations separately, as I did here.
[ Edited: 05 November 2012 04:21 AM by GdB ]
Posted: 05 November 2012 01:13 AM [ Ignore ] [ # 1556 ]
In reality Kkwan is comparing two different situations. $5 and $10, $10 and $20, for instance. He insists there is a need to do that and we agree there is no need .
Imagine we have two amounts, $5 and $10. (Total $15). Imagine I pick $10 first. Oh, but then I look at $10 and $20. (Total $30). Sorry, this is wrong as wrong can be. Depending on what is picked
first, the amounts change.
Correct is: if I have $5 and $10 and I pick $5 then the other amount is $10. And if I pick the $10, then the other is $5. That is the fact kwann wipes under the carpet.
One must compare the situations separately, as I did here.
StephenLawrence Posted: 05 November 2012 01:21 AM [ Ignore ] [ # 1557 ]
Sr. Member There is not ‘no need’, it is just wrong.
Total Posts: 5939 That won’t do as a solution to the problem.
Joined 2006-12-20 Stephen
Posted: 05 November 2012 01:21 AM [ Ignore ] [ # 1557 ]
GdB Posted: 05 November 2012 02:51 AM [ Ignore ] [ # 1558 ]
Sr. Member There is not ‘no need’, it is just wrong.
Total Posts: 4375 That won’t do as a solution to the problem.
Joined 2007-08-31 The explanation follows after the sentence you quote.
Posted: 05 November 2012 02:51 AM [ Ignore ] [ # 1558 ]
There is not ‘no need’, it is just wrong. That won’t do as a solution to the problem.
StephenLawrence Posted: 05 November 2012 06:15 AM [ Ignore ] [ # 1559 ]
Sr. Member There is not ‘no need’, it is just wrong.
Total Posts: 5939 That won’t do as a solution to the problem.
Joined 2006-12-20 The explanation follows after the sentence you quote.
No, the amounts don’t change depending upon what is picked because Kkwan is comparing two different situations that he might be in.
The question is what is wrong with doing that.
Post 1535 contains my thoughts and why I’m still puzzled. Have a go at answering it if you like.
Posted: 05 November 2012 06:15 AM [ Ignore ] [ # 1559 ]
There is not ‘no need’, it is just wrong. That won’t do as a solution to the problem. The explanation follows after the sentence you quote.
No, the amounts don’t change depending upon what is picked because Kkwan is comparing two different situations that he might be in.
Post 1535 contains my thoughts and why I’m still puzzled. Have a go at answering it if you like.
GdB Posted: 05 November 2012 09:21 AM [ Ignore ] [ # 1560 ]
Sr. Member No, the amounts don’t change depending upon what is picked because Kkwan is comparing two different situations that he might be in.
Total Posts: 4375 The question is what is wrong with doing that.
Joined 2007-08-31 Post 1535 contains my thoughts and why I’m still puzzled. Have a go at answering it if you like.
That calculation was already don by Mingy Jongo, a long, long time ago.
Posted: 05 November 2012 09:21 AM [ Ignore ] [ # 1560 ]
No, the amounts don’t change depending upon what is picked because Kkwan is comparing two different situations that he might be in. The question is what is wrong with doing that. Post 1535 contains
my thoughts and why I’m still puzzled. Have a go at answering it if you like.
That calculation was already don by Mingy Jongo, a long, long time ago. | {"url":"http://www.centerforinquiry.net/forums/viewthread/12459/P1545/","timestamp":"2014-04-18T03:02:17Z","content_type":null,"content_length":"95610","record_id":"<urn:uuid:80b8436f-9a15-47ad-9497-cb1b2168235c>","cc-path":"CC-MAIN-2014-15/segments/1398223211700.16/warc/CC-MAIN-20140423032011-00322-ip-10-147-4-33.ec2.internal.warc.gz"} |
The Harmonic Oscillator
Next: The Rigid Rotor Up: Some Analytically Soluble Problems Previous: The Particle in a Contents
The Harmonic Oscillator
Now consider a particle subject to a restoring force
If we choose the energy scale such that
After some effort, the eigenfunctions are
The eigenvalues are
Next: The Rigid Rotor Up: Some Analytically Soluble Problems Previous: The Particle in a Contents David Sherrill 2006-08-15 | {"url":"http://vergil.chemistry.gatech.edu/notes/quantrev/node23.html","timestamp":"2014-04-19T07:28:38Z","content_type":null,"content_length":"8213","record_id":"<urn:uuid:7c9d5682-c903-4d01-8c37-b2993ac78135>","cc-path":"CC-MAIN-2014-15/segments/1397609536300.49/warc/CC-MAIN-20140416005216-00052-ip-10-147-4-33.ec2.internal.warc.gz"} |
When analyzing a questionnaire, one often wants to view the correlation between two or more Likert questionnaire item’s (for example: two ordered categorical vectors ranging from 1 to 5). When
dealing with several such Likert variable’s, a clear presentation of all the pairwise relation’s between our variable can be achieved by inspecting the (Spearman) correlation matrix (easily achieved
in R...
Siegel-Tukey: a Non-parametric test for equality in variability (R code)
Daniel Malter just shared on the R mailing list (link to the thread) his code for performing the Siegel-Tukey (Nonparametric) test for equality in variability. Excited about the find, I contacted
Daniel asking if I could republish his code here, and he kindly replied “yes”. From here on I copy his note at full. p.s: (The R function can be downloaded from...
Barnard’s exact test – a powerful alternative for Fisher’s exact test (implemented in R)
(The R code for Barnard’s exact test is at the end of the article, and you could also just download it from here)About Barnard’s exact test About half a year ago, I was studying various statistical
methods to employ on contingency tables. I came across a promising method for 2×2 contingency tables called “Barnard’s exact test“. Barnard’s test is a non-parametric alternative to Fisher’s exact...
Non-parametric Methods
A statistical method is called non-parametric if it makes no assumption on the population distribution or sample size.This is in contrast with most parametric methods in elementary statistics that
assume the data is quantitative, the population... | {"url":"http://www.r-bloggers.com/tag/non-parametric/","timestamp":"2014-04-20T03:24:07Z","content_type":null,"content_length":"30122","record_id":"<urn:uuid:a589c16c-99f2-4f2a-ac43-dcf0838ca181>","cc-path":"CC-MAIN-2014-15/segments/1397609537864.21/warc/CC-MAIN-20140416005217-00394-ip-10-147-4-33.ec2.internal.warc.gz"} |
A 1 Kg Mass And A 5 Kg Mass Are Connected By A ... | Chegg.com
A 1 kg mass and a 5 kg mass are connected by a 25 cm bar. Thesystem is then rotated horizontally at 300 rpm about an axis 10 cmfrom the 5 kg mass. What is the moment of inertia about this axis?What
is the rotational kinetic energy? | {"url":"http://www.chegg.com/homework-help/questions-and-answers/1-kg-mass-5-kg-mass-connected-25-cm-bar-thesystem-rotated-horizontally-300-rpm-axis-10-cmf-q413006","timestamp":"2014-04-19T18:04:28Z","content_type":null,"content_length":"19624","record_id":"<urn:uuid:9299c00d-ebd3-4433-a610-67234dc3bc60>","cc-path":"CC-MAIN-2014-15/segments/1397609537308.32/warc/CC-MAIN-20140416005217-00075-ip-10-147-4-33.ec2.internal.warc.gz"} |
Trees in groups of exponential growth
up vote 22 down vote favorite
Question: Let $G$ be a finitely generated group with exponential growth. Is there a finite generating set $S \subset G$, such that the associated Cayley graph $Cay(G,S)$ contains a binary tree?
Some background:
1. The existence of such a tree clearly implies exponential growth.
2. Kevin Whyte showed in Amenability, Bilipschitz Equivalence, and the Von Neumann Conjecture, Duke Journal of Mathematics 1999, p. 93-112, that such trees exist if $G$ is non-amenable. So the
question is only open for amenable groups of exponential growth.
3. One good reason for such a binary tree to exist is the existence of a free semigroup inside $G$. In fact, if $G$ is solvable, then the existence of such a semigroup is known to be equivalent to
exponential growth (and equivalent to being not virtually nilpotent). This is part of some version or extension of the Tits alternative. Grigorchuk constructed an amenable torsion group with
exponential growth, which does not contain such a semigroup, but it contains a binary tree.
EDIT: Al Tal pointed out in an answer below that Benjamini and Schramm covered the non-amenable case (this is 2. from above) already in Benjamini and Schramm "Every Graph With A Positive Cheeger
Constant Contains A Tree With A Positive Cheeger Constant", GAFA, 1997.
gr.group-theory open-problem geometric-group-theory
Do you mean contains a tree isometrically? If only up to biLipschitz equivalence, it looks to me like the answer does not depend on the generating set. – Bill Johnson Mar 29 '11 at 19:26
If you can do it in a bi-Lipschitz way, then you can embed it as a graph with a larger generating set. In general, to find an isometric copy is a harder question, but of course related. For the
moment, I am only interested in the question that I asked, i.e. contains means containment in the sense of subgraphs. – Andreas Thom Mar 29 '11 at 19:43
add comment
4 Answers
active oldest votes
Look at Russell Lyons, Random walks and the growth of groups, C. R. Acad. Sci. Paris 320 (1995), 1361--1366 (you can find it on Lyons' Web page). Consider any generating set and for every
vertex take the shortlex smallest path connecting the vertex and 1. Then take the union of all these paths. What you get is a (spanning) subtree which has exponential growth. I think that in
up vote the paper, Lyons proves that this tree contains a binary subtree if the growth function is exponential. The reason for this is that the degree of growth can be expressed in terms of the
8 down so-called "cuts". And if the spanning tree has too many vertices of degree 2, there would be too many cuts consisting of one vertex, and the growth rate would be 0. Of course this tree is not
vote a full subgraph, just a subgraph, but the question asks for a subgraph only.
Thanks, I will check. In fact, I am in Bloomington right now. – Andreas Thom Mar 30 '11 at 1:45
So far, this is not a complete answer. Lyons showed that the branching number of this tree equals the growth rate. Also, the spanning tree is subperiodic, which makes it somewhat
understandable. But it is not clear whether it contains a copy or Lipschitz copy of a binary tree. If someone has other ideas, I would be happy to hear them. – Andreas Thom Mar 30 '11 at
Yes, the answer only shows a possible direction. What needs to be proved (disproved) is whether a tree of exponential growth contains a Lipschitz copy of the binary tree. Lyons has several
papers about various probabilistic properties of trees: percolation, random walks, etc. So you should ask him. If he does not know the answer, I do not think anybody else would know. –
Mark Sapir Mar 30 '11 at 19:26
I think it is easy to construct examples of trees of exponential growth with no such copy. However, I do not not about subperiodic examples with positive branching number. Thanks a lot for
pointing our Lyons' work. – Andreas Thom Mar 30 '11 at 19:31
3 Russell Lyons explained to me an example of a subperiodic tree with branching number bigger than 1, which (for any stretching constant) does not contain stretched copies of finite binary
tree of arbitrary size. In particular, a positive answer to my question is not an easy consequence of his results. – Andreas Thom Mar 30 '11 at 23:49
add comment
Some time ago I was interested in the same question, but for the strengthened, bi-Lipschitz case (mentioned above by Bill Johnson). For non-amenable groups it is true; Victor Guba told me
how prove this, using Gromov's criteria of non-amenability. Also I was told that this result was obtained in a work of Benjamini and Shramm (I don't know the paper).
For amenable groups of exponential growth the answer is unknown to me, but I am very interested in it.
up vote 7
down vote It is also interesting if the same hold for the following little more general case. Graph $\Gamma$ is non necessarily a Cayley graph, but a vertex-transitive graph that has exponential
growth of balls cardinality (we consider balls centered in some fixed point).
This was proved by Kevin Whyte for non-amenable groups. – Andreas Thom Apr 3 '11 at 14:44
4 I've made a small search and found the paper by Benjamini and Schramm "Every Graph With A Positive Cheeger Constant Contains A Tree With A Positive Cheeger Constant", GAFA, 1997. The
mentioned result is a consequence of their theorem 1.5, see also the Remark 1.9. – Al Tal Apr 3 '11 at 15:52
Thanks a lot! I did not know about this paper. Kevin Whyte's paper ("Amenability, bi-Lipschitz equivalence, and the von Neumann conjecture." Duke Math. J. 99 (1999), no. 1, 93–112)
appeared two years later. – Andreas Thom Apr 3 '11 at 16:37
add comment
If G is a finitely generated solvable group with exponential growth, then G contains a quasi-isometrically embedded free semi-group (this is a result of Y. Cornulier and R. Tessera,
up vote 3 Quasi-isometrically embedded free sub-semigroups; Geom. Topol. 12 461-473, 2008, improving on Rosenblatt)
down vote
Thanks, Alain. It's a nice result, but I do not care about the metric. So, the existence of a free subsemigroup already gives the existence of a generating set so that a binary tree
is embedded. – Andreas Thom Apr 19 '11 at 20:46
add comment
This (so nice) question seems to be equivalent with the notorious and old problem of constructing a supraamenable (or superamenable) group of exponential growth. Recall that a supraamenable
group is one such that every non-empty set is not G-paradoxical, or equivalently, given any non-empty subset of G, there exists a finitely additive invariant measure on G that assigns measure
one to the set. All groups of sub-exponential growth are supraamenable, but no other example is known.
Basic defintions are here (before Exercise 8 and Remark 3) http://terrytao.wordpress.com/2009/01/08/245b-notes-2-amenability-the-ping-pong-lemma-and-the-banach-tarski-paradox-optional/
The question is stated eg. as Question 70 here but it is much older http://www.unige.ch/math/folks/delaharpe/articles/18-CGH.pdf
up vote
2 down Non supraamenability seems to be equivalent with the existence of a generating set such that the Cayley graph contains the binary tree. Indeed, if such a generating set $S$ exists then the
vote set $V$ containing the vertices of the tree is paradoxical using elements from $S^{-1}$: take the subset of the left sons and the one of the right sons, they will both cover their mothers.
Conversely, if $X=X_1 \sqcup X_2$ is a paradoxical subset of $G$ and $S$ is the (finite) set of elements involved in the paradox, then $S^{-1}$ will do, as long as one gets sure identity is
not in $S$ (which can be assumed). Start with any $x \in X$ as initial root. A paradox is nothing else than a $2$ to $1$ piecewise $G$- map $f:X \rightarrow X$ so one can choose the left son
the counter image of $x$ in $X_1$ and for the right son the counter image in $X_2$ and continue by induction (there is a little problem, at exactly one point in the process there might be a
cycle ocurring (due to the root trying to connect), but then one can delete the whole infected half...)
add comment
Not the answer you're looking for? Browse other questions tagged gr.group-theory open-problem geometric-group-theory or ask your own question. | {"url":"http://mathoverflow.net/questions/60011/trees-in-groups-of-exponential-growth","timestamp":"2014-04-20T14:07:01Z","content_type":null,"content_length":"79827","record_id":"<urn:uuid:e3eeb3b0-aed0-44c9-b3a9-f6ef8d43107a>","cc-path":"CC-MAIN-2014-15/segments/1397609538787.31/warc/CC-MAIN-20140416005218-00580-ip-10-147-4-33.ec2.internal.warc.gz"} |
Fairfax, VA Science Tutor
Find a Fairfax, VA Science Tutor
...I believe that a good tutor is someone who can help a student see, listen, feel and get a taste of life. I teach a number of different classes including General Biology, Anatomy and
Physiology, Biochemistry, Microarray and research practice. I enjoy working with students individually or in smal...
19 Subjects: including genetics, microbiology, physiology, anatomy
...What has helped me the most is learning to convert an algebraic expression into common english so I can easily determine the solution. This is what I aim to teach students so that they can
solve any expression on their own. I was a chemistry research intern at NASA's Jet Propulsion Laboratory during the summer of 2013.
10 Subjects: including organic chemistry, geology, chemistry, biochemistry
Biology is my passion! I have an advanced degree in Molecular and Microbiology with over 5 years experience in a lab setting. I had taken a few anatomy courses during my undergrad degree and
taught labs for a pre-med anatomy class for 2 years as a graduate student.
13 Subjects: including genetics, geometry, biology, biochemistry
...My experience enables me to quickly ascertain each student's best learning style (visual, audible, or a combination) and then teach accordingly. This quality is essential to facilitate the
learning process as it is directly evidenced by each student's measurable progress and self-confidence. Many students also develop additional learning styles in this process.
23 Subjects: including nutrition, pharmacology, anatomy, physiology
...I have taught Biology, Algebra, AP Biology and related electives. I have also tutored Chemistry and Geometry, in addition to the aforementioned subjects, for several years. My undergraduate
degree is in Biology and I hold a Masters degree in Biomedical Science.
8 Subjects: including biochemistry, SAT math, genetics, microbiology
Related Fairfax, VA Tutors
Fairfax, VA Accounting Tutors
Fairfax, VA ACT Tutors
Fairfax, VA Algebra Tutors
Fairfax, VA Algebra 2 Tutors
Fairfax, VA Calculus Tutors
Fairfax, VA Geometry Tutors
Fairfax, VA Math Tutors
Fairfax, VA Prealgebra Tutors
Fairfax, VA Precalculus Tutors
Fairfax, VA SAT Tutors
Fairfax, VA SAT Math Tutors
Fairfax, VA Science Tutors
Fairfax, VA Statistics Tutors
Fairfax, VA Trigonometry Tutors
Nearby Cities With Science Tutor
Annandale, VA Science Tutors
Arlington, VA Science Tutors
Bethesda, MD Science Tutors
Burke, VA Science Tutors
Centreville, VA Science Tutors
Chantilly Science Tutors
Fairfax Station Science Tutors
Falls Church Science Tutors
Herndon, VA Science Tutors
Manassas, VA Science Tutors
Mc Lean, VA Science Tutors
Oakton Science Tutors
Springfield, VA Science Tutors
Vienna, VA Science Tutors
Woodbridge, VA Science Tutors | {"url":"http://www.purplemath.com/Fairfax_VA_Science_tutors.php","timestamp":"2014-04-18T13:30:13Z","content_type":null,"content_length":"23967","record_id":"<urn:uuid:94de30c8-9211-4452-be10-9c5b721c85cb>","cc-path":"CC-MAIN-2014-15/segments/1397609533689.29/warc/CC-MAIN-20140416005213-00368-ip-10-147-4-33.ec2.internal.warc.gz"} |
Inversive geometry question-ellipse and limacon
October 5th 2009, 01:05 PM #1
Sep 2009
Inversive geometry question-ellipse and limacon
I need to invert an ellipse about one of its foci. The ellipse in question has semi-minor axis of $\frac{\sqrt{2}}{2}$ and semi-major axis of 1.
After doing a little googling I see that the inverse of an ellipse about one of its foci is a "dimpled limacon." However, I am at a loss as to how to obtain the limacon equation for particular a
and b values such as those indicated above.
Could someone please help?
Follow Math Help Forum on Facebook and Google+ | {"url":"http://mathhelpforum.com/geometry/106289-inversive-geometry-question-ellipse-limacon.html","timestamp":"2014-04-19T22:15:58Z","content_type":null,"content_length":"29501","record_id":"<urn:uuid:01a63827-e0df-44d4-a29f-eaf912a4b6e1>","cc-path":"CC-MAIN-2014-15/segments/1397609537754.12/warc/CC-MAIN-20140416005217-00558-ip-10-147-4-33.ec2.internal.warc.gz"} |
Symplectic forms and 1-forms
up vote -4 down vote favorite
Suppose we have a real symplectic manifold $(M,\omega)$. Under what conditions can we find a global 1-form $\alpha$ such that $\omega = \alpha \wedge\alpha$?
Obviously there are some simple obstructions, for example, the cotangent bundle must admit a non-vanishing section (thus, surfaces of genus $>1$ are out). However it does not seem easy to come up
with sufficient conditions.
gt.geometric-topology sg.symplectic-geometry dg.differential-geometry cotangent-bundles
1 For a one-form $\alpha$, $\alpha \wedge \alpha = 0$. – Dan Fox Jun 8 '12 at 9:01
And then you should do an immediate excercise. If ω=α∧β then then M is... – Swiat Gal Jun 8 '12 at 10:06
Do you want to have $w=d \alpha$? – George Jun 9 '12 at 9:39
$\dim M = 0 $ – Allen Knutson Jun 9 '12 at 16:08
This question was incredibly badly phrased, for which I apologize. I meant to ask in the case where we tensor the exterior algebra with something nonabelian. But even then as Gal pointed out the
answer is easy. – Blake Jun 27 '12 at 2:34
add comment
1 Answer
active oldest votes
You can never find such a $1$-form since any $1$-form wedge itself is identically zero.
up vote 5 down vote
add comment
Not the answer you're looking for? Browse other questions tagged gt.geometric-topology sg.symplectic-geometry dg.differential-geometry cotangent-bundles or ask your own question. | {"url":"http://mathoverflow.net/questions/99098/symplectic-forms-and-1-forms?sort=oldest","timestamp":"2014-04-19T05:00:40Z","content_type":null,"content_length":"55142","record_id":"<urn:uuid:4acc258d-d723-43c0-884e-009591cb2175>","cc-path":"CC-MAIN-2014-15/segments/1397609535775.35/warc/CC-MAIN-20140416005215-00597-ip-10-147-4-33.ec2.internal.warc.gz"} |
Got Homework?
Connect with other students for help. It's a free community.
• across
MIT Grad Student
Online now
• laura*
Helped 1,000 students
Online now
• Hero
College Math Guru
Online now
Here's the question you clicked on:
Getting [Math Processing Error] in Latex for every Latex code , what should be done ?
• one year ago
• one year ago
Your question is ready. Sign up for free to start getting answers.
is replying to Can someone tell me what button the professor is hitting...
• Teamwork 19 Teammate
• Problem Solving 19 Hero
• Engagement 19 Mad Hatter
• You have blocked this person.
• ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.
This is the testimonial you wrote.
You haven't written a testimonial for Owlfred. | {"url":"http://openstudy.com/updates/50a0f3c9e4b0e22d17eed503","timestamp":"2014-04-18T10:59:21Z","content_type":null,"content_length":"40027","record_id":"<urn:uuid:c31d915b-4b7d-40ee-9299-4808ddb43623>","cc-path":"CC-MAIN-2014-15/segments/1397609533308.11/warc/CC-MAIN-20140416005213-00342-ip-10-147-4-33.ec2.internal.warc.gz"} |
Physics Forums - Relations between coefficient and exponent of Proth prime [itex]k\cdot 2^n+1[/itex]?
Relations between coefficient and exponent of Proth prime [itex]k\cdot 2^n+1[/itex]?
Definition: Proth number is a number of the form :
[itex]k\cdot 2^n+1[/itex]
where [itex]k[/itex] is an odd positive integer and [itex]n[/itex] is a positive integer such that : [itex]2^n>k[/itex]
My question : If Proth number is prime number are there some other known relations in addition to [itex]2^n>k[/itex] , between exponent [itex]n[/itex] and coefficient [itex]k[/itex] ?
Re: Relations between coefficient and exponent of Proth prime [itex]k\cdot 2^n+1[/it
[itex]( n \equiv 1 \pmod 2 \land n > 1) \Rightarrow \gcd(k-1,3)=1 [/itex]
[itex] n \equiv 0 \pmod 2 \Rightarrow \gcd(k+1,3)=1 [/itex]
clearwater304 Nov30-11 07:45 PM
Re: Relations between coefficient and exponent of Proth prime [itex]k\cdot 2^n+1[/it
I would think it has something to do with the sieve of eratosthenes, where the twin primes revolve around multiples of 6. The formula would give the lesser value for the twin primes.
A few years ago, i decided to look into the riemann hypothesis. I noticed that using the sieve of eratosthenes, there is an obvious pattern for composite numbers. The pattern gets more complex after
regions of primes squared. I started to develop a formula but it got more complex with each region, and didn't seam like a good basis for an equation, so I put it off.
All times are GMT -5. The time now is 12:51 AM.
Powered by vBulletin Copyright ©2000 - 2014, Jelsoft Enterprises Ltd.
© 2014 Physics Forums | {"url":"http://www.physicsforums.com/printthread.php?t=551704","timestamp":"2014-04-20T05:51:41Z","content_type":null,"content_length":"5855","record_id":"<urn:uuid:4c0bc36a-231a-44b7-a490-3c6047d98ce0>","cc-path":"CC-MAIN-2014-15/segments/1397609538022.19/warc/CC-MAIN-20140416005218-00564-ip-10-147-4-33.ec2.internal.warc.gz"} |
Few Trig Problems
February 14th 2010, 01:38 PM #1
Sep 2009
Few Trig Problems
1. (cos^2)T/1-sinT to 1+sinT
Show the steps to get the left side to equal 1+sint
2. find an interval (0,2(pie)) to solve cotT= sqrt3/ 3
3. Determine the width of a river with markers placed at each side in line withe the base of a tower that rises 25m out of the ground. from the top of the tower, the angles of depression are 58
degrees and 38 degrees. how wide is the river?
First, check those parentheses. Please never write that again. Do not separate a function from its arguement.
Second, multiple numerator and denominator by "1+sin(T)"
First, pie is for eating. pi is for mathematics.
Second, cot(T) = cos(T)/sin(T)
Let's see those two. Then we can talk about the third.
I apologize, I wasn't sure how to put the symbols on here. Im sure I confused you in my attempt to post those questions. I was also posting on my iphone, so typos happen frequently. You want me
to rewrite the problems?
No, I was not confused. I already answered and provided methods to proceed. Just learn. There is no harsh judgment here.
I have no idea how to do the first two. Would you mind showing some steps? I tried putting something in to laTex to help make things clearer, but man that is another animal all on its own!
For the last word problem I have the answer to be 40 meters? tan=d/25 d=25*tan58 degrees??
1) I told you exactly how to do the first one in my first post. Did you try it?
2) Show us #1 and we can talk about #2.
3) "tan=d/25" Never write that again. "tan" means nothing by itself.
What is 'd'? Please define your terms.
I think you need two things.
x = Distance between tower and the near shore.
y = Width of the river.
Now it's thinking time.
Angle of depression to the far shore is 38º.
Angle of depression to the near shore is 58º, making the change for crossing the river 20º.
Angle of depression to the bottom of the tower is 90º, making the change for getting there from the river 32º.
$\tan(32^{\circ}) = \frac{x}{25}$
$\tan(52^{\circ}) = \frac{x+y}{25}$
Solve for y.
Let's see what you get.
For number 1 I wrote cos^2 as the Pythagorean identity and then used that as a difference of two squares. Which cancels 1-sin and leaves 1+sin.
Number 2 I got 4(pi)/3 and pi/3.
Number 3 idk yet
What will it look like when solved for y?
1) Assuming that question asked is $Prove \frac{cos^2\theta}{1-sin\theta}=1+sin\theta$
$LHS= \frac{1^2-sin^2\theta}{1-sin\theta}$
$= \frac{(1-sin\theta)(1+sin\theta)}{1-sin\theta}$
$= (1)(1+sin\theta)$
$= 1+sin\theta$ (Proved)
First, check those parentheses. Please never write that again. Do not separate a function from its arguement.
Second, multiple numerator and denominator by "1+sin(T)"
First, pie is for eating. pi is for mathematics.
Second, cot(T) = cos(T)/sin(T)
Let's see those two. Then we can talk about the third.
To prove a question, either prove from left to right or right to left...
Never multiply, divide, minus or add anything to both sides before starting to prove.
February 14th 2010, 02:13 PM #2
MHF Contributor
Aug 2007
February 14th 2010, 02:44 PM #3
Sep 2009
February 14th 2010, 04:50 PM #4
MHF Contributor
Aug 2007
February 14th 2010, 06:42 PM #5
Sep 2009
February 14th 2010, 08:54 PM #6
MHF Contributor
Aug 2007
February 14th 2010, 09:10 PM #7
Sep 2009
February 14th 2010, 09:16 PM #8
Sep 2009
February 14th 2010, 10:27 PM #9
Super Member
Dec 2009
February 14th 2010, 10:29 PM #10
Super Member
Dec 2009 | {"url":"http://mathhelpforum.com/trigonometry/128808-few-trig-problems.html","timestamp":"2014-04-17T13:24:56Z","content_type":null,"content_length":"55524","record_id":"<urn:uuid:6aee4786-0ca7-4aba-8fca-2349772bb462>","cc-path":"CC-MAIN-2014-15/segments/1397609530131.27/warc/CC-MAIN-20140416005210-00106-ip-10-147-4-33.ec2.internal.warc.gz"} |
Two problems with integrals.
April 15th 2009, 03:07 PM #1
Aug 2007
Two problems with integrals.
I'm having difficulties with a few homework problems.
The first one I need to use u substitution to evaluate the definite integral on [-pi/2, pi/2] for ((x^2 * sinx)/(1 + x^6))dx
I'm just lost as to where to use the substitution, if anyone has some pointers that'd be great.
The other problem I'm supposed to evaluate the integral using logarithmic differentiation on the [e,6] for dx/xlnx
Same problem with this one, I just don't know where to begin with it.
Thanks for any advice/help!
I'm having difficulties with a few homework problems.
The first one I need to use u substitution to evaluate the definite integral on [-pi/2, pi/2] for ((x^2 * sinx)/(1 + x^6))dx
I'm just lost as to where to use the substitution, if anyone has some pointers that'd be great.
The other problem I'm supposed to evaluate the integral using logarithmic differentiation on the [e,6] for dx/xlnx
Same problem with this one, I just don't know where to begin with it.
Thanks for any advice/help!
If $f(x)$ is odd on $[-a,a]$ then $\int_{-a}^a f(x)\,dx = 0$ and $f(x) = \frac{x^2 \sin x}{1+x^6}$ is odd on $[-\frac{\pi}{2}, \frac{\pi}{2}]$. For the second problem, try $u = \ln x$.
April 15th 2009, 03:12 PM #2 | {"url":"http://mathhelpforum.com/calculus/83926-two-problems-integrals.html","timestamp":"2014-04-19T12:21:19Z","content_type":null,"content_length":"34780","record_id":"<urn:uuid:5c5895f4-12c0-40b2-b594-ac960396e07c>","cc-path":"CC-MAIN-2014-15/segments/1397609537186.46/warc/CC-MAIN-20140416005217-00567-ip-10-147-4-33.ec2.internal.warc.gz"} |
Animated Sine Curve
A circle, with radius 1, is centred on the origin. A point labelled 'C' rotates around the circle, starting at (1,0)
A point 'A', starting at (0,0), moves along the x axis, so that when C has completed one turn, A has moved (approx) 6.28 units.
Point 'B' is constrained to move so that its x coordinate matches A, whilst its y coordinate matches C. Thus it traces out a sine curve as A and C move.
http://www.bundy.demon.co.uk/images/sinecurve.avi 3M file, needs Windows Media Player.
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei | {"url":"http://www.mathisfunforum.com/viewtopic.php?pid=159593","timestamp":"2014-04-18T21:42:48Z","content_type":null,"content_length":"8714","record_id":"<urn:uuid:13423483-93a8-479c-bbd4-c354fcaa288d>","cc-path":"CC-MAIN-2014-15/segments/1397609535095.9/warc/CC-MAIN-20140416005215-00551-ip-10-147-4-33.ec2.internal.warc.gz"} |
What Kind Of State Secrets Does A President Know? - Page 4 - News, Politics and Current Events
I think the look on BO's face is,
WHAT THE HELL DID I GET MYSELF INTO.IF I NEW THEN WHAT I KNOW NOW I'D NEVER HAVE RUN.
Re: What Kind Of State Secrets Does A President Know?
BIG BEAM wrote:I think the look on BO's face is,
WHAT THE HELL DID I GET MYSELF INTO.IF I NEW THEN WHAT I KNOW NOW I'D NEVER HAVE RUN.
Because of secrets he was briefed on by the CIA?
Re: What Kind Of State Secrets Does A President Know?
Devil505 wrote:
mikeandgerry wrote:The moon's gravitational pull is so weak that only a "gunshot" like blast was needed to propel the LM into orbit.
It's not THAT weak Mike. To be exact, it's 1/7th that of Earth's. Less, to be sure, but still pretty significant to escape.
Gravity is a an accelerative force, meaning that for every unit of distance further away the two bodies are, the attractive force gets weaker by the square of the distance. It takes far less energy
to move away from the moon compared to the earth than 1/7th due to this effect. Also, In an atmosphere that is void, there is even less of an energy requirement to move away.
Examine the Wikipedia video. There is a sharp blast which kicks up some debris and dust that is deflected by the platform (the lower half of the LM) but no need for sustained rocket thrust.
Re: What Kind Of State Secrets Does A President Know?
mikeandgerry wrote:Gravity is a an accelerative force, meaning that for every unit of distance further away the two bodies are, the attractive force gets weaker by the square of the distance.
A bit off topic here Mike but if you're a mathematician (I'm not) here you go:
Let x, v, and a denote distance, velocity, and acceleration respectively of an object along a line. Then, from the chain rule we have:
(1) a = dv/dt = (dv/dx)*(dx/dt) = v*(dv/dx)
and hence
(2) a*dx = v*dv
For convenience let f(x) be the indefinite integral of a*dx.
Consider an object moving position x1 to position x2 with initial velocity v1 and final velocity v2. We integrate both sides of (2) to get
(3) v2**2 - v1**2 = 2 * (f(x2)-f(x1))
Now consider the case where the acceleration of the the object is due to gravitational forces from one or more masses M_i located at positions X_i. The acceleration due to mass M_i is given by
(4) a_i(x) = G*M_i/(x-X_i)**2
Full formulas here:
This link is broken, either the page no longer exists or there is some other issue like a typo.
Re: What Kind Of State Secrets Does A President Know?
Just how much free time to you guys have? This discussion has no ending point. You can take a man to water, but you can't make him drink! You can hold his head under water, but you can't make him
open his mouth. You can argue day and night and what the hell does it prove? That you were/are married, and you haven't learned anything yet? She is ALWAYS right, dummie. They must call you 'devil '
for a reason. The political season is OVER, your side won.....let it die. I thought this was a coal forum, not a "I hit you last" kiddie game. Yup, I'll exercise my rights and stay the hell off this
topic. Thanks for nothing.
Re: What Kind Of State Secrets Does A President Know?
I learned to bypass the threads I'm not interested in. It helps to keep my blood pressure under control.
Re: What Kind Of State Secrets Does A President Know?
Devil505 wrote:
BIG BEAM wrote:I think the look on BO's face is,
WHAT THE HELL DID I GET MYSELF INTO.IF I NEW THEN WHAT I KNOW NOW I'D NEVER HAVE RUN.
Because of secrets he was briefed on by the CIA?
That and he's probably privy to some info from certain select committees that he didn't have access to before.
Re: What Kind Of State Secrets Does A President Know?
Not a mathematician devil? Who knew?
The math you provided is fine if you want to complicate the explanation with calculus. In the hypothetical situation presented, which was launching interstellar probes from Earth-Moon system or the
Moon and the related cost benefit analysis(you must be a sci-fi fan), they sought to calculate velocities but stopped short of forces. I investigated your link. You stopped short of the part that
confirmed what I stated.
What we are talking about is a problem of force, derived from F=ma. While the math you provided was fine for calculating the required velocities for those situations, it only touched on the problem
of calculating the energy required for a mass to leave masses of two considerably different sizes and having considerably different atmospheres. The initial force may differ by the factor of 7 as you
suggested but the sustained force and resulting energy required to escape the gravitational pull is far less than a factor of 7
From the link you posted:
(8) G*M_i = g_i*R_i**2
where R_i is a reference distance which, in subsequent calculations, is the mass body radius and g_i is the surface acceleration of gravity.
From equation (8) and these values we get
G*M_Earth = 398653. km**3/sec**2
G*M_Moon = 4893. km**3/sec**2
This will put it into layman's terms for you, from Wikipedia:
Earth's gravity
Every planetary body (including the Earth) is surrounded by its own gravitational field, which exerts an attractive force on all objects. Assuming a spherically symmetrical planet (a reasonable
approximation), the strength of this field at any given point is proportional to the planetary body's mass and inversely proportional to the square of the distance from the center of the body.
The strength of the gravitational field is numerically equal to the acceleration of objects under its influence, and its value at the Earth's surface, denoted g, is approximately expressed below as
the standard average.
g = 9.8 m/s2 = 32.2 ft/s2
This means that, ignoring air resistance, an object falling freely near the earth's surface increases its velocity with 9.8 m/s (32.2 ft/s or 22 mph) for each second of its descent. Thus, an object
starting from rest will attain a velocity of 9.8 m/s (32.2 ft/s) after one second, 19.6 m/s (64.4 ft/s) after two seconds, and so on, adding 9.8 m/s (32.2 ft/s) to each resulting velocity.
Emphasis mine.
Your cut and paste touches on it in derivation 3 and 4.
Re: What Kind Of State Secrets Does A President Know?
mikeandgerry wrote:Not a mathematician devil? Who knew?
I posted that as a joke Mike.
whistlenut wrote:They must call you 'devil ' for a reason. The political season is OVER, your side won.....let it die. I thought this was a coal forum, not a "I hit you last" kiddie game. Yup,
I'll exercise my rights and stay the hell off this topic. Thanks for nothing.
The election is over & coal is the purpose of this forum....but....Many of us have other interests & just enjoy a friendly debate on various subjects in this....the General OFF-Topic Forum. My advice
is to read only the threads that interest you. What's the problem with that?
Re: What Kind Of State Secrets Does A President Know?
And I got it! Which is why I jibed you back.
I am not a mathematician either but I did study some calculus and physics.
I know just enough to get my self in trouble at times.
Re: What Kind Of State Secrets Does A President Know?
Complicate the explanation with calculus?......complicate??.....that's what makes it fun...it's just starting to get interested!
Re: What Kind Of State Secrets Does A President Know?
O.K. Devil,I am not certain that Oswald acted alone but from my reading , I will give you this. That Mannlicher Carcano rifle was test fired by a team from the F.B.I. ,a civilian group of known
marksman, and the Army Ordnance group.The Army Ordance group fired 47 rounds with rifle serial # C2766 [THE rifle] and found it to be at least as accurate as the M1 and the government issue at the
time ,the M14. It was capable of the time required to get off the shots if using open sights.It was said at the time that it was a cheap piece of"junk".It was manufactured at theTerni Arsenal in
Italy in 1940 and likely used in the war until Italy surrendered, Sept.1943. The Army ordnance people classified the stock as marked,the action as smooth,and the bore as fair.The rifle was the
subject of a possession lawsuit. The federal government prevailed and the rifle is now in the Federal Archives.These are all documented facts and not heresay or myth. I cannot understand what they
are talking about when they say the design of the bolt action contributed to rapid firing. I thought a bolt action was a bolt action??? Since I have not drawn my own conclusion as of yet I will
continue to research one of the most horrendous and sad tradgedys in American history.
Re: What Kind Of State Secrets Does A President Know?
stovepipemike wrote:O.K. Devil,I am not certain that Oswald acted alone
B4 Richard locks this thread for going off topic Mike, I'm going to start a new thread specifically for conspiracy theories, since there seems to be much interest in them.
As far as this statement: ..."I cannot understand what they are talking about when they say the design of the bolt action contributed to rapid firing. I thought a bolt action was a bolt action???"
While I'm far from a firearms expert, (Dr. Atwater from "Tales Of The Gun" is!
Re: What Kind Of State Secrets Does A President Know?
Place would be pretty boring with just coal topics. I think the off coal posts add a little fun.
Re: What Kind Of State Secrets Does A President Know?
ken wrote:Place would be pretty boring with just coal topics. I think the off coal posts add a little fun.
Indeed. Not to mention that there simply aren't enough coal issues to keep us all checking back here as regularly as we do when current events are being discussed.
The simple truth is that, without regular traffic, boards wither and die. If you're a hockey fan, it's sort of like the Rodney Dangerfield quote: "I went to a fight the other night and a hockey game
broke out." | {"url":"http://nepacrossroads.com/about7658-45.html","timestamp":"2014-04-16T21:54:08Z","content_type":null,"content_length":"51948","record_id":"<urn:uuid:3334631a-4b2b-4141-89eb-2c2c9924d3ce>","cc-path":"CC-MAIN-2014-15/segments/1397609525991.2/warc/CC-MAIN-20140416005205-00370-ip-10-147-4-33.ec2.internal.warc.gz"} |
Euler Midpot method
April 7th 2009, 01:17 AM #1
Mar 2009
Euler Midpot method
I have the equation
dy/dx=2e^-x-y^2 with y(0)=1
I have h=0.2 and need to find an approximation of y at x=0.4 using midpoint Eulers method.
So so far i have
and when n=0, t=0.4, x1=0 and x2=1
when n=1, t=0.5, x1=1 and x2=1.5
when n=2, t=0.6, x1=0.8414, x2=2.85
Are these correct? iF not what am i doing wrong!?
Follow Math Help Forum on Facebook and Google+ | {"url":"http://mathhelpforum.com/differential-equations/82672-euler-midpot-method.html","timestamp":"2014-04-19T20:36:28Z","content_type":null,"content_length":"28434","record_id":"<urn:uuid:aef46672-cc81-4f02-a57d-a40d5024b1c2>","cc-path":"CC-MAIN-2014-15/segments/1397609537376.43/warc/CC-MAIN-20140416005217-00295-ip-10-147-4-33.ec2.internal.warc.gz"} |
College of Natural Science and Mathematics
Department of Mathematics and Statistics
Graduate Certificate, M.S. Degrees; Minor
Statistics is a collection of methods and theories for making decisions or estimating unknown quantities from incomplete information. Statistical techniques are useful, for example, in estimating
plant, animal and mineral abundances; forecasting social, political and economic trends; planning field plot experiments in agriculture; performing clinical trials in medical research; and
maintaining quality control in industry. Employment opportunities are excellent for statisticians in many of these areas of application.
1. Complete the following:
STAT F200X--Elementary Probability and Statistics (3)
or STAT F300--Statistics (3)--3 credits
STAT F401--Regression and Analysis of Variance--4 credits
MATH F371--Probability*--3 credits
MATH F408--Mathematical Statistics--3 credits
MATH, STAT or STAT related course work**--3 credits
2. Minimum credits required--16 credits
* MATH F371 requires MATH F200X, F201X and F202X as prerequisites.
** e.g., BA F360, GEOS F430, ANTH F424, MATH F460, etc.
Note: Courses completed to satisfy this minor can be used to simultaneously satisfy other major or general distribution requirements.
Note: Fisheries majors selecting the research option need only complete MATH F371 and MATH F408 in addition to their fisheries requirements to obtain a minor in statistics. | {"url":"http://www.uaf.edu/catalog/catalog_12-13/programs/statistics.html","timestamp":"2014-04-19T01:59:08Z","content_type":null,"content_length":"10816","record_id":"<urn:uuid:7ac99bdb-7ce5-4ed6-87a7-f6244e498302>","cc-path":"CC-MAIN-2014-15/segments/1398223202774.3/warc/CC-MAIN-20140423032002-00488-ip-10-147-4-33.ec2.internal.warc.gz"} |
JCBDigger's Guides
Home XNA Contents Development Blog
I have converted examples of Ray to Triangle and BoundingSphere to Triangle intersections available on the Internet in to a XNA C# triangle class. It also includes a few other triangle related
Download Source Code
Triangle XNA class (4kb) Feb. 2010
The triangle uses an array of Vector3's for the corner points.
public Triangle()
Vertex = new Vector3[3];
Vertex[0] = Vector3.Zero;
Vertex[1] = Vector3.Zero;
Vertex[2] = Vector3.Zero;
The Intersect Ray method is from the Creators club picking with triangle accuracy sample.
// Returns the distance from the origin of the ray to the intersection with
// the triangle, null if no intersect and negative if behind.
public void Intersects(ref Ray ray, out float? distance)
// Set the Distance to indicate no intersect
distance = null;
// Compute vectors along two edges of the triangle.
Vector3 edge1, edge2;
Vector3.Subtract(ref Vertex[2], ref Vertex[1], out edge1);
Vector3.Subtract(ref Vertex[0], ref Vertex[1], out edge2);
// Compute the determinant.
Vector3 directionCrossEdge2;
Vector3.Cross(ref ray.Direction, ref edge2, out directionCrossEdge2);
float determinant;
Vector3.Dot(ref edge1, ref directionCrossEdge2, out determinant);
// If the ray is parallel to the triangle plane, there is no collision.
if (determinant > -float.Epsilon && determinant < float.Epsilon)
float inverseDeterminant = 1.0f / determinant;
// Calculate the U parameter of the intersection point.
Vector3 distanceVector;
Vector3.Subtract(ref ray.Position, ref Vertex[1], out distanceVector);
float triangleU;
Vector3.Dot(ref distanceVector, ref directionCrossEdge2, out triangleU);
triangleU *= inverseDeterminant;
// Make sure it is inside the triangle.
if (triangleU < 0 || triangleU > 1)
// Calculate the V parameter of the intersection point.
Vector3 distanceCrossEdge1;
Vector3.Cross(ref distanceVector, ref edge1, out distanceCrossEdge1);
float triangleV;
Vector3.Dot(ref ray.Direction, ref distanceCrossEdge1, out triangleV);
triangleV *= inverseDeterminant;
// Make sure it is inside the triangle.
if (triangleV < 0 || triangleU + triangleV > 1)
// == By here the ray must be inside the triangle
// Compute the distance along the ray to the triangle.
float length = 0;
Vector3.Dot(ref edge2, ref distanceCrossEdge1, out length);
distance = length * inverseDeterminant;
The Triangle to sphere intersection is an expensive test compared to other intersections. I only use it to create level files. I do not use it in game.
// This is an expensive test.
// The result is true or false.
public void Intersects(ref BoundingSphere sphere, out bool result)
result = false;
// First check if any corner point is inside the sphere
// This is necessary because the other tests can easily miss
// small triangles that are fully inside the sphere.
if (sphere.Contains(A) != ContainmentType.Disjoint ||
sphere.Contains(B) != ContainmentType.Disjoint ||
sphere.Contains(C) != ContainmentType.Disjoint)
// A point is inside the sphere
result = true;
// Test the edges of the triangle using a ray
// If any hit then check the distance to the hit is less than the length of the side
// The distance from a point of a small triangle inside the sphere coule be longer
// than the edge of the small triangle, hence the test for points inside above.
Vector3 side = B - A;
// Important: The direction of the ray MUST
// be normalised otherwise the resulting length
// of any intersect is wrong!
Ray ray = new Ray(A, Vector3.Normalize(side));
float distSq = 0;
float? length = null;
sphere.Intersects(ref ray, out length);
if (length != null)
distSq = (float)length * (float)length;
if (length > 0 && distSq < side.LengthSquared())
// Hit edge
result = true;
// Stay at A and change the direction to C
side = C - A;
ray.Direction = Vector3.Normalize(side);
length = null;
sphere.Intersects(ref ray, out length);
if (length != null)
distSq = (float)length * (float)length;
if (length > 0 && distSq < side.LengthSquared())
// Hit edge
result = true;
// Change to corner B and edge to C
side = C - B;
ray.Position = B;
ray.Direction = Vector3.Normalize(side);
length = null;
sphere.Intersects(ref ray, out length);
if (length != null)
distSq = (float)length * (float)length;
if (length > 0 && distSq < side.LengthSquared())
// Hit edge
result = true;
// If we get this far we are not touching the edges of the triangle
// Calculate the InverseNormal of the triangle from the centre of the sphere
// Do a ray intersection from the centre of the sphere to the triangle.
// If the triangle is too small the ray could miss a small triangle inside
// the sphere hence why the points were tested above.
ray.Position = sphere.Center;
// This will always create a vector facing towards the triangle from the
// ray starting point.
InverseNormal(ref ray.Position, out side);
ray.Direction = side;
Intersects(ref ray, out length);
if (length != null && length > 0 && length < sphere.Radius)
// Hit the surface of the triangle
result = true;
// Only if we get this far have we missed the triangle
result = false;
A good source of intersection code mainly in C/++ and theoretical papers is available from: realtimerendering.com
To get the vertices and triangles from an XNA model:
using XNA 3.1 is available from enchantedage.com
using XNA 4.0 I have a modified version of the above here. | {"url":"http://www.discoverthat.co.uk/games/xna-triangle.htm","timestamp":"2014-04-19T22:11:43Z","content_type":null,"content_length":"13953","record_id":"<urn:uuid:4ccf2c85-3c1a-4431-9b60-5b1b76cd9382>","cc-path":"CC-MAIN-2014-15/segments/1397609537754.12/warc/CC-MAIN-20140416005217-00432-ip-10-147-4-33.ec2.internal.warc.gz"} |
Math Forum Discussions - Re: ZFC and God
Date: Jan 23, 2013 8:36 AM
Author: Jesse F. Hughes
Subject: Re: ZFC and God
WM <mueckenh@rz.fh-augsburg.de> writes:
> On 23 Jan., 12:47, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
>> WM <mueck...@rz.fh-augsburg.de> writes:
>> > On 22 Jan., 21:18, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
>> >> WM <mueck...@rz.fh-augsburg.de> writes:
>> >> > That is potential infinity. That proof is not necessary, because the
>> >> > set is obviously potentially infinite. No, you shoudl give a proof,
>> >> > that there is a larger k than all finite k.
>> >> Er, no. When I say that the union is infinite, I do not mean that it
>> >> contains an infinite number.
>> > But you mean that the tree contains infinite paths. And just that is
>> > impossible without ...
>> > In order to shorten this discussion please have a look at
>> http://math.stackexchange.com/questions/284328/how-to-distinguish-bet...
>> No. It's irrelevant.
> You are in error.
>> We're talking about whether you can prove that
>> U_n=1^oo {1,...,n}
>> is finite. I'm not switching topics to paths in trees (despite the
>> fact that the ignorance of your question is obvious).
> The union of FISs is finite. Yes that is my claim. But I cannot give
> an upper limit, because the finite numbers have no upper limit. This
> is called potentially infinite.
>> > There it has meanwhile turned out ... But see it with your own eyes
>> > what you would not believe if I told you.
>> > The index omega is in reach, it seems.
>> You're playing your usual little game of trying to change the topic.
>> I won't have it.
>> I take it that this new tack is so that you don't have to concede the
>> point: there is no mathematical publication which claims that the
>> above union contains elements larger than any natural, nor any
>> publication which claims that this is what it means to be infinite.
> I know. But if you hace read the discussion, you have seen that two
> matheologians claim just this. Why do they? Because they cannot answer
> the question: What paths are (as subsets of the set of nodes) in a
> Binary Tree that is the union of all its levels? Are there only the
> finite paths? Or are there also the infinite paths?
> Try to answer it, and you will see that you need the omegath level or
> must confess that it is impossible to distinguish both cases. Hence,
> Cantor's argument applies simultaneously to both or to none.
I'm not interested in the web-published claims of two individuals on a
different topic than we're discussing.
Once again, let me remind you what you claimed. You claimed ZF was
inconsistent, and in particular that ZF proves that the union
U_n {1,...,n}
is both finite and infinite.
Now, we've had two competing definitions of infinite in this
particular discussion.
(1) A set S is infinite if there is no natural n such that |S| = n.
(2) A set S is infinite if it contains a number greater than every
natural n.
The first definition is what mathematicians almost always mean, and
they *never* mean the second, but this is mere semantics. Let's talk
We both agree that, using definition (1), the above union is infinite
and (I think) we agree that we cannot show it is finite (=not
infinite). If I'm mistaken on this point, then please show me.
On the other hand we both agree that, per definition (2), the union is
"finite", but I have seen no contradiction result, since you have not
shown that the union is "infinite" in this sense. Nor can you find a
single publication in which a mathematician has claimed the union
above (i.e., the set N of natural numbers) contains an element larger
than every natural.
So, let's not get distracted by paths and whatsits. Just do what you
said you could do: show that ZF proves a contradiction. Either show
me that there is a natural k such that
| U_n {1,...,n} | = k
or show me that there is an element k in U_n {1,...,n} such that k is
larger than every natural number.
But don't distract us from the topic at hand.
Jesse F. Hughes
Mama: "I had a very good steak when I was in Bonn."
Quincy (Age 4): "A stick? I wish you brought it home. Was it very
big and did it look like a gun?" | {"url":"http://mathforum.org/kb/plaintext.jspa?messageID=8129767","timestamp":"2014-04-17T02:14:05Z","content_type":null,"content_length":"6539","record_id":"<urn:uuid:42a71123-0483-4c28-a197-03e19f7a134c>","cc-path":"CC-MAIN-2014-15/segments/1398223201753.19/warc/CC-MAIN-20140423032001-00238-ip-10-147-4-33.ec2.internal.warc.gz"} |
John and Jane started solving a quadratic equation. John mad
Question Stats:
90%9% (01:52)based on 71 sessions
itnas wrote:
John and Jane started solving a quadratic equation. John made a mistake while copying the constant term and got the roots as 5 and 9. Jane made a mistake in the coefficient of x and she got the roots
as 12 and 4.What is the equation?
a. x2 + 4x +14 =0
b. 2x2 +7x -24 =0
c. x2 -14x +48 =0
d. 3x2 -17x +52 =0
e. 2x2 + 4x +14 =0
I just solve it with (x-y)(x-y) aproach not sure if I was just lucky and landed on the right answer or if it does always work
So: John got values 9 and 5 for x; (x-5)(x-9)=0 --> x^2-14x+45=0 (his mistake 45)
Jane got values 12 and 4 for x; (x-12)(x-4)=0 --> x^2-16x+48=0 (her mistake 16x)
Eliminate mistakes and plug in the right values each picked: X^2-14x(from Jonhs equ)+48(from janes)=0
Guess that this might only work when X^2 does not have a multiplier...
Will be adding to my "Blackbook" Viete's formula for the roots.
This approach isn't incorrect. It is perfectly fine and Viete's formula is good to know (I assume it is discussed in detail in high school in most curriculums).
It will work even if the equation has a co-efficient other than 1 for x^2. Lets say, rather than x2 -14x +48 =0, the given equation in options is: 2x^2 - 28x +96 =0. It doesn't matter since 2 is
common to all terms and will be taken out and eliminated. So, in essence, the equation is still x2 -14x +48 =0.
Also if the equation is something like 4x^2 -28x + 45 =0, where nothing is common, the roots you obtain will reflect the co-efficient of x^2. i.e. roots of this equation are 5/2 and 9/2 and when you
put it in the (x-a)(x-b) = 0 form, you get:
(x - 5/2)(x - 9/2) = 0
x^2 - 14/2 x + 45/4 = 0
4x^2 - 28x + 45 = 0
So according to the given roots, you will always get the accurate equation. It might have something common in all the terms but that equation will still be the same.
Veritas Prep | GMAT Instructor
My Blog
Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.
Veritas Prep Reviews | {"url":"http://gmatclub.com/forum/john-and-jane-started-solving-a-quadratic-equation-john-mad-106597.html","timestamp":"2014-04-16T08:03:01Z","content_type":null,"content_length":"194304","record_id":"<urn:uuid:ba3a71de-eca3-46c3-8ac1-82044da26064>","cc-path":"CC-MAIN-2014-15/segments/1397609521558.37/warc/CC-MAIN-20140416005201-00616-ip-10-147-4-33.ec2.internal.warc.gz"} |
Dynamics of Galaxies - Giuseppe Bertin
© CAMBRIDGE UNIVERSITY PRESS 2000
13.5. Equations for the guiding centers
13.5.1. Larmor oscillations and drifts
We briefly recall the basic idea about the guiding center description of particle orbits ^(9) (see Fig. 13.6). Consider a charged particle (charge q, and mass m) moving in a constant magnetic field B
in the presence of a constant force F
Figure 13.6. Qualitative representation of the E × B drift (above) and magnetic gradient drift (below) for charged particles (from Krall, N.A., Trivelpiece, A.W. 1973, Principles of Plasma Physics,
McGraw-Hill, New York, pp.612, 625; with kind permission of the authors).
One can separate the equations in the parallel and perpendicular directions (with respect to the magnetic field)
then one separates the motion of the guiding center v[0] from the Larmor oscillation
so that
The resulting guiding center motion is given by the relation
from which it is evident that a perpendicular force produces a velocity and not an acceleration.
The more general, inhomogeneous and/or time-dependent, case where B and F are not constant can still be worked out with a similar strategy if the resulting drifts turn out to be slow and the basic
gyration frequency is sufficiently fast. For example, a gradient in B can be absorbed in F[] in Eq. (45). Some effects, such as those due to the curvature of the field, may require some detailed
analysis, which we do not need to record here ^(10). When the curvature is negligible, the parallel motion is basically reduced to solving the one-dimensional problem
where U is the potential associated with F[||] and µ = mv[]^2 / 2B is the adiabatic invariant associated with the Larmor gyration. Essentially the condition at the basis of this type of description
is that the variations in the magnetic field encountered by the particle on its orbit be slow with respect to the relevant cyclotron frequency.
13.5.2. Star drifts and stellar hydrodynamics
Much like in the case of Larmor gyrations of charged particles in a magnetic field, the epicyclic theory can be extended to the case of weakly non-axisymmetric and weakly time-dependent fields. This
tool allows one to gain a physical perception of the general properties of orbits without resorting to numerical surveys and well beyond the simple "small oscillations" that are considered in the
standard stability analysis of the Lagrangian points, as we briefly gave in the previous section. The specific theory in the context of stellar dynamics ^(11), formally developed for cool disks in
the vicinity of the relevant corotation radius, is based on the generalization of the definitions of angular and epicyclic frequency as:
where now guiding center orbits [r[0](t), [0](t)] can be derived from an effective Jacobi integral
where E[0] generalizes the concept of energy associated with the circular orbits Eq. (12):
The relevant equations of the motion are:
The second term on the right-hand-side of Eq. (53) corresponds to the well known polarization drift of plasma physics. It should be stressed that in the presence of rotation the perturbation forces
induce drift velocities in the motion of the guiding centers and not accelerations.
The complete properties of the orbits are then obtained by combining the information on the motion of the guiding centers with the fact that the adiabatic invariant µ is essentially constant:
where H is the star "Jacobi integral", which depends on the physical coordinates (r,
When the perturbing potential is time-independent, the guiding center orbits are then simply obtained as contours of the function H[0](r[0], [0]). The Lagrangian points of the star orbit analysis
described above are then recovered as stationary points for H[0]; their stability properties are easily reconstructed by inspection of the relevant Hessian. If one takes as a perturbation a two-armed
spiral potential of the form given in Eq. (32), one finds that the contours of constant H[0] identify two islands at corotation connected by a separatrix passing through the unstable potential minima
(see Fig. 13.7). Outside the islands, moving away from corotation either inside or outside the corotation circle, the contours are in the form of distorted circles. This new shear flow configuration
should be compared with the unperturbed shear flow. The trapped orbits at the stable Lagrangian points define some kind of "cat's eyes" ^(12). There is a clear analogy with the structure of magnetic
islands that originate in plasma configurations via magnetic reconnection ^(13).
Figure 13.7. Vorticity islands marked by the guiding center orbits (in the corotating frame) in an axisymmetric disk in the presence of a two-armed rigidly rotating spiral field (from Berman, R.,
Mark, J.W-K. 1979, Astrophys. J., 231, 388). The structures created are reminiscent of magnetic islands that may result from reconnection in sheared magnetic configurations or cat's eyes that may
originate from a shear flow. The lower frame shows full orbits, which can be seen as a result of the superposition of the slow libration of the guiding center and the rapid epicyclic oscillation (see
also Contopoulos, G. 1973, Astrophys. J., 181, 657).
The concepts introduced in the present short Section find many applications in the context of magnetically confined plasmas, in particular in the description of trapped and circulating particles in
toroidal plasma configurations ^(14). We will not pursue here these sources of analogies any further. In closing, we may just briefly refer to another development, which is conceptually very
interesting. For a collisionless system it is possible to construct fluid equations from the moments of the collisionless Boltzmann equation (see Chapter 8). In the absence of collisions, a well
known problem is how to close the fluid equations into a finite set, or, in more physical terms, how to define an appropriate equation of state. This question has found a solution in plasma physics
in terms of the so-called double adiabatic theory ^(15), which makes use of the conservation of the adiabatic invariant to set a constraint equivalent to that of an equation of state. This leads to
the justification of MHD-like equations for a collisionless plasma, with the peculiarity that pressure is to be considered anisotropic. It should be stressed that the closure is obtained under a set
of assumptions that make the double adiabatic theory applicable only to a rather limited class of perturbations. Still the procedure is very interesting, especially from the physical point of view. A
similar theory has been worked out for the context of the stellar dynamics of galaxy disks ^(16).
^9 For example, see Schmidt, G. (1979), Physics of High Temperature Plasmas, 2nd edition, Academic Press, New York. Back.
^10 See the book by Schmidt mentioned earlier; see also Krall, N.A., Trivelpiece, A.W. (1973), Principles of Plasma Physics, McGraw-Hill, New York Back.
^11 Berman, R.H. (1975), Ph. D. Thesis, Massachusetts Institute of Technology; Berman, R.H., Mark, J. W-K. (1977), Astrophys. J., 216, 257; Berman, R.H., Mark, J. W-K. (1979), Astrophys. J., 231, 388
^12 Kelvin, Lord (1880), Nature, 23, 45 Back.
^13 See, e.g., White, R. (1983), Handbook of Plasma Physics, I, edited by A.A. Galeev, R.N. Sudan, North-Holland. Back.
^14 Bertin, G., Coppi, B., Taroni, A. (1977), Astrophys. J., 218, 92 Back.
^15 Chew, G.F., Goldberger, M.L., Low, F.E. (1956), Proc. R. Soc. London A, 236, 112 Back.
^16 see Berman; Berman and Mark, op.cit. Back. | {"url":"http://ned.ipac.caltech.edu/level5/Sept02/Bertin/Bertin13_5.html","timestamp":"2014-04-16T10:27:27Z","content_type":null,"content_length":"14887","record_id":"<urn:uuid:341df013-76d8-4c69-8dc2-b1c0358a64a2>","cc-path":"CC-MAIN-2014-15/segments/1398223206647.11/warc/CC-MAIN-20140423032006-00217-ip-10-147-4-33.ec2.internal.warc.gz"} |
User Chris Pressey
bio website catseye.tc
visits member for 1 year, 4 months
seen Dec 16 '12 at 20:49
stats profile views 43
My main interest is in the design of pathological programming languages. While this subject is not entirely (perhaps not even primarily) mathematical, it does rely significantly on results from
computability, complexity theory, and formal languages. Results from pretty much any field are welcome additions if they can be applied to the design of a programming language to make it (more)
pathological. Currently I am somewhat interested in the possibilities of abstract algebra in this regard.
Mathematics 183 rep 11
Theoretical Computer Science 150 rep 16
MathOverflow 90 rep 7
Computer Science 76 rep 6
85 Votes Cast
all time by type
85 up 25 question
0 down 60 answer | {"url":"http://mathoverflow.net/users/29482/chris-pressey?tab=stats","timestamp":"2014-04-18T21:53:12Z","content_type":null,"content_length":"55514","record_id":"<urn:uuid:ff950b52-933d-4c08-a600-603bf546c702>","cc-path":"CC-MAIN-2014-15/segments/1398223203235.2/warc/CC-MAIN-20140423032003-00077-ip-10-147-4-33.ec2.internal.warc.gz"} |
rational map becomes a morphism after blow-ups
up vote 1 down vote favorite
In dimension 2, a rational map becomes a morphism after a sequence of blow-ups. Does this still hold in higher dimensions?
2 In light of the comments under abx's answer, it might be a good idea to clarify the question a bit; in particular, do you require the blow-ups to be along smooth centers? – Artie Prendergast-Smith
Nov 23 '13 at 22:21
add comment
1 Answer
active oldest votes
Yes, but this is a very difficult result, due to Hironaka. To be precise : given a rational map $f:X --> Y$, there exists a birational morphism $b:\hat{X}\rightarrow X$, obtained as the
up vote 6 composition of successive blown-up with smooth centers, such that $f\circ b$ is a morphism.
down vote
Thank you. Do you have a reference? Or is this just in Hironaka's article on resolution of singularities? – Timo Keller Nov 23 '13 at 12:59
9 Actually, you do not need Hironaka at all. Let $X$ and $Y$ be projective schemes. Let $f$ be a morphism from a dense open subset $U$ of $X$ to $Y$. Let $\Gamma_f$ be the graph of $f$
inside $X\times Y$. Let $\widehat{X}$ be the Zariski closure of $\Gamma_f$. Then the projection, $b:\widehat{X}\to X$, is a projective, birational morphism. Thus, by a theorem in Chapter
II, Section 7 of Hartshorne's "Algebraic Geometry", the morphism $b$ is (isomorphic to) the blowing up of $X$ along a coherent sheaf of ideals. – Jason Starr Nov 23 '13 at 13:03
3 @Jason: that's right, of course, but I believe the OP meant blow-ups with smooth centers (and rational map of smooth varieties). – Serge Lvovski Nov 23 '13 at 14:56
1 @Timo Keller: Yes, this is in Hironaka's paper (Resolution of singularities of an algebraic variety over a field of characteristic zero", Ann. Of Math. (2) 79, 109–326. The statement is
explained in CH. 0, §5. – abx Nov 23 '13 at 17:40
@Serge and abx: Okay, that makes sense to me. – Jason Starr Nov 23 '13 at 18:14
add comment
Not the answer you're looking for? Browse other questions tagged ag.algebraic-geometry or ask your own question. | {"url":"http://mathoverflow.net/questions/149714/rational-map-becomes-a-morphism-after-blow-ups/149716","timestamp":"2014-04-19T19:45:22Z","content_type":null,"content_length":"57158","record_id":"<urn:uuid:d74f4f87-903b-4fad-9894-58d7349d0648>","cc-path":"CC-MAIN-2014-15/segments/1397609537376.43/warc/CC-MAIN-20140416005217-00142-ip-10-147-4-33.ec2.internal.warc.gz"} |
Paradox Algorithm in Application of a Linear Transportation Problem
Osuji George A.^1, , Opara Jude^2, Nwobi Anderson C.^3, Onyeze Vitus^2, Iheagwara Andrew I.^4
^1Department of Statistics, Nnamdi Azikiwe University, Awka Anambra State Nigeria
^2Department of Statistics, Imo State University, Owerri Nigeria
^3Department of Statistics, Abia State Polytechnic, Aba Nigeria
^4Department of Planning, Research and Statistics, Ministry of Petroleum and Environment Owerri Imo State Nigeria
Paradox seldom occurs in a linear transportation problem, but it is related to the classical transportation problem. For specific reasons of this problem, an increase in the quantity of goods or
number of passengers (as used in this paper) to be transported may lead to a decrease in the optimal total transportation cost. Two numerical examples were used for the study. In this paper, an
efficient algorithm for solving a linear programming problem was explicitly discussed, and it was concluded that paradox does not exist in the first set of data, while paradox exists in the second
set of data. The Vogel’s Approximation Method (VAM) was used to obtain the initial basic feasible solution via the Statistical Software Package known as TORA. The first set of data revealed that
paradox does not exist, while the second set of data showed that paradox exists. The method however gives a step by step development of the solution procedure for finding all the paradoxical pair in
the second set of data.
Keywords: transportation paradox, paradoxical range of flow, transportation problem, linear programming, paradoxical pair, VAM
American Journal of Applied Mathematics and Statistics, 2014 2 (1), pp 10-15.
DOI: 10.12691/ajams-2-1-3
Received December 14, 2013; Revised December 23, 2013; Accepted January 05, 2014
© 2013 Science and Education Publishing. All Rights Reserved.
Cite this article:
• A., Osuji George, et al. "Paradox Algorithm in Application of a Linear Transportation Problem." American Journal of Applied Mathematics and Statistics 2.1 (2014): 10-15.
• A., O. G. , Jude, O. , C., N. A. , Vitus, O. , & I., I. A. (2014). Paradox Algorithm in Application of a Linear Transportation Problem. American Journal of Applied Mathematics and Statistics, 2
(1), 10-15.
• A., Osuji George, Opara Jude, Nwobi Anderson C., Onyeze Vitus, and Iheagwara Andrew I.. "Paradox Algorithm in Application of a Linear Transportation Problem." American Journal of Applied
Mathematics and Statistics 2, no. 1 (2014): 10-15.
Import into BibTeX Import into EndNote Import into RefMan Import into RefWorks
1. Introduction
Paradox occurs when a transportation problem admits of a total cost which is lower than the optimum and is attainable by shipping larger quantities of goods over the same routes that were previously
designated as optimal. This phenomenon which does not occur regularly was discovered by Szwarc (1971). It is obvious that many researchers have discovered independently from each other the following
behavior of the transportation problem. In certain cases of the Transportation Problem (TP), an increase in the supplies and demands may lead to a decrease in the optimal transportation cost. In
other words, by moving bigger amount of goods around, one may save a lot of money. This surely sounds paradoxical (Deineko, et al.; 2003).
The classical transportation problem is the name of a mathematical model which has a special mathematical structure. The mathematical formulation of a large number of problems conforms to this
special structure. Hitchcock (1941) originally developed the basic linear transportation problem. Charnes et al (1953) developed the stepping stone methods which provide an alternative way of
determining the simplex method information. Dantzig (1963) used the simplex method to the transportation problem as the primal simplex transportation method. Appa (1973) also developed the solution
procedure for solving the transportation problem and its variants. Klingman and Russel (1974 and 1975) introduced a specialized method for solving a transportation problem with several additional
linear constraints. Hadley (1987) gave the detailed solution procedure for solving linear transportation problem. Till date, several researchers studied extensively to solve cost minimizing
transportation problem in various ways.
In some situations, if we obtain more flow with lesser cost than the flow corresponding to the optimum cost then we say paradox occurs. Charnes and Klingman (1971), Szwarc (1973), Adlakha and
Kowalski (1998) and Storoy (2007) considered the paradoxical transportation problem. Gupta et al (1993) considered a paradox in linear fractional transportation problem with mixed constraints. Joshi
and Gupta (2010) studied paradox in linear plus fractional transportation problem. In the early day of linear programming problem some of the pioneers observed paradox but by whom no one knows.
In this paper we present a method for solving transportation problem with linear constraints. Thereby, we state the sufficient condition of existence of paradox, paradoxical range of flow and
paradoxical flow for a specified flow in such type of linear transportation problem. We also justify the theory by illustrating a numerical example.
2. Definitions
1. Paradox in a transportation problem: in a transportation problem if we can obtain more flow (F^1) with lesser cost (Z^1) than the optimum flow (F^0) corresponding to the optimum cost (Z^0) i.e. F^
1 > F^0 and Z^1 < Z^0, then we say that a paradox occurs in a transportation problem.
2. Cost-flow pair: if the value of the objective function is Z^0 and the flow is F^0 corresponding to the feasible solution X^0 of a transportation problem, then the pair (Z^0, F^0) is called the
cost-flow pair corresponding to the feasible solution X^0.
3. Paradoxical pair: A cost-flow pair, (Z, F) of an objective function is called paradoxical pair if Z < Z^0 and F > F^0 where Z^0 is the optimum cost and F^0 is the optimum flow of the
transportation problem.
4. Best paradoxical pair: The paradoxical pair (Z*, F*) is called the best paradoxical pair of a transportation problem if for all paradoxical pair (Z, F), either Z* < Z or Z* = Z but F* > F.
5. Paradoxical range of flow: if F^0 be the optimum flow and F* be the flow corresponding to the best paradoxical pair of a transportation problem then [F^0, F*] is called paradoxical range of flow.
3. Review of Related Literature
The transportation paradox is, however, hardly mentioned at all in any of the great number of textbooks and teaching materials where the transportation problem is treated. Apparently, several
researchers have discovered the paradox independently from each other. But most papers on the subject refer to the paper by Charines and Klingman (1971) and Szwarc (1971) as the initial papers. In
Charines and Klingman (1971) name it the more-for-less paradox and they write: “The paradox was first observed in the early days of linear programming history (by whom no one knows) and has been part
of the folklore known to some (e.g. A. Charnes and Cooper; 1953) but unknown to the great majority of workers in the field of linear programming.
Arora and Ahuja (2010) carried out a research work in paradox on a fixed charge transportation problem. In their findings, a paradox arises when the fixed charge transportation problem admits of a
total cost which is lower than the optimum cost, by transporting larger quantities of goods over the same routes. A sufficient condition for the existence of a paradox is established. Paradoxical
Range of flow is obtained for any given flow in which the corresponding objective function value is less than the optimum value of the fixed charge transportation problem.
Ekezie et al (2013) carried out a research on the determination of paradoxical pairs in a linear transportation problem. In their study, an efficient algorithm for solving a linear programming
problem was discussed, and it was concluded that paradox exists. The North-West Corner method was used to obtain the initial basic feasible solution for the optimal solution. They also used the
algorithm discussed to develop a step by step solution procedure for finding all the paradoxical pairs.
According to Appa (1973), the transportation paradox is known as Doigs paradox at the London School of Economics, named after Alison Doig who used it in exams etc around 1959 (Doig did not publish
any paper on it).
Since the transportation paradox seems not to be known to the majority of those who are working with (or teaching) the transportation problem, one may be tempted to believe that this phenomenon is
only an academic curiosity which will most probably not occur in any practical situation. But that seems not to be true. Experiments done by Finke (1978), with randomly generated instances of the
transportation problem of size 100 100 and allowing additional shipments (post-optimal) show that the paradoxical properties. More precisely, the average cost reductions achieved are reported to be
18.6% with total additional shipments of 20.5%.
Ekezie et al (2013) carried out a research on the Paradox sum of a linear and a linear fractional transportation problem using data that were collected from a secondary source. In the study, a
transportation problem with an objective function as the sum of a linear and linear fractional function was considered. A paradoxical situation arises in the sum of a linear and linear fractional
transportation problem, when value of the objective function falls below the optimal value and this lower value is attainable by transporting larger number of passengers. An algorithm is proposed for
finding initial basic feasible solution for the sum of a linear and linear fraction transportation problem and a sufficient condition for the existence of a paradoxical solution is established.
In a recent paper (2003), Deineko et al developed necessary and sufficient conditions for a cost matrix C to be immune against the transportation paradox. As well see in the next section, these
conditions are rather restrictive, supporting the observations by Finke.
4. Problem Formulation
In this paper, we consider the following transportation problem:
Let the transportation problem consists of m sources and n destinations, where
x[ij] = the amount of product transported from the ith source to the jth destination,
c[ij] = the cost involved in transporting per unit product from the ith source to the jth destination,
a[i] = the number of units available at the ith source,
b[j] = the number of units required at the jth destination.
In this paper, we consider the cost minimizing linear transportation problem as:
subject to the constraints
Let [1] and the value of the objective function Z^0 corresponding to the basic feasible solution X^0 is
Let F^0 be the corresponding flow.
Now we consider the dual variables u[i] for i ∈ I and j ∈ I such that u[i] + v[j] = c[ij] corresponding to the basis B.
Also ∀(I, j)∉B, let
Theorem: the sufficient condition for the existence of paradoxical solution of (P[1]) is that if ∃ at least one cell (r, s) ∉ B in the optimum table of (P[1]) where a[r] and b[s] are replaced by a[r]
+ l and b[s] + l respectively (l > 0) then (u[r] + v[s]) < 0.
Proof: Let Z^0 be the value of the objective function and F^0 be the optimum flow corresponding to the optimum solution (X^0) of problem (P[1]). The dual variables u[i] and v[j] are given by
Now, let ∃ at least one cell (r, s)∉B, where a[r] are replaced by a[r] + l and b[s] + l, respectively (l > 0) in such a way that the optimum basis remains same, then the value of the objective
The new flow
Therefore for the existence of paradox we must have [r] and b[s] are replaced by a[r] + l and b[s] + l (l > 0) then l( + v[s]) < 0, i.e. (u[r] + v[s]) < 0.
Now we state the following algorithm to find all the paradoxical pair of the problem (P[1]).
Step 1: Find the cost-flow pair (Z^0, F^0) for the optimum solution X^0.
Step 2: i = 1
Step 3: Find all cells (r, s)∉B such that (u[r] + v[s]) < 0 if it exists otherwise go to step 8.
Step 4: Among all cells (r, s) ∉B satisfying step 3 find min flow for l = 1 which enter into the existing basis whose corresponding cost is minimum. Let (Z^i, F^i) be the new cost flow pair
corresponding to the optimum solution X^i.
Step 5: Write (Z^i, F^i).
Step 6: i = i + 1.
Step 7: go to step 3
Step 8: We write the best paradoxical pair (Z*, F*) = (Z^i, F^i) for the optimum solution X* = X^i.
Step 9: End.
This algorithm gives all the paradoxical pairs. From these pairs we can find the paradoxical pair for a specified flow () also.
5. Data Analysis
In this paper, we shall use three sets of data to enable us achieve our primary aim. Firstly, we shall examine the data gotten from ABC Transport Company, owerri . ABC Transport Company Ltd has many
types of buses that ply different routes in . In this study, we shall restrict the work to only 6 different types of buses that ply 4 different routes in . Table 1 shows the expected number of
passengers each type of bus can carry in a day, and the cost of transporting a passenger from Owerri to the different routes in Nigeria by each of the buses.
Solving the transportation problem in Table 1, the result is displayed in Table 2.
The total cost of transportation is N2, 454,440. We then check the sign of (U[r] + V[s]), where (r, s) ∉ B in Table 2, we observe that all the U[i’s] + V[j’s] > 0. With this result, we can conclude
that paradox does not exist, which implies that the algorithm discussed in this paper will be irrelevant to this set of data.
Let us now consider the second set of data used for this research, which was extracted from Opara (2009), Introduction to Operation Research, Exercises 3 page 28. The estimated supply capacities of
the six warehouses, the demand requirements at the seven markets and the transportation cost of each product are given in Table 3.
Solving the above problem using the Vogel’s Approximation Method (VAM), the optimal transportation table is presented in Table 4.
The total cost is 759. We then check the sign of (U[r] + V[s]), where (r, s) ∉ B in Table 4, we observe that U[5] + V[3] = -3 < 0, and U[5] + V[5] = - 1 < 0. This implies that Paradoxical pair of the
problem (P[1]) exists. So applying the algorithm discussed in this paper, we have;
Applying Step 1: The cost-flow pair is (Z^o, F^o) = (759, 173) corresponding to the optimum solution X = {x[12] = 13, x[13] = 34, x[14] = 13, x[22] = 16, x[25] = 17, x[26] = 6, x[31] = 26, x[34] = 7,
x[41] = 20, x[52] = 3, x[61] = 3, x[67] = 5}.
Applying step 2: set i=1
Applying step 3: Now we check the sign of (U[r] + V[s]) and we obtain for the non-basic cells (5, 3) and (5, 5), the sign that is negative.
Applying step 4: For l = 1
For the cell (5, 3)
The total cost of this transportation problem is 756.
For cell (5, 5), the transportation table is presented in Table 6.
The total cost of this transportation problem is 758.
The min cost = min{756, 758} = 756.
Hence l = 1 enters in the optimum basis from the cell (5, 3) and corresponding table is Table 5, the corresponding paradoxical pair (Z′, F′) = (756, 174).
Employing steps 6 and 7. Then repeating this process, the next table is
Now repeating this process, the final table is presented in Table 8.
Hence, from the above table, the corresponding paradoxical pair (Z′, F′) = (720, 186).
Applying step 8: The best paradoxical pair is (Z*, F*) = (720, 186) corresponding to the optimum solution is X* = {x[12] = 0; x[13] = 47, x[14] = 13, x[22] = 16, x[25] = 17, x[26] = 6, x[31] = 26, x
[34] = 7, x[41] = 20, x[52] = 26, x[61] = 3, x[67] = 5} and the paradoxical range of flow is [F^0, F*] = [173, 186]. Thus, all the paradoxical pairs are {(756, 174), (753, 175), (750, 176), (747,
177), (744, 178), (741, 179), (738, 180), (735, 181), (732, 182), (729, 183), (726, 184), (723, 185) and (720, 186).
Let us consider the third set of data from this hypothetical example for more clarification of the algorithm. The estimated supply capacities of the five warehouses, the demand requirements at the
five markets and the transportation cost of each product are given in Table 8.
Solving the above problem using VAM via TORA Statistical Software Package, the optimal transportation table is presented in Table 10.
The total cost is 320. Again, we then check the sign of (U[r] + V[s]), where (r, s) ∉ B in Table 10, we observe that U[2] + V[5] = -2 < 0, U[3] + V[5] = - 1 < 0, and U[4] + V[5] = - 1 < 0. So,
paradoxical pairs exist.
Applying Step 1: The cost-flow pair is (Z^o, F^o) = (320, 142) corresponding to the optimum solution X = {x[11] = 6, x[12] = 26, x[14] = 3, x[15] = 10, x[21] = 35, x[31] = 3, x[33] = 27, x[44] = 22,
x[52] = 10}.
Applying step 2: set i=1
Applying step 3: Now we check the sign of (U[r] + V[s]) and we obtain for the non-basic cells (2,5), (3,5) and (4,5), the sign that is negative.
Applying step 4: For l = 1
For the cell (2, 5)
The total cost of this transportation problem is 318.
For cell (3, 5), the transportation tableau is presented in Table 12.
The total cost of this transportation problem is 319.
For the cell (4, 5), the transportation tableau is presented in Table 13.
The total cost is 319.
The min cost = min {318, 319, 319} = 318.
Hence l = 1 enters in the optimum basis from the cell (2, 5) and corresponding table is Table 10, the corresponding paradoxical pair (Z′, F′) = (318, 143).
Employing steps 6 and 7. Then repeating this process again, the next tableau is
Now repeating this process, the final table is presented in Table 15.
Hence, from the above table, the corresponding paradoxical pair (Z′, F′) = (308, 148).
Applying step 8: The best paradoxical pair is (Z*, F*) = (308, 148) corresponding to the optimum solution is X* = {x[11] = 0; x[12] = 26, x[14] = 3, x[15] = 16, x[21] = 41, x[31] = 3, x[33] = 27, x
[44] = 22, x[52] = 10} and the paradoxical range of flow is [F^0, F*] = [142, 148]. Thus, all the paradoxical pair are {(318, 143), (316, 144), (314, 145), (312, 146), (310, 147), and (308, 148)}.
6. Conclusion
In this paper, an attempt has been made to discuss an efficient statistical algorithm for computing paradox in a linear transportation problem if paradox does exist. The algorithm gives step by step
development of the solution procedure for finding all the paradoxical pair where paradox exists, well understanding. The statistical software package known as “TORA” was used to obtain the optimal
solution before adopting the algorithm of paradoxical pairs.
Future research should be done on a related work like in this paper, and the author should try to develop a program that will enable one to obtain the best paradoxical pairs instead of solving it
manually, and as well the paradoxical range of flow.
[1] Adlakha V. and Kowalski, K. (1998): A quick sufficient solution to the more-for-less paradox in a transportation problem, Omega 26(4):541-547.
[2] Appa G.M. (1973): The Transportation problem and its variants, Oper. Res. Q. 24:79-99.
[3] Arora S.R. and Ahuja A. (2000): A paradox in a fixed charge transportation problem. Indian J. pure appl. Math., 31(7): 809-822, July 2000 printed in India.
[4] Charnes A.; Cooper W.W. and Henderson (1953): An Introduction to Linear programming (Wiley, New Work).
[5] Charnes A. and Klingman D. (1971): The more-for-less paradox in the distribution model, Cachiers du Centre Etudes de Recherche Operaionelle 13; 11-22.
[6] Deineko, V.G; Klinz, B and Woeginger, G.J. (2003): Which Matrices are Immune against the Transportation Paradox? Discrete Applied Mathematics, 130:495-501.
[7] Dantzig, G.D. (1963): Linear Programming and Extensive (Princeton University Press, NJ).
[8] Dantzig G.B. (1951): Application of the simplex method to a transportation problem, in Activity Analysis of Production and Allocation (T.C. Koopmans, ed.) Wiley, New York, pp.359-373.
[9] Ekezie, D.D.: Ogbonna, J.C. and Opara, J. (2013): The Determination of Paradoxical Pairs in a Linear Transportation Problem. International Journal of Mathematics and Statistics Studies. Vol. 1,
No. 3, p.p.9-19, September 2013.
[10] Finke, G.(1978): A unified approach to reshipment, overshipment and postoptimization problems, lecture notes in control and information science, Vol.7, Springer, Berlin, 1978, p.p.201-208.
[11] Gupta, A. Khanna S and Puri, M.C. (1993): A paradox in linear fractional transportation problems with mixed constraints, Optimization 27:375-387.
[12] Hadley G. (1987): Linear Programming (Narosa Publishing House, New Delhi).
[13] Hitchcock, F.L. (1941): The distribution of a product from several resources to numerous localities, J. Math. Phys. 20:224-230.
[14] Joshi, V. D. and Gupta, N. (2010): On a paradox in linear plus fractional transportation problem, Mathematika 26(2):167-178.
[15] Opara, J. (2009): Manual on Introduction to Operation Research, Unpublished.
[16] Klingman, D. and Russel, R. (1974): The transportation problem with mixed constraints, operational research quarterly, Vol. 25, No. 3: p.p. 447-455.
[17] Klingman, D. and Russel, R. (1975): Solving constrained transportation problems, Oper. Res. 23(1):91-105.
[18] Storoy, S. (2007): The transportation paradox revisited, N-5020 Bergen, Norway.
[19] Szwarc W. (1971): The transportation paradox, Nav. Res. Logist. Q.18:185-202. | {"url":"http://pubs.sciepub.com/ajams/2/1/3/index.html","timestamp":"2014-04-16T13:53:58Z","content_type":null,"content_length":"96708","record_id":"<urn:uuid:7f94d825-a9c5-4904-ae2e-51a372593f15>","cc-path":"CC-MAIN-2014-15/segments/1398223203841.5/warc/CC-MAIN-20140423032003-00425-ip-10-147-4-33.ec2.internal.warc.gz"} |
AARTS, E.H.L.: Simulated Annealing: Theory and Applications
, 2000
"... INTRODUCTION In this paper we consider Simulated Annealing algorithms (SA in what follows) applied to continuous global optimization problems, i.e. problems with the following form f = min x2X f
(x); (1.1) where X ` ! n is a continuous domain, often assumed to be compact, which, combined with ..."
Cited by 30 (1 self)
Add to MetaCart
INTRODUCTION In this paper we consider Simulated Annealing algorithms (SA in what follows) applied to continuous global optimization problems, i.e. problems with the following form f = min x2X f(x);
(1.1) where X ` ! n is a continuous domain, often assumed to be compact, which, combined with the continuity or lower semicontinuity of f , guarantees the existence of the minimum value f . SA
algorithms are based on an analogy with a physical phenomenon: while at high temperatures the molecules in a liquid move freely, if the temperature is slowly decreased the thermal mobility of the
molecules is lost and they form a pure crystal which also corresponds to a state of minimum energy. If the temperature is decreased too quickly (the so called quenching) a liquid metal rather ends up
in a polycrystalline or amorphous state with
- IEEE Transactions on Evolutionary Computation , 2000
"... Finding the degree-constrained minimum spanning tree (d-MST) of a graph is a well studied NP-hard problem which is important in network design. We introduce a new method which improves on the
best technique previously published for solving the d-MST, either using heuristic or evolutionary app ..."
Cited by 11 (0 self)
Add to MetaCart
Finding the degree-constrained minimum spanning tree (d-MST) of a graph is a well studied NP-hard problem which is important in network design. We introduce a new method which improves on the best
technique previously published for solving the d-MST, either using heuristic or evolutionary approaches. The basis of this encoding is a spanning-tree construction algorithm which we call the
Randomised Primal Method (RPM), based on the well-known Prim's algorithm [6], and an extension [4] which we call `d-Prim's'. We describe a novel encoding for spanning trees, which involves using the
RPM to interpret lists of potential edges to include in the growing tree. We also describe a random graph generator which produces particularly challenging d-MST problems. On these and other
problems, we find that an evolutionary algorithm (EA) using the RPM encoding outperforms the previous best published technique from the operations research literature, and also outperforms
- In: 1st Austrian - Hungarian Workshop on Distributed and Parallel Systems , 1996
"... Abstract: This paper describes the static and dynamic task allocation tools in PVM environment for distributed memory parallel systems. For the static mapping the objective function is used to
evaluate the optimality of the allocation of a task graph onto a processor graph. Together with our optimiz ..."
Cited by 2 (0 self)
Add to MetaCart
Abstract: This paper describes the static and dynamic task allocation tools in PVM environment for distributed memory parallel systems. For the static mapping the objective function is used to
evaluate the optimality of the allocation of a task graph onto a processor graph. Together with our optimization method also augmented simulated annealing and heuristic move exchange methods in the
distributed form are implemented. For dynamic task allocation the semidistributed approach was designed based on the division of processor network topology into independent and symmetric spheres.
Distributed static mapping (DSM) and dynamic load balancing (DLB) tools are controlled by user window interface. DSM and DLB tools are integrated together with software monitor (PG_PVM) in GRAPNEL
environment. Optimal planning of parallel program execution in a distributed memory parallel computer (DMPC) solves the response speed. Optimal allocation comes out from the assumption that the
program execution time depends upon uniform load of the processors and upon interprocessor communication minimization. In this paper, our attention is concentrated on the diffusion method for static
mapping and on the semidistributed approach for the dynamic task allocation. In our distributed static mapping tool also augmented simulated annealing and heuristic move exchange methods are
implemented [1], [2]. To specify an appropriate optimization goal it is necessary to create a cost function, which provides a realistic evaluation of the communication and computation overhead. For
the given graphs S (task
"... Development of the high performance parallel computer systems suffers today from lack of the software that would allow simple programmingwith consequent optimal and safe program execution. The
main goal of the research for this scope is to provide a programming environment that allows applicatio ..."
Cited by 1 (0 self)
Add to MetaCart
Development of the high performance parallel computer systems suffers today from lack of the software that would allow simple programmingwith consequent optimal and safe program execution. The main
goal of the research for this scope is to provide a programming environment that allows application programmers to develop parallel programs without worrying about the physical machine they are
programming. This paper presents the mapping algorithm for distributed memory, parallel message passing systems using an objective function to evaluate the optimality of mapping a task graph onto
processor graph. Our optimization method is compared with other ones, some of them issuing from artificial intelligence or operations research. In our experiments randomly generated tasks and
processors graphs are used. Different approaches were compared with regard to these criterions: mapping success, relative difference of solution, relative quality. 1.
"... Abstract. In this paper, we demonstrate the ease in which an adaptive simulated annealing algorithm can be designed. Specifically, we use the adaptive annealing schedule known as the modified
Lam schedule to apply simulated annealing to the weighted tardiness scheduling problem with sequence-depende ..."
Cited by 1 (1 self)
Add to MetaCart
Abstract. In this paper, we demonstrate the ease in which an adaptive simulated annealing algorithm can be designed. Specifically, we use the adaptive annealing schedule known as the modified Lam
schedule to apply simulated annealing to the weighted tardiness scheduling problem with sequence-dependent setups. The modified Lam annealing schedule adjusts the temperature to track the theoretical
optimal rate of accepted moves. Employing the modified Lam schedule allows us to avoid the often tedious tuning of the annealing schedule; as the algorithm tunes itself for each instance during
problem solving. Our results show that an adaptive simulated annealer can be competitive when compared to highly tuned, hand crafted algorithms. Specifically, we compare our results to a
state-of-theart genetic algorithm for weighted tardiness scheduling with sequence-dependent setups. Our study serves as an illustration of the ease with which a parameter-free simulated annealer can
be designed and implemented. 1
"... : This paper describes the mapping algorithm for distributed memory, parallel message passing systems using the objective function to evaluate the optimality of the mapping of a task graph onto
a processor graph. Our optimization method is compared with other ones, some of them issuing from artifici ..."
Add to MetaCart
: This paper describes the mapping algorithm for distributed memory, parallel message passing systems using the objective function to evaluate the optimality of the mapping of a task graph onto a
processor graph. Our optimization method is compared with other ones, some of them issuing from artificial intelligence or operations research. In our experiments randomly generated tasks and
processor graphs are used. Keywords: static and dynamic mapping, multicomputer, scheduling, load balancing, smoothing. 1 Introduction Optimal planning of parallel program execution in distributed
environment of a multicomputer on the basis of message passing solves the response speed. Static and dynamic mappings can be available and effective way of solution. The theory of optimal mapping
comes out from the assumption that the program execution time depends upon uniform load of the processors and upon interprocessor communication minimization. In this paper, our attention is
concentrated on the diffusio...
"... : This paper describes the mapping algorithm for distributed memory, parallel message passing systems using the objective function to evaluate the optimality of the mapping of a task graph onto
a processor graph. Our optimisation method is compared with other ones, some of them issuing from artifici ..."
Add to MetaCart
: This paper describes the mapping algorithm for distributed memory, parallel message passing systems using the objective function to evaluate the optimality of the mapping of a task graph onto a
processor graph. Our optimisation method is compared with other ones, some of them issuing from artificial intelligence or operations research. In our experiments randomly generated tasks and
processor graphs are used. Keywords: static and dynamic mapping, multicomputer, scheduling, load balancing, smoothing. 1 Introduction Optimal planning of parallel program execution in distributed
environment of a multicomputer on the basis of message passing solves the response speed. The theory of optimal mapping comes out from the assumption that the program execution time depends upon
uniform load of the processors and upon interprocessor communication minimisation. In this paper, our attention is concentrated on the diffusion method for static mapping. For static mapping a
parallel program can be re...
"... : This paper describes the static and dynamic task allocation tool under PVM environment for distributed memory parallel systems. For the static allocation the objective function is used to
evaluate the optimality of the allocation of a task graph onto a processor graph. Toghether with our optimisat ..."
Add to MetaCart
: This paper describes the static and dynamic task allocation tool under PVM environment for distributed memory parallel systems. For the static allocation the objective function is used to evaluate
the optimality of the allocation of a task graph onto a processor graph. Toghether with our optimisation method also augmented simulated annealing and heuristic move exchange methods are implemented.
For dynamic task allocation the semidistributed approach was designed based on the division of processor network topology into independent and symmetric spheres. S&D task allocation tool is
controlled by user window interface - allocation toolbox. Keywords: distributed memory parallel systems, static and dynamic allocation, multicomputer, load balancing. 1 Introduction Optimal planning
of parallel program execution in distributed environment of a multicomputer on the basis of message passing solves the response speed. The theory of optimal allocation comes out from the assumption
that the pr... | {"url":"http://citeseerx.ist.psu.edu/showciting?cid=1989662","timestamp":"2014-04-16T13:21:16Z","content_type":null,"content_length":"33305","record_id":"<urn:uuid:c4039899-d1d2-465e-8695-1f82d4ecc8a2>","cc-path":"CC-MAIN-2014-15/segments/1397609523429.20/warc/CC-MAIN-20140416005203-00586-ip-10-147-4-33.ec2.internal.warc.gz"} |
2005-2006 UAF Catalog
College of Natural Science and Mathematics
Department of Mathematical Sciences
(907) 474-7332
Minimum Requirements for Degrees: M.A.T.: 36 credits; M.S.: 30-35 credits; Ph.D.: 18 thesis credits
Downloadable PDF (58K)
The number of new fields in which professional mathematicians find employment grows continually. This department prepares students for careers in industry, government and education.
The M.S. in mathematics prepares students for Ph.D. work, in addition to providing a terminal degree for those planning to enter industry or education. The M.A.T. degree prepares graduates to teach
secondary school mathematics. The aim of the Ph.D. program is to provide the student with the expertise to accomplish significant research in applied or pure mathematics, as well as to provide a
broad and deep professional education.
In addition to the major programs, the department provides a number of service courses in support of other programs within the university. Current and detailed information on mathematics degrees and
course offerings is available from the department.
The department maintains a math lab for all students studying mathematics at the baccalaureate level.
The Department of Mathematical Sciences also offers programs in computer science and statistics (see separate listings).
Graduate Program--M.A.T. Degree
1. Complete the following admission requirements:
a. The department does not require any GRE, but recommends applicants provide GRE general scores.
b. Complete and submit a TOEFL score of at least 600 (this requirement is only for foreign applicants who seek a teaching assistantship).
c. The department gives preference to foreign applicants who also submit results of the Test of Spoken English (TSE).
2. Complete the general university requirements.
3. Complete the M.A.T. degree requirements.
4. Complete the following:
MATH courses* 18
5. Minimum credits required 36
* At least 12 credits must be at the 600-level.
Graduate Program--M.S. Degree
1. Complete the following admission requirements:
a. The department does not require any GRE, but recommends applicants provide GRE general scores.
b. Complete and submit a TOEFL score of at least 600 (this requirement is only for foreign applicants who seek a teaching assistantship).
c. The department gives preference to foreign applicants who also submit results of the Test of Spoken English (TSE).
2. Complete the general university requirements.
3. Complete the master's degree requirements.
4. Complete mathematics courses and electives.
5. Complete a project or thesis.
6. Minimum credits required 30-35
Graduate Program--Ph.D. Degree
1. Complete the following admission requirements:
a. The department does not require any GRE, but recommends applicants provide GRE general scores.
b. Complete and submit a TOEFL. (For teaching assistantship consideration, foreign applicants whose native language is not English. Score of at least 600.)
c. The department gives preference to applicants who also submit results of the Test of Spoken English (TSE).
2. Complete the general university requirements.
3. Complete the Ph.D. degree requirements.
4. Minimum credits required 18 | {"url":"http://www.uaf.edu/catalog/catalog_05-06/programs/math_grad.html","timestamp":"2014-04-19T13:49:41Z","content_type":null,"content_length":"9774","record_id":"<urn:uuid:af1d2410-3a46-4b89-8fce-0d90dbc28d55>","cc-path":"CC-MAIN-2014-15/segments/1398223211700.16/warc/CC-MAIN-20140423032011-00290-ip-10-147-4-33.ec2.internal.warc.gz"} |
Need recommendation for self teaching book
August 16th 2008, 05:00 PM #1
Need recommendation for self teaching book
As the title states, does anyone have an excellent self teaching trig. book they can recommend? Preferably one that proceeds in a logical fashion, tons of examples to work through, and solutions
that dont leave the math impaired guessing as was done.
Many Thanks
Moo once posted a link that had several free useful e-books. One of them was a teach yourself trigonometry book. Check here:
XP Math - Math eBooks
You will have to forgive me, but from a quick glance I do not think that will help me very much. I am very poor with math at the moment. Currently I seem to thrive in self teaching book formats
that first explain the concept/theory, give a few practice problems with in depth solutions, and then offer multiple practice questions to try. I am willing to shell out what ever money I have
to, price is not a limiting factor.
August 16th 2008, 05:08 PM #2
Super Member
Jun 2008
August 16th 2008, 05:50 PM #3 | {"url":"http://mathhelpforum.com/trigonometry/46092-need-recommendation-self-teaching-book.html","timestamp":"2014-04-17T18:45:59Z","content_type":null,"content_length":"35060","record_id":"<urn:uuid:49f5314f-ac3e-47d8-b7e3-fd402f7a224b>","cc-path":"CC-MAIN-2014-15/segments/1398223202548.14/warc/CC-MAIN-20140423032002-00043-ip-10-147-4-33.ec2.internal.warc.gz"} |
state biot savart law
2 answers
Biot-Savart law
A law of physics which states that the magnetic flux density (magnetic induction) near a long, straight conductor is directly proportional to the current in the conductor and inversely proportional
to the distance from the conductor. The field near a straight conductor can be found by application of Ampère's law. The magnetic flux density near a long, straight conductor is at every point
perpendicular to the plane determined by the point and the line of the conductor. Therefore, the lines of induction are circles with their centers at the conductor. Furthermore, each line of
induction is a closed line. This observation concerning flux about a straight conductor may be generalized to include lines of induction due to a conductor of any shape by the statement that every
line of induction forms a closed path.
Recent Unanswered Questions | {"url":"http://www.akaqa.com/question/q19192255777-State-biot-savart-law?page=1","timestamp":"2014-04-19T05:00:05Z","content_type":null,"content_length":"57093","record_id":"<urn:uuid:43b558f3-2ccc-4974-b33d-6122e49b6152>","cc-path":"CC-MAIN-2014-15/segments/1397609535775.35/warc/CC-MAIN-20140416005215-00080-ip-10-147-4-33.ec2.internal.warc.gz"} |
Riemann Integrable?
July 27th 2010, 05:50 PM #1
Jun 2010
Riemann Integrable?
I am asked to show that $\displaystyle \int^{1}_{0} \frac{x^{p - 1}}{1 - x} log \Bigl( \frac{1}{x} \Bigr) dx = \sum^{\infty}_{n = 0} \frac{1}{(n + p)^{2}}$ for p > 0. I have a lot of it so far,
and am basically on the cusp.
$\displaystyle \int^{1}_{0} \frac{x^{p - 1}}{1 - x} log \Bigl( \frac{1}{x} \Bigr) dx = \displaystyle \int^{1}_{0} x^{p - 1} \sum^{\infty}_{n = 0} x^{n} log \Bigl( \frac{1}{x} \Bigr) dx = \sum^{\
infty}_{n = 0} \int^{1}_{0} x^{n + p - 1} log \Bigl( \frac{1}{x} \Bigr) dx$. Now the obvious calculus thing to do is integrate by parts and I'm done. But to do that, assuming I'm treating this
like a Riemann integral, I have to evaluate $log \Bigl( \frac{1}{x} \Bigr) \frac{x^{n + p}}{n + p}$ from 0 to 1. Well okay, 1 is easy. Log of 0 isn't defined, though, and I'm not sure how to do a
proofy demonstration that this is whole thing is zero. So that leads me to think that maybe I shouldn't be treating this like a Riemann integral and instead should find some sequence of step
functions which approaches what I'm trying to integrate, i.e. to argue it as a Lebesgue integral. But finding a sequence of step functions which approaches $x^{n + p - 1} log(1/x)$ seems
daunting. Ideas?
I am asked to show that $\displaystyle \int^{1}_{0} \frac{x^{p - 1}}{1 - x} log \Bigl( \frac{1}{x} \Bigr) dx = \sum^{\infty}_{n = 0} \frac{1}{(n + p)^{2}}$ for p > 0. I have a lot of it so far,
and am basically on the cusp.
$\displaystyle \int^{1}_{0} \frac{x^{p - 1}}{1 - x} log \Bigl( \frac{1}{x} \Bigr) dx = \displaystyle \int^{1}_{0} x^{p - 1} \sum^{\infty}_{n = 0} x^{n} log \Bigl( \frac{1}{x} \Bigr) dx = \sum^{\
infty}_{n = 0} \int^{1}_{0} x^{n + p - 1} log \Bigl( \frac{1}{x} \Bigr) dx$. Now the obvious calculus thing to do is integrate by parts and I'm done. But to do that, assuming I'm treating this
like a Riemann integral, I have to evaluate $log \Bigl( \frac{1}{x} \Bigr) \frac{x^{n + p}}{n + p}$ from 0 to 1. Well okay, 1 is easy. Log of 0 isn't defined, though, and I'm not sure how to do a
proofy demonstration that this is whole thing is zero. So that leads me to think that maybe I shouldn't be treating this like a Riemann integral and instead should find some sequence of step
functions which approaches what I'm trying to integrate, i.e. to argue it as a Lebesgue integral. But finding a sequence of step functions which approaches $x^{n + p - 1} log(1/x)$ seems
daunting. Ideas?
This should get you started
$\int_{0}^{1}\frac{x^{p-1}}{1-x}\log\left( \frac{1}{x}\right)dx=\int_{0}^{1}\int_{x}^{1}\frac {1}{s}\cdot \frac{x^{p-1}}{1-x}dsdx$
Now use Fubini's theorem to switch the order of integration to get
$\int_{0}^{1}\int_{0}^{s}\frac{1}{s}\cdot \frac{x^{p-1}}{1-x}dxds$
Now just use your trick and express $\frac{1}{1-x}$ as geometric series and integrate.
I'm afraid I can't go that route since I don't have Fubini's Theorem or anything about double-integrals.
... However, a similar idea might be to build the step-functions which approximate this integral on intervals [s, 1] where s is ever closer to 0 and the step functions are constant on smaller
partitions as the sequence approaches the function. I'm toying with this idea right now.
How does this sound? I create the sequence of functions defined by $f_{i} = \begin{cases}log \frac{1}{x} \text{ if } \frac{1}{i + 1} \leq x \leq 1 \\ 0 \text{ if } x > \frac{1}{i + 1} \end{cases}
$. Obviously this sequence is increasing and approaching $log \frac{1}{x}$, and each individual function is Riemann integrable and equal to... Hm. I guess I'm stuck here, I don't know how to
integrate log yet. So this looks like the wrong way to go.
Last edited by ragnar; July 27th 2010 at 07:21 PM. Reason: update
Here's another idea not using Fubini's theorem. In the integral $\int_0^1 x^{n+p-1}\log(x^{-1})dx$, change the variable to $u=x^{-1}$. You get, assuming $p>0$, $\int_1^\infty u^{-n-p-1} \log u du
= \int_1^\infty \log u\: d\left(\frac{u^{-n-p}}{-n-p}\right) = \log u\frac{u^{-n-p}}{-n-p} \Big |^{\infty}_1 - \int_1^\infty \frac{u^{-n-p-1}}{-n-p}du = \frac{1}{(-n-p)^2}$.
I am asked to show that $\displaystyle \int^{1}_{0} \frac{x^{p - 1}}{1 - x} log \Bigl( \frac{1}{x} \Bigr) dx = \sum^{\infty}_{n = 0} \frac{1}{(n + p)^{2}}$ for p > 0. I have a lot of it so far,
and am basically on the cusp.
$\displaystyle \int^{1}_{0} \frac{x^{p - 1}}{1 - x} log \Bigl( \frac{1}{x} \Bigr) dx = \displaystyle \int^{1}_{0} x^{p - 1} \sum^{\infty}_{n = 0} x^{n} log \Bigl( \frac{1}{x} \Bigr) dx = \sum^{\
infty}_{n = 0} \int^{1}_{0} x^{n + p - 1} log \Bigl( \frac{1}{x} \Bigr) dx$. Now the obvious calculus thing to do is integrate by parts and I'm done. But to do that, assuming I'm treating this
like a Riemann integral, I have to evaluate $log \Bigl( \frac{1}{x} \Bigr) \frac{x^{n + p}}{n + p}$ from 0 to 1. Well okay, 1 is easy. Log of 0 isn't defined, though, and I'm not sure how to do a
proofy demonstration that this is whole thing is zero. So that leads me to think that maybe I shouldn't be treating this like a Riemann integral and instead should find some sequence of step
functions which approaches what I'm trying to integrate, i.e. to argue it as a Lebesgue integral. But finding a sequence of step functions which approaches $x^{n + p - 1} log(1/x)$ seems
daunting. Ideas?
I think if p>1 your function has a continous extension to [0,1] so integration by parts would be justified. For the other cases (where the function blows up near 0) I think the question would be
if $\ln \left( \frac{1}{x} \right)$ is integrable.
Here's another idea not using Fubini's theorem. In the integral $\int_0^1 x^{n+p-1}\log(x^{-1})dx$, change the variable to $u=x^{-1}$. You get, assuming $p>0$, $\int_1^\infty u^{-n-p-1} \log u du
= \int_1^\infty \log u\: d\left(\frac{u^{-n-p}}{-n-p}\right) = \log u\frac{u^{-n-p}}{-n-p} \Big |^{\infty}_1 - \int_1^\infty \frac{u^{-n-p-1}}{-n-p}du = \frac{1}{(-n-p)^2}$.
This is, I think, a more elegant way of doing essentially what I just figured out how to do. Thank you all!
July 27th 2010, 06:38 PM #2
July 27th 2010, 06:52 PM #3
Jun 2010
July 27th 2010, 06:57 PM #4
Jun 2010
July 27th 2010, 07:45 PM #5
July 27th 2010, 07:52 PM #6
Super Member
Apr 2009
July 27th 2010, 07:55 PM #7
Jun 2010 | {"url":"http://mathhelpforum.com/differential-geometry/152152-riemann-integrable.html","timestamp":"2014-04-19T20:43:07Z","content_type":null,"content_length":"58483","record_id":"<urn:uuid:3d3ef4ff-b66a-4ce8-8268-afa2ad8fb47c>","cc-path":"CC-MAIN-2014-15/segments/1397609537376.43/warc/CC-MAIN-20140416005217-00046-ip-10-147-4-33.ec2.internal.warc.gz"} |
Think Stats
Safari Books Online is a digital library providing on-demand subscription access to thousands of learning resources.
Think Stats: Probability and Statistics for Programmers is a textbook for a new kind of introductory prob-stat class. It emphasizes the use of statistics to explore large datasets. It takes a
computation approach: students write programs in Python as a way of developing and testing their understanding.
Description Content
Visit the catalog page for Think Stats • Catalog Page
Visit the errata page for Think Stats • Errata | {"url":"http://my.safaribooksonline.com/9781449308117?portal=oreilly&cid=orm-cat-readnow-9781449308117","timestamp":"2014-04-18T18:49:16Z","content_type":null,"content_length":"73731","record_id":"<urn:uuid:ed1cd6e7-e76d-4541-af13-3f644956b39d>","cc-path":"CC-MAIN-2014-15/segments/1397609535095.7/warc/CC-MAIN-20140416005215-00404-ip-10-147-4-33.ec2.internal.warc.gz"} |
The Information Theoretic Approach to Cryptography
, 1975
"... A new definition of program-size complexity is made. H(A;B=C;D) is defined to be the size in bits of the shortest self-delimiting program for calculating strings A and B if one is given a
minimal-size selfdelimiting program for calculating strings C and D. This differs from previous definitions: (1) ..."
Cited by 333 (16 self)
Add to MetaCart
A new definition of program-size complexity is made. H(A;B=C;D) is defined to be the size in bits of the shortest self-delimiting program for calculating strings A and B if one is given a
minimal-size selfdelimiting program for calculating strings C and D. This differs from previous definitions: (1) programs are required to be self-delimiting, i.e. no program is a prefix of another,
and (2) instead of being given C and D directly, one is given a program for calculating them that is minimal in size. Unlike previous definitions, this one has precisely the formal 2 G. J. Chaitin
properties of the entropy concept of information theory. For example, H(A;B) = H(A) + H(B=A) + O(1). Also, if a program of length k is assigned measure 2 \Gammak , then H(A) = \Gamma log 2 (the
probability that the standard universal computer will calculate A) +O(1). Key Words and Phrases: computational complexity, entropy, information theory, instantaneous code, Kraft inequality, minimal
program, probab...
- IBM JOURNAL OF RESEARCH AND DEVELOPMENT , 1977
"... This paper reviews algorithmic information theory, which is an attempt to apply information-theoretic and probabilistic ideas to recursive function theory. Typical concerns in this approach are,
for example, the number of bits of information required to specify an algorithm, or the probability that ..."
Cited by 320 (19 self)
Add to MetaCart
This paper reviews algorithmic information theory, which is an attempt to apply information-theoretic and probabilistic ideas to recursive function theory. Typical concerns in this approach are, for
example, the number of bits of information required to specify an algorithm, or the probability that a program whose bits are chosen by coin flipping produces a given output. During the past few
years the definitions of algorithmic information theory have been reformulated. The basic features of the new formalism are presented here and certain results of R. M. Solovay are reported. | {"url":"http://citeseerx.ist.psu.edu/showciting?cid=3244181","timestamp":"2014-04-18T12:20:53Z","content_type":null,"content_length":"15269","record_id":"<urn:uuid:7d6cc701-2ac5-4908-a923-c82678d7d19b>","cc-path":"CC-MAIN-2014-15/segments/1397609533308.11/warc/CC-MAIN-20140416005213-00364-ip-10-147-4-33.ec2.internal.warc.gz"} |
Physics Forums - View Single Post - Target in a shooting gallery
A target in a shooting gallery consists of a vertical square wooden board, 0.220m on a side and with mass 0.800 kg, that pivots on a horizontal axis along its top edge. The board is struck face-on at
its center by a bullet with mass 1.80g that is traveling at 320m/s and that remains embedded in the board.
A)What is the angular speed of the board just after the bullet's impact?
B)What maximum height above the equilibrium position does the center of the board reach before starting to swing down again?
C)What minimum bullet speed would be required for the board to swing all the way over after impact?
I'm just a little confused about how to approach this problem. I wanted to know if I am on the right track and maybe where I should go with my information.
I started off finding the KE of the bullet before it strikes the board. Using KE = (1/2)mv^2 I got (1/2)(.0018kg)(320 m/s)^2 to get KE = 92.16 and I took this to be the force on the board that caused
it to rotate
Then I wanted to know the Torque about the square so I used the equationg Radius X Force. I got (.110m) X (92.16 J) = 10.1376
I'm not exactly sure where to take this information. I thought about using Conservation of Energy but I dont know the PE of the system afterwards because I don't know how high it rises. If someone
could just point in the right direction to find (A) I would greatly appreciate it. thank you | {"url":"http://www.physicsforums.com/showpost.php?p=1676632&postcount=1","timestamp":"2014-04-20T21:22:29Z","content_type":null,"content_length":"9775","record_id":"<urn:uuid:2eb5ffff-fd6c-43ea-aea2-49316497eac2>","cc-path":"CC-MAIN-2014-15/segments/1397609539230.18/warc/CC-MAIN-20140416005219-00380-ip-10-147-4-33.ec2.internal.warc.gz"} |
Got Homework?
Connect with other students for help. It's a free community.
• across
MIT Grad Student
Online now
• laura*
Helped 1,000 students
Online now
• Hero
College Math Guru
Online now
Here's the question you clicked on:
pleaaassee hellpp??
• one year ago
• one year ago
Your question is ready. Sign up for free to start getting answers.
is replying to Can someone tell me what button the professor is hitting...
• Teamwork 19 Teammate
• Problem Solving 19 Hero
• Engagement 19 Mad Hatter
• You have blocked this person.
• ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.
This is the testimonial you wrote.
You haven't written a testimonial for Owlfred. | {"url":"http://openstudy.com/updates/510c25b1e4b0d9aa3c4729b4","timestamp":"2014-04-21T04:44:47Z","content_type":null,"content_length":"96088","record_id":"<urn:uuid:d8231a28-8433-4b1a-95ad-0029add6ec51>","cc-path":"CC-MAIN-2014-15/segments/1398223202457.0/warc/CC-MAIN-20140423032002-00178-ip-10-147-4-33.ec2.internal.warc.gz"} |
Flatness for infinity functors
up vote 8 down vote favorite
It is well known that for ordinary categories, if $C$ has finite limits and $D$ is cocomplete, and $A:C \to D $ is left-exact (i.e. preserves finite limits) then the left-Kan extension of $F$ along
the Yoneda embedding $y:C \hookrightarrow Set^{C^{op}}$ is left-exact. I'm pretty sure this is still true for $\left(\infty,1\right)$-categories, once we replace the role of presheaves with that of $
\infty$-presheaves, but is this written up somewhere?
ct.category-theory higher-category-theory
Allow me to criticize myself here. This is well known for $D$ a TOPOS. If $D$ is not a topos, is it even true? – David Carchedi Dec 14 '11 at 1:39
add comment
1 Answer
active oldest votes
For reference, at least when $D$ is an infinity topos, which I believe is probably necessary, this is Proposition 6.1.5.2 in HTT.
up vote 0 down vote accepted
add comment
Not the answer you're looking for? Browse other questions tagged ct.category-theory higher-category-theory or ask your own question. | {"url":"http://mathoverflow.net/questions/83350/flatness-for-infinity-functors","timestamp":"2014-04-19T18:03:21Z","content_type":null,"content_length":"50292","record_id":"<urn:uuid:d6cefc93-fcda-42a8-b902-2c398da65f42>","cc-path":"CC-MAIN-2014-15/segments/1397609537308.32/warc/CC-MAIN-20140416005217-00487-ip-10-147-4-33.ec2.internal.warc.gz"} |
Garden Grove, CA Algebra 2 Tutor
Find a Garden Grove, CA Algebra 2 Tutor
...Every student has their own challenges and these must be addressed accordingly. I like to start from the beginning with a new student and find out exactly what is causing some lack of
understanding. I sincerely hope every student I work with can develop confidence along with proficiency in mathematics.
14 Subjects: including algebra 2, calculus, statistics, SAT math
...I have been a high school Football coach for the past two years and I am currently a Football Coach at John W. North High School. My students gain a great understanding of football that they
are able to take and use in real world application.I have played football for four years in High School.
12 Subjects: including algebra 2, physics, algebra 1, precalculus
...I have completed nearly every math course offered at my university and have 4+ years of swimming and theatre experience. I have been cooking for 10+ years both as an amateur and professional.
I work as a Teacher's Assistant and Tutor for mathematics and have done so for about 3 years at the university.
14 Subjects: including algebra 2, calculus, physics, algebra 1
...I remember running in races as early as second grade. I joined my track and cross country teams while in grade school, and started doing well against class mates and my region there. In high
school, I received many honors: State Group Champion in Cross-country, First Team All- County, and All- League Honors, among others.
62 Subjects: including algebra 2, English, reading, biology
...I began programming in high school, so the first advanced math that I did was discrete math (using Knuth's book called Discrete Mathematics). I have also participated in high school math
competitions (ie AIME) and a college math competition (the Putnam) for several years, and in both cases the ma...
28 Subjects: including algebra 2, Spanish, chemistry, French
Related Garden Grove, CA Tutors
Garden Grove, CA Accounting Tutors
Garden Grove, CA ACT Tutors
Garden Grove, CA Algebra Tutors
Garden Grove, CA Algebra 2 Tutors
Garden Grove, CA Calculus Tutors
Garden Grove, CA Geometry Tutors
Garden Grove, CA Math Tutors
Garden Grove, CA Prealgebra Tutors
Garden Grove, CA Precalculus Tutors
Garden Grove, CA SAT Tutors
Garden Grove, CA SAT Math Tutors
Garden Grove, CA Science Tutors
Garden Grove, CA Statistics Tutors
Garden Grove, CA Trigonometry Tutors | {"url":"http://www.purplemath.com/Garden_Grove_CA_Algebra_2_tutors.php","timestamp":"2014-04-16T13:34:06Z","content_type":null,"content_length":"24387","record_id":"<urn:uuid:4e76f841-ecee-452a-a912-74fec26b060e>","cc-path":"CC-MAIN-2014-15/segments/1397609523429.20/warc/CC-MAIN-20140416005203-00518-ip-10-147-4-33.ec2.internal.warc.gz"} |
Inverse cotangent: Transformations
Transformations and argument simplifications
Argument involving basic arithmetic operations
Involving cot^-1(- z)
Involving cot^-1(-z) and cot^-1(z)
Involving cot^-1(1/z)
Involving cot^-1(1/z) and cot^-1(z)
Involving cot^-1(z^1/2)
Involving cot^-1(z^1/2) and cot^-1(1/z^1/2)
Involving cot^-1(z^1/2) and cot^-1(1/z^1/2)
Involving cot^-1(z^1/2) and cot^-1(1/1/z^1/2)
Involving cot^-1(1/z^1/2)
Involving cot^-1(1/z^1/2) and cot^-1(z^1/2)
Involving cot^-1(1/z^1/2) and cot^-1(1/z^1/2)
Involving cot^-1(1/z^1/2) and cot^-1(1/1/z^1/2)
Involving cot^-1((z[2])^1/2)
Involving cot^-1((z[2])^1/2) and cot^-1(z)
Involving cot^-1((z[2])^1/2) and cot^-1(1/z)
Involving cot^-1(a (b z^c)^m)
Involving cot^-1(a (b z^c)^m) and cot^-1(a b^m z^m c)
Involving cot^-1(1-z/1+z)
Involving cot^-1(1-z/1+z) and cot^-1(z)
Involving cot^-1(1-z/1+z) and cot^-1(1/z)
Involving cot^-1(z-1/z+1)
Involving cot^-1(z-1/z+1) and cot^-1(z)
Involving cot^-1(z-1/z+1) and cot^-1(1/z)
Involving cot^-1(1+z/1-z)
Involving cot^-1(1+z/1-z) and cot^-1(z)
Involving cot^-1(1+z/1-z) and cot^-1(1/z)
Involving cot^-1(z+1/z-1)
Involving cot^-1(z+1/z-1) and cot^-1(z)
Involving cot^-1(z+1/z-1) and cot^-1(1/z)
Involving cot^-1(2z/1-z^2)
Involving cot^-1(2 z/1-z^2) and cot^-1(z)
Involving cot^-1(2 z/1-z^2) and cot^-1(1/z)
Involving cot^-1(2z/z^2-1)
Involving cot^-1(2z/z^2-1) and cot^-1(z)
Involving cot^-1(2z/z^2-1) and cot^-1(1/z)
Involving cot^-1(1-z^2/2 z)
Involving cot^-1(1-z^2/2 z) and cot^-1(z)
Involving cot^-1(1-z^2/2 z) and cot^-1(1/z)
Involving cot^-1(z^2-1/2z)
Involving cot^-1(z^2-1/2z) and cot^-1(z)
Involving cot^-1(z^2-1/2z) and cot^-1(1/z)
Involving cot^-1(2z^1/2/1-z)
Involving cot^-1(2 z^1/2/1-z) and cot^-1(z^1/2)
Involving cot^-1(2 z^1/2/1-z) and cot^-1(1/z^1/2)
Involving cot^-1(2 z^1/2/1-z) and cot^-1(1/z^1/2)
Involving cot^-1(2 z^1/2/z-1)
Involving cot^-1(2 z^1/2/z-1) and cot^-1(z^1/2)
Involving cot^-1(2 z^1/2/z-1) and cot^-1(1/z^1/2)
Involving cot^-1(2 z^1/2/z-1) and cot^-1(1/z^1/2)
Involving cot^-1(1-z/2 z^1/2)
Involving cot^-1(1-z/2z^1/2) and cot^-1(z^1/2)
Involving cot^-1(1-z/2z^1/2) and cot^-1(1/z^1/2)
Involving cot^-1(1-z/2z^1/2) and cot^-1(1/z^1/2)
Involving cot^-1(z-1/2z^1/2)
Involving cot^-1(z-1/2z^1/2) and cot^-1(z^1/2)
Involving cot^-1(z-1/2z^1/2) and cot^-1(1/z^1/2)
Involving cot^-1(z-1/2z^1/2) and cot^-1(1/z^1/2)
Involving cot^-1((1+z^2)^1/2+c z)
Involving cot^-1((1+z^2)^1/2+z) and cot^-1(z)
Involving cot^-1((1+z^2)^1/2+z) and cot^-1(1/z)
Involving cot^-1((1+z^2)^1/2-z) and cot^-1(z)
Involving cot^-1((1+z^2)^1/2-z) and cot^-1(1/z)
Involving cot^-1(1/(1+z^2)^1/2+c z)
Involving cot^-1(1/(1+z^2)^1/2+z) and cot^-1(z)
Involving cot^-1(1/(1+z^2)^1/2+z) and cot^-1(1/z)
Involving cot^-1(1/(1+z^2)^1/2-z) and cot^-1(z)
Involving cot^-1(1/(1+z^2)^1/2-z) and cot^-1(1/z)
Involving cot^-1((1+z^2)^1/2+a/z)
Involving cot^-1((1+z^2)^1/2+1/z) and cot^-1(z)
Involving cot^-1((1+z^2)^1/2+1/z) and cot^-1(1/z)
Involving cot^-1((1+z^2)^1/2-1/z) and cot^-1(z)
Involving cot^-1((1+z^2)^1/2-1/z) and cot^-1(1/z)
Involving cot^-1(z/(1+z^2)^1/2+a)
Involving cot^-1(z/(1+z^2)^1/2+1) and cot^-1(z)
Involving cot^-1(z/(1+z^2)^1/2+1) and cot^-1(1/z)
Involving cot^-1(z/(1+z^2)^1/2-1) and cot^-1(z)
Involving cot^-1(z/(1+z^2)^1/2-1) and cot^-1(1/z)
Products, sums, and powers of the direct function
Sums of the direct function
Differences of the direct function
Linear combinations of the direct function
Related transformations
Sums involving the direct function
Involving log(z)
Involving sin^-1(z)
Involving cos^-1(z)
Involving tan^-1(z)
Involving csc^-1(z)
Involving sec^-1(z)
Involving sinh^-1(z)
Involving cosh^-1(z)
Involving tanh^-1(z)
Involving coth^-1(z)
Involving csch^-1(z)
Involving sech^-1(z)
Differences involving the direct function
Involving log(z)
Involving sin^-1(z)
Involving cos^-1(z)
Involving tan^-1(z)
Involving csc^-1(z)
Involving sec^-1(z)
Involving sinh^-1(z)
Involving cosh^-1(z)
Involving tanh^-1(z)
Involving coth^-1(z)
Involving csch^-1(z)
Involving sech^-1(z)
Linear combinations involving the direct function
Involving log(z)
Involving sin^-1(z)
Involving cos^-1(z)
Involving tan^-1(z)
Involving csc^-1(z)
Involving sec^-1(z)
Involving sinh^-1(z)
Involving cosh^-1(z)
Involving tanh^-1(z)
Involving coth^-1(z)
Involving csch^-1(z)
Involving sech^-1(z) | {"url":"http://functions.wolfram.com/ElementaryFunctions/ArcCot/16/ShowAll.html","timestamp":"2014-04-18T00:36:57Z","content_type":null,"content_length":"210107","record_id":"<urn:uuid:6699d56a-0c78-49ee-8679-71cf79318940>","cc-path":"CC-MAIN-2014-15/segments/1397609532374.24/warc/CC-MAIN-20140416005212-00546-ip-10-147-4-33.ec2.internal.warc.gz"} |
five lemma
Diagram chasing lemmas
Homological algebra
The five lemma is one of the basic lemmas of homological algebra, useful for example in the construction of the connecting homomorphism in the homology long exact sequence.
Let $\mathcal{A}$ be an abelian category. Consider a commutative diagram in $\mathcal{A}$ of the form
$\array{ A_1 & \to & A_2 & \to & A_3 & \to & A_4 &\to & A_5\\ \downarrow f_1 &&\downarrow f_2 &&\downarrow f_3 &&\downarrow f_4 &&\downarrow f_5 \\ B_1 & \to & B_2 & \to & B_3 & \to & B_4 &\to & B_5
where the top and bottom rows are exact sequences. For simplicity we denote all the differentials in both exact sequences by $d$.
Proposition (the lemma on five homomorphisms or the five lemma)
1. sharp five lemma (essentially the weak four lemma)
1. If $f_2$ and $f_4$ are epi and $f_5$ is mono, then $f_3$ is epi.
2. If $f_2$ and $f_4$ are mono and $f_1$ is epi, then $f_3$ is mono.
2. (weak) five lemma (conjunction of the two statements above)
If $f_2$ and $f_4$ are isos, $f_1$ is epi, and $f_5$ is mono, then $f_3$ is iso.
The four lemma follows immediately from the salamander lemma, as discussed at salamander lemma - impliciations - four lemma. Here is direct proof.
By the Freyd-Mitchell embedding theorem we can always assume that the abelian category is $R$Mod (though this requires the category to be small, one can always take a smaller abelian subcategory
containing the morphism in the diagram which is small). Then we can do the diagram chasing using elements in that setup. We prove only 1) as 2) is dual.
Suppose $b\in B_3$. Since $f_4$ is epi, one can choose an element $a_4\in A_4$ such that $f_4(a_4) = d(b)$. Now $0 = d^2 b = d f_4 (a_4) = f_5 d (a_4)$. Since $f_5$ is a monomorphism that means that
$d a_4 = 0$ as well. By the exactness of the upper row, that means there is $a_3\in A_3$ such that $d a_3 = a_4$, hence also $d f_3 (a_3) = f_4 d (a_3) = f_4(a_4) = d b$. We would like that $f_3(a_3)
$ be equal to $b$ but this is not so, we just see that $d (b-f_3(a_3)) = 0$ and hence by exactness of the lower row there is $b'\in B_2$ such that $d b' = b-f_3(a_3)$. Since $f_2$ is also epi, there
is $a_2\in A_2$ such that $f_2(a_2) = b'$. Now $d a_2+a_3\in A_3$ is such that
$f_3 (d a_2 + a_3) = d f_2(a_2) + f_3(a_3) = d b' + f_3(a_3) = b - f_3(a_3) + f_3(a_3) = b$
demonstrating that $b$ is in the image of $f_3$.
Hence $f_3$ is an epimorphism.
Short five lemma
(short five lemma)
Let $A \to B \to C$ and $A \to \tilde B \to C$ be two exact sequences. If a homomorphism $f \colon B \to \tilde B$ makes the diagram
$\array{ && B \\ & earrow && \searrow \\ A &&\downarrow^{\mathrlap{f}}&& C \\ & \searrow && earrow \\ && \tilde B }$
commute, then $f$ is an isomorphism.
Apply prop. 1 to the diagram
$\array{ 0 &\to& A &\to& B &\to& C &\to& 0 \\ \downarrow^{\mathrlap{=}} && \downarrow^{\mathrlap{=}} && \downarrow^{\mathrlap{f}} && \downarrow^{\mathrlap{=}} && \downarrow^{\mathrlap{=}} \\ 0 &\to&
A &\to& \tilde B &\to& C &\to& 0 }$
Short split five lemma
A special case of the five lemma is the short five lemma where the objects $A_1,B_1,A_5,B_5$ above are all zero objects. It may hold in more general setups, sometimes with additional assumptions.
The short split five lemma is a statement usually stated in the setup of semiabelian categories:
(short split five lemma)
Given a commutative diagram
$\array{L & \overset{l}{\to} & H & \overset{q}{\to} & C\\ ^u\downarrow && \downarrow^w && \downarrow^v \\ K & \underset{k}{\to} & G& \underset{p}{\to} & B}$
where $p$ and $q$ are split epimorphisms and $l$ and $k$ are their kernels, if $u$ and $v$ are isomorphisms then so is $w$.
Early references of the 5-lemma
• (lemma (5,9) in) D. A. Buchsbaum, Exact categories and duality, Transactions of the American Mathematical Society Vol. 80, No. 1 (1955), pp. 1-34 (JSTOR)
• (prop.1.1, page 5) Henri Cartan, Samuel Eilenberg, Homological algebra, Princeton Univ. Press 1956
• (lemma 3.3 in chapter I) S. MacLane, Homology, Springer 1963, 1975
In nonabelian context
The short 5-lemma also appears in various topological algebra contexts; see for example
• Francis Borceux, Maria Manuel Clementino, Topological semi-abelian categories, Adv. Math. 190 (2005), 425-453 (web) | {"url":"http://ncatlab.org/nlab/show/five+lemma","timestamp":"2014-04-19T22:34:45Z","content_type":null,"content_length":"62813","record_id":"<urn:uuid:5f66aef4-271a-4dee-b44a-e6478094c592>","cc-path":"CC-MAIN-2014-15/segments/1397609537754.12/warc/CC-MAIN-20140416005217-00470-ip-10-147-4-33.ec2.internal.warc.gz"} |
newbie ques - check double
"David Harmon" <(E-Mail Removed)> wrote in message
news:(E-Mail Removed)...
> On Tue, 28 Sep 2004 17:43:34 GMT in comp.lang.c++, "Mike Wahler"
> <(E-Mail Removed)> wrote,
> >> if (d == floor(d))
> >> // d is an integer
> >
> >Another alternative is to use 'modf()'.
> And there are others. But testing any floating point result for any
> exact value
OP is not looking for an 'exact value', but simply whether
a real number has a fractional part. Also note that types
'float' and 'double' can indeed represent integers exactly.
> typically indicates wrong thinking in the design anyway.
I don't think it's 'wrong thinking' to try to determine
if a real number has a fractional part (unless of course
it's not really needed by the application being written). | {"url":"http://www.velocityreviews.com/forums/t285914-newbie-ques-check-double.html","timestamp":"2014-04-24T17:02:25Z","content_type":null,"content_length":"50329","record_id":"<urn:uuid:3e9cf32d-711c-4d88-a104-e1dee2826334>","cc-path":"CC-MAIN-2014-15/segments/1398223206647.11/warc/CC-MAIN-20140423032006-00436-ip-10-147-4-33.ec2.internal.warc.gz"} |
Evaluating a Function
August 27th 2012, 06:54 PM #1
Evaluating a Function
For the function f defined by f(x) = $2x^2-3x$
Evaluate: $\frac{f(x+h)-f(x)}{h}$
I'm solving the problem using a book which actually gives me step-by-step instructions. Thing is I have a confusion with the following distribution, and the book is not showing the distribution
$\frac{f(x+h)-f(x)}{h}=\frac{[2(x+h)^2 -3(x+h)]-[2x^2-3x]}{h}$
When I do this step I receive the following:
What the book gives
What am I doing wrong? Everything?
Re: Evaluating a Function
For the function f defined by f(x) = $2x^2-3x$
Evaluate: $\frac{f(x+h)-f(x)}{h}$
I'm solving the problem using a book which actually gives me step-by-step instructions. Thing is I have a confusion with the following distribution, and the book is not showing the distribution
$\frac{f(x+h)-f(x)}{h}=\frac{[2(x+h)^2 -3(x+h)]-[2x^2-3x]}{h}$
When I do this step I receive the following:
What the book gives
What am I doing wrong? Everything?
Try these corrections:
1. $(x + h)^2 = x^2 + 2xh + h^2$, not $(x + h)^2 = x^2 + h^2$
2. The sign on the last 3x is positive, not negative
Re: Evaluating a Function
August 27th 2012, 07:00 PM #2
August 27th 2012, 07:09 PM #3 | {"url":"http://mathhelpforum.com/pre-calculus/202625-evaluating-function.html","timestamp":"2014-04-17T19:17:04Z","content_type":null,"content_length":"40794","record_id":"<urn:uuid:8333c79d-2a6f-4ba4-8a14-4ce38c193a90>","cc-path":"CC-MAIN-2014-15/segments/1397609530895.48/warc/CC-MAIN-20140416005210-00252-ip-10-147-4-33.ec2.internal.warc.gz"} |
red dwarf star
UCB976.1 is
a large terrestrial planet
, on an orbit about 45419*10
km from its star. Its' radius is 8259 km, its' mass is 4506. One year on UCB976.1 lasts 193 earth days, one day on UCB976.1 lasts 21 earth hours. Its' average surface temperature is 437, and it has
17 moons.
UCB976.2 is
a very large terrestrial planet
, on an orbit about 136782*10
km from its star. Its' radius is 9966 km, its' mass is 7918. One year on UCB976.2 lasts 1009 earth days, one day on UCB976.2 lasts 20 earth hours. Its' average surface temperature is 96, and it has
19 moons.
UCB976.3 is
a very large terrestrial planet
, on an orbit about 205173*10
km from its star. Its' radius is 11345 km, its' mass is 11681. One year on UCB976.3 lasts 1855 earth days, one day on UCB976.3 lasts 19 earth hours. Its' average surface temperature is 64, and it
has 21 moons.
UCB976.4 is
a small terrestrial planet
, on an orbit about 307759*10
km from its star. Its' radius is 4492 km, its' mass is 725. One year on UCB976.4 lasts 9 earth years, one day on UCB976.4 lasts 30 earth hours. Its' average surface temperature is 38, and it has 20
UCB976.5 is
a small terrestrial planet
, on an orbit about 461638*10
km from its star. Its' radius is 4504 km, it | {"url":"http://www.galaxiki.org/cgi-bin/local/perl/galaxiki/wiki.pl?mode=star_planets&id=1821976&level=3&coord_x=63&coord_y=62&option=","timestamp":"2014-04-18T05:31:14Z","content_type":null,"content_length":"18824","record_id":"<urn:uuid:88ceac72-ed5d-4b6e-93f4-0f17be37ced8>","cc-path":"CC-MAIN-2014-15/segments/1398223206120.9/warc/CC-MAIN-20140423032006-00615-ip-10-147-4-33.ec2.internal.warc.gz"} |
Wolfram Demonstrations Project
Allan Plot of an Oscillator with Deterministic Perturbations
The Allan deviation is a statistical measure of the relative frequency instability of an oscillator on a sampling period . This Demonstration simulates an oscillator having white frequency noise
plus deterministic perturbations. The upper graph shows the time series of relative frequency fluctuations and the lower graph shows the corresponding Allan plot . You can modify the noise
amplitude, add a drift or an oscillation, and observe the resulting change in Allan deviation. Each of the three perturbations contributes to the Allan deviation as follows: the white frequency
noise gives rise to , the linear drift adds a contribution (green curve), and the oscillation results in (red curve).
Snapshot 1: oscillator with white frequency noise
Snapshot 2: oscillator with white frequency noise plus a deterministic oscillation
Snapshot 3: oscillator with white frequency noise plus a linear drift
The Allan deviation is the square root of the Allan variance defined by:
where is the relative frequency fluctuations average over the integration time .
[1] C. Audoin and B. Guinot,
The Measurement of Time
, Cambridge: Cambridge University Press, 2001.
[2] J. Vanier and C. Audoin,
The Quantum Physics of Atomic Frequency Standards
, Philadelphia: Hilger, 1989.
(Université de Neuchâtel) | {"url":"http://demonstrations.wolfram.com/AllanPlotOfAnOscillatorWithDeterministicPerturbations/","timestamp":"2014-04-16T21:53:58Z","content_type":null,"content_length":"44754","record_id":"<urn:uuid:0f3e15f2-fec5-49d2-b54a-ae48a9df6d44>","cc-path":"CC-MAIN-2014-15/segments/1397609525991.2/warc/CC-MAIN-20140416005205-00581-ip-10-147-4-33.ec2.internal.warc.gz"} |
Patent US7764786 - Protection of a DES algorithm
1. Field of the Invention
The present invention relates to the field of encryption algorithms, in particular of DES type (Data Encryption Standard), executed by integrated circuits. The present invention more specifically
relates to the protection of the execution of a DES algorithm against a differential power analysis (DPA) attack of the circuit which executes the algorithm.
2. Discussion of the Related Art
DES or triple DES algorithms are symmetrical encryption algorithms (with a secret key) used in cryptography, for example, to encrypt data before having them transited on unprotected supports
(Internet, connection between a smart card and a card reader, between a processor and an external memory, etc.). Such algorithms are described, for example, in standards FIPS PUB 46-2 (DES) and FIPS
PUB 46-1, and operating modes (known as Electronic Codebook—ECB, Cipher Block Chaining—CBC, Cipher Feedback—CFB, Output Feedback—OFB) are described in FIPS PUB 81.
These algorithms perform an encryption by blocks (of 64 bits) by using keys (of 64 bits for the DES and of 128 bits for the triple DES) from which are derived sub-keys of 48 bits. The decryption is
performed based on the same key (symmetrical algorithm). In the following description, the DES algorithm will be taken as an example.
A block to be encrypted designated as M is submitted to an initial permutation, designated as IP, then to sixteen iterations of a calculation depending on a key, designated as KEY, and finally to a
permutation inverse to the initial permutation, designated as IP^−1.
The calculation depending on key KEY can be expressed with the following notations:
□ i for the rank of the iteration ranging between 1 and 16;
□ L[i]R[i ]for a 64-bit data block, resulting from the application of function f to a block R[i-1 ]with sub-key K[i], formed of a word or sub-block L[i ]of the 32 left-hand bits b[1 ]to b[32 ]
and of a word or sub-block R[i ]of the 32 right-hand bits b[33 ]to b[64];
□ K[i ]for a 48-bit block extracted from 64-bit key KEY and used in the encryption function of rank i; and
□ f for an encryption function.
With the above notations, the result of the initial permutation IP is a block L[0]R[0 ]and each iteration applies:
□ L[i]=R[i-1]; and
□ R[i]=L[i-1](+)f(R[i-1],K[i]), where (+) designates a bit-to-bit addition modulo 2 (bit-to-bit XOR).
The result of the last iteration is a block R[16]L[16 ]which is submitted to the inverse permutation IP^−1 to provide an encrypted block designated as M′.
Function f comprises three successive steps.
A first step is an expansion, designated as E, of the 32 bits of sub-block R[i-1 ]in 48 bits to combine them, by a bit-to-bit XOR function (+), with the 48 bits of sub-key K[i ]of the concerned
iteration. The result of this expansion and combination provides eight groups of six bits, designated as B[1i ]to B[8i], such that:
B [1i] B [2i] B [3i] B [4i] B [5i] B [6i] B [7i] B [8i] =K [i](+)E(R [i-1]).
A second step applies to the 48 bits provided by the previous step a substitution table, designated as S or SBOX. In this step, each group of six bits resulting from the previous expansion is
transformed, by one of eight substitution functions (primitive functions), noted S[1 ]to S[8], substituting each group B[1i ]to B[8i ]with a group S[1](B[1i]) to S[8](B[8i]), each over 4 bits, to
obtain eight groups of four bits, or again 32 bits. The result can be noted S[1](B[1i])S[2](B[2i])S[3](B[3i]) . . . S[8](B[8i]), substitution functions S[1 ]to S[8 ]being independent from the rank of
the iteration.
A third step is a permutation, noted P, of the 32 bits resulting from the previous step. This permutation provides a 32-bit result sub-block corresponding to the result of function f and that may be
expressed as:
f(R [i-1] ,K [i])=P(S [1](B [1i])S [2](B [2i])S [3](B [3i]) . . . S [8](B [8i])).
Each sub-key K[i ]is obtained by applying a key function KS which is a function specific to key KEY, function KS depending on rank i of the iteration, that is:
K [i] =KS(i,KEY).
The details of primitive functions KS, S[1 ]to S[8 ]and P, as well as of functions E are described in the mentioned standards.
The encryption is performed by submitting a block to be decrypted M′ to initial permutation IP, then to 16 calculation iterations identical to those of the encryption, with the only difference that
the sub-keys are used in an inverse order (it is started from sub-key K[16 ]to end with sub-key K[1]). The first block resulting from the inverse permutation is block R[16]L[16 ]and the block
resulting from the last iteration to be submitted to inverse initial permutation IP^−1 is block L[0]R[0]. Permutation IP^−1 provides decrypted block M.
A weakness of DES-type algorithms appears in attacks by differential power analysis of a circuit executing the algorithm. Such attacks consist of making assumptions about the key to correlate an
intermediary result during the iterations to the power consumption of the integrated circuit. Such attacks enable discovering the secret formed by the key. Indeed, function f is known (DES standard),
as well as the input data applied to the algorithm. Supposing a portion of sub-key K by assumption, an intermediary result L[i]R[i ]is obtained. If a correlation between the intermediary result and
the circuit consumption is obtained at a time t, the assumption as to the key is verified. Computing means enables the hackers to make assumptions in a sufficient number, and thus to hack the secret
of the circuit (the key).
A first known solution to attempt to protect a secret handled by a DES algorithm is to mask the execution by introduction of random numbers in the iterations. This solution has the disadvantage of
requiring a modification of the actual algorithm and is thus not applicable to circuits in which the DES execution cell already exists in non-reconfigurable wired logic. Indeed, for rapidity reasons,
the algorithm is generally executed, at least partially, by a cell in wired logic integrated to the circuit using the data. The key is generally stored in a secure circuit area, for example, in an
integrated circuit personalization phase. Its loading into the cell of execution of the algorithm is performed in protected fashion, for example, by applying the methods described in patents
FR-A-2802668 and FR-A-2802669, which are incorporated herein by reference.
A second known solution consists of masking the execution of the algorithm with the secret key by having it execute among several executions (some ten) using false keys. These keys are permanently
stored in a non-volatile memory associated with the algorithm execution processor or directly hardwired in the circuit. The right key is generally written on personalization of the circuit (for
example, of the smart card) by a person different from the circuit manufacturer, in a generally inaccessible area (secure area of the circuit). Thus, a hacker cannot know, when an assumption about a
key is verified, whether the right key has been used or not. A disadvantage of this solution is that, to preserve the masking, it is necessary to protect all the keys (the false ones as well as the
right one) in their loading into the algorithm execution cell. This takes time and lengthens, in a manner incompatible with the desired fast data manipulation, the algorithm execution. Another
disadvantage of this solution is that it only brings white noise, which is thus easily filterable by the hacker.
The present invention aims at improving the security of encryption algorithms, in particular, of DES type, against differential power analysis attacks of an integrated circuit which executes this
The present invention especially aims at providing a solution compatible with the desired rapidity for the data encryptions and decryptions.
The present invention also aims at providing a solution which does not require modifying the actual algorithm and which is thus compatible with cells of conventional execution of the DES algorithm.
To achieve these and other objects, the present invention provides a method for protecting the execution of an algorithmic calculation taking into account at least one valid piece of data and at
least one secret key by an integrated circuit, and performing several iterations of an encryption calculation, comprising executing the algorithm with the valid data between several executions of the
same algorithm with invalid data corresponding to a combination of the valid data with predetermined masks.
According to an embodiment of the present invention, the position of the execution with the valid data in the general execution is randomly selected.
According to an embodiment of the present invention, said combination is, for each masked execution, a bit-to-bit addition of the bits of a block of the valid data with the mask bits.
According to an embodiment of the present invention, the execution with the valid data corresponds to a combination with a neutral mask for the combination operation.
According to an embodiment of the present invention, said predetermined masks are selected so that the result of the application of the algorithm with the same key is different for at least one bit
from the result of the application of the algorithm to the valid data.
According to an embodiment of the present invention, the algorithm is the DES algorithm, the combination taking place before execution of the first iteration.
According to an embodiment of the present invention, the masks are 64-bit blocks to be combined with the 64-bit blocks of the valid data before application of an encryption iteration, the 64-bit
block of each mask comprising among the bits of positions b[7], b[57], b[49], b[41], b[33], and b[25], between 1 and 6 bits at state 1, the bits of all other positions being at state 0.
The present invention also provides a processor of execution of a DES-type encryption algorithm or the like.
The foregoing and other objects, features, and advantages of the present invention will be discussed in detail in the following non-limiting description of specific embodiments.
FIG. 1 represents, very schematically, an example of an integrated processor to which applies the present invention; and
FIG. 2 is a flowchart of an embodiment of the method according to the present invention.
For clarity, only those steps and elements which are necessary to the understanding of the present invention have been shown in the drawings and will be described hereafter. In particular, the
forming of a calculation processor for the implementation of the present invention has not been described in detail, the present invention being implementable with any conventional processor, by
providing the adapted data thereto.
A feature of the present invention is to mask the execution of the encryption algorithm by executing this algorithm several times with false data, thus masking the encryption of the “right” data. The
right data to be encrypted introduced into the algorithm processing cell are combined with masks, preferably predetermined, to create false data on which the encryption algorithm is applied. The
execution of the algorithm with the unmasked introduced data is interposed, preferably at a random position, in the series of masked executions. Preferably, all encryptions are performed with the
same key which is thus transferred only once into the algorithm processing cell.
The masks are in fact data blocks of same size as the data blocks processed by the algorithm at the step selected for the combination, which are combined, preferably, by an XOR type function
(bit-to-bit addition) with the data block to be encrypted. Preferably, the masks are selected according to the algorithm for the result of the application of the algorithm with the same key to be
different for at least one bit from the result of the application of the algorithm to the valid data.
Accordingly, a hacker introducing data that he knows and making assumptions about the key is incapable of obtaining a proper correlation with the integrated circuit power consumption since this power
consumption is a function of different data.
The present invention will be described hereafter in relation with a preferred embodiment with the DES algorithm. It however more generally applies to any encryption algorithm, provided that the
creation of the masks to create false data by modification of a message to be encrypted can be adapted.
Preferably, the masks manipulated by the algorithm which are used to introduce false correlations over the channel (mask the execution) are prerecorded in the integrated circuit containing the cell.
An advantage of executing the algorithm with several data rather than with several keys is that the data need not be masked for the introduction into the cell. The protection then only negligibly
slows down the encryption or decryption of the introduced data with respect to the conventional solution using several keys.
The present invention takes advantage from the fact that, in any encryption algorithm and especially in the DES algorithm, the progress of the calculation results in that successive values can be
predicted by making assumptions about the key. The false messages (masked data) coming up from the beginning result in that these assumptions are seen as relative to a false key. In the DES
algorithm, at each time of the calculation where the key appears in the form of a sub-key with the message, the data and the sub-key are then linked by a function arbitrarily designated as g to
provide an intermediary result arbitrarily designated as I, which is such that I=g(KEY, D). A power analysis attack consists of attempting to correlate results I with the consumption by making
assumptions about key KEY. Knowing data D that it introduces, and knowing function g (the DES algorithm is known), the hacker calculates a result I based on an assumption about key KEY. If the
correlation between value I and the circuit power consumption is verified, this means that the assumption about the key was the right one.
The fact of executing the algorithm on false data results in that the hacker obtains a correlation on modified data D′. As a result, the correlation appears on a key assumption which is not the right
one. In other words, the hacker believes that the algorithm executes function I=g(KEY, D) while it eventually executes I′=g(KEY, D′), with D′=D(+)A, where A designates the mask providing result I′.
The hacker believes he knows the data (that he has introduced) and thus makes assumptions as to the key, based on power analyses. This power consumption is however altered without him knowing it.
In fact, by combining the input data with a mask, the present invention indirectly masks the key by taking into account the fact that the possible attacker makes assumptions as to this key.
When the result provided by the circuit is altered, the “right” execution must be randomly interposed among a few masked executions (the number of masked executions is selected according to the time
available for the algorithm execution). This is especially necessary to properly operate the circuit in the absence of piracy (the right encryption must be providable in a normal execution). This
proper result is provided in a result area different from that in which the false executions can be found.
Preferably, the execution with the valid data actually corresponds to a combination with a neutral mask as to the combination. Thus, no difference is detectable between executions. The only reference
to be temporarily stored to identify the execution with the valid data is its position in all the executions, which preferably corresponds to the result of a random drawing.
FIG. 1 represents, very schematically, an example of processor 1 for implementing the method according to the present invention. Such a processor comprises a central processing unit 11 (CPU) able to
communicate, through one or several buses 12 for data, addresses and control signals, with one or several memories 13 (MEM) and with an input/output interface circuit 14 (I/O) for communicating with
outside. Other integrated elements 15 (FCT) implementing other functions (among which, for example, a dedicated circuit for performing the algorithm the execution of which is to be protected) are
connected to the bus(es) 12 depending on the application
FIG. 2 is a simplified flowchart of an embodiment of the method according to the present invention implemented, for example, by a processor as represented in FIG. 1. Data to be processed (block 21,
DATA INPUT) are received by the processor 1. In this example, a loop of n executions of the algorithm ALGO is initialized (block 22, i=1). For each iteration of the loop, a mask to be applied to the
data is selected (block 23, SELECT MASK). Such a selection is, for example, randomized and the rank of the right execution (with a neutral mask) is stored. The selected mask is applied to the data
(block 24, MASK(DATA)) and the algorithm is executed with the masked data (block 25, EXECUTE ALGO). The algorithm can be executed by the central processing unit 11 (software implementation) and/or by
a dedicated circuit 15 (hardware implementation) and the results of the computations are for example stored in the memory 13. While the loop is not ended (output N of block 26 (i=n ?)), another
iteration (block 27, i=i+1) is performed with another mask. When the n iterations have been made (output Y of block 26), the result of the right execution (masked with a neutral mask) is selected and
outputted (block 28, SELECT AND OUTPUT RESULT).
In the context of the DES algorithm and according to this preferred embodiment, masks or masking data are stored, for example, in a non-volatile memory area, in the integrated circuit.
The mask construction function is a function of the algorithm and must be such that for any message D likely to be selected by the attacker and for any key K (right) or K′ (false), operation g
(bit-to-bit addition in the DES case) of combination of first sub-key K[1 ]or K[1 ]with an intermediary result designated as I (I=E(R[0]) in the DES case) which is a function of the input data before
application of the first sub-key, is such that:
g(I, K[1]′)=g(I′, K[1]), where I′ designates the intermediary result obtained with the masked data.
The masks are however constructed independently from the data D with which they are likely to be combined, these data being however unknown.
For the DES algorithm, when the bits of the initial message are considered, it can be seen that certain bit positions (determined by IP and E) are combined with the key bits, for example, bits 1, 2,
3, 4, 5, and 6 of sub-key K[1 ]are combined by XOR (+) with bits b[7], b[57], b[49], b[41], b[33], and b[25 ]of the introduced data block D. Thus, a masking by combination of six bits m[1], m[2], m
[3], m[4], m[5], and m[6 ]with bits b[7], b[57], b[49], b[41], b[33], and b[25 ]of the data message provides a new message which, once applied to the input of the encryption cell, achieves the same
result at the end of the step of combination with the sub-key. Thus, the hacker which calculates the correlation between the data processed by the algorithm in the first round under the assumption
corresponding to the right key, obtains no correlation, while under the assumption of a false key, he will see a correlation between the predicted key (its assumption) and the effectively-calculated
For the manipulation of false data not to be locatable, the mask (which can be considered as a predetermined data block—the six masking bits at positions b[7], b[57], b[49], b[41], b[33], and b[25])
must be introduced at the cell input.
According to a preferred embodiment, any combination of states 0 and 1 is selected for the six bits b[7], b[57], b[49], b[41], b[33], and b[25 ]of the masking data block (one combination from among
the 64 possible combinations) and all its other bits are set to state 0 (neutral element of the addition), so that the bits of the real data message, other than bits b[7], b[57], b[49], b[41], b[33],
and b[25], are not modified by the mask. As an alternative, the other block bits will be randomly set. This alternative is however not preferred since its risks introducing a white noise.
The above preferred embodiment takes into account the fact that, in the DES algorithm, the application of first substitution S (SBOX) only affects bits b[7], b[57], b[49], b[41], b[33], and b[25 ]of
the data block. Indeed, by representing the 64-bit data blocks in the form of matrixes of eight words of eight bits and, with the above notations, the input data block can be written as:
b[1], b[2], b[3], b[4], b[5], b[6], b[7], b[8];
b[9], b[10], b[11], b[12], b[13], b[14], b[15], b[16];
b[17], b[18], b[19], b[20 ]b[21 ]b[22], b[23], b[24];
b[25], b[26], b[27], b[28], b[29], b[30], b[31], b[32];
b[33], b[34], b[35], b[36], b[37], b[38], b[39], b[40];
b[41], b[42], b[43], b[44], b[45], b[46], b[47], b[48];
b[49], b[50], b[51], b[52], b[53], b[54], b[55], b[56];
b[57], b[58], b[59], b[60 ]b[61 ]b[62], b[63], b[64].
After application of initial permutation IP, this matrix becomes:
b[58], b[50], b[42], b[34], b[26], b[18], b[10 ]b[2];
b[60], b[52], b[44], b[36], b[28], b[20], b[12], b[4];
b[62], b[54], b[46], b[38], b[30], b[22], b[14], b[6];
b[64], b[56], b[48], b[40], b[32], b[24], b[16], b[8];
b[57], b[49], b[41], b[33], b[25], b[17], b[9], b[1];
b[59], b[51], b[43], b[35], b[27], b[19], b[11 ]b[3];
b[61 ]b[53], b[45], b[37], b[29], b[21], b[13], b[5];
b[63], b[55], b[47], b[39], b[31], b[23], b[15], b[7].
When the left-hand and right-hand portions are submitted to the first round, only the right-hand portion:
b[57], b[49], b[41], b[33], b[25], b[17], b[9], b[1];
b[59], b[51], b[43], b[35], b[27], b[19], b[11], b[3];
b[61], b[53], b[45], b[37], b[29], b[21], b[13], b[5];
b[63], b[55], b[47], b[39], b[31], b[23], b[15], b[7],
is modified and becomes:
b[7], b[57], b[49], b[41], b[33], b[25], b[17];
b[25], b[17], b[9], . . . ;
. . . ;
. . . b[15], b[7], b[57].
At the end of expansion step E, eight words of six bits each are obtained, which have the following expression:
b[32], b[1], b[2], b[3], b[4], b[5];
b[4], b[5], b[6], b[7], b[8], b[9];
b[8], b[9], b[10], b[11], b[12], b[13];
b[12], b[13], b[14], b[15], b[16], b[17];
b[16], b[17], b[18], b[19], b[20], b[21];
b[20], b[21], b[22], b[23], b[24], b[25];
b[24], b[25], b[26], b[27], b[28], b[29];
b[28], b[29], b[30], b[31], b[32], b[1].
Thus, data D can be masked by being combined by XOR with a block having at least one of its bits b[7], b[57], b[49], b[41], b[33], and b[25 ]at 1 and all its other bits at 0. Any bit combination of
bits b[7], b[57], b[49], b[41], b[33], and b[25 ]is valid provided that at least one of them has value one.
All the parts of data D are successively masked by applying the same mask to each 64-bit block introduced into the cell.
Of course, the present invention is likely to have various alterations, modifications, and improvements which will readily occur to those skilled in the art. In particular, although the present
invention has been described in relation with a preferred embodiment of false data generation, its transposition to another generation function is within the abilities of those skilled in the art,
respecting the condition that each portion on which the selection function of the DPA attack applies, that is, each six-bit portion at the beginning of the substitution steps, differs by at least one
bit when it is masked.
Further, the practical forming of an algorithmic execution cell for the implementation of the present invention is within the abilities of those skilled in the art based on the functional indications
given hereabove by using conventional programming tools.
Further, other functions of mask combination with the input data may be envisaged, provided to respect the above-described functionalities. The bit-to-bit addition is however preferred due to its
Such alterations, modifications, and improvements are intended to be part of this disclosure, and are intended to be within the spirit and the scope of the present invention. Accordingly, the
foregoing description is by way of example only and is not intended to be limiting. The present invention is limited only as defined in the following claims and the equivalents thereto. | {"url":"http://www.google.com/patents/US7764786?dq=6,108,703","timestamp":"2014-04-20T12:44:48Z","content_type":null,"content_length":"79908","record_id":"<urn:uuid:801f9119-2de5-4e5a-91e1-156c62045ba3>","cc-path":"CC-MAIN-2014-15/segments/1397609538423.10/warc/CC-MAIN-20140416005218-00006-ip-10-147-4-33.ec2.internal.warc.gz"} |
Given an integer n and a finite extension K of Q , find a polynomial of degree n that is irreducible over K
up vote 1 down vote favorite
Given a positive integer n and a finite extension $K$ of $\mathbb{Q}$, can one always find an irreducible polynomial in $K[x]$ of degree n? What if $n$ is prime?
The natural approach is to take a prime ideal $\mathfrak{p}$ in $\mathcal{O}_K$, choose an element $\alpha \in \mathfrak{p} - \mathfrak{p}^2$, and consider the polynomial $x^n - \alpha$. It is
irreducible over $\mathcal{O}_K$ by Eisenstein's Criterion. If $\mathcal{O}_K$ is a Schreier domain, then Gauss's Lemma applies and $x^n - \alpha$ is irreducible over $K$. The problem is that $\
mathcal{O}_K$ need not be a Schreier domain (and Schreier domains are exactly the domains where Gauss's Lemma works).
polynomials number-fields
I think you are trying to find the polynomial explicitly. If you are just wondering whether it exists, the answer is yes - degree n extensions exist for any n and any number field. Just tack on
enough p power roots of unity for each p dividing n and take an appropriate subextension, which exists since the Galois group is abelian. – Hunter Brooks Aug 25 '10 at 3:34
2 Rather than arguing in $K$ and $\mathcal O_K$, why not first localize at $\mathfrak p$, and then argue in $\mathcal O_{K,\mathfrak p}$ (the localization) and its fraction field. The localization
is a DVR, which is good as you could want for applying tools like Eisenstein's criterion and Gauss's Lemma. – Emerton Aug 25 '10 at 3:39
3 HDK: there is no problem at all. A polynomial that is Eisenstein w.r.t. a prime ideal in O_K is irreducible over K. I never heard of Schreier domains before; that concept is unnecessary. If you
look at K as the fraction field of the localization at $\mathfrak p$ then the standard proof that Eisenstein polynomials w.r.t. a prime in a PID goes through. – KConrad Aug 25 '10 at 3:42
By the way, a Schreier domain is not "exactly the domains where Gauss's Lemma holds." There are various meanings of Gauss's Lemma and some of them even work for polynomials over pretty general
commutative rings. – KConrad Aug 25 '10 at 3:44
I lost some words at the end of my first comment. Should be: the standard proof that Eisenstein polynomials w.r.t. a prime in a PID are irreducible over the fraction field of the PID goes through.
– KConrad Aug 25 '10 at 3:46
add comment
3 Answers
active oldest votes
The question has been well-answered in the comments. Here's another approach, somewhat like that advocated by Hunter Brooks. Let $p$ be a prime congruent to 1 modulo $n$ and such that $K\
up vote 2 cap{\bf Q}(e^{2\pi i/p})=\bf Q$. Then $K(e^{2\pi i/p})$ is a cyclic extension of $K$ of degree a multiple of $n$, so it has a subfield of degree $n$ over $K$.
down vote
add comment
Here is a more general result.
Theorem: Let $(K,|\ |)$ be a non-Archimedean normed field with completion $\hat{K}$. Let $\mathcal{L}/\hat{K}$ be a finite separable extension of degree $d$. Then there exists a degree $d$
separable field extension $L/K$ such that $L\hat{K} = \mathcal{L}$.
In particular, as long as the completion of $K$ admits a separable field extension of a certain degree $d$, so does $K$ itself, necessarily of the form $K[t]/(P(t))$ by the primitive
element theorem. Moreover, as long as $K$ has characteristic zero and carries a nontrivial discrete valuation, it admits finite separable extensions of all finite degrees.
up vote 2 For a proof of this theorem using Krasner's Lemma, see Section 3.5 of
down vote
When the norm corresponds to discrete valuation $v$ (e.g. $| \ | = | \ |_{\mathfrak{p}}$ the $\mathfrak{p}$-adic norm for a prime ideal $\mathfrak{p}$ of a number field $K$) one can get
away with less: by weak approximation, there exists $\alpha \in K$ with $v(\alpha) = 1$. For any positive integer $n$ prime to the characteristic of $K$, by Eisenstein's Criterion the
polynomial $t^n - \alpha \in K[t]$ is (separable and) irreducible even over the completion $\hat{K}$, so is certainly irreducible over $K$.
add comment
Your "$x^n-\alpha$" approach is the "ramified" way to go: the extension you get localizes to a totally ramified extension of the local field $K_{\mathfrak{p}}$, which has degree $n$, so
the global extension must have degree $n$ too.
up vote 1 One might instead go in the "unramified" extension. Let $\mathfrak{p}$ be a prime ideal of $\mathfrak{O}_K$, and $k=\mathfrak{O}_K/\mathfrak{p}$ be the residue field. Then there is an
down vote irreducible polynomial of degree $n$ over the finite field $k$; lifting this to a polynomial over $\mathfrak{O}_K$ gives an irredusible polynomial over $K$.
Robin, is "irredusible" the British spelling, or an error? I know about soluble/solvable and centre/center, but irredusible/irreducible for UK/US spelling is completely unfamiliar to
me. – KConrad Aug 25 '10 at 17:12
1 It must be the accusative, since Robin spells it "irreducible" when it's in the nominative in the line before. – Gerry Myerson Aug 27 '10 at 12:45
add comment
Not the answer you're looking for? Browse other questions tagged polynomials number-fields or ask your own question. | {"url":"http://mathoverflow.net/questions/36617/given-an-integer-n-and-a-finite-extension-k-of-q-find-a-polynomial-of-degree-n","timestamp":"2014-04-18T16:19:30Z","content_type":null,"content_length":"66871","record_id":"<urn:uuid:f74794b5-6b18-4b1a-941e-46fbeda8b5d9>","cc-path":"CC-MAIN-2014-15/segments/1397609533957.14/warc/CC-MAIN-20140416005213-00555-ip-10-147-4-33.ec2.internal.warc.gz"} |
Find The forumula for the inverse of a given function
February 10th 2013, 09:37 AM #1
Jan 2011
Find The forumula for the inverse of a given function
So one problem is f(x)=x^3 , In my head I know its x^(1/3) because
Then i think I Do the third square root to both sides to get that answer but am not sure.
This is the one where Im haveing the most trouble
f(x)=(3x+1)/(2x-5) So I Multipy each side by 2x-5 and get
y(2x-5) which factors into
2xy-5y=3x+1 and am not sure what to do from here
Any help would be greatly appreciated.
The answer in the back of the book is y=(5x+1)/(2x-3)
even with that I cant figure out how they came up with it
Re: Find The forumula for the inverse of a given function
transfer all terms with y to the right side and all x to the left and solve for x ...to be a function of y..the interchange the x with y and thats it...you must find
(5x+1)/(2x-3) as inverse to the original function
Good luck
Re: Find The forumula for the inverse of a given function
I can help you to a certain extent, but the ONLY thing I myself am unsure of is why it's 5x+1 and not 5x-1, or -5x+1 conversely.
First, the easiest way to solve this would be to switch the x's and y's. Equation becomes
You were correct to multiply the denominator, then you get
Isolate all terms with y on one side, so I'll subtract 3y from the right and 5x from the left to keep the formatting of your books answer more intact:
Factor out a y
$y(2x-3)=-5x+1$ and divide by 2x-3
Now you just have to hope that either your book is wrong or somebody can explain to you why it's 5x+1 without a negative.
Hope I helped at least a bit.
Re: Find The forumula for the inverse of a given function
It started out as f(x)=(3x+1)/(2x-5) I think you did f(x)=(3x+1)/(2x+5)
Thank you though i just couldn't wrap my head around it.
I Was failing at getting like terms on their own side I think.
I went through it again and got the correct Answer TYVM
Also where is the reference material for this site to make my math problems look like yours
Re: Find The forumula for the inverse of a given function
Oops, 2x-5 would indeed make a ton more sense as to why it's 5x+1 lol. Not sure why my mind read it as 2x+5.
And the way to format math problems like this is called LaTex, there's a specific sub-forum on this website with how to do it all. Everything goes inside [ tex][/tex] brackets.
February 10th 2013, 10:20 AM #2
Senior Member
Feb 2013
Saudi Arabia
February 10th 2013, 10:27 AM #3
Nov 2012
February 10th 2013, 10:38 AM #4
Jan 2011
February 10th 2013, 10:41 AM #5
Nov 2012 | {"url":"http://mathhelpforum.com/algebra/212874-find-forumula-inverse-given-function.html","timestamp":"2014-04-17T20:44:26Z","content_type":null,"content_length":"40574","record_id":"<urn:uuid:1260a6cb-a658-4741-8493-2c4c0873a640>","cc-path":"CC-MAIN-2014-15/segments/1397609530895.48/warc/CC-MAIN-20140416005210-00013-ip-10-147-4-33.ec2.internal.warc.gz"} |
Thevenin-Norton equivalencies
Since Thevenin's and Norton's Theorems are two equally valid methods of reducing a complex network down to something simpler to analyze, there must be some way to convert a Thevenin equivalent
circuit to a Norton equivalent circuit, and vice versa (just what you were dying to know, right?). Well, the procedure is very simple.
You may have noticed that the procedure for calculating Thevenin resistance is identical to the procedure for calculating Norton resistance: remove all power sources and determine resistance between
the open load connection points. As such, Thevenin and Norton resistances for the same original network must be equal. Using the example circuits from the last two sections, we can see that the two
resistances are indeed equal:
Considering the fact that both Thevenin and Norton equivalent circuits are intended to behave the same as the original network in suppling voltage and current to the load resistor (as seen from the
perspective of the load connection points), these two equivalent circuits, having been derived from the same original network should behave identically.
This means that both Thevenin and Norton equivalent circuits should produce the same voltage across the load terminals with no load resistor attached. With the Thevenin equivalent, the open-circuited
voltage would be equal to the Thevenin source voltage (no circuit current present to drop voltage across the series resistor), which is 11.2 volts in this case. With the Norton equivalent circuit,
all 14 amps from the Norton current source would have to flow through the 0.8 Ω Norton resistance, producing the exact same voltage, 11.2 volts (E=IR). Thus, we can say that the Thevenin voltage is
equal to the Norton current times the Norton resistance:
So, if we wanted to convert a Norton equivalent circuit to a Thevenin equivalent circuit, we could use the same resistance and calculate the Thevenin voltage with Ohm's Law.
Conversely, both Thevenin and Norton equivalent circuits should generate the same amount of current through a short circuit across the load terminals. With the Norton equivalent, the short-circuit
current would be exactly equal to the Norton source current, which is 14 amps in this case. With the Thevenin equivalent, all 11.2 volts would be applied across the 0.8 Ω Thevenin resistance,
producing the exact same current through the short, 14 amps (I=E/R). Thus, we can say that the Norton current is equal to the Thevenin voltage divided by the Thevenin resistance:
This equivalence between Thevenin and Norton circuits can be a useful tool in itself, as we shall see in the next section.
• REVIEW:
• Thevenin and Norton resistances are equal.
• Thevenin voltage is equal to Norton current times Norton resistance.
• Norton current is equal to Thevenin voltage divided by Thevenin resistance.
Related Links | {"url":"http://www.allaboutcircuits.com/vol_1/chpt_10/10.html","timestamp":"2014-04-21T10:27:52Z","content_type":null,"content_length":"14554","record_id":"<urn:uuid:d9509646-4580-402d-8a1f-bd6296f95c0c>","cc-path":"CC-MAIN-2014-15/segments/1398223203841.5/warc/CC-MAIN-20140423032003-00064-ip-10-147-4-33.ec2.internal.warc.gz"} |
Subsums of a Zero-sum Free Subset of an Abelian Group
Let $G$ be an additive finite abelian group and $S \subset G$ a subset. Let f$(S)$ denote the number of nonzero group elements which can be expressed as a sum of a nonempty subset of $S$. It is
proved that if $|S|=6$ and there are no subsets of $S$ with sum zero, then f$(S)\geq 19$. Obviously, this lower bound is best possible, and thus this result gives a positive answer to an open problem
proposed by R.B. Eggleton and P. Erdős in 1972. As a consequence, we prove that any zero-sum free sequence $S$ over a cyclic group $G$ of length $|S| \ge {6|G|+28\over19}$ contains some element with
multiplicity at least ${6|S|-|G|+1\over17}$.
Full Text: | {"url":"http://www.combinatorics.org/ojs/index.php/eljc/article/view/v15i1r116/0","timestamp":"2014-04-21T13:20:46Z","content_type":null,"content_length":"14922","record_id":"<urn:uuid:bfaf9a0e-0eee-4e18-ac0b-99a903836a5a>","cc-path":"CC-MAIN-2014-15/segments/1398223201753.19/warc/CC-MAIN-20140423032001-00295-ip-10-147-4-33.ec2.internal.warc.gz"} |
Section: Linux Programmer's Manual (3) Updated: 2010-09-20 Local index Up
tgamma, tgammaf, tgammal - true gamma function
#include <math.h>
double tgamma(double x);
float tgammaf(float x);
long double tgammal(long double x);
Link with -lm.
Feature Test Macro Requirements for glibc (see feature_test_macros(7)):
tgamma(), tgammaf(), tgammal():
_XOPEN_SOURCE >= 600 || _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L;
or cc -std=c99
The Gamma function is defined by
Gamma(x) = integral from 0 to infinity of t^(x-1) e^-t dt
It is defined for every real number except for nonpositive integers. For nonnegative integral m one has
Gamma(m+1) = m!
and, more generally, for all x:
Gamma(x+1) = x * Gamma(x)
Furthermore, the following is valid for all values of x outside the poles:
Gamma(x) * Gamma(1 - x) = PI / sin(PI * x)
On success, these functions return Gamma(x).
If x is a NaN, a NaN is returned.
If x is positive infinity, positive infinity is returned.
If x is a negative integer, or is negative infinity, a domain error occurs, and a NaN is returned.
If the result overflows, a range error occurs, and the functions return HUGE_VAL, HUGE_VALF, or HUGE_VALL, respectively, with the correct mathematical sign.
If the result underflows, a range error occurs, and the functions return 0, with the correct mathematical sign.
If x is -0 or +0, a pole error occurs, and the functions return HUGE_VAL, HUGE_VALF, or HUGE_VALL, respectively, with the same sign as the 0.
See math_error(7) for information on how to determine whether an error has occurred when calling these functions.
The following errors can occur:
Domain error: x is a negative integer, or negative infinity
errno is set to EDOM. An invalid floating-point exception (FE_INVALID) is raised (but see BUGS).
Pole error: x is +0 or -0
errno is set to ERANGE. A divide-by-zero floating-point exception (FE_DIVBYZERO) is raised.
Range error: result overflow
errno is set to ERANGE. An overflow floating-point exception (FE_OVERFLOW) is raised.
glibc also gives the following error which is not specified in C99 or POSIX.1-2001.
Range error: result underflow
An underflow floating-point exception (FE_UNDERFLOW) is raised.
errno is not set for this case.
These functions first appeared in glibc in version 2.1.
C99, POSIX.1-2001.
This function had to be called "true gamma function" since there is already a function gamma(3) that returns something else (see gamma(3) for details).
If x is negative infinity, errno is not set (it should be set to EDOM).
In glibc versions 2.3.3 and earlier, an argument of +0 or -0 incorrectly produced a domain error (errno set to EDOM and an FE_INVALID exception raised), rather than a pole error.
gamma(3), lgamma(3)
This page is part of release 3.27 of the Linux man-pages project. A description of the project, and information about reporting bugs, can be found at http://www.kernel.org/doc/man-pages/.
This document was created by man2html, using the manual pages.
Time: 21:57:23 GMT, April 16, 2011 | {"url":"http://www.makelinux.net/man/3/T/tgammaf","timestamp":"2014-04-17T01:41:55Z","content_type":null,"content_length":"12381","record_id":"<urn:uuid:2b612b24-d262-4ff5-be6e-8a5a8cdf0f34>","cc-path":"CC-MAIN-2014-15/segments/1398223203841.5/warc/CC-MAIN-20140423032003-00597-ip-10-147-4-33.ec2.internal.warc.gz"} |
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional
development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here. | {"url":"http://nrich.maths.org/public/leg.php?group_id=40&code=218","timestamp":"2014-04-17T01:20:28Z","content_type":null,"content_length":"57143","record_id":"<urn:uuid:c06793ac-e8dd-4ec0-8751-8e78d9992922>","cc-path":"CC-MAIN-2014-15/segments/1398223207985.17/warc/CC-MAIN-20140423032007-00499-ip-10-147-4-33.ec2.internal.warc.gz"} |
Help needed with martices and conics
June 25th 2007, 12:24 PM #1
Jun 2007
I'm not sure this is where I should put this, but I didn't see anywhere else:
Using the determinant of a matrix representing a conic,
[a b d]
[b c e]
[d e f]
where the equation of the conic is
and the determinant of the top left 2-by-2 matrix, how would you classify the conic?
2) (Refering to the d and e of the previous question)
Show that d^2+e^2 stays the same under a rotation of axes, in other words, the matrix is multiplied by
[cos(z) -sin(z) 0]
[sin(z) cos(z) 0]
[0 0 1]
Note: It's a 3x3 matrix
Thanks in advance!
1) Check the sign of the discriminant:
$b^2-ac \begin{cases} <0: \mbox{ellipse}\cr =0: \mbox{parabola} \cr >0: \mbox{hyperbola} \end{cases}$
2) Let $d', \ e'$ be the respective coefficients after the rotation. Calculate to get $d'=dcosz+esinz, \ d'=ecosz-dsinz.$ So $d'^2+e'^2=d^2+e^2$.
July 9th 2007, 07:42 AM #2 | {"url":"http://mathhelpforum.com/advanced-algebra/16268-help-needed-martices-conics.html","timestamp":"2014-04-17T07:38:14Z","content_type":null,"content_length":"32872","record_id":"<urn:uuid:48282d27-1a8f-4107-836c-669adad2fc1d>","cc-path":"CC-MAIN-2014-15/segments/1397609526311.33/warc/CC-MAIN-20140416005206-00418-ip-10-147-4-33.ec2.internal.warc.gz"} |
Posts by
Total # Posts: 13
A particle starts at the point (5,0) at t=0 and moves along the x-axis in such a way that at time t>0 its velocity v(t) is given by v(t)= t/(1+t^2). a). Determine the maximum velocity of the
particle. Justify your answer. b). Determine the position of the particle at t=6. c...
ALGEBRA 1 HELP
a). 4^(-1) is the same as 1/4. Since this is the diameter, you divided it by the 2 to get the radius. So the radius is 1/8. Now the expression is: A= pi*(1/8)^2 or A=(1/64)*pi b). In part a, the
expression is for the area of one punched hole. Since you have three punched holes...
1. The first thing you need to do is convert 60km to meters, or 10,000m to kilometers; whichever you prefer. Next,it helps if you draw a right triangle. The plane is at a height of 10,000m; this is
the vertical leg of the triangle. It is 60 km away from the airport; this is th...
In the interval (0 is less than or equal to x which is less than or equal to 5), the graphs of y=cos(2x) and y=sin(3x) intersect four times. Let A, B, C, and D be the x-coordinates of these points so
that 0<A<B<C<D<5. Which of the definite integrals below repres...
Algebra 1
Whenever you have a number raised to a negative power, you have to divide it. So 6y^-3 becomes (6)/(y^3)
Algebra 1 HELP
So you have (8^6)/((8^4)*(8^2)). I would start with the denominator. When you are multiplying exponents with the same base, you add the exponents. So the above equation becomes (8^6)/(8^6). This
simplifies to 1. For the second problem, it's slightly different. You have (4^...
What is the integral of (x*f(x))dx?
Thank you!
I'm a little confused with this integration problem: If the definite integral from 0 to 2 of (e^(x^2)) is first approximated by using two inscribed rectangles of equal width and then approximated by
using the trapezoidal rule with n=2, the difference between the two approx...
state the error and rewrite the sentence.who did max always want you to meet
misplaced nodifier
The mystery has been solved after ten years of a missing portrait.
misplaced nodifier
i dont understand
misplaced nodifier
we finally found the fire extinguisher we had been hunting for behind a pile of logs | {"url":"http://www.jiskha.com/members/profile/posts.cgi?name=rasheda","timestamp":"2014-04-19T07:33:35Z","content_type":null,"content_length":"8750","record_id":"<urn:uuid:6086ff8a-7daa-4d0a-8f08-626f5a7344b1>","cc-path":"CC-MAIN-2014-15/segments/1397609536300.49/warc/CC-MAIN-20140416005216-00097-ip-10-147-4-33.ec2.internal.warc.gz"} |
Math Forum - Ask Dr. Math Archives: Elementary Multiplication
This page:
Dr. Math
See also the
Dr. Math FAQ:
multiplication facts
order of operations
Internet Library:
T2T FAQ:
learning to multiply
3D and higher
Golden Ratio/
Fibonacci Sequence
Number Sense/
About Numbers
large numbers
place value
prime numbers
square roots
Word Problems
Browse Elementary Multiplication
Stars indicate particularly interesting answers or good places to begin browsing.
Selected answers to common questions:
Flashcards/worksheets on the Web.
Learning to multiply.
Least common multiple, Greatest common factor.
Number sentences.
Order of operations.
We said: 568 x 11 and after about 5 seconds she said the answer was 6248. How did she do it so quickly?
How come when you multipy 0.36 and 88 you get 9.4270, which is less than what it should be?
Why is the sum of the two digits 9 when you multiply 9 times any number between 1 and 10?
Why does any number times zero equal zero?
Why does counting up the total decimal places when multiplying decimal numbers work?
Why does multiplying by a decimal decrease the answer? How can you have less than what you started with when you multiply?
If multiplication is defined as repeated addition, why is the product of two fractions smaller than either of the fractions?
8541 * 4372 = 37340252 - How can I check my answer?
Can you multiply mixed numbers without changing them into improper fractions?
Why do you need to convert mixed numbers to improper fractions before multiplying them together? What is the mathematical reason behind this operation?
Multiplying negative integers by breaking each negative number into a positive number multiplied by -1.
An adult ponders his elementary school lessons of multiplication and negative numbers. We can rewrite -2*3 as -2 + -2 + -2, but how can we re- write -2 * -3?
If you are multiplying three sets of 8 do you write the problem 3x8 or 8x8?
I don't know what 6 times 6 is.
Can you show me how to multiply two-digit numbers like 39 x 98?
How do you use Napier's Bones to do multiplication?
How do Napier's bones work?
Let's say 3 x 2 = 6. Three is how many kids there are in a 'group.' Two is how many 'groups' there are, and six is the answer. Now let's say 3 x (-2) = -6. How can you have negative two 'groups'
of three kids?
When you multiply decimals, why is there always the same number of decimal places in the answer as in the problem?
What are the definitions for addition and multiplication of: closure, commutative, associative, and identity?
Find the smallest possible natural number that ends in 6 such that if the 6 is erased and placed in front of the remaining digits, the resulting number is 4 times as large as the original number.
How do you do problems like 14 x 7?
Write 1,000,000,000 as the product of two numbers, neither of which contains any zeros.
Why does the order of operations have to be in that order? Who set that specific order of operations?
Why do we learn to multiply starting with the least significant digits in the ones place, instead of starting with the larger place values?
Evaluate the expression: 30 - 5^2 + 4^3.
How do I solve (8.2 - 3.6)(3 * 3.6 + 6)?
Given a+3 and b+5, is 105 / ab 7 or 175?
I need help figuring out the steps in this expression: 5-{-4[2^4-11(-9- 1)]}=
Is the associative property an exception to the order of operations, a corollary, or something totally unrelated?
Does the distributive property contradict the rules of order of operations? When we have a(b + c) order of operations says we should add first in the parentheses, then multiply, but the
distributive property says we can multiply first to get ab + ac, then add.
How can I do two-digit multiplications (e.g., 99*98) without having to use paper?
What are the numbers 4 and 1 called in the subtraction 4 - 1 = 3?
I need a page of information on the commutative, associative, and F.O.I.L. properties.
At the high school level it is difficult to prove that -1 x -1 = 1. Is there a published proof somewhere that is appropriate for kids that age?
Doctor Vogler describes the "accumulator" method for finding products of two multi-digit terms, then works through an example.
I teach fourth grade math. Are rectangular arrays the best way to teach multiplication?
I have a project to do on "Russian" or "peasant" multiplication.
What is Russian peasant multiplication?
Can you explain what a square number is?
Page: [<prev] 1 2 3 4 5 [next>] | {"url":"http://mathforum.org/library/drmath/sets/elem_multiplication.html?start_at=121&num_to_see=40&s_keyid=39606828&f_keyid=39606829","timestamp":"2014-04-16T04:41:00Z","content_type":null,"content_length":"21364","record_id":"<urn:uuid:768f0a11-a60d-400d-8934-9dbc1e109c57>","cc-path":"CC-MAIN-2014-15/segments/1397609521512.15/warc/CC-MAIN-20140416005201-00006-ip-10-147-4-33.ec2.internal.warc.gz"} |
Le Monde puzzle [#827]
ack to R (!) for the current Le Monde puzzle:
Given an unknown permutation of the set {1,…,6}, written on the faces of a cube, there exist a sequence of summits such that increasing by one unit the three numbers of the faces sharing the
successive summits in the sequence leads to identical values over all faces. What was the initial permutation? What is the minimal number of steps to reach equality?
My initial worry was to rewrite the summit constraint(s) in a manageable way. I tried with a 6×8 matrix, calling 1 the bottom face and 6 the top face (which are thus the only two that cannot get
changed at the same time):
for (i in 2:5){
First, I sought a random exploration of the faces. However, I did impose the smallest and largest values on the top and bottom faces as they are the ones getting most and least updated compared with
the other faces (?):
for (alea in 1:10^3){
for (T in 1:100){
if (diff(range(faces))==0) break()
if (diff(range(faces))==0){
The outcome is unsurprising in that the smallest number of summits is then 5, making all faces equal to 6. For a starting value equal to, e.g., {1,2,3,5,4,6}. (Something that tooks a [wee] while for
me to understand was why removing the sample(2:5) in the above makes a difference.) The solution in Le Monde spells out the solution more clearly as a cube whose opposite faces should sum up to 7… | {"url":"http://xianblog.wordpress.com/2013/07/03/le-monde-puzzle-827/","timestamp":"2014-04-20T06:45:55Z","content_type":null,"content_length":"36251","record_id":"<urn:uuid:ee4222a6-90ae-4cdb-9fbd-a45025d20dfb>","cc-path":"CC-MAIN-2014-15/segments/1398223202548.14/warc/CC-MAIN-20140423032002-00256-ip-10-147-4-33.ec2.internal.warc.gz"} |
Help solving linear equations - Math and Physics
Hi I'm trying to implement a fast triangle-triangle intersection algorithm (Tropp06,
In Stage 4 of the paper I have found the line of intersection between the plane of triangle B and triangle A, this a vector t emenating from a point T.
The edge of B that I'm looking for intersection with is defined as a point in B, P plus an edge vector p.
So the equation as given in the paper is of the from
P + d p = T + g t
where d and g are scalar multiples of the vectors p and t.
P,p,T and t are all known. d and g are the unknown scalars I need to solve for.
The goal here is to save operations and avoid using divides. The paper also hints at using determinants to save calculations.
The result is a point where the line T+t and P+p cross.
I re-write the equation to look like this -d p + g t = (P-T) in an attempt to make it look more like what I find in linear algebra texts.
I look at this as a series of 3 equations of 2 variables. Something like:
-d * p.x + g * t.x = (P-T).x
-d * p.y + g * t.y = (P-T).y
-d * p.z + g * t.z = (P-T).z
Now, all the examples I can find show how to solve for 3 equations and 3 variables, or 2 equations and 2 variables, not 3 equations and 2 variables.
Also, the paper says that since the vectors lie in the same plane "2 x 2 equations sets are solved".
Thanks to anyone who can help with this. | {"url":"http://www.gamedev.net/topic/607554-help-solving-linear-equations/","timestamp":"2014-04-20T08:26:26Z","content_type":null,"content_length":"107990","record_id":"<urn:uuid:96c4a279-8264-4e72-a2df-5021e7c2b942>","cc-path":"CC-MAIN-2014-15/segments/1397609538110.1/warc/CC-MAIN-20140416005218-00108-ip-10-147-4-33.ec2.internal.warc.gz"} |
ModelDB: Medial reticular formation of the brainstem: anatomy and dynamics (Humphries et al. 2006, 2007)
This code is freely available for modifcation and extension, please
cite the original sources (see below). For discussion and assistance
please contact: m.d.humphries@shef.ac.uk or drmdhumphries@gmail.com
This MATLAB code builds the medial reticular formation (mRF) anatomy
models detailed in Humphries, Gurney & Prescott (2006) [HGP06]. The
main function (discrete_cluster1.m) constructs either form of the
"stochastic" model from HGP06. The function pruning_model.m constructs
either form of the "pruning" model from HGP06: it calls
discrete_cluster1.m to construct the first, overgrowth phase of the
The main function (discrete_cluster1.m) also includes options to
simulate the constructed model as a network of leaky integrator
neurons (aka firing rate units) to examine its basic dynamics. This
simulation model is sketched in Humphries, Gurney & Prescott (2010)
[HGP10]; in that paper we looked at how the fidelity of input-output
encoding in the mRF model depended on the scale of inputs and outputs
one was considering. The MSc thesis of Donoso (2008) is a preliminary
study of the relationship between the mRF model's structure and the
oscillatory dynamics that result.
The reasons for studying the mRF as a potential brainstem action
selection system are reviewed in Humphries et al (2007) and Humphries,
Gurney & Prescott (2010)
Main Files:
discrete_cluster1.m: builds the mRF anatomy model using the
"stochastic" algorithm; optionally runs that
model as a dynamic system
pruning_model.m: builds the mRF anatomy model using the "pruning"
algorithm example_run_of_model.m: shows how to specify all the
parameters, and run a single instance of the model, with
interesting dynamics.
example_script_using_parameters_from_MNAS_book_chapter: an alternative
specification of the model, as used in HGP10
cluster_input_IO_patterns: runs the complete set of cluster input
simulations, examining the fidelity of input-output responses
(from HGP10, Fig5c,d) proj_input_IO_patterns: runs the complete
set of projection-unit input simulations, examining the fidelity
of input-output responses (from HGP10, Fig5a,b)
Support Functions (folder LI_network_toolbox, make sure this is on
your MATLAB path):
LI_network.m: called by discrete_cluster1.m to run the mRF anatomy
model as a network of leaky integrators; this in turn
calls the MEX function LI_network_C
LI_network_C.c: the source C-code for the MEX function; this is
supplied compiled as both 32-bit (.dll) and 64-bit
(.mexw64) Windows versions. It is strongly suggested
that this function is recompiled for your platform to
avoid problems: type "help mex" for information at the
MATLAB prompt
LI_network_ode.m: optionally called by discrete_cluster1.m to run the
mRF model as a network of leaky integrators, using
MATLAB's built-in ODE solver, rather than the custom
MEX file. Useful for checking the consistency of
results, but orders-of-magnitude slower than the MEX
Statistics Toolbox (for normrnd and gamrnd functions: these are easily
replaced or found)
Open questions - some suggestions for ideas to pursue
(1) How do the graph properties of the network scale with the number
of neurons? Due to computational limitations at the time, the mRF
anatomy model was built up to a maximum of 3750 nodes (75 clusters and
50 neurons per cluster). Yet the number of neurons-per-cluster is
likely to be at least an order of magnitude bigger than this. [Any
anatomical model]
(2) What are the effects of changing the power-law exponent on
connectvity in the distance-dependent model? [Stochastic model]
(3) The pruning model has numerous parameters that remain unexplored:
(i) Choice of starting model (spatially-uniform vs
distance-dependent probability of connections)
(ii) choice of initial weight distribution (width of Gaussian;
log-normal distributions etc)
(iii) Choice of parameters for weight updating
(iv) Threshold for pruning
(4) How might we alter the weight update algorithm for the pruning
(1) What are the effects of weight choice and distribution on the
intrinsic dyna mics? (Oscillations, stability etc)
(2) How do the different construction algorithms affect the resultant
(3) What are the parameter regimes dividing stable from oscillatory
(4) How could the intrinsic dynamics of the model support "selection
of actions" ?
(5) And, of course, what are the dynamics of the system if we using
spiking neuron models?
Humphries, M. D., Gurney, K. & Prescott, T. J. (2006) The brainstem
reticular formation is a small-world, not scale-free,
network. Proceedings of the Royal Society B. Biological Sciences, 273,
503-511. [PDF supplied with code]
Humphries, M. D., Gurney, K. & Prescott, T. J. (2007) Is there a
brainstem substrate for action selection? Phil Trans R Soc B, 2007,
362, 1627-1639. [PDF supplied with code]
Donoso, J. R. (2008) Dynamics of the brainstem action selection
systems. MSc Thesis, University of Sheffield. Supervisor: Dr M
Humphries. [PDF supplied with code]
Humphries, M. D., Gurney, K. & Prescott, T. (2010) The medial
reticular formation: a brainstem substrate for simple action
selection? In A. K. Seth, T. J. Prescott and J. J. Bryson (Eds)
Modelling Natural Action Selection. Cambridge, UK: CUP. In press. [PDF
supplied with code] | {"url":"http://senselab.med.yale.edu/ModelDB/ShowModel.asp?model=128816","timestamp":"2014-04-21T09:41:05Z","content_type":null,"content_length":"20997","record_id":"<urn:uuid:70fb9083-58da-4fc0-af16-230ee712b114>","cc-path":"CC-MAIN-2014-15/segments/1397609539705.42/warc/CC-MAIN-20140416005219-00459-ip-10-147-4-33.ec2.internal.warc.gz"} |
Got Homework?
Connect with other students for help. It's a free community.
• across
MIT Grad Student
Online now
• laura*
Helped 1,000 students
Online now
• Hero
College Math Guru
Online now
Here's the question you clicked on:
The product of n whole numbers 1 x 2 x 3 x 4 x ... x (n-1) x n, has twenty-eight consecutive zeros. Find the largest value of n.
Best Response
You've already chosen the best response.
what are zeros??
Best Response
You've already chosen the best response.
"0". This is a zero. Consecutive zeros are zeros that appear consecutively, i.e. The product of 10 x 10x 10 has 3 consecutive zeros (1ooo)
Best Response
You've already chosen the best response.
It's somewhat tedious to explain the whole thing. One interesting observation is there would be only trailing zeroes.
Best Response
You've already chosen the best response.
@ffm i'll try before you
Best Response
You've already chosen the best response.
Just tell me how you work it out, or the solution/methodology. The answer is not so important.
Best Response
You've already chosen the best response.
i think between 1 and 10, you will have 2 zeros.
Best Response
You've already chosen the best response.
I have used binary search along with the usual De Polignac's formula (just) twice to yield 124 as the answer. Ref: http://en.wikipedia.org/wiki/De_Polignac%27s_formula
Best Response
You've already chosen the best response.
"Consecutive zeros are zeros that appear consecutively, i.e. The product of 10 x 10x 10 has 3 consecutive zeros (1ooo)" You haven't understood the problem.
Best Response
You've already chosen the best response.
sorry, 139
Best Response
You've already chosen the best response.
@ffm is it correct??
Best Response
You've already chosen the best response.
33 for 139.
Best Response
You've already chosen the best response.
I have posted the correct answer.
Best Response
You've already chosen the best response.
ah ... where did i screwed up??
Best Response
You've already chosen the best response.
@FoolforMath, how did you manage to get 124?
Best Response
You've already chosen the best response.
3 zeros ,,,?? how 25*22 = 00 => two zeros were coming from here. so all the factors of 100 or 1000 or 10000 ... were causing problem for my idea.
Best Response
You've already chosen the best response.
1-10 : 2 zeros 10-20: 2 20-30: 3 (25 is factor of 100) 30-40: 2 40-50: 3 (50 is factor of 100) 60-60: 2 60-70: 2 70-80: 3 (at some point 75 will give two zeros) 80-90: 2 90-100: 3 (100 itself
gives two) ----------------------- so from 0 to 100 we have: 24 zeros 100-110: 2 110-120: 2 ----------------------- I guess that would give 28 zeros screw you ---> minions of 100
Best Response
You've already chosen the best response.
the answer was n = 120
Best Response
You've already chosen the best response.
The largest power of 5 dividing n must be 5^28.Now use De Polignac's Formula.
Best Response
You've already chosen the best response.
120! =
Of course you need an analytic proof of that using 2 and 5.
Best Response
You've already chosen the best response.
Should the question be, find the smallest n to achieve that?
Your question is ready. Sign up for free to start getting answers.
is replying to Can someone tell me what button the professor is hitting...
• Teamwork 19 Teammate
• Problem Solving 19 Hero
• Engagement 19 Mad Hatter
• You have blocked this person.
• ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.
This is the testimonial you wrote.
You haven't written a testimonial for Owlfred. | {"url":"http://openstudy.com/updates/4f82a1b5e4b0505bf083e6b7","timestamp":"2014-04-17T06:52:24Z","content_type":null,"content_length":"76548","record_id":"<urn:uuid:2d49c146-1ec6-4678-93e8-029269883441>","cc-path":"CC-MAIN-2014-15/segments/1397609526311.33/warc/CC-MAIN-20140416005206-00354-ip-10-147-4-33.ec2.internal.warc.gz"} |
Material Results
Search Materials
Return to What's new in MERLOT
Get more information on the MERLOT Editors' Choice Award in a new window.
Get more information on the MERLOT Classics Award in a new window.
Get more information on the JOLT Award in a new window.
Go to Search Page
View material results for all categories
Click here to go to your profile
Click to expand login or register menu
Select to go to your workspace
Click here to go to your Dashboard Report
Click here to go to your Content Builder
Click here to log out
Search Terms
Enter username
Enter password
Please give at least one keyword of at least three characters for the search to work with. The more keywords you give, the better the search will work for you.
select OK to launch help window
cancel help
You are now going to MERLOT Help. It will open a new window.
College Algebra or Liberal Arts math students are presented with two Questions of the Day and a write-pair-share activity...
see more
Material Type:
James Rutledge
Date Added:
Sep 29, 2009
Date Modified:
Aug 14, 2012
This is a Stand Alone Powerpoint on Fractions, Decimals, and Percents. It is intended for fifth grader learners, after the...
see more
Material Type:
Lisa Napierala
Date Added:
Nov 26, 2011
Date Modified:
Dec 14, 2011
This is a Goal Directed Instructional Design Plan created to be used with the Algebra Equation web app at MathPlayground.com.
see more
Material Type:
Sophia Borden
Date Added:
Oct 30, 2012
Date Modified:
Oct 30, 2012
Goal-directed Instructional Design Plan
Material Type:
Scott Hudson
Date Added:
Mar 22, 2011
Date Modified:
Apr 08, 2011
This classroom activity presents Calculus II students with some Flash tutorials involving work and pumping liquids along with...
see more
Material Type:
James Rutledge
Date Added:
Sep 29, 2009
Date Modified:
Aug 14, 2012
This classroom activity presents Calculus II students with some Flash tutorials involving work and pumping liquids along with...
see more
Material Type:
James Rutledge
Date Added:
Sep 29, 2009
Date Modified:
Aug 14, 2012
In this cooperative learning activity, students are presented with a real-world problem: Given a mirror and laser pointer,...
see more
Material Type:
Joanne Nelson
Date Added:
Dec 16, 2009
Date Modified:
Nov 05, 2013
A lesson that reinforces the major ideas involving linear functions through the real world situation of choosing between cell...
see more
Material Type:
Kristina Badgley
Date Added:
Nov 06, 2010
Date Modified:
Dec 15, 2010
Here is a lesson plan and assignment to teach students the concept of finding percent of a number through the application of...
see more
Material Type:
Liz Klein
Date Added:
Jan 21, 2012
Date Modified:
Jul 21, 2012
Es el OA del Histograma con su actividad correspondiente
Material Type:
Date Added:
Jul 18, 2011
Date Modified:
Jul 18, 2011 | {"url":"http://www.merlot.org/merlot/materials.htm?nosearchlanguage=&pageSize=&page=4&materialType=Assignment&category=2513&sort.property=overallRating","timestamp":"2014-04-17T20:39:29Z","content_type":null,"content_length":"178646","record_id":"<urn:uuid:3f23bae3-123c-4c65-88c1-821c2b8ce0f1>","cc-path":"CC-MAIN-2014-15/segments/1397609530895.48/warc/CC-MAIN-20140416005210-00636-ip-10-147-4-33.ec2.internal.warc.gz"} |
Homework Help
Posted by Alex on Saturday, February 21, 2009 at 4:39pm.
How do I solve lim(x-->pi/4)(sinx-cosx)/cos(2x)
The (x-->pi/4) goes below the lim.
Should i just substitute the x's with pi/4??
• Calculus - Alex, Saturday, February 21, 2009 at 5:07pm
This question is related to limits.
• Calculus - drwls, Saturday, February 21, 2009 at 5:15pm
If you do that, you will get 0/0. You have to take the ratio of the derivatives.
= lim(x->pi/4)(cosx+sinx)/-2 sin(2x)
= sqrt 2/(-2) = -0.707
• Calculus - drwls, Saturday, February 21, 2009 at 5:18pm
That's called using L'Hopital's rule for indeterminate-ratio limits. It works for 0/0 or infinity/infinity. Try it with a number close to pi/4, such as 0.785, and you will see that it gives the
right answer.
• Calculus - bobpursley, Saturday, February 21, 2009 at 5:20pm
if you put in PI/4 in to the x, you will get an indeterminate form 0/0.
Lim (sinx/cos2x - cosx/cos2x)
multiply numerator and denominator by (sinx+cosx)
lim (sin^2x -cos^2x)/cos2x(sinx+cosx)
lim (sin^2x-cos^2x)/(sin^2x-cos^2x)(sinx+cosx)
lim 1/(sinx+cosx)= 1/sqrt2
check that.
• Calculus - bobpursley, Saturday, February 21, 2009 at 5:22pm
looking at drwls answer, using L'Hopitals rule (I assumed you had not gotten to it yet), I see I must have made a sign error, you can find it.
• Calculus - Rina, Saturday, February 21, 2009 at 5:33pm
Thanks. Actually i did not learn that other rule yet and I don't think we will but thanks anyway it was helpful.
I solved using bobpursley's idea and got sqrt2/2=1/sqrt2.
• Calculus - Alex, Saturday, February 21, 2009 at 5:39pm
Thanks everyone!
• Calculus - Alex, Saturday, February 21, 2009 at 5:48pm
I have a similar question relating to limits that I solved
lim(x-->0) (1-cosx)/2x^2
I multiplied the numerator and denominator by (1+cosx) to get
lim(x->0) (1-cos^2x)/2x^2(1+cosx)
= lim(x->0)sin^2x/2x^2(1+cosx)
the lim(x->0) (sinx/x)^2 would =1
I then substituted the remaining portion with 0 and got 1/4
Is this answer right??
Related Questions
CALCULUS - Could someone please solve these four problems with explanations? I'd...
Calculus..more help! - I have a question relating to limits that I solved lim(x...
calculus - calculate the lim as x-> pi (cos(x)+1)/(x-pi) using the special ...
math - i need some serious help with limits in pre-calc. here are a few ...
calculus - The limit represents the derivative of some function f at some number...
Calculus - Below are the 5 problems which I had trouble in. I can't seem to get ...
Calculus - Find the following limits algebraically or explain why they don’t ...
Calculus - Using L'Hopital's rule find the limit if exists of; lim x->1 (cosx...
Calculus - Evaluate the following limit: lim x->(pi/2) [((pi/2)-(x))/cosx] ...
Maths Calculus Derivatives & Limits - Using the definition of the derivative ... | {"url":"http://www.jiskha.com/display.cgi?id=1235252355","timestamp":"2014-04-21T04:01:07Z","content_type":null,"content_length":"10830","record_id":"<urn:uuid:3620ded9-20ee-4515-8a8c-ed49310f861c>","cc-path":"CC-MAIN-2014-15/segments/1398223206147.1/warc/CC-MAIN-20140423032006-00407-ip-10-147-4-33.ec2.internal.warc.gz"} |
April 20th
April 20th
Basic Algebraic Operations and Simplification
We can say that the basic algebraic operations you must master are:
• addition (of two or more terms or expressions)
• subtraction (of one term or expression from another)
• multiplication (of one term or expression by another) In the case of multiplication, it turns out to be useful not only to start with two expressions and be able to write down the result of
multiplying them together, but also, to be able to start with an expression and rewrite it as the product of two or more factors.
• division (of one term or expression by another this leads to the whole subject of working with fractions containing literal symbols.)
• manipulating radicals or roots, particularly square roots, of algebraic expressions
Because the presence of literal symbols in algebraic expressions can lead to considerable (indeed terrifying) complexity when some of these basic operations are performed, a very important algebraic
skill is the ability to simplify algebraic expressions of various sorts, whenever such a thing is possible. Simplification is something you do a lot in algebra (and in mathematics in general), though
it is a bit difficult to define precisely what is meant by one expression being simpler than another in all situations. Also, exactly how one might achieve a simplification depends on the features of
the algebraic expression with which you are dealing. In general:
one expression is simpler than another if it has fewer terms, or if its parts have fewer terms (for example, in the case of fractions)
The catch is that in the process of simplifying an expression, we must make sure that the new simpler expression is mathematically equivalent to the original expression it evaluates to the same
value as the original expression whenever the same values are substituted for corresponding literal symbols in the two. The rules and strategies for simplification that we will describe are intended
to ensure that this requirement is satisfied. By imposing this requirement, we are able to discard the original more complicated expressions and continue to work with the simplified version since in
the end the simplified version must give exactly the same results.
When doing algebra, it is generally expected that where an obvious simplification of an expression is possible, you will carry out that simplification before stating a final solution to a problem.
What are obvious possible simplifications to check for depends on the situation. The most important and common strategies for simplification of various types of expressions will be described with
examples in the next few sections of these notes. | {"url":"http://www.algebra-online.com/tutorials-2/algebraic-operations-simplification-1.htm","timestamp":"2014-04-20T03:38:54Z","content_type":null,"content_length":"19501","record_id":"<urn:uuid:bcb88187-ac83-4662-8a78-75bdf380df40>","cc-path":"CC-MAIN-2014-15/segments/1397609537864.21/warc/CC-MAIN-20140416005217-00087-ip-10-147-4-33.ec2.internal.warc.gz"} |
Homework Help
Posted by Anonymous on Friday, August 14, 2009 at 9:21pm.
What is the exact value of cot(5(pi)/6)?
• MATH - MathMate, Friday, August 14, 2009 at 9:58pm
= cos(5π/6) / sin(5π/6)
= sin(π/2 - 5π/6)/ cos(π/2 - 5π/6)
= sin(-π/3)/cos(-π/3)
= -sin(π/3)/cos(π/3)
= -(sqrt(3)/2)/(1/2)
= -sqrt(3)
• MATH - drwls, Friday, August 14, 2009 at 10:04pm
Use Google, if you don't have a calculator. Type
tan(5*pi/6) =
in the search box.
Then take the reciprocal of that answer, for the cotangtent.
You may recognize the answer as the square root of 3.
5 pi/6 is a 150 degree angle. The reference angle is 30 degrees, but cosine is negative in the second quadrant.
Related Questions
pre-calc - Can someone help me find the exact value of 4csc(3pi/4)-cot(-pi/4)? ...
Pr-Cal/Trig - 1)if the graph of f(x)=cotx is transformed by a horizontal shrink ...
trig - Find the exact value of the trigonometric function. -cot(pi/4 + 16pi)
PreCalculus - Hi I need some assistance on this problem find the exact value do ...
nicole - 1. determine the exact value.. cot 7pi/6 and sec(-210degrees) 2. ...
Trig - Find the exact value of cot(-pi/6). I don't have a lot of work for this ...
Math - What is the exact value of cot(5pi/6)?
Math - What is the exact value of cot(5pi/6)?
math repost - 1. What is the exact value of csc^2 210degrees - cot^2 210degrees...
Math - What is the exact value of csc^2 210degrees - cot^2 210degrees? Can you ... | {"url":"http://www.jiskha.com/display.cgi?id=1250299286","timestamp":"2014-04-18T04:40:23Z","content_type":null,"content_length":"8720","record_id":"<urn:uuid:1ff38063-4626-4d5c-bc55-d1015ee53236>","cc-path":"CC-MAIN-2014-15/segments/1397609532480.36/warc/CC-MAIN-20140416005212-00546-ip-10-147-4-33.ec2.internal.warc.gz"} |
Results 1 - 10 of 33
- IN ISSCC DIGEST OF TECHNICAL PAPERS , 1995
"... A CMOS 64 x 64 pixel area image sensor chip using Sigma-Delta modulation at each pixel for A/D conversion is described. The image data output is digital. The chip was fabricated using a 1.2µm
two layer metal single layer poly n-well CMOS process. Each pixel block consists of a phototransistor and ..."
Cited by 26 (7 self)
Add to MetaCart
A CMOS 64 x 64 pixel area image sensor chip using Sigma-Delta modulation at each pixel for A/D conversion is described. The image data output is digital. The chip was fabricated using a 1.2µm two
layer metal single layer poly n-well CMOS process. Each pixel block consists of a phototransistor and 22 MOS transistors. Test results demonstrate a dynamic range potentially greater than 93dB, a
signal to noise ratio (SNR) of up to 61dB, and dissipation of less than 1mW with a 5V power supply.
- IEEE TRANSACTLONS ON SIGNAL PROCESSING, VOL. 41. NO. 7. JULY 1993 , 1993
"... In this paper we propose a framework for stability analysis of EA modulators, and argue that limit cycles for constant inputs are natural objects to investigate in this context. We present a
number of analytical and approximate techniques to aid the stability analysis of the double loop and interpol ..."
Cited by 15 (2 self)
Add to MetaCart
In this paper we propose a framework for stability analysis of EA modulators, and argue that limit cycles for constant inputs are natural objects to investigate in this context. We present a number
of analytical and approximate techniques to aid the stability analysis of the double loop and interpolative modulators, and use these techniques to propose ways of improved design that explicitly
take stability into account.
- IEEE Transactions on Signal Processing , 1994
"... Abstract-We consider the application of EA modulators to analog-todigital conversion. We have previously shown that for constant input signals, optimal nonlinear decoding can achieve large gains
in signal-to-noise ratio (SNR) over linear decoding. In this paper we show a similar result for band-limi ..."
Cited by 11 (1 self)
Add to MetaCart
Abstract-We consider the application of EA modulators to analog-todigital conversion. We have previously shown that for constant input signals, optimal nonlinear decoding can achieve large gains in
signal-to-noise ratio (SNR) over linear decoding. In this paper we show a similar result for band-limited input signals. The new nonlinear decoding algorithm is based on projections onto convex sets
(POCS), and alternates between a time-domain operation and a band limitation to find a signal invariant under both. The time-domain operation results in a quadratic programming problem. The band
limitation can be based on singular value decomposition of a certain matrix. We show simulation results for the SNR.performance of a POCS-based decoder and a linear decoder for the single loop,
double loop and two-stage CA modulators and for a specific fourth-order interpolative modulator. Depending on the modulator and the oversampling ratio, improvements in SNR of up to 1&20 dB can be
achieved. I.
"... this paper, we propose a systematic design method for continuous-time Sigma-Delta modulators. The -transform technique is used to take into account any variation occuring between two sampling
instants in the continuous-time DAC feedback signal. The proposed discretetime to continuous-time transfor ..."
Cited by 10 (8 self)
Add to MetaCart
this paper, we propose a systematic design method for continuous-time Sigma-Delta modulators. The -transform technique is used to take into account any variation occuring between two sampling
instants in the continuous-time DAC feedback signal. The proposed discretetime to continuous-time transformation method is general and well-suited to design automation. A fifth-order lowpass as well
as a sixth order bandpass modulators with RZ and NRZ feedback signals are given as design examples. I.
- IEEE Trans. Circuits Syst. II , 1995
"... A dynamic element matching algorithm, data weighted averaging, is introduced for use in multi-bit \Delta\Sigma data converters. Using this algorithm, distortion spectra from DAC linearity errors
are shaped by first-order noise shaping, resulting in a dynamic range improvement of 9 dB/octave when DAC ..."
Cited by 9 (0 self)
Add to MetaCart
A dynamic element matching algorithm, data weighted averaging, is introduced for use in multi-bit \Delta\Sigma data converters. Using this algorithm, distortion spectra from DAC linearity errors are
shaped by first-order noise shaping, resulting in a dynamic range improvement of 9 dB/octave when DAC errors dominate. Combining this technique with random dithering eliminates the aliasing of the
DAC errors into baseband. Simulations show that with only 1% element matching 110 dB signal-to-noise ratio (18 bits) is achieved for a third-order 3-bit modulator with an oversampling ratio of 128. 1
Introduction Oversampling \Delta\Sigma data converters have displaced traditional converter architectures in audio and instrumentation applications where low frequency, high-resolution and high
linearity conversion is required [1]. The high resolution obtained from these converters is attributed to the inherent linearity of a single-bit quantizer in the \Delta\Sigma modulator. This high
linearity mak...
- In Proc. IEEE International Conference on Electronics, Circuits, and Systems , 1999
"... In this paper, the design procedure for a thirdorder continuous-time \Sigma\Delta modulator with RZ feedback is described. The circuit is realized using continuous-time current-mode integrators
and DACs with switched-current sources. A design method to find the minimum biasing current required to ac ..."
Cited by 6 (3 self)
Add to MetaCart
In this paper, the design procedure for a thirdorder continuous-time \Sigma\Delta modulator with RZ feedback is described. The circuit is realized using continuous-time current-mode integrators and
DACs with switched-current sources. A design method to find the minimum biasing current required to achieve the desired dynamic range is presented. With a sampling frequency of 25:6MHz, the circuit
is expected to achieve 84dB of dynamic range for a 100kHz bandwidth input signal. The circuit operates from a power supply of 1:7V and consumes 7:4mW in a 0:35m CMOS process.
, 1993
"... Analog-to-digital conversion (ADC) which consists in a double discretization of an analog signal in time and in amplitude is increasingly used in modern data acquisition. However, the conversion
process always implies some loss of information due to amplitude quantization. Oversampling is the techni ..."
Cited by 6 (0 self)
Add to MetaCart
Analog-to-digital conversion (ADC) which consists in a double discretization of an analog signal in time and in amplitude is increasingly used in modern data acquisition. However, the conversion
process always implies some loss of information due to amplitude quantization. Oversampling is the technique currently used to reduce this loss of accuracy. The error reduction can be performed by
lowpass filtering the quantized signal, thus eliminating the high frequency components of the quantization error signal. This is the classical method used to reconstruct the analog signal from its
oversampled and quantized version. This reconstruction scheme yields a mean squared error (MSE) inversely proportional to the oversampling ratio R. The fundamental question pursued in this thesis is
the following: how much information is available in the oversampled and quantized version of a bandlimited signal for its reconstruction? In order to identify this information, it is essential to go
back to the original description of quantization which is typically deterministic. We show that a reconstruction scheme fully takes this information into account
- IEEE Trans. Ind. Elect , 2001
"... Abstract—Conducted electromagnetic interference (EMI) is a major cause of concern in switch-mode power supplies (SMPSs) which commonly use standard pulsewidth modulation (PWM). In this paper,
Sigma–Delta (61) modulation is proposed as an alternative switching technique to reduce conducted EMI from a ..."
Cited by 4 (0 self)
Add to MetaCart
Abstract—Conducted electromagnetic interference (EMI) is a major cause of concern in switch-mode power supplies (SMPSs) which commonly use standard pulsewidth modulation (PWM). In this paper,
Sigma–Delta (61) modulation is proposed as an alternative switching technique to reduce conducted EMI from an SMPS. The result of using 61 modulation is a spread in the spectrum of the conducted
emissions so that large concentrations of power at discrete frequencies are avoided. Experimental time-domain waveforms and spectra of the switching function of first-order and second-order 61
modulators are presented to prove the viability of the scheme for EMI mitigation. These modulators are then applied to a dc–dc converter in an off-the-shelf computer power supply and experimental
results show a reduction of roughly 5–10 dB V in EMI emissions over standard PWM modulators. Index Terms—Electromagnetic compatibility, electomagnetic conducted interference, Sigma–Delta modulation,
, 2002
"... High-performance analog-to-digital converters, digital-to-analog converters, and fractional- frequency synthesizers based on delta--sigma (16) modulation---collectively referred to as data
converters---have contributed significantly to the high level of integration seen in recent commercial wirel ..."
Cited by 4 (2 self)
Add to MetaCart
High-performance analog-to-digital converters, digital-to-analog converters, and fractional- frequency synthesizers based on delta--sigma (16) modulation---collectively referred to as data
converters---have contributed significantly to the high level of integration seen in recent commercial wireless handset transceivers. This paper presents a tutorial on data converters and their uses
and implications with respect to wireless transceiver architectures.
, 2003
"... A novel application and generalization of sigma--delta (61) modulation has emerged in three-phase power-electronic converters. A conventional modulator with scalar signals and binary quantizer
is generalized to a modulator with vector signals and a hexagonal quantizer. Indeed, power-electronic ..."
Cited by 3 (1 self)
Add to MetaCart
A novel application and generalization of sigma--delta (61) modulation has emerged in three-phase power-electronic converters. A conventional modulator with scalar signals and binary quantizer is
generalized to a modulator with vector signals and a hexagonal quantizer. Indeed, power-electronic switching states may be thought of as determining the quantizer outputs. The output spectrum is a
key performance measure for both communications and power electronics. This paper analytically derives the output spectrum of the hexagonal modulator with a constant input using ergodic theory and
Fourier series on the hexagon. The switching rate of the modulator is important for power-electronic design and formulas for the average switching rate are derived for constant and slowly varying
sinusoidal inputs. Index Terms---Ergodic, power electronics, quantization, sigma--delta (61) modulation, spectral analysis. | {"url":"http://citeseerx.ist.psu.edu/showciting?cid=1327751","timestamp":"2014-04-18T14:28:40Z","content_type":null,"content_length":"38011","record_id":"<urn:uuid:b3095462-8c9f-4eca-b6db-49581c1c6263>","cc-path":"CC-MAIN-2014-15/segments/1398223203422.8/warc/CC-MAIN-20140423032003-00221-ip-10-147-4-33.ec2.internal.warc.gz"} |
[plt-scheme] call/cc puzzle
From: Jon Rafkind (rafkind at cs.utah.edu)
Date: Sat Jan 17 14:22:00 EST 2009
Henk Boom wrote:
> 2009/1/17 Jos Koot <jos.koot at telefonica.net>:
>> Is that a quation or just a nice gesture?
>> Jos
> The latter. I had fun coming up with it and figuring out why it did
> what it did, and I thought maybe other people would as well. =)
I think I figured out at least part of it. Hope I don't spoil it for
(let ([f (call/cc1 call/cc2)])
(printf "f is ~a\n" f)
(f (lambda (x) (printf "x is ~a\n" x))))
I wrote call/cc1 and call/cc2 to mean call/cc but so I could identify
them in the explanation. The result of this prints
f is #<continuation>
f is #<procedure:/home/jon/tmp/x.ss:17:5>
x is #<procedure:/home/jon/tmp/x.ss:17:5>
The flow is this: call/cc1 passes its continuation to call/cc2 which
invokes the first continuation with the second. So f is now equal to the
continuation of call/cc2 and it prints #<continuation> as expected. Now
f is invoked with the continuation of call/cc2 with (lambda (x) ...)
which starts the computation at (let ([f ...]) ...) so f is now bound to
(lambda (x) ...). Printing this results in <procedure>, and then the f
[which is now (lambda (x) ...)] is applied to (lambda (x) ...) which
prints #<procedure> again.
So at the end it does ((lambda (x) (printf "x is ~a\n" x)) (lambda (x)
(printf "x is ~a\n" x))). Maybe this is obvious to some people but it
took me at least 15 minutes to figure out.
Posted on the users mailing list. | {"url":"http://lists.racket-lang.org/users/archive/2009-January/029808.html","timestamp":"2014-04-19T17:28:51Z","content_type":null,"content_length":"6677","record_id":"<urn:uuid:a4491a3a-1160-4d39-836d-f1a17db5650f>","cc-path":"CC-MAIN-2014-15/segments/1397609537308.32/warc/CC-MAIN-20140416005217-00367-ip-10-147-4-33.ec2.internal.warc.gz"} |
Physics Forums - Pressure, Buoyant Force problem
ChunkymonkeyI Nov13-11 04:07 PM
Pressure, Buoyant Force problem
1. The problem statement, all variables and given/known data
A cube of metal(density=6.00 kg/dm^3) has a cavity inside it. It weighs 2.40 times as much in air as it does when completely submerged in water. What fraction of the cube's volume is the cavity?
2. Relevant equations
Fb=Density of fluid times volume of fluid times g
3. The attempt at a solution
I first made two equations:
Density=m/v (for water) Density=m/v
6.00 kg/dm^3=m/1000 kg 6.00 kg/dm^3/2.40m/V
Idk what 2 do from there because I think I set the equations up wrong could someone please explain 2 me what I should do cuz what's really bugging me is the amount of information that is given to me?
Re: Pressure, Buoyant Force problem
The information is enough to work out the answer (as long as you also know the density of water). And you could either assume the density of air is approximately zero or you could use the actual
value, to get a more accurate answer.
To start this question, you should use what they give you. They are saying that the apparent weight of the cube is 2.4 times as much in air than in water. And you know the equation for the apparent
weight. So you can use this to find the actual weight of the cube in terms of the volume of the cube. And then you can use this along with the equation for the actual weight of the cube due to the
masses contained, to find the fraction of the cube that is hollow.
ChunkymonkeyI Nov14-11 08:48 PM
Re: Pressure, Buoyant Force problem
I still kinda dont get what ur saying can u show me ur work because I dervived Fw=Density of object times g times V and I made this equation equal to Fa plus 9800 times volume of the fluid and I
really need help please
Re: Pressure, Buoyant Force problem
So you wrote:
[tex]Weight_{object} = F_{apparent} + 9800 V[/tex]
Is this the apparent weight when its underwater? what does the 9800 mean?
Maybe I should go through it step-by-step, since there are a few steps which could get confusing when written all in one paragraph.
So first, you need the equation for the actual weight of the object. the object has two parts. an air cavity and a metal shell. I think you should write an equation for the total weight of the object
in terms of the volumes of the metal part and cavity part and the density of air and metal.
ChunkymonkeyI Nov16-11 05:12 PM
Re: Pressure, Buoyant Force problem
Quote by BruceW (Post 3617095)
So you wrote:
[tex]Weight_{object} = F_{apparent} + 9800 V[/tex]
Is this the apparent weight when its underwater? what does the 9800 mean?
Maybe I should go through it step-by-step, since there are a few steps which could get confusing when written all in one paragraph.
So first, you need the equation for the actual weight of the object. the object has two parts. an air cavity and a metal shell. I think you should write an equation for the total weight of the object
in terms of the volumes of the metal part and cavity part and the density of air and metal.
Could u show each step if u dont mind because I'm getting the wrong answer for 3 times now and I think it would be helpful 2 c each steps
Re: Pressure, Buoyant Force problem
Quote by BruceW (Post 3617095)
So first, you need the equation for the actual weight of the object. the object has two parts. an air cavity and a metal shell. I think you should write an equation for the total weight of the object
in terms of the volumes of the metal part and cavity part and the density of air and metal.
This is the first step. Write out this equation. It is essentially using the principle that total mass is sum of the constituent masses. In this case, the constituent masses are that of the cavity
and the metal bit.
And just use symbols for now. (I find it is easier to use symbols in calculations until you get to the end of the problem). So you could use something like [itex]V_m[/itex] for the volume taken up by
the metal (for example).
ChunkymonkeyI Nov19-11 12:58 PM
Re: Pressure, Buoyant Force problem
Quote by BruceW (Post 3619932)
This is the first step. Write out this equation. It is essentially using the principle that total mass is sum of the constituent masses. In this case, the constituent masses are that of the cavity
and the metal bit.
And just use symbols for now. (I find it is easier to use symbols in calculations until you get to the end of the problem). So you could use something like [itex]V_m[/itex] for the volume taken up by
the metal (for example).
This is what I did:
Fa=m(object)g-(density of fluid)(volume of fluid)(g)
Fa=(Density of the object)(Volume of the object)(g)-(Density of fluid)(volume of the fluid)(g)
Fa=g((density of object)(volume of the object)-(density of fluid)(volume of fluid))
m(a)=(density of object)(volume of object) minus (density of fluid)(volume of fluid)
m(a)=(6000 kg/m^3)(V of object) minus (1000 kg/m^3)(Volume of fluid)
Idk what 2 do from there but the only other thing Ik is that since its submerged the volume of the fluid is equal to the volume of the object and the apparent mass=m/2.40 but idk what 2 do from there
please show me the steps and the math out :)
Re: Pressure, Buoyant Force problem
Quote by ChunkymonkeyI (Post 3624395)
This is what I did:
Fa=m(object)g-(density of fluid)(volume of fluid)(g)
Fa=(Density of the object)(Volume of the object)(g)-(Density of fluid)(volume of the fluid)(g)
Fa=g((density of object)(volume of the object)-(density of fluid)(volume of fluid))
m(a)=(density of object)(volume of object) minus (density of fluid)(volume of fluid)
m(a)=(6000 kg/m^3)(V of object) minus (1000 kg/m^3)(Volume of fluid)
Almost right. The object has an air cavity inside it, so if we assume the air density is negligible, the mass of the object equals the density of metal times the volume which the metal actually takes
up. In other words, the volume of the cavity isn't contributing to the mass of the object. If you change this, you will then have the apparent weight in water. To get the apparent weight in air, its
just the same equation, but the fluid is now air.
All times are GMT -5. The time now is 01:37 PM.
Powered by vBulletin Copyright ©2000 - 2014, Jelsoft Enterprises Ltd.
© 2014 Physics Forums | {"url":"http://www.physicsforums.com/printthread.php?t=550151","timestamp":"2014-04-20T18:37:45Z","content_type":null,"content_length":"14368","record_id":"<urn:uuid:27823e2b-9279-49e8-8b17-ffd11c59c837>","cc-path":"CC-MAIN-2014-15/segments/1398223202548.14/warc/CC-MAIN-20140423032002-00351-ip-10-147-4-33.ec2.internal.warc.gz"} |
A Resistor On A Wheatstone Bridge Is Replaced With ... | Chegg.com
A resistor on a Wheatstone bridge is replaced with a strain gage which has a nominal resistance of 120 Ohms and a gage factor of 2.06. The remaining resistors on this quarter-bridge Wheatstone bridge
circuit are 120 Ohm fixed resistors. What will the output voltage be for a strain of 1000 ?strain and for a supply voltage of 3 V?
Electrical Engineering | {"url":"http://www.chegg.com/homework-help/questions-and-answers/resistor-wheatstone-bridge-replaced-strain-gage-nominal-resistance-120-ohms-gage-factor-20-q2799554","timestamp":"2014-04-17T12:47:16Z","content_type":null,"content_length":"20766","record_id":"<urn:uuid:a3913c39-7820-4f9c-b2be-24d2bcae86ae>","cc-path":"CC-MAIN-2014-15/segments/1397609530131.27/warc/CC-MAIN-20140416005210-00613-ip-10-147-4-33.ec2.internal.warc.gz"} |
comparitive bar chart
July 30th 2010, 02:00 PM
comparitive bar chart
Given the following data, if a comparative bar chart were to be made with percentages along the vertical axis, would row total or column total be used to calculate the percentages. The answer key
says row total. How do you know that because the percentages could be of the class or domestic/international?
Attachment 18389
July 30th 2010, 02:45 PM
Its true you could make the x-axis be type and compare the classes within or be classes and compare the type within.
Was that all the info given? Was there a first part to the question you have not shown?
July 31st 2010, 03:05 PM
part a got me to state $H_o$
part b says "If the vertical axis will show the Percentage of Passengers, would you use row, column or table totals to calculate the percentages?"
Apparently the answer is row because it is the independent variable. But is that a rule that the horizontal axis in a comparitive bar chart is the independent variable (and I guess the bars would
be the dependent)? | {"url":"http://mathhelpforum.com/statistics/152396-comparitive-bar-chart-print.html","timestamp":"2014-04-18T21:20:11Z","content_type":null,"content_length":"4744","record_id":"<urn:uuid:ee845cdc-8608-42d2-b9c9-acac5f58260c>","cc-path":"CC-MAIN-2014-15/segments/1397609535095.9/warc/CC-MAIN-20140416005215-00097-ip-10-147-4-33.ec2.internal.warc.gz"} |
The influence of network structure on correlations
Pernice et al. have developed an approach to analyze the influence of different network motifs on correlations between the activity of a pair of nodes.
To get the flavor of their approach, let's imagine a very simplified model, where the $N$-dimensional $\vc{x}$ is the activity of the $N$ network nodes. Image that, if the network were uncoupled the
activity of the nodes would be $\vc{x}_0$. With the coupling, the activity $\vc{x}$ satisfies this simple linear self-consistency equation $$\vc{x} = \vc{x}_0 + wA\vc{x},$$ where $A$ is the adjacency
matrix and the scalar $w$ is the weighting of the effect of each connection.
We can easily solve this equation for $\vc{x}$ in terms of the uncoupled activity $\vc{x}_0$. $$\vc{x} = (I-wA)^{-1}\vc{x}_0$$
For simplicity, assume that the $\vc{x}$ are all mean zero. We can calculate their correlation as $E(\vc{x}\vc{x}^T)$, where $E(\cdot)$ is the expected value from measuring the activity over many
The correlation satisfies $$E(\vc{x}\vc{x}^T) = (I-wA)^{-1}E(\vc{x}_0\vc{x}_0^T)(I-wA^T)^{-1}$$ which we can rewrite as $$C= (I-wA)^{-1}C_0(I-wA^T)^{-1}$$
$C_0$ the correlation if there were no coupling. Since the nodes would be independent in this case, it is a diagonal matrix. Let's assume that the network is statistically homogeneous so that all
diagonal entries of $C_0$ are the same, equal to the constant $c_0$: $C_0 = c_0 I$. Then we can rewrite our equation as $$\frac{C}{c_0}= (I-wA)^{-1}(I-wA^T)^{-1}.$$
If we assume weak coupling so that $wA$ is small, then we can expand in a power series. $$\frac{C}{c_0} = \sum_{i,j=0}^\infty w^{i+j} A^i(A^T)^i.$$
Each term $A^i(A^T)^i$ represents different network motifs. For example $AA^T$ represents divergence motif, and $A^2$ or $(A^T)^2$ represent chains of two edges. In this way, you can examine how
different motifs influence the correlations.
For example, if you consider just motifs of two edges, then you find that just the divergent motif and the chain motif influence correlations. | {"url":"http://mathinsight.org/influence_network_structure_correlations","timestamp":"2014-04-19T19:36:22Z","content_type":null,"content_length":"13868","record_id":"<urn:uuid:9cf4aae1-9ec0-496f-99bd-9961a3f9ecc4>","cc-path":"CC-MAIN-2014-15/segments/1398223202774.3/warc/CC-MAIN-20140423032002-00386-ip-10-147-4-33.ec2.internal.warc.gz"} |
Angle of Photon after Compton Scattering
Ignore the Compton formula. I am referring to your own equations that you posted. You can write
sinφ = ...
cosφ = ...
(I was wrong adding the p
up front), square and add. This gives one equation with two unknowns, p
and λ'. The energy conservation equation will allow you to eliminate p
and you will end up with an equation in λ' only. Actually, since you are asked to find the energy of the scattered photon, I would replace 1/λ' with E'/hc in my expressions and solve for E'. | {"url":"http://www.physicsforums.com/showthread.php?t=336947","timestamp":"2014-04-23T20:46:03Z","content_type":null,"content_length":"47370","record_id":"<urn:uuid:6678466d-4097-4602-b6ee-cb3ad3a73e60>","cc-path":"CC-MAIN-2014-15/segments/1398223203422.8/warc/CC-MAIN-20140423032003-00362-ip-10-147-4-33.ec2.internal.warc.gz"} |
Got Homework?
Connect with other students for help. It's a free community.
• across
MIT Grad Student
Online now
• laura*
Helped 1,000 students
Online now
• Hero
College Math Guru
Online now
Here's the question you clicked on:
What is the solution of the system of equations?
• one year ago
• one year ago
Your question is ready. Sign up for free to start getting answers.
is replying to Can someone tell me what button the professor is hitting...
• Teamwork 19 Teammate
• Problem Solving 19 Hero
• Engagement 19 Mad Hatter
• You have blocked this person.
• ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.
This is the testimonial you wrote.
You haven't written a testimonial for Owlfred. | {"url":"http://openstudy.com/updates/5083927fe4b041b051b96755","timestamp":"2014-04-18T10:39:21Z","content_type":null,"content_length":"85729","record_id":"<urn:uuid:e77db5a2-c582-4248-a5de-f44578908256>","cc-path":"CC-MAIN-2014-15/segments/1397609533308.11/warc/CC-MAIN-20140416005213-00165-ip-10-147-4-33.ec2.internal.warc.gz"} |
Got Homework?
Connect with other students for help. It's a free community.
• across
MIT Grad Student
Online now
• laura*
Helped 1,000 students
Online now
• Hero
College Math Guru
Online now
Here's the question you clicked on:
Good Night Open Study!
• one year ago
• one year ago
Your question is ready. Sign up for free to start getting answers.
is replying to Can someone tell me what button the professor is hitting...
• Teamwork 19 Teammate
• Problem Solving 19 Hero
• Engagement 19 Mad Hatter
• You have blocked this person.
• ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.
This is the testimonial you wrote.
You haven't written a testimonial for Owlfred. | {"url":"http://openstudy.com/updates/50d12f79e4b01186104983ca","timestamp":"2014-04-21T02:13:08Z","content_type":null,"content_length":"53807","record_id":"<urn:uuid:4d46e0ff-2bbc-482d-b4bd-ddbd0d187546>","cc-path":"CC-MAIN-2014-15/segments/1397609539447.23/warc/CC-MAIN-20140416005219-00009-ip-10-147-4-33.ec2.internal.warc.gz"} |
Express Eigenvectors in terms of Eigenkets.
1. The problem statement, all variables and given/known data
One of the problems in our test is this.
Express the eigenvectors of [itex] J_y [/itex] in terms of the eigenkets of [itex] J^2 [/itex] and [itex] J_z [/itex] .
2. Relevant equations
3. The attempt at a solution
I know the matrix of [itex] J_y [/itex] and the operators or eigenkets for [itex] J_y [/itex] ,[itex] J^2 [/itex] and [itex] J_z [/itex]. I just don't seem to understand the question. Can someone
please explain it to me please? What should I do? | {"url":"http://www.physicsforums.com/showthread.php?t=586480","timestamp":"2014-04-17T07:20:36Z","content_type":null,"content_length":"20033","record_id":"<urn:uuid:81f492e4-3b1a-47b4-976f-131e9b3cede3>","cc-path":"CC-MAIN-2014-15/segments/1397609526311.33/warc/CC-MAIN-20140416005206-00061-ip-10-147-4-33.ec2.internal.warc.gz"} |
dissection (mathematics)
Cutting apart one or more figures and rearranging the pieces to make another figure. Dissection puzzles have been around for thousands of years. The problem of dissecting two equal squares to form
one larger square using four pieces dates back to at least the time of Plato (427–347 BC). In the 10th century, Arabian mathematicians described several dissections in their commentaries on Euclid's
Elements. The 18th-century Chinese scholar Tai Chen presented an elegant dissection for approximating the value of pi. Others worked out dissection proofs of Pythagorean theorem.
In the 19th century, dissection puzzles by Sam Loyd, Henry Dudeney, and others became tremendously popular in magazine and newspaper columns. A classic example is the Haberdasher's Puzzle.
Dissections can get quite elaborate: an eight-piece octahedron becomes a hexagon, a nine-piece five-pointed star becomes a pentagon, and so on.
See also:
1. Lindgren, Harry. Geometric Dissections. New York: Van Nostrand Reinhold, 1964.
2. Lindgren, Harry. Recreational Problems in Geometrical Dissections and How to Solve Them. New York: Dover Publications, 1972.
3. Frederickson, Greg N. Dissections: Plane and Fancy. Cambridge: Cambridge University Press, 1997.
Related entry
Related categories
GAMES AND PUZZLES | {"url":"http://www.daviddarling.info/encyclopedia/D/dissection.html","timestamp":"2014-04-21T07:23:54Z","content_type":null,"content_length":"8326","record_id":"<urn:uuid:8bda8d24-701e-4dd6-9ab7-2f96222cbb24>","cc-path":"CC-MAIN-2014-15/segments/1398223203235.2/warc/CC-MAIN-20140423032003-00570-ip-10-147-4-33.ec2.internal.warc.gz"} |
Charged Molecules
Next: Preliminary Investigations Up: Computational Techniques Previous: Supercells
If the molecular species to be modelled is charged special consideration must be given to obtaining a converged total energy, as the energy of a periodically repeated system with net charge diverges.
The limit of the energy of the molecule in an infinitely large supercell is the quantity of interest. It may be shown that this is identical to the system containing the original charged molecule and
a uniform background charge which fills the supercell and neutralises the charge on the molecule [9].
The energy per unit cell of this new system will converge as a power law in the size of the supercell L. The terms of this series to
The charge density of the system consists of the density of the charged system
where q is the charge on the molecule and V is the volume of the supercell. This may be split into two components, adding and subtracting a point charge at
The position
The energy of interaction may be divided into three components:
This is the Madelung energy of a system of point charges on a cubic lattice immersed in a neutralising background [10],
It may be shown that the energy of interaction of a neutral charged system with no net dipole moment on a cubic lattice will converge as 2]
Makov and Payne [2] show that this may itself be divided into two components. The interaction of the point charge with
The second component is due to the interaction of
Therefore the total calculated energy for a simple cubic lattice is given by
where 2.3.
Figure 2.3: Graph demonstrating the effect of the charged molecule corrections on the convergence of the energy of an
Next: Preliminary Investigations Up: Computational Techniques Previous: Supercells
Mr. Matthew D. Segall
Fri Jul 21 15:33:30 BST 1995 | {"url":"http://www.tcm.phy.cam.ac.uk/~mds21/report/node14.html","timestamp":"2014-04-16T19:01:12Z","content_type":null,"content_length":"6706","record_id":"<urn:uuid:0fa7aab6-065f-4a34-9f50-17de6159a469>","cc-path":"CC-MAIN-2014-15/segments/1398223203841.5/warc/CC-MAIN-20140423032003-00490-ip-10-147-4-33.ec2.internal.warc.gz"} |
Probability Test
Gah i posted 2 questions about my test earlier, cud u pls check it
Last edited by andrew2322; May 10th 2008 at 07:51 PM.
Hello, Questions 1, 2 and 3 are ok. Question 4 : a.) The first marble picked is black and the second is red: 5/36 I don't see any black marble :/ b.) Obtaining 2 white marbles: 1/16 Ok.
Last edited by andrew2322; May 10th 2008 at 07:52 PM.
Yes ^^ Unless I made mistakes too, but all the reasoning is correct !
haha i doubt two people can make the exact same mistake
So far #1 and #2 are correct, but #3 has an error... 3.) A red and a black die labelled 1 - 6 are thrown simultaneously, find the probability of: a.) A number less than 5 on the red die: 2/3 b.) A
number less than 5 on the red die but a totla of 10 altogether: 1/36 c.) Both die adding to 10: 1/12 a) is correct given that, b) should be equal to $\frac{2}{3}*\frac{1}{6} = \frac{1}{9}$ c) is
correct, three possibilities out of thirty-six 4.) There is 3 white marbles, 4 blue marbles and 5 red marbles in a bag. Find the probabilty of if marbles are picked WITH REPLACEMENT: a.) The first
marble picked is black and the second is red: 5/36 b.) Obtaining 2 white marbles: 1/16 a) 0, there are no black marbles b) $\frac{3}{12}^2 = \frac{9}{144}$, Remember, the white marble is replaced by
another white marble. #5, #6 and #7 are all correct Note: Best way to solve #7 is by using a Venn diagram
He said it was blue b) $\frac{3}{12}^2 = \frac{9}{144}$, Remember, the white marble is replaced by another white marble. The probability to get a white marble is 3/12=1/4 Since there is replacement,
the probability to get 2 marbles will be the product of the probabilities of getting 1 marble, that is to say 1/4²=1/16, isn't it ? Actually, 9/144 is 1/16... | {"url":"http://mathhelpforum.com/statistics/35634-probability-test.html","timestamp":"2014-04-17T15:15:09Z","content_type":null,"content_length":"67177","record_id":"<urn:uuid:c1fbf09a-5f15-4e8e-af33-ea8de6b07a7e>","cc-path":"CC-MAIN-2014-15/segments/1397609539493.17/warc/CC-MAIN-20140416005219-00480-ip-10-147-4-33.ec2.internal.warc.gz"} |
River Grove Statistics Tutor
...I currently tutor two students in Prealgebra and like to instill confidence in them so they know that math is something you can be good at if you do it enough. When I took the Basic Skills test
for my teaching certificate I received a perfect score on the math section. Currently I am taking a L...
17 Subjects: including statistics, reading, Spanish, English
...I started off my college career as a math major. Although that was a long time ago, I have helped several students with their pre-calculus courses. The precalculus student that I helped just
last academic year went from getting Cs and Bs in her tests to As.
13 Subjects: including statistics, geometry, algebra 2, algebra 1
...I have a BS degree in biology. I have a BS degree in biology, and have studied biochemistry in college and medical school. I have two full years of chemistry in college.
17 Subjects: including statistics, chemistry, geometry, reading
...I have taught high-school and college aged students various subjects, ranging from math to law to reading and writing. As a Forensics Instructor at two different national institutes and as a
practicing attorney, I have gained significant experience in helping high-school or college aged students...
39 Subjects: including statistics, English, reading, physics
I am a PhD Psychology student specializing in Social and Industrial/Organizational Psychology. I am looking to find tutoring jobs locally in the Chicago suburbs. I absolutely love statistics and
11 Subjects: including statistics, GRE, GED, grammar | {"url":"http://www.purplemath.com/River_Grove_Statistics_tutors.php","timestamp":"2014-04-20T07:04:28Z","content_type":null,"content_length":"23929","record_id":"<urn:uuid:f73dd110-5c28-4420-9471-c08b3140d683>","cc-path":"CC-MAIN-2014-15/segments/1397609538022.19/warc/CC-MAIN-20140416005218-00220-ip-10-147-4-33.ec2.internal.warc.gz"} |
Foundations of Electrical Engineering 2nd Edition Chapter 7.3 Solutions | Chegg.com
In a common emitter configuration, the output is considered across the collector –emitter terminals.
Write the equation for the voltage
It is clear from the equation (1) that as the output voltage across collector-emitter terminals changes, the value of the collector current changes.
Write the equation for the relation between input and output current as shown in the equation (2).
It is clear from the equation (2) that as
It is clear that as base current changes, the input voltage across the base-emitter terminals also changes.
Therefore, the output of the transistor has the little influence on the input. Hence, the answer is | {"url":"http://www.chegg.com/homework-help/foundations-of-electrical-engineering-2nd-edition-chapter-7.3-solutions-9780130927019","timestamp":"2014-04-16T05:44:42Z","content_type":null,"content_length":"26385","record_id":"<urn:uuid:daee5631-7be7-4cbd-9200-a134f0240591>","cc-path":"CC-MAIN-2014-15/segments/1397609521512.15/warc/CC-MAIN-20140416005201-00079-ip-10-147-4-33.ec2.internal.warc.gz"} |
Measurement of Characteristics of Sound Reflection and Scattering by Elastic Cylindrical Shells in Conditions of Hydroacoustic Basin
St. Petersburg State Marine Technical University, St. Petersburg, Russia
A method and experimental setup intended for measurement the amplitude and phase of acoustic field in the near zone a scatterer are described. The results of measurement the scattering
characteristics of low-frequency sound signals scattered by elastic cylindrical shells are analyzed.
At a glance: Figures
Keywords: diffraction, Fresnel zone, Fraunhofer zone, Cylindrical shell, boundary conditions
International Journal of Physics, 2013 1 (1), pp 5-14.
DOI: 10.12691/ijp-1-1-2
Received January 30, 2013; Revised March 04, 2013; Accepted March 10, 2013
© 2013 Science and Education Publishing. All Rights Reserved.
Cite this article:
• Kleshchev, A.. "Measurement of Characteristics of Sound Reflection and Scattering by Elastic Cylindrical Shells in Conditions of Hydroacoustic Basin." International Journal of Physics 1.1 (2013):
• Kleshchev, A. (2013). Measurement of Characteristics of Sound Reflection and Scattering by Elastic Cylindrical Shells in Conditions of Hydroacoustic Basin. International Journal of Physics, 1(1),
• Kleshchev, A.. "Measurement of Characteristics of Sound Reflection and Scattering by Elastic Cylindrical Shells in Conditions of Hydroacoustic Basin." International Journal of Physics 1, no. 1
(2013): 5-14.
Import into BibTeX Import into EndNote Import into RefMan Import into RefWorks
1. Introduction
The following two problems are solved on the basis of experimental data on the amplitude - phase characteristics of the scattered sound field in the near zone of a scatterer made in the form of an
elastic finite cylindrical shell ^[1, 2]:
1). determination of the nature of sound scattering by the shell at low sounding frequencies;
2). calculation of the angular scattering in the Fraunhofer zone from the results of measurement the amplitude and phase of the scattered field in the Fresnel zone
2. The Criterions of the Acoustical Diffracted Measurements
The measurement of the characteristics of the sound reflection and scattering very offen conduct at the models with an use for these intentions of the hydroacoustic basins and the shallow ponds and
the water areas ^[3, 4]. A principal difference of the diffracted experiment (DE) in the conditions of the hydroacoustic basin (HB) and the shallow water area (SWA) along a comparison with the
natural conditions of a deep sea consistes in a presence of the reflective boundaries disposed near to the source and scatterer (a free surface, a bottom, the walls of the basin). As a rule, the
experimenters are interested by the characteristics of the reflection of a Fraunhofer zone (of a distant field) correspond-ding an infinite medium in that from the infinitely removed source on the
scatterer falls a sound plane wave.
Therefore by the DE in the conditions of the HB or of the SWA by the principal problem is an except of an influence of the reflective boundaries of the division of the mediums on the characteristics
of the scatterer. The solution of the this problem is begun witch a choise of the form of the sound signal. The optimum properties with this point of view has a pulse signal with a harmonic or
frequency – modulated filling. An use of the signal of the such type permits distinguish at a time the useful reflected signal by the body on a background of the preventing reflections from the
boundaries. Therefore we are sparing the principal attention in the future the signals of the pulse type.
A distance between the source of pulse signal and the scatterer we will choose so as the wave, falling on the body, at least in the limits of the scatterer, could be received for the plane wave
(littlely from it differed). A receiver (a hydrophone) of the reflected signal we will place in the Fraunhofer zone. The criterions of the minimum distance between the combined antenna and the
scatterer answering the two brought demands and founded on a known formula D is the maximum dimension of the scatterer, λ is the length of the sound wave in the medium) were considered in ^[3, 5].
However in the diffracted measurements the criterion of the minimum distance can be found with the help of the radial wave functions being by the fundamental solutions of the of the scalar Helmholtz
equation ^[6, 7]. We are showing this on the example of the bodies of the simplest form (a sphere, an infinite cylinder, prolate and oblate spheroids) or the bodies round that can circumscribe the
spherical, cylindrical or spheroidal surfaces. At first we are determining a difference in the angular characteristics of the scattering by these bodies of the plane and spherical sound waves (for
the cylinder we will conduct the comparison between the plane and cylindrical waves). For this we are write the decomposition of a potential of the spherical (or cylindrical) wave in series at the
own functions of the Helmholtz equation ^[8]:
1). in the spherical coordinate system
where R - the distance between the source and the point of an observation; r - the radial coordinate of the point of an observation; r[1] - the radial coordinate of the source; θ - the angular
coordinate of the point of the observation relatively of a polar axis;
2). in the circular cylindrical coordinate system
where r[1], r and R form a tringle by that the angle φ is concluded between sides r and r[1];
3). in the prolate spheroidal coordinate system
where ξ[1], η[1](η[1]=cos θ[1]), φ[1]=0 - the spheroidal coordinates of the source;
Analogously (3) will look the decomposition of the potential of the spherical wave and in the oblate spheroidal coordinate system, only С must substitute on –iC, ξ[1] on iξ[1] and
The formulas for the potential of the plane wave are got from (1) - (3), if r[1] and ξ[1] direct to the infinite and instead of the radial functions of third type and the Hankel functions use by
their asymptotical meanings ^[2, 6]. We are writing these asimptotics for the radial functions in the chosen us coordinate systems ^[2, 6]:
1). in the spherical coordinate system
2). in the cylindrical coordinate system
3). in the prolate spheroidal coordinate system
In the real situations we have an affair with the terminal meanings r[1] and ξ[1], however and in this case we can accomplish correctly a passage from the spherical (or cylindrical) wave to the plane
wave (the field of the falling wave) or from the Fresnel zone in the Fraunhofer zone (the field of scattered wave). We apply to the decompositions (1) - (3). The convergence of the serieses standing
in the right parts of these formulas depends from this as quickly are diminiched (over the modulus) with a growth of the indexes of the summing up the productes of the radial functions of the first
and third types. The number of the member of the series (n[lim], m[lim]), on that must finish the summing up can be determined from the tables of the radial functions, it will by the function of the
wave dimension kr[0] (the sphere, the cylinder) or С (the spheroid), of the coordinate r or ξ [in the given case it corresponds the coordinate of the external surface of the scatterer (r[0] or ξ[0])
or circumscribed round it the the coordinate surface] and of the requisite precision. For a practical intention we can be limited by the members by that the modulus of the product of the radial
functions of the first and third types at 3 - 4 order less of the biggest modu-lus of the product of these functions by the less meanings of the indexes. Now at the tables of the radial functions we
are finding the limital meanings of the indexes of the summing up to that the and the sphere n[lim] has the order kr[0], by the spheroid n[lim][0] (m=0) of the order Cξ[0], by m>0 the meaning n[lim][
][m] is diminiched with the growth m, in other words n[lim][ ][m]≥ n[lim][ ][m][+1] has one and the same order what and Cξ[0]/2. We are showing an use of the given method of the choise of the
position of the point source relatively of the scatterer on example of the prolate spheroid with the coordinate of the external surface ξ[0]=1,005, the wave dimension of the body С we are placing
equal 10,0. The angular coordinates of the source will invariable (θ[0]=90^˚, φ[0]=0˚), but the it radial coordinate ξ[1] are giving two meanings m=0; n=0; 1; 2; 3;…; 13; m=1; n=1; 2;…; 13; m=2; n=2;
3;…; 12; m=3; n=3; 4;…; 11; m=4; n=4; 5;…; 10; m=5; n=5; 6; 7; 8. In the tables 1 and 2 are presented the tabulated and asymptotical [from (6)] meanings of the radial functions of the third type with
the indexes m=0; n=0-13 and the radial coordinate ξ[1]= 2,4; 10,0. The difference between the tabulated and asymptotical meanings of the functions of the third type by ξ[1]= 2,4 leads to the
difference of the angular characteristics of the backscattering of the soundsoft spheroid of the wave from the point source with these radial coordinates, over the comparison with the angular
characteristics of the scattering of the plane falling wave (Figure 1). As well can be placed the boundary of the Fraunhofer zone for the ideal scatterers in the form of the sphere, the cylinder or
the spheroid (or near to them forms). Howerer in this case the numbers of the indexes n[lim] (the sphere, the cylinder) or n[lim] and m[lim] (the spheroid) of the radial functions of the third type
for that must be fulfilled the asimtotical formulas (4) - (6) are determined more complicated combination of the radial functions of the first and third types (by the hard scatterer appear and the
derivatives of these functions), entering in the coefficients of the decomposition of the pressure in the scattered wave over the own functions of the Helmholtz equation. The concrete formula for
these coefficients is settled proceeded from the form of the boundary conditions and the type of the source of the falling on the body wave. For the ideal scatterer in the form of the prolate
spheroid the combination of the radial functions has the following form:
the point source
а) the soft spheroid
б) the hard spheroid
the plane wave
а) the soft spheroid
б) the hard spheroid
If used by the formulas (9) and (10), we are finding the boundary ξ of the Fresnel zone and Fraunhofer zone of the scattered pressure for the plane falling wave and place on this boundary the point
source (ξ[1]=ξ), that as is seen from the comparison (7) and (8) with (9) and (10), this boundary will general for both types indignation. In a confirmation of this in Figure 2 come up the angular
characteristics of the sound scattering by the hard spheroid of the pressure in the Fraunhofer zone for the plane and spherical waves. In Figure 2 the curve 1 corresponds the modulus of the angular
characteristic of the sound scattering by the hard spheroid for the plane falling wave; the curve 2 corresponds the point source with the coordinate ξ[1]=10,0 and the distribution of the modulus of
the scattered pressure for the radial coordinate ξ[1]=10,0 by the falling plane wave^*; the curve 3 characterises the distribution of the modulus of the scattered pressure for the radial coordinate ξ
[1]=10,0 (it is by the coordinate of the source).
The fulfiled numerical estimations shown, what the minimal distance R[min] from the scatterer to the boundaries of the Fresnel and Fraunhofer zones submits to an inequality R[min]≥2(D^2/λ).
We see, what for the scatterers of the spheroidal form the linear distance from the surface of the scatterer ξ[0] until a line of the boundary ξ[2] depends from the angle of the observation θ: by
biggest it will for the angle θ=0˚ and by least for the angle θ=90º (the oblate spheroid, for the prolate spheroid– backwards: maximum by θ=90º, minimum by θ=0˚).
We are noticing as well, what by the angle θ=0˚ (the axially symmetric problem), the index m in the all higher written formulas has one meaning m =0.
By the diffracted measurements in the natural ponds must remember about the following principal demands that they must answer ^[3]: 1) have enough the big dimensions so as an interference evoked by
the reflections from the way of an use of the pulse regime; 2) posses by a low level of a surrounded noise; 3) the liquid medium must be free from all, what can evoke the refraction or the scattering
of the sound (of the flows, of the gradients of the temperarature, of the sea organisms, of the bubles and of the soilings).
For a securing of the low level of the surrounded noise, of a stability of a platform and of the conveniences of a production of the measurements must be fulfilled a protection from rainy weather.
By the source of the noise are the ships, disposed near from the basin, the industrial plants (especially the connected with a water pumps), a freight transport, the railroads, a rain, and the waves.
The auxiliary platforms, using by the measurements, are different: the piers, the bridges, the barges, but as well the ships. The piers and the bridges secure the best conveniences and the stability
of the conditions of a work. If the basin is big and deep must use a sailing construction, but the stability and the conveniences must secure by a vertical dimension of the construction and by the
service lines going under the water or coming to a shore.
Of the simple criterion for a definition of the minimal acceptable depth by the production of the measurements in the basin is not, but the requisite depth in a first turn is determined by the
frequency range of the reflective body.
A quality of the hydroacoustic basin depends from that in which degree can remove an influence of the reflections or of the hindrance from the reflections. If the reflections are abolished or
absorbed by the absorbes an the boundaries of the basin then last is named by drowned.
The big part of the such hydroacoustic basins are not above and they are similar the natural basins, but less them at the dimensions. By an exeption is the reserved drowned basin, in that can imitate
the conditions of the measurements of the deep ocean given the high static pressures and the low temperature of the water.
By the pulse regime of the work the form of the basin is not important. By a limiting factor is the distance until reflective boundaries surfaces nearest to the way of the propagation of the straight
acoustic signal from a source to ta scatterer and to a receiver.
3. The Structure Schema of the Experiment and it Methodology
The block diagram of the plant for the amplitude - phase measurements of the reflected (scattered) signal is presented in Figure 3. The block diagram includes in itself the radiating section, the
scatterer (model) and the liquid medium. We explain the principle its work, used the time diagrams of voltages in the radiating section (Figure 4). The generator of the harmonic oscillations G
creates the harmonic signal of the frequency ω (see the diagram I on the Figure 4), the frequency that is controled by the crystal - controlled digital frequency meter Fr. Entered on the modulator
Mod, creating the rectangular video pulse by the durationn τ (see the diagram II in Figure 4), the harmonic signal is turned in the pulse signal with the rectangular envelope and the harmonic filling
of the frequency ω (see the diagram III in the Figure 4). This pulse signal with the help of the source S exposes to the sound the liquid medium of the the basin or of the water area and the finding
in it model M. The hydrophone H (the receiver in Figure 3) can receive the different signals (in the dependence from the situation). If turns out well divide the useful signal p[s] (reflected from
the model) and the hindrance p[p] (the reflection from the boundaries of the division of the mediums), then the receiver fixes the signal p[s], scattered of the model. If the model is absent, then
the hydrophone receives only the straight signal p[i]. If the receiver is disposed near of the model, then the division of the straight and scattered signals can not and the hydrophone fixes the
diffracted pulse signal.
At the low frequencies, interfering reflections can be avoided only near the model. In this case, it is almost impossible to separate the direct and reflected signals and the measurement receiver
detects the total (diffracted) signal. If the undistorted signal (obtained without the model) is known at the same points, the scattered signal can be determined as the difference between the
diffracted and straight signals (under the condition that the amplitudes and phases of these signals are measured simultaneously). From the distributions of the scattered or diffracted signals,
measured near the model, it is possible to calculate the angular charactristics (the characteristics of the far field of the scatterer) by using the Kirchhof integral ^[7, 9, 10]. In acoustics, the
method of extrapolating the near - field data to the far field was first applied to hydroacoustics arrays (in the literature, this method has been called the DRL method) ^[3, 5, 8, 11]).
The sound pulse (p[s], p[i] or p[Σ]), turned by the hydrophone in electric signal, dos at the preliminary amplifier >, but after at the spectrometer Sp of the ultrasonics frequencies, tuned in the
frequency of the filling of the pulse ω. Further the signal follows over the two channels: over the first channel the signal filtered out by the spectrometer Sp is given at the time selector TS that,
cuts out 1 - 2 the periods of the placing part of the pulse. The pulse signal with the time selector and the harmonic signal with the generator G of the harmonic oscillations do at the two entrances
of the digital phase - meter DPh, that measures the phase of the signal, receiving by the hydrophone, relatively of the supportal signal with the generator G.поступают Simultaneously the signal with
the spectrometer Sp dos at the first entrance of the commutator C, at it the second entrance dos the signal with the time selector TS and in the dependence from the position of the relay of the
commutator on the screen of the cathode - ray oscilloscope EOs we observe either the all time picture of the pulses in the liquid medium (in the time of the time - base) or the placing part of the
useful signal cut out by the time selector TS.
We are telling about the method DRL on the example of the diffracted problem ^[7, 9]. If we know the distribution of the scattered p[s] or diffracted S, surrounding the scatterer, then with the help
of the Kirchhoff integral we can determine Р ^[1, 2, 3, 5, 7, 9, 10]:
where: the index d is s or Σ, Q - the point of the surface S; G(P; Q) - the Green function, submitting to the non - homogeneous Helmholtz equation ^[2].
For the surfaces S of the spheroidal or spherical forms the formulas for G[1] and G[2] have according the following form ^[2]:
where ξ, η, φ; r, θ, φ – the spheroidal and spherical coordinates of the point of the observation Р; Q of the surface S; in the given case ξ=ξ[0] and
An advantage of the termal integrals (12) and (13) at the comparison with the binominal (11) obviously: for the definition of the pressure in the distant field enough know the distribution only of
the pressure S. The formulas (14)–(17) get simplified ^[13] for the account of the substitution of the radial functions
By the use of the binominal integral (11) as the Green function G(P;Q) we choose
where r - the distance between the points Р и Q. Besides that, from the absence the enough miniature receivers of the oscillatory velocity use one from two approximation:
1) the scattered wave near of the surface S we account by plane and spreading normally to it, in the result the measurement of the normal derivative
2) the measurement of the derivative Δq between the surfaces of the measurements S[1] and S[2]:
In the Fraunhofer zone (r is enough big) are fair the usual approximations ^[6]:
where R - the distance from the beginning of the coordinates of the system О to the point of the observation; D(θ,φ) - the angular characteristic of the scattering in the spherical coordinates θ, φ;
In the distant zone the single vector from Q in Р can substitute by the single vector О in the point Р, so what
On the practice the continuous distributions of the pressure ^[1, 2, 7, 9]
where L and М – the number of the nodes after the coordinates A[l] and D[m] – the main coefficients; the formulas for В are given in ^[8]. By the use (22) for the calculation of the relation λ in the
liquid). For the exception of the influence of the nonhomo-geneous flexural waves (for the scatterers in the form of the elastic shells) the distance from the surface of the scatterer to the nearest
(main) point must not be λ/2, the distance between the main points so as we could evoid of the false additional maximums must be less λ/2.
The measurement of the distributions of the diffracted pressure near of the model can be fulfield with the help of the construction, presented in Figure 5. The model 1 is suspended to the
construction 2 with the help of the metallic strings. The miniature hydrophones 3 are fixed to the strings of angular gear 4 made from hollow (water - filled) metal tubes. For correct phase
meas-urements, the hydrophone size should be small compared to the wavelength of sound. The low-speed electric motor 5 served to rotate the angular gear around the model at the required step in
angle. At each fixed position of the system, the amplitude - phase distribution of the diffracted pressure was measured with the use of switch 6 and the receiving channel of the experimental setup
(see Figure 5). Through the A/D converter, the distribution was sent to the PC, where the angular characteristic was calculated.
The field, scattered by the elastic shell, was measured in the Fresnel zone by using the setup shown in Figure 5 and the structure shown in Figure 6. The latter consisted of the rigid template fixed
above the water surface. The paper sheet was glued to the upper surface of the template. On the paper, the contour of a cylindrical shell with flat ends, the approximating contour of an elliptic
shape, the measuring elliptic contour and the measurement lines AB, CD, EF and OM were drawn. Along the shell contour, the measuring elliptic contour and the AB, CD, EF and OM directions, holes
served to suspend miniature spherical hydrophones with the diameter d = 5mm. The strings were strained with the use of a load, which was positioned near the bottom of the tank to eliminate its effect
on the scattered sound field measurements ^[10].
In both types of the experimental setup, the angle at which the model was insonified could be varied by varying the position of the source with respect to the scatterer. The insonifying pulse length
was always greater than the maximal size of the model.
As in the setup shown in Figure 1, the measurements were performed twice: first, in the pre-sence of the shell, the magnitude of the diffracted pressure and its phase were measured, then the shell
was lifted to the surface and the pressure magnitude and the phase of the incident wave were measured at the same points as before.
4. The Analysis of the Results of the Measurements
The measured amplitude – phase distributions of the diffracted or scattered field near the scattered allow determination of the factors that govern the scatterer field formation. Figure 7 shows the
meanings of the magnitude and the phase of the scattered pressure for the finite cylinnddrical shell insonified along its rotation axis. At this axis (the OM direction in Figure 6), the distributions
of the magnitude and the phase were measured at different wave distances kz from the end of the shell with the radius a. Curves 1 and 2 represent the experimental values of thmag-nitude and the phase
of the scattered pressure respectively. Curves 3 and 4 represent the corresponding distributions for the elastic hollow oblate spheroidal shell with the major semiaxis a in the case of its
insonification along the OM direction ^[14]. Distributions 5 and 6 characterize the magnitude and the phase of the scattered pressure soft oblate spheroid, the wave size of the body С = ka = 3,1.
Figure 8 shows similar distributions of the magnitude and the phase of the scattered pres-sure for aforementioned spheroidal shell along the OM direction with another wave size C = 1,0.
Figure 9 and Figure 10 compare the experimental and calculated (for the acoustically soft in-finite cylinder) distnticributions of the magnitude and the phase of the diffracted pressure, the
distributions were measured along the EF direction, the data were obtained for bounded cylinders with the wave size C = ka = 1,0 (Figure 9) and C = ka = 3,1 (Figure 10). In addition, Figure 9
compares the distributions of the magnitude and phase of the diffracted pressure obtained for two shells (model 1 and model 2) with identical lengths and diameters but with different thicknesses of
their ends. In both cases, the shells were insonified along the EF direction.
The structure represented in Figure 6 makes it possible (by recalculating the near field to the far field) to obtain the angular scattering characteristic D(θ) for axisymmetric models insoni- fied
along their rotation axis, because, in this case, it is not necessary to measure ψ[s] for different values of the angle φ. As the illustration, Figure 11 displays the results of the measure- ments
the magnitude of the angular chararacteristic
5. Conclusions
If the pulsed signal from the scatterer can be singled out in the Fraunhofer zone (the deep- water region), the angular scattering characteristic can be measured directly. Howerer, this procedure is
rather complicated, as compared to the method described above, be-cause it requires scanning of the great number of points at the uniform step on the spherical surface in the far zone. In addition,
it is necessary to select the useful scattered signal against interfering reflegtions at all of the measurement points. Therefore, in experiments, as the rule, only two - dimensional (rather than
three - dimensional) scattering characteristics are measured (or only parts of these characteristics).
The work was supported as of research under State Contract no P242 of April 21, 2010, within the Federal Target Program “Scientific and scientific - pedagogical personnel of innova-tive Russia for
the years 2009 - 2013”.
^1*By writing down (11) – (13)took into account, what the Kirchhoff integral for the pressurep[i]in the falling wave equally zero [12].
[1] Kleshchev A. A., “Scattering of Low - Frequency Pulsed Sound Signals from Elastic Cylindrical Shells”, Acoust. Physics. 57(3): 375-380, 2011.
[2] Kleshchev A. A., Hydroacoustic Scatterers, Prima, St. Petersburg, 2012 [in Russian].
[3] Bobber R., Underwater Electroacoustic Measurements, Peace, Moscow, 1974 [in Russian].
[4] Klyukin I. I., Kolesnikov A. E., Acoustic Measurements in Shipbuilding, Shipbuil- ding, Leningrad, 1982 [in Russian].
[5] Horton C. W., “Acoustic Impedance of an Outgoing Cylindrical Wave”, J. Acoust. Soc. Am. 34 (10). 1663. Oct. 1962.
[6] KleshchevA. A., Klyukin I. I., Principles of Hydroacoustics, Shipbuilding, Lenin- grad, 1987 [in Russian].
[7] Kleshchev A. A., Klyukin I. I., “The experimental method of the production of the characteristics of the far - field of the scatterers”, Tr. LKI. 77: 37-40, 1972.
[8] Horton C. W., Innis G. S., “The Comparison of Far - Field Radiation Patterns from Measurements Made Near the Source”, J. Acoust. Soc. Am. 33(7): 877-880, 1961.
[9] Kleshchev A. A., Klyukin I. I., “The use of the diffracted Kirchhoff integral for the calculation of the angular characteristics of scattering”, in 7^th All - Union Acoustic Conference, Nauka,
Leningrad, 123-125, 1973.
[10] Kleshchev A. A., “The experimental characteristics of the scattering of the non - sta- tionary sound signal by the cylindrical shells at the low frequencies in the Fresnel zone”, in 21^st Session
of Russ. Acoust. Soc. Geos, Moscow, 163-166, 2009.
[11] Baker D. D., “Determination of Far - Field Characteristics of Large Underwater Sound Transduccers from Near - Field Measurements”, J. Acoust. Soc. Am. 34 (11): 1737-1744. Nov. 1962.
[12] Shenderov E. L., Wave Problems of Hydroacoustic, Shipbuilding, Leningrad, 1982 [in Russian].
[13] Kleshchev A. A., “The some criterions of the acoustical diffracted measurements”, in 7^th All - Union Acoustic Conference. Nauka, Leningrad, 143-146, 1973.
[14] Kleshchev A. A., “The scattering of the sound by the elastic oblate spheroidal shell”, Sov. Phys. Acoust. 21 (6): 571-573, 1975. | {"url":"http://pubs.sciepub.com/ijp/1/1/2/index.html","timestamp":"2014-04-18T16:17:00Z","content_type":null,"content_length":"115760","record_id":"<urn:uuid:a85c5822-6275-40ff-9ad1-dd2d9674cf4c>","cc-path":"CC-MAIN-2014-15/segments/1398223203841.5/warc/CC-MAIN-20140423032003-00594-ip-10-147-4-33.ec2.internal.warc.gz"} |
Matrix multiplication help
12-05-2007 #1
Registered User
Join Date
Oct 2007
Matrix multiplication help
I have to do a program to multiply two matrices using 1d arrays, but I am not sure how to begin. What would I need to get from the user--the number of rows in the first array and cols in the
second or just how many elements he/she will be inputting?
Also, say the user decides to use 3 rows for array for matrix 1, would I need to create 3 arrays to get the input?
any suggestions are appreciated. Thank you.
What would I need to get from the user--the number of rows in the first array and cols in the second or just how many elements he/she will be inputting?
Probably the rows and columns, because from that information you can determine the total number of elements (rows*cols), but from the total you can't determine the number of rows and cols.
(Assuming I've understood you correctly.)
Also, say the user decides to use 3 rows for array for matrix 1, would I need to create 3 arrays to get the input?
It sounds like you might want to use dynamic memory allocation. You can use something like this to dynamically allocate a 2D array.
int rows, cols;
std::cin >> rows >> cols;
int **data = new int * [rows];
for(int x = 0; x < rows; x ++) {
data[x] = new int [cols];
Seek and ye shall find. quaere et invenies.
"Simplicity does not precede complexity, but follows it." -- Alan Perlis
"Testing can only prove the presence of bugs, not their absence." -- Edsger Dijkstra
"The only real mistake is the one from which we learn nothing." -- John Powell
Other boards: DaniWeb, TPS
Unofficial Wiki FAQ: cpwiki.sf.net
My website: http://dwks.theprogrammingsite.com/
Projects: codeform, xuni, atlantis, nort, etc.
would this work with a 1 d array as well?
Umm, sure. 1D arrays are simple.
int *array = new int[size];
// ... use array ...
delete [] array;
But I'm going to guess that you don't want 1D arrays. Matricies are 2D, are they not?
Seek and ye shall find. quaere et invenies.
"Simplicity does not precede complexity, but follows it." -- Alan Perlis
"Testing can only prove the presence of bugs, not their absence." -- Edsger Dijkstra
"The only real mistake is the one from which we learn nothing." -- John Powell
Other boards: DaniWeb, TPS
Unofficial Wiki FAQ: cpwiki.sf.net
My website: http://dwks.theprogrammingsite.com/
Projects: codeform, xuni, atlantis, nort, etc.
If you assume the matrix multiplication is valid (which is definitely an assumption), then you have three dimensions: the left is i x j, and the right is j x k. The result will be i x k. So you
would need to get those three numbers, and i x j numbers for the first matrix, and j x k numbers for the second, and compute i x k answers for the result.
You can represent these as 1D arrays if you have to (representing A[2][3] as A[2*j+3], etc.), but I would hope you don't have to.
I have to use 1d arrays. I still don't get how it would behave like as the 2 d array above, though--can anyone explain?
In other words, how would I input data row by row using this index (A[2*j+3] ) in a for loop?
- also, in that case, I would be asking the user for the number of columns (j), right?
Thank you.
Last edited by Fredir; 12-05-2007 at 02:22 PM.
dwks, just a minor question, i would have to declare int array to be of a specific size before doing that right?
If you have to use 1d arrays, you're going to have to flatten your grid out somehow. For instance, let's look at a 3x3 thing:
a[0][0] a[0][1] a[0][2]
a[1][0] a[1][1] a[1][2]
a[2][0] a[2][1] a[2][2]
There are nine entries, so if we do this we need to use a[0] through a[8]. The question is, are you going to fill in your list: across, or down? Once you do that, then you know how to get from
the two-dimensional version to the one-dimensional version.
If you don't know i, j, and k at compile time, well, that just makes the question more interesting.
I have to input it across--how would I implement the index in this case? I having a hard time visualizing how to set up the indexes...
offset = row * width + column;
row = offset / width;
column = offset % width;
For row major matrices (I think).
I am not sure how the whole col/row thing is being played out in an array, though. I would appreciate if anyone could explain...thanks.
dwks, just a minor question, i would have to declare int array to be of a specific size before doing that right?
No, you don't. That's the beauty of dynamically allocated data structures (like arrays). You can make them any size, and that size can be determined at run-time.
Here's an example. If I declare an array like so
int number[100];
and read numbers into this array, the user can only enter 100 numbers, and then my program will crash (or at least give an error message if I've written it well). But if I say, "how many numbers
do you want?", I can allocate that many numbers, and the user can enter that many numbers.
cout << "How many numbers? ";
int numbers;
cin >> numbers;
int *number = new int[numbers];
// ...
delete [] number; // quite important
There's a third approach, of course: read in numbers until your array is full, and then resize the array if and when you run out of space. That way the user can change the number of numbers that
they want at any time. It's a little more complicated to code in C++, however (unlike C . . .), so I'll leave it out for now.
As for that "quite important" comment? One caveat (and benefit) of dynamically allocated memory is that you need to free it. You have to tell the compiler when you're done using the memory. Use
delete for memory allocated with new, and delete[] for memory allocated with new[]. (Basically, whether you allocated an array or just a single object.)
So, how can you flatten a 2D array into a 1D array?
First, let's consider how 2D arrays work. When you declare a 2D array of dimensions [X][Y], you get X*Y elements. (Each element might take up 4 bytes, for a int under most platforms, say -- or
one byte, for chars, or hundreds of bytes, for more complex elements like classes.) So you get X*Y*sizeof(array[0][0]) bytes of memory.
Now, when you access array[0][0], you're accessing the first element in the array. array[0][1] is the second (if it exists, of course). And so on, until you access array[0][Y-1], the Y-th
element. But what is element number Y+1? It's array[1][0]. And then array[1][1] and so on, until you get to the X*Y-th element, the last element, which is array[X-1][Y-1].
Are you familiar with the pointer-like syntax for accessing elements in an array? It goes like this. array[0][0] is the same as **array. array[1][2] is the same as *(*(array + 1) + 2). Right. Of
To elaborate: *(*array + 1) is just one element beyond *array, which is the same as array[0]: that is to say, array[0][1]. If you wanted [1][2], you'd take array[0] and add one to get *array + 1,
and dereference that to get array[1][0], and add 2 to get array[1][2]. In short, *(*(array + 1) + 2). If this point needs more clarification, let me know.
Now, you can actually do all of this stuff with a 1D array. How? Well, if you declare a 1D array of X*Y elements, you're taking up the same amount of memory as a 2D array of X by Y. You just have
to change how you index it. For the first values between (0,0) and (0,Y-1), it's simple. You access 1Darray[0] through 1Darray[Y-1]. Then what? For (1,0) you use 1Darray[Y], and for (1,1) you use
1Darray[Y+1], and so on.
But it turns out that there's an easier way to represent this. Make every pair have a unique index -- a sequential index, so you don't waste any memory. Simple. *(1Darray + x * Y + y). Lost yet?
array[1][2] would be 1Darray[1 * Y + 2] in this scheme. It really works. It's sort of like a different base, if you are familiar with numerical bases. Once your Y index reaches its max, you wrap
it around to zero and increment the X index. Every X index is equal to Y Y-indicies.
Anyhow, that should give you enough information to figure it out. If not, ask away.
Last edited by dwks; 12-05-2007 at 05:26 PM.
Seek and ye shall find. quaere et invenies.
"Simplicity does not precede complexity, but follows it." -- Alan Perlis
"Testing can only prove the presence of bugs, not their absence." -- Edsger Dijkstra
"The only real mistake is the one from which we learn nothing." -- John Powell
Other boards: DaniWeb, TPS
Unofficial Wiki FAQ: cpwiki.sf.net
My website: http://dwks.theprogrammingsite.com/
Projects: codeform, xuni, atlantis, nort, etc.
thank you so much for the elaborate post. I will see how it goes from here.
dwks, can you give me a brief example of how to declare such an array? I am assuming we need Y (the number of columns) from the user, correct?
-- I am not sure what the y in *(1Darray + x * Y + y) got introduced.
Last edited by Fredir; 12-05-2007 at 06:13 PM.
It's either this:
row * width + column
column * width + row
depending on how your array is arranged.
Since your doing this in C++, you should probably wrap you matrix in an object. Then overload operator [] to return a pointer to the correct row.
Something like this:
class Matrix{
int *m_buffer;
int m_rows, m_cols;
Matrix(int rows, int cols):m_rows(rows),m_cols(cols){
m_buffer=new int[row*col];
int *operator [] (int row){
return m_buffer+row*m_cols;
Last edited by King Mir; 12-05-2007 at 10:26 PM. Reason: Bin doing too much java recently.
It is too clear and so it is hard to see.
A dunce once searched for fire with a lighted lantern.
Had he known what fire was,
He could have cooked his rice much sooner.
12-05-2007 #2
12-05-2007 #3
Registered User
Join Date
Oct 2007
12-05-2007 #4
12-05-2007 #5
12-05-2007 #6
Registered User
Join Date
Oct 2007
12-05-2007 #7
Registered User
Join Date
Oct 2007
12-05-2007 #8
12-05-2007 #9
Registered User
Join Date
Oct 2007
12-05-2007 #10
12-05-2007 #11
Registered User
Join Date
Oct 2007
12-05-2007 #12
12-05-2007 #13
Registered User
Join Date
Oct 2007
12-05-2007 #14
12-05-2007 #15
Registered User
Join Date
Apr 2006 | {"url":"http://cboard.cprogramming.com/cplusplus-programming/96637-matrix-multiplication-help.html","timestamp":"2014-04-17T05:08:21Z","content_type":null,"content_length":"104277","record_id":"<urn:uuid:9dbc407a-a467-44c2-b6c4-21a407057a22>","cc-path":"CC-MAIN-2014-15/segments/1397609526252.40/warc/CC-MAIN-20140416005206-00053-ip-10-147-4-33.ec2.internal.warc.gz"} |
Math vocab chapter 8
14 terms · chapter 8 cpm math vocab
Ajacent Angles
angles which share a common side and vertex but no common interior parts
Associative Property
Changing the grouping of the numbers does not change the result in adddition
Associative Property for Multiplication
changing the grouping of the numbers does not chnage the result in addition
combining like terms
when working with an expression, terms with the same variable can be combined into one equantity Ex: 3x + 5x + 10 + 5 = 8x + 15
Communative property
the property of an operation such that changing the order of the numbers does not change the result of the operation
Complementary Angles
Two angles whose sum is 90 degrees.
In order
Distributive Property
for any a, b and c, a(b+c) = ab + ac
To evaluate an expression substitute the value given for the variable and perform the operations according to the order of operations
Like terms
terms, that have the same variable part and corresponding exponet
to combine like terms; to express the quanity using as few smybols as possible; to put a fraction in lowest terms
Straight angle
a 180 degree angle
Supplemetary angle
two angles whose measurements give a sum of 180 degrees
each part of the expression seoarated by addition or subtraction signs is a term | {"url":"http://quizlet.com/2333508/math-vocab-chapter-8-flash-cards/","timestamp":"2014-04-19T19:52:41Z","content_type":null,"content_length":"57396","record_id":"<urn:uuid:2ebed3ac-e657-4e1c-a8b7-97035ba8f607>","cc-path":"CC-MAIN-2014-15/segments/1397609537376.43/warc/CC-MAIN-20140416005217-00155-ip-10-147-4-33.ec2.internal.warc.gz"} |
n A
Degree Name
Master of Science (MSc)
Physics and Astronomy
Committee Member
Erik Sorensen, Duncan O'Dell
In Part I, the relationship between the topology of the Fermi surface and the entanglement entropy S is examined. Spinless fermionic systems on one and two dimensional lattices at fixed chemical
potential are considered. The lattice is partitioned into sub-system of length L and environment, and the entanglement of the subsystem with the environment is calculated via the correlation matrix.
S is plotted as a function of the next-nearest or next-next nearest neighbor hopping parameter, t. In 1 dimension, the entanglement entropy jumps at lifshitz transitions where the number of Fermi
points changes. In 2 dimensions, a neck-collapsing transition is accompanied by a cusp in S, while the formation of electron or hole-like pockets coincides with a kink in the S as a function of the
hopping parameter. The entanglement entropy as a function of subsystem length L is also examined. The leading order coefficient of the LlnL term in 2 dimensions was seen to agree well with the Widom
conjecture. Of interest is the difference this coefficient and the coefficient of the term linear in L near the neck-collapsing point. The leading order term changes like |t-t[c]|^1/2 whereas the
first sub-leading term varies like |t-t[c]|^1/3, where t[c] is the critical value of the hopping parameter at the transition.
In Part II, we study the statistics of fractionalized excitations in a bosonic model which describes strongly interacting excitons in a N-band insulator. The elementary excitations of this system are
strings, in a large N limit. A string is made of a series of bosons whose flavors are correlated such that the end points of a string carries a fractionalized flavor quantum number. When the tension
of a string vanishes, the end points are deconfined. We determine the statistics of the fractionalized particles described by the end points of strings. We show that either bosons or Fermions can
arise depending on the microscopic coupling constants. In the presence of the cubic interaction in the Hamiltonian as the only higher order interaction term, it was shown that bosons are emergent. In
the presence of the quartic interaction with a positive coupling constant, it was revealed that the elementary excitations of the system possess Fermion statistics.
Recommended Citation
Rodney, Marlon A., "THE ENTANGLEMENT ENTROPY NEAR LIFSHITZ QUANTUM PHASE TRANSITIONS & THE EMERGENT STATISTICS OF FRACTIONALIZED EXCITATIONS" (2012). Open Access Dissertations and Theses. Paper 7487.
McMaster University Library
Files over 3MB may be slow to open. For best results, right-click and select "save as..."
Included in | {"url":"http://digitalcommons.mcmaster.ca/opendissertations/7487/","timestamp":"2014-04-21T04:38:31Z","content_type":null,"content_length":"24590","record_id":"<urn:uuid:8afe14dc-0c49-43ff-b570-40ba7c9d5681>","cc-path":"CC-MAIN-2014-15/segments/1397609539493.17/warc/CC-MAIN-20140416005219-00082-ip-10-147-4-33.ec2.internal.warc.gz"} |
• Online Information article about DETERMINANT definition of the determinant, and it is interesting to show how from these properties, assumed for the definition of, the determinant, it at once
appears that- the determinant is a function serving for the solution of a system. — “DETERMINANT - Online Information article about DETERMINANT”,
• Determinant - Definition. In linear algebra, the determinant is a function that associates a scalar det(A) to every square matrix A. The fundamental geometric meaning of the determinant is as the
scale factor for volume when A is regarded as a linear transformation. — “Determinant - Definition”,
• In algebra, the determinant is a special number associated with any square matrix. The fundamental geometric meaning of a determinant is a scale factor for measure when the matrix is regarded as
a linear transformation. Thus a 2 2 matrix with. — “Determinant Information (Linear Transformation) @ ”,
• DETERMINANT, in mathematics, a function which presents itself in the 2. It is easy, by induction, to arrive at the general results: A determinant of the order n is the sum of the 1.2.3 n products
which can be formed with n elements out of n 2 elements arranged in the form of a square, no two of. — “Determinant - LoveToKnow 1911”, 1911
• This section shows how determinants can be used to solve a system of simultaneous linear equations (Cramer's Rule). — “1. Determinants”,
• We called this number the determinant of A. It is clear from this, that we would like to have a similar result for bigger matrices (meaning higher orders). So is there a similar notion of
determinant for any square matrix, which determines whether a square matrix is invertible or not?. — “Introduction to Determinants”,
• Thus a 2 × 2 matrix with determinant 2 when applied to a set of points with finite area will transform those points into a set with twice the area. Determinants are important both in calculus,
where they enter the substitution rule for several variables, and in multilinear algebra. — “Determinant - Wikipedia, the free encyclopedia”,
• The determinant is an algebraic operation that transforms a square matrix $M$ into a scalar. For example, the determinant is zero if and only the matrix $M$ is singular (no inverse exists). —
“PlanetMath: determinant”,
• In algebra, a determinant is a function depending on n that associates a scalar, det(A), to every n×n square matrix A. The fundamental geometric meaning of a determinant is as the scale factor
for volume when A is regarded as a linear transformation. — “Determinant - Mirror of Wikipedia - ”,
• In algebra, a determinant is a function depending on n that associates a scalar det(A) to every n×n square matrix A. The fundamental geometric meaning of a determinant is as the scale factor for
volume when A is regarded as a linear transformation. — “Determinant - Wikipedia, the free encyclopedia”,
• Determinant definition, a determining agent or factor. See more. — “Determinant | Define Determinant at ”,
• A determinant is a scalar number which is calculated from a matrix. Determinants are perhaps most comonly associated with matricies but it does have a geometric interpretaion that is completely
independant of matricies (this geometric interpretation is discussed on this page). — “Maths - Matrix Algebra - Determinants - Martin Baker”,
• If all the entries on one row or one column of a determinant are multiplied by the same If all the entries in a row (or a column) of a determinant are zero, the value of the. — “Determinant”,
• Determinant. Before plunging into the theory of determinants we are going to make an attempt at defning them in a more geometric fashion.This works well in low dimensions and will serve to
motivate our more algebraic constructions of subsequent sections. — “Determinant”,
• Encyclopedia article about Determinant. Information about Determinant in the Columbia Encyclopedia, Computer Desktop Encyclopedia, computing dictionary. — “Determinant definition of Determinant
in the Free Online”, encyclopedia2
• The determinant of a matrix (written |A|) is a single number that depends on the elements of the matrix A. Determinants exist only for square matrices (i.e., ones where the number of rows equals
the number of Determinants are a basic building block of linear algebra, and are. — “Determinant - Conservapedia”,
• This page lists our free online video tutorials on determinant, determinant word problems, and printable determinant worksheets. — “Determinant Help : Videos | Worksheets | Word Problems”,
• The determinant "determines" whether the system has a unique solution (which occurs precisely if the determinant is non-zero). In this sense, two-by-two determinants were considered by Cardano at
the end of the 16th century and larger ones by Leibniz about 100 years later. — “Determinant - Wikinfo”,
• Definition of word from the Merriam-Webster Online Dictionary with audio pronunciations, thesaurus, Word of the Day, and word games. Definition of DETERMINANT. 1 : an element that identifies or
determines the nature of something or that fixes or conditions an outcome. 2 :. — “Determinant - Definition and More from the Free Merriam”, merriam-
• The determinant is a number assigned to a system of linear equations and unknowns. Define the determinant of a square matrix to be. where is the Levi. — “Linear algebra/determinant - Mathematics
• Wikipedia determinant (plural determinants) A determining factor; an element that determines the nature of something (linear algebra) The unique scalar function over square matrices which is
distributive over matrix multiplication, multilinear. — “determinant - Wiktionary”,
• Translations of determinant. determinant synonyms, determinant antonyms. Information about determinant in the free online English 1. An influencing or determining element or factor: "Education is
the second most important determinant of recreational participation" (John P. Robinson). — “determinant - definition of determinant by the Free Online”,
• In algebra, a determinant is a function depending on n that associates a scalar, det(A), to every n×n square matrix A. The fundamental geometric meaning of a determinant is as the scale factor
for volume when A is regarded as a linear transformation. — “Determinant”, schools-
• By Multiple of Row Added to Row of Determinant, we can subtract row 1 from each of the other rows and leave unchanged: From Determinant with Unit Element in Otherwise Zero Row, we can see that
this directly gives us:. — “Vandermonde Determinant - ProofWiki”,
• This lesson This lesson describes how to calculate the determinant of a square matrix for 2 x 2 matrices, 3 x 3 matrices, and n x n matrices. Also describes matrix determinant notation. — “Matrix | {"url":"http://crosswords911.com/determinant.html","timestamp":"2014-04-20T11:20:55Z","content_type":null,"content_length":"77706","record_id":"<urn:uuid:9705ee9a-8ab5-4707-b38d-f57d63894e40>","cc-path":"CC-MAIN-2014-15/segments/1397609538423.10/warc/CC-MAIN-20140416005218-00097-ip-10-147-4-33.ec2.internal.warc.gz"} |
Tractatus 3.318 + MM comments
3.318 Like Frege and Russell I construe a proposition as a function of the expressions contained in it.
Perhaps there is a likeness, but surely there are also many differences. The problem with "a function of the expressions contained in it" is that it then becomes unclear what a proposition is: this
seems a per obscurum explanation at best.
Besides, what Frege and Russell maintained is, much rather, that both the meaning and the truth-value of a proposition depend functionally on the terms of the proposition, more or less in the sense
that if one knows the meanings of all terms and the truth-values of all propositions that do not contain logical operators, then one can infer the meaning and the truth-value of the proposition. (The
general idea coming down to: One knows what "cow", "eats", "grass", "sun" and "shines" mean; so one knows what "the cow eats grass and the sun shines" means, and since it is night one knows "the sun
shines" is false and therefore so is the conjunction even if "the cow eats grass" is true.) | {"url":"http://www.maartensz.org/philosophy/wittgenstein/Tractatus/3/T3.318.html","timestamp":"2014-04-17T12:29:19Z","content_type":null,"content_length":"3885","record_id":"<urn:uuid:e071de5a-d9be-486d-b94d-db59ec3b6f94>","cc-path":"CC-MAIN-2014-15/segments/1397609530131.27/warc/CC-MAIN-20140416005210-00168-ip-10-147-4-33.ec2.internal.warc.gz"} |
Got Homework?
Connect with other students for help. It's a free community.
• across
MIT Grad Student
Online now
• laura*
Helped 1,000 students
Online now
• Hero
College Math Guru
Online now
Here's the question you clicked on:
Factor the following expression. 198q3r2 – 184q2r2 + 18qr2
• one year ago
• one year ago
Your question is ready. Sign up for free to start getting answers.
is replying to Can someone tell me what button the professor is hitting...
• Teamwork 19 Teammate
• Problem Solving 19 Hero
• Engagement 19 Mad Hatter
• You have blocked this person.
• ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.
This is the testimonial you wrote.
You haven't written a testimonial for Owlfred. | {"url":"http://openstudy.com/updates/50be0920e4b09e7e3b858931","timestamp":"2014-04-20T08:46:52Z","content_type":null,"content_length":"49129","record_id":"<urn:uuid:68205ee5-a83b-4ff0-96a1-add14222d249>","cc-path":"CC-MAIN-2014-15/segments/1398223206770.7/warc/CC-MAIN-20140423032006-00498-ip-10-147-4-33.ec2.internal.warc.gz"} |
Re: [TowerTalk] Feedpoint Impedance
> Radiation resistance should be fixed..
Oh, right...duh.
The current equation will do - but the radiator (I may have confused things
by referring to it as a "dipole") may be anywhere between one-half and one
wavelength long, so the current won't be a simple cosine function. It
*will* be zero at the ends :-)
73, Ward N0AX
----- Original Message -----
From: "Jim Lux" <jimlux@earthlink.net>
To: "Ward Silver" <hwardsil@gmail.com>; "Towertalk Reflector"
Sent: Monday, July 28, 2008 4:16 PM
Subject: Re: [TowerTalk] Feedpoint Impedance
> -----Original Message-----
>>From: Ward Silver <hwardsil@gmail.com>
>>Sent: Jul 28, 2008 12:46 PM
>>To: Towertalk Reflector <towertalk@contesting.com>
>>Subject: [TowerTalk] Feedpoint Impedance
>>While we're on the math subject, does anyone know of an equation that
>>either feedpoint impedance or radiation resistance as a function of
>>along a linear radiator of known electrical length? Free space would be
>>fine, I can work in the effects of ground later.
> Radiation resistance should be fixed.. it's a function of the size and
> shape of the radiator. Feedpoint impedance will change with position, of
> course (essentially, it's some transformation of the combination of
> radiation resistance, loss resistance and the reactance of the antenna)
> I don't think there's a nice analytical expression for it. One could
> start with the Schelkunoff formulation (the one using sine and cosine
> integrals, which are series expansions). Do you need the reactive part?
> If not, you could assume that the current has a sinusoidal distribution,
> and once you know the radiation resistance, the feedpoint R at the center
> will be the Rrad+Rloss.. Moving away from the center, it would scale as
> 1/cos(distance), becoming infinite at the very end.
> Orfanidis's online book might be a good source.. he has equations for the
> current at various places along the element, and that's really what you're
> looking for. http://www.ece.rutgers.edu/~orfanidi/ewa/ Chapter 16 or 22,
> I suspect.
> Practically, I've done this kind of thing with NEC.. run a series of cases
> with systematic variation in the position, generate a table, and then do
> interpolation.
> Jim, W6RMK
TowerTalk mailing list | {"url":"http://lists.contesting.com/_towertalk/2008-07/msg00774.html?contestingsid=484l0us4tj4uk7krkumrulhg15","timestamp":"2014-04-21T05:18:50Z","content_type":null,"content_length":"10975","record_id":"<urn:uuid:60165c75-5957-49f4-8684-3cd849e904a5>","cc-path":"CC-MAIN-2014-15/segments/1397609539493.17/warc/CC-MAIN-20140416005219-00417-ip-10-147-4-33.ec2.internal.warc.gz"} |
River Grove Statistics Tutor
...I currently tutor two students in Prealgebra and like to instill confidence in them so they know that math is something you can be good at if you do it enough. When I took the Basic Skills test
for my teaching certificate I received a perfect score on the math section. Currently I am taking a L...
17 Subjects: including statistics, reading, Spanish, English
...I started off my college career as a math major. Although that was a long time ago, I have helped several students with their pre-calculus courses. The precalculus student that I helped just
last academic year went from getting Cs and Bs in her tests to As.
13 Subjects: including statistics, geometry, algebra 2, algebra 1
...I have a BS degree in biology. I have a BS degree in biology, and have studied biochemistry in college and medical school. I have two full years of chemistry in college.
17 Subjects: including statistics, chemistry, geometry, reading
...I have taught high-school and college aged students various subjects, ranging from math to law to reading and writing. As a Forensics Instructor at two different national institutes and as a
practicing attorney, I have gained significant experience in helping high-school or college aged students...
39 Subjects: including statistics, English, reading, physics
I am a PhD Psychology student specializing in Social and Industrial/Organizational Psychology. I am looking to find tutoring jobs locally in the Chicago suburbs. I absolutely love statistics and
11 Subjects: including statistics, GRE, GED, grammar | {"url":"http://www.purplemath.com/River_Grove_Statistics_tutors.php","timestamp":"2014-04-20T07:04:28Z","content_type":null,"content_length":"23929","record_id":"<urn:uuid:f73dd110-5c28-4420-9471-c08b3140d683>","cc-path":"CC-MAIN-2014-15/segments/1398223211700.16/warc/CC-MAIN-20140423032011-00220-ip-10-147-4-33.ec2.internal.warc.gz"} |
Summary: Math 3130 Midterm: Due Wednesday October 22 in Class
Remember to show your work!
Directions This is a take home, open notes test. There are eight problems on the test. You must
answer carefully and completely any five of the problems. You answer must be your own; you
are free to discuss problems with other students but must write up your own answers. Excessive
similarity of answers will be noted and dealt with appropriately.
Problem 1 Find all possible cycle types in S5 and say how many permutations there are with
each cycle type.
Problem 2 Compute GCD(54, 45) = 54x + 45y using the Euclidean algorithm and solving for
x and y by back substitution through the Euclidean algorithm.
Problem 3 Let A be a group with two elements and so that A consists of all possible products
in any order of and . If and satisfy the following relations:
= 3
= ()2
= e
Prove the following identities hold in A.
(i) = 2
, (ii) = 2 | {"url":"http://www.osti.gov/eprints/topicpages/documents/record/585/1725488.html","timestamp":"2014-04-18T04:19:26Z","content_type":null,"content_length":"8045","record_id":"<urn:uuid:8ff2cbf5-f289-4f6b-a47a-01bee684da8b>","cc-path":"CC-MAIN-2014-15/segments/1397609532480.36/warc/CC-MAIN-20140416005212-00010-ip-10-147-4-33.ec2.internal.warc.gz"} |
Sierra Madre SAT Math Tutor
Find a Sierra Madre SAT Math Tutor
...I received my high school's Spanish award for excellence in both spoken Spanish and classwork. Since high school, I have regularly practiced Spanish with friends who are native speakers.
Further, I have always had a great interest in grammar, so my Spanish grammar continues to improve in advanced grammar topics.
28 Subjects: including SAT math, chemistry, Spanish, calculus
...I love working with students and have experience teaching a wide range of classes from pre-Algebra to Advanced Engineering Mathematics. I am currently at Fuller Seminary in Pasadena preparing
for a career in community work as a pastor. Here is a testimonial from one of my students: “I love this teacher.
9 Subjects: including SAT math, calculus, algebra 1, algebra 2
...Unlike the SAT Math sections, ACT Math requires the test takers to solve more problems in less time, and asks simpler (less tricky) questions. The strategy here is to learn to work quickly by
becoming familiar with the math topics. I have been teaching this subject for over 10 years, and I can help you to score higher.
38 Subjects: including SAT math, reading, English, writing
...I have enabled students to reach their maximum potential on standardized examinations (up to a 650 point increase on the SAT exams!) as well as on school work, and to get into the college of
their dreams! To provide some more details on my academic background, I have listed my experiences in the...
43 Subjects: including SAT math, English, writing, reading
...I took a term of basic linear algebra covering the basic things such as vector spaces, subspaces, quotient spaces, orthogonal complements, linear transformations, matrices, determinant, trace,
change of basis, Gramm-Schmidt orthogonalization, vector spaces over more general fields, inner products...
35 Subjects: including SAT math, chemistry, calculus, geometry | {"url":"http://www.purplemath.com/sierra_madre_sat_math_tutors.php","timestamp":"2014-04-17T13:16:03Z","content_type":null,"content_length":"24107","record_id":"<urn:uuid:c917512f-c969-47a4-9d42-625b5c6cf78a>","cc-path":"CC-MAIN-2014-15/segments/1397609530131.27/warc/CC-MAIN-20140416005210-00172-ip-10-147-4-33.ec2.internal.warc.gz"} |
Mount Hamilton Algebra 2 Tutor
Find a Mount Hamilton Algebra 2 Tutor
...These distractions may include other students, other stimuli, whether audio or visual, or any mental or physical unpreparedness on the student's part at the time. All these factors combined can
result in an undesirable learning environment for some students. One-on-one tutoring eliminates many types of distractions.
5 Subjects: including algebra 2, geometry, Chinese, prealgebra
...I do have a passion for Math because I have my Bachelors of Science in Mathematics and Masters of Science in Actuarial Science. I look forward to hearing from you on how I can help you with
Math!I currently work at a health care and consulting firm and have used Microsoft Outlook on a daily basi...
9 Subjects: including algebra 2, geometry, algebra 1, trigonometry
EDUCATION- B.Tech Electrical Engineering Pursuing MS in Software Engineering Experience: I have a passion for learning and teaching math and science, having tutored high school science and math
for over 1 year. Having the experience of helping people from various background, I am able ...
15 Subjects: including algebra 2, calculus, statistics, geometry
...I have taught Algebra 1, Algebra 2, Earth Science, Biology, Biology Honors, Chemistry, Physics and Zoology. I am a patient person and I try to understand each student's needs and what they will
need to be most successful. I understand the importance of truly teaching the material so that the st...
16 Subjects: including algebra 2, chemistry, physics, geometry
I am a Yale graduate with a diverse background and major in Film Studies. I have taught English literature and writing courses for a full academic year and two summers. I have spent a year at a
college prep school, tutoring in a variety of subjects (English, Spanish, Biology, Chemistry, Physics, A...
20 Subjects: including algebra 2, English, chemistry, writing | {"url":"http://www.purplemath.com/Mount_Hamilton_Algebra_2_tutors.php","timestamp":"2014-04-21T04:56:36Z","content_type":null,"content_length":"24243","record_id":"<urn:uuid:d9d4f0c9-f1e1-49b6-a218-1eefb8dd179e>","cc-path":"CC-MAIN-2014-15/segments/1398223205375.6/warc/CC-MAIN-20140423032005-00616-ip-10-147-4-33.ec2.internal.warc.gz"} |
FOM: What is the standard model for PA?
Vladimir Sazonov sazonov at logic.botik.ru
Wed Mar 18 12:21:44 EST 1998
Torkel Franzen wrote:
> Validimir Sazonov says:
> >You don't see anything indeterminate or unclear about the notion
> >"natural number" or you see that and how it is determinate?
> I don't see anything indeterminate or unclear about the notion
> "natural number". "Seeing that it is determinate", as far as I can
> determine, amounts only to not seeing anything indeterminate or
> unclear about it. This doesn't exclude the possibility that you might
> convince me that there is something indeterminate or unclear about
> it.
Probably this corresponds to what I described as an illusion of
the standard model. Of course I also have some such illusion.
(You probably will not agree to call it this way.) As any
illusion it has some objective roots (on which we probably can
agree). It is interesting to discuss such roots, to understand
how they work in the creation of this illusion. For example, we
know some geometrical illusions arising from some simple figures
on a sheet of paper (stairs or the like). Who considers
corresponding images in our mind as real?
> >No, I do not know. More precisely, I know that I may consider both
> >alternative, each being reasonable in its own way. Let us fix that
> >there is NO last natural number because this is usually *postulated*
> >for "the standard model". This still does not fix this standard
> >model, just how *long* is it.
> "The standard model" is jargon. You knew everything that I know about
> the natural numbers (from the present philosophical point of view) long
> before you had heard of "the standard model". One of the things you
> learned was that there isn't any largest natural number - given any number
> k, there is a larger one, k+1. It's not clear to me what you consider
> "unfixed".
>From the point of view of the above discussed illusion, when
we concentrate *only* on it, we will hardly see anything
unfixed. It comes in mind the "full" induction axiom on
"arbitrary" properties of natural numbers which would fix the
standard model completely (up to isomorphism) as in the
framework of set theory. You know that the term "arbitrary" is
too problematic here. It bothers me too much to consider this
model as "really" fixed.
Also I would like to have the following picture of "creating"
the natural numbers which seems do not contradict to the
traditional view, but is of somewhat different flavour. We
count 0,1,2, etc. We iterate successor operation to get + and
iterate + to get * and then exponential, etc. We realize that
the more is "operative" ability of considered operations, the
"longer" is the row of arising in this way natural numbers. We
consider these operations as abstract, non-realistic ones. We
introduce them only in the hope to overcome the currently
considered infinity. E.g. if we have only addition operation
(as *total* recursive function) then multiplication is only
partial recursive and 2^1000 will hardly arise in this row, even
if we consider it as infinite (no last number). Then we
postulate that * is also total and get 2^1000 reachable with the
help of multiplication by two. However, we will never consider
2^1000 as reachable by the direct (feasible) iteration of the
successor operation. Thus, we have many different infinite
natural number series. I do not see how we will get "all"
natural numbers in this process even potentially. Also I do not
understand what does it mean this "all". All the attention is
concentrated here on fuzziness of all these intermediate
infinities and in the most degree of the "whole" process. The
simplest one is the first infinity corresponding to feasible
> >Yes, I do know that it [for all x, log log x < 10] does not hold
> >according to such and such axioms.
> Axioms are secondary. People who have never heard of the Peano
> axioms and wouldn't be interested in hearing about them learn and
> apparently accept that log is an unbounded function, on the basis of
> their informal understanding of "natural number". Is there some
> confusion or unclarity in this?
I believe that the main feature of mathematics is *provability*
of their results. I cannot imagine proofs without some kind of
proof rules and axioms. We learn mathematics even at school by
some training repeated again and again how to do something
*correctly* (of course, together with corresponding intuitions).
That is why we are able to recognize correct proof from
incorrect one (even without knowing, say what is the name of the
rule modus ponens, reductio ad absurdum, etc.; however, e.g. my
students, even not the best ones, actually know after school
even the name of the latter rule). In particular we implicitly
learned at school some (idea of) induction or iteration rule, i.e.,
essentially Peano Arithmetic, which allows us to *deduce* easily
that exponential (= iterated multiplication) is total function
and logarithm is bounded.
> >If you say "all", I do not understand what does this mean. It is unclear
> >what is "all" EVEN in the more reliable case of feasible numbers which
> >have a physical, perceiving meaning in our real world.
> Then we're back to the beginning. All the natural numbers are 0,s(0),s(s(0))
> and so on. What's unclear or indeterminate about this?
> As for the "feasible numbers", I don't know what you mean by "the
> more reliable case". The notion of "feasible number" is very unclear
> and indeterminate - isn't that so?
This notion is *comparatively* clearer that an illusory idea of
standard model. Who do not know what is *physically* written
string in a finite alphabet? It is less clear about f.n. how to
work with them in a formal axiomatic system like PA. However,
how many peoples did try to do this? On the other hand, there
were some attempts which show that this is possible. I believe
that only (let, say, hypothetical) possibility of formalization
of feasibility concept gives us some hope on including it in
mathematics as a "first-class citizen".
> >I have some llusion of understanding.
> Well, I would say that you rather have an illusion of not
> understanding. Or, in less confrontational terms, I would say that
> you have certain ideas about what is required to understand something,
> or what is required for something to make determinate sense. I am
> certainly not in a position to say that these ideas are wrong, that
> you are mistaken, that your pursuits are misguided. On the contrary, I
> think it's a good thing that people pursue such ideas and
> inclinations, including stuff like Yesenin-Volpin's consistency proof
> for ZFC (or NF). Where I think you are plain wrong is only in
> presenting your ideas and inclinations as though they revealed some
> defect in standard practice.
It is rather not in standard practice but around it. I would not
like to assert anything global. But I really feel rather strong
discomfort when I see some assertions on "absolute truth" (not in
the technical sense of model theory) and the like.
Vladimir Sazonov
Program Systems Institute, | Tel. +7-08535-98945 (Inst.),
Russian Acad. of Sci. | Fax. +7-08535-20566
Pereslavl-Zalessky, | e-mail: sazonov at logic.botik.ru
152140, RUSSIA | http://www.botik.ru/~logic/SAZONOV/
More information about the FOM mailing list | {"url":"http://www.cs.nyu.edu/pipermail/fom/1998-March/001584.html","timestamp":"2014-04-20T23:27:50Z","content_type":null,"content_length":"10595","record_id":"<urn:uuid:2e4af850-8956-4a1a-9025-5c1a09384b2d>","cc-path":"CC-MAIN-2014-15/segments/1397609539337.22/warc/CC-MAIN-20140416005219-00137-ip-10-147-4-33.ec2.internal.warc.gz"} |