content stringlengths 86 994k | meta stringlengths 288 619 |
|---|---|
Lesson outline
A pentomino is a shape made up of 5 individual squares. There are twelve different types, all of which are available as tiles within Polypad. Pentominoes can be used recreationally to complete
various puzzles. This task explores the perimeter of shapes made from pentominoes, and offers students opportunities to work systematically and construct reasoned arguments.
Lesson objective: Understand that shapes with the same area can have different perimeter
Lesson activity
If students haven’t seen pentominoes before, you may wish to start with a quick overview. Use Polypad to display all pentominoes, and enable the square grid to help students see the lengths of each
side more clearly.
Invite students to calculate the area and the perimeter of each of the twelve pentominoes, and find the “odd one out”. They should notice that all shapes have the same area (5), but not the same
perimeter. Most shapes have a perimeter of 12, except for the P-pentomino which has a perimeter of 10. Can students explain what’s different about this pentomino?
Main Activity
Now introduce the idea of joining two or more pentominoes together. Explain that we want to stay within the squares of the grid and match up the squares of pentominoes as we join them. You may wish
to show them an example, such as this one. Remind students that the two pentominoes are not allowed to overlap.
Invite students to make some shapes of their own by joining together two different pentominoes (but they can use the same pentomino more than once in different pairs). For each shape, can they work
out its perimeter?
Consider sharing this Polypad with students as a starting point.
If students are struggling (for example, counting the “joins” as part of the perimeter), they could use the ruler tool to trace around the pentominoes, and then delete the tiles underneath so that
only the outline remains.
Once students have created a few examples, pose the following questions:
1. What is the smallest perimeter of a shape made by joining two pentominoes together?
2. What is the largest perimeter of a shape made by joining two pentominoes together?
3. Which perimeters in between can you make?
4. Can you make a perimeter of 15?
5. What are the areas of your shapes?
Give students some time to explore, reminding them of the importance of recording their findings so that they are ready to share with the class later. If students have their own devices, they can use
the pen tool to annotate the shapes they make or the text tool to record the perimeters and areas.
It might be useful to keep the 12 pentominoes visible on the board or print a copy of the pentominoes so that students working on squared paper can remind themselves of the shapes they are working
with. At the end of this document is a diagram of all pentominoes with a side-length of 1 cm.
Towards the end of the lesson, bring the class together to share findings. You could encourage students to share some of the shapes they found with the whole class and explain their reasoning. If
students are working on Polypad, you can share their work via the "Class" tab on Polypad. Here are some useful prompts for drawing the discussion together:
1. How do you know that you have found the smallest/largest possible perimeter?
2. How did you work out the perimeters?
3. What were the areas of your shapes?
4. Why are all the perimeters even numbers?
5. How can you be certain that no other perimeters could be made?
Finish off the lesson by emphasising that when we join two shapes together the area of the new shape is the sum of the original areas, but the perimeter of the new shape depends on how much of the
original shapes’ perimeters are touching.
Possible solutions
Here are some of the shapes students might have found for each of the possible perimeters, from the smallest possible (14) to the largest possible (22).
22 is the largest possible, because every pentomino has a perimeter of either 10 or 12, and the maximum perimeter is made by joining together two pentominoes with a perimeter of 12 so that they only
touch by one unit.
14 is the smallest possible perimeter, and there are three different ways to make this (excluding rotations and reflections):
As every pentomino has an area of 5 square units, two pentominoes form a shape with area 10 square units.
As every pentomino has an even perimeter, and joining pentominoes reduces their combined perimeter by twice the length of the overlap, every combination of pentominoes will also have an even
Support and extension
The same activity can be adapted to use the tetrominoes rather than pentominoes, which may help students who are overwhelmed by thinking about twelve different pieces at once.
An important part of this activity is that pentominoes are not allowed to overlap. At some point, you could show the class an example with a perimeter smaller than 14, and that you’ve “beaten”
everyone to the smallest perimeter. See if students notice that you overlapped the pieces and discuss how the class feels about that – should it be “allowed” or not?
As an extension, students could explore what happens when you join together more than two pentominoes, perhaps working up to the question “What is the maximum perimeter of a shape made from all
twelve pentominoes?” | {"url":"https://polypad.amplify.com/he/lesson/pentomino-perimeters","timestamp":"2024-11-09T21:00:53Z","content_type":"text/html","content_length":"27361","record_id":"<urn:uuid:b2017422-6d06-4d82-a081-e014decb0552>","cc-path":"CC-MAIN-2024-46/segments/1730477028142.18/warc/CC-MAIN-20241109182954-20241109212954-00242.warc.gz"} |
Area of an irregular quadrangle with the given sides
Calculates an area of an irregular quadrangle with the given sides
This content is licensed under Creative Commons Attribution/Share-Alike License 3.0 (Unported). That means you may freely redistribute or modify this content under the same license conditions and
must attribute the original author by placing a hyperlink from your site to this work https://planetcalc.com/2804/. Also, please do not modify any references to the original work (if any) contained
in this content.
Users of Planetcalc are persistently asking us to create a calculator for an area of irregular quadrangles for which the only lengths of the sides are known. So, I've decided to make this joke
calculator(Press "pause" button to calculate a quadrangle area with given sides which you liked most.
The area of an irregular quadrangle cannot be calculated with the length of the sides only. I hope this demonstration will help those who asked about the calculator to understand this.
Similar calculators
PLANETCALC, Area of an irregular quadrangle with the given sides | {"url":"https://planetcalc.com/2804/?license=1","timestamp":"2024-11-03T18:22:48Z","content_type":"text/html","content_length":"54842","record_id":"<urn:uuid:2e3951fb-8a9f-461b-8312-8dec95790a1f>","cc-path":"CC-MAIN-2024-46/segments/1730477027782.40/warc/CC-MAIN-20241103181023-20241103211023-00480.warc.gz"} |
Unusual Report Gives The Important Points to You on math websites for kids That Only A Few People Know Exist - Prompt Packways
But if these aren’t sufficient, take a glance at the Class Central catalog, which has over 150K on-line programs, many of them free or free-to-audit. This series provides the necessary mathematical
background for majors in Computer Science, Economics, Mathematics, Mathematical and Computational Science, and most Natural Sciences and some Engineering majors. Those who plan to main in Physics or
in Engineering majors requiring Math 50’s beyond Math 51 are really helpful to take Math 60CM. This collection provides the required mathematical background for majors in all disciplines, especially
for the Natural Sciences, Mathematics, Mathematical and Computational Science, Economics, and Engineering. Knowledge of Math 21 content material is prime to university-level quantitative work, and is
predicted by the surface world for anybody incomes a level in a quantitative subject right here.
• It offers a complete and engaging strategy to math learning, making it an effective device for students.
• Axiomatic, analytic, transformational, and algebraic approaches to geometry might be used.
• These materials enable personalized follow alongside the brand new Illustrative Mathematics eighth grade curriculum.
• In truth, many college students use on-line courses to satisfy arithmetic prerequisites for superior pc science degrees.
After signing up with Khan Academy, learners can study decimals, fractions, powers of ten algebraic considering, and different math ideas at their own tempo. Alongside Scratch, Python, JavaScript,
and Java programs, the corporate provides lessons introducing children to popular subjects similar to synthetic intelligence, information science, and robotics. Group lessons start at $122.50 per
person per unit (four 55-min sessions). If you need your youngsters to sharpen their math skills while studying to code, Create & Learn is an impressive option.
Not known Facts About ixl learning center Unveiled By The Experts
If you discover any of these indicators, they doubtless need additional help. But that is solely one of many the reason why mother and father are selecting to put money into on-line math lessons for
their younger ones. Juni Learning offers children aged 7 to 18 with self-study courses, 1-on-1 classes, and boot camps in laptop science, math, and English. But although the videos and interactive
workouts assist self-directed learning, Mathletics doesn’t provide a lot guidance for children. As a end result, Kids can answer questions incorrectly over and over again. Nevertheless, Mathletics is
great for getting your youngsters thinking about learning math outdoors of sophistication.
Kids, Work and ixl reviews
Learning arithmetic is an inevitable part of pre-school life. Imagine, most of the professions must be proficient in maths. For occasion, engineers, finance professionals, scientists, etc.
Topics embody vectors and the geometry of area, purposes of integration, integration strategies, L’Hopital’s Rule, improper integrals, parametric equations, polar coordinates, conic sections and
infinite series. The course includes study of trigonometric functions, inverse trigonometric features, trigonometric identities and trigonometric equations. Complex numbers, De Moivre’s Theorem,
polar coordinates, vectors and other topics in algebra are also addressed, together with conic sections, sequences and collection. In addition to the lesson itself, you will also receive in return
all the mandatory notes and a roadmap for the next classes.
The study of arithmetic and logic as a self-discipline provides as much as a lot more than what you learned in highschool algebra. A math education might help you understand the ideas that guide the
world you live in. Studying this discipline not only develops your mathematical pondering ixlmath.com 4th grade skills, but in addition your problem-solving abilities. You can learn to have a look at
a problem, think about the relationships between various factors, and are available to a logical conclusion.
Learn seventh grade math—proportions, algebra basics, arithmetic with unfavorable numbers, likelihood, circles, and extra. This exploration will also embody the development and sequential nature of
every of these branches of arithmetic and the means it pertains to the various ranges inside the algebra arithmetic curriculum. An introduction to mathematical logic and proof within the context of
discrete constructions. Topics embrace basic mathematical logic, elementary number concept, primary set theory, capabilities, and relations. Writing proficiency is required for a passing grade on
this course. A pupil who doesn’t write with the talent usually required of an upper-division student will not earn a passing grade, regardless of how well the scholar performs in other areas of the
This characteristic is useful for K-12 math learners, as it helps them construct confidence and motivation whereas improving their math expertise. Think Academy’s highly-qualified academics follow a
set curriculum and provide personalised stories to keep you up to date together with your kids’ progression. Yet as its programs are only available at certain instances, it’s not as versatile as
different e-learning platforms. If you’re taking our calculus collection, and you are a highschool scholar, you can take the AP Calculus exam to show that you’ve learned calculus to a degree required
by most colleges and universities.
When students gather a thousand points in a single week, they can trade them for certificates and credits to update their avatars. Parents of “mathletes” obtain weekly reviews to trace their
progress. In a survey of Preply students, 92% of respondents agreed that Preply’s 1-on-1 lessons are more fun than a method they used before. | {"url":"https://promptpack.com/unusual-report-gives-the-important-points-to-you-on-math-websites-for-kids-that-only-a-few-people-know-exist/","timestamp":"2024-11-10T09:29:30Z","content_type":"text/html","content_length":"49878","record_id":"<urn:uuid:f9a829f1-a240-4277-9335-25baa288c0bd>","cc-path":"CC-MAIN-2024-46/segments/1730477028179.55/warc/CC-MAIN-20241110072033-20241110102033-00764.warc.gz"} |
Bioequivalence and Bioavailability Forum
To round or not to round… [Software]
Hi ElMaestro,
❝ ❝ Haha, I know this game and therefore, always round before the comparison.
❝ or never bring yourself into a situation where you need to compare floats.
Did I tell to how
significant digits I round?
❝ I've taken the worst way out and written functions that check if x is simar to y plus/minus a wee faction like 1e-8 or something.
I don’t know which kind of measurements you are comparing. Sumfink ultra-precise (according to the International Bureau of Weights and Measures:
Zizou (I guess) and I were talking about concentrations. AP according to the GLs 20% at the LLOQ and 15% above. Hence,
reported substantially beyond that is not relevant (shall I call it noise?). What substantially means, depends on the field. Some people go crazy with 6
, physicists are fine with just 3
x <- pi
p <- 15
s <- 8
mult <- c(3, 6)
sigma <- x * p / 100
sigma.m <- sigma * mult
lo <- x - sigma.m
hi <- x + sigma.m
df <- data.frame(x = rep(x, 2), prec = p,
sigma = sigma, mult = mult,
sigma.m = sigma.m,
lo = lo, hi = hi)
df <- signif(df, s)
names(df)[2] <- "prec. (%)"
print(df, row.names = FALSE)
x prec. (%) sigma mult sigma.m lo hi
3.141593 15 0.4712389 3 1.413717 1.7278760 4.555309
3.141593 15 0.4712389 6 2.827433 0.3141593 5.969026
Do you get the idea? The true value might be somewhere between our self-imposed limits. Therefore, I don’t give a shit whether I get 3.14
or 3.141 592 653 589 793 in an electronic file. However, I insist in a CRC-checksum
to verify the data-transfer. If I deal with bloody Excel, I round to one decimal beyond what is given in the analytical report
being aware that it is
beyond the analytical AP. If the data-transfer of analytical results to stats was done electronically in “full numeric precision” (haha), I want to see validation for it.
❝ It is ugly and clumsy, it works, and it feel everytime like I am suffering defeat.
Well, you are the C-man here. What about
printf("%.yg\n", x);
is the desired number of significant digits? With
options("digits" = 15)
x <- 12345678.999999
y <- 0.12345678999999
prec <- 8
fmt1 <- "%33.17f"
fmt2 <- paste0("%.", prec, "g")
cat(x, "\n",
y, "\n",
sprintf(fmt1, x), "\u2190 fake news\n",
sprintf(fmt1, y), "\u2190 fake news\n",
sprintf(fmt1, signif(x, prec)), "\u2190", prec, "significant digits\n",
sprintf(fmt1, signif(y, prec)), "\u2190", prec, "significant digits\n",
sprintf(fmt2, x), "\u2190", "directly with", paste0("'", fmt2, "'\n"),
sprintf(fmt2, y), "\u2190", "directly with", paste0("'", fmt2, "'\n"))
12345678.99999899975955486 ← fake news
0.12345678999999000 ← fake news
12345679.00000000000000000 ← 8 significant digits
0.12345679000000000 ← 8 significant digits
12345679 ← directly with '%.8g'
0.12345679 ← directly with '%.8g'
If you are interested whether rubbish in ≈ rubbish out, ask for a checksum and verify it. Probably better than diving into the murky waters of (likely irrelevant) rounding.
1. I would be fine with just 3.1 for π. The RE is –1.32%, again much below what is achievable in bioanalytics.
2. SHA-256 or higher preferred (collisions reported for SHA-1, i.e., different input give the same hash). MD5 is better than nothing.
3. That’s the only GxP-compliant (dated/signed, released by QUA) document, right? Did you ever see result-tables with 15 significant digits?
4. Here it gets tricky. These data are different to what is given in the analytical report. Now what? At least I expect a statement about this discrepancy in the protocols (analytical and/or
statistical). Regularly I see something like “calculations were performed in full numeric precision”. How could one ever hope to verify that having only the analytical report with rounded
Dif-tor heh smusma 🖖🏼 Довге життя Україна! []
Helmut Schütz
The quality of responses received is directly proportional to the quality of the question asked.
🚮 Science Quotes
Complete thread: | {"url":"https://forum.bebac.at/forum_entry.php?id=20412&order=time","timestamp":"2024-11-10T03:20:20Z","content_type":"text/html","content_length":"27636","record_id":"<urn:uuid:5858766a-64c4-49c7-a19a-d7fdb37c7f0f>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.3/warc/CC-MAIN-20241110005602-20241110035602-00202.warc.gz"} |
An Elementary Treatise on Algebra
An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms
Benjamin Peirce
From inside the book
Results 1-5 of 11
Page 49 ... questions into equations , which is universally applicable . The fol- lowing rule can , however , be used in most cases , and problems , in which it will not succeed , must be con-
sidered as ... Problems into Equations (76, 77),
Page 50 To which are Added Exponential Equations and Logarithms Benjamin Peirce. Examples of putting Questions into Equations . stead $ 50 ; a short time after , from the sum thus increased he took
away the fourth part , and put again in its ...
Page 51 To which are Added Exponential Equations and Logarithms Benjamin Peirce. Examples of putting Questions into Equations ... QUESTIONS INTO EQUATIONS . 51 Least common multiple (51), 36.
Page 52 To which are Added Exponential Equations and Logarithms Benjamin Peirce. Examples of putting Questions into Equations . 6. A hostile corps has set out two days ago from a certain place , and
goes 27 miles daily . Another corps wishes to ...
Page 53 To which are Added Exponential Equations and Logarithms Benjamin Peirce. Examples of putting Questions into Equations ... QUESTIONS INTO EQUATIONS . 53.
Subtraction 23 24 104
CHAPTER IV 110
SECTION IV 138
SECTION V 152
CHAPTER VI 181
CHAPTER VII 197
Popular passages
In any proportion the terms are in proportion by Composition and Division ; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference.
There is a number consisting of two digits, the second of which is greater than the first, and if the number be divided by the sum of its digits, the quotient is 4...
Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Problem. To find the last term of an arithmetical progression when its first term, common difference, and number of terms are known. Solution. In this case a, r, and n are supposed to be known, and I
is to be found.
The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
A term may be transposed from one member of an equation to the other by changing its sign.
Arrange the terms in the statement so that the causes shall compose one couplet, and the effects the other, putting ( ) in the place of the required term. II. If the required term be an extreme,
divide the product of the means by the given extreme ; if the required farm be a mean, divide the product of the extremes by the given mean.
Likewise, the sum of the antecedents is to their difference, as the sum of the consequents is to their difference.
What fraction is that, whose numerator being doubled, and denominator increased by 7, the value becomes §; but the denominator being doubled, and the numerator increased by 2, the value becomes f?
The sum of the squares of the extremes of four numbers in arithmetical progression is 200, and the sum of the squares of the means is 136. What are the numbers ? Ans.
Bibliographic information | {"url":"https://books.google.com.jm/books?id=GN42AAAAMAAJ&q=Questions+into+Equations&dq=editions:ISBN1404787283&output=html&source=gbs_word_cloud_r&cad=5","timestamp":"2024-11-05T08:46:33Z","content_type":"text/html","content_length":"77805","record_id":"<urn:uuid:17000b21-0845-4c43-9be1-82fbc10b46b7>","cc-path":"CC-MAIN-2024-46/segments/1730477027878.78/warc/CC-MAIN-20241105083140-20241105113140-00039.warc.gz"} |
1480 (1 to 25)
View count: 1
The recently celebrated discovery of the Higgs boson has captivated the public's imagination with the promise that it can explain the origins of everything in the universe. It's no wonder that the
media refers to it grandly as the "God particle." Yet behind closed doors, physicists are admitting that there is much more to this story, and even years of gunning the Large Hadron Collider and
herculean number crunching may still not lead to a deep understanding of the laws of nature. In this fascinating and eye-opening account, theoretical physicist Alexander Unzicker and science writer
Sheilla Jones offer a polemic. They question whether the large-scale, multinational enterprises actually lead us to the promised land of understanding the universe. The two scientists take us on a
tour of contemporary physics and show how a series of highly publicized theories met a dead end. Unzicker and Jones systematically unpack the recent hot theories such as "parallel universes," "string
theory," and "inflationary cosmology," and provide an accessible explanation of each. They argue that physics has abandoned its evidence-based roots and shifted to untestable mathematical theories,
and they issue a clarion call for the science to return to its experimental foundation.
View count: 1
This article is about the enigmatic situation in modern physics. An alternative to the special theory of relativity is presented, and it is demonstrated that we do not need the concept dilation of
time, and also that the reason to existing confusion is due to misunderstandings of stellar aberration and of the experiments done by Michelson and Morley. It is also demonstrated that bound
electrons generate POTENTIAL force that becomes real when a second electron is introduced, which demands energy from the ether. This explains why bound electrons do not loose energy, and explains
also why 2 light waves in opposite phase can produce zero light.
Infinite Universe Theory presents the ultimate alternative to the Big Bang Theory and the common assumption that the universe had an origin. Author Glenn Borchardt starts with photos of the “elderly”
galaxies at the observational edge of the universe. These contradict the current belief that the universe should have increasingly younger objects as we view greater distances. He restates the
fundamental assumptions that must underlie the new paradigm. Notably, by assuming infinity he is able to adapt classical mechanics to “neomechanics” and its insistence that phenomena are strictly the
result of matter in motion. He shows in detail how misinterpretations of relativity have aided current flights of fancy more in tune with religion than science.
Borchardt demonstrates why only Infinite Universe Theory can provide answers to questions untouched by currently regressive physics and cosmogony. His new modification of gravitation theory gets us
closer to its physical cause without calling upon attraction or curved spacetime or “immaterial fields.”
This is the book for you if you have doubts about the universe exploding out of nothing and expanding in all directions at once, that the universe has more than three dimensions, or that light is a
massless wave-particle that defies the Second Law of Thermodynamics. Borchardt has put forth a solid case for an Infinite Universe that extends in all directions and exists everywhere and for all
“What a great read! Thanks so much for a book full of great ideas. I love the Q&A format; it’s very satisfying to have good answers to clearly stated questions.” -Rick Dutkiewicz
“Truly brilliant.” -Jesse Witwer
“A radical, daring, and innovative demolition of regressive physics, from the creation of ‘something out of nothing’ to the ‘God Particle.’” -William Westmiller
"Glenn Borchardt's book uses the hammer of Infinity to explain and destroy the junk theories that plague 'Official' physics today. This is a book that should be used in college courses, to give
students a basic understanding of how physics is done. Physics has 'gone off the rails' for a century and it is books like Borchardt's that will return physics from its current unscientific and
anti-materialist base and back on to a scientific and materialist road." -Mike Gimbel
“What a fascinating read!” -Juan Calsiano
by Alphonsus G. Kelly
Publisher: Brown Walker Press
Year: 2005
ISBN: 1581124376
ISBN: 978-1581124378
Newton's Laws held for 300 years until Einstein developed the 'special theory of relativity' in 1905. Experiments done since then show anomalies in that theory.
This book starts with a description of the special theory of relativity. It is shown that Einstein was not the first to derive the famous equation E = mc^2, which has become synonymous with his name.
Next, experimental evidence that cannot be explained by special relativity is given. In the light of this evidence, the two basic postulates of the special theory of relativity on the behaviour of
light are shown to be untenable. A new theory (universal relativity) is developed, which conforms to the experimental evidence.
The movement of a conductor near a pole of a magnet and the movement of that pole near the conductor does not always give the same result. It has been claimed that this contradicts relativity theory.
Experiments described in this book show that it is not special relativity but another basic law of physics that is contradicted - Faraday's Law.
The Big Bang theory of the beginning of the universe is questioned and an alternative proposed. The source of much of the mysterious missing 'dark matter' that has been sought for decades by
astronomers is located. An explanation of the shapes of some galaxies is proffered.
Relativity theory has become one of the icons of Twentieth Century science. It's reckoned to be a difficult subject, taught as a layered series of increasingly difficult mathematics and increasingly
abstract concepts. We're told that relativity theory is supposed to be this complicated and counter-intuitive. But how much of this historical complexity is really necessary? Can we bypass the
interpretations and paradoxes and pseudoparadoxes of Einstein's special theory and jump directly to a deeper and more intuitive description of reality? What if curvature is a fundamental part of
physics, and a final theory of relativity shouldn't reduce to Einstein's "flat" 1905 theory //on principle//? "Relativity..." takes us on a whistlestop tour of Twentieth Century physics - from black
holes, quantum mechanics, wormholes and the Big Bang to the workings of the human mind, and asks: what would physics look like without special relativity? 394 printed pages, 234?156 mm, ~200 figures
and illustrations, includes bibliography and index
View count: 1
Researches undertaken during the last 20 years have confirmed that space possesses physical properties even where it is devoid of ordinary matter. In addition to the well known properties of
permittivity, permeability and the ability to transmit electromagnetic waves, other features have been more recently associated with the nature of space. These include the Casimir Effect and a
significant amount of energy. This medium, devoid of any trace of ordinary matter, is usually referred to as "Physical Vacuum", "Plenum" or "Cosmic Substratum" along with other appellations. Despite
the veil of equivalent terms, these names obviously refer to the Ether, a medium conceived in antiquity, which received much attention from Science between the 17th and early 20th centuries. Today it
is commonly understood throughout the academic community that Einstein excluded once and for all the ether from modern physics with his Special Theory of 1905. There is a widespread, unjustified
assumption that ether is conceptually incompatible with Relativity, though Einstein developed an equivalent concept in the context of the General Theory and his later work. We may add that Einstein?s
ether concept has inspired many modern physicists though others follow another direction of thought. The aim of this first volume of papers is to examine the different paths by which the modern ether
concept has been developed and to highlight the part it plays in major departments of 21st C physics. The evidence for its existence is reviewed, and it is hoped, widespread misconceptions concerning
ether are corrected. It is anticipated that the emerging modern concept of ether will play a fundamental part in the development of 21st C physical science. - Back cover
A book dealing with experimental and theoretical studies devoted to the exploration of the modern ether concept, evidence of its reality and implications for modern physics.
-5- Editor's Foreword
-7- Introduction
-13- Ether as a Disclosing Model, Michael C. Duffy
-47- Einstein's New Ether 1916-1955, Ludwik Kostro
-69- Basic Concepts for a Fundamental Aether Theory, Joseph Levy
-125- Aether Theory and the Principle of Relativity, Joseph Levy
-139- Ether Theory of Gravitation, Why and How, Mayeul Arminjon, Laboratoire Sols, Solides, Structures, Risques, CNRS & Universite de Grenoble, BP 53, F-38041, Grenoble Cedex 9 France
-203- A Dust Universe Solution to the Dark Energy Problem, James G. Gilson, school of mathematical sciences, Queen Mary University of London, Mile End Road, London E14NS, United Kingdom E-mail:
-217- Eddington Ether and Number, Raul A. Simon, LAMB, Santiago Chile
-257- The dynamical Space-time as a Field Configuration in a Background Space-time, A. N. Petrov, Department of Physics and Astronomy, University of Missouri,-Columbia, Columbia MO 65211, USA and
Sternberg Astronomical Institute, Universitetskii pr., 13 Moskow 119992 Russia E-mail: anpetrov@rol.ru
-305- Locality and Electromagnetic Momentum in Critical Tests of Special Relativity, Gianfranco Spavieri, Jesus Quintero, Arturo Sanchez, Jose Ayazo, & Georges T. Gillies, Department of Mechanical
and Aerospace Engineering, University of Virginia, PO Box 400746, Charlottesville, Virginia 22904, USA E-mail: gtg@Virginia.edu
-357- Correlations Leading to Space-time Structure in an Ether, J. E. Carroll, Engineering Department, University of Cambridge, CB2 1PZ, United Kingdom, E.mail: jec1000@cam.ac.u
-407- Reasons for Gravitational Mass and the Problem of Quantum Gravity, Volodymyr Krasnoholovets
This book presents a comprehensive exposition of the theory of electromagnetic retardation and offers a significant novel approach to the formulation, development and use of the theory of special
relativity. The book is divided into two parts. The first part, Chapters 1 to 5, presents the fundamentals of the theory of electromagnetic retardation with emphasis on recently developed
electromagnetic relations and mathematical techniques. Employing as the starting point the retarded electromagnetic field integrals rather than the traditional Lienard-Wiechert potentials and using
the newest mathematical methods for operations with retarded integrals, the theory is presented in a clear and logical manner, and the applications of the theory are demonstrated by numerous
well-chosen original illustrative examples.
As Professor Jefimenko shows, the theory of electromagnetic retardation leads to, and duplicates, many electromagnetic relations that are customarily considered to constitute consequences of
relativistic electrodynamics. Much of the first part of the book is devoted to establishing a bridge between the theory of electromagnetic retardation and the theory of relativity. In the second part
of the book, Chapters 6 to 11, all the fundamental equations of the special relativity theory, including equations of relativistic electrodynamics and mechanics, are derived in a natural and direct
way from equations of electromagnetic retardation and from electromagnetic force and energy equations without any postulates, conjectures, or hypotheses. As a result, the theory of special relativity
acquires a new physical and mathematical base and becomes united with Maxwellian electromagnetism into one simple, clear, and harmonious theory of electromagnetic phenomena and mechanical
interactions between rapidly moving bodies. Numerous well-chosen original illustrative examples demonstrate various applications of the relativistic electrodynamics and relativistic mechanics
developed in this part of the book.
The new approach to the formulations of the theory of relativity presented in this book makes it necessary to reexamine the conventional interpretation of some of the key aspects of the special
relativity theory. One of the most significant results of this reexamination is that, although the idea of Lorentz length contraction played an important part in Einstein's approach to the
formulation of the theory of relativity, this idea is not an integral part of the theory of relativity itself. Another equally significant result of this reexamination, based on an analysis of a
dozen elementary electromagnetic clocks, is that the rate of the moving clocks depends both on the velocity and on the construction of the clocks, so that although all the clocks examined in the book
run slow when in motion, only some clocks conform to Einstein's time-dilation formula; others do not.
Finally, the novel approach to the formulation of the special relativity theory developed in this book leads to the conclusion that gravitational phenomena are subject to essentially the same
relativistic relations as are the electromagnetic phenomena. Based on this conclusion, a covariant formulation of Newton-Heaviside's gravitational theory is developed and presented in the last
chapter of the book.
An Appendix to the book contains an analysis of the physical nature of electric and magnetic forces and presents a novel interpretation of the "near-action" mechanism of electromagnetic interactions.
This book is one of the best I have ever seen. More than 40 physicists, among them one Nobel laureate, presented their new theories and new experimental evidence.
Kotelnikov suggested an electrodynamics which can describe also particles which are faster than light. This suggestion is in agreement with special relativity.
We know Hector Munera from his interpretation of the Michelson-Morley experiment which, according to Munera, did show an aether drift. In this book, he presented a new approach to the electromagnetic
Caroline Thompson presented, for the first time, her phi-wave aether model.
Most revolutionary and far-reaching is K?hne's quantum electromagnetodynamics. His theory is a generalization of quantum electrodynamics. It includes Dirac magnetic monopoles and two kinds of photon,
the conventional one which he named "electric photon" and a new one which he named "magnetic photon". His theory is the only quantum field theory of the electromagnetic interaction which can explain
the quantization of electric charge, which is local, which is manifestly Lorentz invariant, which describes electrism and magnetism symmetrically, which does not require the Dirac string, and which
makes testable predictions.
K?hne's theory predicts that the magnetic photon couples with electric charges, where the coupling strength depends on the absolute motion of the electric charge. As a consequence, the creation,
shielding and absorption of magnetic photons is suppressed by a factor of 700 000 with respect to electric photons of the same energy.
As K?hne pointed out, his theory violates the relativity principle.
But what is more: K?hne had presented his theory and suggested an experiment to test his theory already in 1997 (http://arxiv.org/abs/hep-ph/9708394). Now, in his contribution to this book he
discussed three independent experiments which confirm his magnetic photon rays.
The far-reaching consequences of this probable discovery include:
1. The discovery of a new elementary particle (magnetic photon)
2. The discovery of a new radiation (magnetic photon rays)
3. Possible applications in medicine (examinations via magnetic photon rays instead of X rays)
4. The first proof for the violation of the relativity principle of special relativity
5. Indirect evidence for magnetic monopoles
6. Indirect evidence for an aether
Wow, could this mean a Nobel prize within the near future?
Anyway, this book is very good. I recommend this book to everyone who is interested in physics and/or the philosophy of science. - Peter M?ller, Amazon
• Foreword
• Preface
• Introduction: The de Broglie-Bohm-Vigier Approach in Quantum Mechanics
• Model of the Causal Interpretation of Quantum Theory in Terms of a Fluid with Irregular Fluctuations
• Dirac?s Aether in Relativistic Quantum Mechanics
• Superluminal Propagation of the Quantum Potential in the Causal Interpretation of Quantum Mechanics
• Model of Quantum Statistics in Terms of a Fluid with Irregular Stochastic Fluctuations Propagating at the Velocity of Light: A Derivation of Nelson?s Equations
• Relativistic Hydrodynamics of Rotating Fluid Masses
• Causal Superluminal Interpretation of the Einstein-Podolsky-Rosen Paradox
• Action-at-a-Distance and Causality in the Stochastic Interpretation of Quantum Mechanics
• De Broglie?s Wave Particle Duality in the Stochastic Interpretation of Quantum Mechanics: A Testable Physical Assumption
• Nonlinear Klein-Gordon Equation Carrying a Nondispersive Solitonlike Singularity
• Relativistic Wave Equations with Quantum Potential Nonlinearity
• Causal Particle Trajectories and the Interpretation of Quantum Mechanics
• New Theoretical Implications of Neutron Interferometric Double Resonance Experiments
• Positive Probabilities and the Principle of Equivalence for Spin-Zero Particles in the Causal Stochastic Interpretation of Quantum Mechanics
• Markov Process at the Velocity of Light: The Klein-Gordon Statistic
• Description of Spin in the Causal Stochastic Interpretation of Proca-Maxwell Waves: Theory of Einstein?s "Ghost Waves"
• Possible Test of the Reality of Superluminal Phase Waves and Particle Phase Space Motions in the Einstein-de Broglie-Bohm Causal Stochastic Interpretation of Quantum Mechanics
• Possible Experimental Test of the Wave Packet Collapse
• Testing Wave-Particle Dualism with Time-Dependent Neutron Interferometry
• Energy Conservation and Complementary in Neutron Single-Crystal Interferometry
• Time-Dependent Neutron Interferometry: Evidence in Favour of de Broglie Waves
• Causal Stochastic Prediction of the Nonlinear Photoelectric Effects in Coherent Intersecting Laser Beams
• Fundamental Problems of Quantum Physics
• Bibliography of works by Jean-Pierre Vigier
This book serves as a useful reminder that the widespread belief that the quantum world is irreducibly weird, indeterministic, unvisualizable, and dependent on human observation, is not required by
experimental results, and that a causal, more rational and intuitive interpretation is possible.
The book was compiled as a tribute to Jean-Pierre Vigier on the occasion of his 80th birthday. It begins with a preface by Stanley Jeffers outlining Vigier's life. He worked closely with Louis de
Broglie and David Bohm, and helped to pioneer the de Broglie-Bohm-Vigier approach to quantum physics, also known as the causal stochastic interpretation. The main features of this approach and how it
evolved are explained in an introduction by Lev Chebotarev. The bulk of the book consists of 22 facsimile reprints of papers on quantum mechanics authored or coauthored by J.P. Vigier. There is also
a biography of Vigier's works. Most of the papers are, at least in part, highly technical, but much of the discussion and analysis of the contending interpretations of quantum physics can be readily
understood by nonspecialists.
As Chebotarev points out, while quantum mechanics works impeccably as a mathematical tool, 'the conceptual situation in quantum mechanics appears to be the most disturbing in modern physics'. Seventy
years after the advent of quantum theory, 'there is still no clear idea as to what its mathematics is actually telling us' (p. 1).
A central tenet of the standard Copenhagen interpretation of quantum mechanics, as developed by Bohr, Heisenberg, Born, and Pauli, is that 'There is no quantum world, there is only an abstract
quantum physical description'. But what does the mathematical formalism actually describe? It is hard to believe that the quantum world underlying our material, macroscopic world consists of nothing
but abstract 'probability waves' that somehow 'collapse' into particle-like objectivity whenever a measurement is made (or, according to some theorists, whenever a measurement is registered by a
conscious human mind).
Each time the position of, say, an electron is measured, it is found in only one place. In between measurements we do not know exactly where the electron is, but the wave function can be used to
calculate the probability of it being found in any particular region of space. On the assumption that the wave function provides a complete description of quantum objects, many physicists believe
that a particle does not follow a definite trajectory in between measurements, but dissolves into 'superposed probability waves', which then 'collapse' instantaneously, discontinuously, and quite
inexplicably when the next measurement is made.
This probabilistic approach was strongly opposed by Einstein, Planck, and Schr?dinger, but it was de Broglie and later Bohm and Vigier who played the main role in developing an alternative.
Chebotarev writes:
The central idea of the Stochastic Interpretation of Quantum Mechanics consists in treating a microscopic object exhibiting a dual wave-particle nature as composed of a particle in the proper
sense of the word (a small region in space with a high concentration of energy), and of an associated wave that guides the particle's motion. Both the particle and the wave are considered to be
real, physically observable, and objectively existing entities. (p. 2)
Particles are pictured as oscillators (or solitons) beating in phase with their surrounding pilot waves, which in turn result from the superposition of superluminal phase waves carried by a
subquantal etheric medium subject to constant stochastic fluctuations. The force, or quantum potential, determining particle motions therefore carries information from the entire environment,
accounting for the 'wholeness' of quantum phenomena.
The causal stochastic approach can account for all the quantum properties of matter, including all the so-called paradoxes. It therefore disproves the claim that the quantum formalism requires us to
abandon not only the quest for an explanation of quantum phenomena but also the concepts of causality, continuity, and the objective reality of individual microobjects. In Vigier's view, the
Copenhagen interpretation is based on 'arbitrary philosophical assumptions', and its insistence on the absolute and final character of indeterminacy is dogmatic.
The causal stochastic approach is 'the only known interpretation of quantum mechanics in terms of which all quantum effects can be explained on the basis of causal continuous motions in space and
time' (p. 142). It has no place for the ill-defined notion of wave-packet collapse. There is only a 'pseudo-collapse', which 'simply represents a change of our knowledge and does not correspond to
any real physical changes in the state of the system' (p. 147). Vigier says that even if the quantum-potential approach 'is not taken as a fully satisfactory description of quantum mechanical
reality, it at least shows in a clear way the features that such a description must entail' (p. 169).
In the causal approach, therefore, 'the material world has an existence independent of the knowledge of observers' (p. 170). Vigier does not discuss possible explanations for genuine psychokinesis
('mind over matter'). However, invoking the abstract notion of wave-function collapse certainly contributes nothing to a concrete understanding of such phenomena (see Pratt, 1997). Bohm believed that
the causal interpretation opened the door to the creative operation of deeper, subtler, more mindlike levels of reality. Like Bohm, Vigier stresses that it is by no means a return to the classical
mechanistic worldview. Some of his statements, however, seem to deny the existence of free will (pp. 50-51, 99-100), though he acknowledges that, given the fundamental complexity of nature, 'The
ghost cannot be exorcized from the machine' (p. 169).
Vigier shows how, in stark contrast to the Copenhagen interpretation, the causal interpretation is able to provide an intelligible and visualizable explanation of key experiments such as the
double-slit experiment and neutron-interferometry experiments (pp. 137-72). In the double-slit experiment, if both slits are open an interference pattern builds up on the screen even if electrons
approach the slits one at a time. In the Copenhagen interpretation, a single particle supposedly passes in some indefinable sense through both slits and interferes with itself, whereas in the causal
approach each particle passes through only one slit whereas the pilot wave passes through both. If a device is used to detect through which slit each particle travels, the interference pattern
disappears. In the Copenhagen interpretation, the measurement collapses the wave function, whereas in the causal approach it affects the real pilot wave. The Copenhagen interpretation claims that any
path-determining measurement will destroy the interference pattern, whereas the causal interpretation predicts that interference will persist if future techniques allow a sufficiently subtle,
nondemolition measurement to be performed.
Neutron-interferometry experiments reproduce the double-slit configuration with massive particles and introduce new interaction possibilities through neutron spin. In these experiments, something
exchanges energy with the spin-flip coils in the two arms of the interferometer, and this interaction almost certainly involves real neutrons rather than nebulous probability waves. Although such
experiments cannot yet determine the path of each individual neutron, they prove 'the incompleteness of the quantum-mechanical Copenhagen description because the persistence of an interference
pattern is combined with the existence of a definite trajectory for each particle, a fact forbidden in the Copenhagen interpretation' (p. 257). In other words, the wave and particle aspects of matter
can manifest simultaneously in the same experimental setup, thereby contradicting the complementarity principle.
Vigier argues that quantum entanglement (EPR-type) experiments leave no doubt that quantum mechanics is a nonlocal theory, i.e. that quantum systems can show correlations that cannot be explained in
terms of classical forces or signals propagating at or slower than the speed of light. However, the EPR experiments conducted to date still contain loopholes, and Chebotarev puts the probability of
nonlocal connections at about 90% (for a dissident view, see Thompson, 1998). Vigier proposes that nonlocal interactions are not absolutely instantaneous but causal and superluminal; they are
mediated by the quantum potential, carried by superluminal phase waves in a Dirac-type ether consisting of superfluid states of particle-antiparticle pairs. (If superluminal connections were brought
about by individual particles rather than phase waves, this would contradict relativity theory, which Vigier upholds.)
Vigier writes:
In my opinion the most important development to be expected in the near future concerning the foundations of quantum physics is a revival, in modern covariant form, of the ether concept of the
founding fathers of the theory of light. [I]t now appears that the vacuum is a real physical medium which presents some surprising properties. (p. 272)
In several places he refers to the 'negative result' of the Michelson-Morley ether-drift experiment of 1887 (pp.63, 192). However, contrary to what numerous textbooks and popular science books claim,
this famous experiment did not give a null result.
Vigier (1997a) himself acknowledges this in an article not included in the book, or even mentioned in the bibliography. In it he states: 'the observed effect was not zero in Michelson's famous
experiment, as later confirmed by a (presently almost forgotten) set of very detailed and very careful experiments by Morley and Miller [Miller, 1933].' He presents a brief overview of the 'long set
of remarkable experiments' conducted from 1881 to 1926, which 'are now completely ignored in the physics community'. These experiments detected a small but consistent and systematic ether drift of
about 9 km/s.
Although relativity theory assumed a zero ether drift (and a constant velocity of light), Vigier (1997b) argues that a positive ether drift is compatible with special relativity if photons are
assumed to have a very small mass. He also argues that Sagnac's discovery in 1910 of fringe shifts in rotating interferometers (the Sagnac effect) can be reconciled with general relativity on the
same assumption. Whether the results of ether-drift experiments, including more recent ones (e.g. Silvertooth & Whitney, 1992), are best understood in terms of standard relativity theory is hotly
contested (e.g. Galeczki, 1995; Hazelett & Turner, 1979; M?nera, 1997; Spolter, 1993).
Vigier points out the radical implications of non-zero-mass photons, as originally proposed by Einstein, Schr?dinger, and de Broglie:
If confirmed by experiment, it would necessitate a complete revision of present cosmological views. The associated tired-light models could possibly replace the so-called expanding Universe
models. Non-velocity redshifts could explain the anomalous quasar-galaxy associations, etc., and the Universe would possibly be infinite in time (p. 273).
Vigier's book is an important contribution to the debate on fundamental aspects of quantum physics.
David Pratt
E-mail: dp5@compuserve.com
Journal of Scientific Exploration, vol. 16, no. 2, pp. 283-7, 2002
This book is the first to describe a very successful objective unified field theory which emerged in 2003 and which is already mainstream physics - Einstein Cartan Evans (ECE) field theory. The
latter completes the well known work of Einstein and Cartan, who from 1925 to 1955 sought to unify field theory in physics with the principles of general relativity. These principles are based on the
need for objectivity in natural philosophy, were first suggested by Francis Bacon in the sixteenth century and developed into general relativity in about 1915. In this year, using Riemann geometry,
Einstein and Hilbert independently arrived at an objective field equation for gravitation.Since then there have been many attempts to unify the 1915 gravitational theory with the other three
fundamental fields: electromagnetism, the weak and strong fields. As described for the first time in this book, unification is achieved straightforwardly with the principles of standard Cartan
geometry and the Evans Ansatz. The latter shows that electromagnetism is spinning spacetime, gravitation is curving spacetime and that they are unified with the structure (or master) equations of
Cartan. Quantum mechanics is unified with general relativity using the Evans Lemma and wave equation.Technical appendices and charts are provided which show how all the major equations of physics are
obtained from the ECE field theory and two introductory chapters describe the background mathematics from an elementary level. In this third volume, ECE theory is extended to the Sagnac effect and
Faraday disc generator to show that electrodynamics is spinning space-time in general relativity. These two effects are difficult to explain with special relativity. A simplified dielectric ECE
theory is developed and applied for example to cosmology.One chapter is dedicated to a convenient summary of all the details of Cartan geometry needed to develop ECE theory. The important topic of
spin connection resonance (SCR) is introduced and applied to new energy and counter-gravitation. Finally wave mechanics is developed in ECE theory.
Proceedings of an International Conference held 1994 in Olympia, Greece
• Michele Barone, The Underwater Neutrino Telescopes 1
• Jenner Barretto Bastos-Filho & R. M. X. de Araujo, Dimensional Analysis and Fundamental Physical Constants in N-Dimensional Spaces for Real N 11
• G. F. Sanger, On Mechanisms of Ambiguity and Adaptation in Nature and Their Dimensions 23
• Ruggero Maria Santilli, An Introduction to Hadronic Mechanics 69
• Roland H. Dishington, Cause and Effect in Special Relativity 187
• Joseph Levy, Is the Invariance of the Speed of Light Compatible with Quantum Mechanics? Some New Arguments 203
• Constantin I. Mocanu, Hertzian Extension of Einstein Special Relativity to Non-Uniform Motions 217
• A. Panaitescu, On the Electromagnetic State Quantities in Electrodynamics of Moving Media 241
• A. Paparodopoulos, The Law of Universla Gravitation in a G Variant Universe 265
• Simon J. Prokhovnik, The Nature of Friedmann Universes 277
• Horst E. Wilhelm, Physical Foundations of Galilei Covariant Electrodynamics 283
• A. Afriat, Correlations Involving Several Subsystems 2999
• Co. Antonopoulos, On Measurements with Contradictory Results; Tracing the Roots of the Original Wholeness 313
• A. K. Aringazin, K. M. Aringazin, A. Baskoutas, G. Brodimas, A. Jannusis & E. Vlachos, q-Deformed Harmonic Oscillator in Phase Space 329
• M. Damjanonvic & Z. Maric, Relativistic Dynamics and Space-Time Structure of Few-Body Processes 349
• J. Foadi, A Geometrical Approach to Bell Inequalities 357
• L. C. B. Ryff, Some Reflections and Conjectures on E.P.R. Correlations and Realism 369
• Franco Selleri, Complementarity vs. Causality in Space and Time 381
• James Paul Wesley, Light Radiates as Stochastic Bursts of Photons 399
• V. P. Ivankin, On the Origin and Development of the Solar System 409
• Martin Kokus, Red-Shift Quantization and the Fractal Geometry of the Universe 425
• H. G. Owen, Speculations on the Physical State of the Earth's Inner Core 429
• Giovanni Scalera, Relocation of Paleopoles on Variable Radius Earth Models 463
In 1905, Albert Einstein published his Theory of Special Relativity within which he described the now famous mass-energy formula E=mc^2. This theoretical construction revolutionized the classical
perspective of the universe as understood since the time of Isaac Newton. No longer were the classical concepts of Absolute Space and Absolute Time valid irrespective of observation point. Now the
concepts of Length Contraction and Time Dilation were in vogue and Physics would never be the same. Until now!
In an easy to read format along with many illustrations, Michael Strauss leads the reader in a comprehensive description of the history leading up to Special Relativity Theory. He points out errors
in the original assumptions, documents and ideas which led to the acceptance of this theory. However, his most powerful argument against Special Relativity is none other than the equations of Special
Relativity! As a result, E=mc^2 is no longer relative!
View count: 1
This book presents 26 papers concerning important fundamental questions in mathematics and physics. Is a line a continuum or a dense set of points? Is space empty or does it contain an ether? Is the
ether a sea of virtual particles or a gravitational field? Does quantum theory say nature is actually unpredictable? Can alternative logics resolve paradoxes in physics? Are the space-time ideas of
relativity tenable? Can absolute velocities be measured? Can conservation of energy be violated? Why are gravitational and inertial masses equal? Does mass really change with velocity? The authors do
not agree with each other. Some accept relativity, while others say it is wrong. The observed force between suspended antennas and the results of many other experiments contradict Maxwell theory and
special relativity and are predicted by classical Weber electrodynamics. Some claim quantum behavior is intrinsically unpredictable; while others claim microphysical reality and suggest crucial
experiments to prove their point. There is a claim to having observed cold nuclear fusion in a spark discharge. There is a claim to having violated the conservation of momentum and energy
experimentally. The Weber potential (so successful in electrodynamics) when applied to gravitation predicts the mass-times-acceleration force as an induction force due to the far mass in the
universe, verifying Mach?s principle and proving the identity of gravitational and inertial mass. A unipolar device is described that is supposed to extract energy from space. The Weber potential
also predicts the result of the Kaufmann-Bucherer experiments; so mass may not, in fact, vary with velocity. This book presents some new important concrete results. It may not provide the reader with
the particular answers he seeks; but many of the important fundamental questions are presented; and it provides a gold mine of references to facilitate the search for further answers.
View count: 1
by Paul Wesley
Publisher: Benjamin Wesley
Year: 2002
ISBN: 3980094294
Scientific Physics is physics based upon ordinary empirical scientific principles. Traditional orthodox physics has become mired down in mystical ideas, anti-scientific principles, and denials of
obvious experimental facts. The evidence reviewed in this book proves space-time is absolute ? no "special relativity" nonsense. A cosmology is presented for an eternal, infinite, uniform
in-the-large, steady-state, nonexpanding universe that fits all of the facts ? no impossible "big bang", no "curved space", no "expanding universe", no "bounded universe", etc. The far-reaching
consequences of mass-energy equivalence (known in the 1800?s) are explored, yielding neomechanics in absolute space-time, a new gravitational theory, etc. An electrodynamic field theory is presented
that agrees with Ampere?s original force law, with Weber electrodynamics for slowly varying effects, and predicts longitudinal electrodynamic K waves (recently observed), yields the force that drives
the Marinov motor and that explains the Aharonov-Bohm effect ? no error-ridden Maxwell theory, no Faraday law of electromagnetic induction, no absurd Biot-Savart law, etc. The conditions for creating
thermodynamic order are presented, which indicate why low entropy life exists, why stars are born from high entropy gas and dust, why territorial behavior of all organisms and man, etc. It is shown
how quantum particles move along discrete trajectories as explicit function of time to yield all observed wave behavior. The empirically correct Wesley wave, Y = sin [p?(r-vt)/h], for free particles
is generalized to yield wave equations for bound particles ? no "wave-particle duality", no single particle interfering with itself, no single particle going through both slits to produce
interference, no "uncertainty principle", no intrinsic "probability amplitudes", no superposition of physical states, no "complementarity", no astrological "nonlocality", no thoughts affecting
experimental results, no "indistinguishable" particles, no "expectation values" as observables, no "operator approach", etc.
Book Review: Selected Topics in Scientific Physics by Dr. Thomas E. Phipps Jr.
by Milo M. Wolff
Publisher: Technotran Press
Year: 1989 / Revised 1994
ISBN: 0962778710
ISBN: 978-0962778711
Part I describes the fundamental laws underlying science. The emphasis is on intuitive understanding of the foundations of scientific knowledge to enable deciphering of Mother Nature's designs for
the physical universe. It explains the six fundamental laws: Conservation of Energy, Gravity, Coulomb's force, Newton's laws, Quantum Mechanics, and Special Relativity. The book follows a trail of
scientific ideas and clues from the Greeks to Newton, Mach, Clifford, Einstein, Dirac, and Feynman to Modern galactic astronomy.
Part II discusses cosmology, space and the universe. It explores their enigmas and paradoxes. Dr Wolff's role is a friendly guide to the reader, enabling her/him to understand the machinery behind
Nature's laws, and to help solve the puzzles which have confounded scientists over the years. The century-old controversy of wave structure or substance structure of particles is examined and it is
shown that a wave structure is the origin of the natural laws. The mysterious role of space itself is explored and the reader is asked and helped to choose between truth and prejudice.
"A major fallacy unique in scientific history." Have you ever read the book Has Hawking Erred written by Gerhard Kraus in 1993 with that daring statement about Einstein's time dilation?
"The fact that nearly all academic physicists support Special Relativity proves nothing about its validity," said by John Chappell Jr., chairman of NPA, in 1996. Did you know that 90 years after
Einstein's Relativity publication, physicists still fail to stop their own colleagues' criticism against the theory?
"All motions may be accelerated and retarded, but the flowing of absolute time is liable to no change," said Isaac Newton. Did you know that all so-called evidence thought to confirm Einstein's time
dilation, in fact only confirm Newton's law that motion can be changed, but time is still absolute?
• Have you ever wondered what time is?
• What is time dilation?
• What is space curvature?
• Why can our space be curved?
• Did you ever feel sick of hearing physicists admit how confused they are about time, yet they can be so sure of time dilation?
• Did you ever feel convinced listening to physicists describe what 4-dimensional space-time is like, while saying you cannot draw it?
• Did you ever feel stupid for not understanding Einstein and Relativity but still happily accepting it?
• Did you ever dare think Einstein is wrong, but not dare say it due to your limited Math and Physics?
• Whatever your favourite excuse, do you ever believe one day you CAN understand Einstein and realize he is wrong?
• If you never bother asking those questions, don't read this book for this book is nothing but a challenge to Einstein's Relativity!
"This book, in 10 Chapters and 191 pages, describes the "tour de force" of a common sensed person, with average scientific education but not a physicist himself, in search for an understanding of
Einstein's Relativity theory. He is convinced that at least three important points of the theory are total flaws: 1-time dilation; 2-space curvature; and 3-the absolute constancy of light speed,
regardless of source velocity or observer velocity. The first two chapters set the dialectical stage, quote some dissidents of RT (Relativity Theory) including my own group (Natural Philosophy
Alliance) and Gerhard Kraus, and anticipates some of the author's theses, but without much reasoning. In fact these two initial chapters appear to me somehow vague and slow. It is in Chap. 3 (an
imaginary interview with Einstein) where we start reading some solid arguments, mostly describing the disconcerting variety of opinions that 20 relativistic authors explored by John Doan hold respect
Time Dilation. On page 35 John Doan presents the critique. It is not original but is forcefully expressed and repeated along the entire book as a leitmotiv, namely, that asymmetric time aging as
usually claimed by a group of relativists when one clock moves back and forth, showing "less" time than an identical clock that remained at "rest" at the origin, is a logical impossibility . Since
relative motion is perfectly reciprocal, symmetric and interchangeable, there is no way to say which clock must really go slower. They can both get slower, leading to a>b and a<b simultaneously.
"The arguments against space-curvature and light speed constancy are less forcefully presented. John Doan even dares to give his own version of 4-D space which I personally cannot approve (it is
still 3-D). Concerning light speed he describes the relativistic position as claiming that c+v = c, or that c+c = c. These, of course, are inaccurate expressions which relativists do not endorse. But
the reader gets the hint that in practice this is what RT concludes using its velocity composition expression, (which the author does not quote). After an imaginary interview with Einstein and asking
him twenty questions that he cannot answer the author is ready to "divorce" Relativity and return to Newtonian absolute space and time.
"In an equally imaginary interview with Newton Time Dilation is replaced by "motion change". John Doan does not question the possibility of Time Dilation provided it is due to an asymmetric physical
cause, not to Einstein's uniform motion only, and provided we refer it to a physical change in a clock, not in "Time", whatever Time means. Newton's affirmations sound a bit authoritarian but his
absolute space, time and simultaneity win the day in the author's view.
"The next Chapter, (7), is a grand detour into the "relativity of language" which, to this reviewer, seems the weakest portion of the book, and not too much needed at all, though it contains a high
dose of human insights and situations. The following two Chapters present the final attack on Time Dilation and the replacement of Einstein by Newton. Topics like asymmetry vs. symmetry, relative vs
absolute, are discussed. The author uses the method of analogical comparisons to guide the reader through the intricacies of relativistic thought. In the final chapter an unexpected biographical
experience, concerning a friend killed at war who was a relativistic dissident since adolescence, moves the reader almost to compassion. The plea for understanding rises here to its climax, but only
to conclude that no matter what is done, Relativity will always "win". In an Epilogue the author asks Stephen Hawking, whom he praises, to become a new Einstein, but against Einstein." - Francisco M?
'Requiem' ist ein treffender Titel f?r dieses Buch ?ber eine Kulttheorie, die seit ihren Anf?ngen von Widerspr?chen geplagt ist. Die Autoren, beide Physiker, zeigen streng wissenschaftlich und doch
unterhaltend, da? die Krise der heutigen Physik durch die "spezielle" Relativit?t mitverschuldet wird. Sie weisen aber auch auf Wege aus dieser Sackgasse: F?r die aus dem relativistischen
Prokrustes-Bett befreite Physik stehen empirisch korrekte und widerspruchsfreie L?sungen zur Verf?gung. Dynamik, Elektrodynamik, Quantenmechanik und Thermodynamik fordern ein globales ausgew?hltes
Bezugssystem, damit Energie- und Impulserhaltung, Strahlung, Sternaberration, Unipolarinduktion, Temperatur usw. konsistent beschrieben werden k?nnen. Galilei hat Recht: Die Erde bewegt sich - sie
bewegt sich im absoluten Sinne! Das Buch ist eine aufmunternde Rechtfertigung f?r alle, die nicht einer absurden Lehrmeinung, sondern ihrem gesunden Verstand vertrauen.
English reviews:
This book gives a good overview of arguments against the Special Relativity Theory. Despite a few loose ends and some fuzzy reasoning the authors do a good job convincing the reader that all is not
well in SRT land. Reference is made to theoretical and experimental proofs (with a good reference list) against Einstein's interpretation of the relativity theory. But even Lorentz' version of the
relativity theory is put in doubt, and some old ("forgotten") and new electrodynamics theories are discussed. A good addition to standard text books, to compensate for their SRT cult!
I felt very confirmed in my own evaluation of special and general relativity. My approach was to use logic and linguistic analysis to arrive at the same conclusions that are derived in the book using
experiments, historical and mathematical analyis. The authors are invited to to read my critique and to compare our two approaches. I would like to discuss this with them further. From Annalen Der
Physik I received the response - we will not publish or even consider any critique of relativity as the subject is closed for us!
by John Frank Johnson
Publisher: Lifetime Press
Year: 1989
ISBN: 0931571057
ISBN: 978-0931571053
View count: 1
The Relativity Question can be regarded as a continuation of the story begun in Herbert Dingle's dissident classic, Science at the Crossroads (1972). It may be "the only reasonably comprehensive
account of Professor Dingle's crusade against special relativity, by anyone other than himself. Even then, much of the story is told in Professor Dingle's own words, in the form of letters written by
him to various people, copies of which he sent to [the author] in hopes that they would eventually be published. There are also some letters written by [or with] a collaborator, Mr. Mark Haymon...
Replies to many of these letters are also included, and most of the correspondence is presented without detailed comment from [the author]. If the presentation of the correspondence seems somewhat
one-sided, part of the reason is that some of those to whom letters were written... did not reply, and some of those who did reply would not give permission to publish their letters." - From the
In addition to the correspondence, Dr. McCausland also presents criticisms of the theory of relativity itself. He details logical flaws in the arguments of Dingle's adversaries that can be understood
by scientists and non-scientists alike. From their own words we can witness their case falter and ultimately fail.
Arguably more than any other book, Einstein Plus Two helped launch the dissident revolution of the 1990s. As a consequence of this book, Beckmann founded Galilean Electrodynamics in 1990, a time when
several other dissident journals made their start. Beckmann's concept of the relativity principle without Einsteinian observer dependence serves as the major unifying theme. It stresses the idea of
motion with respect to the local field rather than to the observer of special relativity theory.
The book is divided into three sections: Einstein Plus Zero, One and Two. In Einstein Plus Zero, Beckmann reexamines the historic experiments of Bradley, Fresnel, Fizeau, Airy, and of course,
Michelson with Morley and Gale, and shows how understanding motion with respect to the local field makes sense of them all. In Einstein Plus Zero, he considers quantization of electron orbits,
electromagnetic mass, the meaning of Planck's constant and the Schr?dinger Equation from a proper understanding of central motion. Finally in Einstein Plus Two, the large questions of gravitation,
Mercury's perihelion, the Titius-Bode Series and inertia are addressed.
"There is so much to enjoy in this book. If you get your hands on this book, even for a moment, at least read the preface and the introduction. They are brilliant and short. His 'Grandiose Theory of
the Railroad Track' shows Beckmann's humor and his insight. I also love Mr. Beckmann's simple statement that 'a theory that does not recognize the equality of action and reaction cannot, without
apology, invoke the conservation of momentum.'" [p.77] - Larry Koler, Amazon
by Franco Selleri
Publisher: C. Roy Keys Inc. (Apeiron)
Year: 1998
ISBN: 0968368913
ISBN: 978-0968368916
Proceedings of an international conference on Special Relativity and Some of its Applications, held in Athens, Greece, June 25-28, 1997. The papers gathered in these proceedings discuss the
historical background and conceptual as well as empirical difficulties with conventional relativity theory, while some new approaches to understanding electromagnetism and gravitation are presented.
This volume includes 38 papers by authors from 17 different countries.
Velocity of Light
History and Philosophy
Structures in Space and Time
Cosmology and Astrophysics
Quantum Theory and Relativity
The Olympia conference Frontiers of Fundamental Physics was a gathering of about a hundred scientists who carry on research in conceptually important areas of physical science (they do "fundamental
physics"). Most of them were physicists, but also historians and philosphers of science were well represented. An important fraction of the participants could be considered "heretical" because they
disagreed with the validity of one or several fundamental assumptions of modern physics. Common to all participants was an excellent scientific level coupled with a remarkable intellectula honesty:
we are proud to present to the readers this certainly unique book.
Alternative ways of considering fundamental matters should of course be vitally important for the progress of science, unless one wanted to admit that physics at the end of the XXth century has
already obtained the final truth, a very unlikely possibility even if one accepted the doubtful idea of the existence of a "final" truth. The merits of the Olympia conference should therefore not be
judged a priori in a positive or in a negative way depending on one's refusal or acceptance, respectively, of basic principles of contemporary sience, but considered after reading the actual new
proposals and evidence there presented. They seem very important to us... - From the Preface.
Index 597
View count: 1
Professor Dingle's reputation in the world of science, in Britain and further afield, is considerable, as have been his achievements. It is therefore a matter of fundamental importance that after
much of a lifetime subscribing to what is regarded as a central part of modern physics "Einstein's Special Theory of Relativity" a scientist of Professor Dingle's wisdom and experience should now
cast grave doubt on it, and ask for basic reconsideration. He writes: "The habit has developed of assuming that a physical theory is necessarily sound if its mathematics is impeccable: the question
of whether there is anything in nature corresponding to that impeccable mathematics is not regarded as a question; it is taken for granted."
Professor Dingle's views have become widely known through a series of extraordinary, sometimes bitter, correspondences in Nature and the Listener. In the latter, much of the argument centred on the
matter of the now famous 'travelling clocks'. His technical argument is reserved for the second part of this book. The first part will cause shock and dismay to many, whether scientists or not. In
his attempts over recent years to raise the basic question of Special Relativity's rightness or otherwise, the author has found himself obstructed and progressively disregarded by key figures in the
world of scientific responsibility and information. He gives chapter and verse to this, and the whole story is damning to a discipline that has claimed so much. Professor Dingle issues a grave
warning against the perils that exist to us all as a result of this indifference and lessening of scientific honesty.
by John Philip Claybourne
Publisher: Xlibris Corporation
Year: 2003
ISBN: 1413403921
ISBN: 978-1413403923
ISBN: 1413403913
ISBN: 978-1413403916
Erroneous conclusions and gaps in modern physical theory are revealed. Perceived conflicts between classical and quantum are eliminated, partly as a result of a new theory of electric fields. The new
theory explains relativistic mass increase and mass decrement in the nucleus, identifying a supplementary term needed in Einstein's famous equation E = mc^2. The theory also provides a logical
explanation of electron diffraction. The book challenges concepts of particle / wave duality, provides an alternate explanation of nuclear forces and proves that all verified predictions of special
relativity theory are a sole result of Einstein's relativistic mass increase theory.
by Richard A. Waldron
Publisher: F. Muller
Year: 1977
ISBN: 0584101481
ISBN: 978-0584101485
Waldron developed a ballistic theory of light on his own before learning that Walter Ritz had already done it at about the time that A. Einstein developed his 'Special Relativity'. Waldron shows with
mathematical accuracy and in excruciating detail, one by one, that all the so called proofs of Einsteinian relativity (approx. 20) aren't proof at all but that the experimental and observational
results can be just as well explained with the more pedestrian Ritzian relativity. Unfortunately the books writing style is extremely dry and the backreferencing to figures and what was said earlier
is hard to follow (References are to sections, but the pages have no section headers). But he is so detailed and conscientous in his proofs, that its a book worth having for any 'dissenter' regarding
Einsteinian Relativity, special or general. Quasi a 'dissenters' bible'. I finally decided to get my hands on the book after seeing it being quoted in many 'dissenter' articles. - Walter G. Hecker,
1480 (1 to 25) | {"url":"https://db.naturalphilosophy.org/books/?tab0=Scientists&tab1=Scientists&tab2=Display&id=1291","timestamp":"2024-11-14T10:30:35Z","content_type":"text/html","content_length":"124966","record_id":"<urn:uuid:4cc290a3-ea16-4aa8-8390-4ebcebef5bc4>","cc-path":"CC-MAIN-2024-46/segments/1730477028558.0/warc/CC-MAIN-20241114094851-20241114124851-00737.warc.gz"} |
Mastering the NORM.DIST Formula in Excel: A Comprehensive Guide - THINK Accounting
If you've ever found yourself perplexed by the NORM.DIST formula in Excel, fear not my fellow spreadsheet warriors! In this comprehensive guide, we will break down the complexities of this
statistical function, giving you the confidence you need to conquer any data analysis task. So grab your thinking caps and let's dive right into the world of NORM.DIST!
Understanding NORM.DIST
Before we can unleash the full potential of NORM.DIST, it's important to grasp the underlying concept. NORM.DIST is a nifty little function that allows you to calculate the cumulative distribution of
a specified value in a normal distribution. Translation: it helps you figure out the likelihood of a certain value occurring within a given range. Pretty neat, right?
But let's dive a little deeper into the world of NORM.DIST. Understanding how this function works can open up a whole new realm of possibilities in data analysis and decision-making.
Imagine you're a scientist studying the growth patterns of plants. By using NORM.DIST, you can determine the probability of a plant reaching a certain height within a specific timeframe. This
information can help you make informed decisions about plant care and optimize growth conditions.
Or picture yourself as a business analyst trying to forecast sales for a new product. With NORM.DIST, you can estimate the likelihood of achieving different sales targets, allowing you to set
realistic goals and allocate resources effectively.
Exploring the Syntax of NORM.DIST
Now, let's get down to the nitty-gritty of how to actually use this formula. The syntax of NORM.DIST is surprisingly straightforward. It goes like this: =NORM.DIST(x, mean, standard_dev, cumulative).
Don't worry, we'll explain what each of those variables mean in a moment. Just hang in there!
First up, we have 'x' - the value for which you want to calculate the distribution. This could be anything from the height of your office plant to the number of pizza slices you can devour in one
sitting. The choice is yours!
Next, we have the 'mean' (μ) - the average value of the distribution. Think of it as the center of the bell curve. It's like finding out the average number of times your cat naps during the day.
Fascinating, isn't it?
Then, we have the 'standard_dev' (σ) - a measure of how spread out the data is. Essentially, it tells you how wide or narrow the bell curve is. It's like determining the standard deviation of the
amount of coffee your colleagues consume daily. Good luck with that!
Lastly, we have 'cumulative' - a logical value that determines whether you want to calculate the cumulative distribution or just the probability density function. It's like deciding whether you want
to eat the entire pizza or just a slice. Hungry yet?
But let's not stop there. Let's explore some practical examples of how NORM.DIST can be used in real-life scenarios.
Practical Examples of NORM.DIST in Action
Enough theory, let's see NORM.DIST in action! Imagine you're a basketball coach and you want to predict the probability of your star player making a certain number of free throws. With the power of
NORM.DIST, you can calculate the likelihood of them sinking 8 out of 10 free throws, or nailing every single one. It's like having a crystal ball for sports statistics!
Now, let's explore a more intriguing example. You're planning a surprise party for your friend, and you want to determine the chances of them arriving at the party between 8:00 PM and 9:00 PM. By
utilizing NORM.DIST, you can estimate the probability of your friend being fashionably late or promptly on time. It's like playing a mathematical game of hide-and-seek!
But wait, there's more! Let's delve into some tips and tricks for using NORM.DIST effectively.
Tips and Tricks for Using NORM.DIST Effectively
So, you've got the basics down, but we all know that true mastery comes with practice. Here are some handy tips and tricks to make the most of NORM.DIST:
1. Experiment with different values: Don't be afraid to mix things up and see how the results change. It's like adding extra toppings to your pizza - the possibilities are endless!
2. Use cell references: Make your formulas dynamic by referencing cells containing the necessary values. It's like having a secret sauce that can be adjusted in a flash!
3. Check your assumptions: Remember, NORM.DIST assumes a standard normal distribution. If your data doesn't fit this assumption, you might end up with questionable results. It's like trying to fit a
square peg into a round hole - not always a perfect fit!
By following these tips, you can become a NORM.DIST wizard and unlock even more insights from your data. But beware of common mistakes that can trip you up along the way.
Avoiding Common Mistakes with NORM.DIST
Even the best of us stumble from time to time, but fear not! Here are some common pitfalls to avoid when using NORM.DIST:
• Double-check your input: Ensure that you're using the correct values for 'mean' and 'standard_dev'. Mixing them up can lead to some wonky results. It's like baking a cake with salt instead of
sugar - not exactly a sweet surprise!
• Watch out for negative values: Remember, NORM.DIST doesn't play nice with negative values. It's like trying to throw a basketball into the wrong hoop - you might miss the mark entirely!
• Be mindful of the 'cumulative' parameter: For cumulative calculations, use TRUE. For probability density functions, use FALSE. Switching them up can make your formulas go haywire. It's like
trying to drive a car with the gas pedal and brake reversed - a recipe for disaster!
Now, let's address a common issue that many users encounter when working with NORM.DIST.
Troubleshooting NORM.DIST: Why Isn't It Working?
Uh-oh, encountering some difficulties? Don't panic! Here are some troubleshooting techniques to get NORM.DIST back on track:
1. Check your arguments: Double-check that you've entered the correct values for 'x', 'mean', 'standard_dev', and 'cumulative'. It's like solving a puzzle - sometimes the missing piece is right in
front of you!
2. Verify your data: Make sure your data is formatted correctly and doesn't contain any hidden characters or spaces. It's like searching for your keys - sometimes they're right where you left them!
3. Consult the Excel gods: If all else fails, consult the sacred texts of Excel documentation or visit your friendly neighborhood search engine for guidance. It's like calling in reinforcements -
sometimes a fresh pair of eyes can work wonders!
Exploring Related Formulae to NORM.DIST
Now that you're a NORM.DIST wizard, let's explore some other statistical functions that can complement your mastery:
Other Statistical Functions You Should Know
Excel is full of statistical treasures waiting to be discovered. Here are some other handy functions to add to your repertoire:
• NORM.INV: The inverse of NORM.DIST, allowing you to find the value that corresponds to a given probability in a normal distribution. It's like having a magic wand that reveals hidden secrets!
Imagine this: you're analyzing a dataset and you want to know the value that corresponds to a specific probability in a normal distribution. With NORM.INV, you can wave your magic wand and
instantly uncover the hidden treasure. It's like being a detective solving a mystery, but instead of clues, you have probabilities and formulas at your disposal.
• AVERAGE: Calculate the arithmetic mean of a range of values. It's like finding the average number of times your office plant is complimented on its foliage. Leaf it to Excel!
Picture this: you have a range of values representing the number of times your office plant is complimented on its beautiful foliage. With the AVERAGE function, you can effortlessly calculate the
average number of compliments received. It's like having a green thumb for statistics, finding the sweet spot where compliments bloom like flowers.
• STDEV.P: Calculate the standard deviation of a population based on a sample of data. It's like measuring the variability in the number of unanswered emails in your inbox. Keep calm and calculate!
Imagine you're staring at your inbox, filled with unanswered emails. You want to understand the variability in the number of unanswered emails you receive. With the STDEV.P function, you can
analyze a sample of data and calculate the standard deviation. It's like having a compass that guides you through the stormy sea of unanswered emails, helping you navigate the waves of
Now that you're armed with knowledge and a sprinkle of humor, go forth and conquer the realm of NORM.DIST! May your spreadsheets be error-free and your formulas be as smooth as freshly brewed coffee.
Happy Excel-ing!
Hi there!
I'm Simon, your not-so-typical finance guy with a knack for numbers and a love for a good spreadsheet. Being in the finance world for over two decades, I've seen it all - from the highs of bull
markets to the 'oh no!' moments of financial crashes. But here's the twist: I believe finance should be fun (yes, you read that right, fun!).
As a dad, I've mastered the art of explaining complex things, like why the sky is blue or why budgeting is cool, in ways that even a five-year-old would get (or at least pretend to). I bring this
same approach to THINK, where I break down financial jargon into something you can actually enjoy reading - and maybe even laugh at!
So, whether you're trying to navigate the world of investments or just figure out how to make an Excel budget that doesn’t make you snooze, I’m here to guide you with practical advice, sprinkled with
dad jokes and a healthy dose of real-world experience. Let's make finance fun together! | {"url":"https://www.think-accounting.com/formulas/mastering-the-norm-dist-formula-in-excel-a-comprehensive-guide/","timestamp":"2024-11-08T20:51:26Z","content_type":"text/html","content_length":"101761","record_id":"<urn:uuid:d5387b2b-f28b-4e3c-86bc-b27fbcd942e3>","cc-path":"CC-MAIN-2024-46/segments/1730477028079.98/warc/CC-MAIN-20241108200128-20241108230128-00715.warc.gz"} |
Let’s Build a Computer #1 (Binary Numbers)
Bookmark (0)
Please login to bookmarkClose
In this series you will learn how computers work from the ground up. You will learn by actually building it piece by piece (on paper) in a series of weekly articles. If you continue and follow along,
you will fully understand how a modern computer operates down to the smallest detail!
Let’s Start!
Computers only understand numbers, so we need to come up with a way of representing them. Since computers are built using only on/off switches, we need to use something very simple. Computer
designers came up with a number system called Binary.
Our computer will be very basic and just handle the numbers 0 through 7. However, the same concept can be expanded to handle any number. The binary code scientists came up with to count is as follows
and uses base 2 (0-1 digits) instead of base 10 (0-9 digits) concepts. Don’t worry if that confuses you now. You will understand it later by doing examples.
One way to visualize it is to pretend you were an alien on another planet who did not understand anything except the number ‘0’ and ‘1’, but needed a way to count things. The system below would give
you that ability.
Binary Numbers 0 – 7
• 000 = 0
• 001 = 1
• 010 = 2
• 011 = 3
• 100 = 4
• 101 = 5
• 110 = 6
• 111 = 7
Take a minute to see if you can discover the pattern. The first column multiplies by 4, the second by 2, and the first by 1. In mathematical terms, it is all based on powers of 2, like 2^0=1, 2^1=2,
and 2^2=4. If we added another column to handle 4 digit binaries, it would be 2^3 = 8. We can represent an infinite amount of numbers using this system.
The number 5 is 101 in binary. This is the same as= 1×4 + 0x2 + 1×1 = 4 + 0 + 1 = 5
It may look very strange, but you do this all the time without realizing it using normal math and base 10. Example: 25 = 2×10 + 5×1 = 25
Here is a video that talks about converting decimals numbers to binary with more details. However, if you have faith in the 0-7 binary list above, it is good enough to continue our computer journey.
Binary Math
Now that we have a way to represent numbers with 1’s and 0’s, we need a way to do math on them. Let’s start by adding, which is actually very simple and works like the way you add normal numbers,
except you can’t go higher than 1.
If you want to add 1 + 2 in binary, you first need to convert the numbers to binary (you can just use our list):
1 = 001
2 = 010
001 +
You add it like normal numbers. The answer is 011 which translates to 3 in human readable form.
Here is a more advanced one: 3 + 3
3 = 011
011 +
Just like normal addition, we start on the right side: 1 + 1 = 2. We know 2 = ‘010’ in binary, so we put down the 0 and carry the 1. This is similar to how you can only go up to 9 with regular
numbers (base 10) and carry the 10’s place if the number is over 9.
011 +
The middle column now adds up to 3. We can represents this as “011” in binary and need to put down a ‘1’ and carry the ‘1’ over.
We now have 110 = 4×1 + 2×1 + 1×0 = 4 + 2 + 0 = 6, which is the correct answer when converted to our normal base 10 system. Here is another way of looking at it (Source: Carrying Binary Digits).
Below is a good video to review binary addition. You really need to understand this concept well before we can move on and actually build the hardware that will add numbers for us. It is one the most
important parts of a computer.
Take some time to understand binary numbers and adding them. Next week we will start building our computer adder, or ALU (Arithmetic Logic Unit) that will perform math for us. The good news is that
you don’t need to understand any more math. This is the most complex it gets. Computers only know how to add. We will talk about subtraction, multiplication, and division later, but it is just done
using binary addition and some special tricks!
If you have any questions, please comment below. I look forward to taking you on this wonderful journey to understand how computers really work.
11 Comments
Oldest Most Voted
Inline Feedbacks
View all comments | {"url":"https://net.kidzsearch.com/lets-build-a-computer-1-binary-numbers/","timestamp":"2024-11-07T04:27:02Z","content_type":"text/html","content_length":"276420","record_id":"<urn:uuid:5f328044-7c39-49b4-b0ec-91e49430bd43>","cc-path":"CC-MAIN-2024-46/segments/1730477027951.86/warc/CC-MAIN-20241107021136-20241107051136-00388.warc.gz"} |
Research details
In the past two decades, cosmology has transformed into a precision science, with important new questions revealed or brought into focus by a wealth of observational data. Among the most prominent
issues are the cause of late-time accelerated expansion and the nature of early universe inflation. New observations, including data of the Planck and Euclid satellite experiments, are making various
novel observational tests possible, and require increasingly precise treatment of cosmological inhomogeneities. Another topical field is cosmology related to electroweak physics, probed at the LHC at
Late universe inhomogeneities
The discovery of the accelerated expansion of the universe at late times was rewarded with the Nobel prize in physics in 2011, and the Nobel prize committee characterised its cause as perhaps the
biggest enigma in physics today. While simple vacuum energy fits the observations well, there are many alternatives, which will face increasingly tight tests in the coming decade. One possibility is
that the observed acceleration is due to the effect of structure formation on the expansion of the universe and on light propagation. Even if the impact of inhomogeneities is too small to explain the
accelerated expansion, detailed modelling of the effect is important for precision analysis of observations, particularly gravitational lensing. The study of inhomogeneities also ties in with
theoretical questions such as the Newtonian limit of general relativity in a cosmological setting and the inclusion of general relativistic effects in cosmological simulations.
Inflationary perturbations and LHC cosmology
Inflation is recognised as the most successful scenario for the early universe. Originally proposed to account for homogeneity, isotropy and spatial flatness of the universe, the biggest success of
inflation has been in explaining the origin of inhomogeneity from quantum fluctuations. Inflation is the only area of physics where the interface of general relativity and quantum physics is probed
observationally. There are numerous interesting questions related to quantum effects, such as loop corrections, possible quantum non-equivalence of classically equivalent coordinatisations of field
space and decoherence.
Cosmology related to electroweak physics is particularly topical as the LHC is taking data. The most plausible points of contact between cosmology and particle physics at the LHC are inflationary
models involving the electroweak scale, such as Higgs inflation, and models of the electroweak phase transition and dark matter.
Cosmological observations and simulations
The transformation of cosmology in the past two decades has been driven by the increasing breadth and precision of observations, rather than theoretical sophistication. It has become possible to
accurately test fundamental properties such as homogeneity, isotropy and spatial flatness in a model-independent way, by combining measurements of distance with those of expansion rate, gravitational
lensing or, with upcoming observations of the Gaia satellite, cosmic parallax. Model-independent comparison of qualitatively different observations will be an increasingly important check on the
current cosmological paradigm. Another crucial change has been the increased feasibility of running large cosmological simulations to access the non-linear regime of cosmological evolution. This
makes it possible to use observations of various aspects of structure formation and matter distribution on large scales for novel cosmological tests, such as comparing homogeneity properties of
simulations and observations, or using voids as sensitive probes of vacuum energy. The BOSS survey of the Sloan Digital Sky Survey, which is scheduled to conclude in 2014, provides improved data on
distances, expansion rates and lensing. In particular, the CODEX survey will yield the largest X-ray cluster catalogue to date. Spectroscopy of strong lensing features will be available from ESO
telescopes. The Euclid satellite is the premier next generation large scale structure survey. Euclid is scheduled to launch in 2020, and there is a lot of theoretical work to be done, including on
modelling non-linear effects of inhomogeneities and determining different cosmological tests to be done with the data. | {"url":"https://www.hip.fi/cosmology-of-the-early-and-late-universe/research-details/","timestamp":"2024-11-12T00:51:52Z","content_type":"text/html","content_length":"51388","record_id":"<urn:uuid:e75076b8-87f5-448a-8db7-75cf7905359e>","cc-path":"CC-MAIN-2024-46/segments/1730477028240.82/warc/CC-MAIN-20241111222353-20241112012353-00011.warc.gz"} |
Math Problem Statement
Carmen opens a savings account after starting her summer job and deposits money into it each month. The graph represents the relationship between y , the total amount of money in her account, and x
the number of months since she began saving.
Which equation best represents the relationship between x and y ? A.y=50x+100
© 202
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Linear Equations
Linear Equation Theorem
Suitable Grade Level
Grades 6-8 | {"url":"https://math.bot/q/linear-equation-savings-account-time-amount-FMXUmyzw","timestamp":"2024-11-06T23:46:39Z","content_type":"text/html","content_length":"86060","record_id":"<urn:uuid:32a84785-9451-43dd-ade2-bee68eec9c5b>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.54/warc/CC-MAIN-20241106230027-20241107020027-00591.warc.gz"} |
51作业君 | 代写程序，保原创包教会 | 代写Java, Python, C++, Matlab,程序代写
辅导案例-ENG 4061/7060-Assignment 4
ELEC ENG 4061/7060 Image Processing Page 1 of 10 7060 Image Sensors & Processing / 4061 Image Processing Assignment 4 May 2020 (Assignment Value: 18%) (note: there are no written questions for this
assignment) Overview This assignment is intended to give you some hands-on experience with thresholding, morphological cleaning, feature estimation and classification as covered in lectures. In this
assignment work you will be required to modify several functions which implement thresholding, clean up and feature estimation stages of a classification system. NOTE: Unlike previous assignments you
may use any of the functions in the MATLAB image processing toolbox except for graythresh (unless otherwise instructed by me – see comments in red in exercise 4B) to achieve this. Background A
manufacturer of different types of steel bolts, washers and attachment hooks has a approached your company to develop an automated sorting system for their production lines to deal with the large
number of items that are currently manually sorted as they travel along a conveyor belt. The intent is to develop a camera based classification system which can identify the metal parts. However due
to conditions on the production line space and lighting is limited and only small noisy imagery of the parts can be obtained. As your company’s key trouble-shooter, you have been assigned the task of
developing a simple demonstrator to show that such a system might work. To this end you have been given some example imagery of some 6 metallic parts of the many dozen which they sell. Example images
are shown on the next page. To solve this problem, you will need to firstly threshold and filter out the region containing the metal parts and then implement a feature extraction step stage that
extracts shape estimates from the data. The thresholding will be performed using Otsu’s method and an Euler number feature will be used to discriminate classes 2,4 and 6 from 1,3 and 5. It is up to
you which of the other simple shape measures covered in class you might use to separate out the other shapes. Your resulting shape measures will then be fed into a KNN classifier which you have been
given to test if the approach works. ELEC ENG 4061/7060 Image Processing Page 2 of 10 Class 1 Class 2 Class 3 Class 4 Class 5 Class 6 Above: example images of the 6 metallic parts (1 Bolt, 2 Eye
Bolt, 3 Hook Bolt, 4 Carabiner, 5 U- bolt and 6 Washer). Note the noise present in the captured images. The images in the dataset are identified by the file prefixes bolt, eyeb, hook, loop, ubol and
wash respectively. Assignment Submission Assignments are to be submitted via MyUni as a ZIP archive file containing the four key MATLAB functions ( otsu_threshold.m, simple_euler.m, object_extract.m
and feature_extract.m plus any others you modify) and a Word or PDF document summarising your results with comments on the performance of the processing steps employed. Marks will be deducted for
late submission. IMPORTANT: DO NOT INCLUDE THE SUPPLIED IMAGE DATABASE IN YOUR ASSIGNMENT SUBMISSION. I WILL DEDUCT MARKS IF YOU DO !!! Source Materials Source code, test functions and example
imagery for this assignment are located on the MyUni website (https://www.myuni.adelaide.edu.au). The image data is contained in the noisy_data subdirectory and includes some 150 images per object
type (900 in all) which should give you plenty of examples to work with. ELEC ENG 4061/7060 Image Processing Page 3 of 10 Exercise 4A (5%) – Image Thresholding (Otsu’s Method) Modify the supplied
function [B,th]=otsu_threshold(I) such that it thresholds an image using Otsu’s method as described below. Here I is the input image, B is the binary image output and th is the estimated threshold.
An optional argument N can also be supplied which defines the number of thresholds tested by the algorithm (see below). Otsu’s thresholding method is a form of automatic class clustering based on
maximising the variance between the greylevel of pixels in the thresholded and un-thresholded regions of the image whilst minimising the grey-level variance between pixels within each region. That
is, for all possible values of t, we week a threshold t that minimises: )()()()( ttNttN oobb + Where )(tN b number of pixels below the threshold t )(tb is the standard deviation of the values
below t )(tN o number of pixels above (or equal to) the threshold t )(to is the standard deviation of the values above (or equal to) t However, the solution for this turns out to be the same as
maximising for the between class variance. This can be easily calculated as follows: For each potential threshold T (between the max and min values of the image) 1. Separate the pixels into two
groups according to the current threshold T. 2. Find the mean of each group )(tb and )(to . 3. Square the difference between the two means ( )2)()( tt ob − . 4. Multiply this value by the number
of pixels in one cluster )(tN b times the number in the other )(tNo . 5. Record the result and the threshold T used The best threshold is the value T associated with the largest calculated result.
Modify the function [B,th] = otsu_threshold(I) such that it implements the algorithm given above. Test your algorithm on some example images including those from the test database and the supplied
function otsu_test.m IMPORTANT: Do not use ‘greythresh’ or any other thresholding technique for this part of the assignment or you will receive zero marks for part 4A. ELEC ENG 4061/7060 Image
Processing Page 4 of 10 Above: the Otsu algorithm given earlier applied to two test images (see otsu_test.m). Exercise 4B (3%) – Region (Object) Extraction Modify the supplied function B =
object_extract(I) such that it thresholds the supplied image I using Otsu’s method and returns a "cleaned up" binary image B representing the metal part. The function should remove artefacts from the
thresholded imagery such as point noise and merge fragmented regions together to form a good representation of the irrigation object. You will need to use morphological filters to achieve this.
Important Note: One problem you may face is in dealing with the excessive noise in the raw imagery and this may adversely affect the threshold result. You may wish to reduce this noise before
considering the threshold step. So in effect the steps are: 1. Reduce noise 2. Threshold 3. Cleanup using morphological filtering (eg. erode/dilate/open/close etc) The resulting binary image should
ideally contain one connected region representing the plastic part to make it easy for your feature extraction processing. An example of this processing is given below (note: your own solutions may
not look exactly like this): ELEC ENG 4061/7060 Image Processing Page 5 of 10 Illustrate your processing results using examples from the image datasets and write this up in your assignment report.
Take special note of any situations where the thresholding may be problematic. You can use the supplied test script object_extract_all to check your thresholding on the 6 sets of test images (but be
warned it will take some time to go through all 900 images). Comments: The quality of the thresholding and cleanup stages will have an impact on any features you estimate from the regions and hence
the quality of the final classification performances in exercises 4D. You may need to revisit this step once you have the classifier working to do some fine tuning. SPECIAL NOTE: If you are unable to
get the Ostu thresholder going in part 4A you can temporarily use the function greythresh() to obtain a threshold. If you do so please make it very clear in your code and write up that you have done
so otherwise marks will be deducted. Exercise 4C (3.5%) – Feature Estimation (Euler Number) As described in lectures the Euler number of a binary image is the number of binary regions minus the
number of holes. There are several ways of estimating the Euler number for a binary image, but the easiest is to estimate the number of convex and concave corner-like regions in the binary image by
performing a series of tests on 2x2 neighbourhoods around each pixel in the image. Geometrically, each region or hole will have some factor of 4 of these. This simple algorithm for 4-connected
regions is as follows: 1. Set convex count and concave count to zero. ELEC ENG 4061/7060 Image Processing Page 6 of 10 2. For each pixel (i,j) examine the local 2x2 patch of image data a. If the 2x2
patch contains 1 set pixel increment the convex count by 1. b. If the 2x2 patch contains 3 set pixels increment the concave count by 1. c. If the 2x2 patch contains 2 set pixels diagonally opposite
one another (ie [10;01] or [01;10]) then increment the convex count by 2. 3. The final Euler number is the convex count minus the concave count divided by 4. To loosely explain how this works.
Imagine a simple box shape (Euler number = 1). The above algorithm will only increment the convex count at each corner of the box giving a total value of 4 convex to 0 concave → (4-0)/4 = 1. Next
imagine this same box now has a square hole in it (ie. Euler=0). In this case the above algorithm will give a convex count of 4 and also a convex count of 4 at the 4 corners of the hole → (4-4)/4 =0.
If instead there were 2 square holes rather than two then the convex count would be 8 leading to an Euler number estimate of -1. Geometrically speaking this reasoning can be extended for any number
or shape of hole or object. In each case the differences in count will always come down to a factor of 4, the only exception being when the object is touching the image boundary. To handle this case
a 1 pixel wide empty border is usually added to the image before applying the above algorithm. Case (c) is included above to improve the estimate in the presence of small adjacent holes etc. Modify
the supplied file simple_euler.m such that it implements the algorithm shown above. Make sure you also add the 1 pixel boundary mentioned above before doing the calculation. Use the script
euler_test.m to check you code and write up your results. Above: Example Euler number calculations (see euler_test). Note: you do not need this solution to complete Exercise 4E. If you wish to use
the Euler number for exercise 4E then you may use regionprops() to get an estimate. Euler Number 1 (est 1) 20 40 60 20 40 60 Euler Number 0 (est 0) 20 40 60 20 40 60 Euler Number 3 (est 3) 20 40 60
20 40 60 Euler Number 5 (est 5) 20 40 60 80 100 120 20 40 60 80 100 120 ELEC ENG 4061/7060 Image Processing Page 7 of 10 Exercise 4D (3.5%) – Feature Estimation (Eccentricity) The eccentricity of an
object can be used to distinguish between rounded and elongated objects. There are several ways of computing such a measure. Here we will use an approximation based on the central image moments
discussed in class. The measure for eccentricity is as follows: = (2,0 − 0,2) 2 + 41,1 2 (2,0 + 0,2) 2 From the lecture notes recall that the central moments are defined as follows: Where xc and yc
are the centres of mass defined as: Modify the supplied function simple_eccentricity.m to implement this estimate of eccentricity and test your results using the script eccentricity_test.m and write
up your results. The supplied code includes a call to meshgrid() to supply you with the x and y coordinates. An example output is shown below: Above: Example eccentricity calculations (see
eccentricity_test). NOTE: this estimate does not match the one used in regionprops() so don’t try comparing the two. Note: you do not need this solution to complete Exercise 4E. If you wish to use
eccentricity for exercise 4E then you may use regionprops() to get an estimate. ELEC ENG 4061/7060 Image Processing Page 8 of 10 Exercise 4E (3%) – Shape Measure Classification As already noted the
Euler number could be used as a simple shape measure to distinguish classes 2,4 and 6 from classes 1,3 and 5. However to distinguish between all 5 classes we will need to make use of some of the
other shape measures described in class. Modify the function F=feature_extract(B) such that when it is given the cleaned up binary image B it returns a row vector of shape measurements of your choice
(which may or may not include the Euler number). To assist you many of the shape simple measures described in class can be constructed from values returned by the MATLAB function regionprops() which
works with binary images. Your task is to figure out which ones can be used to successfully classify the 6 shapes. The function regionprops takes a binary region B and returns a record with fields
including such measurements as Area, MajorAxis, MinorAxis EulerNumber etc. However, be warned that if your object is fragmented into several regions the function will return estimates for each
fragment rather than a single result (make sure your solution for part 4B does the right thing). Suggested measurements from the notes that you might like to try include: • Euler number • Minor axis
/ major axis • Perimeter / square root of the area • Area / convex area Note your estimates should be, if possible, invariant to translation scale and rotation. To test if your proposed shape
measures might work, use the supplied function: [F,C] = feature_extract_all(); If this runs to completion without producing an error (which it should unless you have a bug in your feature_extract.m
file) then the values F and C will contain the feature measurements and class numbers for each of the 900 images in the dataset. The function cplot(F,C) can then be used to generate scatterplots of
the features you have created. You can use tricks like cplot(F(:,4:5),C) to just plot features 4 and 5 of your data. ELEC ENG 4061/7060 Image Processing Page 9 of 10 Above: illustration of feature
clustering based on two possible shape measures (created using cplot.m). Your own feature plots will differ from the example shown here. Once you are satisfied that your feature measurements are
working well enough you can use the supplied KNN classifier script as a final test: [C_est,C_true] = knn_classify_all(F,C,k); Where F and C are previously calculated features and class numbers and
‘k’ is the number of nearest neighbours to test to see if your solution works (eg. 3). C_est and C_true are the estimates and true class labels based on a 30% train 70% test split of the data. An
example screen shot of the run-time plot and resulting confusion summary generated by this script are shown below. ELEC ENG 4061/7060 Image Processing Page 10 of 10 Above: sample screenshots of
knn_classify_all.m. Your own results and feature plots will differ from what is shown here. Ideally the higher the numbers along the diagonal in the confusion matrix the better. Unlike most
real-world problems you are ever likely to encounter, this dataset is relatively easy to classify. If you get this working correctly, you should be able to easily achieve over 90% correct
classification (and probably into the high nineties). Important: Plot histograms and/or scatterplots of the feature values for each class and record your classification scores and put these in your
report. Try different combinations of feature measures and see what happens. What did you find were the best combinations? | {"url":"https://51zuoyejun.com/caseDetail/1903.html","timestamp":"2024-11-06T00:54:11Z","content_type":"application/xhtml+xml","content_length":"37005","record_id":"<urn:uuid:b1a8f7d7-f545-41da-a0e9-f6363f82116a>","cc-path":"CC-MAIN-2024-46/segments/1730477027906.34/warc/CC-MAIN-20241106003436-20241106033436-00265.warc.gz"} |
Mathematical Operatives
What is a Mathematical operator?
This page will guide you through using Excel to create basic mathematical operations. This is very similar to creating a function or formula except that we are not using the function's operative such
as (=Sum) or (=Average) or any of the other function operative.
If we wanted the sub-total for a given range we can use the function operative (SUM):
however if we wanted to write this the super long manual way (but still using cell references), in plain mathematical operatives it would be:
We could also write out, instead of the cell references, with the values found within these cells:
(lets assume A1's value is 1, A10's Value is 10 and the numbers between count up between the two)
To have Excel calculate the value of a mathematical equation you must start by adding the equals sign (=) as shown above, after this we may use any of the mathematical operatives displayed below to
calculate the values we need:
┃+ (plus sign) │Addition │=3+3 ┃
┃- (minus Sign) │Subtraction │=3-1 ┃
┃*(asterisk) │Multiplication │=3*3 ┃
┃/ (Forward Slash)│Division │=3/3 ┃
┃% (Percent Sign) │Percent │=100*50%┃
┃^ (caret) │Exponentiation (to the power of) │=3^2 ┃
Using these operators we can create almost any function (in long hand) we wish to. We can also replace the values (like I have used in my example) with cell references that will update the whole
function when I update a value in their original cell. However you may have to consider the order of operations. As certain functions will mean you have to use parenthesis (brackets) to tell Excel
which part of the function to calculate first.
The Order of Operations
If you combine several operators in a single formula, Excel performs the operations in the order shown in the following table. If a formula contains operators with the same precedence — for example,
if a formula contains both a multiplication and division operator — Excel evaluates the operators from left to right.
│Operator │Description │
│: (colon) │ │
│ │ │
│(single space)│Reference operators │
│ │ │
│, (comma) │ │
│– │Negation (as in –1) │
│% │Percent │
│^ │Exponentiation │
│* and / │Multiplication and division │
│+ and – │Addition and subtraction │
│& │Connects two strings of text (concatenation) │
│= │ │
│< > │ │
│<= │Comparison │
│>= │ │
│<> │ │
Use of Parentheses (brackets)
To change the order of evaluation, enclose in parentheses the part of the formula to be calculated first. For example, the following formula produces 11 because Excel calculates multiplication before
addition. The formula multiplies 2 by 3 and then adds 5 to the result.
In contrast, if you use parentheses to change the syntax, Excel adds 5 and 2 together and then multiplies the result by 3 to produce 21.
In the example below, the parentheses around the first part of the formula force Excel to calculate B4+25 first and then divide the result by the sum of the values in cells D5, E5, and F5.
You can watch this video on Operator order in Excel to learn more | {"url":"https://help.chi.ac.uk/mathematical-operatives","timestamp":"2024-11-03T18:49:23Z","content_type":"text/html","content_length":"76328","record_id":"<urn:uuid:eecf10fb-4bcf-4a1f-a067-3a06bafa3ced>","cc-path":"CC-MAIN-2024-46/segments/1730477027782.40/warc/CC-MAIN-20241103181023-20241103211023-00165.warc.gz"} |
Inscribed Angles Worksheets - 15 Worksheets.com
Inscribed Angles Worksheets
About These 15 Worksheets
These worksheets will help students understand and practice the concept of inscribed angles in circles. An inscribed angle is formed by two chords in a circle that share an endpoint on the circle.
The vertex of the inscribed angle lies on the circle, and the angle itself intercepts an arc between the endpoints of the chords. These worksheets aim to provide students with a solid understanding
of this geometric concept through a variety of exercises and practice problems. By working through these worksheets, students learn to identify inscribed angles, apply related geometric theorems, and
solve problems involving circles and angles.
What Are Inscribed Angles?
Inscribed angles are angles formed by two chords in a circle that meet at a common endpoint on the circle’s circumference. The vertex of an inscribed angle lies on the circle itself, and its sides,
or arms, extend to intersect the circle at two other points. A key property of inscribed angles is that they subtend, or “cut off,” an arc of the circle. This means that the measure of the inscribed
angle is half the measure of the arc it intercepts. Inscribed angles that intercept the same arc or congruent arcs are always equal. This property is useful in solving various geometric problems and
proving theorems related to circles. Inscribed angles are fundamental in the study of circles and play a significant role in understanding cyclic quadrilaterals, where all vertices lie on the
circumference of a circle. Recognizing and working with inscribed angles helps in grasping more complex geometric relationships and properties within circles.
Math Skills Explored
Inscribed angle worksheets cover a range of important math skills that are fundamental to geometry. Firstly, students learn to identify inscribed angles and distinguish them from other types of
angles in circles, such as central angles. This skill is crucial for accurately applying geometric principles and solving related problems. The worksheets reinforce the understanding that the measure
of an inscribed angle is always half the measure of the intercepted arc. This principle is a key geometric theorem that students must master to solve problems involving circles.
In addition to identifying and measuring inscribed angles, students practice calculating the measures of intercepted arcs and other related angles. These calculations often involve applying the
properties of inscribed angles, central angles, and the relationships between different angles in a circle. By combining these principles, students can solve for unknown measures in complex diagrams.
These exercises help develop algebraic skills, as students frequently set up and solve equations to find the measures of unknown angles and arcs.
Another important skill explored in these worksheets is the ability to use geometric notation correctly. Students learn to label angles, arcs, chords, and points accurately, which is essential for
clear communication in geometry. This notation practice supports their ability to follow and create geometric proofs, an advanced skill that is crucial for higher-level math courses.
Types of Exercises
Inscribed angle worksheets feature a variety of exercises and practice problems designed to reinforce the concepts and skills mentioned above. These problems range from basic identification tasks to
more complex calculations and proof-based questions. Here are some common types of exercises found on inscribed angle worksheets:
Identification of Inscribed Angles – One of the foundational exercises in these worksheets involves identifying inscribed angles in various diagrams. Students are presented with circles containing
multiple angles and chords and are asked to mark or color the inscribed angles. This exercise helps them visually recognize the geometric relationships and understand the concept of inscribed angles
being half the measure of their intercepted arcs. Often, these identification problems serve as the first step before moving on to calculation-based questions.
Calculating the Measure of Inscribed Angles – A significant portion of inscribed angle worksheets focuses on calculating the measures of inscribed angles. These problems typically provide the measure
of an intercepted arc or a central angle, and students must use the property that an inscribed angle is half the measure of its intercepted arc to find the angle measure. These exercises often
require setting up and solving algebraic equations, reinforcing both geometric and algebraic skills.
Finding Intercepted Arc Measures – Some worksheets include problems where students are given the measure of an inscribed angle and must find the measure of the intercepted arc. This exercise requires
students to apply the inscribed angle theorem in reverse, multiplying the angle measure by two to find the arc measure. These problems help students understand the direct relationship between
inscribed angles and their intercepted arcs and develop their ability to manipulate geometric relationships.
Word Problems – Some worksheets incorporate word problems that require the application of inscribed angle principles to real-world scenarios. For instance, a problem might describe a situation
involving a Ferris wheel, and students must calculate angles or arc measures based on given information. These word problems help students see the practical applications of inscribed angles and
enhance their problem-solving abilities by requiring them to translate verbal descriptions into geometric diagrams and equations.
Angle Relationships in Circles – Some worksheets extend the concept of inscribed angles to explore relationships between different angles and arcs in circles. For example, students might work with
problems involving central angles, inscribed angles, and angles formed by intersecting chords or tangents. These exercises require students to apply multiple geometric principles and understand the
interplay between different types of angles and arcs in a circle. Solving these problems helps students develop a comprehensive understanding of angle relationships in circles.
Proofs Involving Inscribed Angles – Advanced inscribed angle worksheets might include proof-based problems where students must use logical reasoning to demonstrate geometric theorems involving
inscribed angles. These exercises develop critical thinking and understanding of geometric properties. Proofs might involve multiple steps and the use of other geometric principles, such as the
relationships between inscribed angles and opposite arcs, or the properties of cyclic quadrilaterals. Writing out these proofs helps students articulate their reasoning and understand the logical
flow of geometric arguments.
Mixed Review Problems – To reinforce learning and ensure mastery, many inscribed angle worksheets include mixed review problems that combine different types of exercises. These worksheets might
present a series of diagrams where students need to identify inscribed angles, calculate unknown measures, find intercepted arc measures, and prove angle relationships in one comprehensive activity.
Mixed review problems help students apply their knowledge in varied contexts and build confidence in their geometric skills.
Benefits of These Worksheets
Enhanced Understanding of Circle Geometry
Inscribed angle worksheets play a crucial role in enhancing students’ understanding of circle geometry. By working through these worksheets, students become familiar with the properties and
relationships specific to inscribed angles and their intercepted arcs. This foundational knowledge is essential for grasping more advanced concepts related to circles, such as the relationships
between central angles, chords, and tangents. Through consistent practice, students develop a comprehensive understanding of how inscribed angles function within the broader context of circle
geometry, preparing them for more complex mathematical studies.
Development of Analytical Skills
Inscribed angle worksheets require students to apply logical reasoning and critical thinking to solve problems. As they work through various exercises, students must identify inscribed angles,
calculate their measures, and understand their relationships with intercepted arcs and other angles. This analytical approach helps students develop strong problem-solving skills, which are valuable
not only in mathematics but also in other academic disciplines and real-life situations. By learning to approach problems methodically and think critically, students enhance their overall cognitive
abilities and become more adept at tackling challenging tasks.
Reinforcement of Key Geometric Concepts
These worksheets reinforce key geometric concepts by providing numerous opportunities for students to apply their knowledge of inscribed angles in different contexts. For example, students might be
asked to prove that inscribed angles intercepting the same arc are congruent or to use inscribed angles to solve for unknown measures in geometric figures. This repetition and variation help solidify
students’ understanding and improve their ability to recall and apply geometric principles. Reinforcing these concepts through practice ensures that students retain the information and can use it
effectively in future mathematical endeavors.
Practical Application of Mathematical Skills
Inscribed angle worksheets provide practical applications of mathematical skills, particularly in the context of geometry. Students practice measuring angles, calculating arc lengths, and
understanding the relationships between different geometric elements within a circle. These skills are not only essential for academic success but also have practical applications in fields such as
engineering, architecture, and design. By working through real-world problems involving inscribed angles, students see the relevance of geometry in everyday life and gain a deeper appreciation for
the subject.
Visual Learning and Comprehension
The visual nature of inscribed angle worksheets caters to visual learners and helps students understand abstract concepts through diagrams and illustrations. Visual aids, such as circle diagrams with
marked inscribed angles and arcs, make it easier for students to grasp the relationships between different geometric elements. This visual approach enhances comprehension and retention by making
abstract geometric principles more concrete and accessible. By seeing the concepts in action, students can better understand how inscribed angles function and how to apply their properties in various
Versatility in Teaching
Inscribed angle worksheets are versatile tools that teachers can use in various instructional settings, including individual practice, group activities, homework assignments, and assessments. This
versatility makes them valuable resources in the classroom, allowing educators to tailor their teaching strategies to meet the needs of their students. For instance, worksheets can be used to
introduce new concepts, reinforce previously learned material, or assess students’ understanding of inscribed angles. This flexibility ensures that students receive comprehensive instruction and
multiple opportunities to practice and master the concepts.
Progressive Difficulty for Skill Building
The progressive nature of inscribed angle worksheets ensures that students can build their skills gradually. Starting with basic identification and measurement tasks and progressing to more complex
problems involving proofs and applications helps ensure a thorough understanding of the topic. This gradual increase in difficulty allows students to build confidence as they master each level before
moving on to more challenging tasks. By scaffolding the learning process, these worksheets support continuous improvement and mastery of geometric concepts, preparing students for more advanced
Engagement and Motivation
Inscribed angle worksheets often include engaging and interactive elements that keep students motivated and interested in learning. Activities such as puzzle-solving, real-world problem scenarios,
and creative design tasks make learning about inscribed angles enjoyable and relevant. By incorporating elements of fun and challenge, these worksheets encourage active participation and sustained
interest in geometry. This engagement is critical for maintaining students’ motivation and fostering a positive attitude towards mathematics, which can lead to greater academic success and a lifelong
interest in the subject. | {"url":"https://15worksheets.com/worksheet-category/inscribed-angles/","timestamp":"2024-11-14T14:58:20Z","content_type":"text/html","content_length":"138005","record_id":"<urn:uuid:536053e4-f38c-4da4-ae8a-9c723b0e4a2b>","cc-path":"CC-MAIN-2024-46/segments/1730477028657.76/warc/CC-MAIN-20241114130448-20241114160448-00336.warc.gz"} |
If two ping pong balls are suspended near each other class 11 physics JEE_Main
Hint: As a fast stream of air is produced between the balls, the velocity of the air molecules between the balls change. This leads to change in pressure. Try to figure out whether pressure will
increase or decrease and accordingly answer.
Complete step by step answer:
Important point to understand here is that when pressure between the balls will decrease then the balls will move towards each other. And if the pressure between the balls increases, the balls move
away from each other.
Now we have to find an equation which relates velocity, pressure and that equation holds for viscous fluids like air or water. Since we are dealing with air, we have Bernoulli’s equation.
As per Bernoulli’s principle, an increase in a fluid’s speed creates a pressure decrease and a decrease in fluid’s speed creates an increase in pressure.
From the above discussion let’s use Bernoulli’s principles, we have:
$ \Rightarrow {P_2} = {P_1} + \dfrac{1}{2}\rho ({v_1}^2 - {v_2}^2)$ -- equation \[1\]
Where ${P_1},\,{P_2}$ are the initial and final pressures respectively.
$\rho $ is the density of the air which will be same
${v_1},\,{v_2}$ are the initial and final velocities respectively.
It must be noted here that
${v_2} > {v_1}$ as a fast stream of air is produced in the second case.
Using this in equation we have:
$ \Rightarrow {P_2} = {P_1} + \dfrac{1}{2}\rho ({v_1}^2 - {v_2}^2)$
Now as we have achieved earlier that ${v_2} > {v_1}$ hence, the term $({v_1}^2 - {v_2}^2)$ will be negative
$ \Rightarrow {P_2} = {P_1} + (negative\,quantity)$
$ \Rightarrow {P_2} < {P_1}$
Therefore, the pressure after a fast stream of air is produced will be lower.
As a result, the balls will Come nearer to each other. Option (A) is the correct option.
Note: While dealing with such questions, try to find some definitions or formulas which relate the given quantities. Remember that when velocity of air increases, pressure decreases and when velocity
of air decreases then pressure will increase. | {"url":"https://www.vedantu.com/jee-main/if-two-ping-pong-balls-are-suspended-near-each-physics-question-answer","timestamp":"2024-11-12T12:14:08Z","content_type":"text/html","content_length":"147239","record_id":"<urn:uuid:6333d9a2-144b-4daa-9255-fee4d684a53e>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.45/warc/CC-MAIN-20241112113320-20241112143320-00696.warc.gz"} |
Mind Mappings: Enabling Efficient Algorithm-Accelerator Mapping Space Search
Mar 02, 2021
Modern day computing increasingly relies on specialization to satiate growing performance and efficiency requirements. A core challenge in designing such specialized hardware architectures is how to
perform mapping space search, i.e., search for an optimal mapping from algorithm to hardware. Prior work shows that choosing an inefficient mapping can lead to multiplicative-factor efficiency
overheads. Additionally, the search space is not only large but also non-convex and non-smooth, precluding advanced search techniques. As a result, previous works are forced to implement mapping
space search using expert choices or sub-optimal search heuristics. This work proposes Mind Mappings, a novel gradient-based search method for algorithm-accelerator mapping space search. The key idea
is to derive a smooth, differentiable approximation to the otherwise non-smooth, non-convex search space. With a smooth, differentiable approximation, we can leverage efficient gradient-based search
algorithms to find high-quality mappings. We extensively compare Mind Mappings to black-box optimization schemes used in prior work. When tasked to find mappings for two important workloads (CNN and
MTTKRP), the proposed search finds mappings that achieve an average $1.40\times$, $1.76\times$, and $1.29\times$ (when run for a fixed number of steps) and $3.16\times$, $4.19\times$, and $2.90\
times$ (when run for a fixed amount of time) better energy-delay product (EDP) relative to Simulated Annealing, Genetic Algorithms and Reinforcement Learning, respectively. Meanwhile, Mind Mappings
returns mappings with only $5.32\times$ higher EDP than a possibly unachievable theoretical lower-bound, indicating proximity to the global optima.
* Appears in the proceedings of the 26th ACM International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS '21), April 19-23, 2021, Virtual, USA | {"url":"https://www.catalyzex.com/paper/mind-mappings-enabling-efficient-algorithm","timestamp":"2024-11-03T23:14:59Z","content_type":"text/html","content_length":"57891","record_id":"<urn:uuid:ed742332-51a6-4592-be3c-8817d4c9a509>","cc-path":"CC-MAIN-2024-46/segments/1730477027796.35/warc/CC-MAIN-20241103212031-20241104002031-00404.warc.gz"} |
Numerical reasoning Tests - Sheffield Tutor CompanyNumerical reasoning Tests
Sheffield Tutor Company will soon be providing information about Numerical Reasoning Tests and Aptitude Tests to help people prepare for Graduate scheme jobs, police tests, fireman tests as well as
Maths tests for nurses. Stay tuned for updates and information on Numerical Reasoning Tests.
Further to our recent news, Sheffield Tutor Company is happy to announce that we have updated our numerical reasoning offer. Whether you are preparing for the KPMG numerical reasoning test or are
looking for practice numerical reasoning tests then Sheffield Tutor Company can help. Contact us today for more information about our numerical reasoning test tutors and how we can help you to pass
your exam.
The numerical reasoning test is quite a tricky test as it requires people to be sharp with their mental arithmetic and your knowledge of percentages and ratio has to be strong. One specific test,
called the professional numeracy skills test has to be taken and passed by those on the Teach First program but also anyone who wants to become a qualified teacher in England or Wales, regardless of
which access route they take. As far as numerical reasoning tests go, the QTS Maths test is a little different as the first 12 questions are audio questions which require you to have quick mental
Maths skills. At Sheffield Tutor Company we can help people pass their professional numeracy skills test by providing expert qts maths tutors in Sheffield.
The following employers provide numerical reasoning tests as part of their assessment process. If you need help with your numerical reasoning remember to contact Sheffield Tutor Company as we have
expert Maths tutors in Sheffield.
• KPMG
• John Lewis
• ALDI
• Barclays
• BBC
• EY
• GSK
• Tesco
• Unilever
• J.P. Morgan
• P&G
• Rolls-Royce
• Jaguar
• L’OREAL
• Lidl
• Shell
• Boots
• CITI
• Deutsche
• Nestle
• Sky
• UBS
• McKinsey and Co
• Sainsburys
• Transport for London
• Diageo
• British Airways
• HP
• Atkins
• American Express
• Bain & Company
• Balfour Beatty
• Black Rock
• Ford
• Schlumberger
• Aviva
• Axa
• Capital One
• Mercer
• Santander
• National Audit Office
• FCA
• DHL
• Yorkshire Water
• BNP PARIBAS
• Standard Life
• Next
• TK maxx
• Vodafone
• FujitsuEE
• IKEA
• B&Q
• Admiral
• ANZ
• Chevron
• Atos
• Novo nordisk
• Macquarie
• Science & Technology Facilities Council
• Grant Thornton
• O2 (Telefonica)
• Airbus Group
• Credit Suisse
• Bank of America Merrill Lynch
• Siemens
• Centrica
• Arcadia
• Savills
• Dyson
• BDO
• Baker Tilly
• Smith & Williamson
• Amazon
• NGDP
• British Council
• EDF ENERGY
• Hilton Worldwide
• Samsung
• BMW
• E.ON
• GCHQ
• HM Revenue & Customs
• Intel
• Mercedes-Benz
• Mondelez International
• BT | {"url":"https://sheffieldtutorcompany.co.uk/numerical-reasoning-tests/","timestamp":"2024-11-03T13:20:04Z","content_type":"text/html","content_length":"47192","record_id":"<urn:uuid:9bd371ef-e248-460d-bb47-652df7c7851b>","cc-path":"CC-MAIN-2024-46/segments/1730477027776.9/warc/CC-MAIN-20241103114942-20241103144942-00528.warc.gz"} |
Finding Good Coordinates for Sampling: The Importance of Geometry
Probability that a random point in an \(n\)-dimensional cube lies inside the inscribed sphere
W. S. B. Woolhouse, Educational Times 18 (1865), p. 189
W. S. B. Woolhouse, The Lady's and Gentleman's Diary 158 (1861), p. 76
If the vertices of the triangle are chosen from the standard Gaussian on \(\mathbb{R}^2\), then
Obtuseness is scale-invariant, so pick a perimeter \(P\) and we have \(a+b+c=P\).
J.J. Sylvester, Phil. Trans. R. Soc. London 154 (1864), p. 654, footnote 64(b)
W.S.B. Woolhouse, Mathematical Questions with Their Solutions VII (1867), p. 81
A. De Morgan, Trans. Cambridge Phil. Soc. XI (1871), pp. 147–148
W.S.B. Woolhouse, Mathematical Questions with Their Solutions VI (1866), p. 52
C.M. Ingleby, Mathematical Questions with Their Solutions V (1865), p. 82
G.C. De Morgan, Mathematical Questions with Their Solutions V (1865), p. 109
W.S.B. Woolhouse, Mathematical Questions with Their Solutions VIII (1868), p. 105
J.M. Wilson, Mathematical Questions with Their Solutions V (1866), p. 81
W.A. Whitworth, Mathematical Questions with Their Solutions VIII (1868), p. 36
Report on J.J. Sylvester’s presentation of his paper “On a Special Class of Questions on the Theory of Probabilities” to the British Association for the Advancement of Science, 1865
Sampling action-angle coordinates uniformly is equivalent to sampling equilateral polygons uniformly.
We can generate random equilateral \(n\)-gons in expected time \(\Theta(n^2)\).
In any reasonable model of random knots parametrized by a “size,” the probability of knotting goes to 1 as the size goes to infinity.
Synthetic chemists can now produce simple topological polymers in usable quantities. | {"url":"https://slides.com/shonk/cu24/fullscreen","timestamp":"2024-11-12T12:33:37Z","content_type":"text/html","content_length":"186956","record_id":"<urn:uuid:f60233e8-1866-4ac9-adcd-581fedef938f>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.45/warc/CC-MAIN-20241112113320-20241112143320-00440.warc.gz"} |
Civil Engineering Tutorials and Solutions
58 Replies to “Tutorials/Solutions”
1. nice work ……if any one need any kind of help relating autocad can contact me ….i will try my best if it is up to my knowledge…
2. can we make structure drafting on cad
3. i need some books and videos about arcGIS software…pleas help me….best regards
4. hi i need project title for construction managment
5. i want this
Structural Analysis (8th Edition) By R.C.Hibbeler Solution Manual
Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16.
plz how could i get this from ur site.
6. account details bro.. im unable to send money.. please give correct details as in bank acccount
7. Whether member ship is compulsory to see all the excel projects
8. i need civil engineering FE exam material can you provide me???
☆ Uploading a reference book for it
☆ fundamentals of engineering exam material same as PE exam
9. can you provide design of highway bridges barker and puckett 3rd edition???
□ that is available will be uploading
10. and also i need Designing with geosynthetivs by koerner,robert M 6th edition and Masonry structural design by richard klinger?
11. hello 🙂
I know it is sorry to you, can you provide “solutions manual to accompany matrix analysis of structures (Robert E. Sennett)” ? I’m really need it.
I wanna get your favor.
□ I think its not available on our site
12. can i have the solution manual for the designing with geosynthetics 5th edition. urgent plz
13. hi i need mechanic of materials 4th ed by R.C hibbleler manual solution pleas help!
□ when we have 8th edition solution then y u need 4th edition ?
☆ i know but my professor teach us from 4th ed 🙁
■ so do you have it in your website or not?
14. hi
how can i find “principles of geotechnical engineering 8th edition solution manual”?plz help me
15. hello 🙂 i really need Structural Analysis (8th Edition) By R.C.Hibbeler Solution Manual
Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16. the problem is I don’t have
my own email address so i had to use my sister’s account can you still please allow me to be your member?
16. dear i am student and want to awail the service….
any discount?
how much data will be allow to save in local harddrive?
from peshawar,pakistan
□ All data available. No limit.
□ you can do googling for it. We dont have it yet
18. do u have midas civil software with crack
19. I cant download hibbeler it says on google drive that i need permissions in order to download that. Thank you very much for your help
□ Yes because you are not a member
20. Sir can i ask a pdf on this one. Instructor’s Solution Manual to Accompany Matrix Analysis of Structures By Aslam Kassimali (2nd Edition) (322 Pages).
i really need it sir. hoping for your respond immediately. THANK YOU AND MORE POWER.
□ You can have it but membership is required
21. I’m Civil Engineering student and want all these tutorials and solution manuals…
22. etabs ke tutorial open ni ho rhe…..you need permission ka option arha ?
halanke mai ne registration bhi karai hovi he
□ Are u signed in by ur gmail id ?
23. hellow… can i have permission at Structural Analysis (8th Edition) By R.C.Hibbeler Solution Manual??? thank you….
□ Yes but u have to be our member
24. Sir i need matlab codes or book for Structural dynamics. If anyone expert in matlab. We can adjust if you want any money. Please help me here my id is
25. plz snd me solution of r.c hibbler 8th eddition | {"url":"https://civilengineerspk.com/tutorials/","timestamp":"2024-11-07T12:35:21Z","content_type":"text/html","content_length":"176903","record_id":"<urn:uuid:01e966f1-7400-4856-9c9c-8495bf76f03b>","cc-path":"CC-MAIN-2024-46/segments/1730477027999.92/warc/CC-MAIN-20241107114930-20241107144930-00030.warc.gz"} |
Lesson 8
Rewriting Quadratic Expressions in Factored Form (Part 3)
Lesson Narrative
So far, the quadratic expressions that students have transformed from standard form to factored form have at least a squared term and a linear term. In this lesson, students encounter quadratic
expressions without a linear term and consider how to write them in factored form.
Students begin by studying numerical examples and noticing that expressions such as \((20+1)(20-1)\) and \(20^2-1^2\) (which is a difference of two squares) are equivalent. Through repeated
reasoning, students are able to generalize the equivalence of these two forms as \((x+m)(x-m) =x^2-m^2\) (MP8). Then, they make use of the structure relating the two expressions to rewrite
expressions (MP7) from one form to the other.
Along the way, they encounter a variety of quadratic expressions that can be seen as differences of two squares, including those in which the squared term has a coefficient other than 1, or
expressions that involve fractions.
Students also consider why a difference of two squares (such as \(x^2 - 25\)), can be written in factored form, but a sum of two squares (such as \(x^2+25\)) cannot be, even though both are quadratic
expressions with no linear term.
After this lesson, students will have the tools they need to solve factorable quadratic equations given in standard form by first rewriting them in factored form. That work begins in the next lesson.
Learning Goals
Teacher Facing
• Understand that multiplying a sum and a difference, $(x+m)(x-m)$, results in a quadratic with no linear term and explain (orally) why this is the case.
• When given quadratic expressions with no linear term, write equivalent expressions in factored form.
Student Facing
• Let’s look closely at some special kinds of factors.
Student Facing
• I can explain why multiplying a sum and a difference, $(x+m)(x-m)$, results in a quadratic expression with no linear term.
• When given quadratic expressions in the form of $x^2+bx+c$, I can rewrite them in factored form.
CCSS Standards
Building On
Building Towards
Additional Resources
Google Slides For access, consult one of our IM Certified Partners.
PowerPoint Slides For access, consult one of our IM Certified Partners. | {"url":"https://curriculum.illustrativemathematics.org/HS/teachers/1/7/8/preparation.html","timestamp":"2024-11-14T11:35:14Z","content_type":"text/html","content_length":"78775","record_id":"<urn:uuid:a6ece51d-a890-4c33-ab9e-3214c2ed7bca>","cc-path":"CC-MAIN-2024-46/segments/1730477028558.0/warc/CC-MAIN-20241114094851-20241114124851-00215.warc.gz"} |
[Solved] A triangle is drawn with its vertices on the circle C such t
A triangle is drawn with its vertices on the circle C such that one of its sides is a diameter of C and the other two sides have their lengths in the ratio a : b. If the radius of the circle is r,
then the area of the triangle is
1. \(\rm \frac{2abr^2}{a^2+b^2}\)
2. \(\rm \frac{4abr^2}{a^2+b^2}\)
3. \(\rm \frac{abr^2}{a^2+b^2}\)
4. \(\rm \frac{abr^2}{4(a^2+b^2)}\)
Answer (Detailed Solution Below)
Option 1 : \(\rm \frac{2abr^2}{a^2+b^2}\)
India's Super Teachers for all govt. exams Under One Roof
Demo Classes Available*
Enroll For Free Now
Here BC is the diameter and ∠ABC = 90°
Area of the triangle \(\rm =\frac{1}{2}\times (ax)\times (bx)=\frac{ab}{2}x^2\)
Diameter (BC) = \(\rm \sqrt{(ax)^2+(bx)^2}=2r\)
⇒ (ax)^2 + (bx)^2 = 4r^2
⇒ x^2 [a^2 + b^2] = 4r^2
⇒ \(\rm x^2=\frac{4r^2}{a^2+b^2}\)
Hence, the area = \(\rm \frac{abx^2}{2}=\frac{ab}{2}\times \frac{4r^2}{a^2+b^2}=\frac{2abr^2}{a^2+b^2}\)
Ace your Quantitative Aptitude and
preparations for Plane Figures with us and master Circle or Semi Circle for your exams. Learn today!
India’s #1 Learning Platform
Start Complete Exam Preparation
Trusted by 6.3 Crore+ Students
More Plane Figures Questions
More Mensuration Questions
More Quantitative Aptitude Questions | {"url":"https://testbook.com/question-answer/a-triangle-is-drawn-with-its-vertices-on-the-circl--6687bff59362dece75ab75c8","timestamp":"2024-11-07T18:27:31Z","content_type":"text/html","content_length":"217078","record_id":"<urn:uuid:c1d43e97-ce89-43a3-9b5c-4bdddec88ef7>","cc-path":"CC-MAIN-2024-46/segments/1730477028009.81/warc/CC-MAIN-20241107181317-20241107211317-00260.warc.gz"} |
External Service Desk Knowledge Base
Flux and bandpass calibration
MeerKAT makes use of J1939-6342 and J0408-6545 as the flux and bandpass calibrators. Due to MeerKAT’s wide field of view and sensitivity, there is structure introduced into the bandpass response from
secondary sources in the field. It is necessary to use a multi-component model for the primary calibrators in order to derive a stable bandpass calibration and accurate flux scale. This is vital at
the UHF band, as shown below, but it is also advisable to do so at L-band for accurate bandpass calibration.
The L-and UHF-band calibrator models used by the SDP pipeline, in wsclean format, can be found here.
J1939-6342 (Figure 1) has an additional ~20% flux contribution from other sources in the field at 900 MHz, and up to 40% at 600 MHz with its spectrum turning over at ~1 GHz. These sources cause
time-variable ripples across the bandpass in both phase and amplitude (examples shown in Figure 2). While the standard CASA flux density models can be used for L-band data reduction, it is essential
to use multi-component models for UHF observations.
Figure 2: Effects of off-axis sources surrounding J1939-6342, in the UHF band, on visibility amplitudes on a selection of baselines. Multiple scans are overplotted to illustrate the time-variability.
A full discussion of the observations and models are included in this commissioning report. The SDP calibrator pipeline is currently using 90 components. This is sufficient for most cases.
This source has somewhat lower interference from other sources in the field (1% contribution at L-band); there is a bright double-lobed source at the 1% (integrated flux) level 5.5 arcmin away from
the central source.
Using CASA setjy for non-standard flux models
There isn’t a standard flux model available for J0408-6545 in CASA. The code below shows how to set the model (using only the primary source in the field).
def casa_flux_model(lnunu0, iref, *args): """ Compute model: iref * 10**lnunu0 ** (args[0] + args[1] * lnunu0 + args[1] * lnunu0 ** 2 + args[0] * lnunu0 ** 3) """ exponent = np.sum([arg * (lnunu0 **
(power )) for power, arg in enumerate(args)], axis=0) return iref * (10**lnunu0) **(exponent) def fit_flux_model(nu, s, nu0, sigma, sref, order=5): from scipy.optimize import curve_fit from
scipy.special import binom """ Fit a flux model of given order from : S = fluxdensity *(freq/reffreq)**(spix[0]+spix[1]*log(freq/reffreq)+..) Very rarely, the requested fit fails, in which case fall
back to a lower order, iterating until zeroth order. If all else fails return the weighted mean of the components. Finally convert the fitted parameters to a katpoint FluxDensityModel: log10(S) = a +
b*log10(nu) + c*log10(nu)**2 + ... Parameters ---------- nu : np.ndarray Frequencies to fit in Hz s : np.ndarray Flux densities to fit in Jy nu0 : float Reference frequency in Hz sigma : np.ndarray
Errors of s sref : float Initial guess for the value of s at nu0 order : int (optional) The desired order of the fitted flux model (1: SI, 2: SI + Curvature ...) """ init = [sref, -0.7] + [0] *
(order - 1) lnunu0 = np.log10(nu/nu0) for fitorder in range(order, -1, -1): try: popt, _ = curve_fit(casa_flux_model, lnunu0, s, p0=init[:fitorder + 1], sigma=sigma) except RuntimeError: log.warn
("Fitting flux model of order %d to CC failed. Trying lower order fit." % (fitorder,)) else: coeffs = np.pad(popt, ((0, order - fitorder),), "constant") return [nu0] + coeffs.tolist() # Give up and
return the weighted mean coeffs = [np.average(s, weights=1./(sigma**2))] + [0] * order return [nu0]+ coeffs.tolist() def convert_flux_model(nu=np.linspace(0.9,2,200)*1e9 , a=1,b=0,c=0,d=0,Reffreq=
1.0e9) : """ Convert a flux model from the form: log10(S) = a + b*log10(nu) + c*log10(nu)**2 + ... to an ASA style flux model in the form: S = fluxdensity *(freq/reffreq)**(spix[0]+spix[1]*log(freq/
reffreq)+..) Parameters ---------- nu : np.ndarray Frequencies to fit in Hz a,b,c,d : float parameters of a log flux model. Reffreq : float Reference frequency in Hz returns :
reffreq,fluxdensity,spix[0],spix[1],spix[2] """ MHz = 1e6 S = 10**(a + b*np.log10(nu/MHz) +c*np.log10(nu/MHz)**2 + d*np.log10(nu/MHz)**3) return fit_flux_model(nu, S , Reffreq,np.ones_like(nu),sref=1
,order=3) #name=0408-65 epoch=2016 ra=04h08m20.4s dec=-65d45m09s a=-0.9790 b=3.3662 c=-1.1216 a=-0.9790 b=3.3662 c=-1.1216 d=0.0861 reffreq,fluxdensity,spix0,spix1,spix2 = convert_flux_model
(np.linspace(0.9,2,200)*1e9,a,b,c,d) f_cal_alt = 'J0408-6545' setjy(vis=msfile, field=f_cal_alt, spix=[spix0, spix1, spix2, 0], fluxdensity = fluxdensity, reffreq='%f Hz'%(reffreq), standard=
Applying a full sky model to a CASA measurement set
The calibrator models are in wsclean format.
The crystalball package can be used to populate the ‘MODEL_DATA' column of a measurement set. This replaces CASA’s own setjy task as crystalball utilises all the components in the sky model. setjy by
default assumes a single point source model at the phase center of the flux calibrator field. A model image may also be provided for use with setjy.
crystalball can be used as follows:
$ crystalball observation.ms -sm skymodel.txt -f 0
for the measurement set “observation.ms”, sky model “skymodel.txt” and flux calibrator field ID “0”.
Calibration can proceed as normal after this step. | {"url":"https://skaafrica.atlassian.net/wiki/spaces/ESDKB/pages/1481408634/Flux+and+bandpass+calibration","timestamp":"2024-11-08T07:35:44Z","content_type":"text/html","content_length":"972075","record_id":"<urn:uuid:609cde23-1994-473f-ad0c-11ed15d3608f>","cc-path":"CC-MAIN-2024-46/segments/1730477028032.87/warc/CC-MAIN-20241108070606-20241108100606-00320.warc.gz"} |
FLTRCK - Editorial
Author: samhenry97
Editorialist: samhenry97
What is the largest amount of items of an array that sums to a number <= a given value?
We can construct a sum array, and then use binary searches for each query.
First, we read the integers and sort them. Then, we create an array sum, which is a cache of the sums of each subarray 0…i.
Now, for each query, we can run a binary search to see where the largest sum is that fits the weight. | {"url":"https://discusstest.codechef.com/t/fltrck-editorial/19058","timestamp":"2024-11-11T01:21:56Z","content_type":"text/html","content_length":"20724","record_id":"<urn:uuid:ba03d0bb-be8f-4838-b212-b802052908da>","cc-path":"CC-MAIN-2024-46/segments/1730477028202.29/warc/CC-MAIN-20241110233206-20241111023206-00510.warc.gz"} |
Planck radiation law - Mono Mole
Planck radiation law
The Planck radiation law explains how a blackbody emits electromagnetic radiation at a specific temperature, based on the assumption that the energy of each oscillator in the body can only have
discrete values.
In June 1900, Lord Rayleigh published the Rayleigh-Jeans law, which is now known as a flawed attempt in physics to describe the spectral radiance of electromagnetic radiation as a function of
wavelength from a blackbody at a given temperature. The mistake that he made was to use the equipartition theorem to assume that each oscillation mode within a blackbody has an average energy of $\
overline{E}=kT$. In December of the same year, the German physicist Max Planck presented the Planck radiation law, which assumed that the energy of an oscillator of frequency $u$ came in discrete
where $n=0,1,2,\cdots$ and $h$ is a proportionality constant called the Planck constant.
According to the Boltzmann distribution, the probability of a mode $P_{n,u}$ with frequency $u$ associated with the state $E_{n,u}$ is
The average energy $\overline{E}$ of the mode of frequency $u$ is
Let $\small{x=e^{-\frac{hu}{kT}}}$.
$\overline{E}=hu\frac{\sum_{n=0}^{\infty}nx^n}{\sum_{n=0}^{\infty}x^n}=hu\biggr\(\frac{x+2x^2+3x^3+\cdots}{1+x+x^2+\cdots}\biggr\)=hu x\biggr\(\frac{1+2x+3x^2+\cdots}{1+x+x^2+\cdots}\biggr\)$
Substituting the Taylor series of $\small{\frac{1}{1-x}=1+x+x^2+\cdots}$ and $\small{\frac{1}{(1-x)^2}=1+2x+3x^2+\cdots}$ in the above equation gives
$\overline{E}=\frac{hu x}{1-x}=\frac{hu}{x^{-1}-1}=\frac{hu}{e^{\frac{hu}{kT}}-1}\;\;\;\;\;\;\;\;4$
Substituting eq4 in eq2 yields
$u(u)du=\frac{8\pi hu^3}{c^3}\frac{1}{e^{\frac{hu}{kT}}-1}du\;\;\;\;\;\;\;\;5$
which is the mathematical expression of the Planck distribution law.
Show that in the classical limit, the average energy of a mode in eq4 is consistent with the equipartition theorem.
In the classical limit, $\small{hu\rightarrow 0}$ and we can expand $\small{e^\frac{hu}{kT}}$ as the Taylor series $\small{e^\frac{hu}{kT}=1+\frac{hu}{kT}+\frac{1}{2!}\biggr\(\frac{hu}{kT}\biggr\)^2+
\cdots}$. Substituting the series in eq4 and ignoring the higher powers of the series because $\small{\frac{hu}{kT}\rightarrow 0}$, we have $\overline{E}=kT$. | {"url":"https://monomole.com/planck-radiation-law/","timestamp":"2024-11-03T10:52:38Z","content_type":"text/html","content_length":"101459","record_id":"<urn:uuid:ba8ebbe9-91dd-421b-af62-08689d7da9f3>","cc-path":"CC-MAIN-2024-46/segments/1730477027774.6/warc/CC-MAIN-20241103083929-20241103113929-00891.warc.gz"} |
2001 AMC 12 Problems/Problem 23
A polynomial of degree four with leading coefficient 1 and integer coefficients has two zeros, both of which are integers. Which of the following can also be a zero of the polynomial?
$\text{(A) }\frac {1 + i \sqrt {11}}{2} \qquad \text{(B) }\frac {1 + i}{2} \qquad \text{(C) }\frac {1}{2} + i \qquad \text{(D) }1 + \frac {i}{2} \qquad \text{(E) }\frac {1 + i \sqrt {13}}{2}$
Let the polynomial be $P$ and let the two integer zeros be $z_1$ and $z_2$. We can then write $P(x)=(x-z_1)(x-z_2)(x^2+ax+b)$ for some integers $a$ and $b$.
If a complex number $p+qi$ with $qot=0$ is a root of $P$, it must be the root of $x^2+ax+b$, and the other root of $x^2+ax+b$ must be $p-qi$.
We can then write $x^2+ax+b = (x-p-qi)(x-p+qi) = (x-p)^2 - (qi)^2 = x^2 - 2px + p^2 + q^2$.
We can now examine each of the five given complex numbers, and find the one for which the values $-2p$ and $p^2+q^2$ are integers. This is $\boxed{\frac {1 + i \sqrt {11}}{2}}$, for which we have
$-2p = -2\cdot\frac 12 = -1$ and $p^2+q^2 = \left( \frac 12 \right)^2 + \left( \frac {\sqrt{11}}2 \right)^2 = \frac 14 + \frac {11}4 = \frac {12}4 = 3$.
(As an example, the polynomial $x^4 - 2x^3 + 4x^2 - 3x$ has zeroes $0$, $1$, and $\frac {1 \pm i \sqrt {11}}{2}$.)
Solution 2
By Vieta, we know that the product of all four zeros of the polynomial equals the constant at the end of the polynomial. We also know that the two imaginary roots are a conjugate pair (I.E if one is
a+bi, the other is a-bi). So the two imaginary roots must multiply to give you an integer. Taking the 5 answers into hand, we find that $\boxed{\frac {1 + i \sqrt {11}}{2}}$ is our only integer
giving solution.
Note: I think this solution is not correct. the products of the roots are integers do not mean the product of the two complex roots are integers.
Note: I believe this solution is correct. We know that the two real solutions are integers and that the final product is an integer. The product of the real solutions multiplied by the product of the
complex solutions equals the final product, so we know that the product of the two complex solutions must be integers. We know the two complex solutions are conjugates, so we can test all the answer
choices and find that A is the answer. ~A1597412
Note: No, the solution is not correct. Here's a counterexample: the product of the two integer roots is 4 and the product of the two complex roots is $1/2$. The product of all four roots is $2$,
which is clearly an integer.
FINAL CLARIFICATION: The note above is accurate. This solution is not fully complete in writing, but is valid nonetheless. If the 2 complex roots multiply to a non-integer, the sum of all 4 roots MAY
STILL produce an integer. However, if the 2 complex roots multiply to an integer, all 4 roots MUST produce an integer. So we know that $\boxed{ A) \frac {1 + i \sqrt {11}}{2}}$ MUST be the solution.
There is a simple fix: The complex roots must be algebraic integers, so the product of the root and its conjugate must be an integer.
Solution 3
After dividing the polynomial out by $(x-p)$ and $(x-q)$, where p and q are the real roots of the polynomial, we will obtain a quadratic with two complex roots. We can then use the quadratic formula
to solve for these complex roots.
Let's start by using synthetic division to divide $x^4+ax^3+bx^2+cx+d$ by $(x-p)$. Using this method, the quotient becomes $1x^3+(a-p)x^2+(b-pa+p^2)x+(c-bp+ap^2-p^3)+\frac{d-pc+bp^2-ap^3+p^4}{x-q}$.
However, we know that there should be no remainder because $(x-p)$ is a factor of the polynomial, so $\frac{d-pc+bp^2-ap^3+p^4}{x-q}$ must equal 0, so $d=-pc+bp^2-ap^3+p^4$. When we divide the
expression on the left by -p, we get $c-bp+ap^2-p^3$, so we can replace it in our original synthetic division equation with $\frac {d}{-k}$.
We then want to synthetically divide $x^3+(a-p)x^2+(b-pa+p^2)x+\frac {d}{-k}$ by the next factor, $(x-q)$. Using the same method as before, we can simplify the quotient to $x^2+(a-p-q)x+\frac{d}{pq}$
. Now for the easy part!
Use the quadratic formula to determine the form of the complex roots.
Now this is starting to look a lot like answers A and E. Noticing that the real part in each answer choice is $\frac{1}{2}$, $(k+n-a)=1$ and $(a-k-n)^2=1$, and the imaginary part is positive.
Furthermore, by Vieta's Formulas, we know that d must be a multiple of p and q, so $\frac{4d}{pq}$ is a multiple of 4. Rearranging the expression, we get:
The radicand therefore must be one less than a multiple of four, which is only the case in $\frac {1 + i \sqrt {11}}{2}$ or $\boxed{A}$.
Solution 4 (answer choices)
According to the Complex Conjugate Root Theorem, if $a+bi$ is a root then so is $a-bi$. Then the quadratic $(x-(a+bi))(x-(a-bi))$ is also a polynomial factor of the quartic in question. Let's check
what that expanded quadratic looks like for each answer choice:
$\[ \begin{array}{|c|c|} \hline \textbf{Answer Choice} & \textbf{Quadratic Expression} \\ \hline \text{A} & \left(x - \frac{1 + \sqrt{-11}}{2}\right)\left(x - \frac{1 - \sqrt{-11}}{2}\right) = x^2 -
x + 3 \\ \text{B} & \left(x - \frac{1 + \sqrt{-1}}{2}\right)\left(x - \frac{1 - \sqrt{-1}}{2}\right) = x^2 - x + \frac{1}{2} \\ \text{C} & \left(x - \frac{1 + 2\sqrt{-1}}{2}\right)\left(x - \frac{1 -
2\sqrt{-1}}{2}\right) = x^2 - x + \frac{5}{4} \\ \text{D} & \left(x - \frac{2 + \sqrt{-1}}{2}\right)\left(x - \frac{2 - \sqrt{-1}}{2}\right) = x^2 - 2x + \frac{5}{4} \\ \text{E} & \left(x - \frac{1 +
\sqrt{-13}}{2}\right)\left(x - \frac{1 - \sqrt{-13}}{2}\right) = x^2 - x + \frac{7}{2} \\ \hline \end{array} \]$
Noting that only choice $\textbf{(A)}$ has all integer coefficients, we can clearly see that for the two other integer roots $p$, and $q$, $(x-p)(x-q)(x^2 - x + 3)$ will always give us a polynomial
of degree four with leading coefficient 1 and integer coefficients. Thus the answer must be $\boxed{\textbf{(A)} = \frac {1 + i \sqrt {11}}{2}}$.
Solution 5
Suppose $P(x) = (x-z_1)(x-z_2)(x^2+ax+b)$
Expand P(x): $P(x) = x^4 + ((z_1+z_2)+a)x^3+(-(z_1+z_2)a+b+z_1z_2)x^2+(-(z_1+z_2)+az_1z_2)x$.
Notice that the coefficients of $P(x)$ are integers. Comparing the coefficients, we can know that $a$ and $b$ are integers
Suppose $p+qi$ and $p-qi$ are the two complex roots of p(x).
Using $z\overline{z} =$|z|$^ 2$ and $b = (p+qi)(p-qi)$ (using Vieta only on $x^2+ax+b=0$)
so $p^2+q^2$ is an integer
select (A)
See Also
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. | {"url":"https://artofproblemsolving.com/wiki/index.php/2001_AMC_12_Problems/Problem_23","timestamp":"2024-11-05T06:21:08Z","content_type":"text/html","content_length":"59014","record_id":"<urn:uuid:a7164eab-c094-42eb-b7c8-5b730f7276fe>","cc-path":"CC-MAIN-2024-46/segments/1730477027871.46/warc/CC-MAIN-20241105052136-20241105082136-00445.warc.gz"} |
期刊界 All Journals 搜尽天下杂志 传播学术成果 专业期刊搜索 期刊信息化 学术搜索
收费全文 3416篇
免费 358篇
国内免费 184篇
化学 150篇
晶体学 8篇
力学 287篇
综合类 47篇
数学 2310篇
物理学 1156篇
2023年 27篇
2022年 67篇
2021年 60篇
2020年 61篇
2019年 66篇
2018年 65篇
2017年 98篇
2016年 110篇
2015年 77篇
2014年 177篇
2013年 217篇
2012年 129篇
2011年 212篇
2010年 213篇
2009年 191篇
2008年 228篇
2007年 265篇
2006年 209篇
2005年 169篇
2004年 179篇
2003年 163篇
2002年 118篇
2001年 93篇
2000年 91篇
1999年 95篇
1998年 71篇
1997年 71篇
1996年 46篇
1995年 58篇
1994年 38篇
1993年 29篇
1992年 32篇
1991年 28篇
1990年 17篇
1989年 18篇
1988年 20篇
1987年 19篇
1986年 9篇
1985年 23篇
1984年 15篇
1983年 12篇
1982年 8篇
1981年 10篇
1980年 9篇
1979年 9篇
1978年 6篇
1977年 8篇
1976年 5篇
1975年 4篇
1973年 3篇
排序方式：共有3958条查询结果，搜索用时 15 毫秒
The age of information (AoI) metric was proposed to measure the freshness of messages obtained at the terminal node of a status updating system. In this paper, the AoI of a discrete time status
updating system with probabilistic packet preemption is investigated by analyzing the steady state of a three-dimensional discrete stochastic process. We assume that the queue used in the system is
, which represents that the system size is 2 and the packet in the buffer can be preempted by a fresher packet with probability
. Instead of considering the system’s AoI separately, we use a three-dimensional state vector
to simultaneously track the real-time changes of the AoI, the age of a packet in the server, and the age of a packet waiting in the buffer. We give the explicit expression of the system’s average AoI
and show that the average AoI of the system without packet preemption is obtained by letting
. When
is set to 1, the mean of the AoI of the system with a
queue is obtained as well. Combining the results we have obtained and comparing them with corresponding average continuous AoIs, we propose a possible relationship between the average discrete AoI
with the
queue and the average continuous AoI with the
queue. For each of two extreme cases where
, we also determine the stationary distribution of AoI using the probability generation function (PGF) method. The relations between the average AoI and the packet preemption probability
, as well as the AoI’s distribution curves in two extreme cases, are illustrated by numerical simulations. Notice that the probabilistic packet preemption may occur, for example, in an energy harvest
(EH) node of a wireless sensor network, where the packet in the buffer can be replaced only when the node collects enough energy. In particular, to exhibit the usefulness of our idea and methods and
highlight the merits of considering discrete time systems, in this paper, we provide detailed discussions showing how the results about continuous AoI are derived by analyzing the corresponding
discrete time system and how the discrete age analysis is generalized to the system with multiple sources. In terms of packet service process, we also propose an idea to analyze the AoI of a system
when the service time distribution is arbitrary.
A new Markov process describing crystal growth in three dimensions is introduced. States of the process are configurations of the crystal surface, which has a terrace-edge-kink structure. The states
are continuous along edges but discrete across edges, in accordance with the very different rates for the two types of captures of particles. Stationary distributions, describing steady crystal
growth, are found in general. To our knowledge, these are the first examples of stationary distributions for layered crystal growth in three dimensions. The steady growth rate and other quantities
are obtained explicitly for two interacting edges. For many interacting edges, growth behavior is determined (a) in various asymptotic regimes including thermodynamic limits, (b) via simulations, and
(c) using series (cluster) expansions in the slope of the surface, the first three coefficients being computed. The theoretical growth rates show a marked dependence on surface dimensions. This may
contribute to the size dependence and dispersion in the observed growth rate of small crystals.
It is known that at the critical temperature the Curie-Weiss mean-field model has non-Gaussian fluctuations and that internal fluctuations can be Gaussian. Here we compute the distribution of the
-mode magnetization fluctuations as a function of the temperature, the wave vector
, and a fading out external field. We obtain new classes of probability distributions generated by this external field as well as new critical behavior in terms of its rate of fading out. We discuss
also the susceptibility as the limit
tending to zero.
Recently developed methods of qualitative analysis for regenerative processes arising in queueing are presented. These methods are essentially qualitative and use notions such as coupling,
probability metrics, etc. They are developed for studying various properties of regenerative models, including convergence rate to a stationary regime, continuity of their characteristics with
respect to some parameters and first-occurrence time of an event such as queue overflowing. In spite of their qualitative nature they lead to good quantitative estimates of underlying properties with
computer methods available to calculate them.
In this paper, we investigate the exact distribution of the waiting time for the
-th ℓ-overlapping occurrence of success-runs of a specified length in a sequence of two state Markov dependent trials. The probability generating functions are derived explicitly, and as asymptotic
results, relationships of a negative binomial distribution of order
and an extended Poisson distribution of order
are discussed. We provide further insights into the run-related problems from the viewpoint of the ℓ-overlapping enumeration scheme. We also study the exact distribution of the number of
ℓ-overlapping occurrences of success-runs in a fixed number of trials and derive the probability generating functions. The present work extends several properties of distributions of order
and leads us a new type of geneses of the discrete distributions.
The article provides a refinement for the volume-corrected Laplace-Metropolis estimator of the marginal likelihood of DiCiccio
et al.
The correction volume of probability α in DiCiccio
et al.
is fixed and suggested to take the value α=0.05. In this article α is selected based on an asymptotic analysis to minimize the mean square relative error (MSRE). This optimal choice of α is shown to
be invariant under linear transformations. The invariance property leads to easy implementation for multivariate problems. An implementation procedure is provided for practical use. A simulation
study and a real data example are presented.
Contrary to the common sense in economics and financial engineering, price fluctuations at very fine level of motion exhibit various evidences against the efficient market hypothesis. We attempt to
investigate this issue by studying extensive amount of foreign currency exchange data for over five years at the finest level of resolution. We specifically focus on the proposed stability in
binomial conditional probabilities originally found in much smaller examples of financial time series. In order to handle very large data, we have written an efficient program in C that automatically
generates those conditional probabilities. It is found that the stability is maintained for extremely large time duration that covers almost the entire period. Based on the length of conditions for
which the conditional probabilities are distinguishable each other, we identify the length of memory being less than 3 movements.
By combining the Kramers-Moyal expansion with fractional Brownian motion of order
, in a formal symbolic calculus, one can obtain an approximation for the solution of some stochastic differential equations involving both Gaussian and Poissonian white noises, in terms of rotating
Gaussian white noises on the grid defined by the complex roots of the unity. Illustrative examples are outlined. | {"url":"https://slh.alljournals.cn/search.aspx?subject=mathematical_chemical&major=sx&orderby=referenced&field=key_word&q=ruin+probability&encoding=utf8","timestamp":"2024-11-14T00:56:41Z","content_type":"application/xhtml+xml","content_length":"64416","record_id":"<urn:uuid:73704071-363f-49ff-8a8e-ce3aec7b6b2a>","cc-path":"CC-MAIN-2024-46/segments/1730477028516.72/warc/CC-MAIN-20241113235151-20241114025151-00707.warc.gz"} |
Free data analysis using R
In this blog post, Alan Parker – scientific consultant and physical chemist at Rational Formulation – explains how the free software ‘R’ can be used for data analysis
Data analysis is one of the most frequently mentioned training needs on AuthorAID. To do data analysis, we need software. I strongly advocate the use of R, an open source programming language.
Here I will outline several good reasons to use R, which is totally free. However, the fact R is free does not mean it is of low quality. It is written, and used daily, by many of the world’s best
statisticians and data scientists. A highly professional team ensures regular upgrades and bug fixes. It runs on Windows, Mac and Linux. For big problems, it can even run on clusters of computers.
The well-known data analyst Nate Silver uses R extensively to predict the results of US elections. Check out his web site: fivethirtyeight.com.
Figure 1 - Graph showing distribution of capsule properties. Created with R
R is extremely powerful, but it can also be used for small data sets, because you can type one line programmes straight in and they will run immediately. For example, plotting a histogram on R is
easy (unlike on Excel). Here’s how to do it: let’s say that you have some data in a list that you’ve named x. You just type hist (x) and a neat histogram is created instantly. R has hundreds of
powerful commands to do data analysis.
Figure 1 is an example of a graph that I made with R. You can find many others by Googling “R graphics gallery”. I had data for the size and shape (“circularity” on the y axis) of thousands of
perfume capsules. I wanted to show how these capsule properties were distributed. Colour is used to indicate how often capsules with a particular size/shape pair are found in the sample. Pink
indicates very common. Green means rare. The graph shows that small, circular particles are most frequent (top left). But there are also a few large, non-circular particles (middle right). We used
this graph to immediately identify unusual samples.
Figure 2 is another beautiful graph, this time taken from the online R graph gallery. This graph compares how seven varieties of plant responded to two treatments. There were many plants in each
sample, so each variety/treatment combination is presented as symbol that has: 1) a bar for the mean; 2) a box that includes values between the first and third quartiles; and 3) a thin line that
includes one standard deviation above and below the mean. Outliers are shown as black blobs. There is a lot of information presented in a very clear and attractive way here.
R’s community and resources
Figure 2 - 'Grouped boxplot with ggplot2'. Graph created with R
One of the best things about R is its great user community. There are tons of tutorials, blogs and forums covering every imaginable subject. You can find many (about 500) blogs gathered on the
umbrella site “R bloggers”.
Probably the main reason for R’s success is its system of add-ons, called “packages”. There are now an incredible 11,000 of these, all free. Each package extends R by adding extra functions that are
ready to run. Just download the package and it’s ready to go. Also included in the packages are help for each extra function and a tutorial introduction. There are packages for many different types
of analysis, for example: “Spatial Designs for Ecological and Environmental Surveys” and “Stochastic Mortality Modelling”. There is even a package that imitates the hand-drawn graph style of the
popular scientific cartoon strip “xkcd”.
To navigate the mountain of add-on packages, there is a special site: CRAN. Inside CRAN you will find 35 “task views”. Each of these is a summary of the key packages devoted to a single area of data
analysis, such as “Environmetrics”, “Meta Analysis” or “Social Sciences”. “Spatial” is a task view that covers the creation of maps with data included. If CRAN is a bit overwhelming, you can find a
shorter, more user-friendly list at “Awesome R” (https://awesome-r.com/ ).
I must say that using R alone is not much fun. You just get a lonely “>” symbol, waiting for you to type something (like the console of Linux or MS-DOS). However, in the last few years, a great free
user interface has been developed: “R Studio”. In my opinion, no one should use R without R Studio. It gives you a screen with four windows: one to type in, another for your scripts (bits of
programme that you want to save), a third showing your plots and a last one showing the history of what you’ve already done. With all this at your fingertips, you can easily flip back and forth:
trying things, making mistakes, correcting them and moving forward.
R scripts and reproducible research
In R, there are several kinds of script. The one that I use is called “Rmarkdown”. I write a mixture of working code and comments, with simple symbols to separate them. This script is already an
exact record of what I did and why. Even better, at the touch of a button, I can convert my script into a nice-looking Word or HTML file. These can easily be turned into a report or blog post.
Scripts are essential, because documentation is a vital part of data analysis, both for you (“Why did I do that?”) and, more generally, to conform to the norms of reproducible research. Reproducible
research – i.e. the capacity to repeat a study and the data analysis anywhere by anybody – is the gold standard. It is key to any scientific method, including in applied social sciences. To meet this
standard, your publications must include the data that you gathered and the data analysis, so that anyone can replicate exactly what you did. At the moment, very few papers meet this standard.
However, due to the recent “crisis of reproducibility” caused by discovering that many studies cannot be repeated, more and more journals will insist upon it. To make data analysis repeatable, the
programming tool must be freely available and open source, so R is ideal.
I hope that this brief introduction has given you the motivation to download R (and don’t forget R Studio) and try it. I should say that I am not a trained statistician or computer programmer. I
picked up R because I needed a tool that was more powerful than Excel. I must admit that the transition needs a little commitment, but once you are up and running, I guarantee that you’ll impress
your colleagues with the results.
Alan Parker is a scientific consultant for Rational Formulation, Annecy, France. He is a physical chemist who has worked in R&D in a range of industries over more than 35 years. He has 40
peer-reviewed publications and six patents, and he recently founded his own scientific consultancy.
Useful links
R Project homepage (with free download links)
R Studio
R Bloggers
CRAN packages | {"url":"https://www.authoraid.info/en/news/details/1277/","timestamp":"2024-11-02T11:36:01Z","content_type":"text/html","content_length":"31770","record_id":"<urn:uuid:ff3a178d-bcee-40e5-b8f7-8e4206caad34>","cc-path":"CC-MAIN-2024-46/segments/1730477027710.33/warc/CC-MAIN-20241102102832-20241102132832-00254.warc.gz"} |
QYLD Yields 11.5%, Pays Monthly, and Could Be Considered a "Buy" Right Now | Daily Trade Alert
I read recently that if you’re looking for high yield in today’s markets, one of the first things to consider is funds that are based on selling covered calls. These funds hold a basket of stocks and
then sell call options against those stocks. The premiums on the options generate high income.
That’s what NASDAQ-100 Covered Call ETF (QYLD) does. This is an ETF offered by a company called Global X, which offers many products of this type.
QYLD is not a dividend-growth ETF. Most of its assets don’t even pay dividends. Rather, as we’ll see, QYLD generates income by selling call options against its stocks.
QYLD is one of a growing number of ETFs that might be called “new wave.” In the early years of ETFs (the 1990s), most ETFs were based on simply holding well-established stock baskets like the S&P
500, Dow Jones Industrial Average, and similar venerable indexes.
That meant that early ETFs were relatively passive investments. The investor simply bought shares of the ETF, and the ETF, in turn, held the stocks of a slowly-changing index.
Nowadays, however, many indexes are created for the purpose of marketing ETFs based upon them. These are not the staid indexes of yore. In fact, some of them can be quite active. These are not your
father’s ETFs.
Covered-Call ETFs
The index on which QYLD is based is not an old-fashioned list of stocks passively held.
QYLD is based on a covered call index, meaning that it generates returns by trading options according to the specifications in the index it follows. An investor cannot hold an index directly. An
index is more like an academic paper. An index holds no stocks. Its portfolio is hypothetical, and it ignores the fees and expenses that would be involved in actually buying the stocks and doing the
trading that the index suggests.
That’s where ETFs come in. They buy the actual stocks and options specified in the index, charge for their work, and thus become real investments that we can buy.
The primary purpose of a covered-call strategy is to generate income. Call options are financial instruments that give the call buyers the right to buy a stock from their counter-party (the seller or
writer of the option) at an agreed-upon price and date. The agreed price is called the strike price.
When a covered-call writer (QYLD in our case) sells a call option, it earns an immediate premium. It keeps that premium no matter the outcome of the option. If the strike price is reached by the
stock, the buyer of the option will call away the stock, because they can get it cheaper from the option-writer than from the open market.
So, selling call options is a way to generate income based on the risk that a stock will be called away. Therefore, price volatility is the biggest total-return risk in a covered-call strategy.
Volatility makes it more likely that the call option will be exercised, because it makes it more likely that the strike price is hit. And since markets tend to rise over time, calls written near the
current price of the stock (which is QYLD’s practice) will tend to be called away more often than not.
Usually when you hold an ETF, you are said to own the stocks in the fund. That is true, but notice that there is an important caveat with a covered-call fund. From the call-writer’s point of view, a
risk of selling options is that potential profits from the rising prices of the stocks in the portfolio will not accrue to your benefit. Once the stock’s price passes the strike price, further price
increases go to the option buyer. As Global X says, “Covered call strategies inherently forfeit upside in exchange for current income.” (Source)
And beyond that, the ETF’s holders are exposed to all of the price downside that may occur, because the stocks are not called away.
Many call options expire without hitting the strike price, in which case the writer keeps both the stock and the premium.
The ideal scenario for a covered-call writer (QYLD in our case) is for the stock price to stay under the strike price for the duration of the option contract, without going down very far. That way,
the option writer keeps both the premium and the shares, and does not lose money to price declines in the shares.
QYLD in a Nutshell
The NASDAQ-100 Covered Call ETF (QYLD) was launched on December 11, 2013. It has become a very popular fund among retail investors. QYLD is the largest covered-call ETF, with $4.5 B in assets. That’s
about two-thirds the combined value of all 20 covered-call ETFs.
QYLD pays a monthly dividend (or distribution) from the income generated by selling call options against the NASDAQ-100 index.
Therefore, QYLD offers investors a simple way to participate in a covered-call income strategy based on securities in the NASDAQ-100. The investor just owns QYLD. The ETF takes care of everything
The big attraction is the income return: QYLD provided investors a gross distribution yield of just over 12% over the past 12 months.
A secondary attraction is QYLD’s monthly distributions. Some investors like monthly payouts. (Personally, I don’t care if dividends come to me quarterly or monthly.)
QYLD’s Operations
The index followed by QYLD is the CBOE NASDAQ-100 Buy-Write Index. “Buy-Write” means the same thing as “covered call.” The seller of the option buys the stocks first, then they write options to sell
Here is how Global X illustrates how QYLD works. First, in a down market, QYLD will generally benefit from the premium it receives, because the month will end with the index (against which the calls
are sold) below the strike price, so QYLD keeps both the stocks and the premium. The premium will offset some (or even all) of the decline in the index’s price.
In a flat market, the calls are not exercised either, so again QYLD keeps both the premium and the stocks.
A rising market, however, brings the risk of selling covered calls into play. If the index price rises by the end of the month, above the strike price, QYLD still keeps the option premium, but it
won’t benefit from the increase in the index’s value.
Here is how Global X diagrams its operations. It does this every month:
Notice that the diagram states that QYLD distributes “a portion” of the income from writing the calls to QYLD’s shareholders. To be more specific, Global X states elsewhere that “[T]he fund expects
to distribute on a monthly basis one-half of the premiums received by writing calls on the Nasdaq 100, capped at 1% of the Fund’s net asset value (NAV). (Source)
In words:
• QYLD buys all the stocks in the NASDAQ-100 index.
• QYLD sells call options against the index itself (not the individual stocks).
• The options are priced at or slightly above the index’s value at the time of writing the options.
• The options are one-month in duration. New ones are written monthly, which provides the monthly cash flow stream to QYLD’s investors.
• QYLD targets approximately 1% per month in distributions.
• Importantly, price changes in the index during the month do not matter if they exceed the strike price. The type of options sold cannot be exercised early, so all that matters is the price of the
index at the end of the month.
The options are settled in cash; no shares of stock or of the index change hands. The cash settlement amount is determined from relation between the value of the index and the strike price.
So, QYLD’s covered calls may partially protect it from a decline in the price of the index via the premiums collected for the options. However, if the stock market is rallying, QYLD will underperform
the index, because the calls prevent QYLD from participating in the index’s rising price above the strike price. And the option premiums may not be sufficient to offset losses or underperformance of
the strategy over time.
The magnitude of risk from not participating in price rises during a market rally is related to the percentage of stocks against which calls are written. Since QYLD sells options on the entire
NASDAQ-100, it is effectively optioning 100% of the stocks that it owns. That means that it maximizes the risk of underperforming the index, but also that it generates the maximum income for its
shareholders from the premiums that it collects from selling the calls.
Now let’s take a look at the two indexes that determine QYLD’s performance: (1) The NASDAQ-100 index of stocks, and (2) the buy-write index that determines how and when covered calls are written
against the index of stocks.
The Stock Index: NASDAQ-100
NASDAQ – which originally stood for National Association of Securities Dealers Automated Quotation system – is now written as an ordinary name rather than an acronym. It’s a stock market, launched in
1971, that offered the first all-electronic system for trading stocks.
The NASDAQ-100 index is a selection of the largest, most active companies traded on NASDAQ. It excludes financial companies, and its stocks are weighted in a certain way that you do not need to
understand for QYLD’s purposes.
As we said earlier, you can’t own an index, because it is a theoretical construct. But you can own an index through an ETF that replicates it in real life. The NASDAQ-100 can be owned and traded
through Invesco’s QQQ Trust (QQQ) ETF.
The NASDAQ-100 is dominated by tech stocks. Here (per Morningstar) are the top 10 holdings in the index. They are all tech or tech-like companies. These top-10 companies account for 53% of the index.
The next display shows that the NASDAQ-100 holds high-quality companies as measured by Morningstar’s moat rating. Per the table, 57% of the fund’s assets have wide-moat ratings and another 37% have
narrow-moat ratings. Other Morningstar grades are high as well.
The next display shows the overall distribution of the index’s stocks by sector.
The three largest sectors – Information Technology, Communication Services, and Consumer Discretionary – account for 85% of the index. Note also that Amazon and Tesla are in the Consumer
Discretionary sector, even though many (if not most) investors think of them as tech stocks.
Because of this concentration in holdings, QYLD is classified as a “non-diversified” investment company under the Investment Company Act of 1940. In practical terms, the fund is prone to be more
volatile than a more-diversified fund would be.
The Strategy Index: CBOE NASDAQ-100 Buy-Write Index
The CBOE NASDAQ-100 BuyWrite Index (“BXN”) is a benchmark index that measures the performance of a theoretical portfolio that holds the stocks in the NASDAQ-100 and writes (sells) a succession of
one-month covered call options against the index.
QYLD replicates BXN’s processes, which we already covered above.
Despite the fact that most investors buy QYLD for its monthly income, the underlying CBOE index is really a total-return strategy. QYLD has simply redeployed the buy-write mechanism to distribute
cash to shareholders rather than reinvest it into the Nasdaq-100 index (or its component stocks).
QYLD’s Performance vs. Its Objectives
According to its home page, these are QYLD’s objectives:
(1) High income potential. QYLD seeks to generate income through covered call writing.
(2) Monthly distributions. QYLD is designed to make monthly distributions rather than quarterly.
(3) Efficient options execution. QYLD writes and manages the call options, saving investors the time and potential expense of doing so individually.
Note that QYLD does not list total return as one of its three purposes. Of course, total returns are very important to many investors, so we will look at them later. Here, we’ll just focus on QYLD’s
three stated objectives.
(1) High income potential
QYLD has hit its goal of high potential income in spades. This chart shows its yield since 2015. It has spent most of its time in the 9-12% range. Right now its current yield is around 11.5%.
At 10% average yield, an investor in QYLD would make back their entire initial investment in 10 years. At 11% average yield, the payback period falls to 9 years.
(2) Monthly distributions
This chart shows QYLD’s dividends since inception. Other than a couple skipped months early in its life, QYLD, has paid monthly dividends since inception in 2014.
As with all ETF’s, QYLD’s dividends vary from payment to payment. Just eyeballing a trend line, it looks like QYLD’s monthly payment has averaged about $0.15-0.20 per share per month since inception.
(3) Efficient options execution
QYLD is designed for an investor like me, who wants equity income but does not want the labor of trading options to get it. I don’t want to be tied to my computer that much. QYLD charges 0.60% in
fees to do it for me.
Overall, it’s fair to say that QYLD has hit its three objectives since it was released:
• High income
• Monthly payments
• Efficient execution of covered-call operation
QYLD’s Total Return Performance
Even income investors don’t like to lose capital while they are generating income. Therefore, let’s examine QYLD’s total returns.
We know from earlier discussion that a covered-call strategy sacrifices total return in exchange for high yield. With that in mind, what is “good” total return for an investment that’s generating 12%
per year in income?
QYLD presents an interesting case, because it goes all-in on the covered-call strategy. We saw earlier that applying that strategy to 100% of a portfolio’s stocks maximizes the likely damage to total
returns. So clearly, one would employ this strategy if one is striving for very high yields, knowing the trade-offs. Just from its design and descriptive literature, QYLD does not present itself as a
buy-and-hold investment designed to amass wealth. It does present itself as a source of reliable high yields that are paid monthly.
Keeping that in mind, here are four total-return comparisons that you might find useful.
(1) S&P 500
Here are QYLD’s price returns – without dividends or dividend reinvestment – compared to SPDR S&P 500 ETF Trust (SPY), an ETF that tracks the S&P 500. The timeframe starts at the beginning of 2014,
which is just after QYLD was commenced.
Remember, this shows changes only in price. SPY pays a dividend of only 1.3% in contrast to QYLD’s dividend of 11.5%.
You can see that QYLD’s price-only returns are negative in the nearly eight years of its existence. That may be surprising, given that the underlying stocks it owns are dominated by the red-hot
technology sector. But they are not surprising when considering how a covered-call strategy limits upward price rewards.
In all of the comparisons, QYLD’s negative price-only returns have been the worst. QYLD is designed to be a dividend-generating machine, and price-only comparisons ignore that income. So let’s
account for those dividends by displaying total returns with dividends reinvested (i.e., dripping the dividends back into buying more shares).
Even taking dividends and reinvestment into account, we can see that QYLD’s total returns have only achieved about half of simply holding the S&P 500 itself via SPY.
Of course, if you did that and needed income, you would have to sell shares of SPY every month to turn some of your paper gains into cash. That works fine when prices are going up; it can be
uncomfortable when prices are going down.
(2) Covered-call ETF for S&P 500
Global-X offers a covered-call ETF where the stock index is the S&P 500. This ETF – Global-X S&P 500 Covered Call ETF (XYLD) – is attracting a lot of money from investors. It has a current yield of
about 6.3%.
Here is the total-return comparison with dividends reinvested:
XYLD has achieved about 80% of the total returns of the S&P 500. Note also that XYLD’s total return (75%) is less than QYLD’s total return (94%) shown earlier over the same time period.
(3) QQQ itself
Since QYLD uses the NASDAQ-100 as its stock portfolio, it’s fair to ask how QYLD’s returns compare to Invesco QQQ Trust (QQQ), the ETF that tracks that same portfolio without embellishments. QQQ’s
current yield is about 0.5%.
Here’s the total return comparison with dividends reinvested:
QYLD, even accounting for dividends and reinvesting them, has barely exceeded ¼ of the total returns of the same index of stocks that it invests in. That is an extreme example of the foregone price
returns from applying a covered-call strategy to a portfolio of high-flying stocks. QQQ has been on an almost continuous bull-market run since 2009.
Again, however, remember that to generate income, if you need it, you would need to continually trim QQQ shares and realize the paper gains. Every time you trim, you would reduce future gains,
because you would own fewer shares.
(4) Closed-End fund
As I said earlier, I was surprised to discover the proliferation of covered-call ETFs that are available to investors. I usually associate that kind of strategy with closed-end funds (CEFs).
There is not space here to get into how CEFs operate. Suffice it to say, they too are designed to “convert” total returns into income for investors, and some of them use covered-call strategies to do
And, lo and behold, one of them uses a covered-call strategy on the NASDAQ-100, just as QYLD does. It is Nuveen NASDAQ 100 Dynamic Overwrite Dividend (QQQX). Quick facts about it:
• Introduced in 2007
• Designed to offer regular distributions by replicating the price movements of the NASDAQ 100 Index, as well as selling call options on an average of 55% of the Fund’s equity portfolio. (Remember
that applying covered calls to about 50% of a portfolio garners half the premium income but also allows participation in about half the upside of the underlying stocks.)
• Pays quarterly
• Current yield = 6.2%
• Payouts are much smoother
This chart shows QQQX’s payouts since inception.
Because QQQX applies the covered-call strategy to about half of its portfolio, we would expect its total returns to be about 2x better than QYLD’s. That’s the payoff for generating about half the
yield that QYLD generates. QQQX sells covered calls on about 55% of its holdings, which allows it to participate in more price upside.
As you can see, the Nuveen CEF almost doubles QYLD’s total return performance while yielding about half as much (12% to 6%).
Summarizing Everything
I know this is a long report, so to make everything more understandable, here is a summary of the results:
What are the takeaways?
1. Total returns tend to be inversely related to yield: Higher yields tend to be associated with lower total returns and vice-versa. If you need income and don’t get much from organic yield, you
will need to generate it by selling shares; you need to hope that the pace of positive returns exceeds your pace of selling shares off.
2. QYLD forfeits a great deal of price return, and therefore of total return, in exchange for the income generated through the covered-call strategy.
3. That said, QYLD’s income is significant: Figure on 10-12% yield most of the time.
4. QYLD generates income from a selection of stocks (mostly tech stocks) that normally do not provide much income. Thus, an investment in QYLD could be seen as a way for an income-focused investor
to diversify risk by participating in a sector that usually provides little in the way of dividends. However, much of the potential upside of that sector is lost because of the covered-call
strategy, so the historical benefit of holding lots of tech stocks is mostly wiped out.
5. QYLD pays monthly, which some investors will find attractive. The payments can vary significantly month-to-month.
QYLD’s Possible Role in a Dividend Growth Portfolio
Most dividend-growth investors understand that high yields usually accompany slow growth. For example, Verizon (VZ), which is high-yield as dividend-growth stocks go (4.7%) has slow dividend growth
(2% per year over the past five years). Its price doesn’t grow very much either.
But high yields have the obvious charm of the copious dividends themselves. That money can be used to reinvest back into the stock or fund that pays it, which turbo-charges portfolio growth by adding
more shares even without adding new money. Similarly, one can reinvest that dividend money into other stocks that have high quality, decent yields, better growth rates, and other attractive
If one needs the income for living expenses – which may be the case with some retirees – the attractiveness of the high yield expands. In that case, you are not reinvesting the dividends, you are
living off them. The concept of “converting” some of the fund’s total return into regular dividends can be very attractive, because you don’t have to sell shares to generate cashflow for living
It is hard to value an ETF, because of all the moving parts. At the current time, Morningstar values QYLD’s current price as fair, with a valuation ratio of 1.05 (meaning 5% overvalued).
As shown below (purple line), QYLD has generally traded in the $20-25 range for the past several years except for the Covid crash last year. Yield and price are inversely related, so the lower the
price you buy QYLD at, the higher the yield (orange line) you’ll get on the purchase.
For a rule of thumb, you might want to limit purchases to when QYLD’s yield is 11% or 11.5% or above. If you were to buy $10,000 worth of QYLD at 11.5% yield, that would produce $1150 in dividend
income in a year, assuming the payments stayed relatively steady.
Lastly, most distributions by covered call funds are not qualified dividends under tax law. The tax implications of this sort of income are too complex to cover here, but note that most of QYLD’s
income does not qualify for lower tax rates that apply to the dividends from common dividend-growth companies such as JNJ and VZ. That said, it may be “return of capital” that lowers your cost basis
and delays taxes until you sell the shares. Global X advises that “Particularly tax-sensitive investors may want to consider holding covered call ETFs in a tax-advantaged account or consult with a
tax accountant prior to investing.”
This is not a recommendation to buy, hold, sell, trim, or add to QYLD. Any investment requires your own due diligence. Always be sure to match your stock and fund picks to your personal financial
— Dave Van Knapp | {"url":"https://dailytradealert.com/qyld-yields-11-5-pays-monthly-and-is-a-buy-right-now/","timestamp":"2024-11-08T12:30:51Z","content_type":"text/html","content_length":"90987","record_id":"<urn:uuid:3824460a-d09f-4a36-9097-8cdbfabda518>","cc-path":"CC-MAIN-2024-46/segments/1730477028059.90/warc/CC-MAIN-20241108101914-20241108131914-00052.warc.gz"} |
How can you convert centimeters to millimeters? | Socratic
How can you convert centimeters to millimeters?
1 Answer
Quick Answer: Multiply by 10.
To do any conversion, you find the relationship between the two units.
In this case,
$\text{100 cm" = "1 m}$ and $\text{1000 mm" = "1 m}$
$\text{100 cm" = "1000 mm}$ or $\text{1 cm" = "10 mm}$
This gives you two conversion factors:
$\text{1 cm"/"10 mm}$ and $\text{10 mm"/"1 cm}$
and if you look at the equation, you'll see that
$\text{1 cm"/"10 mm}$ = $\text{10 mm"/"1 cm} = 1$
Convert 3.1 cm into millimetres.
You multiply by a conversion factor: $\text{1 cm"/"10 mm}$ or $\text{10 mm"/"1 cm}$.
Choose the one that gives you the correct units for the answer.
#3.1 cancel("cm") × "10 mm"/(1 cancel("cm")) =" 31 mm"#
Note that the "cm" cancels out and leaves you with the answer in “mm”. If you had chosen the other conversion factor, you would have gotten
$\text{3.1 cm" × "1 cm"/"10 mm" = "0.31 cm"^2"/mm}$
The strange units for the answer tell you that you have made a mistake.
If you can’t remember that $\text{1 cm" = "10 mm}$, you can always use the definitions of milli and centi:
$\text{milli} = {10}^{-} 3$; so $\text{1 mm" = 10^-3 "m}$
$\text{centi } = {10}^{-} 2$, so $\text{1 cm" = 10^-2 "m}$
Then you can convert “cm” to “m” and “m” to “mm”.
#3.1 cancel("cm") × (10^(-2) cancel("m"))/(1 cancel("cm")) × "1 mm"/(10^(-3) cancel("m")) = "31 mm"#
It's an extra step, but it always works.
Impact of this question
43277 views around the world | {"url":"https://api-project-1022638073839.appspot.com/questions/how-can-you-convert-centimeters-to-millimeters","timestamp":"2024-11-05T22:17:41Z","content_type":"text/html","content_length":"37354","record_id":"<urn:uuid:9aa1c76e-3cab-45de-a1ed-bbc31f392a14>","cc-path":"CC-MAIN-2024-46/segments/1730477027895.64/warc/CC-MAIN-20241105212423-20241106002423-00087.warc.gz"} |
My Review of SubjectMath.com
I actually went ahead and bought the practice tests (hey more material is always good right?) and I have previewed his course, so I figured you all could use a review of the materials --- especially
with the rather hefty price tag!
First, the practice tests themselves. While the material is in fact very thorough and does cover the same topics, it would be a lie to say that it's as closely aligned with the test as is advertised.
Most math subject GRE's start off with (relatively) easy and routine problems, and generally build gradually in difficulty; on the other hand, SubjectMath.com's tests are designed so that almost
every question needs a "trick" to solve it in any reasonable amount of time. Have to find a double integral under a plane? Gotcha! Just use the volume formula for a pyramid. Horrible Riemann sum?
Gotcha! Just turn it into log(n)/n which goes to zero. Tricks are good to have, yes, but you don't need them for the entire test. In addition, the problems are worded in a much more verbose manner,
with gratuitous notation and obfuscated expressions thrown in just to confuse you (reminds me of math competitions a bit). As a side note, the author is in serious need of an editor (e.g. "aspires to
zero", "devisable by", "hight of 2") --- not that it takes away from the actual content, but it does take away a bit from the professionalism.
Also, after skimming through the online modules, I would say the only ones that are worthwhile are the Additional Topics and Advanced modules. There's a LOT of good stuff in those, especially the
Advanced one. Most of the other stuff you can figure out yourself with a bit of Wikipedia searching for basic facts, or is already covered in the existing books. (Hint: Learn everything you can about
eigenvalues and rings. Ever.
tl;dr: While the tricks presented are definitely valuable if you already have a high score and want to raise it by those elusive last few points, it's not really correct to say that the material is
representative of the GRE subject test as a whole.
Last edited by DMAshura on Thu Sep 03, 2015 7:15 pm, edited 1 time in total.
Re: My Review of SubjectMath.com
Thanks a lot for this! Much appreciated. How would you rank the available review materials out there? Would this be close:
1. ETS Practice Tests 0568, 1268
2. Undergrad Textbooks (Stewart, Dummit, Insel)
3. Princeton Review
4. ETS Practice Tests 8767, 9367, 9768 (Too Easy)
5. Subjectmath.com
6. REA Mathematics (Too Difficult)
Re: My Review of SubjectMath.com
I would put Subjectmath.com as a tie with 87/93/97 for #4 and REA as #5. Both 87/93/97 and Subjectmath.com are off the mark in terms of difficulty --- just each in a different direction. They're both
good practice, but not to be taken as representative. But also yes, Subjectmath.com is leagues better than REA.
Re: My Review of SubjectMath.com
No offense, but why are you buying all this crap? You've already taken it multiple times and gotten a pretty high score, right?
Re: My Review of SubjectMath.com
I tutor students who are going to be taking the math GRE, so I try to keep current with the test and the materials that are out there.
Re: My Review of SubjectMath.com
Thanks for reviewing. A while back I found a pdf that Charlie Marshak put together with problems he pulled from all over the place as well as a solutions doc. And like you say, many of them are trick
problems that are not that representative of the real thing; BUT, it's free, so why not! The solutions are a bit sloppy and careless and have some errors in some places for sure, but in general
enough hints to go on.
http://www.math.ucla.edu/~cmarshak/GREB ... oblems.pdf
http://www.math.ucla.edu/~cmarshak/GREB ... utions.pdf | {"url":"https://mathematicsgre.com/viewtopic.php?f=1&t=3511","timestamp":"2024-11-12T03:01:51Z","content_type":"text/html","content_length":"31287","record_id":"<urn:uuid:141b23b7-1885-443f-8883-8c9d4d8d00db>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.50/warc/CC-MAIN-20241112014152-20241112044152-00822.warc.gz"} |
6) Considering that the aircraft with the following characteristics on
6) Considering that the aircraft with the following characteristics only makes a pitching motion: a) Write the linearized differential equation in matrix format for fixed rudder. (Za=0) Ax=AAx b)
Find the
undamped natural frequency. c) If the solution of the characteristic equation is as follows, λ=-0.020±0.1954i Find the period and damping ratio. d) For initial values = 0,ȧ, Irad/s, solve a(t). a(t)=
e" (c, cost+c₂ sin cot) e) Draw the graph of change in angle of attack with time.
Fig: 1 | {"url":"https://tutorbin.com/questions-and-answers/6-considering-that-the-aircraft-with-the-following-characteristics-only-makes-a-pitching-motion-a-write-the-linearized","timestamp":"2024-11-11T10:05:59Z","content_type":"text/html","content_length":"61961","record_id":"<urn:uuid:b6002932-095c-4543-9591-13be85c2ba8d>","cc-path":"CC-MAIN-2024-46/segments/1730477028228.41/warc/CC-MAIN-20241111091854-20241111121854-00059.warc.gz"} |
Visual Basic 2012 Lesson 25– Drawing Polygon and Pie - Visual Basic Tutorial
Visual Basic 2012 Lesson 25– Drawing Polygon and Pie
We have learned how to draw rectangle, ellipse, circle and text in the preceding chapters, now let’s learn how to draw polygons on the screen. Besides that, we shall also learn how to draw pie.
25.1: Drawing Polygons
Polygon is a closed plane figure bounded by three or more straight sides. In order to draw a polygon on the screen, we need to define the coordinates of all the points (also known as vertices) that
joined up to form the polygon.
The syntax to defines the points of a polygon with vertices A1, A2, A3, A4…….An is as follows;
Dim A1 As New Point(X1,Y1)
Dim A2 As New Point(X2,Y2)
Dim A3 As New Point(X3,Y3)
Dim A4 As New Point(X4,Y4)
Dim An as New Point(Xn,Yn)
After declaring the points, we need to define a point structure that group all the points together using the following syntax:
Dim myPoints As Point() = {A1, A2, A3,....,An}
.Finally, create the graphics object and use the DrawPolygon method to draw the polygon using the following syntax:
Dim myGraphics As Graphics = Me.CreateGraphics
myGraphics.DrawPolygon(myPen, myPoints)
where myPen is the Pen object created using the following syntax:
myPen = New Pen(Drawing.Color.Blue, 5)
Example 25.1 Drawing a Triangle
A triangle is a polygon with three vertices. Here is the sample code:
Dim myPen As Pen
Dim A As New Point(10, 10)
Dim B As New Point(100, 50)
Dim C As New Point(60, 150)
Dim myPoints As Point() = {A, B, C}
myPen = New Pen(Drawing.Color.Blue, 5)
Dim myGraphics As Graphics = Me.CreateGraphics
myGraphics.DrawPolygon(myPen, myPoints)
Running the program produces the image below:
Example 25.2: Drawing a Quadrilateral
A quadrilateral is a polygon consist of four sides, so you need to define four vertices. The following is the code:
Dim myPen As Pen
Dim A As New Point(10, 10)
Dim B As New Point(100, 50)
Dim C As New Point(120, 150)
Dim D As New Point(60, 200)
Dim myPoints As Point() = {A, B, C, D}
myPen = New Pen(Drawing.Color.Blue, 5)
Dim myGraphics As Graphics = Me.CreateGraphics
myGraphics.DrawPolygon(myPen, myPoints)
The output image is as shown below:
25.2: Drawing Pie
In order to draw a pie, you can use the DrawPie method of the graphics object. As usual, you need to create the Graphics and the Pen objects. The syntax for drawing a pie is:
myGraphics.DrawPie(myPen, X, Y, width,height, StartAngle, SweepAngle)
Where X and Y are the coordinates the bounding rectangle, other arguments are self-explanatory. Both StartAngle and SweepAngle are measured in degree. SweepAngle can take possible or negative values.
If the value is positive, sweeps through clockwise direction while negative means it sweep through anticlockwise direction.
Example 25.3
Drawing a pie that starts with 0 degrees and sweeps clockwise through 60 degrees.
Dim myPen As Pen
myPen = New Pen(Drawing.Color.Blue, 5)
Dim myGraphics As Graphics = Me.CreateGraphics
myGraphics.DrawPie(myPen, 50,50, 150,150,0,60)
The output image is as shown below: | {"url":"https://www.vbtutor.net/index.php/visual-basic-2012-lesson-25/","timestamp":"2024-11-09T19:55:53Z","content_type":"text/html","content_length":"47959","record_id":"<urn:uuid:c4593b9a-1f31-4a88-b558-7a6f272bfd1a>","cc-path":"CC-MAIN-2024-46/segments/1730477028142.18/warc/CC-MAIN-20241109182954-20241109212954-00889.warc.gz"} |
Eigenvalues, Eigenvectors: Stable Vectorial Planes
Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
This lecture covers the concept of stable vectorial planes, where a function f is given from R³ to R³ along with a subspace V of R³. It discusses the proposition that a vector is an eigenvector of A
if and only if it is not a multiple of another vector in V. The lecture also explores the properties of the transpose of A, such as having the same trace, determinant, and characteristic polynomial.
Various equations and proofs are presented to illustrate the stability of vectorial planes under the given function.
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website.
Please make sure to verify the information with EPFL's official sources. | {"url":"https://graphsearch.epfl.ch/en/lecture/0_89riqac4","timestamp":"2024-11-09T20:55:33Z","content_type":"text/html","content_length":"109505","record_id":"<urn:uuid:510008cf-68ce-4040-92ef-50448487a1f6>","cc-path":"CC-MAIN-2024-46/segments/1730477028142.18/warc/CC-MAIN-20241109182954-20241109212954-00138.warc.gz"} |
MathSciDoc: An Archive for Mathematician
We introduce a pictorial approach to quantum information, called holographic software. Our software captures both algebraic and topological aspects of quantum networks. It yields a bi-directional
dictionary to translate between a topological approach and an algebraic approach. Using our software, we give a topological simulation for quantum networks. The string Fourier transform (SFT) is our
basic tool to transform product states into states with maximal entanglement entropy. We obtain a pictorial interpretation of Fourier transformation, of measurements, and of local transformations,
including the n-qudit Pauli matrices and their representation by Jordan-Wigner transformations. We use our software to discover interesting new protocols for multipartite communication. In summary,
we build a bridge linking the theory of planar para algebras with quantum information. | {"url":"https://archive.ymsc.tsinghua.edu.cn/pacm_category/0129?show=time&size=3&from=5&target=searchall","timestamp":"2024-11-03T02:38:19Z","content_type":"text/html","content_length":"62569","record_id":"<urn:uuid:a8925833-7224-4285-9a45-f3e94cbe551d>","cc-path":"CC-MAIN-2024-46/segments/1730477027770.74/warc/CC-MAIN-20241103022018-20241103052018-00696.warc.gz"} |
FLASH Code
The FLASH code is a modular, adaptive, parallel simulation code capable of handling general compressible flow problems in astrophysical environments. It has been designed to allow users to configure
initial and boundary conditions, change algorithms, and add new physical effects with minimal effort. It uses the PARAMESH library to manage a block-structured adaptive grid, placing resolution
elements only where they are needed most. It uses the Message-Passing Interface (MPI) library to achieve portability and scalability on a variety of different message-passing parallel computers.
Available via
Operating Systems
Programming Languages | {"url":"https://orms.mfo.de/project@all_keywords=1&terms=networks&id=277.html","timestamp":"2024-11-04T11:11:02Z","content_type":"application/xhtml+xml","content_length":"10841","record_id":"<urn:uuid:aaa2ece3-f77a-4e64-9f92-5a90206ec7f6>","cc-path":"CC-MAIN-2024-46/segments/1730477027821.39/warc/CC-MAIN-20241104100555-20241104130555-00616.warc.gz"} |
Category: algorithms Component type: function
template <class ForwardIterator, class Predicate, class T>
void replace_if(ForwardIterator first, ForwardIterator last, Predicate pred
const T& new_value)
Replace_if replaces every element in the range [first, last) for which pred returns true with new_value. That is: for every iterator i, if pred(*i) is true then it performs the assignment *i =
Defined in the standard header algorithm, and in the nonstandard backward-compatibility header algo.h.
Requirements on types
• ForwardIterator is a model of Forward Iterator.
• ForwardIterator is mutable.
• Predicate is a model of Predicate.
• ForwardIterator's value type is convertible to Predicate's argument type.
• T is convertible to Forward Iterator's value type.
• T is Assignable.
• [first, last) is a valid range.
Linear. Replace_if performs exactly last - first applications of pred, and at most last - first assignments.
Replace every negative number with 0.
vector<int> V;
replace_if(V.begin(), V.end(), bind2nd(less<int>(), 0), 0);
assert(V[1] == 0 && V[3] == 0);
See also
replace, replace_copy, replace_copy_if
STL Main Page | {"url":"http://ld2014.scusa.lsu.edu/STL_doc/replace_if.html","timestamp":"2024-11-12T08:48:40Z","content_type":"text/html","content_length":"5788","record_id":"<urn:uuid:19280ea9-f656-42a5-a138-e7cf7a4c535f>","cc-path":"CC-MAIN-2024-46/segments/1730477028249.89/warc/CC-MAIN-20241112081532-20241112111532-00622.warc.gz"} |
The Taub Faculty of Computer Science
Thursday, 07.11.2024, 15:30
Flow matching models, ODE-based generative models, generate samples by gradually morphing a simple source distribution into a target distribution. In practice, these models still fall short of
perfectly replicating the target distribution, mainly due to imperfections of the learned mapping. Previous work mainly focus on alleviating discretization error, which rises from sampling a
continuous trajectory with a finite number of steps. In this work we ...
[ Full version ]
Sunday, 17.11.2024, 18:30
You are Invited to Intel's practical Gen AI workshop. Registration: ...
[ Full version ]
Wednesday, 20.11.2024, 10:30
DNA data storage presents an efficient solution for archiving, though synthesis time and cost pose challenges.This seminar focuses on cyclic synchronized synthesis technologies like photolithography,
introducing performance metrics based on synthesis cycles.We extend prior work on channel capacity, achieving higher rates and capacities through improved encoding.Additionally, we analyze cost
bounds and explore alphabet sizes larger than the standard four, inspired by...
[ Full version ]
Thursday, 31.10.2024, 11:00
Mechanistic interpretability research seeks to explain the internal mechanisms that operate within AI models as they perform different tasks. A widely used strategy to uncover and analyze those
mechanisms is by identifying circuits within the model. A circuit is a sub-graph of the model’s computational graph, believed to be critical for executing a specific task. In recent years, several
methods have been proposed for automaticall...
[ Full version ]
Tuesday, 15.10.2024, 11:00
Machinery for data analysis often requires a numeric representation of the input. Towards that, a common practice is to embed components of structured data into a high-dimensional vector space. We
study the embedding of the tuples of a relational database, where existing techniques are often based on optimization tasks over a collection of random walks from the database. The focus of this
paper is on the recent FoRWaRD algorithm that is designed for...
[ Full version ]
Sunday, 13.10.2024, 10:30
Suppose that n forecasting experts are providing daily rain/no-rain predictions, and the best among them is mistaken in at most k many days. For how many days will an optimal learner allowed to
observe the predictions mis-predict? This is a fundamental problem in online learning, and other important classification problems can be reduced to it. It was studied in the 90’s by Cesa-Bianchi,
Freund, Helmbold, and Warmuth who gave fine-grained bounds for the case where the lea...
[ Full version ]
Sunday, 13.10.2024, 10:30
Suppose that n forecasting experts are providing daily rain/no-rain predictions, and the best among them is mistaken in at most k many days. For how many days will an optimal learner allowed to
observe the predictions mis-predict? This is a fundamental problem in online learning, and other important classification problems can be reduced to it. It was studied in the 90’s by Cesa-Bianchi,
Freund, Helmbold, and Warmuth who gave fine-grained bounds for the case where the lea...
[ Full version ]
Wednesday, 09.10.2024, 10:30
Motion planning is a central challenge in robotics, with learning-based approaches gaining significant attention in recent years. This thesis focuses on a specific aspect of these approaches: using
machine-learning techniques, particularly Support Vector Machines (SVM), to evaluate whether robot configurations are collision-free, an operation termed "collision detection". Despite the growing
popularity of these methods, there is a lack of theoretical guarantees supporting their...
[ Full version ]
Tuesday, 24.09.2024, 19:00
According to the instructions from the Home Front Command, we regret to inform that we must postpone the excellence ceremony scheduled for Tuesday, September 24, 2024. We will provide further details
later. We all hope for better and quieter days....
[ Full version ]
Monday, 23.09.2024, 17:00
Graduation Ceremony Monday, September 23, 2024 Lev HaCampus 17:00 Technion Ceremony 19:00 Gathering and Refreshments 20:00 Ceremony Begins Parking is available on a first-come, first-served basis.
The number of guests is limited to 4 due to space constraints....
[ Full version ]
Wednesday, 18.09.2024, 14:30
The algorithmic study of the principal-agent framework is an emerging frontier for algorithmic game theory. We extend this model by incorporating knapsack constraints to capture real-world resource
limitations. To address the computational challenges arising from these constraints, we develop approximation algorithms that guarantee near-optimal outcomes for both the principal and agents. Our
research contributes to the understanding of contract desi...
[ Full version ]
Prof. Yuliy Baryshnikov (University of Illinois at Urbana-Champaign)
Wednesday, 18.09.2024, 11:30
Hyperbolic Geometry of Google Maps:Navigation of the Google Maps (not to confuse with *driving with* Google Maps) on smartphones is perhaps the most intuitive and efficient UI in existence, – and the
reason, as I will show, is the underlying structure of the 3D hyperbolic space.Professor Yuliy Baryshnikov’s short bio is here...
[ Full version ]
Sunday, 15.09.2024, 16:00
How can two parties jointly sample from a source of correlated randomness (X,Y), say two hands of cards in a poker game, without leaking any extra information? This secure sampling question is
strongly motivated by the design of efficient protocols for secure computation, allowing the two parties to compute a function of their secret inputs without revealing their inputs to each
other.While there has been major progress on securely sampling some useful correlations, others ...
[ Full version ]
Wednesday, 11.09.2024, 11:30
Deep neural networks are successful in various tasks but are also susceptible to adversarial examples: malicious input perturbations designed to deceive the network. Many adversarial attacks on image
classifiers involve making imperceptible changes bounded by a small ε with respect to an Lₚ norm (e.g., p = 0, 1, 2, ∞), by a small interval neighborhood, or by semantic feature perturbations, such
as adjustments in brightness, translation, or rotation. To unde...
[ Full version ]
Monday, 09.09.2024, 18:00
Information Session for students who interested in advanced degrees in Artificial Intelligence and Machine Learning Whether you're contemplating how to enter the field and unsure where to start, or
if you've already completed a Master's degree and are considering starting a PhD, we invite you to join us! Date: Monday, September 9th at 6:00 PMProgram: Scientific lectures, student panel, and
mingling. ...
[ Full version ]
Wednesday, 04.09.2024, 11:30
The emerging paradigm of in-network computing leverages programmable network hardware, such as switches, to enhance the performance, reliability, and functionality of distributed systems.
Traditionally, networks in distributed systems have been treated merely as conduits for data, with limited assumptions about their capabilities. However, by introducing higher-level abstractions that
utilize the potential of programmable network devices, significant improvements in distributed...
[ Full version ]
Wednesday, 04.09.2024, 10:30
Unsupervised latent variable models serve as highly effective tools for representing complex data such as images or videos, relevant for applications such as robotic manipulation, video generation,
novelty detection, and many more. Variational Autoencoders (VAEs) provide compact latent representations with stability and efficiency. In this talk, we will explore modern VAEs that mitigate
shortcomings of classical approaches such as blurry images, and can be used as a basis for s...
[ Full version ]
Monday, 02.09.2024, 14:30
Traditional discriminative Machine-Learning approaches often formulate problems as optimization of a parameterized function mapping from a given input space to some desired output space. While this
formulation is applicable to many theoretical and practical problems, it is inherently reliant on the assumption that the dataset X is constant. The world around us is abundant with scenarios where
this is either not the case, or where dropping this a...
[ Full version ]
Sunday, 01.09.2024, 11:30
Metric theory offers powerful tools for analysing and processing shapes on curved manifolds, with Riemannian metrics being the most commonly used due to their simplicity and success in many
applications. However, Riemannian metrics are limited by their symmetric nature, where lengths of paths are independent of traversal direction. Finsler metrics, a generalisation including asymmetric
distances, provide broader tools but are rarely applied in practice, perhaps due to their the...
[ Full version ]
Wednesday, 28.08.2024, 15:30
Automated deductive reasoning plays an important role in software verification, optimization, and mathematical theorem discovery. This talk explores novel applications and extensions of equality
saturation, a technique for efficiently representing and manipulating large sets of equivalent expressions, to enhance automatic deductive reasoning across various domains.In this talk, we present a
collection of three works: A symbolic theory exploration system, dubbed Thes...
[ Full version ]
Tuesday, 27.08.2024, 13:00
This talk will cover two topics:First, we suggest a new interpretation of Spearman correlation using k-subset permutations. We characterize the distribution of the Spearman correlation of a
permutation that starts with the identity permutation over n elements and is perturbed by uniformly shuffling a random subset of k indices. We present some key aspects of this distribution, including
its expected value and variance for every k between 1 and n. We then generalize it to an...
[ Full version ]
Tuesday, 27.08.2024, 11:00
In this talk, I will present topics from my PhD work. The talk consists of three topics:Feature selection is a core process in building machine learning models. It is often essential for optimizing
performance and sometimes essential to support practical use, such as when the number of features to be measured in the execution stage is limited by hardware or other factors. We examined the
procedure in challenging situations: feature selection on ...
[ Full version ]
Friday, 23.08.2024, 11:30
Diagnosing Crohn's Disease (CD) typically involves examining 2D slices from magnetic resonance enterography (MRE). However, the anisotropic resolution of MRE complicates precise 3D measurements and
visualization. The absence of automated 3D measurement systems further complicates assessment. Previous methods for generating isotropic volumes from anisotropic data often rely on extensive 3D data
and focus solely on interslice ...
[ Full version ]
Wednesday, 21.08.2024, 17:30
The rapid growth of data-intensive applications and high-speed I/O devices has led to increasing demands on I/O performance in both virtualized cloud environments and bare metal setups. But existing
systems struggle to fully exploit the potential of modern hardware due to inefficiencies at various I/O stack layers. This thesis presents three novel techniques that optimize I/O performance across
virtualized and bare metal environments: IOctopus, cint...
[ Full version ]
Tal Yankovitz (Tel Aviv University)
Wednesday, 21.08.2024, 13:00
A q-locally correctable code (LCC) C:{0,1}^k->{0,1}^n is a code in which it is possible to correct every bit of a (not too) corrupted codeword by making at most q queries to the word. The cases in
which q is constant are of special interest, and so are the cases that C is linear. In a breakthrough result Kothari and Manohar (STOC 2024) showed that for linear 3-LCC n=2^Ω(k^1/8) . In this work
we prove that n=2^Ω(k^1/4) . As Reed-Muller codes yield 3-...
[ Full version ]
Wednesday, 21.08.2024, 12:30
Hello everyone, We are pleased to invite you to the annual projects fair of the Taub Faculty of Computer Science, along with the Outstanding Project competition—Wednesday, August 21, starting at
12:30 PM in the Taub Lobby - Floor 0. Everyone is welcome to support the competing teams and be impressed by significant and creative projects. We look forward to seeing you!...
[ Full version ]
Wednesday, 21.08.2024, 10:30
Geometric Deep Learning attempts to apply deel learning methodlogies to domains where a grid structure doesn't exit. We advocate for using principled methods to define the primitives of these
networks. As such we define networks that stem from the symmetries of geometric representations, And show how analyzing some of these primitives spectrally reveals that combining allows for SOTA
performance. This is finally complemented by the introduction of a suite of identity losses tha...
[ Full version ]
Ben Finkelshtein (University of Oxford)
Tuesday, 20.08.2024, 11:30
Graph neural networks are popular architectures for graph machine learning, based on iterative computation of node representations of an input graph through a series of invariant transformations. A
large class of graph neural networks follow a standard message-passing paradigm: at every layer, each node state is updated based on an aggregate of messages from its neighborhood. In this work, we
propose a novel framework for training graph neural networks, where every node is view...
[ Full version ]
Thursday, 15.08.2024, 10:50
Did you do an innovative, interesting, groundbreaking project? You are invited to apply at the link: https://tinyurl.com/cs-projects24 Apply by August 15, 2024 The final phase will take place on
August 21, 2024 - noon on Wednesday, in the format of a project fair - the participation of the contestants is mandatory. The...
[ Full version ]
Wednesday, 14.08.2024, 19:00
Invitation to Band Night You are invited to Band Night of the Faculty of Computer Science!!Talented students and faculty members from our department will perform in a variety of musical ensembles and
styles. Join us for an unforgettable evening of live performances and amazing energy. Wednesday, August 14th at 7:00 PM on the Taub Terrace. There are sheltered areas, excellent air quality, so get
your strings ready – entrance is free!...
[ Full version ]
Monday, 12.08.2024, 12:30
The field of information design studies strategic information revelation by a certain sender to receivers. The Bayesian persuasion model, introduced by Kamenica and Gentzkow, assumes that the sender
can trustworthily commit to a randomized information revelation policy, called a signaling scheme. In contrast, the cheap talk model assumes that the sender does not have such a commitment power. The
research focuses on optimizing the sender’s util...
[ Full version ]
Thursday, 08.08.2024, 13:30
A sequence of recent works, concluding with Mu et al. (Eurocrypt, 2024) has shown that every problem $\Pi$ admitting a non-interactive statistical zero-knowledge proof (NISZK) has an efficient
zero-knowledge \emph{batch verification} protocol. Namely, an NISZK protocol for proving that $x_1, \dots, x_k \in \Pi$ with communication that only scales poly-logarithmically with $k$. A caveat of
this line of work is that the prover runs in exponential-time, whereas for NP problems it ...
[ Full version ]
Shir Landau Feibish (The Open University)
Wednesday, 07.08.2024, 11:30
Collecting network telemetry is essential for detecting problems in the network. In recent years we have seen an abundance of research on network telemetry in the data plane. Many of these solutions
analyze traffic continuously over a long period of time, while resetting the structure from time to time. If shorter time intervals are needed, sliding windows are usually used, yet these incur
significant resource and management overhead. However, often in order to unders...
[ Full version ]
Tuesday, 06.08.2024, 18:30
Taub balcony + the transparent hall in the student house
The Computer Science Student Council brings you the "The Good, the Bad and the Ugly" festivalTuesday, August 66:30 p.m. Lecturers pour beers, free food and drink, karaoke and surprises (admission for
students from MDAMH only), on the Taub terrace.9:00 p.m. party in the transparent hall (with ticket presentation only) The event is sponsored by Plus500...
[ Full version ]
Tuesday, 06.08.2024, 11:00
Statistical enrichment tools are highly useful in biological research. Current approaches to statistical enrichment in ranked or ordered lists such as, for example, GSEA and GOrilla, are limited to
the suffix (prefix) of the list. These methods assess extreme density of 1s in binary vectors on either side. Statistical significance can be assigned using, e.g, Wilcoxon Rank Sum and mHG
statistics.In this work we extend the mHG approach to also add...
[ Full version ]
Tuesday, 06.08.2024, 10:00
Modern programming languages rely on advanced and intricate type systems.Expressive type systems support more language features but often result in unexpected language capabilities. For example, we
know that the Java type system is Turing complete, which means it is so complex that Java compilers cannot guarantee termination. But a powerful type system can also be a blessing in disguise. Over
the years, crafty programmers found wa...
[ Full version ]
Yoel Shkolnisky (Tel Aviv University)
Monday, 05.08.2024, 15:30
Detecting unknown objects in noisy data is a key task in many problems. A natural model for the unknown objects is the linear subspace model, which assumes that the objects can be expanded in some
known basis (such as the Fourier basis). In this talk, I will present an object detection algorithm that under the linear subspace model is asymptotically guaranteed to find all objects while making
only a small percentage of false discoveries. We demonstrate our derivations for the p...
[ Full version ]
Friday, 02.08.2024, 10:00
Do you know someone who wants to do something big? Orientation day for a bachelor's degree in the Faculty of Computer Science at the Technion is approaching and you are all invited! Friday 2.8 |
Sharona, Tel Aviv For more details and to register: ...
[ Full version ]
Tuesday, 30.07.2024, 14:30
The computations required for deep learning research have been doubling every few months, resulting in an estimated 5,000x increase from 2018 to 2022. This trend has led to unprecedented success in a
range of AI tasks. In this talk I will discuss a few troubling side-effects of this trend, touching on issues of lack of inclusiveness within the research community, and an increasingly large
environmental footprint. I will then present Green AI – an ...
[ Full version ]
Tuesday, 30.07.2024, 10:00
Famously, multiset neural networks based on sum-pooling can separate all distinct multisets, and as a result can be used by message passing neural networks (MPNNs) to separate all pairs of graphs
that can be separated by the 1-WL graph isomorphism test. However, the quality of this separation may be very weak, to the extent that the embeddings of "separable" multisets and graphs might even be
considered identical when using fixed finite pre...
[ Full version ]
Sunday, 28.07.2024, 18:30
The CTF Technipwn group invites you to a special guest lecture:RingHopper - the SMM weaknesses we found in billions of devices - a security researcher from Intel An attacker who manages to penetrate
the SMM mode can bypass almost any security mechanism, steal confidential information, install malware, and even disable the entire system. In this lecture, security researcher Benny Seltzer from
Intel will present a study presented at the international DEFCON conference, we wil...
[ Full version ]
Wednesday, 24.07.2024, 14:30
This paper studies two problems that are motivated by the novel recent approach of composite DNA that takes advantage of the DNA synthesis property which generates a huge number of copies for every
synthesized strand. Under this paradigm, every composite symbols does not store a single nucleotide but a mixture of the four DNA nucleotides. In the first problem, our goal is study how to carefully
choose a fixed number of mixtures of the DNA nucleotides such that the decoding prob...
[ Full version ]
Arnold Filtser (Bar-Ilan university)
Wednesday, 24.07.2024, 12:45
A partition mathcal{P} of a metric space (X,d_X) is (sigma,tau,Delta)-sparse if each cluster has a diameter at most Delta, and every ball of radius Delta/sigma intersects at most tau clusters. In
this talk, we will explore the construction and different applications of sparse partitions in their various forms over the years. As time allows, we will discuss applications to: Universal TSP,
Steiner point removal, universal Steiner tree, and facility location....
[ Full version ]
Wednesday, 24.07.2024, 11:00
In LLMs, the ability to update factual knowledge of the model is an important and attractive ability, due to the need to deal with everchanging nature of information in the world. However, predicting
whether an edit applied to a LLM will be successful or not is difficult. In this work, we suggest two metrics that can predict the editing success: (1) where the knowledge is stored in the parameters
as reflected by the logit-lens technique; (2) the proba...
[ Full version ]
Monday, 22.07.2024, 19:00
Please register here: https://docs.google.com/forms/d/e/1FAIpQLSe8pYE1eVqgTK1xTf-4xyCEca4-bx12RuXtkXMcC5-4-ue_sQ/viewform ...
[ Full version ]
Noga Alon (Princeton and Tel Aviv University)
Monday, 22.07.2024, 15:30
"Noga Alon is being awarded the 2024 Wolf Prize for his profound impact on Discrete Mathematics and related areas." I will describe a recent joint work with Matia Bucic and Lisa Sauermann about the
investigation of extremal problems in discrete geometry for typical norms. The results include surprisingly tight solutions of the unit and distinct distances problems for typical norms, as well as a
determination of the chromatic number of the unit distance grap...
[ Full version ]
Wednesday, 17.07.2024, 13:00
Calling all Code Wizards! Ever wondered what it's like to be a software engineer at the heart of Google's innovation? Well, grab your coding wands and get ready to find out!Get a behind-the-scenes
look on how Google connects 2 billion daily users through the OneGoogle team....
[ Full version ]
Wednesday, 17.07.2024, 13:00
The talk will focus on the d-dimensional vector bin packing problem. The input for the problem is a set of items, each associated with a d-dimensional weight vector. The objective is to partition the
items into a minimal number of bins, such that the total weight of items in a bin is at most one in every dimension. The problem...
[ Full version ]
Wednesday, 17.07.2024, 09:30
Zoom Lecture:
& Computational Robotics Lab (CRL), 1st floor, Taub building
In this work we introduce the problem of task assistance planning where we are given two robots Rtask and Rassist. The first robot, Rtask, is in charge of performing a given task by executing a
precomputed path. The second robot, Rassist, is in charge of assisting the task performed by Rtask using on-board sensors. The ability of Rassist to provide assistance to Rtask depends on the
locations of both robots. Since Rtask is moving along its path, Rassist may also need to move to...
[ Full version ]
Tuesday, 16.07.2024, 13:00
Hardware Reverse Engineering (HRE) involves gate-level Netlist extraction and specification discovery, wherein graph-based methods play a crucial role in identifying sub-circuits. We propose a novel
approach for Subcircuit Recognition, essential for specification discovery in HRE, leveraging existing graph similarity kernels. Focusing on the reduced problem we formulate as Subgraph Localization,
we delineate two key components: graph similarity metr...
[ Full version ]
Tuesday, 16.07.2024, 11:30
Room 1061, Meyer Building
The rapid growth of generative models allows an ever-increasing variety of capabilities. Yet, these models may also produce undesired content suc...
[ Full version ]
Thursday, 11.07.2024, 16:30
Cryptocurrencies have gained popularity in recent years. They are often implemented on one or more of the over 1000 existing blockchain networks, including the popular Bitcoin and Ethereum networks.
Recently, various technologies known as blockchain interoperability have been developed to connect these different blockchains, creating an interconnected blockchain ecosystem. Interoperability
refers to the ability of blockchains to share information with each other. Decentralized Exc...
[ Full version ]
Shai Ben-David (University of Waterloo)
Wednesday, 10.07.2024, 13:00
Characterizing learnability by a combinatorial dimension is a hallmark of machine learning theory. Starting from the fundamental characterization of binary classification PAC by the VC-dimension,
through the characterization of online mistake bound learnability by the Littlestone dimension, all the way to recent papers characterizing multi-class learning and differential privacy. However, for
some basic learning setup no such characterizations have been provided. ...
[ Full version ]
Wednesday, 10.07.2024, 12:30
In this seminar, I will discuss two of my papers (published in ICLR 2023) on uncertainty estimation and class-out-of-distribution detection. We present a novel framework to benchmark the ability of
image classifiers to detect class-out-of-distribution (C-OOD) instances (i.e., instances whose true labels do not appear in the training distribution) at various levels of detection difficulty. We
apply this technique to ImageNet, and benchmark 500+ pretrained, publicly available, Image...
[ Full version ]
Wednesday, 10.07.2024, 12:30
First spotlight day of the semester!! Nvidia is coming to meet you in Taub Wednesday, July 10, between 12:30-2:30 PM in the Taub lobby In the program: a meeting with the recruitment team, the
engineers waiting for you!!...
[ Full version ]
Wednesday, 10.07.2024, 12:30
While language models (LMs) show impressive text manipulation capabilities, they also lack commonsense and reasoning abilities and are known to be brittle. In this talk, I will suggest a different
LMs design paradigm, inspired by how humans understand it. I will present two papers, both shedding light on human-inspired NLP architectures aimed at delving deeper into the meaning beyond words.
The first paper [1] accounts for the lack of commonsense and reasoning abilities by pr...
[ Full version ]
Roy Ganz - The Andrew and Erna Viterbi Faculty of Electrical & Computer Engineering
Tuesday, 09.07.2024, 11:30
Deep learning has revolutionized computer vision, achieving unprecedented performanc in tasks like classification and detection. However, these models are highly susceptible to adversarial attacks,
prompting the development of robust training methods. A notable outcome of such training is the phenomenon of Perceptually Aligned Gradients (PAG), where input gradients align semantically with human
perception. Our research explores both the practical and theoretical implications of...
[ Full version ]
Wednesday, 03.07.2024, 11:00
Message Passing Graph Neural Networks (MPGNNs) have emerged as the standard method for modeling complex interactions across diverse graph entities. While the theory of such models is widely
investigated, their aggregation module has not received sufficient attention. Sum-based aggregators have solid theoretical foundations regarding their separation capabilities. However, practitioners
often prefer using more complex aggregations and mixtures of diverse aggregations. In this resea...
[ Full version ]
Tuesday, 02.07.2024, 17:00
Technipwn Group flies you to Vegas!This August, the faculty CTF group is participating in the DEFCON conference in Las Vegas and invites you to join!This coming tuesday we will hold a competition
aimed at choosing the team that will fly to represent us at the conference.The topics of the competition are the usual topics of the ctf competitions such as: web, reverse, crypto, pwn and more!You
are invited to prepare and come to compete ...
[ Full version ]
Prof. Oded Margalit (Ben Gurion University)
Tuesday, 02.07.2024, 14:30
In this talk, we'll explore intriguing parallels between incorrect mathematical proofs and critical failures in technology, demonstrating their impact and lessons learned, like: 1. Mathematical
Proofs and Social Engineering: How hand-waving a mathematical proof is similar to social engineering, and why larger hardware implementations might surprisingly be more efficient. 2. Cybersecurity
and Mathematical Proofs: The surprising connection between a cyber attack that nearly caused a...
[ Full version ]
Monday, 01.07.2024, 14:00
Cycle-accurate simulations, frequently used by computer architects, incur substantial overheads. To mitigate this, recent virtual memory studies have adopted a lighter-weight methodology that
leverages partial simulations of only the memory subsystem. This approach feeds simulation outputs into a mathematical linear model to predict execution runtimes. While this methodology accelerates
the simulation process, its accuracy has traditionally been assumed rather than rigorously v...
[ Full version ]
Sunday, 30.06.2024, 18:30
Come be part of the Faculty's Capture The Flag - CTF group!! The faculty CTF group, Technipwn, holds bi-weekly meetings where we solve challenges, train for competitions and have fun The meetings are
suitable for both beginners and experienced participants, and are held on Sundays at Taub 9. Organized and managed by students, and intended for all students (not only from computer science!), with
and without CTF experience. The sessions include practical experience in solving chal...
[ Full version ]
Sunday, 30.06.2024, 14:30
As data storage challenges grow and existing technologies approach their limits, synthetic DNA emerges as a promising storage solution due to its remarkable density and durability advantages. While
cost remains a concern, emerging sequencing and synthetic technologies aim to mitigate it, yet introduce challenges such as errors in the storage and retrieval process. One crucial task in a DNA
storage system is clustering numerous DNA reads into groups that represent the original i...
[ Full version ]
Sunday, 30.06.2024, 14:30
The memory wall bottleneck is throttling the performance of data-intensive applications as the data transfer between the processing units (e.g., CPU, GPU cores) and the memory is significantly slower
than the compute itself. Therefore, emerging digital processing-in-memory systems overcome this bottleneck by performing parallel bitwise logic within the memory arrays themselves. This enables a
drastic reduction in data transfer for vectored operations since the same instruction may...
[ Full version ]
Sunday, 30.06.2024, 10:30
Computer systems that facilitate tight integration of data storage and processing can eliminate the "memory wall" and "power wall" bottlenecks. The memristive Memory Processing Unit (mMPU)
architecture contains memory cells that can also execute logical functions, such as Memristor-Aided Logic (MAGIC) NOR gates. The mMPU supports both general-purpose computing and application-specific
acceleration. This research contributes to both these aspects of the mMPU.First, we intro...
[ Full version ]
Thursday, 27.06.2024, 10:00
Deep learning has revolutionized drug development by enhancing various stages of the process, yet traditional optimization goals often lack the sophistication required for real-world applications.
This work tackles more complex and nuanced problems beyond conventional property enhancement, focusing on optimizing under patentability constraints and translating preclinical success in animals to
human clinical trials. In addressing patentability, we introduce a patent loss mechanism ...
[ Full version ]
Wednesday, 26.06.2024, 13:00
We consider the problem of approximate counting of triangles and longer fixed length cycles in undirected and directed graphs. We provide an algorithm which is faster as t, the number of copies of
the searched subgraph, increases. Our running time, which significantly improves upon the state of the art (Tětek [ICALP’22]), is the same as that of multiplying an n x (n/t) matrix by an (n/t) x n
matrix, up to polylogarithmic factors. Finally, we show that under popular fine-graine...
[ Full version ]
Wednesday, 26.06.2024, 11:30
The arrival of persistent memory devices to consumer market has revived the interest in transactional durable algorithms. Persistent memory is touted as having two attributes that distinguish it from
other storage technologies: fine access granularity and fast persistece.In the first part of the talk we investigate how these attributes differentiate persistent memory from block storage in the
context of buffered durability – a relaxed approach that allows some progres...
[ Full version ]
Tuesday, 25.06.2024, 11:30
Computed tomography (CT) aims to recover the volumetric three dimensional (3D) structure of heterogeneous objects. Traditionally, CT refers to a medical imaging modality. There the object, radiation
source and detector array are fully controlled. This results in a linear image formation model. In contrast, we seek CT of natural objects, acquired outdoors, in an uncontrolled environment. We focus
on underwater plankton and cloud droplets, which strongly affect climate. Cloud imagin...
[ Full version ]
Thursday, 20.06.2024, 16:30
Multivariate time series forecasting is a pivotal task in several domains, including financial planning, medical diagnostics, and climate science. This paper presents the Neural Fourier Transform
(NFT) algorithm, which combines multi-dimensional Fourier transforms with Temporal Convolutional Network layers to improve both the accuracy and interpretability of forecasts. The Neural Fourier
Transform is empirically validated on fourteen diverse datasets, showing superior performance ...
[ Full version ]
Thursday, 20.06.2024, 08:00
The annual Faculty Hackathon is underway! CS Hackathon - Doing Good Reserve the dates: June 20-21, in Taub. This year, in accordance with the order of the day, we will focus on developing
technological solutions to increase mental resilience in cooperation with the Ministry of Defense's rehabilitation department, associations and initiatives. Opening of registration, development
ideas, and preparation workshops - very soon. For details and more informat...
[ Full version ]
Omri Weinstein (Hebrew University)
Wednesday, 19.06.2024, 13:00
We develop a new framework, Polyform, for fast approximate matrix multiplication (AMM), through sums of sparse polynomial multiplications, using (variants of) FFT. Using this framework, we obtain new
data-dependent speed-accuracy tradeoffs, which often improve on the worst-case accuracy of randomized sketching algorithms. Meanwhile, Polyform can be viewed as a cheap alternative bilinear operator
to matrix multiplication in Deep Neural Networks, which is our motivating applicati...
[ Full version ]
Sunday, 16.06.2024, 14:30
Jumping automata are finite automata that read their input in a non-sequential manner, by allowing a reading head to “jump” between positions on the input, consuming a permutation of the input word.
We argue that allowing the head to jump should incur some cost. To this end, we propose three quantitative semantics for jumping automata, whereby the jumps of the head in an accepting run define the
cost of the run. The three semantics correspond to different interpretations of ju...
[ Full version ]
Sunday, 16.06.2024, 13:00
Neural network optimization is a challenging task, in large part because of the nonconvexity, in general, of the loss function. Various algorithms have been proposed to solve this task, but most of
them focus on the convex subspaces of the loss function to avoid the challenge of finding the optimal step in concave subspaces. In addition to avoiding the concave spaces entirely (which can bear a
significant computational burden!), they also simply take the minimizer of a second-d...
[ Full version ]
Sunday, 16.06.2024, 11:00
In this paper, we present a novel approach for test-time domain adaptation via online self-training, consisting of two components. First, we introduce a statistical framework that detects
distribution shifts in the classifier's entropy values obtained on a stream of unlabeled samples. Second, we devise an online adaptation mechanism that utilizes the evidence of distribution shifts
captured by the detection tool to dynamically update the classifier's parameters. The resulting adap...
[ Full version ]
Adi Vainiger, The Andrew and Erna Viterbi Faculty of Electrical & Computer Engineering
Monday, 10.06.2024, 15:00
Room 1061, EE Meyer Building
Atmospheric lidars are important remote sensing tools in aerosols and climate research. A pulsed time-of-flight lidar continuously samples vertical atmospheric profiles, through day and night,
yielding a spatiotemporal atmospheric map. However, lidar analysis is challenged by low signal-to-noise ratios, sunlight interference, and need for frequent calibration. We advance lidar analysis. We
develop a framework for simulating realistic spatiotemporal lidar data under diverse atmosph...
[ Full version ]
Sunday, 09.06.2024, 14:30
DNA emerges as a promising medium for the exponential growth of digital data due to its density and durability. This study extends recent research by addressing the coverage depth problem in
practical scenarios, exploring optimal error-correcting code pairings with DNA storage systems to minimize coverage depth. Conducted within random access settings, the study provides theoretical
analyses and experimental simulations to examine the expectation and probability distribution of sa...
[ Full version ]
Ronen Shaltiel (Haifa University)
Wednesday, 05.06.2024, 12:45
In the talk I will survey a research direction which combines coding-theory and computational complexity. This direction was introduced by Lipton, and refined by Guruswami and Smith. The goal is to
construct error correcting codes which correct errors that are introduced by computationally bounded channels. This is in contrast to Hamming’s standard model which assumes a bound on the fraction of
bits that a channel may flip, but allows the channel to be computationally unbounded....
[ Full version ]
Wednesday, 05.06.2024, 11:30
In recent years, machine learning (ML) has fueled extraordinary advances in fields such as natural language processing and computer vision. These results have encouraged researchers to utilize ML in
additional application domains, such as computer and networked systems, with varying degrees of success. In this talk I will focus on the prominent challenge of rate control in computer networking,
and devising a practical ML toolkit for the safe deployment of deep-learning-based solut...
[ Full version ]
Tuesday, 04.06.2024, 18:30
The CTF group of the faculty - Technipwn invites you to the semester opening lecture - a year of offensive security: attacks on OpenAI, Atlassian, Apple and more! Speaker>> Ron Massas, Vulnerability
Researcher at Imperva During his work at Imperva, security researcher Ron Massas uncovered a number of fascinating vulnerabilities and hacks in a number of large companies. In the lecture, he will
take us on a fascinating journey in the world of offensive security, and will present c...
[ Full version ]
Sunday, 02.06.2024, 13:30
In the last two decades, a main way to improve performance of computer processors has been producing processors with multiple cores, on which tasks may execute concurrently. Software is required to
keep up with the hardware advances and supply concurrent algorithms for programs that run on multiple cores. This talk will focus on a fundamental building block of concurrent algorithms: concurrent
data structures, designed with improved efficiency while also satisfying strong correctn...
[ Full version ]
Friday, 31.05.2024, 10:00
An open day for undergraduate studies at the Technion will be held on May 31 from 10:00 am to 1:00 pm in Sarona, Tel Aviv. At the event you can meet the representatives of the faculty, consult, get
an impression and get answers about the studies. Register for the open day at the ...
[ Full version ]
Theory group members and interested people
Wednesday, 29.05.2024, 12:45
This week we plan to get acclimated to our seminar's new location (outside of Taub, due to construction work), in a more social atmosphere. This includes introductions of current and prospective
members of the group,* and talk about plans for the semester, including theory courses scheduled. Come meet established theorists and folks interested in theory research! * if you know students doing
or interested in theory who are not (or might not be) registered to this mailing list, pl...
[ Full version ]
Wednesday, 29.05.2024, 11:30
Multi-label neural networks are important in various tasks, including safety-critical tasks. Several works show that these networks are susceptible to adversarial attacks, which can remove a target
label from the predicted label list or add a target label to this list. However, no verifier can deterministically determine the list of labels for which a multi-label neural network is locally
robust. The main challenge is that the complexity of the analysis increases by a factor expon...
[ Full version ]
Wednesday, 29.05.2024, 11:30
Multi-label neural networks are important in various tasks, including safety-critical tasks. Several works show that these networks are susceptible to adversarial attacks, which can remove a target
label from the predicted label list or add a target label to this list. However, no verifier can deterministically determine the list of labels for which a multi-label neural network is locally
robust. The main challenge is that the complexity of the analysis increases by a factor expon...
[ Full version ]
Wednesday, 22.05.2024, 13:00
A meeting of those interested in graduate studies at the Taub Faculty of Computer Science at the Technion will be held on Wednesday, May 22, 2024, 1:00 p.m., room 337 Outstanding bachelor's graduates
from all universities! This is your opportunity to participate and be impressed by the Faculty of Computer Science at the Technion, Meet faculty members and graduate students and hear fascinating
lectures. Event schedule: 13:00-13:30 Opening remarks: The words of t...
[ Full version ]
Wednesday, 22.05.2024, 11:30
Payment Channel Networks (PCNs) are a leading method to scale the transaction throughput in cryptocurrencies. Two participants can use a bidirectional payment channel for making multiple mutual
payments without committing them to the blockchain. Opening a payment channel is a slow operation that involves an on-chain transaction locking a certain amount of funds. These aspects limit the
number of channels that can be opened or maintained. Users may route payments through a multi-ho...
[ Full version ]
Thursday, 16.05.2024, 14:00
In the past few years, software has been at the heart of many applications ranging from appliances to virtual services. Helping software developers to write better code is a crucial task. In
parallel, recent developments in machine learning and deep learning in particular have shown great promise in many fields, and code-related tasks in particular. The main challenge is how to represent
code in a way that can be used by deep learning models effectively. While code can be treated ...
[ Full version ]
Wednesday, 15.05.2024, 15:30
Zoom lecture:
, password: OmerMSC and room 601
We introduce and study jumping automata over infinite words, a fascinating twist on traditional finite automata. These machines read their input in a non-consecutive manner, defying conventional word
order. We explore three distinct semantics: one ensuring every letter is accounted for, another permitting word permutation within fixed windows, and a third allowing permutation within windows of an
existentially-quantified bound. Our work covers expressiveness, closure properties, a...
[ Full version ]
Sunday, 05.05.2024, 15:00
Methods in question-answering (QA) that transform texts detailing processes into an intermediate code representation, subsequently executed to generate a response to the presented question, have
demonstrated promising results in analyzing scientific texts that describe intricate processes. The limitations of these existing text-to-code models are evident when attempting to solve QA problems
that require knowledge beyond what is presented in the input text. We propose a novel domai...
[ Full version ]
Sunday, 21.04.2024, 16:00
Distributed lending protocols are major financial mechanisms that match borrowers and lenders without the need for intermediaries. Smart contracts deployed on blockchains ensure the security of such
loans. Borrowers mitigate the risk of default by providing collateral in the form of cryptocurrencies or by limiting the loan duration. In the first part of the talk, we describe various loan types,
major platforms, and financial models that allow them. In the second part of the talk,...
[ Full version ]
Elias Nehme - The Andrew and Erna Viterbi Faculty of Electrical & Computer Engineering
Tuesday, 16.04.2024, 14:30
Room 1061, EE Meyer Building & Zoom Lecture:
In biological imaging, fast acquisition of depth information is crucial e.g. for accurate 3D tracking of sub-cellular elements and for 3D super-resolution. In the first part of this talk, we present
a series of works enhancing the success of snapshot depth sensing in the revolutionary field of single-molecule localization microscopy (Nobel Prize in Chemistry 2014). Specifically, we present an
approach for jointly designing the “optics” of the microscope and the 3D reconstructi...
[ Full version ]
Monday, 15.04.2024, 14:00
The standard formulation of Markov decision processes (MDPs) assumes that the agent's decisions are executed immediately. However, in numerous realistic applications such as robotics or healthcare,
actions are performed with a delay whose value can even be stochastic. In this work, we introduce stochastic delayed execution MDPs, a new formalism addressing random delays without resorting to
state augmentation. We show that given observed delay values, it is sufficient to perform a ...
[ Full version ]
Monday, 15.04.2024, 10:00
Graduates of the faculty are invited with their children to a day of lectures, workshops and information regarding registration and admission - for children; and a nostalgic tour (for parents)
Monday, April 15, starting at 10:00 at the Technion In the program: 1. The wonders of infinity - the Faculty of Mathematics 2. What is the Internet of Things? - Faculty of Computer Science 3. Games
and Virtual Reality - Fac...
[ Full version ]
Yara Mulla ( NVidia - IBC Barracuda)
Wednesday, 10.04.2024, 11:30
Due to their increasing aggressiveness, recent congestion control algorithms (CCAs) can quickly starve standard TCP flows in their shared router queues. Existing solutions based on fair queueing are
not scalable enough, and those based on admission control do not fit all CCAs. Independently, building on the popularization of machine learning, recent papers have designed several CCA
classifiers.In this seminar, we introduce a buffer isolation mode where incoming flows first...
[ Full version ]
Tom Bekor - The Andrew and Erna Viterbi Faculty of Electrical & Computer Engineering
Tuesday, 09.04.2024, 11:30
Room 1061, EE Meyer Building
Graduate Seminar Data augmentation has become an integral part of deep learning, as it is known to improve the generalization capabilities of neural networks.Since the most effective set of image
transformations differs between tasks and domains, automatic data augmentation search aims to alleviate the extreme burden of manually finding the optimal image transformations. However, current
methods are not able to jointly optimize all degrees of freedom: (1)...
[ Full version ]
Tuesday, 09.04.2024, 11:00
In the landscape of data stream processing, the challenges posed by online problems are of paramount importance. This paper introduces a pioneering method tailored to address these challenges within
the context of data streams. While our initial focus centered on Complex Event Processing (CEP) problems, it is essential to underscore the versatility of our approach, as it is equally applicable to
a diverse range of online problems. To the best of our knowledge, there exists no comp...
[ Full version ]
Michal Dory, Haifa University
Monday, 08.04.2024, 13:30
Assume that you have a huge graph, where edges and vertices may fail, and you want to answer questions about this graph quickly, without inspecting the whole graph. A fault-tolerant labeling scheme
allows us to do just that. It is a distributed data structure, in which each vertex and edge is assigned a short label, such that given the labels of a pair of vertices s,t, and a set of failures F,
you can answer questions about s and t in G\F. For example, determine if s and t are con...
[ Full version ]
Sunday, 07.04.2024, 10:00
Language Models (LMs) excel in many tasks, but understanding discourse – how sentences connect to form coherent text – remains a challenge. This is especially true for smaller models aiming to match
the abilities of their larger counterparts in handling long and complex inputs. To address this, we introduce DEPTH, a new encoder-decoder model designed to foster robust discourse-level
representations during the pre-training phase. DEPTH uniquely combines hierarchical sentence re...
[ Full version ]
Gal Chechik, Bar-Ilan University and NVIDIA
Thursday, 04.04.2024, 10:30
Between training and inference, lies a growing class of AI problems that involve fast optimization of a pre-trained model for a specific inference task. These are not pure “feed-forward” inference
problems applied to a pre-trained model, because they involve some non-trivial inference-time optimization beyond what the model was trained for; neither are they training problems, because they
focus on a specific input. These compute-heavy inference workflows raise new challenges i...
[ Full version ]
Wednesday, 03.04.2024, 12:30
The 12th CS Research Day for graduate studies will be held on Wednesday, April 03, 2024 between 12:30-14:30, at the lobby of the CS Taub Building. Research Day events are opportunity for our graduate
students to expose their researches using posters and presentations to CS faculty and all degrees students, Technion distinguished representatives and to high-ranking delegates from the hi-tech
leading industry companies in Israel and abroad. The participating researches will be on...
[ Full version ]
Or Meir (Haifa University)
Wednesday, 03.04.2024, 12:15
One of the major open problems in complexity theory is proving super-logarithmic lower bounds on the depth of circuits. Karchmer, Raz, and Wigderson (Computational Complexity 5(3/4), 1995) suggested
approaching this problem by proving that depth complexity of a composition of two functions is roughly the sum of their individual depth complexities. They showed that the validity of this conjecture
would imply the desired lower bounds.The intuition that underlies the KRW conj...
[ Full version ]
Wednesday, 03.04.2024, 11:30
In the past year, numerous companies have incorporated Generative AI (GenAI) capabilities into new and existing applications, forming interconnected Generative AI (GenAI) ecosystems consisting of
applications powered by GenAI services.While ongoing research highlighted risks associated with the GenAI layer of agents (e.g., dialog poisoning, membership inference, prompt leaking, jailbreaking),
a critical question emerges: Can attackers develop malware to exploit the GenAI c...
[ Full version ]
Hadar Averbuch-Elor, Tel-Aviv University
Tuesday, 02.04.2024, 14:30
Foundation models that connect vision and language have recently shown great promise for a wide array of tasks such as text-to-image generation. Significant attention has been devoted towards
utilizing the visual representations learned from these powerful vision and language models. In this talk, I will present an ongoing line of research that focuses on the other direction, aiming at
understanding what knowledge language models acquire through exposure to images during pretraini...
[ Full version ]
Anton Agafonov (Graduate Seminar)
Tuesday, 02.04.2024, 11:30
Room 608, Zisapel Building
In various applications, such as virtual reality and gaming, simulating the deformation of soft tissues in the human body during interactions with external objects is essential. Traditionally, Finite
Element Methods (FEM) have been employed for this purpose, but they tend to be slow and resource-intensive. In this paper, we propose a unified representation of human body shape and soft tissue with
a data-driven simulator of non-rigid deformations. This approach enables rapid simula...
[ Full version ]
Monday, 01.04.2024, 12:30
The graduate students' lounge, room 225
Engineering the Future of Blockchain 1.4.23 | 12:30-14:30 | The graduate students' lounge, Taub, 2nd floor 12:30 - Mingling and Snacks 13:00 - Oded Naor, Ph.D., Product Manager - Btockchain
reinvented: a deep dive into StarkWare's game-changing sotutions 13:30 - Noa Oved, MSC, Software Team Lead - Coding the future: Transforming algorithmic insights into real-wortd sotutions 14:00- Q&A
Plese RSVP at...
[ Full version ]
Thursday, 28.03.2024, 09:30
An open day for studies at the Technion will be held on Thursday, March 28, starting at 09:30 For details and registration, go to the registration and admission website at the link ...
[ Full version ]
Tomer Koren (Tel-Aviv University)
Wednesday, 27.03.2024, 12:15
In machine learning, there has been considerable interest over the past decade in understanding the ability of optimization algorithms to generalize—namely, to produce solutions (models) that extend
well to unseen data—particularly in the context of overparameterized problems. I will survey several recent theoretical studies that explore generalization in classical convex optimization, that
reveal intriguing behavior of common optimization methods and shed some light on the c...
[ Full version ]
Prof. Daniel Jackson, MIT
Wednesday, 27.03.2024, 12:00
I will explain how successful innovations in software can usually be traced to just one or two "concepts" that offer new scenarios that, with seemingly small shifts, radically change how an
application is used. I give examples from apps such as Zoom, WhatsApp and Calendly. I explain how concepts, each with their own characteristic scenarios, can be composed to form apps. I explain how
this idea can be used to make software more usable, modular and consistent. More information at:...
[ Full version ]
Eytan Modiano - Laboratory for Information and Decision Systems Massachusetts Institute of Technology
Wednesday, 27.03.2024, 11:30
Age of Information (AoI) is a recently proposed performance metric that captures the freshness of the information from the perspective of the application. AoI measures the time that elapsed from the
moment that the most recently received packet was generated to the present time. In this talk, we explore the AoI optimization problem in wireless networks.We start by considering a wireless network
with a number of nodes transmitting information to a base station and develop l...
[ Full version ]
Wednesday, 27.03.2024, 10:00
Intel's tech experience is coming to campus! Ready for the most innovative technological picnic you've ever seen? We have loaded technological tools and our greatest minds to the track and we are on
our way to you Wednesday 27.3 | Mayer building, 3rd floor 10:00 - AR | VR | HR Come and get to know us and our technologies 12:30 - FPGA MicroPython The number of places is limited, register at the
[ Full version ]
Tuesday, 26.03.2024, 11:30
Room 1061, EE Meyer Building
We propose a new approach for generative modeling based on training a neural network to be idempotent. An idempotent operator is one that can be applied sequentially without changing the result
beyond the initial application, namely f(f(z))=f(z). The proposed model f is trained to map a source distribution (e.g, Gaussian noise) to a target distribution (e.g. realistic images) using the
following objectives: (1) Instances from the target distribution should map to themselves, namel...
[ Full version ]
Thursday, 21.03.2024, 10:30
In this lecture we will explore collaborative caching algorithms in order to boost the effectiveness of caches in a distributed storage system. I'll introduce a scheme that partitions each node’s
cache into two conceptual regions: an egoistic area whose goal is to contain the most valuable data for the node that owns the cache, and an altruistic area whose goal is to contain the most valuable
data for the system as a whole. Each node’s division between these two regions is dyn...
[ Full version ]
Elnatan Kadar (Graduate Seminar)
Wednesday, 20.03.2024, 14:30
Room 1061, EE Meyer Building
We propose a new way to explain and to visualize neural network classification through a decomposition-based explainable AI. Instead of providing an explanation heatmap, our method yields a
decomposition of the image into class-agnostic and class-distinct parts, with respect to the data and chosen classifier. Following a fundamental signal processing paradigm of analysis and synthesis,
the original image is the sum of the decomposed parts. We thus obtain a radically different way ...
[ Full version ]
Ilan Newman (University of Haifa)
Wednesday, 20.03.2024, 13:15
A finite metric space $(X,d)$ on a set of points $X$ is just the shortest path metric $d$ on a positively weighted graph $G=(X,E)$. In the online setting, the vertices of the input finite metric
space $(X,d)$ are exposed one by one, together with their distances $d(*,*)$to the previously exposed vertices. The goal is to embed (map) $X$ into a given host metric space $(H,d_H)$ (finite or not)
and so to distort the distances as little as possible (distortion is the worst cas...
[ Full version ]
Wednesday, 20.03.2024, 12:30
You are invited to the spotlight day of the Mobileye company at the Technion Wednesday 20.3 | 12:30 | Taub Building...
[ Full version ]
(George Washington University) Adam J Aviv
Wednesday, 20.03.2024, 11:30
The surveillance economy, where tracking and collecting data on uses for the purpose of advertising and other actions, is central to much of the money-making enterprises of the modern technology
ecosystem. Due to regulations and other forces, some of the largest companies, such as Google and Apple, have prioritized mechanisms for users to better manage and receive information about the kinds
of data that is being collected about them. In this talk, I will explore how effective the...
[ Full version ]
Tuesday, 19.03.2024, 12:30
Yahoo holds a dedicated meeting with graduate students Tuesday, March 19 at 12:30 p.m. at the CS Grads Club In the program: an introduction to Yahoo's research in Israel and the summer internship
program. Register to the event here waiting for you!!...
[ Full version ]
Yarden Zuckerman, SW Security Manager, Nvidia
Monday, 18.03.2024, 18:00
Join us for a lecture and pizza! Cyber Security Challenges In The Modern Era by Yarden Zuckerman, SW Security Manager, Nvidia Monday | March 18, 2024 | 18:00 p.m. | Piano Auditorium Taub Building ...
[ Full version ]
Monday, 18.03.2024, 13:30
I'll present our paper about the role that null messages play in synchronous systems with and without failures. Our work provides necessary and sufficient conditions on the structure of protocols for
information transfer and coordination there. We start by introducing a new and more refined definition of null messages. A generalization of message chains that allow these null messages is provided
and is shown to be necessary and sufficient for information transfer in reliable syste...
[ Full version ]
Hilla Schefler (Technion)
Wednesday, 13.03.2024, 12:15
Differential Privacy (DP) is a mathematical framewirk for ensuring the privacy of individuals in a dataset. Roughly speaking, it guarantees that privacy is protected in data analysis by ensuring that
the output of an analysis does not reveal sensitive information about any specific individual, regardless of whether their data is included in the dataset or not.This talk presents a unified
framework for characterizing both pure and approximate differentially private learnabi...
[ Full version ]
Wednesday, 13.03.2024, 10:30
To deploy and operate deep neural models in production, the quality of their predictions, which might be contaminated benignly or manipulated maliciously by input distributional deviations, must be
monitored and assessed. Specifically, we study the case of monitoring the healthy operation of a deep neural network (DNN) receiving a stream of data, with the aim of detecting input distributional
deviations over which the quality of the network’s predictions is potentially damaged. ...
[ Full version ]
Tuesday, 12.03.2024, 14:30
Multi-rotor aerial autonomous vehicles (MAVs) primarily rely on vision for navigation purposes. However, visual localization and odometry techniques suffer from poor performance in low or direct
sunlight, a limited field of view, and vulnerability to occlusions. Acoustic sensing can serve as a complementary or even alternative modality for vision in many situations, and it also has the added
benefits of lower system cost and energy footprint, which is especially important for micr...
[ Full version ]
Or Avitan (Graduate Seminar)
Tuesday, 12.03.2024, 11:30
Room 1061, EE Meyer Building
We propose that spaceborne polarimetric imagers can be calibrated, or self-calibrated using zodiacal light (ZL). ZL is created by a cloud of interplanetary dust particles. It has a significant degree
of polarization in a wide field of view. From space, ZL is unaffected by terrestrial disturbances. ZL is insensitive to the camera location, so it is suited for simultaneous cross-calibration of
satellite constellations. ZL changes on a scale of months, thus being a quasi-constant tar...
[ Full version ]
Monday, 11.03.2024, 13:30
I will share some of my learnings from working on problems on the intersection of Distributed Computing and Cryptography.On the one hand, I will show how some cryptographic protocols (MPC and DKG)
can be improved by using distributed computing counterparts for notions such as zero knowledge proofs and proofs of knowledge. On the other hand, I will show how distributed computing protocols (ABA)
can be improved by carefully using notions of binding from cryptography. One rec...
[ Full version ]
Monday, 11.03.2024, 10:30
Most works on modeling the conversation history in Conversational Question Answering (CQA) report a single main result on a common CQA benchmark. While existing models show impressive results on CQA
leaderboards, it remains unclear whether they are robust to shifts in setting (sometimes to more realistic ones), training data size (e.g. from large to small sets) and domain. In this work, we
design and conduct the first large-scale robustness study of history modeling approaches for...
[ Full version ]
Sunday, 10.03.2024, 18:00
Nvidia invites you to a virtual spotlight day where the company's engineers will talk about the different groups and open positions Sunday, March 10, from 18:00 to 19:30 To register for the event
[ Full version ]
Wednesday, 06.03.2024, 12:30
Cadence company is coming to a spotlight day at the faculty Wednesday 6/3 | 12:30-14:30 | Lobby Taub In the program: a meeting with the recruitment teams, the engineers for a 1:1 conversation about
employment opportunities and tips for writing a report. And of course merch and sweets. waiting for you!!...
[ Full version ]
Yair Carmon (Tel-Aviv university)
Wednesday, 06.03.2024, 12:15
We design a new stochastic first-order algorithm for approximately solving matrix games as well as the more general problem of minimizing the maximum of smooth convex functions. Our central tool is
ball oracle acceleration: a technique for minimizing any convex function with a small number of calls to a ball oracle that minimizes the same function restricted to a small ball around the query
point. To design an efficient ball oracle for our problems of interest we leverage stochast...
[ Full version ]
Tuesday, 05.03.2024, 15:00
Early time classification algorithms aim to label a stream of features without processing the full input stream, while maintaining accuracy comparable to that achieved by applying the classifier to
the entire input. In this paper, we introduce a statistical framework that can be applied to any sequential classifier, formulating a calibrated stopping rule. This data-driven rule attains
finite-sample, distribution-free control of the accuracy gap between full and early-time classifi...
[ Full version ]
Mor Filo, a graduate of the faculty and a developer at Amazon
Monday, 04.03.2024, 18:30
You have been accepted as a student! What now? The student community at the SHE S faculty invites you to a meeting on: First time student job: about the opportunities, challenges and skills you
acquire in your first job Monday, 4/3 at 6:30 pm in the piano auditorium Please register in advance: here Speaker: Moore Philo, graduate of the faculty and developer at Amazon The meeting is suitable
for thos...
[ Full version ]
Thursday, 29.02.2024, 15:00
We study the problem of computing an embedding of the tuples of a relational database in a manner that is extensible to dynamic changes of the database. In this problem, the embedding should be
stable in the sense that it should not change on the existing tuples due to the embedding of newly inserted tuples (as database applications might already rely on existing embeddings); at the same
time, the embedding of all tuples, old and new, should retain high quality. This task is chall...
[ Full version ]
Wednesday, 28.02.2024, 12:30
Spotlight day for Nvidia at the Technion on February 28, 2024 Nvidia is coming to meet the students of the Faculty of Computer Science at the Technion! Come and meet the company's engineers face to
face Wednesday February 28, 2024 | 12:30-14:30 | Taub lobby, floor 0...
[ Full version ]
Sarel Cohen (Tel-Aviv Academic College)
Wednesday, 28.02.2024, 12:15
Theory Seminar: An f-edge fault-tolerant distance sensitivity oracle (f-DSO) is a data-structure that, when queried with two vertices (s, t) and a set F of at most f edges of a graph G with n
vertices, returns an estimate tilde{d}(s,t,F) of the distance d(s,t,F) from s to t in G – F. The oracle has stretch alpha if the estimate satisfies d(s,t,F) le tilde{d}(s,t,F) le alpha cdot d(s,t,F)
. In the last two decades, extensive research has focused on developing efficient f-DSOs. Th...
[ Full version ]
Naama Ben-David, Technion
Monday, 26.02.2024, 13:30
Locks are frequently used in concurrent systems to simplify code and ensure safe access to contended parts of memory. However, they are also known to cause bottlenecks in concurrent code, leading
practitioners and theoreticians to sometimes opt for more intricate lock-free implementations. In this talk, I’ll show that, despite the seeming contradiction, it is possible to design practically
and theoretically efficient lock-free locks; I'll present a lock-free lock algorithm with ...
[ Full version ]
Thursday, 22.02.2024, 15:00
In this talk, we delve into several fundamental questions in deep learning. We start by addressing the question, "What are good representations of data?" Recent studies have shown that the
representations learned by a single classifier over multiple classes can be easily adapted to new classes with very few samples. We offer a compelling explanation for this behavior by drawing a
relationship between transferability and an emergent property known as neural collapse. Later, we expl...
[ Full version ]
Wednesday, 21.02.2024, 17:00
In the last decade, DNA-based storage systems emerged as a potential data archival solution due to their high data density and durability. This research delves into intrinsic error characteristics of
DNA storage systems to devise robust coding strategies and innovative algorithms for enhanced reliability, efficiency, scalability, and cost-effectiveness. The research propels DNA storage
feasibility while contributing to foundational theory.The work analyzes combinatorial st...
[ Full version ]
Wednesday, 21.02.2024, 15:00
High-dimensional data is increasingly available in diverse applications, ranging from images to shapes represented as point clouds. Such data raises novel questions and offers a unique opportunity to
study them by developing new machine-learning tools. While the analysis of an individual sample may be challenging, leveraging the power of the data collection can be effective in tackling complex
tasks. This talk delves into the challenges associated with studying such data, particul...
[ Full version ]
Gal Arnon (Weizmann institute)
Wednesday, 21.02.2024, 12:15
We show that every language in NP has an Interactive Oracle Proof (IOP) with inverse polynomial soundness error and small query complexity. This achieves parameters that surpass all previously known
PCPs and IOPs. Specifically, we construct an IOP with perfect completeness, soundness error 1/n, round complexity O(loglog n), proof length poly(n) over an alphabet of size O(n), and query complexity
O(loglog n). This is a step forward in the quest to establish the sliding-scale conjec...
[ Full version ]
Monday, 19.02.2024, 13:30
This talk focuses on the distributed task of constructing an approximate \emph{maximum weight independent set (MWIS)}. Specifically, we are interested in deterministic CONGEST algorithms whose
approximation guarantees are expressed as a function of the graph's \emph{arboricity} $\alpha$.Generally speaking, efficient deterministic non-trivial approximation algorithms for MWIS were not known
until the recent breakthrough of Faour et al.~[SODA 2023] that obtained an $O(\Delta...
[ Full version ]
Thursday, 15.02.2024, 11:00
Zoom Lecture:
and Taub 401
In clinical settings, a significant portion of ECG data is typically available in printed form, and the most convenient means of digitizing this information involves utilizing a mobile device.
Despite notable progress in AI-based techniques for paper-based 12-lead ECG analysis, their adoption in clinical practice remains limited primarily due to challenges such as inadequate accuracy in
clinical settings and a restricted ability to diagnose various cardiac conditions. Our objectiv...
[ Full version ]
Wednesday, 14.02.2024, 12:15
Suppose that n forecasting experts (or functions) are providing daily rain/no-rain predictions, and the best among them is mistaken in at most k many days. For how many days will a person allowed to
observe the predictions, but has no weather-forecasting prior knowledge, mispredict?In this talk, we will discuss how such classical problems can be reduced to calculating the (average) depth of
binary trees, by using newly introduced complexity measures (aka dimensions) of the...
[ Full version ]
Wednesday, 14.02.2024, 11:30
With the rapid increase of storage demands and working sets of modern mobile apps, maintaining high I/O performance in mobile SSDs under strict resource constraints is challenging. The Flash
Translation Layer (FTL) must increase the capacity of the Logical-To-Physical (L2P) address translation cache to keep up with the new workloads, but it comes at the cost of scaling the on-die SRAM,
resulting in higher chip area, power consumption, and costs.In this talk, I will present...
[ Full version ]
Tuesday, 13.02.2024, 18:30
Come be part of a new Capture The Flag-CTF group at the Faculty The meetings are held every Tuesday at 18:30 at Taub 9 and include guest lectures and practical experience in solving challenges.
Everybody is invited! Beginners and experienced For details: Technionctf.com This week - February 13, 2024: 18:30 | Taub 2 | Omar Atias - security researcher, lecturer at BlackHat USA & DEFCON The
price of con...
[ Full version ]
Monday, 12.02.2024, 12:00
QUIC is an emerging transport protocol, offering multiple advantages over TCP. Yet, to fully unleash QUIC’s potential, a paradigm shift is needed in existing network infrastructure. We propose a
novel 0-RTT-aware load balancing algorithm. 0-RTT is crucial for web performance, particularly on mobile networks. Our load balancing algorithm ensures 0-RTT while maintaining near-optimal load
balancing performance.Through extensive simulations, using both synthetic and real-wor...
[ Full version ]
Wednesday, 07.02.2024, 12:30
You are invited to Final spotlight day Wednesday 07.02.2024 | 12:30-14:30 | Visitor Center Auditorium 012, Floor 0 12:30 - Come meet engineers, researchers and the recruitment team at Final, and get
to know the day-to-day life at Final. 13:15 - Meeting on options, probabilities and the world of algorithm trading | Noam Horowitz - researcher at Final To register for the lecture click ...
[ Full version ]
Konstantin Zabaranyi (Technion)
Wednesday, 07.02.2024, 12:15
Come be part of a new Capture The Flag-CTF group at the Faculty The meetings are held every Tuesday at 18:30 at Taub 9 and include guest lectures and practical experience in solving challenges.
Everybody is invited! Beginners and experienced For details: Technionctf.com The week of February 6, 2024: Beginners: Forensics & Networks | Taub 9 experienced: Challenges from 2023 LA CTF | Tau...
[ Full version ]
Tuesday, 06.02.2024, 18:30
Come be part of a new Capture The Flag-CTF group at the Faculty The meetings are held every Tuesday at 18:30 at Taub 9 and include guest lectures and practical experience in solving challenges.
Everybody is invited! Beginners and experienced For details: Technionctf.com The week of February 6, 2024: Beginners: Forensics & Networks | Taub 9 experienced: Challenges from 2023 LA CTF | Taub
[ Full version ]
Tuesday, 06.02.2024, 12:30
Many object-oriented applications in algorithm design rely on objects never changing during their lifetime. This is often tackled by marking object references as read-only, e.g., using the const
keyword in C++. In other languages like Python or Java where such a concept does not exist, programmers rely on best practices that are entirely unenforced. While reliance on best practices is
obviously too permissive, const-checking is too restrictive: it is possible for a method to mutat...
[ Full version ]
Guy Gaziv (DiCarlo Lab at MIT)
Tuesday, 06.02.2024, 11:30
Room 1061, EE Meyer Building
The visual object category reports of artificial neural networks (ANNs) are notoriously sensitive to tiny, adversarial image perturbations. Because human category reports (aka human percepts) are
thought to be insensitive to those same small-norm perturbations — and locally stable in general — this argues that ANNs are incomplete scientific models of human visual perception. Consistent with
this, we show that when small-norm image perturbations are generated by standard ANN mo...
[ Full version ]
Gilad Asharov (Bar Ilan University)
Thursday, 01.02.2024, 11:30
We study secure multiparty computation in the asynchronous setting with perfect security and optimal resilience (less than one-fourth of the participants are malicious). It has been shown that every
function can be computed in this model [Ben-OR, Canetti, and Goldreich, STOC'1993]. Despite 30 years of research, all protocols in the asynchronous setting require $\Omega(n^2C)$ communication
complexity for computing a circuit with $C$ multiplication gates. In contrast, for nearly 15...
[ Full version ]
Wednesday, 31.01.2024, 12:30
We study several graph layout problems with a min max objective. Here, given a graph we wish to find a linear ordering of the vertices that minimizes some worst case objective over the natural cuts
in the ordering; which separate an initial segment of the vertices from the rest. A prototypical problem here is cutwidth, where we want to minimize the maximum number of edges crossing a cut. The
only known algorithm here is by [Leighton-Rao J.ACM 99] based on recursively partitioning ...
[ Full version ]
Dor Katzelnick (Technion)
Wednesday, 31.01.2024, 12:15
We study several graph layout problems with a min max objective. Here, given a graph we wish to find a linear ordering of the vertices that minimizes some worst case objective over the natural cuts
in the ordering; which separate an initial segment of the vertices from the rest. A prototypical problem here is cutwidth, where we want to minimize the maximum number of edges crossing a cut. The
only known algorithm here is by [Leighton-Rao J.ACM 99] based on recursively partitioning ...
[ Full version ]
Dr. Yaniv David (Columbia University)
Wednesday, 31.01.2024, 11:30
Racing to be first to market and deploy new features, developers rely on many external libraries to underpin their software. Each library uses more libraries, creating vast networks of dependencies
that the developers know little about and have no control over, forming a knowledge gap that quickly turns into technical debt. Repaying this debt is difficult, as analyzing or examining all
libraries is infeasible, and worse, the debt keeps growing due to frequent library updates. Atta...
[ Full version ]
Wednesday, 31.01.2024, 10:30
When training large neural networks, there are typically many solutions that perfectly fit the training data. Nevertheless, gradient-based methods often have a tendency to reach those which
generalize well, namely, perform well also on test data. Thus, the training algorithm seems to be implicitly biased towards certain networks, which exhibit good generalization performance.
Understanding this “implicit bias” has been a subject of extensive research recently. Moreover, in con...
[ Full version ]
Monday, 29.01.2024, 15:30
Text-to-image diffusion models (T2I) use a latent representation of a text prompt to guide the image generation process. However, the encoder that produces the text representation is largely
unexplored. We propose the Diffusion Lens, a method for analyzing the text encoder of T2I models by generating images from its intermediate representations. Using the Diffusion Lens, we perform an
extensive analysis of two recent T2I models.We find that the text encoder gradually build...
[ Full version ]
Sunday, 28.01.2024, 10:30
Hyperproperties are system properties that relate multiple execution traces to one another. Hyperproperties are essential to express a wide range of system requirements such as information flow and
security policies; epistemic properties like knowledge in multi-agent systems; fairness; and robustness. With the aim of verifying program correctness, the two major challenges are (1) providing a
specification language that can precisely express the desired properties; and (2) providin...
[ Full version ]
Wednesday, 24.01.2024, 12:15
Stochastic convex optimization is one of the most well-studied models for learning in modern machine learning. Nevertheless, a central fundamental question in this setup remained unresolved: How many
data points must be observed so that any empirical risk minimizer (ERM) shows good performance on the true population? This question was proposed by Feldman who proved that Ω(\frac{d}{ϵ} + \frac{1}{ϵ
^2}) data points are necessary (where d is the dimension and ε > 0 is the accurac...
[ Full version ]
Tuesday, 23.01.2024, 18:30
The Technion CTF Team opens at the Faculty We invite you to join the Capture The Flag - CTF meetings. CTF is a cyber challenge competition and information security on the topics: cryptography,
reverse engineering, forensics, web, etc. The meetings will include guest lectures and practical experience in solving challenges. Beginner and experienced students are welcome to join. The first
introductory meeting will be held on Tuesday, January 23 at 6:30 pm at Taub 9. In the f...
[ Full version ]
Prof. Misha Kazhdan (Computer Science, Johns Hopkins University)
Thursday, 18.01.2024, 11:30
Taub 012 (Learning Center Auditorium)
In this talk we consider the problem of manifold reconstruction from oriented point clouds for embedded manifolds of co-dimension larger than one. Using the framework of Poisson Surface
Reconstruction, and formulating the problem in the language of alternating products, we show that the earlier approach for reconstructing hyper-surfaces extends to general manifolds, at the cost of
replacing a quadratic energy with a multi-quadratic energy. We provide an efficient iterative hierarc...
[ Full version ]
Wednesday, 17.01.2024, 12:15
Vizing’s Theorem provides an algorithm that edge colors any graph of maximum degree Δ using Δ+1 colors, which is necessary for some graphs, and at most one higher than necessary for any graph. In
online settings, the trivial greedy algorithm requires 2Δ-1 colors, and Bar-Noy, Motwani and Naor in the early 90s showed that this is best possible, at least in the low-degree regime. In contrast,
they conjectured that for graphs of superlogarithmic-in-n maximum degree, much better ...
[ Full version ]
Tuesday, 16.01.2024, 11:00
Blockchains have ignited interest in Internet-scale consensus as a vital building block for decentralized applications and services that promise egalitarian access and robustness to faults and abuse.
While the study of consensus has a 40+ year tradition, the new Internet-scale setting requires a fundamental rethinking of models, desiderata, and protocols. An emergent key challenge is to
simultaneously serve clients with different requirements regarding the two fundamental aspects ...
[ Full version ]
Thursday, 04.01.2024, 12:30
Faculty of Biomedical Engineering, Silver Building, Room 201
12-lead electrocardiogram (ECG) recordings can be collected in any clinic and the interpretation is performed by a clinician. Modern machine learning tools may make them automatable. However, a large
fraction of 12-lead ECG data is still available in printed paper or image only and comes in various formats. To digitize the data, smartphone cameras can be used. Nevertheless, this approach may
introduce various artifacts and occlusions into the obtained images.Here, I will p...
[ Full version ]
Monday, 01.01.2024, 10:30
I will present a theoretical framework for analyzing learning algorithms which rely on dependent, rather than independent, observations. While a common assumption is that the learning algorithm
receives independent datapoints, such as unrelated images or texts, this assumption often does not hold. An example is data on opinions across a social network, where opinions of related people are
often correlated, for example as a consequence of their interactions. I will present a line o...
[ Full version ] | {"url":"https://cs.technion.ac.il/events/","timestamp":"2024-11-04T06:03:12Z","content_type":"text/html","content_length":"321947","record_id":"<urn:uuid:86f4db27-527f-4a78-a3bb-cb1798920caf>","cc-path":"CC-MAIN-2024-46/segments/1730477027812.67/warc/CC-MAIN-20241104034319-20241104064319-00178.warc.gz"} |
Development of a Model for Hydrogen-Assisted Fatigue Crack Growth of Pipeline Steel1
Hydrogen has been proposed as a potential partial solution to the need for a clean-energy economy. In order to make this a reality, large-scale hydrogen transportation networks need to be engineered
and installed. Steel pipelines are the most likely candidate for the required hydrogen transportation network. One historical barrier to the use of steel pipelines to transport hydrogen was a lack of
experimental data and models pertaining to the fatigue response of steels in gaseous hydrogen. Extensive research at NIST has been performed in conjunction with the ASME B31.12 Hydrogen Piping and
Pipeline committee to fill this need. After a large number of fatigue crack growth (FCG) tests were performed in gaseous hydrogen, a phenomenological model was created to correlate the applied
loading conditions, geometry, and hydrogen pressure to the resultant hydrogen-assisted fatigue crack growth (HA-FCG) response of the steels. As a result of this extensive data set, and a
simplification of the above-mentioned phenomenological model, the ASME B31.12 code was modified to enable the use of higher strength steels without penalty, thereby resulting in the potential for
considerable installation cost savings. This paper details the modeling effort that led to the code change.
Hydrogen will likely play a key role in transitioning the world away from the use of fossil fuels as a primary energy source. There are multiple ways in which hydrogen may be used to accomplish this
goal. First, hydrogen may be produced with excess power at solar, wind, and other clean power-generation facilities that produce power regardless of demand. In this way, the excess energy generated
during times of off-peak demand may be stored as hydrogen. The hydrogen would then be transported throughout the U.S. to be converted to usable energy via electrochemical fuel cells once demand
arises. As a second option, hydrogen may be used as a simple energy carrier, i.e., hydrogen production and distribution for the sake of distributed electricity generation rather than simply as an
energy storage mechanism. In either scenario, hydrogen must be transported long distances in order for it to achieve its potential usefulness.
Steel pipelines are the most economical means of transporting fuels in the U.S., including hydrogen [1]. Currently, the length of hydrogen-dedicated pipelines in the U.S. comprises only one-half of
one percent of the total length of operating U.S. natural gas pipelines [2,3]. Considering the current U.S. natural gas transportation system as a benchmark, one recognizes the need for far more
hydrogen-specific pipelines to be operational in the near future in order to meet similar energy needs. According to the ASME B31.12 committee on hydrogen piping and pipelines, a major barrier to the
design and installation of steel pipelines for hydrogen transportation has historically been the lack of information on hydrogen-assisted fatigue crack growth (HA-FCG) in pipeline materials. Though
noncyclic fracture studies of pipeline steels in gaseous hydrogen have been performed to provide a baseline understanding of the effect of hydrogen upon these loading and failure scenarios [4–8],
test results on HA-FCG were lacking because of the expense and difficulty associated with the tests. As such, the ASME committee tasked with creating the hydrogen transportation pipeline design and
engineering criteria based the original ASME B31.12-2008 code [9] on the relative response of pipeline steels to monotonic loading in a gaseous hydrogen environment.
An inverse relationship was found between material strength and the adverse effect of hydrogen on ductility, known as hydrogen embrittlement, in tensile tests. Therefore, the use of monotonic data
resulted in design thickness penalties, which were assessed to any steel having a specified minimum yield strength (SMYS) greater than 360MPa (52 ksi). Research at NIST and Sandia National
Laboratories, however, has shown that unlike other material properties (e.g., ductility), strength is not correlated to the response of a material to HA-FCG [10]. The recent HA-FCG results produced
by the two laboratories indicate that the design penalty placed upon higher strength steels is overly conservative and without justification. Studies have shown that allowing pipeline steels with a
SMYS of up to 480MPa (70 ksi) without penalty could reduce material and installation costs by approximately 25% [11]. As a result, the forthcoming version of the ASME B31.12 code will remove the
design penalties on materials with a SMYS between 360MPa and 480MPa (52 ksi and 70 ksi). This work details the recent data analysis and modeling studies performed at NIST that were used to inform
the ASME B31.12 committee during the code revision process. This work also outlines the HA-FCG modeling background and implementation for both predictive and engineering design purposes.
Hydrogen-Assisted Fatigue Crack Growth Results
The HA-FCG experiments performed at NIST include pipeline base materials, which have a SMYS between 360MPa and 690MPa (52 ksi and 100 ksi), as well as on welds and heat-affected zones in pipeline
steels with an SMYS between 360MPa and 480MPa (52 ksi and 70 ksi). A selection of the data collected at NIST on the base materials from pipeline steels is shown in Fig. 1 [12–14]. The data in Fig.
1, and those in Refs. [12], [13], and [15–17] indicate that the presence of hydrogen can increase the fatigue crack growth rate (FCGR) of pipeline steels as much as an order of magnitude over the
FCGR in air, depending upon the applied load and geometry (ΔK). The HA-FCG results also indicate that the effect of hydrogen on the FCG is not dependent upon SMYS, at least between values of 360MPa
(52 ksi) and 690MPa (100 ksi), as the “X52 New” material at 5.5MPa data falls right on the response of X70B at 5.5MPa, for example.
The data presented in Fig. 2 are delineated by the American Petroleum Institute (API) steel designation (e.g., X52), NIST internal naming convention if applicable (e.g., Alloy J, Vintage, New), and
hydrogen pressure in MPa. Note that the API naming convention includes the SMYS of the material such that X52 designates an API pipeline steel that has an SMYS of 360MPa (52 ksi). Fatigue crack
growth (FCG) data shown in these figures have da/dN as the dependent variable (y-axis), which is the crack growth per load cycle, and ΔK is the independent variable (X-axis), where ΔK is the
stress-intensity-factor range. When delineating the results by material type, there appears to be a correlation between increased hydrogen pressure and increased HA-FCG, shown in Fig. 3(a).
For modeling purposes, analysis of the data in Figs. 1–3 shows that (a) HA-FCG is increased over FCG in air for ΔK values larger than some threshold value, (b) HA-FCG rates are not SMYS dependent,
(c) HA-FCG rates appear to increase with hydrogen pressure for a given material, and (d) the HA-FCG data appear to have multiple linear regions of FCG response (shown specifically in Fig. 4). A full
description of the HA-FCG test methodology, tests performed, and test results produced at NIST, can be found in Ref. [18].
Fatigue Crack Surface Morphology
Figure 4 details the separation of the HA-FCG response of an API X100 pipeline steel into three regions for discussion purposes. The regions are referred to as regions A, B, and C. The curve for air
falls outside the three regions.
In these three regions in Fig. 4, the fracture surfaces produced as a result of the HA-FCG within each region differ markedly. For reference, Fig. 5 provides the FCG surfaces of three representative
pipeline materials tested in hydrogen. The ΔK values delineating each region are approximated in the following discussion. The FCG surface in region A (ΔK<∼8MPa m^1/2) closely matches that
produced in air. The response in region B (∼8MPa m^1/2 <ΔK<∼15MPa m^1/2) produces an FCG surface dominated by crystallographic faceting, indicative of a more brittle FCG response and some
hydrogen attack at grain boundaries. Representative crystallographic facets are indicated by arrows in this regime for all three materials shown in Fig. 5. The FCG surface produced in region C (ΔK>
∼15MPa m^1/2), while also exhibiting a small amount of crystallographic faceting, shows a return to much of the character of the FCG surface of air. That is, the existence of quasi-cleavage and
“river” marks, as well as the relative amount of crack branching within region C, more closely resembles that of region A. The FCG surface in region C is indicative of a transition to a more ductile
fatigue behavior, in contrast to that produced in the middle regime (region B). Specifically, the failure surface morphology in region C indicates that the effect of hydrogen has effectively
saturated, in which case the failure surface morphology in region C has components of maximum hydrogen-induced damage (region B) plus an additional ductile-type character similar to that found in
region A. The HA-FCG surfaces produced from the different regions for three representative materials are shown in Fig. 5. The FCG surface morphologies found here are similar to those detailed in
Refs. [19–21]. Details of quasi-brittle fatigue fracture of a low-carbon steel in hydrogen, where predominantly transgranular cracking was seen, showed that what appeared to be brittle fracture was a
combination of extensive slip and localized ductile cracking [22]. An explanation of microstructural details of quasi-cleavage with crystallographic faceting in a low-carbon steel tested in hydrogen
gas can be found in the literature [17].
Not only do the images in Fig. 5 indicate a transition in relative amounts of crystallographic faceting between the three regions, the images also indicate a change in the out-of-plane crack
branching as a function of crack growth. Crack branching is manifested in Fig. 5 as fissures that traverse into the pictures. As an example, region A exhibits little or no crack branching, region B
exhibits considerable branching, while region C exhibits some amount of out-of-plane branching between that of regions A and B for all three materials. This supports the notion of a transition in FCG
morphology as the crack traverses the specimen (growing from region A to B to C). It is understood that the HA-FCGR of pipeline steels is sensitive to loading frequency. The test frequency presented
here, 1Hz, was chosen as it provides baseline for understanding of the deformation mechanisms present, while providing a sufficient amount of time for hydrogen diffusion during each loading
incursion. A complete discussion of the test frequency as it applies to pipeline operation is provided in Ref. [18].
Dominant Damage Mechanisms
Each of the three regimes discussed above is produced as a result of different dominant damage mechanisms. Each damage mechanism dominates at different times depending upon the rate of crack growth
per cycle (da/dN). Given that the FCG regime of region A (ΔK<∼8MPa m^1/2) produces a fatigue surface that matches that of tests in air, it is presumed that this FCG regime is dominated by a
fatigue-only mechanism. Suresh and Ritchie hypothesized that there exists a threshold stress intensity value, $KmaxT$, below which hydrogen does not affect the FCG response of steels [21]. It is
believed that the region A results are due to the stress intensity factor falling below the threshold value, $KmaxT$.
It is understood that the combined HA-FCG response (region A+region B+region C) results from the superposition of a mechanism not affected by hydrogen (region A) and a FCG response affected by
hydrogen (region B+region C). This overarching formulation follows the underpinnings of Ref. [23]. The HA-FCG response that is affected by the presence of hydrogen, region B+region C, is
comprised of a bi-linear trend when plotting da/dN versus ΔK, which will be discussed further. Similar bi-linear trends, or transitions in FCG response, have been attributed to the following
• Crack growth beyond the short-crack regime exhibited by most crystalline metals, i.e., crack extension per cycle greater than the material's grain size [24].
• Crack extension per cycle greater than the Widmanstatten packet size for titanium alloys [24].
In both cases, the transition between bi-linear trends in FCGRs results from an interaction between the length of crack extension per cycle and a characteristic length scale of the material
microstructure. In the case of HA-FCG, it is believed that the characteristic length scale that determines the transition between region B and region C of HA-FCG,
, is a function of the cyclic plastic zone, or fatigue process zone (FPZ) size. The FPZ is the region in front of the crack tip that experiences large-scale plasticity as a result of cyclic loading.
This zone is also associated with high levels of hydrostatic stress. Experimental results indicate that the characteristic transition length, as a function of the fatigue process zone size,
, is on the order of
where the Irwin estimate of the FPZ size [
] is defined as a function of the material yield strength
where the variable
is the maximum stress intensity factor and is related to Δ
where R is the load ratio of the test and is defined as R=K[min]/K[max]. Equation (1), by use of Eq. (2), is plotted as a dashed line along with the HA-FCG results of API X100 steel in Fig. 6.
Equation (1) correlates well with the transition between the two bi-linear HA-FCG regimes (region B and region C). It is hypothesized here that when the value of da/dN is smaller than x[tr], the
HA-FCG response is dominated by the stress-assisted hydrogen accumulation within the FPZ. Specifically, while hydrogen accumulation far-field in front of the crack tip is increased due to hydrostatic
stresses, the hydrogen concentration within the FPZ is exponentially proportional to the hydrostatic stress. As such, when the da/dN is within the zone of increased hydrogen concentration produced by
the 1/r dependence of the hydrostatic stress, the FCG falls in region B and is termed the transient HA-FCG regime. Transient is used here given that these materials exhibit this particular HA-FCG
response for a finite amount of crack extension per cycle. The presumed interaction between da/dN and the FPZ, which produces the response in the transient regime, is shown graphically in Fig. 7(a).
Specifically, when the crack extension, per cycle, falls within the FPZ having size $xtr$, the resulting FCGR is enhanced. In which case, the presence of the accumulated hydrogen at the crack tip
dominates the damage response in this HA-FCG regime. This results in a more brittle material response than that produced in the region A, ultimately leading to an FCG surface that is dominated by
crystallographic faceting. While crack extension per cycle within region A also occurs within the FPZ and its associated region of increased hydrogen concentration, it is hypothesized that the
HA-FCGR is not increased over that of air because the critical K-value for environmental-assisted mechanisms to occur (termed K[max] by Suresh and Ritchie [21]) has not yet been reached.
On the other hand, when the crack extension per cycle, da/dN, extends beyond the FPZ transition length, x[tr], with its associated enhanced hydrogen accumulation, the crack extension is affected
primarily by the far-field hydrogen accumulation in the material. This leads to the HA-FCG response that is dominated by traditional fatigue mechanisms; albeit at an accelerated rate due to the
initial crack extension per cycle occurring within the FPZ. This hypothesis is supported by the evidence that the FCG surface in this regime closely matches that of FCG surfaces tested in air. This
HA-FCG regime (region C) is termed the steady-state regime. The relationship between the per-cycle crack extension and the FPZ that correlates to region C is shown in Fig. 7(b). Specifically, in this
regime, the per-cycle crack extension grows through and extends beyond the FPZ. While the FCG surface produced by this regime appears to be mixed mode, it exhibits far more transgranular crack growth
than intergranular, and, therefore, more closely resembles FCG surfaces of materials tested in air.
Predictive Model
Based upon the above findings, a predictive model was sought to correlate the HA-FCGR of API pipeline steels to the applied load and geometry (together defining ΔK), and hydrogen pressure. The
purpose of such a model is to predict the remaining useful lifetime of steel components (e.g., pipes), given an understanding of the boundary conditions and initial conditions placed upon the
component. The following outlines the derivation of the predictive model intended for that purpose.
The HA-FCG response of API steels appears to follow a multilinear trend on the conventional log-log axes used to plot FCGR data. As an example, one could argue that the X100 data collected in
hydrogen gas pressurized to 1.72MPa follows a tri-linear trend, as proposed in Fig. 8.
Figure 8 proposes the existence of one HA-FCG trend for ΔK<∼8MPa m^1/2, a separate trend for ∼8MPa m^1/2 <ΔK<∼15MPa m^1/2, and a third trend for ΔK>∼15MPa m^1/2. In order of increasing ΔK,
the three regions are termed the “air,” “transient,” and “steady-state” regimes for the remainder of this work. These regimes correlate with regions A, B, and C, respectively. Given that the
steady-state regime is presumed to be dominated by the same damage mechanisms that occur in air, it is not surprising that the slope of the linear region in the steady-state regime matches that of
Based upon the understanding that the FCG response in hydrogen results as a superposition of a fatigue-only component and a hydrogen-assisted component, the following model framework has been
is the resultant FCG response,
is the FCG response for the material in air, given by
and $(da/dN)H$ is the hydrogen-assisted FCG response. The framework outlined in Eq. (4) views the two separate mechanisms as if occurring in parallel; that is, they occur concurrently and without
interaction. The Heaviside step function, δ, simply turns the hydrogen FCG response on when the ambient hydrogen pressure, P[H] is above a threshold value of $PHth=0.02MPa$ [26]. Although it is
likely that hydrogen affects the FCG response of steels at pressures below 0.02MPa, this value is used here, as it is the lowest hydrogen pressure for which steel HA-FCG results are known to have
been published [27].
As discussed above, the HA-FCG is understood to occur as a result of the interaction between two hydrogen-assisted mechanisms; namely a mechanism dominated by hydrogen accumulation at the crack tip,
which results in hydrogen-dominated FCG, and FCG aided by hydrogen, yet dominated by traditional fatigue-in-air damage mechanisms. The HA-FCG response is thought to result from an interaction between
a hydrogen-dominated damage mechanism and a damage mechanism dominated by the deformation state at the crack tip. The basis of this modeling technique is derived in the cumulative damage model
literature. The cumulative damage reasoning states that if damage mechanisms occur concurrently, the cumulative effect must incorporate damage mechanisms interactions. The two interacting HA-FCG
mechanisms are therefore modeled as springs in parallel such that the overall response
results from whichever mechanism is dominant and thereby providing a damage mechanism as the weak link for crack extension, while also being informed by the less dominant mechanism. The term is
defined as
is the HA-FCG response dominated by the hydrogen accumulation within the FPZ (transient regime), and
is the HA-FCG response dominated by crack-tip deformation (steady-state regime). The HA-FCG dominated by hydrogen accumulation in the FPZ is given by
$dadNPH=a1ΔKB1(PHm1 exp(−Q+VσhRT))d1$
is the activation energy for hydrogen diffusion (
=27.1kJ/mol) [
is the partial molar volume of hydrogen in the metal (
/mol) [
is the universal gas constant;
is the absolute temperature;
is the hydrostatic stress at a critical distance in front of the crack tip (Eq.
is the ambient hydrogen pressure; and
1, and
1 are fitting parameters. The stress intensity factor is used here to capture the information regarding the crack-tip stress and deformation state for lack of a better surrogate. The stress
intensity-driven component of the HA-FCG response was initially described by [
$dadNΔK=a2ΔKB2(PHm2 exp(−Q+VσhRT))d2$
2, and
2 are fitting parameters and all other parameters are defined above. It was found, however, that the HA-FCG results all converged at larger values of Δ
regardless of the ambient hydrogen pressure, thereby minimizing the effect of the terms within the parenthesis and driving the value of
2 toward 0 [
]. As such, the following functional form is proposed here for the stress intensity-driven HA-FCG:
The robust HA-FCG predictive model must be calibrated for each material of interest. A minimum of three FCG tests at three different hydrogen pressures and one FCG test in air are required to
calibrate the model. As extrapolation beyond the calibration data is not suggested, all four data sets should be created by use of ΔK values that bound the loading and boundary conditions of interest
to be subsequently modeled. Once calibrated, the model can predict HA-FCG as a function of geometry and load (ΔK), as well as hydrogen pressure. If the stress intensity for the geometry of interest
is known, e.g., a pipe with an internal thumbnail-shaped crack, one can then use the model to predict the cycles to failure, given particular loading and initial conditions. Furthermore, given a
crack of known size and geometry at known stress intensity, one may quantify the effect of an increase or decrease in hydrogen operating pressure upon the lifetime of the component. The full model
applied to an X100 pipeline steel is provided in Fig. 9. Additional implementation examples can be found in Ref. [31]. Model calibrations to several materials are provided in the Appendix. When
calibrated, the model fits HA-FCGR data to within a factor of 2.
Simplified Model
The full model implementation was presented to the ASME B31.12 committee on several occasions between 2012 and 2015. The committee determined that a simplified engineering version of the model should
be developed for potential B31.12 code implementation. The simplified version of the model divides the FCG response into three sections, applies power law relationships to each section, and couples
the three sections in the same mathematical framework as the full version of the model [
]. Specifically, the architecture of the simplified model is identical to that of the full version, as shown below:
The first term is again defined by Eq.
, and the hydrogen-assisted FCG again follows Eq.
, but the individual terms are simplified as follows:
Note that the simplified model is no longer predictive as a function of hydrogen pressure. As such, model calibrations must be performed for each material of interest, at all hydrogen pressures of
There are two ways in which the simplified model may be calibrated to experimental data. First, power law relationships may be fit to each of the three regions (air, transient, and steady-state),
using the relationships in Eqs. (5), (11), and (12). Specifically, the variables a, a3, a4, B, B3, and B4 are all determined as if each region of interest exists independent of the others. When
combining the power law relationships in this way, the transitions between each linear region of interest are more gradual, as shown in Fig. 10(a). Pseudo code that can be used to create the
parameter values a, a3, a4, B, B3, and B4, while minimizing user bias is provided in the Appendix as PseudoCode1.
The second way to calibrate the simplified model is to first fit power law relationships to the three individual regions of interest (as discussed above), followed by a second fitting of the
parameters in which the final parameter values for each region are determined by enabling neighboring regions to influence the others. In this way, the calibration more closely fits the transition
between regions exhibited by the experimental data. This technique was performed on a representative data set and the results are provided in Fig. 10(b). Pseudo code that can be used to create the
second-fit parameter values a1, a3, a4, B1, B3, and B4, while minimizing user bias, is provided in the Appendix as PseudoCode2 and 3.
While the second calibration technique does a far better job of correlating the data, it is more cumbersome to implement than the first. Simplified model calibrations for all materials tested to date
at NIST are provided in the Appendix.
ASME B31.12 Code Implementation
Upon review of both the full and simplified model implementations presented above, the ASME B31.12 committee determined that a single, upper-bound simplification should be employed within the code.
That is, given the vast number of microstructural constituents potentially found within pipeline steels and their respective FCGRs (see Fig. 2), the committee determined that use of the worst-case
model representation was the safest course of action. Use of this upper bound simplification would then enable the engineer to use materials having SMYS up to 480MPa (70 ksi) at design pressures up
to 20.7MPa (3000 psi) without penalty. The upper-bound solution utilizes Eqs. (5), (6), and (10)–(12), in conjunction with the parameter values provided in Table 1. The graphical representation of
the upper-bound FCG prediction, as well as a representative pipeline steel HA-FCG response, is provided in Fig. 11. Note that the upper bound curve provides an upper bound for all data tested at
NIST, including the data provided in Fig. 2.
Table 1
Upper bound for all materials tested
a B a3 B3 a4 B4
English (ksi in^1/2 in/cycle)
2.1746×10^−10 3.2106 2.9637×10^−12 6.4822 2.7018×10^−9 3.6147
Metric (MPa m^1/2 mm/cycle)
4.0812×10^−9 3.2106 4.0862×10^−11 6.4822 4.8810×10^−8 3.6147
Upper bound for all materials tested
a B a3 B3 a4 B4
English (ksi in^1/2 in/cycle)
2.1746×10^−10 3.2106 2.9637×10^−12 6.4822 2.7018×10^−9 3.6147
Metric (MPa m^1/2 mm/cycle)
4.0812×10^−9 3.2106 4.0862×10^−11 6.4822 4.8810×10^−8 3.6147
Although the upper bound appears to be conservative with respect to the experimental data shown in Fig. 11, it provides an upper bound for all potential HA-FCG data sets in existence for the boundary
and loading conditions of interest. As such, one may use the upper-bound model implementation with confidence that the FCG prediction will be conservative for any potential pipeline steel.
Future Work
The full HA-FCG model detailed in Eqs. (4)–(8) can predict the life of a component as a function of hydrogen pressure, provided that (a) there is a closed-form solution for ΔK for the geometry and
loading conditions of interest, and (b) the model is calibrated to that particular material. Both provisions are nontrivial. As was detailed in Ref. [31], depending upon which closed-form solution
one uses for an internal thumbnail-shaped crack (as an example), the resulting life estimate may be upward of 2× different than if another estimate was chosen. Additionally, full model calibrations
require a minimum of one test in air and one test at three different hydrogen pressures for each pipeline steel of interest. As can be seen in Fig. 2 and was discussed previously, the HA-FCG response
of pipeline steels is not correlated with their API designation. That is, the HA-FCG response is not correlated to the SMYS of the material. The HA-FCG response does appear to correlate with the
microstructure of the material, however. Specifically, the HA-FCGR for a material increases with increasing percent polygonal ferrite, as shown in Fig. 12.
To address the two provisions discussed above, NIST is supporting a concerted effort to create and calibrate microstructure-specific models, implemented into a finite element (FE) platform. Once
completed, the FE analysis will enable the user to calculate the HA-FCGR for any geometry and loading condition, not just those for which a closed-form K-solution exists. Furthermore, the
microstructure-based model will enable the engineer to calculate HA-FCGR for any material, with any microstructure, given that the microstructure of the pipeline material is known. Finally, the
implemented FE model would enable material design for improved HA-FCG response.
This paper, in conjunction with Ref. [18], provides a detailed accounting of the work performed at NIST to support a modification of the ASME B31.12 code to enable the use of higher strength pipeline
steels for hydrogen transportation. Specific conclusions from this work are as follows:
• A phenomenological model has been created to predict HA-FCG of pipeline steels. In the simplified engineering form, the model is capable of predicting HA-FCG for each material that it has been
calibrated to (see Table 2).
• A single, upper bound solution set of the phenomenological model has been chosen to be implemented within the ASME B31.12 code. While still somewhat conservative, if chosen to be utilized by the
design engineer, this model will enable the use of API steels having SMYS up to 70 ksi without penalty.
• The phenomenological model may also be used, in conjunction with the data in Table 2, to enable pipeline design engineers to more accurately predict pipeline-specific HA-FCG for engineering
Table 2
Material Section Frequency (Hz) R-value Hydrogen pressure (MPa) Paris prefactor (ai) Paris exponent (Bi)
X52 Alloy J All 1 0.5 0 2.43×10^−9 3.3085
Transient 1 0.5 6.89 1.80×10^−12 8.195
Steady-state 1 0.5 6.86 1.65×10^−7 3.224
Transient 1 0.5 20.68 9.32×10^−17 11.696
Steady-state 1 0.5 20.68 4.88×10^−8 3.6147
* Transient 1 0.5 5.5 6.77×10^−17 11.513
* Steady-state 1 0.5 5.5 1.24×10^−8 3.9786
* Transient 1 0.5 21 1.25×10^−13 8.7596
* Steady-state 1 0.5 21 2.63×10^−8 3.757
* All 1 0.5 0 1.66×10^−9 3.6111
X100 All 1 0.5 0 9.84×10^−9 2.8285
Transient 1 0.5 1.72 3.92×10^−15 9.5469
Steady-state 1 0.5 1.72 3.09×10^−8 3.5035
Transient 1 0.5 6.89 6.70×10^−13 7.8635
Steady-state 1 0.5 6.89 1.10×10^−7 3.1639
Transient 1 0.5 20.68 4.09×10^−11 6.4822
Steady-state 1 0.5 20.68 2.40×10^−7 3.05
Transient 0.1 0.5 6.89 9.41×10^−13 7.9222
Steady-state 0.1 0.5 6.89 1.46×10^−7 3.2187
X52 New All 1 0.5 0 1.61×10^−9 3.5021
Transient 1 0.5 5.51 1.59×10^−12 7.1574
Steady-state 1 0.5 5.51 6.80×10^−8 3.2774
Transient 1 0.5 34.47 2.93×10^−12 7.3247
Steady-state 1 0.5 34.47 5.78×10^−7 2.5876
X52 Vintage ALL 1 0.5 0 1.82×10^−9 3.3934
Transient 1 0.5 5.51 2.52×10^−14 8.2592
Steady-state 1 0.5 5.51 4.20×10^−8 3.3123
Transient 1 0.5 34.47 1.13×10^−15 10.63
Steady-state 1 0.5 34.47 1.89×10^−7 3.0779
X70B ALL 1 0.5 0 4.08×10^−9 3.2106
Transient 1 0.5 5.51 1.31×10^−15 9.9163
Steady-state 1 0.5 5.51 2.53×10^−8 3.6545
Transient 1 0.5 34.47 7.58×10^−14 8.812
Steady-state 1 0.5 34.47 2.31×10^−7 2.9292
X70A ALL 1 0.5 0 1.73×10^−9 3.4426
Transient 1 0.5 5.51 4.82×10^−14 8.5428
Steady-state 1 0.5 5.51 3.42×10^−8 3.575
Transient 1 0.5 34.47 — —
Steady-state 1 0.5 34.47 4.54×10^−7 2.762
Material Section Frequency (Hz) R-value Hydrogen pressure (MPa) Paris prefactor (ai) Paris exponent (Bi)
X52 Alloy J All 1 0.5 0 2.43×10^−9 3.3085
Transient 1 0.5 6.89 1.80×10^−12 8.195
Steady-state 1 0.5 6.86 1.65×10^−7 3.224
Transient 1 0.5 20.68 9.32×10^−17 11.696
Steady-state 1 0.5 20.68 4.88×10^−8 3.6147
* Transient 1 0.5 5.5 6.77×10^−17 11.513
* Steady-state 1 0.5 5.5 1.24×10^−8 3.9786
* Transient 1 0.5 21 1.25×10^−13 8.7596
* Steady-state 1 0.5 21 2.63×10^−8 3.757
* All 1 0.5 0 1.66×10^−9 3.6111
X100 All 1 0.5 0 9.84×10^−9 2.8285
Transient 1 0.5 1.72 3.92×10^−15 9.5469
Steady-state 1 0.5 1.72 3.09×10^−8 3.5035
Transient 1 0.5 6.89 6.70×10^−13 7.8635
Steady-state 1 0.5 6.89 1.10×10^−7 3.1639
Transient 1 0.5 20.68 4.09×10^−11 6.4822
Steady-state 1 0.5 20.68 2.40×10^−7 3.05
Transient 0.1 0.5 6.89 9.41×10^−13 7.9222
Steady-state 0.1 0.5 6.89 1.46×10^−7 3.2187
X52 New All 1 0.5 0 1.61×10^−9 3.5021
Transient 1 0.5 5.51 1.59×10^−12 7.1574
Steady-state 1 0.5 5.51 6.80×10^−8 3.2774
Transient 1 0.5 34.47 2.93×10^−12 7.3247
Steady-state 1 0.5 34.47 5.78×10^−7 2.5876
X52 Vintage ALL 1 0.5 0 1.82×10^−9 3.3934
Transient 1 0.5 5.51 2.52×10^−14 8.2592
Steady-state 1 0.5 5.51 4.20×10^−8 3.3123
Transient 1 0.5 34.47 1.13×10^−15 10.63
Steady-state 1 0.5 34.47 1.89×10^−7 3.0779
X70B ALL 1 0.5 0 4.08×10^−9 3.2106
Transient 1 0.5 5.51 1.31×10^−15 9.9163
Steady-state 1 0.5 5.51 2.53×10^−8 3.6545
Transient 1 0.5 34.47 7.58×10^−14 8.812
Steady-state 1 0.5 34.47 2.31×10^−7 2.9292
X70A ALL 1 0.5 0 1.73×10^−9 3.4426
Transient 1 0.5 5.51 4.82×10^−14 8.5428
Steady-state 1 0.5 5.51 3.42×10^−8 3.575
Transient 1 0.5 34.47 — —
Steady-state 1 0.5 34.47 4.54×10^−7 2.762
Funding Data
• Material Measurement Laboratory (Hydrogen pipelines).
• Pipeline and Hazardous Materials Safety Administration (Grant No. DTPH56-09-T-000005).
Simplified model calibrations performed to date are provided in Table 2. Table 3 provides the chemical compositions, tensile properties, and microstructural constituents of all materials in which
HA-FCG tests have been performed at NIST.
Table 3
Al C Co Cr Cu
X52 Alloy J 0.034 0.06 — 0.03 0.03
X52 Vintage 0.002 0.238 0.004 0.014 0.085
X52 New 0.017 0.071 0.002 0.033 0.016
X70A 0.015 0.048 0.002 0.24 0.22
X70B 0.012 0.053 0.002 0.23 0.25
X100 0.012 0.064 0.003 0.023 0.28
Fe Mn Mo N Nb
X52 Alloy J — 0.87 0.00 — 0.03
X52 Vintage 98.48 0.96 0.004 0.003 0.001
X52 New 98.37 1.06 0.003 0.004 0.026
X70A 97.51 1.43 0.005 0.005 0.054
X70B 97.41 1.53 0.003 0.005 0.054
X100 96.9 1.87 0.23 0.003 0.017
Ni P Si Ti V
X52 Alloy J 0.02 0.011 0.12 0.000 0.002
X52 Vintage 0.05 0.011 0.064 0.002 0.002
X52 New 0.016 0.012 0.24 0.038 0.004
X70A 0.14 0.009 0.17 0.027 0.004
X70B 0.14 0.01 0.16 0.024 0.004
X100 0.47 0.009 0.099 0.017 0.002
Al C Co Cr Cu
X52 Alloy J 0.034 0.06 — 0.03 0.03
X52 Vintage 0.002 0.238 0.004 0.014 0.085
X52 New 0.017 0.071 0.002 0.033 0.016
X70A 0.015 0.048 0.002 0.24 0.22
X70B 0.012 0.053 0.002 0.23 0.25
X100 0.012 0.064 0.003 0.023 0.28
Fe Mn Mo N Nb
X52 Alloy J — 0.87 0.00 — 0.03
X52 Vintage 98.48 0.96 0.004 0.003 0.001
X52 New 98.37 1.06 0.003 0.004 0.026
X70A 97.51 1.43 0.005 0.005 0.054
X70B 97.41 1.53 0.003 0.005 0.054
X100 96.9 1.87 0.23 0.003 0.017
Ni P Si Ti V
X52 Alloy J 0.02 0.011 0.12 0.000 0.002
X52 Vintage 0.05 0.011 0.064 0.002 0.002
X52 New 0.016 0.012 0.24 0.038 0.004
X70A 0.14 0.009 0.17 0.027 0.004
X70B 0.14 0.01 0.16 0.024 0.004
X100 0.47 0.009 0.099 0.017 0.002
Material σ[y] MPa (ksi) σ[UTS] MPa (ksi) Pearlite (%) Polygonal ferrite (%)
X52 Alloy J 442 (64.1) 576 (83.5) ∼20 ∼80
X52 Vintage 325 (47) 526 (76.3) ∼30 ∼70
X52 New 487 (70.6) 588 (85.3) ∼90
X70A 553 (80.2) 640 (92.8) ∼90
X70B 509 (73.8) 609 (88.3) ∼90
X100 689 (99.9) 811 (117.6)
Material Acicular ferrite (%) Bainite (%) Grain size (um)
X52 Alloy J ∼15
X52 Vintage ∼10
X52 New ∼10 ∼1
X70A ∼10 ∼1
X70B ∼10 ∼1
X100 ∼35 ∼65
Material σ[y] MPa (ksi) σ[UTS] MPa (ksi) Pearlite (%) Polygonal ferrite (%)
X52 Alloy J 442 (64.1) 576 (83.5) ∼20 ∼80
X52 Vintage 325 (47) 526 (76.3) ∼30 ∼70
X52 New 487 (70.6) 588 (85.3) ∼90
X70A 553 (80.2) 640 (92.8) ∼90
X70B 509 (73.8) 609 (88.3) ∼90
X100 689 (99.9) 811 (117.6)
Material Acicular ferrite (%) Bainite (%) Grain size (um)
X52 Alloy J ∼15
X52 Vintage ∼10
X52 New ∼10 ∼1
X70A ∼10 ∼1
X70B ∼10 ∼1
X100 ∼35 ∼65
Clear all previous data and variables
Prompt user for data range within file
Store the Delta K and da/dN data points as variables x and y respectively
Plot x versus y data on a logarithmic scale in both axis so that the user can view the data set
Prompt the user to select a point in which they think is part of region 1 the _________ based region
Store this point as variable PickedPoint
Create variables up and low and set both equal to zero
These will be used to turn on and off specific parts of the tolerance check loop
Create variable resetBounds and set equal to 1
This will be used to turn on and off the loop which determines the initial line fit for a region
Create variable nextRegion and set equal to 1
This variable keeps the program in a large loop until all three regions have been found
Create variable count and set equal to zero
This variable keeps track of how many times the main loop has been executed (how many regions have been found)
Create variable tolerance and set equal to desired initial tolerance.
This will be turned into a percentage later
Create main loop that will run while nextRegion is equal to 1
Create variable accepted and set equal to zero
This variable will keep the program in the next loop until the user has accepted the fit for the region being worked with
Create variable stop and set equal to zero
This variable will keep the program in the tolerance loop until a point on the fitted line exceeds the set tolerance
Create accepted loop that will run while accepted equals zero
Create conditional statement so that program will only advance here if resetBounds equals 1
Create variable lower and set equal to PickedPoint-1
Create conditional statement so that if lower is less than 1 then lower equals 1
This will keep the tolerance checks from indexing beyond the dataset
Create variable upper and set equal to PickedPoint+1
Create conditional statement so that if upper is greater than the number of x data points then upper equals the highest index of x
This will keep the tolerance checks from indexing beyond the dataset
Create sub set of data xx which contains all x points from the lower index to the upper index
Create sub set of data yy which contains all y points from lower index to upper index
Find a power fit line (y=αx^β) of (xx,yy) and store alpha and beta as variables a and b
Create variable yfitstart and set equal to the y values of the power fit line for x values 1 through the number of x points from raw data
End the resetBounds section by setting resetBounds equal to zero
Create variable yfit and set equal to yfitstart
Create variable toleranceAbove and set equal to 1+(tolerance/100)
Create variable toleranceBellow and set equal to 1-(tolerance/100)
Create a loop that will run as long as stop equals zero
Create conditional statement so that if the upper index of yfit is greater than toleranceAbove times the upper index of y or less than toleranceBelow times the upper index of y then setup equal to 1
Create conditional statement so that if the lower index of yfit is greater than toleranceAbove times the lower index of y or less than toleranceBelow times the lower index of y then set low equal to
Create conditional statement so if up and low both equal 1 then stop equals 1 which will exit the tolerance checking loop
Create conditional statement so that if up equals zero upper equals upper plus one
Create conditional statement so that if upper is greater than the number of x data points then upper equals the highest index of x
Create conditional statement so that if low equals zero lower equals lower plus one
Create conditional statement so that if lower is less than 1 then lower equals 1
Change sub set xx to contain all x points from the new lower index to the new upper index
Change sub set yy to contain all y points from the new lower index to the new upper index
Find a power fit line (y=αx^β) of (xx,yy) and store alpha and beta as variable a and b
Change variable yfit to equal to the y values of the power fit line for x values 1 through the number of x points from raw data
On a logarithmic plot in both axis plot (x,y) and (x,yfit)
(x,y) should be plotted as individual data points. (x,yfit) should be plotted as a line
Prompt user for feed back
Ask user if they accept the fit
Ask user if they would like to change the picked point
Ask user if they would like to adjust the tolerance
Create conditional statement so that if the user picked a new point then store the new point as variable PickedPoint and set resetBounds equal to 1
Create conditional statement so that if the user accepts the fit stop equals 1
Otherwise set accepted, stop, up, and low all equal to zero. Set yfit equal to yfitstart
Set variable lower equal to PickedPoint-1
Create conditional statement so that if lower is less than 1 then lower equals 1
Set variable upper equal to PickedPoint+1
Create conditional statement so that if upper is greater than the number of x data points then upper equals the highest index of x
Create conditional statement if count equals 1
Create variable R1upper and set equal to upper
Create variable R1lower and set equal to lower
Create variable R1yfit and set equal to yfit
Create variable a1 and set equal to a
Create variable b1 and set equal to b
Plot raw (x,y) data on a logarithmic scale in both axis so that the user can view the data set
Prompt the user to select a point in which they think is part of region 2 the _________ based region
Store this point as variable PickedPoint
Set variable resetBounds equal to 1
Create conditional statement if count equals 1
Create variable R2upper and set equal to upper
Create variable R2lower and set equal to lower
Create variable R2yfit and set equal to yfit
Create variable a2 and set equal to a
Create variable b2 and set equal to b
Plot raw (x,y) data on a logarithmic scale in both axis so that the user can view the data set
Prompt the user to select a point in which they think is part of region 3 the _________ based region
Store this point as variable PickedPoint
Set variable resetBounds equal to 1
Create conditional statement if count equals 3
Create variable R3upper and set equal to upper
Create variable R3lower and set equal to lower
Create variable R3yfit and set equal to yfit
Create variable a3 and set equal to a
Create variable b3 and set equal to b
Set variable nextRegion equal to zero
Create variables R12x and R12y and store the x and y values of the intercept between regions 1&2
Create variables R23x and R23y and store the x and y values of the intercept between regions 2&3
Preform any required operations required to trim regions to intercepts and combine the three trimmed regions into one x and one y array called xMeasured and yMeasured respectively.
Create array ycalculated and store all y values for all three regions based on the equation________
Plot on a logarithmic plot in both axis (x,y), (x,ycalculated), (xMeasured,yMeasured)
(x,y) should be plotted as individual points. (x,ycalculated) and (xMeasured,yMeasured) should be plotted as solid lines in separate colors
PseudoCode2 and 3- to be used together
Clear all previous data, variables, etc.
Call code provided in pseudo code 1 and carry over variables a1, a2, a3, b1, b2, b3, data, x, ycalculated, xMeasuered, and yMeasured.
Prompt user to answer yes or no to the question “Do you have Paris values for the material ran in air?”
Create variable air and set equal to 1 if user entered yes or 0 if user entered no
Create conditional statement for value of air
Prompt user for “Paris prefactor for air” and overwrite a1 from pseudo code 1
Prompt user for “Paris exponent for air” and overwrite b1 from pseudo code 1
Create a 3x2 matrix data1 and populate with $a1b1a2b2a3b3$
Create a 3x2 matrix data1 and populate with $a1b1a2b2a3b3$
End conditional statement
Create variable data2 and set equal to data
Create cell data3 and populate with {data1,data2}
Create variable opt_parameteres and set equal to the output from the function described in pseudo code 3 using data3 as an input
Plot on a logarithmic plot in both axis (xMeasured,yMeasured) and (x,ycalculated)
Create variable airf and set equal to opt_parameters(1,1)*10̂(-10) * data2(:,1)̂opt_parameters(1,2)
Where (1,1) is (row number, column number) and: means all
Create variable transf and set equal to opt_parameters(2,1) *10̂-19 *data2(:,1)̂opt_parameters(2,2)
Create variable ssf and set equal to opt_parameters(3,1)*10̂-10*data2(:,1).̂opt_parameters(3,2)
Create variable fitlifef and set equal to airf+((transf).̂(-1)+(ssf).̂(-1)).̂(-1)
Plot on a logarithmic plot in both axis (data2(:,1), fitlifef) and (x,y)
Create variable piecewise_values and set equal to data1
Create 3x2 matrix
and populate with
$opt_parameters(1,1)*10 ̂−10opt_parameters(1,2)opt_parameters(2,1)*10 ̂−19opt_parameters(2,2)opt_parameters(3,1)*10 ̂−10opt_parameters(3,2)$
Create function that takes data3 as an input and outputs opt_parameters
Create variable data1 and set equal to cell one of data3
Create variable data2 and set equal to cell two of data3
Create variable expnt_air and set equal to the exponent on data1(1,1)
Where (1,1) is (row number, column number). This format will be used going forward
Create variable expnt_trans and set equal to the exponent on data1(2,2)
Create variable expnt_ss and set equal to the exponent on data1(3,2)
Create 3x2 matrix ab and populate with $data11,1*10 ̂expnt_airdata(1,2)data12,1*10 ̂expnt_airdata(2,2)data13,1*10 ̂expnt_airdata(3,2)$Create 3x2 matrix lb and populate with$ab1,1*.999ab1,2*.75ab2,1*10 ̂
Create 3x2 matrix ub and populate with $ab1,1*10ab1,2*3ab2,1*1.1ab2,2*5ab3,1*10ab3,2*1.25$
Create function that will minimize a residual function error1 based on ab, lb, ub, with a tolerance 1e-8 and stores the resulting optimized values of ab as opt_parameters
Note: an example of such a function is fmincon in matlab
Create the residual function error(params,data2)
Where params is a variable filled with variable set to be optimized, ab. Params should be fed back into minimization function until the tolerance is reached.
Create variable a1 and set equal to params(1,1)*10̂-10;
Create variable b1 and set equal to params(1,2);
Create variable a2 and set equal to params(2,1)*10̂-19;
Create variable b2 and set equal to params(2,2);
Create variable a3 and set equal to params(3,1)*10̂-10;
Create variable b3 and set equal to params(3,2);
Create a loop to go from 1 to the number of rows in data2
Create variable air(index#) and set equal to a1*data2(index #,1)̂b1
Where index # is the number of times through the loop and air will become an array of size 1 x number of rows in data2. This format will be used going forward
Create variable trans(index #) and set equal to a2*data2(index #,1)̂b2
Create variable ss(index #) and set equal to a3*data2(index #,1)̂b3;
Create variable fitlife(index #) and set equal to air(index #)+((trans(index #))̂(-1)+(ss(index #))̂(-1))̂(-1)
Create variable residual (index #) and set equal to fitlife(index #)-data2(index #,2)
, “
American Energy Independence, Safety Means More Pipelines
,” Washington Examiner, Washington, DC, accessed July 10, 2013,
U.S. DOE,
, “The Impact of Increased Use of Hydrogen on Petroleum Consumption and Carbon Dioxide Emissions,” U.S. Energy Information Administration, U.S. Department of Energy, Washington, DC, Report No.
H. J.
, and
J. H.
, “Sensitivity of Steels to Degradation in Gaseous Hydrogen,” Hydrogen Embrittlement: Prevention and Control, ASTM, West Conshohocken, PA, Standard No.
ASTM STP 962
, “Tensile Testing of Carbon Steel in High Pressure Hydrogen,”
Paper No. PVP2007-26736.
B. P.
D. K.
, and
San Marchi
, “
Sustained Load Cracking of Steels for Hydrogen Storage and Delivery
International Hydrogen Conference,
Moran, WY, Sept. 7–10, pp.
, and
, “
Damage Under High Pressure Hydrogen Environment of a High Strength Pipeline Steel X80
International Hydrogen Conference
, Moran, WY, Sept. 7–10, pp. 357–364.
, and
, “
Tensile and Fracture Properties of Carbon and Low Alloy Steels in High Pressure Hydrogen
International Hydrogen Conference,
Moran, WY, Sept. 7–10, pp. 349–356.
Hydrogen Piping and Pipelines
American Society of Mechanical Engineers
New York
, p.
A. J.
E. S.
D. G.
R. L.
D. S.
A. E.
, and
L. E.
, “The Effect of Microstructure on the Hydrogen-Assisted Fatigue of Pipeline Steels,”
Paper No. PVP2013-97217.
J. R.
J. W.
, and
R. L.
, “
Economic Impact of Applying High Strength Steels in Hydrogen Gas Pipelines
Int. J. Hydrogen Energy
), pp.
A. J.
E. S.
N. E.
Y. S.
J. D.
R. L.
, and
A. E.
, “
Fatigue Crack Growth of Two Pipeline Steels in a Pressurized Hydrogen Environment
Corros. Sci.
, pp.
E. S.
A. J.
R. L.
, and
D. S.
, “FCGR of Pipeline Steels in Pressurized Hydrogen Gas: A Comparison of Cyclic Loading Rates,”
SteelyHydrogen, 2nd International Conference on Metals and Hydrogen
, Ghent, Belgium, May 5–7, pp. 403–416.
E. S.
R. L.
D. S.
L. E.
D. G.
, and
, “Summary of an ASME/DOT Project on Measurements of Fatigue Crack Growth Rate of Pipeline Steels,”
Paper No. PVP2014-28938.
E. S.
A. J.
R. L.
D. S.
L. E.
, and
D. G.
, “
Fatigue Crack Growth Rates of API X70 Pipeline Steel in a Pressurized Hydrogen Gas Environment
Fract. Fatigue Eng. Mater. Struct.
), pp.
A. J.
E. S.
D. S.
D. S.
R. L.
D. G.
, and
, “
Fatigue Crack Growth of Two X52 Pipeline Steels in a Pressurized Hydrogen Environment
International Hydrogen Conference
, Moran, WY, Sept. 9–12, pp. 299–307.
, and
, “
Small Fatigue Crack Growth Characteristics and Fracture Surface Morphology of Low Carbon Steel in Hydrogen Gas
Int. J. Fract.
(1–2), pp.
A. J.
E. S.
R. L.
L. E.
D. G.
D. S.
, and
N. W.
, 2018, “
Fatigue Measurement of Pipeline Steels for the Application of Transporting Gaseous Hydrogen
ASME J. Pressure Vessel Technol.
(1), p. 011407.
R. L.
K. O.
E. S.
, and
A. J.
, “
Fatigue Crack Growth of X100 Pipeline Steels in Gaseous Hydrogen
Int. J. Fatigue
, pp.
San Marchi
D. G.
B. P.
K. A.
, and
, “Fracture and Fatigue of Commercial Grade API Pipeline Steels in Gaseous Hydrogen,”
Paper No. PVP2010-25825.
, and
R. O.
, “
Mechanistic Dissimilarities Between Environmentally Influenced Fatigue-Crack Propagation at Near-Threshold and Higher Growth Rates in Lower Strength Steels
Met. Sci.
), pp.
, and
, “
Microscopic Characterization of Hydrogen-Induced Quasi-Brittle Fatigue Fracture in Low-Strength Carbon Steel
Mater. Lett.
), pp.
R. P.
, and
, “
Reconsideration of the Superposition Model for Environmentally Assisted Fatigue Crack Growth
Scr. Metall.
), pp.
R. W.
Deformation and Fracture Mechanics of Engineering Materials
4th ed.
Hoboken, NJ
L. T.
Fracture Mechanics, Fundamentals and Applications
3rd ed.
CRC Press
Boca Raton, FL
B. P.
, “Technical Reference on Hydrogen Compatibility of Materials-Plain Carbon Ferritic Steels: C-Mn Alloys (Code 1100),” Sandia National Laboratories, Livermore, CA, Report No.
G. H.
, “
On the Mechanism of Hydrogen-Enhanced Crack Growth in Ferritic Steels
Second Conference on the Mechanical Behavior of Materials,
Boston, MA, Aug. 16–20, pp.
H. G.
, and
J. E.
, “Gas-Phase Hydrogen Permeation Through Alpha Iron, 4130 Steel, and 304 Stainless Steel From Less Than 100 C to Near 600 C,” NASA Ames Research Center, Moffett Field, CA, Technical Report No.
S. X.
, and
, “
Mechanics and Thermodynamics on the Stress and Hydrogen Interaction in Crack Tip Stress Corrosion: Experiment and Theory
J. Mech. Phys. Solids
), pp.
, “
Effects of Hydrogen on the Properties of Iron and Steel
Metall. Mater., Trans. A
), pp.
R. L.
E. S.
, and
A. J.
, “
Fatigue Crack Growth Modeling of Pipeline Steels in High Pressure Gaseous Hydrogen
Int. J. Fatigue
, pp.
R. L.
E. S.
N. E.
Y. S.
, and
A. J.
, “
Fatigue Crack Growth of Pipeline Steels in Gaseous Hydrogen-Predictive Model Calibrated to API-5L X52
International Hydrogen Conference
, Moran, WY, Sept. 9–12, pp. 329–337.
R. L.
E. S.
, and
A. J.
, “Development of an Engineering-Based Hydrogen-Assisted Fatigue Crack Growth Design Methodology for Code Implementation,”
Paper No. PVP2014-28943. | {"url":"https://vibrationacoustics.asmedigitalcollection.asme.org/pressurevesseltech/article/140/2/021403/383751/Development-of-a-Model-for-Hydrogen-Assisted","timestamp":"2024-11-14T18:22:03Z","content_type":"text/html","content_length":"406037","record_id":"<urn:uuid:98bc48f0-a5c4-4384-b378-fca355f32190>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00081.warc.gz"} |
Math Colloquia - <학부생을 위한 ɛ 강연> Convergence of Fourier series and integrals in Lebesgue spaces
Convergence of Fourier series and integrals is the most fundamental question in classical harmonic analysis from its beginning. In one dimension convergence in Lebesgue spaces is fairly well
understood. However in higher dimensions the problem becomes more intriguing since there is no canonical way to sum (and integrate) Fourier series (and integrals, respectively), and convergence of
the multidimensional Fourier series and integrals is related to complicated phenomena which can not be understood in perspective of convergence in one dimension. The Bochner-Riesz conjecture may be
regarded as an attempt to understand multidimensional Fourier series and integrals. Even though the problem is settled in two dimensions, it remains open in higher dimensions. In this talk we review
developments in the Bochner-Riesz conjecture and discuss its connection to the related problems such as the restriction and Kakeya conjectures. | {"url":"http://my.math.snu.ac.kr/board/index.php?mid=colloquia&l=en&sort_index=speaker&order_type=asc&page=6&document_srl=786572","timestamp":"2024-11-02T05:15:59Z","content_type":"text/html","content_length":"43730","record_id":"<urn:uuid:c9c040cd-f173-4ea7-8e11-cd2604de5e52>","cc-path":"CC-MAIN-2024-46/segments/1730477027677.11/warc/CC-MAIN-20241102040949-20241102070949-00228.warc.gz"} |
ncert solutions for class 7th mathematics Archives - MATHS GLOW
Exponents and Powers Exercise 11.3 solutions NCERT class 7 maths NCERT 7th class maths solutions chapter 11 Exponents and Powers Exercise 11.3 are given. You should study the textbook lesson
Exponents and Powers very well. You must observe and practice all example problems and solutions are given in the textbook. You can observe the solutions […]
NCERT Class 7 maths chapter 11 Exponents and Powers exercise 11.3 solutions Read More »
NCERT solutions for class 7th maths Chapter 1/Integers solutions,problems with solutions of Integers vii class
NCERT SOLUTIONS FOR CLASS 7th MATHS CHAPTER 1 INTEGERS Integers class 7 chapter 1 NCERT Maths solutions are given. You should study the textbook lesson very well. You can observe and practice example
problems and solutions given in the textbook. CA foundation maths solutions CBSE SOLUTIONS FOR CLASS 7th MATHS CHAPTER 1 INTEGERS Important points
NCERT solutions for class 7th maths Chapter 1/Integers solutions,problems with solutions of Integers vii class Read More »
Exercise 6.4 solutions class 7 maths NCERT The Triangle and its Properties
The Triangle and its Properties Exercise 6.4 solutions NCERT class 7 NCERT mathematics class 7 The Triangle and its Properties Exercise 6.4 solutions are given. First you should study the textbook
lesson The Triangle and its Properties very well. You should practice all example problems and solutions are given in the textbook. You can observe
Exercise 6.4 solutions class 7 maths NCERT The Triangle and its Properties Read More »
NCERT Maths solutions for chapter 9 Perimeter and Area exercise 9.2 class 7
NCERT maths solutions for chapter 9 Perimeter and Area exercise 9.2 solutions NCERT Mathematics class 7th textbook chapter 9 exercise 9.2 solutions are given. You should study the textbook lesson
Perimeter and Area very well. You should also observe and practice all example problems and solutions are given in the textbook. You can observe the
NCERT Maths solutions for chapter 9 Perimeter and Area exercise 9.2 class 7 Read More »
Symmetry Exercise 12.3 class 7 Maths NCERT solutions
Symmetry exercise 12.3 solutions class 7 NCERT NCERT class 7 mathematics chapter 12 Symmetry Exercise 12.3 solutions are given. You should read and study the textbook lesson very well. You should
practice all problems and solutions are given in the textbook. You can observe the solutions given below and try them in your own method.
Symmetry Exercise 12.3 class 7 Maths NCERT solutions Read More »
NCERT solutions for Maths class 7 Chapter 7 exercise 7.2 Comparing Quantities
Comparing Quantities exercise 7.2 solutions NCERT maths class 7 NCERT mathematics class 7 chapter 7.2 exercise 7.2 solutions are given. You should read the textbook lesson Comparing Quantities very
well. You should also practice all example problems and solutions given in the textbook. You can observe the solutions and try them in your own method.
NCERT solutions for Maths class 7 Chapter 7 exercise 7.2 Comparing Quantities Read More »
NCERT Maths Class 7 solutions
Maths class 7th NCERT Solutions NCERT mathematics Class 7th solutions for some chapters are given. You should study the textbook lessons very well. Read and study every lesson. You should observe and
practice all example problems and solutions are given in the textbook. You can observe the given solutions and try them in your own
NCERT Maths Class 7 solutions Read More »
NCERT Maths Solutions class 7 Exercise 12.2 Symmetry
Symmetry exercise 12.2 solutions class 7 NCERT NCERT class 7 mathematics chapter 12 Symmetry Exercise 12.2 solutions are given. You should practice all problems and solutions are given in the
textbook. You can observe the given solutions and try them in your own method. You can see. NCERT maths class 7 solutions Symmetry Exercise 12.1
NCERT Maths Solutions class 7 Exercise 12.2 Symmetry Read More »
NCERT solutions class 7 maths chapter 12 Symmetry Exercise 12.1
Symmetry exercise 12.1 solutions class 7 NCERT NCERT class 7 mathematics chapter 12 Symmetry Exercise 12.1 solutions are given. You should practice all problems and solutions are given in the
textbook. You can observe the given solutions and try them in your own method. You can see. NCERT maths class 7 solutions Symmetry Exercise 12.1
NCERT solutions class 7 maths chapter 12 Symmetry Exercise 12.1 Read More »
Chapter 6 Exercise 6.5 NCERT maths class 7 The Triangle and its Properties
The Triangle and its Properties Exercise 6.5 solutions NCERT class 7 NCERT mathematics class 7 The Triangle and its Properties Exercise 6.1 solutions are given. First you should study the textbook
lesson The Triangle and its Properties very well. You should practice all example problems and solutions are given in the textbook. You can observe
Chapter 6 Exercise 6.5 NCERT maths class 7 The Triangle and its Properties Read More » | {"url":"https://www.mathsglow.com/category/ncert-solutions-for-class-7th-mathematics/","timestamp":"2024-11-13T20:43:08Z","content_type":"text/html","content_length":"110787","record_id":"<urn:uuid:614dd34c-01bd-44a9-87c2-b6c4ce40ee16>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00576.warc.gz"} |
Domino Standard Environments
Each Domino installation comes with a standard Environment known as the Domino Analytics Distribution (DAD). Periodically, Domino publishes a new set of standard Environments with updated libraries
and packages. These Environments include some common data science packages and libraries pre-configured for use in Domino.
Domino also makes a Domino Minimal Distribution (DMD) available that includes only the packages required to work in Domino. These are a good option if you want to build a Domino-compatible
Environment from scratch. This helps speed Environment build times and execution start times.
Domino Cluster Environments work like a Domino Standard Environments, but have additional libraries to support specific types of clusters. They contain the same workspace tools and general packages
as the DSE to support general data science workflows. You can use these Environments with any Domino execution like a Workspace or Job, but they are best used in a distributed compute cluster
alongside a Domino Cluster Environment. These are smaller and simpler Environments and are only suitable for use in the worker nodes of the cluster. DSEs cannot be used for worker nodes in a cluster.
Domino Environments (abstractions on top of Docker images). Users can create Environments, use those provided by Domino, or edit existing ones.
Domino Analytics Distribution (DAD)
The Domino Analytics Distributions can handle most of what a typical data science workflow needs out of the box. They include the most common Python and R packages. Several versions are available
if you need CUDA support.
quay.io/domino/base hosts the built images unless otherwise stated in the READMEs for the corresponding image. The version of the Domino Environment indicates the version of Domino that the
Environment is shipped with, but typically any image will work on any version of Domino.
Domino Minimal Distribution (DMD)
While the DAD includes most of what a data scientist needs to do their work, the DMD includes only the bare necessities required to work in Domino.
The DMD provides an image that allow you to:
• Open Jupyter and Jupyterlab.
• Batch run Python and R jobs.
• Host a Shiny web app.
• Publish a Python and R Model API.
• Use Domino’s Git integration.
• Install Python and R packages.
To shrink the DMD, remove workspaces that you won’t use or remove Python or R.
The images are hosted on quay.io/domino/base unless otherwise stated in the READMEs for the corresponding image. The version of the Domino Environment indicates the version of Domino that the
Environment is shipped with, but typically any image will work on any version of Domino.
By default, the DSE includes fewer packages than the DAD, giving it a smaller footprint and making it faster and easier to work with. See Environments for more information about how to add packages
to the DSE. The DSE comes with a GPU version that includes CUDA support and common packages for taking advantage of GPUs. WARNING: Domino recommend using an Environment with explicit GPU support when
using GPU hardware tiers.
The version of the Domino Environment indicates the version of Domino that the Environment is shipped with, but typically any image will work on any version of Domino.
Domino Minimal Environment (DME)
The DME has fewer packages and is lighter weight than the Domino Standard Environment (DSE).
The Domino Minimal Environment includes Jupyter and JupyterLab workspace support, but does not include several packages that are included in the DSE. Domino recommends using the DME if you will
be doing several custom installations on top of a base Environment image, because its smaller size speeds build times and avoids conflicting dependencies. See Environments for information about
how to add packages to the DME.
The version of the Domino Environment indicates the version of Domino that the Environment is shipped with, but typically any image will work on any version of Domino.
The following Environments are designed to be used with compute cluster Environments. You can use these Environments with any Domino execution like a Workspace or Job, but they are best used in a
distributed compute cluster alongside a Domino Compute Cluster Environment.
Compute Cluster Environments work like the Domino Standard Environments, but they have additional libraries to support a specific cluster type. They contain the same workspace tools and general
packages as the DSE to support general data science workflows.
A cluster won’t work correctly if the worker nodes are not using the appropriate Domino Cluster Environment for cluster workers and compatible Domino Compute Environment for Job or Workspace.
The Domino Spark Environment is built specifically for workspaces that control a Spark cluster. It includes Scala and Spark on top of the typical DSE functionality. This Environment is best used
alongside a Spark cluster Environment. To ensure compatibility between the Spark compute Environment and Spark cluster Environment, the Spark and Python versions must match across Environment images.
The version of the Domino Environment indicates the version of Domino that the Environment is shipped with, but typically any image will work on any version of Domino.
The Domino Ray Environment is built specifically for workspaces that control a Ray cluster. It includes Ray on top of the typical DSE functionality. This Environment is best used alongside a Ray
cluster Environment. To ensure compatibility between the Ray compute Environment and Ray cluster Environment, the Ray and Python versions must match across Environment images.
See the compute Environment catalog to access Domino Minimal Environment images. The version of the Domino Environment indicates the version of Domino that the Environment is shipped with, but
typically any image will work on any version of Domino.
The Domino Dask Environment is built specifically for workspaces that control a Dask cluster. It includes Dask on top of the typical DSE functionality. This Environment is best used alongside a Dask
cluster Environment. To ensure compatibility between the Dask compute Environment and Dask cluster Environment, the Dask and Python versions must match across Environment images.
See the compute Environment catalog to access Domino Minimal Environment images. The version of the Domino Environment indicates the version of Domino that the Environment is shipped with, but
typically any image will work on any version of Domino.
The Domino Standard Environment also includes a GPU version with support for CUDA and common GPU specific libraries like Torch and Tensorflow. These GPU-enabled Environment images are larger, so
Domino recommends that you use them only if you are using a GPU-enabled hardware tier.
The DSE Environment also has a version that includes FileSystem in Userspace (FUSE) binaries to enable Goofys and SSHFS support. You can add these commands to your Environment Dockerfile to enable
FUSE functionality:
USER root
# Goofys
ADD https://github.com/kahing/goofys/releases/download/v0.24.0/goofys /usr/bin/
RUN chmod a+x /usr/bin/goofys
# SSHFS
RUN apt-get update && apt-get install -y sshfs &&
sed -i "s/^#user_allow_other/user_allow_other/" /etc/fuse.conf
USER ubuntu
How can I tell which image I’m currently using?
The URI for the image will be listed on your compute Environment’s overview page. If your Environment is built on top of another Environment, you may need to click through to the parent
Environment before seeing the underlying docker image.
I have a third-party Docker image, can I use that in Domino?
Maybe, but not likely without some customization. The DSE and DME are tested and configured to meet the Domino platform requirements and conventions. For example, by convention Domino uses /mnt
as the default working directory. It is much easier to use the DME as your base Environment to build on top of than it is to try to get a 3rd party Environment to work directly in Domino.
However, this is not the case for Environments for compute cluster worker nodes. In most cases, these Environments can be plugged directly into Domino with no modifications, as they do not need
to support the same workflows as the Domino Compute Environments.
How can I learn about new versions of the DSE and make feature requests?
See the Compute Environment Catalog for the list of environments. To make feature requests, submit a request to Domino support. | {"url":"https://docs.dominodatalab.com/en/4.5/user_guide/0d73c6/domino-standard-environments/","timestamp":"2024-11-07T23:13:02Z","content_type":"text/html","content_length":"61894","record_id":"<urn:uuid:1bb7b838-f74c-4345-80a0-0f3ac59ad5fe>","cc-path":"CC-MAIN-2024-46/segments/1730477028017.48/warc/CC-MAIN-20241107212632-20241108002632-00077.warc.gz"} |
How to read a Learning curve?
Learning curves help understand the evolution of a model's performance with the amount of data used to train that model. They can be used for instance to know whether more data would help the model
be better or not. They also enable you to know whether the model is a good fit, underfitting, or overfitting.
What is a learning curve
To produce a learning curve, many models are trained using a different proportion of the data available for training. For each proportion, the model performance metric (mean square error in our case)
will be calculated. In some cases, to avoid having too much variability in the results, it is possible to train multiple models for the same proportion of data and get an average (see curve on test
data on the left).
On the Figure shown below for instance, you can see that training a model with more data will improve the model's performance as the mean square error (MSE) keeps going down for the test data. Point
1 shows the MSE when the model is trained on 50% of the available data, and point 2 shows the MSE when the model is trained on 100% of the available data.
How to read a learning curve?
In the examples below, we trained 3 models (linear regression, polynomial regression and decision tree regression) on the same data and we plotted the learning curve for each model:
Example for an underfitting model: Linear regression
• Trend in data neither covered in train nor test set. Error for both sets very high (small gap between the two curves).
• Bringing more data won’t help. You need to use a more complex model to capture the trends in the data.
Example for a suitable model: Polynomial regression
• Trend in data captured well for both data sets. Low train set error and similar test set error (small gap between the two curves, or gap that becomes smaller).
• Bringing more data can help if the curves are not fully converged.
Example for an overfitting model: Decision Tree Regression
• Train set captured very well, test set very bad. Low train set error, high test set error (large gap between the two curves).
• Use a less complex model to reduce overfitting. If you are sure you’re using the right model bringing more data also helps to reduce overfitting.
Read here to find out what “less” or “more complex” means in practical.
Was this article helpful?
That’s Great!
Thank you for your feedback
Sorry! We couldn't be helpful
Thank you for your feedback
Feedback sent
We appreciate your effort and will try to fix the article | {"url":"https://support.monolithai.com/support/solutions/articles/80001014316-how-to-read-a-learning-curve-","timestamp":"2024-11-14T21:37:08Z","content_type":"text/html","content_length":"177743","record_id":"<urn:uuid:a1f3197c-a221-4e19-82d3-aee021afdcc5>","cc-path":"CC-MAIN-2024-46/segments/1730477395538.95/warc/CC-MAIN-20241114194152-20241114224152-00076.warc.gz"} |
COVARIANCE.P Excel
What Is COVARIANCE.P Excel Function?
The COVARIANCE.P Excel function measures how two sets of data points are linearly related. It returns population covariance, which is the average of the derivations’ products of deviations for
each pair of data points in two data sets. It is useful in financial analysis and portfolio management to understand the co-movement between assets. It assumes the data represents the entire
population, providing a more accurate estimate of covariance compared to COVARIANCE.S.
The example shows how to calculate the covariance of numbers in a range, given two sets of values, using the COVARIANCE.P function in Excel.
Enter the formula =COVARIANCE.P(A2:A5, B2:B5) in cell D2. You get the result as 1.125, which is the covariance.
Key Takeaways
• COVARIANCE.P in Excel measures how two sets of data points move together. It is especially useful in financial analysis and portfolio management to understand how assets co-move.
• The COVARIANCE.S function is accessible in MS Excel 2010, serving as an enhanced iteration of the COVAR function found in previous Excel editions.
• The syntax of the COVARIANCE.P function is COVARIANE.P(array1, array2)
• By using this function, analysts can assess the degree to which changes in one variable are related to changes in another, helping them make informed decisions regarding portfolio
diversification, asset allocation, and risk mitigation strategies.
• The COVARIANCE.P function is used in quantitative analysis and decision-making processes for professionals across various industries.
1. Array1 – (Mandatory) This is the first cell range of integers.
2. Array2 – (Mandatory) This is the second cell range of integers.
How To Use COVARIANCE.P Function in Excel?
To effectively utilize the COVARIANCE.P function in Excel, please follow the steps outlined below.
#1 – Access from the Excel ribbon
1. Select the cell in which the answer is to be displayed. Navigate to the Formulas tab and click on it.
2. Select the More Functions option from the function library.
3. To utilize statistical functions, first click on “Statistical” in the drop-down menu, then select “COVARIANCE.P” from the options provided.
4. Input the values for the arguments in the Function Arguments window and then proceed by clicking OK to continue.
#2 – Enter the worksheet manually
Step 1: To calculate the result using Excel, start by selecting an empty cell and entering the formula =COVARIANCE.P(). Alternatively, you can start typing =C and then double-click on the
COVARIANCE.P function from the Excel suggestions.
Step 2:
1. Enter the values for the arguments.
2. Close the braces.
3. Click on the Enter key to see the results.
Let us look at an example of how to use the COVARIANCE.P function in Excel in different scenarios.
Example #1
To gain a better understanding COVARIANCE.P function, let us look at two different stocks, ABC and XYZ, and their rate of returns for ten days. Let us calculate the covariance of the stocks. Look at
the values provided in the table below.
Let us proceed with the following steps:
Step 1: To calculate the co-variance, enter the formula shown below in cell E2.
= COVARIANCE.P(B2:B11,C2:C11)
Step 2: You get the population covariance value in cell E2.
When calculating the covariance of two stocks using the COVARIANCE.P Excel function, it provides valuable insights into the relationship between the two.
The covariance value indicates how the returns of one stock move in relation to the returns of another stock.
A positive covariance implies that when one stock’s return increases, and other hand, while a negative covariance suggests an inverse relationship. In the result below, we have a negative value,
showing an inverse relationship between the two stocks.
Example #2
In this example, we will explore the COVARIANCE.P function using the share prices of two companies, X and Y, for 12 months. We will be calculating the covariance between the shares of these
companies. Please refer to the table for the values needed for this calculation.
Look at the table above. To utilize the COVARIANCE.P Excel function, please follow the steps outlined below:
Step 1: In cell E2, enter the following formula.
= COVARIANCE.P(B2:B13,C2:C13)
Step 2: The resulting value is $7,63,173.17 is displayed in cell E2, as shown in the image below.
When comparing the share prices of two companies using the COVARIANCE.P Excel function, investors can gain valuable insights into the relationship between their returns. A positive covariance as seen
above, indicates that the share prices tend to move in tandem, i.e., when the prices of company X move up, the share prices of company Y also move up.
Example #3
The below example delves into the COVARIANCE.P function by analyzing the marks of two subjects: Science and Accounts. Our goal is to calculate the covariance between these subjects for the students.
The table for the values is below.
To use the COVARIANCE.P Excel function, just follow these simple steps.
Step 1: Enter the formula shown below in cell E2 and calculate the result.
= COVARIANCE.P(B2:B13,C2:C13)
Step 2: The calculated result value is displayed in cell E2, as shown in the image below.
When comparing the marks of two subjects of students using the COVARIANCE.P Excel function, one can obtain a measure of how these two variables change together. A negative covariance indicates an
inverse relationship.
Important Things To Note
1. The COVARIANCE.P function in Excel ignores text or logical values in arrays. It only works with numeric data in arrays of the same size, with non-empty cells and non-zero standard deviation.
2. The #VALUE! error arises when either one or both provided data arrays are devoid of values.
3. The #N/A error emerges when the arrays provided are of unequal lengths.
4. The COVARIANCE.P function is a tool in statistical analysis, particularly in the fields of finance, economics, and risk management.
5. This function allows professionals to calculate the covariance between two sets of data points, providing valuable insights into the relationship and level of co-movement between variables.
Frequently Asked Questions (FAQs)
1. What is the function for Covariance in Excel?
In Excel, covariance is a statistical measure used to quantify the degree to which two random variables change together. Specifically, it measures the direction of the linear relationship between two
sets of numbers. The function for Covariance in Excel is commonly used in data analysis, especially when examining the relationship between variables.
2. What is the difference between COVARIANCE.P and COVARIANCE.S in Excel?
In this example, we have a turnover of Peter’s company and Albert’s company from 2010 to 2015; we are calculating the covariance using the COVARIANCE.P Excel function. Look at the table below.
Enter the COVARIANCE.P Excel formula in the cell E2 as
=COVARIANCE.P(B2:B7, C2:C7), and the result obtained is $13.83.
Enter the COVARIANCE.S Excel formula in the cell F2 as
=COVARIANCE.S(B2:B7, C2:C7), and the result obtained is $16.60.
When comparing the results of COVARIANCE.P and COVARIANCE.S in Excel, it is important to note the method of calculation utilized by each function. COVARIANCE.P calculates the covariance based on the
population parameters, making it ideal for large datasets that encompass an entire population. On the other hand, COVARIANCE.S computes the covariance using sample data, which is useful when working
with smaller sets of data or subsets of a population.
3. What are the limitations of using the COVARIANCE.P function?
The limitations of using the COVARIANCE.P function are;
• It is important that the function only calculates the covariance between two sets of data and not a complete matrix like the COVAR or COVARIANCE.S functions.
• The function assumes that both sets of data are samples from a larger population rather than the entire population itself. If the data represents the entire population, consider using the COVAR
function instead for a more accurate result.
• It is essential to ensure that both data sets have equal lengths and no missing values to avoid any errors in calculation.
Download Template
This article must help us understand the COVARIANCE.P Excel Function’s formula and examples. You can download the template here to use it instantly.
Recommended Articles
Guide to COVARIANCE.P Excel Function. Here we explain how to use COVARIANCE.P function with examples & downloadable excel template. You can learn more from the following articles. – | {"url":"https://www.excelmojo.com/covariance-p-excel/","timestamp":"2024-11-05T19:26:20Z","content_type":"text/html","content_length":"221182","record_id":"<urn:uuid:e7ac837b-da8b-40b0-9222-bb1dff527d00>","cc-path":"CC-MAIN-2024-46/segments/1730477027889.1/warc/CC-MAIN-20241105180955-20241105210955-00340.warc.gz"} |
Break-Even Point Calculator
Find your break-even point with ease using our online calculator. Input your data and get instant results for informed financial decision-making.
Result Break Even Units 0 units Break Even Value 0 units Profit 0 units
Related Calculators:
Additional Funds Needed (AFN) Calculator
Total Asset Turnover Calculator
Capital Budgeting Calculator
Cost of Capital Calculator
Cost of Goods Sold (COGS) Calculator
Straight Line Depreciation Calculator (with Charts)
DuPont Analysis Calculator
EBITDA Calculator
Enterprise Value (EV) Calculator
Operating Cash Flow (OCF) Calculator
Payback Period Calculator
Profit Margin Calculator
Break-Even Point Formula
Calculating your break-even point can seem daunting, but it's a crucial step in managing your business finances. Fortunately, the formula is simple:
Break-Even Point = Fixed Costs ÷ (Price - Variable Costs)
Remember, your fixed costs are the expenses that stay the same no matter how many units you sell. Variable costs, on the other hand, change based on the number of units sold.
Don't let financial jargon intimidate you! Our Break-Even Point Calculator makes it easy to understand your business's financial situation and make informed decisions.
Break-Even Point Example
Let's say you run a small business selling handmade crafts. You sell each item for $50, and it costs you $20 in materials and labor to make each item. You also have fixed costs of $2,000 per month to
cover rent, utilities, and other expenses.
To find your break-even point, we'll use the formula:
Break-Even Point = Fixed Costs ÷ (Price - Variable Costs)
Plugging in our numbers, we get:
Break-Even Point = $2,000 ÷ ($50 - $20) = 67 units
This means you need to sell at least 67 units per month to cover your fixed and variable costs and break even. If you sell fewer units, you'll be operating at a loss. If you sell more units, you'll
start making a profit.
Using our Break-Even Point Calculator, you can quickly and easily calculate your break-even point and make informed decisions about your business finances. | {"url":"https://www.chooseinvesting.com/calc/breakeven/","timestamp":"2024-11-11T23:05:17Z","content_type":"text/html","content_length":"27309","record_id":"<urn:uuid:0c9e0e0f-5f5a-449c-99f5-327e5ad71aec>","cc-path":"CC-MAIN-2024-46/segments/1730477028240.82/warc/CC-MAIN-20241111222353-20241112012353-00615.warc.gz"} |
Project Euler 188 Solution: A tetration calculation
Project Euler 188: Find the last digits of a tetration calculation.
Problem Description
The hyperexponentiation or tetration of a number a by a positive integer b, denoted by a↑↑b or ^ba, is recursively defined by:
a↑↑1 = a,
a↑↑(k+1) = a^(a↑↑k).
Thus we have e.g. 3↑↑2 = 3^3 = 27, hence 3↑↑3 = 3^27 = 7625597484987 and 3↑↑4 is roughly 10^3.6383346400240996*10^12.
Find the last 8 digits of 1777↑↑1855.
Using the optional third parameter of Python’s pow(x, y [,z]) function which calculates the modulo z of x to the power y (computed more efficiently than pow(x, y) % z) we loop through the pow
function b times to calculate the tetration of a↑↑b. Modding the result by some power of 10, 10^8 in this case, we can reduce this unwieldy number to its last 8 digits.
We can exit the loop early, reducing the number of iterations, when the modded result begins to repeat.
Project Euler 188 Solution
Runs < 0.001 seconds in Python 2.7.
Project Euler 188 Solution Python 2.7 source
Project Euler 188 Solution last updated
No comments yet. | {"url":"https://blog.dreamshire.com/project-euler-188-solution/","timestamp":"2024-11-11T16:19:20Z","content_type":"application/xhtml+xml","content_length":"37298","record_id":"<urn:uuid:731f0353-19e8-4e42-beef-2278f52d1a31>","cc-path":"CC-MAIN-2024-46/segments/1730477028235.99/warc/CC-MAIN-20241111155008-20241111185008-00702.warc.gz"} |
ystem download
Axiom is a general purpose Computer Algebra system. It is useful for research and development of mathematical algorithms.
(1) · Free · Linux
Jul 15, 2022 · Download Axiom Computer Algebra System for free. Axiom is a computer algebra system. It consists of an interpreter, a compiler and a library ...
Axiom is free and open source software. It is copyrighted code that is released under the Modified BSD license.
You can now run Axiom on a Windows box. Basically all Axiom needs to run is an X server and a linux install.
The first release of Axiom is under development. Some snapshots of the current source tree are available in the Download section for Axiom on Savannah.
Axiom is a general purpose Computer Algebra system. It was originally ... It is also useful for engineering or scientific purposes. Download. Categories.
Axiom is a computer algebra system. It consists of an interpreter, a compiler and a library of algorithms. Axiom is an excellent research…
(12) · Free · Developer
Apr 22, 2024 · Download Axiom Computer Algebra System - Axiom is a computer algebra system. It consists of an interpreter, a compiler and a library of ...
What are the 5 basic axioms of algebra?
What is the axiom programming language?
Sep 1, 2007 · AXIOM: open source computer algebra system. Author: William S. Page ... Download PDF · View Issue's Table of Contents. Figures Tables. Close ...
Axiom Computer Algebra System free download Windows app and run it online in OnWorks over OS online like Ubuntu, Fedora, Debian, Kali OS wine. | {"url":"https://www.google.bg/search?sca_esv=778fd8ccaca240ed&ie=UTF-8&q=Axiom+computer+algebra+system+download&sa=X&ved=2ahUKEwiKyrb3nYyJAxVgP2IAHShQPdwQ1QJ6BAgHEA4","timestamp":"2024-11-03T05:52:51Z","content_type":"text/html","content_length":"94078","record_id":"<urn:uuid:37f1bce2-7e21-496c-8b6f-c935166b36e1>","cc-path":"CC-MAIN-2024-46/segments/1730477027772.24/warc/CC-MAIN-20241103053019-20241103083019-00387.warc.gz"} |
Python List - Longest common sub-sequence in two lists
Python List Advanced Exercise - Longest common sub-sequence in two lists
Python List Advanced: Exercise-11 with Solution
Write a Python function to find the longest common sub-sequence in two lists.
Sample Solution:
Python Code:
# Define a function to find the longest common subsequence between two lists
def longest_common_subsequence(lst1, lst2):
# Get the lengths of both input lists
m, n = len(lst1), len(lst2)
# Initialize a 2D table 'jh' to store the lengths of common subsequences
jh = [[0 for j in range(n+1)] for i in range(m+1)]
# Fill in the 'jh' table using dynamic programming
for i in range(1, m+1):
for j in range(1, n+1):
if lst1[i-1] == lst2[j-1]:
jh[i][j] = 1 + jh[i-1][j-1]
jh[i][j] = max(jh[i-1][j], jh[i][j-1])
# Initialize a result list to store the common subsequence
result = []
i, j = m, n
# Reconstruct the longest common subsequence
while i > 0 and j > 0:
if lst1[i-1] == lst2[j-1]:
i -= 1
j -= 1
elif jh[i-1][j] > jh[i][j-1]:
i -= 1
j -= 1
# Return the result list in reverse order to get the correct sequence
return result[::-1]
# Create two lists of numbers
nums1 = [1, 2, 3, 4, 5, 6, 7, 8]
nums2 = [6, 7, 5, 6, 7, 8]
# Print the original lists of numbers
print("Original lists:")
# Call the longest_common_subsequence function with the two number lists and store the result in 'result'
result = longest_common_subsequence(nums1, nums2)
# Print the result, which is the longest common subsequence between the two lists
print("Longest common sub-sequence in two lists:")
# Create two more lists of numbers
nums1 = [3, 5, 1, 8, 8]
nums2 = [3, 3, 5, 3, 8]
# Print the original lists of numbers
print("\nOriginal lists:")
# Call the longest_common_subsequence function with the second pair of number lists and store the result in 'result'
result = longest_common_subsequence(nums1, nums2)
# Print the result, which is the longest common subsequence between the two lists
print("Longest common sub-sequence in two lists:")
# Create two lists of numbers that have no common elements
nums1 = [1, 3, 5, 7]
nums2 = [2, 4, 6, 8]
# Print the original lists of numbers
print("\nOriginal lists:")
# Call the longest_common_subsequence function with the third pair of number lists and store the result in 'result'
result = longest_common_subsequence(nums1, nums2)
# Print the result, which is an empty list since there is no common subsequence
print("Longest common sub-sequence in two lists:")
# Create two lists of numbers with some common elements
nums1 = [1, 3, 5, 7]
nums2 = [1, 2, 4, 6, 8]
# Print the original lists of numbers
print("\nOriginal lists:")
# Call the longest_common_subsequence function with the fourth pair of number lists and store the result in 'result'
result = longest_common_subsequence(nums1, nums2)
# Print the result, which is the longest common subsequence between the two lists
print("Longest common sub-sequence in two lists:")
Sample Output:
Original lists:
[1, 2, 3, 4, 5, 6, 7, 8]
[6, 7, 5, 6, 7, 8]
Longest common sub-sequence in two lists:
[5, 6, 7, 8]
Original lists:
[3, 5, 1, 8, 8]
[3, 3, 5, 3, 8]
Longest common sub-sequence in two lists:
[3, 5, 8]
Original lists:
[1, 3, 5, 7]
[2, 4, 6, 8]
Longest common sub-sequence in two lists:
Original lists:
[1, 3, 5, 7]
[1, 2, 4, 6, 8]
Longest common sub-sequence in two lists:
What is the time complexity and space complexity of the following Python code?
def longest_common_subsequence(lst1, lst2):
m, n = len(lst1), len(lst2)
jh = [[0 for j in range(n+1)] for i in range(m+1)]
for i in range(1, m+1):
for j in range(1, n+1):
if lst1[i-1] == lst2[j-1]:
jh[i][j] = 1 + jh[i-1][j-1]
jh[i][j] = max(jh[i-1][j], jh[i][j-1])
result = []
i, j = m, n
while i > 0 and j > 0:
if lst1[i-1] == lst2[j-1]:
i -= 1
j -= 1
elif jh[i-1][j] > jh[i][j-1]:
i -= 1
j -= 1
return result[::-1]
Time complexity - The time complexity of the said code is O(mn), where m and n are the lengths of the input lists “lst1” and “lst2”, respectively. The code uses dynamic programming to compute the
length of the longest common subsequence of “lst1” and “lst2”, which requires filling in a table with dimensions (m+1) x (n+1). The loop that fills in this table has O(mn) iterations, and each
iteration takes constant time, so the overall time complexity is O(mn). The loop that constructs the result list by backtracking through the table also takes O(m+n) time, but this is dominated by the
O(mn) time complexity of the dynamic programming loop.
Space complexity - The space complexity of the said code is O(mn), where m and n are the lengths of the input lists “lst1” and “lst2”, respectively. This is because the code creates a two-dimensional
list jh with dimensions (m+1) x (n+1) to store the dynamic programming table. Each element of “jh” is a single integer, so the total space used by “jh” is proportional to its dimensions, which are O
(mn). The result list also has space complexity proportional to the length of the longest common subsequence, which is at most min(m, n), so we can consider it to be O(min(m, n)) space complexity.
However, since this is a constant factor that does not depend on the size of the input lists, we can ignore it and say that the overall space complexity is O(mn).
Python Code Editor:
Previous: Minimum sum sub-sequence in a list.
Next: First non-repeated element in a list.
What is the difficulty level of this exercise?
Test your Programming skills with w3resource's quiz.
It will be nice if you may share this link in any developer community or anywhere else, from where other developers may find this content. Thanks.
• Weekly Trends and Language Statistics | {"url":"https://www.w3resource.com/python-exercises/list-advanced/python-list-advanced-exercise-11.php","timestamp":"2024-11-09T20:16:19Z","content_type":"text/html","content_length":"142366","record_id":"<urn:uuid:bd79975e-024d-4451-b977-4ab07e7fc5d8>","cc-path":"CC-MAIN-2024-46/segments/1730477028142.18/warc/CC-MAIN-20241109182954-20241109212954-00138.warc.gz"} |
How To Calculate The EMA Of A Stock With Python
In this article, I will be showing you how you can calculate the Exponential Moving Average of a stock using Python.
Step 1. Install the modules
The modules that we will be needing are listed below and you can simply install them with a pip3 install.
pip3 install numpy==1.20.0\
pip3 install pandas==1.1.4\
pip3 install pandas-datareader==0.9.0\
pip3 install matplotlib==3.3.3
Step 2. Understanding Exponential Moving Average
Although I won't be going too deep into the concept of EMA (Exponential Moving Average), I will be giving you a brief overview of what it is. EMA is a type of moving average indicator that gives
greater weight or importance to previous stock prices. The essential difference between EMA and SMA is that EMA responds faster to upward price movement compared to SMA. The formula for calculating
EMA is as follows.
The smoothing factor can be altered upon preference, but a common choice for this variable is 2 and that is what we will be using. Traders use various day lengths when calculating EMA, but a common
one is a 10-day period and that is what we will be using.
Step 3. How to calculate EMA
In Step 2, we established that we would be calculating EMA for every 10 day observations. The first step to calculating EMA is to actually calculate the SMA of the day length constant. In our case,
we will first calculate the SMA of the first 10 stock prices. We will then consider the 10 day SMA to be our first EMA value. Now we will calculate the EMA for the 11th day price using the formula I
mentioned earlier. You can repeat the process of using the EMA formula repeatedly until you have finished calculating for all the stock prices.
Step 3.1. Example
In this example, we will be calculating the 5-day EMA of the following set of numbers with a smoothing value of 2.
10, 11, 11.5, 10.75, 12, 11.75, 12.25, 14, 16, 17, 15.6, 15.75, 16, 14, 16.5, 17, 17.25, 18, 18.75,
The first thing we will do is find the SMA of the first 5 numbers.
EMA = []\
(10 + 11 + 11.5 + 10.75 + 12) / 5 = 11.05
Let's add 11.05 to our EMA list.
EMA = [11.05]
Now we will use the EMA formula to calculate the EMA for the 6th number.
(11.75 x (2 / (1 + 5))) + 11.05 x (1 - (2 / (1 + 5))) = 11.28\
Add 11.28 to our list of EMA: [11.05, 11.28]
Continue the process of using the EMA formula for all the numbers in the set and that is how you calculate the EMA of a stock.
11.05, 11.28, 11.61, 12.40, 13.60, 14.73, 15.02, 15.26, 15.51, 15.01, 15.50, 16.00, 16.42, 16.95,
17.55, 18.36
Step 4. Coding Setup
Now its time to start coding. We can start by setting up the basic things we will need.
1. Import all the necessary modules
2. Create an empty function calculate_ema(prices, days, smoothing=2)
3. Get the stock price data for a certain stock - (MSFT, 2015--01--01, 2016--01--01)
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import pandas_datareader as web
def calculate_ema(prices, days, smoothing=2):
symbol = 'MSFT'
df = web.DataReader(symbol, 'yahoo', '2015-01-01', '2016-01-01')
Step 5. Calculating EMA
Remember that the first step to calculating the EMA of a set of number is to find the SMA of the first numbers in the day length constant. There are two simple ways we can go about this.
def calculate_ema(prices, days, smoothing=2):
ema = [sum(prices[:days]) / days] # First method
ema = []
ema.append(sum(prices[:days]) / days) # Second method
Now we need to loop through the numbers that are not in the range of the day length constant and repeatedly calculate the EMA for them and add them to our EMA list.
def calculate_ema(prices, days, smoothing=2):
ema = [sum(prices[:days]) / days]
for price in prices[days:]:
ema.append((price * (smoothing / (1 + days))) + ema[-1] * (1 - (smoothing / (1 + days))))
return ema
By the end of this step, your code should look something like this.
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import pandas_datareader as web
def calculate_ema(prices, days, smoothing=2):
ema = [sum(prices[:days]) / days]
for price in prices[days:]:
ema.append((price * (smoothing / (1 + days))) + ema[-1] * (1 - (smoothing / (1 + days))))
return ema
symbol = 'MSFT'
df = web.DataReader(symbol, 'yahoo', '2015-01-01', '2016-01-01')
ema = calculate_ema(df['Close'], 10) # Add this line to save EMA values in a list
Step 6. Plotting the results
We can plot the actual stock prices and the calculated EMA with matplotlib.
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import pandas_datareader as web
def calculate_ema(prices, days, smoothing=2):
ema = [sum(prices[:days]) / days]
for price in prices[days:]:
ema.append((price * (smoothing / (1 + days))) + ema[-1] * (1 - (smoothing / (1 + days))))
return ema
symbol = 'MSFT'
df = web.DataReader(symbol, 'yahoo', '2015-01-01', '2016-01-01')
ema = calculate_ema(df['Close'], 10)
price_X = np.arange(df.shape[0]) # Creates array [0, 1, 2, 3, ..., df.shape[0]]
ema_X = np.arange(10, df.shape[0]+1) # Creates array [10, 11, 12, 13, ..., df.shape[0]+1]
# We start at 10, because we use the first 10 values to calculate the SMA,
# then we calculate EMA form the 11th value
plt.plot(price_X, df['Close'], label='Closing Prices')
plt.plot(ema_X, ema, label='EMA')
Your plot should look something like this.
Conclusion. How to use EMA for stocks?
While there are many ways to use the Exponential Moving Average of a stock for technical analysis, a basic usage of it is recognizing a buy signal when the EMA line goes underneath and stock line and
is heading in an upward direction. A sell signal can be recognized when the EMA line goes over the stock line and it is heading in a downward direction. To conclude, I hope you learned something new
and useful from this article which you can use later in your Python projects. | {"url":"https://plainenglish.io/blog/how-to-calculate-the-ema-of-a-stock-with-python","timestamp":"2024-11-07T03:14:57Z","content_type":"text/html","content_length":"73585","record_id":"<urn:uuid:1f252007-f084-47d1-8728-75d2242b959d>","cc-path":"CC-MAIN-2024-46/segments/1730477027951.86/warc/CC-MAIN-20241107021136-20241107051136-00554.warc.gz"} |
The Interior of Intersections of Sets in a Metric Space
The Interior of Intersections of Sets in a Metric Space
Recall from the Interior and Boundary Points of a Set in a Metric Space page that if $(M, d)$ is a metric space and $S \subseteq M$ then a point $a \in S$ is said to be an interior point of $S$ if
there exists an $r > 0$ such that:
\quad B(a, r) \subseteq S
In other words, a point $a$ is an interior point of $S$ if there exists an open ball centered at $x$ that is fully contained in $S$. Furthermore, the set of all interior points of $S$ is called the
interior of $S$ and is denoted $\mathrm{int} (S)$.
We will now look at some very important theorems regarding the interiors of both finite intersections and arbitrary intersections.
Theorem 1: Let $(M, d)$ be a metric space and let $S_1, S_2, ..., S_n \subseteq M$ be a finite collection of subsets of $M$. Then $\displaystyle{\mathrm{int} \left ( \bigcap_{i=1}^{n} S_i \right )= \
bigcap_{i=1}^{n} \mathrm{int} (S_i)}$.
• Proof: Let $x \in \mathrm{int} \left ( \bigcap_{i=1}^{n} S_i \right )$. Then there exists an $r > 0$ such that:
\quad B(x, r) \subseteq \bigcap_{i=1}^{n} S_i
• But $\displaystyle{\bigcap_{i=1}^{n} S_i \subseteq S_i}$ for each $i \in \{ 1, 2, ..., n \}$ and so $B(x, r) \subseteq S_i$ for each $i$. But this implies that $x \in \mathrm{int} (S_i)$ for each
$i$ and thus $\displaystyle{x \in \bigcap_{i=1}^{n} \mathrm{int} (S_i)}$. This shows that:
\quad \mathrm{int} \left ( \bigcap_{i=1}^{n} S_i \right ) \subseteq \bigcap_{i=1}^{n} \mathrm{int} (S_i)
• Now let $x \in \bigcap_{i=1}^{n} \mathrm{int}(S_i)$. Then $x \in \mathrm{int} (S_i)$ for all $i \in \{1, 2, ..., n \}$. So for each $i$ there exists an $r_i > 0$ such that:
\quad B(x, r_i) \subseteq S_i
• Let $r = \min \{ r_1, r_2, ..., r_n \}$. Then $B(x, r) \subseteq S_i$ for all $i \in \{ 1, 2, ..., n \}$ which shows that $\displaystyle{B(x, r) \in \bigcap_{i=1}^{n} S_i}$. Thus $\displaystyle{x
\in \mathrm{int} \left ( \bigcap_{i=1}^{n} S_i \right )}$. This shows that:
\quad \mathrm{int} \left ( \bigcap_{i=1}^{n} S_i \right ) \supseteq \bigcap_{i=1}^{n} \mathrm{int} (S_i)
• We conclude that then $\displaystyle{\mathrm{int} \left ( \bigcap_{i=1}^{n} S_i \right )= \bigcap_{i=1}^{n} \mathrm{int} (S_i)}$. $\blacksquare$
Theorem 2: Let $(M, d)$ be a metric space and let $\mathcal F$ be a finite collection of subsets of $M$. Then $\displaystyle{\mathrm{int} \left ( \bigcap_{S \in \mathcal F} S \right ) \subseteq \
bigcap_{S \in \mathcal F} \mathrm{int} (S) }$.
• Proof: Let $\displaystyle{x \in \mathrm{int} \left ( \bigcap_{S \in \mathcal F} S \right )}$. Then $x$ is an interior point of $\displaystyle{\mathrm{int} \left ( \bigcap_{S \in \mathcal F} S \
right )}$ and so there exists an $r > 0$ such that:
\quad B(x, r) \subseteq \mathrm{int} \left ( \bigcap_{S \in \mathcal F} S \right )
• Therefore $B(x, r) \subseteq S$ for all $S \in \mathcal F$, so $x \in \mathrm{int} (S)$ for all $S \in \mathcal F$. This implies that $\displaystyle{x \in \bigcap_{S \in \mathcal F} \mathrm{int}
(S)}$ and so:
\quad \mathrm{int} \left ( \bigcap_{S \in \mathcal F} S \right ) \subseteq \bigcap_{S \in \mathcal F} \mathrm{int} (S) \quad \blacksquare
Note that in Theorem 1 we relied on the fact that were looking at a finite intersection to show equality. Equality in Theorem 2 does not hold in general though. | {"url":"http://mathonline.wikidot.com/the-interior-of-intersections-of-sets-in-a-metric-space","timestamp":"2024-11-04T20:07:32Z","content_type":"application/xhtml+xml","content_length":"19122","record_id":"<urn:uuid:93fe9913-6d33-4a5c-806d-9bf5aa8d11d6>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.16/warc/CC-MAIN-20241104194528-20241104224528-00674.warc.gz"} |
Introduction to Calculated tags
Calculated input Group Logic
Calculated input is about setting up a calculation expression with one of more tags, like adding the readings from 2 tags together. In the following article, you will get an introduction to
Calculated input groups.
Accessing the interface
Navigate to "DIAPs" and select it.
Choose the DIAP which you wish to add Calculated inputs for:
Choose the "+ Add calculated input group" in order to add a group for creating calculated tags. A calculated input group is basically a kind of virtual/software PLC, that can be setup and run inside
the DIAP. It is a way for logical grouping a set of tags and it is needed to keep the relation between DIAP, tags' groups and tags.
A pop-up will occur:
• Name: The name of the calculated tags group (The virtual/software PLC)
• Location: Just enter something here because this isn't used.
• Description: A description of the calculated tags group.
• Scan Rate (ms): The default scan rate, that will be used when adding a new input into this calculated tags group (This can be overwritten in the tag setting).
• Stop tag: This setup is for when the tags in the group shouldn't collect data. Just set it to No stop tag, this will stop the tag from collecting data, when its reading is equal to that in the
Stop value.
• Stop value: This value is used to check if the tag shouldn't collect data.
• Is Active: Sets the calculated tag group active or inactive. Tags in an inactive active group won't collect data.
Once the group has been created, then it can be expanded in order to add new inputs. Click "Add calculated input".
A calculated input is basically a tag, where one defines an expression to it, that will be calculated like a math formula. You must select a Sensor type, enter a Name for the calculated input:
Now you must specify the expression, that should be calculated, this expression most likely involves the use of other tags. To add a tag to the expression, click "Add new tag":
Press the button "+ Add new input" and select the PLC and tag.
The added tag can now be seen in a list below:
Repeat this for each tag needed in the expression.
To insert a tag into the expression, copy it's TagId, into the expression input:
Here is an example of getting the sum of 2 tags, where Sum tag returns the sum of tag Shift 0<-> and irregular int:
The rest of the settings for the calculated input are standard tag settings, which you can read more about here: Configuration of tags (PLC).
Basic usage examples
Here are some examples of use, using only three tags:
• t997 - a simple boolean (can hold value 0 or 1).
• t998 - a value between -127 and 128.
• t999 - a simple boolean (can hold value 0 or 1) on another PLC.
Tags as shown above where:
t997 = 0
t998 = -3
t999 = 1
t999 + t997 = 1
t997 - t998 = 3
t999 / t998 = 1 / -3 = -0.3333~
Adding more complexity:
t998 * - t999 = 1 * - -3 = 3
Adding constants:
10 * t998 + t999 = 10 * -3 + 1 = -29
Adding parentheses:
10 * (t998 + t999) = 10 * (-3 + 1) = -20
Tags as shown above where:
t997 = 0
t998 = 1
t999 = 1
t997 & t998 = t997 and t998 = 0
t997 | t998 = t997 or t998 = 1
not t997 = 1
not t998 = 0
not(t997 & t998) = 1
not(t998 & t999) = 0
not(t997 | t998) = 0
not(t998 | t999) = 0
"not(A & B)" acts as a NAND gate:
A B A NAND B
"not(A | B)" acts as a NOR gate:
A B A NOR B
The following logic operators can be used in the expression:
Logic operator Description
& Logic and operator
| Logic or operator
not(A & B) NAND gate
not(A | B) NOR gate
Tags as shown above where:
t997 = 0.7
t998 = 1.3
t999 = 2.3
You can use functions, like round, cos, acos, floor and others:
round(t999) = round(2.3) = 2
Combining them with math:
10 * round(t997) + floor(t998) + 10 = 10 * round(0.7) + floor(1.3) = 10* 1 + 1 = 12
You can only pass 1 parameter to the functions:
1 parameter (OK)
2 parameters (Not OK)
The following functions can be used in the expression:
Function Description
acos Returns the arc cosine of a number
asin Returns the arc sine of a number
atan Returns the arc tangent of a number in radians
atan2 Returns the arc tangent of y/x in radians
ceil Rounds a number up to the nearest integer
cos Returns the cosine of a number
cosh Returns the hyperbolic cosine of a number
exp Returns E raised to the power of x
fabs Returns the absolute value of a number
floor Rounds a number down to the nearest integer
log Returns the natural logarithm of a number, or the logarithm of number to base
log10 Returns the base-10 logarithm of x
sin Returns the sine of a number
sinh Returns the hyperbolic sine of a number
sqrt Returns the square root of a number
tan Returns the tangent of a number
tanh Returns the hyperbolic tangent of a number
bool Returns the boolean value of the specified object
int Returns an integer number
round Rounds a number
random Returns a random float number between 0 and 1 (Don't take a parameter, like this random())
omega(X) - is a function that emulates periodical events and with given rotational speed expressed as a period of 1 rotation per X ms, returns angle that can be used in trigonometric
functions as an input parameter.
Sine wave = amplitude * sin(omega(period of wave expressed in ms))
Example of using omega:
Then the calculated input will generate a sine wave like this:
Test expression
The expression is evaluated with python by passing the expression to pythons eval function; because of this, you can test your expression in python. You can run python code online here:
First import the math library, it has a lot of the math function you can call:
Now to simulate the tagId, you can declare variables to hold the reading from your tags like this:
Next you can see the result of your expression by writing it in a print function like this (round is a built in function and floor is a function in the math library):
Click the Run button:
And see the result of your expression:
It properly seems confusing to see the floor function called as math.floor on the web site and it called as floor in the expression of calculated input. It is because the math library is included in
the calculated input and will be searched when a function is called. This means that you don't have to worry about whether the function is builtin or a math library function, you just type the name
of the function in the expression.
In python the function are located here:
Function Python Location
acos math library
asin math library
atan math library
atan2 math library
ceil math library
cos math library
cosh math library
exp math library
fabs math library
floor math library
log math library
log10 math library
sin math library
sinh math library
sqrt math library
tan math library
tanh math library
bool built in function
int built in function
round built in function
random Random library
omega Not a Python function
Underlying lexer and parser rules
* Parser Rules
: expression EOF
: high_op_expression
| expression (OP_LOWER | BIN_OR_UN) high_op_expression
: temp_expression
| high_op_expression OP_HIGH temp_expression
: brackets
| function_call
| un_op_with_brackets
| un_op_with_term
| terminal
: '(' expression ')'
: FUNC '(' expression ')'
: (UN_OP | BIN_OR_UN)+ '(' expression ')'
: (UN_OP | BIN_OR_UN)+ terminal
: NUMBER
| BOOLEAN
| TAG
* Lexer Rules
: 'and'
| '&'
| '*'
| '/'
| '^'
: 'or'
| '+'
| '|'
: '-'
: 'not'
| '~'
: [tT][0-9]+
: '0' ([xX] [0-9a-fA-F]+ ([lL] | [eE] [+-]? [0-9]+)?
| [oO] [0-7]+ [lL]?
| [bB] [01]+ [lL]?)
| ([0-9]+ '.' [0-9]* | '.' [0-9]+) ([eE] [+-]? [0-9]+)? [jJ]?
| [0-9]+ ([lL] | [eE] [+-]? [0-9]+ [jJ]? | [jJ])?
: 'True'
| 'False'
: 'acos'| 'asin'| 'atan'| 'atan2'| 'ceil'| 'cos'
| 'cosh'| 'exp'| 'fabs'| 'floor'| 'log'| 'log10'
| 'sin'| 'sinh'| 'sqrt'| 'tan'| 'tanh'|'bool'
| 'int'| 'round'| 'random'| 'omega'
: (' '|'\t')+ -> skip ;
Recommended setup.
Combining the readings from several tags, can give behavior that seems strange, to avoid this you should set the scan rate of the calculated input and the tags used in the expression of the
calculated input to the same value and the tags should come from the same PLC.
• Scan rate should be the same for calculated input and tags used by it.
• The tags used by the calculated input, should come from the same PLC.
Why the scan rate should be the same for calculated input and tags used by it
The reason why the scan rate should be the same, is because the calculated input has to use simultaneous values from the tags else the results can be incorrect. Imagine that you have a tag measuring
current and other one measuring voltage. Now you want to calculate the power from these tags, you think "Simple, I just multiple them" after all the power formula is:
P(t) = U(t)* I(t)
And your current and voltage are waves:
And you scan your Current every 2 seconds and Voltage every 3 seconds:
Now image that we don't care when the scan happens and take values that are not simultaneous, then the question comes, which values do we pair with each other:
And even if we made a choice here, no matter which choice we take, the result would be wrong, because it the Current's value isn't neither of the choices, when we use a Voltage reading(This is also
true, if we try paring from Current to Voltage):
And lastly, we must also take into account, when the calculated input is set to calculate the result via its scan rate, this also has to match the values from the tags. For example say that you set
the scan rate of the calculated input to 5 seconds:
As you can see above, the calculated input toggles between having the Current and Voltage and therefore it isn't possible for it to make the calculation and as just explain before, we can't pair
values that are not simultaneous.
The way we handle different scan rate on tags and calculated input, is to use the lowest common denominator for all of the scan rates. In the example before this would mean, that you would first get
a result after 30 seconds, because that is the lowest common denominator between 2, 3 and 5. So if you want the results fast, when you have to think about setting their scan rate to the same or to
something, where the common denominator is low enough for you.
Why the tags used by the calculated input, should come from the same PLC
The reason why the tags used by the calculated input, should come from the same PLC, is because the clocks should be synchronized between the tags. Lets look at the Current and Voltage example, say
that the Current tag is measured from PLC P1 and Voltage tag is measured from PLC P2:
And image, that the clock on PLC P1 is 1 second late:
This can cause simultaneous values to appear not simultaneous, when the tags are read:
and not simultaneous values appear simultaneous, when the tags are read:
Tolerance on simultaneous values
Because clocks are not perfect synchronized with each other in the DIAP and PLCs, we have added a tolerance for when values between tags and calculated input are seen as simultaneous. This tolerance
is 100 milliseconds, if tag's values are within 100 milliseconds of when they are read by the calculated input, then they are seen as simultaneous values and used by the calculated input: | {"url":"https://kb.dataintel.dk/introduction-to-calculated-inputs","timestamp":"2024-11-08T12:53:31Z","content_type":"text/html","content_length":"89556","record_id":"<urn:uuid:c05b0e24-60ce-4650-b16b-78793c5eab88>","cc-path":"CC-MAIN-2024-46/segments/1730477028059.90/warc/CC-MAIN-20241108101914-20241108131914-00478.warc.gz"} |
Finding Zeros Of Quadratic Functions Worksheet - Function Worksheets
Finding Zeros Of Quadratic Functions Worksheet – The Quadratic Functions Worksheet will help individuals to know the characteristics of quadratic features. This worksheet is helpful … Read more
Zeros Of Quadratic Function Worksheet
Zeros Of Quadratic Function Worksheet – The Quadratic Characteristics Worksheet can help students to know the qualities of quadratic functions. This worksheet is helpful for … Read more | {"url":"https://www.functionworksheets.com/tag/finding-zeros-of-quadratic-functions-worksheet/","timestamp":"2024-11-08T14:02:40Z","content_type":"text/html","content_length":"58611","record_id":"<urn:uuid:84498844-948f-4970-86d7-674f0c782d62>","cc-path":"CC-MAIN-2024-46/segments/1730477028067.32/warc/CC-MAIN-20241108133114-20241108163114-00667.warc.gz"} |
Section: Research Program
Mean-field approaches
Modeling neural activity at scales integrating the effect of thousands of neurons is of central importance for several reasons. First, most imaging techniques are not able to measure individual
neuron activity (microscopic scale), but are instead measuring mesoscopic effects resulting from the activity of several hundreds to several hundreds of thousands of neurons. Second, anatomical data
recorded in the cortex reveal the existence of structures, such as the cortical columns, with a diameter of about 50$\mu m$ to 1$mm$, containing of the order of one hundred to one hundred thousand
neurons belonging to a few different species. The description of this collective dynamics requires models which are different from individual neurons models. In particular, when the number of neurons
is large enough averaging effects appear, and the collective dynamics is well described by an effective mean-field, summarizing the effect of the interactions of a neuron with the other neurons, and
depending on a few effective control parameters. This vision, inherited from statistical physics requires that the space scale be large enough to include a large number of microscopic components
(here neurons) and small enough so that the region considered is homogeneous.
Our group is developing mathematical and numerical methods allowing on one hand to produce dynamic mean-field equations [1] [36] from the physiological characteristics of neural structure (neurons
type, synapse type and anatomical connectivity between neurons populations), and on the other so simulate these equations. | {"url":"https://radar.inria.fr/report/2016/mathneuro/uid12.html","timestamp":"2024-11-04T13:47:18Z","content_type":"text/html","content_length":"35799","record_id":"<urn:uuid:dd57693c-568a-4f9e-a68a-2553d988ce71>","cc-path":"CC-MAIN-2024-46/segments/1730477027829.31/warc/CC-MAIN-20241104131715-20241104161715-00171.warc.gz"} |
CSCE 222 Chapter 1.3
Jump to navigation Jump to search
« previous | Sunday, February 20, 2011 | next »
A "function" that takes one or more inputs and evaluates to either true or false
EX: Let ${\displaystyle P(x)=x>3}$; ${\displaystyle P(1)={\mbox{false}}}$; ${\displaystyle P(5)={\mbox{true}}}$
• Higher precedence than all logical operators
• Distribute across parenthesized terms: ${\displaystyle \forall x(P(x)\wedge Q(x))\equiv \forall xP(x)\wedge \forall xQ(x)}$
Universal Quantification
If a predicate ${\displaystyle P(x)}$ is true for all values of ${\displaystyle x}$ in the domain,
${\displaystyle \forall xP(x)\equiv P(x_{1})\wedge P(x_{2})\wedge \ldots \wedge P(x_{n})}$
To be contradicted, we need to find only one value of ${\displaystyle x}$ such that ${\displaystyle P(x)}$ is false.
Existential Quantification
If a predicate ${\displaystyle P(x)}$ is satisfiable for at least one value of ${\displaystyle x}$ in the domain,
${\displaystyle \exists xP(x)\equiv P(x_{1})\vee P(x_{2})\vee \ldots \vee P(x_{n})}$
To be contradicted, every value of ${\displaystyle x}$ has to be false.
Variable Binding
A variable is bound if a quantifier is used on that variable. For example, in ${\displaystyle \exists x(x+y=1)}$, ${\displaystyle x}$ is bound, but ${\displaystyle y}$ is free (not bound). To fix
this, we would write ${\displaystyle \exists x\exists y(x+y=1)}$.
Negating Quantifiers
"Every student in your class has taken a course in calculus" could be written as ${\displaystyle \forall xP(x)}$.
Negation would be "There is a student in your class who has not taken a course in calculus", which could be written ${\displaystyle \exists xeg P(x)}$
{\displaystyle {\begin{aligned}eg \forall xP(x)&\equiv \exists xeg P(x)\\eg \exists xP(x)&\equiv \forall xeg P(x)\end{aligned}}} | {"url":"https://notes.komputerwiz.net/wiki/CSCE_222_Chapter_1.3","timestamp":"2024-11-13T02:02:50Z","content_type":"text/html","content_length":"44638","record_id":"<urn:uuid:d44360ad-d4ee-442d-8f30-dbd3279b023e>","cc-path":"CC-MAIN-2024-46/segments/1730477028303.91/warc/CC-MAIN-20241113004258-20241113034258-00317.warc.gz"} |
"Wave_ana" (wavelet analysis) is a program for time series analysis. ^[1] The program is written in standard Fortran-77 and has been ported to a number of Unix machines. The program has two input
menu sections: one to select the input data and to perform some signal manipulation (input menu), and one to analyse the data (analysis menu). The program is interactive, although it can be run in
batch mode using a switch in the input file (wave_ana.dat). The program has a built-in help facility.
The program can read a number of input signals. The number of signals read is controlled by the Norm/cross/triple input switch ("0" = 1 signal,"1" = 2 signals, "2" = 3 signals). These signals can be
text files in a number of formats, or in the TJ-II database format (VXI). Several other but mostly obsolete formats are also available (e.g., unformatted binary data). The input menu also provides
options for time window selection, subsampling, additive noise (for testing purposes), data amplitude normalisation (so that the RMS = 1), and, importantly, filtering. A number of filters is
available, both FFT-based (sharp in frequency space) and smoothing-based. When several signals are read that are not on the same time base, the signals are resampled onto the time base of the first
Several analysis options are offered:
1. Mean, RMS, skewness, kurtosis, probability distribution, cross correlation
2. Wavelet or Fourier spectrum
3. Wavelet or Fourier spectrum with time resolution
4. Wavelet or Fourier bicoherence
5. Bicoherence at fixed sum frequency
6. Summed bicoherence
7. Bicoherence with time resolution
8. Wavelet cross coherence
Several types of wavelet are available (Morlet, ...)
Program output
The program produces two types of output:
• ASCII text data files
• Graphical plots
In batch mode, the graphical output is suppressed. Graphics output routines are available for PV-Wave and for gnuplot.
The program is easily portable and freely available from its author (B.Ph. van Milligen) | {"url":"http://wiki.fusenet.eu/wiki/Wave_ana","timestamp":"2024-11-14T21:31:49Z","content_type":"text/html","content_length":"19467","record_id":"<urn:uuid:3df5b468-3db4-46f6-a96e-0b240f463f07>","cc-path":"CC-MAIN-2024-46/segments/1730477395538.95/warc/CC-MAIN-20241114194152-20241114224152-00341.warc.gz"} |
Maple 2023 Questions and Posts
I am using fsolve() to solve a highly nonlinear system of 6 equations in 6 variables: lambda_d1, lambda_i1, lambda_d2, lambda_i2, lambda_d3, lambda_i3.
fsolve() doesn't "solve"! I usually help fsolve() with some initial conditions and with the expected signs of the solution but in this case it's not enough. I noticed that if I comment out the
expected signs line (that is, if I don't impose my 6 lambdas to be strictly positive), the fsolve() works.
How do I help fsolve() to pin down only positive solutions at each iteration? I have no reasons to believe that there aren't any positive solutions for all 6 lambdas...
Worksheet: fsolve_help.mw
thank you. | {"url":"https://wamp.mapleprimes.com/products/Maple/Maple%202023?page=3","timestamp":"2024-11-02T08:28:26Z","content_type":"text/html","content_length":"610911","record_id":"<urn:uuid:941bd635-1cfb-4831-9c1f-9392784a424f>","cc-path":"CC-MAIN-2024-46/segments/1730477027709.8/warc/CC-MAIN-20241102071948-20241102101948-00218.warc.gz"} |
An exponential encounter
I recently learned about a neat technique, invented by John von Neumann, for generating random samples from an exponential distribution (probability density $e^{-x}$). The algorithm can be
generalized to sample from a normal distribution. One notable feature of von Neumann's approach, in addition to its simple brilliance, is that no logarithms are involved in the computation. While
this algorithm is now mainly of historical interest, it's still a fun exercise in probability and computation. Here, I'll walk through von Neumann's reasoning and present the algorithm.
A decreasing trend
A decreasing sequence of 3 uniformly distributed random numbers in the unit interval.
Generate a random number $u_1$ from a uniform distribution over the unit interval $(0, 1)$. The probability that $u_1$ has a value in the infinitesimal range $(u_1, u_1 + du_1)$ is $du_1$. Now pick a
second random number $u_2$ in exactly the same way. Given the value of $u_1$, what is the probability that $u_1 > u_2$? Call this probability $P_2(u_1)$. For the inequality to hold, $u_2$ must have a
value from 0 to $u_1$, and so the probability is
P_2(u_1) = \int_{0}^{u_1} du_{2} = u_1~.
Choose a third number $u_3$. What is the probability $P_3(u_1)$ that $u_1 > u_2 > u_3$? When $u_1$ is fixed, $u_2$ can take any value from 0 to $u_1$. Similarly, given $u_2$, the value of $u_3$ is
between 0 and $u_2$. The probability that $u_1 > u_2 > u_3$ is then
P_3(u_1) = \int_{0}^{u_1} du_{2} \int_{0}^{u_2} du_{3} = \frac{u_1^2}{2}~.
A pattern is starting to emerge!
For any $n$, the probability that $u_1 > u_2 > \ldots > u_n$ is
P_n(u_1) = \frac{u_1^{n - 1}}{(n - 1)!}~.
We've already seen that this holds for $n = 2$ and 3. Apply inductive reasoning to prove it for all $n$. Here's the inductive step:
P_{n + 1}(u_1)
&= \int_{0}^{u_1} du_{2} \int_{0}^{u_2} du_{3} \ldots \int_0^{u_n} du_{n + 1} \\
&= \int_{0}^{u_1} du_{2} \left[ \int_{0}^{u_2} du_{3} \ldots \int_0^{u_n} du_{n + 1} \right] \\
&= \int_0^{u_1} du_2\, P_n(u_2)~. \\
&= \int_0^{u_1} du_2\, \frac{u_2^{n - 1}}{(n - 1)!} \\
&= \frac{u_1^n}{n!}~. \\
Mathematically, it seems that $P_1(u_1) = 1$. The probabilisitic justification is that a sequence with only $u_1$ is already in order, and the probability is 1 for a decreasing sequence with $n = 1$.
A decreasing trend at its end
A decreasing sequence from $u_1$ to $u_4$ that is ended with $u_5 > u_4$.
Because $n!$ increases rapidly with $n$, the probability of generating a long decreasing sequence is low. We expect to quickly encounter a number that is out of order. What is the probability that a
decreasing sequence terminates after $n$ random draws? This is the joint probability that $u_1 > \ldots > u_n$ and $u_n \le u_{n + 1}$, where the last number, $u_{n + 1}$, ends the decreasing trend.
Denote this probability by $S_n(u_1)$ and write it as
S_n(u_1) = \int_0^{u_1} du_1 \ldots \int_0^{u_{n-1}} du_n \int_{u_n}^1 du_{n + 1}~.
After some simple manipulation, we find
S_n(u_1) &= ~ \int_0^{u_1} du_1 \ldots \int_0^{u_{n-1}} du_n \left(1 - \int_0^{u_n} du_{n + 1}\right) \\
&= ~ \, P_n(u_1) - P_{n + 1}(u_1) \\
&= ~ \, \frac{u_1^{n-1}}{(n - 1)!} - \frac{u_1^n}{n!}~.
This is an interesting exercise and a tidy result, but how does this relate to sampling from an exponential distribution?
An odd result
What is the probability of obtaining and odd-length decreasing sequence (OLDS) for a given $u_1$? Sum $S_n(u_1)$ over odd values of $n$ to get:
S_1(u_1) + S_3(u_1) + \ldots = 1 - u_1 + \frac{u_1^2}{2!} - \frac{u_1^3}{3!} + \ldots ~.
Does this look familiar? Here's a big hint: the Taylor series expansion of $e^{-u_1}$ is
e^{-u_1} = \sum_{n = 0}^\infty \frac{(-u_1)^n}{n!} = 1 - u_1 + \frac{u_1^2}{2!} - \frac{u_1^3}{3!} + \ldots~.
We now arrive at an interesting and useful result: A series of random numbers uniformly distributed over $(0, 1)$, starting with $u_1$, makes an OLDS with probability $e^{-u_1}$. In other words, if
many decreasing sequences are generated that terminate with odd length, and only $u_1$ is retained in each case, then the collection of $u_1$ values will be a sample from the exponential distribution
over $(0, 1)$.
So, we're on the right track. But how do we sample $e^{-x}$ over its entire domain from 0 to $\infty$?
A do-over
For a given value of $u_1$, the probability of an OLDS is $e^{-u_1}$. The probability of an OLDS when $u_1$ is in the infinitesimal range $(u_1, u_1 + du_1)$ is $du_1 e^{-u_1}$. Integration over
$u_1$ gives the probability of an OLDS for any $u_1$: $\int_0^1 du_1 e^{-u_1} = 1 - e^{-1}$. It follows that the probability of an even-length decreasing sequence for any $u_1$ is $e^{-1}$. If $u_1$
is accepted as a random draw from the exponential distribution only when the length of the decreasing sequence is odd, then $e^{-1}$ represents the probability that a sequence is rejected. A rejected
even-length sequence doesn't mean all is lost. It just means we start the process over, but with a small additional twist.
Suppose we encounter an even-length decreasing sequence in the first pass. Reject this sequence and start over by creating a new decreasing sequence with a freshly chosen value of $u_1$. If this new
sequence has an odd length, accept the new $u_1$. The probability of rejecting the first sequence and accepting the second is $e^{-1} e^{-u_1} = e^{-(u_1 + 1)}$. Because $u_1$ is drawn from $(0, 1)$,
a rejection followed by an acceptance samples from the exponential distribution in the interval $(1, 2)$. Similarly, the probability of accepting $u_1$ after two rejections is $e^{-(u_1 + 2)}$. And
so on.
A complete recipe
The complete algorithm is shown below as a flow diagram. Each draw is initialized by choosing a random $x$ in the unit interval ($u_1$ in the discussion above), setting the initial sequence length to
$n = 1$, and setting the initial rejection count to $k = 0$. In the diagram, $u$ and $u'$ represents, respectively, the previous and most recent random numbers. When a decreasing sequence of random
numbers terminates with an odd length, the algorithm returns $x + k$.
A flow diagram representing von Neumann's algorithm for sampling from the exponential distribution.
An Elixir implementation of von Neumann's algorithm can be found in this gist.
It's unlikely to generate long decreasing sequences or for there to be many rejections. It can be shown that the expected number of random draws before the algorithm returns is approximately 4.3. The
standard technique for sampling from an exponential distribution is to compute $-\ln (1 - u)$, where $u$ is a uniform random number on $(0, 1)$. While von Neumann's approach is significantly less
efficient, it avoids an explicit computation of a logarithm. Also, it's straightforward to show that the the algorithm can be adapted to any probability density of the form $a e^{-f(x)}$ for constant
Until next time, keep it random! | {"url":"https://www.ericpfahl.com/a-chance-encounter/","timestamp":"2024-11-05T13:55:28Z","content_type":"text/html","content_length":"28640","record_id":"<urn:uuid:6fd5f2d3-98d6-46fd-ae6f-38b7d9b1b8df>","cc-path":"CC-MAIN-2024-46/segments/1730477027881.88/warc/CC-MAIN-20241105114407-20241105144407-00334.warc.gz"} |
BoTorch · Bayesian Optimization in PyTorch
Posterior APIs¶
Abstract Posterior API¶
Abstract base module for all botorch posteriors.
class botorch.posteriors.posterior.Posterior[source]¶
Bases: abc.ABC
Abstract base class for botorch posteriors.
class botorch.posteriors.posterior.PosteriorList(*posteriors)[source]¶
Bases: botorch.posteriors.posterior.Posterior
A Posterior represented by a list of independent Posteriors.
A Posterior represented by a list of independent Posteriors.
☆ *posteriors – A variable number of single-outcome posteriors.
☆ posteriors (Posterior) –
Return type
>>> p_1 = model_1.posterior(test_X)
>>> p_2 = model_2.posterior(test_X)
>>> p_12 = PosteriorList(p_1, p_2)
Note: This is typically produced automatically in ModelList; it should generally not be necessary for the end user to invoke it manually.
property base_sample_shape: torch.Size¶
The shape of a base sample used for constructing posterior samples.
property device: torch.device¶
The torch device of the posterior.
property dtype: torch.dtype¶
The torch dtype of the posterior.
property event_shape: torch.Size¶
The event shape (i.e. the shape of a single sample).
property mean: torch.Tensor¶
The mean of the posterior as a (b) x n x m-dim Tensor.
property variance: torch.Tensor¶
The variance of the posterior as a (b) x n x m-dim Tensor.
rsample(sample_shape=None, base_samples=None)[source]¶
Sample from the posterior (with gradients).
○ sample_shape (Optional[torch.Size]) – A torch.Size object specifying the sample shape. To draw n samples, set to torch.Size([n]). To draw b batches of n samples each, set to
torch.Size([b, n]).
○ base_samples (Optional[torch.Tensor]) – An (optional) Tensor of N(0, I) base samples of appropriate dimension, typically obtained from a Sampler. This is used for deterministic
A sample_shape x event-dim Tensor of samples from the posterior.
Return type
GPyTorch Posterior¶
Posterior Module to be used with GPyTorch models.
class botorch.posteriors.gpytorch.GPyTorchPosterior(mvn)[source]¶
Bases: botorch.posteriors.posterior.Posterior
A posterior based on GPyTorch’s multi-variate Normal distributions.
A posterior based on GPyTorch’s multi-variate Normal distributions.
mvn (MultivariateNormal) – A GPyTorch MultivariateNormal (single-output case) or MultitaskMultivariateNormal (multi-output case).
Return type
property base_sample_shape: torch.Size¶
The shape of a base sample used for constructing posterior samples.
property device: torch.device¶
The torch device of the posterior.
property dtype: torch.dtype¶
The torch dtype of the posterior.
property event_shape: torch.Size¶
The event shape (i.e. the shape of a single sample) of the posterior.
rsample(sample_shape=None, base_samples=None)[source]¶
Sample from the posterior (with gradients).
○ sample_shape (Optional[torch.Size]) – A torch.Size object specifying the sample shape. To draw n samples, set to torch.Size([n]). To draw b batches of n samples each, set to
torch.Size([b, n]).
○ base_samples (Optional[torch.Tensor]) – An (optional) Tensor of N(0, I) base samples of appropriate dimension, typically obtained from a Sampler. This is used for deterministic
A sample_shape x event_shape-dim Tensor of samples from the posterior.
Return type
property mean: torch.Tensor¶
The posterior mean.
property variance: torch.Tensor¶
The posterior variance.
botorch.posteriors.gpytorch.scalarize_posterior(posterior, weights, offset=0.0)[source]¶
Affine transformation of a multi-output posterior.
☆ posterior (botorch.posteriors.gpytorch.GPyTorchPosterior) – The posterior over m outcomes to be scalarized. Supports t-batching.
☆ weights (torch.Tensor) – A tensor of weights of size m.
☆ offset (float) – The offset of the affine transformation.
The transformed (single-output) posterior. If the input posterior has
mean mu and covariance matrix Sigma, this posterior has mean weights^T * mu and variance weights^T Sigma w.
Return type
Example for a model with two outcomes:
>>> X = torch.rand(1, 2)
>>> posterior = model.posterior(X)
>>> weights = torch.tensor([0.5, 0.25])
>>> new_posterior = scalarize_posterior(posterior, weights=weights)
Determinstic Posterior¶
Deterministic (degenerate) posteriors. Used in conjunction with deterministic models.
class botorch.posteriors.deterministic.DeterministicPosterior(values)[source]¶
Bases: botorch.posteriors.posterior.Posterior
Deterministic posterior.
values (Tensor) –
Return type
property base_sample_shape: torch.Size¶
The shape of a base sample used for constructing posterior samples.
This function may be overwritten by subclasses in case base_sample_shape and event_shape do not agree (e.g. if the posterior is a Multivariate Gaussian that is not full rank).
property device: torch.device¶
The torch device of the posterior.
property dtype: torch.dtype¶
The torch dtype of the posterior.
property event_shape: torch.Size¶
The event shape (i.e. the shape of a single sample).
property mean: torch.Tensor¶
The mean of the posterior as a (b) x n x m-dim Tensor.
property variance: torch.Tensor¶
The variance of the posterior as a (b) x n x m-dim Tensor.
As this is a deterministic posterior, this is a tensor of zeros.
rsample(sample_shape=None, base_samples=None)[source]¶
Sample from the posterior (with gradients).
For the deterministic posterior, this just returns the values expanded to the requested shape.
○ sample_shape (Optional[torch.Size]) – A torch.Size object specifying the sample shape. To draw n samples, set to torch.Size([n]). To draw b batches of n samples each, set to
torch.Size([b, n]).
○ base_samples (Optional[torch.Tensor]) – An (optional) Tensor of N(0, I) base samples of appropriate dimension, typically obtained from a Sampler. Ignored in construction of the
samples (used only for shape validation).
A sample_shape x event-dim Tensor of samples from the posterior.
Return type
Higher Order GP Posterior¶
class botorch.posteriors.higher_order.HigherOrderGPPosterior(mvn, joint_covariance_matrix, train_train_covar, test_train_covar, train_targets, output_shape, num_outputs)[source]¶
Bases: botorch.posteriors.gpytorch.GPyTorchPosterior
Posterior class for a Higher order Gaussian process model [Zhe2019hogp]. Extends the standard GPyTorch posterior class by overwriting the rsample method. The posterior variance is handled
internally by the HigherOrderGP model. HOGP is a tensorized GP model so the posterior covariance grows to be extremely large, but is highly structured, which means that we can exploit Kronecker
identities to sample from the posterior using Matheron’s rule as described in [Doucet2010sampl].
In general, this posterior should ONLY be used for HOGP models that have highly structured covariances. It should also only be used internally when called from the HigherOrderGP.posterior(…)
method. At this time, the posterior does not support gradients with respect to the training data.
A Posterior for HigherOrderGP models.
☆ mvn (gpytorch.distributions.multivariate_normal.MultivariateNormal) – Posterior multivariate normal distribution
☆ joint_covariance_matrix (gpytorch.lazy.lazy_tensor.LazyTensor) – Joint test train covariance matrix over the entire tensor
☆ train_train_covar (gpytorch.lazy.lazy_tensor.LazyTensor) – covariance matrix of train points in the data space
☆ test_train_covar (gpytorch.lazy.lazy_tensor.LazyTensor) – covariance matrix of test x train points in the data space
☆ train_targets (torch.Tensor) – training responses vectorized
☆ output_shape (torch.Size) – shape output training responses
☆ num_outputs (int) – batch shaping of model
Return type
property base_sample_shape¶
The shape of a base sample used for constructing posterior samples.
property event_shape¶
The event shape (i.e. the shape of a single sample) of the posterior.
rsample(sample_shape=None, base_samples=None)[source]¶
Sample from the posterior (with gradients).
As the posterior covariance is difficult to draw from in this model, we implement Matheron’s rule as described in [Doucet2010sampl]-. This may not work entirely correctly for deterministic
base samples unless base samples are provided that are of shape n + 2 * n_train because the sampling method draws 2 * n_train samples as well as the standard n. samples.
○ sample_shape (Optional[torch.Size]) – A torch.Size object specifying the sample shape. To draw n samples, set to torch.Size([n]). To draw b batches of n samples each, set to
torch.Size([b, n]).
○ base_samples (Optional[torch.Tensor]) – An (optional) Tensor of N(0, I) base samples of appropriate dimension, typically obtained from a Sampler. This is used for deterministic
A sample_shape x event_shape-dim Tensor of samples from the posterior.
Return type
Multitask GP Posterior¶
class botorch.posteriors.multitask.MultitaskGPPosterior(mvn, joint_covariance_matrix, test_train_covar, train_diff, test_mean, train_train_covar, train_noise, test_noise=None)[source]¶
Bases: botorch.posteriors.gpytorch.GPyTorchPosterior
Posterior class for a Kronecker Multi-task GP model using with ICM kernel. Extends the standard GPyTorch posterior class by overwriting the rsample method. In general, this posterior should ONLY
be used for MTGP models that have structured covariances. It should also only be used internally when called from the KroneckerMultiTaskGP.posterior(…) method.
☆ mvn (gpytorch.distributions.multivariate_normal.MultivariateNormal) – Posterior multivariate normal distribution
☆ joint_covariance_matrix (gpytorch.lazy.lazy_tensor.LazyTensor) – Joint test train covariance matrix over the entire tensor
☆ train_train_covar (gpytorch.lazy.lazy_tensor.LazyTensor) – covariance matrix of train points in the data space
☆ test_obs_covar – covariance matrix of test x train points in the data space
☆ train_diff (torch.Tensor) – difference between train mean and train responses
☆ train_noise (Union[gpytorch.lazy.lazy_tensor.LazyTensor, torch.Tensor]) – training noise covariance
☆ test_noise (Optional[Union[gpytorch.lazy.lazy_tensor.LazyTensor, torch.Tensor]]) – Only used if posterior should contain observation noise. testing noise covariance
☆ test_train_covar (gpytorch.lazy.lazy_tensor.LazyTensor) –
☆ test_mean (torch.Tensor) –
property base_sample_shape: torch.Size¶
The shape of a base sample used for constructing posterior samples.
property device: torch.device¶
The torch device of the posterior.
property dtype: torch.dtype¶
The torch dtype of the posterior.
rsample(sample_shape=None, base_samples=None, train_diff=None)[source]¶
Sample from the posterior (with gradients).
○ sample_shape (Optional[torch.Size]) – A torch.Size object specifying the sample shape. To draw n samples, set to torch.Size([n]). To draw b batches of n samples each, set to
torch.Size([b, n]).
○ base_samples (Optional[torch.Tensor]) – An (optional) Tensor of N(0, I) base samples of appropriate dimension, typically obtained from a Sampler. This is used for deterministic
○ train_diff (Optional[torch.Tensor]) –
A sample_shape x event_shape-dim Tensor of samples from the posterior.
Return type
Transformed Posterior¶
class botorch.posteriors.transformed.TransformedPosterior(posterior, sample_transform, mean_transform=None, variance_transform=None)[source]¶
Bases: botorch.posteriors.posterior.Posterior
An generic transformation of a posterior (implicitly represented)
An implicitly represented transformed posterior
☆ posterior (Posterior) – The posterior object to be transformed.
☆ sample_transform (Callable[[Tensor], Tensor]) – A callable applying a sample-level transform to a sample_shape x batch_shape x q x m-dim tensor of samples from the original posterior,
returning a tensor of samples of the same shape.
☆ mean_transform (Optional[Callable[[Tensor, Tensor], Tensor]]) – A callable transforming a 2-tuple of mean and variance (both of shape batch_shape x m x o) of the original posterior to the
mean of the transformed posterior.
☆ variance_transform (Optional[Callable[[Tensor, Tensor], Tensor]]) – A callable transforming a 2-tuple of mean and variance (both of shape batch_shape x m x o) of the original posterior to
a variance of the transformed posterior.
Return type
property base_sample_shape: torch.Size¶
The shape of a base sample used for constructing posterior samples.
property device: torch.device¶
The torch device of the posterior.
property dtype: torch.dtype¶
The torch dtype of the posterior.
property event_shape: torch.Size¶
The event shape (i.e. the shape of a single sample).
property mean: torch.Tensor¶
The mean of the posterior as a batch_shape x n x m-dim Tensor.
property variance: torch.Tensor¶
The variance of the posterior as a batch_shape x n x m-dim Tensor.
rsample(sample_shape=None, base_samples=None)[source]¶
Sample from the posterior (with gradients).
○ sample_shape (Optional[torch.Size]) – A torch.Size object specifying the sample shape. To draw n samples, set to torch.Size([n]). To draw b batches of n samples each, set to
torch.Size([b, n]).
○ base_samples (Optional[torch.Tensor]) – An (optional) Tensor of N(0, I) base samples of appropriate dimension, typically obtained from a Sampler. This is used for deterministic
A sample_shape x event-dim Tensor of samples from the posterior.
Return type | {"url":"https://botorch.org/v/0.6.0/api/posteriors.html","timestamp":"2024-11-05T20:28:11Z","content_type":"text/html","content_length":"72005","record_id":"<urn:uuid:9053e992-1958-47a6-bc96-271182b3b8ea>","cc-path":"CC-MAIN-2024-46/segments/1730477027889.1/warc/CC-MAIN-20241105180955-20241105210955-00032.warc.gz"} |
VGSL Specs - rapid prototyping of mixed conv/LSTM networks for images
Variable-size Graph Specification Language (VGSL) enables the specification of a neural network, composed of convolutions and LSTMs, that can process variable-sized images, from a very short
definition string.
Applications: What is VGSL Specs good for?
VGSL Specs are designed specifically to create networks for:
• Variable size images as the input. (In one or BOTH dimensions!)
• Output an image (heat map), sequence (like text), or a category.
• Convolutions and LSTMs are the main computing component.
• Fixed-size images are OK too!
Model string input and output
A neural network model is described by a string that describes the input spec, the output spec and the layers spec in between. Example:
[1,0,0,3 Ct5,5,16 Mp3,3 Lfys64 Lfx128 Lrx128 Lfx256 O1c105]
The first 4 numbers specify the size and type of the input, and follow the TensorFlow convention for an image tensor: [batch, height, width, depth]. Batch is currently ignored, but eventually may be
used to indicate a training mini-batch size. Height and/or width may be zero, allowing them to be variable. A non-zero value for height and/or width means that all input images are expected to be of
that size, and will be bent to fit if needed. Depth needs to be 1 for greyscale and 3 for color. As a special case, a different value of depth, and a height of 1 causes the image to be treated from
input as a sequence of vertical pixel strips. NOTE THAT THROUGHOUT, x and y are REVERSED from conventional mathematics, to use the same convention as TensorFlow. The reason TF adopts this convention
is to eliminate the need to transpose images on input, since adjacent memory locations in images increase x and then y, while adjacent memory locations in tensors in TF, and NetworkIO in tesseract
increase the rightmost index first, then the next-left and so-on, like C arrays.
The last “word” is the output specification and takes the form:
O(2|1|0)(l|s|c)n output layer with n classes.
2 (heatmap) Output is a 2-d vector map of the input (possibly at
different scale). (Not yet supported.)
1 (sequence) Output is a 1-d sequence of vector values.
0 (category) Output is a 0-d single vector value.
l uses a logistic non-linearity on the output, allowing multiple
hot elements in any output vector value. (Not yet supported.)
s uses a softmax non-linearity, with one-hot output in each value.
c uses a softmax with CTC. Can only be used with s (sequence).
NOTE Only O1s and O1c are currently supported.
The number of classes is ignored (only there for compatibility with TensorFlow) as the actual number is taken from the unicharset.
Syntax of the Layers in between
NOTE that all ops input and output the standard TF convention of a 4-d tensor: [batch, height, width, depth] regardless of any collapsing of dimensions. This greatly simplifies things, and allows the
VGSLSpecs class to track changes to the values of widths and heights, so they can be correctly passed in to LSTM operations, and used by any downstream CTC operation.
NOTE: in the descriptions below, <d> is a numeric value, and literals are described using regular expression syntax.
NOTE: Whitespace is allowed between ops.
Functional ops
C(s|t|r|l|m)<y>,<x>,<d> Convolves using a y,x window, with no shrinkage,
random infill, d outputs, with s|t|r|l|m non-linear layer.
F(s|t|r|l|m)<d> Fully-connected with s|t|r|l|m non-linearity and d outputs.
Reduces height, width to 1. Connects to every y,x,depth position of the input,
reducing height, width to 1, producing a single <d> vector as the output.
Input height and width *must* be constant.
For a sliding-window linear or non-linear map that connects just to the
input depth, and leaves the input image size as-is, use a 1x1 convolution
eg. Cr1,1,64 instead of Fr64.
L(f|r|b)(x|y)[s]<n> LSTM cell with n outputs.
The LSTM must have one of:
f runs the LSTM forward only.
r runs the LSTM reversed only.
b runs the LSTM bidirectionally.
It will operate on either the x- or y-dimension, treating the other dimension
independently (as if part of the batch).
s (optional) summarizes the output in the requested dimension, outputting
only the final step, collapsing the dimension to a single element.
LS<n> Forward-only LSTM cell in the x-direction, with built-in Softmax.
LE<n> Forward-only LSTM cell in the x-direction, with built-in softmax,
with binary Encoding.
In the above, (s|t|r|l|m) specifies the type of the non-linearity:
s = sigmoid
t = tanh
r = relu
l = linear (i.e., No non-linearity)
m = softmax
Cr5,5,32 Runs a 5x5 Relu convolution with 32 depth/number of filters.
Lfx128 runs a forward-only LSTM, in the x-dimension with 128 outputs, treating the y dimension independently.
Lfys64 runs a forward-only LSTM in the y-dimension with 64 outputs, treating the x-dimension independently and collapses the y-dimension to 1 element.
Plumbing ops
The plumbing ops allow the construction of arbitrarily complex graphs. Something currently missing is the ability to define macros for generating say an inception unit in multiple places.
[...] Execute ... networks in series (layers).
(...) Execute ... networks in parallel, with their output concatenated in depth.
S<y>,<x> Rescale 2-D input by shrink factor y,x, rearranging the data by
increasing the depth of the input by factor xy.
**NOTE** that the TF implementation of VGSLSpecs has a different S that is
not yet implemented in Tesseract.
Mp<y>,<x> Maxpool the input, reducing each (y,x) rectangle to a single value.
Full Example: A 1-D LSTM capable of high quality OCR
[1,1,0,48 Lbx256 O1c105]
As layer descriptions: (Input layer is at the bottom, output at the top.)
O1c105: Output layer produces 1-d (sequence) output, trained with CTC,
outputting 105 classes.
Lbx256: Bi-directional LSTM in x with 256 outputs
1,1,0,48: Input is a batch of 1 image of height 48 pixels in greyscale, treated
as a 1-dimensional sequence of vertical pixel strips.
[]: The network is always expressed as a series of layers.
This network works well for OCR, as long as the input image is carefully normalized in the vertical direction, with the baseline and meanline in constant places.
Full Example: A multi-layer LSTM capable of high quality OCR
[1,0,0,1 Ct5,5,16 Mp3,3 Lfys64 Lfx128 Lrx128 Lfx256 O1c105]
As layer descriptions: (Input layer is at the bottom, output at the top.)
O1c105: Output layer produces 1-d (sequence) output, trained with CTC,
outputting 105 classes.
Lfx256: Forward-only LSTM in x with 256 outputs
Lrx128: Reverse-only LSTM in x with 128 outputs
Lfx128: Forward-only LSTM in x with 128 outputs
Lfys64: Dimension-summarizing LSTM, summarizing the y-dimension with 64 outputs
Mp3,3: 3 x 3 Maxpool
Ct5,5,16: 5 x 5 Convolution with 16 outputs and tanh non-linearity
1,0,0,1: Input is a batch of 1 image of variable size in greyscale
[]: The network is always expressed as a series of layers.
The summarizing LSTM makes this network more resilient to vertical variation in position of the text.
Variable size inputs and summarizing LSTM
NOTE that currently the only way of collapsing a dimension of unknown size to known size (1) is through the use of a summarizing LSTM. A single summarizing LSTM will collapse one dimension (x or y),
leaving a 1-d sequence. The 1-d sequence can then be collapsed in the other dimension to make a 0-d categorical (softmax) or embedding (logistic) output.
For OCR purposes then, the height of the input images must either be fixed, and scaled (using Mp or S) vertically to 1 by the top layer, or to allow variable-height images, a summarizing LSTM must be
used to collapse the vertical dimension to a single value. The summarizing LSTM can also be used with a fixed height input. | {"url":"https://tesseract-ocr.github.io/tessdoc/tess4/VGSLSpecs","timestamp":"2024-11-11T10:36:55Z","content_type":"text/html","content_length":"13777","record_id":"<urn:uuid:c3084a1e-a4d4-4ced-b7bd-d83d8c718d32>","cc-path":"CC-MAIN-2024-46/segments/1730477028228.41/warc/CC-MAIN-20241111091854-20241111121854-00479.warc.gz"} |
Pendulum Problems
Carlson, Robert Providence Catholic H.S.
1. To review the terms pendulum, period, cycle, frequency, independent
variable, dependent variable, damping, and displacement.
2. To review the graphs of the functions: f(x)=x^0, f(x)=x^1, f(x)=x^2
3. To determine experimentally the relationship between the length
(L) and the period (T) of a simple pendulum.
4. To derive the mathematical equation which represents the
5. To observe the graphical relationship between the period (T) and
the displacement (d) of a simple pendulum.
weights (uniform mass)- one per student
strings (increments of 10cm)- one per student
overhead projector
graph paper
Apple computer/gameport/100k linear potentiometer (see Radio Shack)
`Pendulum Plotter' disc
meter stick
Recommended Strategy
1. Construct a simple pendulum in front of class. Begin a dialogue
concerning the motion of the pendulum. Use the words, period,
frequency, cycle, independent and dependent variable, and control
and try to elicit questions. After discussing the effects of
modifying a pendulum, conclude that it is the length (under small
displacement) that determines the period.
2. Provide each student with a pendulum. Have them determine the
period of their pendulum. Discuss the significance of the number of
cycles used to determine the period. Record data on the board. Also
graph the period (dependent variable-T) versus the length (independent
variable-L) using the vertical axis for (T) and the horizontal axis for
(L). But instead of plotting points, tape each student's pendulum to
the board. A curve is generated by the pendulum bobs but in this manner
we see, maybe more convincingly, that it is the length of the pendulum
that determines the period of the pendulum.
3. Distribute graph paper and, using the overhead projector, help
the class to graph f(x)=x^0, f(x)=x^1, and f(x)=x^2. Compare these
graphs with the graph generated in strategy 2 above. Lead class to
discover that the new function 'fits' between f(x)=x^0 and f(x)=x^1.
At this point, speculate that the new function could have a factor of
x^1/2. Now try to get the kids to look back at the table to guess
what must be done to the 'L' values to get the 'T' values. With
'good' data you'll arrive at T= L^1/2/5.
4. Fit the potentiometer to one end of a meter stick and affix this
apparatus to a ringstand. Using the gameport, wire the apparatus to
the computer. Boot the Pendulum Plotter program. Displace the meter
stick and observe the monitor for a graph which shows simple harmonic
motion. Allow time for experiments regarding the displacement of the
meterstick. What is being graphed now? Ask students to form conjectures
from their experiments.
Return to Physics Index | {"url":"https://smileprogram.info/ph8802.html","timestamp":"2024-11-13T17:46:46Z","content_type":"text/html","content_length":"3550","record_id":"<urn:uuid:6fc14cf5-9240-4ccb-960d-cb859b3b4fd3>","cc-path":"CC-MAIN-2024-46/segments/1730477028387.69/warc/CC-MAIN-20241113171551-20241113201551-00292.warc.gz"} |
ERC School on Free Discontinuity Problems*
communication: The rigidity problem for symmetrization inequalities
Filippo Cagnetti (University of Sussex)
abstract: Steiner symmetrization is a very useful tool in the study of isoperimetric inequality. This is also due to the fact that the perimeter of a set is less or equal than the perimeter of its
Steiner symmetral. In the same way, in the Gaussian setting, it is well known that Ehrhard symmetrization does not increase the Gaussian perimeter.
We will show characterization results for equality cases in both Steiner and Ehrhard perimeter inequalities.
We will also characterize rigidity of equality cases. By rigidity, we mean the situation when all equality cases are trivially obtained by a translation of the Steiner symmetral (or, in the Gaussian
setting, by a reflection of the Ehrhard symmetral).
We will achieve this through the introduction of a suitable measure-theoretic notion of connectedness, and through a fine analysis of the barycenter function for a special class of sets.
These results are obtained in collaboration with Maria Colombo, Guido De Philippis, and Francesco Maggi.
Tue 8 Jul, 16:30 - 17:00,
Aula Dini << Go back | {"url":"https://crm.sns.it/course/4322/","timestamp":"2024-11-03T08:49:33Z","content_type":"text/html","content_length":"8955","record_id":"<urn:uuid:2b19641d-4031-4c1b-8303-7cd41af9bdc8>","cc-path":"CC-MAIN-2024-46/segments/1730477027774.6/warc/CC-MAIN-20241103083929-20241103113929-00710.warc.gz"} |
Two corners of an isosceles triangle are at (4 ,2 ) and (1 ,5 ). If the triangle's area is 64 , what are the lengths of the triangle's sides? | HIX Tutor
Two corners of an isosceles triangle are at #(4 ,2 )# and #(1 ,5 )#. If the triangle's area is #64 #, what are the lengths of the triangle's sides?
Answer 1
#color(blue)(a=b=sqrt(32930)/6 and c=3sqrt(2)#
Let #A=(4,2)# and #B=(1,5)#
If #AB# is the base of an isosceles triangle then #C=(x,y)# is the vertex at the altitude.
Let The sides be # a,b,c#, #a=b#
Let h be the height, bisecting AB and passing through point C:
Length #AB = sqrt((4-1)^2+(2-5)^2)=sqrt(18)=3sqrt(2)#
To find #h#. We are given area equals 64:
So the lengths of the sides are:
#color(blue)(a=b=sqrt(32930)/6 and c=3sqrt(2)#
Sign up to view the whole answer
By signing up, you agree to our Terms of Service and Privacy Policy
Answer 2
To find the lengths of the sides of the isosceles triangle, we first need to determine the coordinates of the third vertex. Since the triangle is isosceles, the third vertex will be directly below
the midpoint of the base.
Let's find the midpoint of the base:
Midpoint = (\left(\frac{{x_1 + x_2}}{2}, \frac{{y_1 + y_2}}{2}\right))
Midpoint = (\left(\frac{{4 + 1}}{2}, \frac{{2 + 5}}{2}\right))
Midpoint = (\left(\frac{5}{2}, \frac{7}{2}\right))
Now, we have the midpoint of the base. To find the length of the altitude (height) of the triangle, we can calculate the distance between the midpoint and the top vertex.
Distance formula:
(d = \sqrt{{(x_2 - x_1)^2 + (y_2 - y_1)^2}})
(d = \sqrt{{\left(\frac{5}{2} - 4\right)^2 + \left(\frac{7}{2} - 2\right)^2}})
(d = \sqrt{{\left(\frac{-3}{2}\right)^2 + \left(\frac{3}{2}\right)^2}})
(d = \sqrt{{\frac{9}{4} + \frac{9}{4}}})
(d = \sqrt{{\frac{18}{4}}})
(d = \sqrt{{\frac{9}{2}}})
(d = \frac{3\sqrt{2}}{2})
Now, we can use the formula for the area of a triangle:
Area = (\frac{1}{2} \times \text{base} \times \text{height})
64 = (\frac{1}{2} \times \text{base} \times \frac{3\sqrt{2}}{2})
Base = (\frac{{2 \times 64}}{{3\sqrt{2}}})
Base = (\frac{{128}}{{3\sqrt{2}}})
Now, we have the base of the triangle. Since the triangle is isosceles, the lengths of the other two sides are equal to the base. Therefore, the lengths of the sides of the triangle are (\frac{{128}}
{{3\sqrt{2}}}) and (\frac{{128}}{{3\sqrt{2}}}).
Sign up to view the whole answer
By signing up, you agree to our Terms of Service and Privacy Policy
Answer from HIX Tutor
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
Not the question you need?
HIX Tutor
Solve ANY homework problem with a smart AI
• 98% accuracy study help
• Covers math, physics, chemistry, biology, and more
• Step-by-step, in-depth guides
• Readily available 24/7 | {"url":"https://tutor.hix.ai/question/two-corners-of-an-isosceles-triangle-are-at-4-2-and-1-5-if-the-triangle-s-area-i-8f9afa38f8","timestamp":"2024-11-06T02:04:14Z","content_type":"text/html","content_length":"578759","record_id":"<urn:uuid:c3d9780d-4271-4567-9d92-ac5a4f27c430>","cc-path":"CC-MAIN-2024-46/segments/1730477027906.34/warc/CC-MAIN-20241106003436-20241106033436-00865.warc.gz"} |
5 (number) - New World Encyclopedia (2024)
List of numbers â Integers
Cardinal 5
Ordinal 5th
Numeral system quinary
Factorization prime
Divisors 1, 5
Roman numeral V
Roman numeral (Unicode) â ¤, â ´
Arabic Ù¥
Arabic (Urdu) Ûµ
Ge'ez á
Bengali ৫
Chinese numeral äº ï¼ ä¼
DevanÄ garÄ« ५
Hebrew × (He)
Khmer á ¥
Thai à¹
penta-/pent- (from Greek)
quinque-/quinqu-/quint- (from Latin)
Binary 101
Octal 5
Duodecimal 5
Hexadecimal 5
Vigesimal 5
5 (five) is a number, numeral, and glyph that represents the number. It is the natural number^[1] that follows 4 and precedes 6. It is an integer and a cardinal number, that is, a number that is used
for counting.^[2] In addition, it is classified as a real number,^[3] distinguishing it from imaginary numbers.
• 1 Evolution of the glyph
• 2 In mathematics
□ 2.1 Numbering systems
□ 2.2 List of basic calculations
• 3 In science
□ 3.1 Chemistry
□ 3.2 Biology
□ 3.3 Meteorology
□ 3.4 Astronomy
• 4 In technology
• 5 In religion
□ 5.1 Judaism
□ 5.2 Christianity
□ 5.3 Islam
□ 5.4 Other religions
• 6 In music
• 7 In sports
• 8 Miscellaneous fields
• 9 See also
• 10 Notes
• 11 References
• 12 External links
• 13 Credits
Evolution of the glyph
The evolution of our modern glyph for five cannot be neatly traced back to the Brahmin Indians quite the same way one can trace the glyphs for 1 to 4. The (later) Kushana and Gupta Indians had among
themselves several different glyphs that bear no resemblance to the modern glyph. The Nagari and Punjabi took these glyphs and all came up with glyphs that look like a lowercase "h" rotated 180°.
The Ghubar Arabs transformed the glyph in several different ways, coming up with glyphs that look more like 4s or 3s than 5s.^[4] It was from those characters that the Europeans finally came up with
the modern 5, though from purely graphical evidence, it would be much easier to conclude that the modern 5 came from the Khmer. The Khmer glyph develops from the Kushana/Ã ndhra/Gupta numeral, its
shape looking like a modern day version with an extended swirled "tail."^[4]
While the shape of the 5 character has an ascender in most modern typefaces, in typefaces with text figures the character usually has a descender, for example, in .
In mathematics
Five is between 4 and 6 and is the third prime number, after 2 and 3, and before 7. Because it can be written as 2^(2^1)+1, five is classified as a Fermat prime. 5 is the third Sophie Germain prime,
the first safe prime, and the third Mersenne prime exponent. Five is the first Wilson prime and the third factorial prime, also an alternating factorial. It is an Eisenstein prime with no imaginary
part and real part of the form . It is also the only number that is part of more than one pair of twin primes.
Five is conjectured to be the only odd untouchable number.
The number 5 is the 5th Fibonacci number, being 2 plus 3. 5 is also a Pell number and a Markov number, appearing in solutions to the Markov Diophantine equation: (1, 2, 5), (1, 5, 13), (2, 5, 29),
(5, 13, 194), (5, 29, 433), ....^[5] Whereas 5 is unique in the Fibonacci sequence, in the Perrin sequence 5 is both the fifth and sixth Perrin numbers.
5 and 6 form a Ruth-Aaron pair under either definition.
There are five solutions to Znám's problem of length 6.
Five is the second Sierpinski number of the first kind, and can be written as S2=(2^2)+1
While polynomial equations of degree 4 and below can be solved with radicals, equations of degree 5 and higher cannot generally be so solved. This is the Abel-Ruffini theorem. This is related to the
fact that the symmetric group S[n] is a solvable group for n â ¤ 4 and not solvable for n â ¥ 5.
While all graphs with 4 or fewer vertices are planar, there exists a graph with 5 vertices which is not planar: K[5], the complete graph with 5 vertices.
Five is also the number of Platonic solids.
A polygon with five sides is a pentagon. Figurate numbers representing pentagons (including five) are called pentagonal numbers. Five is also a square pyramidal number.
Five is the only prime number to end in the digit 5, because all other numbers written with a 5 in the ones-place under the decimal system are multiples of five. As a consequence of this, 5 is in
base 10 a 1-automorphic number.
Vulgar fractions with 5 or 2 in the denominator do not yield infinite decimal expansions, as is the case with most primes, because they are prime factors of ten, the base. When written in the decimal
system, all multiples of 5 will end in either 5 or 0.
There are five Exceptional Lie groups.
Numbering systems
• In binary, code five is 101
• In ternary, code five is 12
• In quaternary, numeral system code five is 11
• In quinary, five is 10; and in senary, code and all codes above (such as decimal, duodecimal and vigesimal) five is 5.
• The Roman numeral for five is V, which comes from a representation of an outstretched hand.
• In the Arabic alphabet, Ù¥â (hÄ Ê¼) has numerical value of 5.
• In the Greek alphabet, ε (epsilon) has numerical value of 5.
• In the Hebrew alphabet, × (heh) has numerical value of 5.
• In the Cyrillic alphabet, Ð has numerical value of 5.
• In the Glagolitic alphabet, (dobro) has numerical value of 5.
• The kanji and Chinese character for five are both äº , and its formal writing in Chinese is ä¼ (pinyin wÇ ).
List of basic calculations
Multiplication 1 2 3 4 5 6 7 8 9 10
Multiplication 11 12 13 14 15 16 17 18 19 20
Multiplication 21 22 23 24 25 50 100 1000
Division 1 2 3 4 5 6 7 8 9 10
5 2.5 1.25 1 0.625 0.5
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Division 11 12 13 14 15
2.2 2.4 2.6 2.8 3
Exponentiation 1 2 3 4 5 6 7 8 9 10
Exponentiation 11 12 13
In science
• The atomic number of boron is five.
• The smallest atomic mass number (the sum of protons and neutrons) for which no stable isotopes exist for any element.
• Humans and other primates have five digits on each hand and five toes on each foot.
• Five is the number of appendages on most starfish, which exhibit pentamerism.
• The most destructive known tornadoes rate an F-5 on the Fujita scale.
• The most destructive known hurricanes rate as Category 5 on the Saffir-Simpson scale.
• Messier object M5, a magnitude 7.0 globular cluster in the constellation Serpens.
• The Saros number of the solar eclipse series which began on April 4, 2720 B.C.E. and ended on May 24, 1422 B.C.E. The duration of Saros series 5 was 1298.17 years, and it contained 73 solar
• The Saros number of the lunar eclipse series which began on December 22, 2455 B.C.E. and ended on March 24, 1084 B.C.E. The duration of Saros series 5 was 1370.29, and it contained 77 lunar
• The Roman numeral V (usually) stands for the fifth-discovered satellite of a planet or minor planet (such as Jupiter V).
• The Roman numeral V stands for dwarfs (main sequence stars) in the Yerkes spectral classification scheme.
In technology
• Five is the resin identification code used in recycling to identify polypropylene.
• In radio communication, the term "Five by five" is used to indicate perfect signal strength and clarity.
• The Pentium, coined by Intel Corporation, is a fifth-generation x86 architecture microprocessor.
• On almost all devices with a numeric keypad such as telephones and computers, the 5 key has a raised dot or raised bar to make dialing easier. Persons who are blind or have low vision find it
useful to be able to feel the keys of a telephone. All other numbers can be found with their relative position around the 5 button. (On computer keyboards, the 5 key of the numpad has the raised
dot or bar, but the 5 key that shifts with theÂ% symbol does not.)
• 5 is a common number of gears for automobiles with manual transmission.
In religion
• The Torah contains five books: Genesis, Exodus, Leviticus, Numbers, and Deuteronomy. They are collectively called the Five Books of Moses, the Pentateuch (Greek for "five containers," referring
to the scroll cases in which the books were kept), or Humash (× × × ×©, Hebrew for "fifth").
• The book of Psalms is arranged into five books, paralleling the Five Books of Moses.
• The Khamsa, an ancient symbol shaped like a hand with five fingers, is used as a protective amulet by Jews.
• In Greek Orthodox Christian mysticism, the number 5 symbolizes the Holy Spirit as the bearer of all life. In the monastic tradition of Mount Athos there exists a "hymn" to the Holy Spirit
composed entirely and solely of repetitions of the word "pente" (Greek for "five")
• There are five basic "pillars" of Islam.
• Muslims pray to Allah five times a day *In Islam, particularly Shia Islam, the Panjetan or the Five Holy Purified Ones are the members of Muhammad's family including: Muhammad, Ali, Fatima,
Hasan, Husayn and is often symbolically represented by an image of the Khamsa.
Other religions
• The five sacred Sikh symbols prescribed by Guru Gobind Singh are commonly known as Panj Kakars or the "Five Ks" because they start with letter K representing Kakka in the Punjabi language. They
are: Kesh (unshorn hair), Kangha (the comb), Kara (the steel bracelet), Kachh (the soldiers shorts), and Kirpan (the sword).
• According to some traditions of Maya mythology, we are now living in the Fifth World.
• In East Asian tradition, there are five elements: Water, fire, earth, wood, and metal. The Japanese names for the days of the week, Tuesday through Saturday, come from these elements via the
identification of the elements with the five planets visible with the naked eye. Also, the traditional Japanese calendar has a five-day weekly cycle that can be still observed in printed mixed
calendars combining Western, Chinese-Buddhist and Japanese names for each weekday.
• In some cultures there are five cardinal directions, including the center.
• In Cantonese, "five" sounds like the word "not" (symbol: å ). When five appears in front of a lucky number, for example, "58," the result is considered unlucky.
• In Discordianism, 5 is seen as a very important number as demonstrated in the Law of Fives and The Pentabarf, which contains five rules. Each page of the Principia Discordia, the primary
religious document in Discordianism, is also labeled with 5 digits.
In music
• A perfect fifth is the most consonant harmony, and is the basis for most western tuning systems.
• Modern musical notation uses a musical staff made of five horizontal lines.
• Using the Latin root, five musicians are called a quintet, for example, the Jackson Five. (In an episode of Will & Grace guest-starring Janet Jackson, she declared that 5 is a mystical number and
for that reason she must have precisely 5 backup dancers).
• The Five is the name of a nineteenth-century Russian Group of nationalistic composers who included César Cui, Aleksandr Borodin, Mily Balakirev, Modest Mussorgsky, and Nikolay Rimsky-Korsakov.
• The name of the band The Fifth Dimension implies that they are transcending beyond even the fourth dimension (time) into a new inner dimension.
• Take Five is a famous jazz standard composed by Paul Desmond. It counts five beats per bar.
• The number of completed, numbered piano concertos of Ludwig van Beethoven and Camille Saint-Saëns.
• In harmonicsâ The fifth partial (or 4th overtone) of a fundamental has a frequency ratio of 5/1 to the frequency of that fundamental. This ratio corresponds to the interval of 2 octaves + a pure
major third. Thus, the interval of 5/4 is the interval of the pure third. A major triad chord when played in just intonation (most often the case in a cappella vocal ensemble singing), will
contain such a pure major third.
In sports
• The number of players of a basketball team on the court at a given time.
• Also used in basketball to represent the position of center.
• The Olympic Games have five interlocked rings as their symbol, representing the number of inhabited continents represented by the Olympians (counting North America and South America as one
• The number of kyu (pupil) grades in judo
• In rugby union, the number of the lock forward who usually jumps at number 4 in the line-out. It is also the number of points awarded for a try.
• In rugby league, the number of the left wing, and also the number of tackles the attacking team has to score a try before the handover.
• In baseball, five represents the third baseman's position.
• In hockey, the area between the goaltender's legs is known as the five-hole.
Miscellaneous fields
International maritime signal flag for 5
A hand holding the four 5's in a standard deck of cards: Diamonds, Clubs, Hearts, Spades
• Five is the number of oceans in the world.
• The five senses are sight, smell, sound, touch and taste.
• The five basic tastes are sweet, salty, sour, bitter and umami.
• In various early cultures, the universe was thought to be comprised of five classical elements: water, earth, air, fire, and ether.
• Pentameter is verse with five repeating feet per line; iambic pentameter was the most popular form in Shakespeare.
• In the United States legal system, the Fifth Amendment to the United States Constitution can be referred to in court as "pleading the fifth," absolving the defendant from self-incrimination.
• Five is the number of permanent members with veto power on the UN Security Council.
• Five is the least number of justices needed to make a majority decision in the U.S. Supreme Court.
• Five babies born at one time are quintuplets. The most famous set of quintuplets were the Dionne Quintuplets born in the 1930s.
• Quintessence, meaning "fifth element," refers to the elusive fifth element that completes the basic four elements (water, fire, air and earth).
• Five is the number of dots in a quincunx.
• There are five points in a pentagram.
• The Garden of Cyrus 1658, by Sir Thomas Browne is a Pythagorean Discourse based upon the number 5.
• The word "punch" comes from the Hindi word for five. Being true to the designation of punch, the drink Five Alive is named for its five ingredients.
• Five is an informal term for the British Security Service, MI5.
• There are five vowels in the English alphabet: A, e, i, o and u.
See also
1. â A natural number is any number that is a positive integer, such as 1, 2, 3, 4, and so forth. Often, the number 0 is also called a natural number.
2. â A cardinal number indicates the quantity of things, but not the order in which they occur. By contrast, ordinal numbers are first, second, third, and so on, indicating their positions in a
3. â A real number is a number that can be given by a finite or infinite decimal representation. The term "real number" was coined to distinguish it from an "imaginary number." The set of real
numbers includes rational and irrational numbers, which can be positive, negative, or zero.
4. â ^4.0 ^4.1 Georges Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer (New York: Wiley, 2000, ISBN 0471393401).
5. â The Online Encyclopedia of Integer Sequences, A030452: Markov numbers satisfying region 5 (x=5) of the equation x^2 + y^2 + z^2 = 3xyz. Retrieved October 7, 2022.
6. â NASA Eclipse Website, Saros Series 5 Saros Series Catalog of Solar Eclipses. Retrieved October 7, 2022.
7. â NASA Eclipse Website, Saros Series 5 Catalog of Lunar Eclipse Saros Series. Retrieved October 7, 2022.
ISBN links support NWE through referral fees
External links
All links retrieved June 13, 2023.
New World Encyclopedia writers and editors rewrote and completed the Wikipedia article in accordance with New World Encyclopedia standards. This article abides by terms of the Creative Commons
CC-by-sa 3.0 License (CC-by-sa), which may be used and disseminated with proper attribution. Credit is due under the terms of this license that can reference both the New World Encyclopedia
contributors and the selfless volunteer contributors of the Wikimedia Foundation. To cite this article click here for a list of acceptable citing formats.The history of earlier contributions by
wikipedians is accessible to researchers here:
The history of this article since it was imported to New World Encyclopedia:
Note: Some restrictions may apply to use of individual images which are separately licensed. | {"url":"https://klausaudio.com/article/5-number-new-world-encyclopedia","timestamp":"2024-11-08T08:58:21Z","content_type":"text/html","content_length":"99782","record_id":"<urn:uuid:9f3645e4-5343-4926-9aab-4e2bd541ca7c>","cc-path":"CC-MAIN-2024-46/segments/1730477028032.87/warc/CC-MAIN-20241108070606-20241108100606-00879.warc.gz"} |
Using Double Angle Identities to Evaluate a Trigonometric Expression
Question Video: Using Double Angle Identities to Evaluate a Trigonometric Expression Mathematics • Second Year of Secondary School
Find, without using a calculator, the value of (sin 2π ΅)/(2 cos 2π ΅) given cos π ΅ = 4/5 where 3π /2 < π ΅ < 2π .
Video Transcript
Find, without using a calculator, the value of sin two π ΅ divided by two multiplied by cos two π ΅ given that the cos of angle π ΅ is equal to four-fifths, where π ΅ is greater than three π
over two and less than two π .
Before focusing on the expression we need to calculate, letβ s look at the information we have been given. We are told that the cos of angle π ΅ is equal to four-fifths and that this angle π ΅
lies between three π over two and two π radians. The CAST diagram shown helps us identify whether the sine, cosine, and tangent of any angle between zero and two π is positive or negative.
In this question, we know that the angle π ΅ lies in the fourth quadrant. In this quadrant, the cosine of the angle is positive, whereas both the sine of the angle and tangent of the angle are
negative. We are also told in the question that the cos of angle π ΅ is equal to four-fifths. We can use this information together with our trigonometrical identities to calculate the sin of angle π
΅ and the tan of angle π ΅.
We recall that sin squared π plus cos squared π is equal to one. This means that sin squared π ΅ plus four-fifths squared is equal to one. We can square four-fifths by squaring the numerator
and denominator separately, giving us 16 over 25. We can then subtract this from both sides of our equation. sin squared π ΅ is therefore equal to nine over 25. We can then square root both sides of
this equation such that the sin of angle π ΅ is equal to the positive or negative square root of nine over 25. This simplifies to positive or negative three-fifths. Recalling that the sin of angle π
΅ must be negative, this is equal to negative three-fifths.
We know that the tan of any angle π is equal to the sine of that angle divided by the cosine of the angle. This means that the tan of angle π ΅ is equal to negative three-fifths divided by
four-fifths. The right-hand side simplifies to negative three-quarters. We now have values for the sin of angle π ΅, the cos of angle π ΅, and the tan of angle π ΅. Our next step is to try to
substitute these into the expression sin of two π ΅ divided by two multiplied by the cos of two π ΅. We can do this using our knowledge of the double-angle formulae. The sin of two π is equal to
two multiplied by the sin of π multiplied by the cos of π . And the cos of two π is equal to cos squared π minus sin squared π .
The expression sin two π ΅ over two multiplied by cos two π ΅ can be rewritten as shown. Dividing the numerator and denominator by two, we are left with sin π ΅ multiplied by cos π ΅ all divided
by cos squared π ΅ minus sin squared π ΅. We can now substitute the values negative three-fifths and four-fifths into this expression. The numerator becomes negative three-fifths multiplied by
four-fifths, and the denominator is four-fifths squared minus negative three-fifths squared. Negative three-fifths multiplied by four-fifths is equal to negative twelve twenty-fifths. And four-fifths
squared minus negative three-fifths squared is equal to seven twenty-fifths. This simplifies to negative 12 over seven. The value of sin two π ΅ divided by two multiplied by the cos of two π ΅ is
negative twelve-sevenths.
An alternative method here would be to recognize that sin two π ΅ divided by cos two π ΅ is equal to tan of two π ΅. Our expression could therefore be rewritten as tan of two π ΅ divided by two.
We could then have used the fact that the tan of two π is equal to two multiplied by the tan of π divided by one minus tan squared π . Our expression would therefore have simplified to the
tan of π ΅ divided by one minus tan squared π ΅. Substituting negative three-quarters for the tan of π ΅ would once again have given us an answer of negative twelve-sevenths. | {"url":"https://www.nagwa.com/en/videos/742196784106/","timestamp":"2024-11-03T02:51:36Z","content_type":"text/html","content_length":"254200","record_id":"<urn:uuid:194f9816-1d7e-480c-88db-f66d4d7fcb6c>","cc-path":"CC-MAIN-2024-46/segments/1730477027770.74/warc/CC-MAIN-20241103022018-20241103052018-00240.warc.gz"} |
lation. If it
Ans: Given, 2tan−1(c... | Filo
Question asked by Filo student
lation. If it Ans: Given,
Not the question you're searching for?
+ Ask your question
Video solutions (1)
Learn from their 1-to-1 discussion with Filo tutors.
7 mins
Uploaded on: 2/21/2024
Was this solution helpful?
Found 8 tutors discussing this question
Discuss this question LIVE for FREE
6 mins ago
One destination to cover all your homework and assignment needs
Learn Practice Revision Succeed
Instant 1:1 help, 24x7
60, 000+ Expert tutors
Textbook solutions
Big idea maths, McGraw-Hill Education etc
Essay review
Get expert feedback on your essay
Schedule classes
High dosage tutoring from Dedicated 3 experts
Practice more questions on Trigonometry
View more
Students who ask this question also asked
View more
Stuck on the question or explanation?
Connect with our Mathematics tutors online and get step by step solution of this question.
231 students are taking LIVE classes
Question Text lation. If it Ans: Given,
Updated On Feb 21, 2024
Topic Trigonometry
Subject Mathematics
Class Class 12
Answer Type Video solution: 1
Upvotes 134
Avg. Video Duration 7 min | {"url":"https://askfilo.com/user-question-answers-mathematics/lation-if-it-ans-given-37313939383833","timestamp":"2024-11-06T04:38:03Z","content_type":"text/html","content_length":"444589","record_id":"<urn:uuid:1a4ff282-bff8-47f9-adb0-4e3f2ea6f7d2>","cc-path":"CC-MAIN-2024-46/segments/1730477027909.44/warc/CC-MAIN-20241106034659-20241106064659-00734.warc.gz"} |
Section: Research Program
The behavior of the monitored continuous system is assumed to be described by a parametric model $\left\{{𝐏}_{\theta }\phantom{\rule{0.166667em}{0ex}},\phantom{\rule{0.166667em}{0ex}}\theta \in \
Theta \right\}$, where the distribution of the observations (${Z}_{0},...,{Z}_{N}$) is characterized by the parameter vector $\theta \in \Theta$. An estimating function, for example of the form :
${𝒦}_{N}\left(\theta \right)=1/N\phantom{\rule{0.166667em}{0ex}}\sum _{k=0}^{N}K\left(\theta ,{Z}_{k}\right)$
is such that ${𝐄}_{\theta }\left[{𝒦}_{N}\left(\theta \right)\right]=0$ for all $\theta \in \Theta$. In many situations, $𝒦$ is the gradient of a function to be minimized : squared prediction error,
log-likelihood (up to a sign), .... For performing model identification on the basis of observations $\left({Z}_{0},...,{Z}_{N}\right)$, an estimate of the unknown parameter is then [63] :
${\stackrel{^}{\theta }}_{N}=arg\left\{\theta \in \Theta \phantom{\rule{0.166667em}{0ex}}:\phantom{\rule{0.166667em}{0ex}}{𝒦}_{N}\left(\theta \right)=0\right\}\phantom{\rule{4pt}{0ex}}$
In many applications, such an approach must be improved in the following directions : | {"url":"https://radar.inria.fr/report/2014/i4s/uid25.html","timestamp":"2024-11-14T20:28:51Z","content_type":"text/html","content_length":"44051","record_id":"<urn:uuid:2d84535a-4f1d-4c79-98de-9e3c40f055c3>","cc-path":"CC-MAIN-2024-46/segments/1730477395538.95/warc/CC-MAIN-20241114194152-20241114224152-00198.warc.gz"} |
Vertical Elastic Design Spectrum per ASCE 7-16 with ideCAD
How does ideCAD define vertical elastic design spectrum, according to ASCE 7-16?
• Using the coefficients obtained from the map, the vertical elastic spectrum curve is automatically calculated.
• The design vertical response spectral acceleration, S[av], is taken as two-thirds of the value of S[aMv].
S[MS] = The MCE[R] spectral response acceleration parameter at short periods
S[aMv] = The vertical response spectral acceleration
S[av] = The design vertical response spectral acceleration
T[v] = The vertical period of vibration. [s]
C[v] = is defined in terms of S[S] in Table 11.9-1
With the spectral response acceleration parameters obtained from USGS depending on the coordinates, the vertical response spectrum S[aMv] is calculated according to the formula below.
For vertical periods less than or equal to 0.025 s, S[aMv] is determined with Eq. 11.9-1.
For vertical periods T>0.025 s and T≤0.05 s, S[aMv] is determined with Eq. 11.9-2.
For vertical periods T>0.05 s and T≤0.15 s, S[aMv] is determined with Eq. 11.9-3.
For vertical periods T>0.15 s and T≤2.0 s, S[aMv] is determined Eq. 11.9-4.
The vertical coefficient, C[v], is determined according to Table 11.9-1 using straight-line interpolation for intermediate values.
Values of Vertical Coefficient C[v]
S[s] Site Class A, B Site Class C Site Class D, E, F
S[s] ≥ 2.0 0.9 1.3 1.5
S[s] = 1.0 0.9 1.1 1.3
S[s] = 0.6 0.9 1.0 1.1
S[s] = 0.3 0.8 0.8 0.9
S[s] ≤ 0.2 0.7 0.7 0.7
The design vertical response spectral acceleration, S[av], is taken as two-thirds of the value of S[aMv]. | {"url":"https://help.idecad.com/ideCAD/11-9-2-vertical-elastic-design-spectrum","timestamp":"2024-11-05T19:44:58Z","content_type":"text/html","content_length":"83117","record_id":"<urn:uuid:bf83a032-2596-40ec-944e-2c318ce4d24b>","cc-path":"CC-MAIN-2024-46/segments/1730477027889.1/warc/CC-MAIN-20241105180955-20241105210955-00413.warc.gz"} |
William Jevons
William Jevons (1835–1882)
William Stanley Jevons (1835–1882) was an English economist and logician, a major figure, both in Britain and internationally, in the fields of political economy and social reform. Jevons is most
often credited with being the first theorist to make economics a mathematical discipline, and he is regarded as one of the founders of the form of neo-classical economics, that dominates our current
economic thinking and political discourse.
The most interesting for us aspect of his life is the designed in 1869 logical machine for doing logic inference, called Logic Piano, which is the best-known logic machine of the 19^th century.
The work of Devons on Logic Piano was inspired by Stanhope’s Demonstrator. The construction of the device was announced in his 1869 logic textbook, Substitution of Similars. It was the culmination of
a long series of inventions and aids to the calculation of syllogisms: logical alphabet, logical slate, logical stamp, and logical abacus-all tools to write quickly the lines of a truth table in a
logical argument.
The interest of Jevons to Logic as a science began as early as in 1860, when he worked as an assayer at the Sydney Mint, Australia. Jevons wrote in his 1860 diary:
As I awoke in the morning the sun was shining brightly into my room, there was a consciousness on my mind that I was the discoverer of the true logic of the future I felt a delight such as one can
seldom hope to feel. I remembered only too soon though how unworthy and weak an instrument I was for accomplishing so great a work and how hardly I could expect to do it.
The title page of Substitution of Similars of Jevons
Jevons’ serious involvement and subsequent passion for Logic came about when, on his return to England, he met up with his former undergraduate teacher of mathematics, the famous logician Augustus de
Morgan. It seems Jevons was one of the first in Britain to catch on to the importance of the newly developed formal logical systems of Boole and De Morgan.
Jevons read the Mathematical Analysis of Logic and An Investigation of the Laws of Thought of Boole and was fascinated. But he also saw problems with it, and by 1861 he was developing his own system
of logic based on what he eventually called the Substitution of Similars, whereby philosophy would be shown to consist solely in pointing out the likeness in things. In 1863 he published his first
work on the subject, Pure Logic, which was hardly a success, with four copies sold in 6 months. But Jevons was a great one for persistence.
The Logic Piano of William Jevons
In his 1869 logic textbook, The Substitution of Similars Jevons described the Logical Abacus: as a series of wooden boards with various combinations of true and false terms. It was intended that they
be arranged on a rack and a ruler used to remove certain excluded combinations. This was the basic outline of the device that, with the addition of levers and pulleys, Jevons had a Salford clock
maker construct for him in 1869. Fitted within a wooden case, and with a keyboard mounted on the front to operate the substitution mechanism, this was his Logic Piano.
The logic piano (see the nearby image) was a wooden box approximately 90 cm high. A faceplate above the keyboard displayed the entries of the truth table. Just like a piano, the keyboard had
black-and-white keys, but here they were used for entering premises. As the keys were struck, rods would mechanically remove from the face of the piano the truth-table entries inconsistent with the
premises entered on the keys.
The Logic Piano can deal with up to 4 terms. Jevons had in fact wanted to build a machine capable of dealing with up to 16 terms, but it would have been too large and taken up a whole wall in his
office. The logic expressions are typed (or perhaps played) via the keys of the keyboard (see the nearby image), and hitting full stop removes all impossible combinations from the screen. The copula
is the equals key, while the finis key resets the machine.
A truth-table for n proposition requires 2^n entries. The table for n = 4 has 16 entries and is as follows if we represent the truth of a proposition by an upper case letter, and its falsity by the
same letter in lower case:
The truth-table for n=4
PQRS PQRs PQrs PQrs
PqRS PqRs Pqrs Pqrs
pQRS pQRs pQrs pQrs
pqRS pqRs pqrS pqrs
The proposition if P, then Q, is true just in case P is false or Q is true. If this proposition were entered on the keyboard of the logic piano, the face would show:
The truth-table for proposition if P, then Q, is true just in case P is false or Q is true, when n=4
PQRS PQRs PQrs PQrs
(second line is removed)
pQRS pQRs pQrs pQrs
pqRS pqRs pqrS pqrs
As propositions were entered on the keyboard, representing additional premises that must be satisfied simultaneously, other inconsistent entries would disappear from the face.
The action of the logic piano actually did not result in a conclusion stated in the form of a proposition, but only in the truth table entries consistent with the conclusion. Jevons worked
unsuccessfully to resolve this problem, which he termed the inverse problem and which he somewhat misleadingly associated with the process of mathematical induction.
As Jevons’ adversary John Venn noted, the logic piano has no practical purpose, for there are no circumstances in which difficult syllogisms arise or in which syllogisms must be resolved repeatedly
enough to justify mechanization of the process. Jevons countered that it was a convenience to his personal work and useful in his logic classes. | {"url":"http://www.computer-timeline.com/timeline/william-jevons/","timestamp":"2024-11-13T03:08:31Z","content_type":"text/html","content_length":"78328","record_id":"<urn:uuid:75c482ca-d87b-4cfa-a543-e219a45c531c>","cc-path":"CC-MAIN-2024-46/segments/1730477028303.91/warc/CC-MAIN-20241113004258-20241113034258-00443.warc.gz"} |
What is the benefit of studying computer science?
The most important aspect of computer science is problem solving, an essential skill for life. Students study the design, development and analysis of software and hardware used to solve problems in a
variety of business, scientific and social contexts.
What is Mathematics for computer science?
Discrete Mathematics is the Foundation of Computer Science While Boolean Algebra is used in Logic Gates, Relational Algebra is used in Databases. In case you need another example, Number Theory has
multiple applications in Cryptography and Cryptanalysis.
Why is math important to computer science?
The math courses play a critical role in helping students understand programming languages, data structures, differential equations, and more. Calculus is often used in computer graphics, scientific
computing, and computer security.
Can I major in computer science if I’m bad at math?
You can be bad at it at first, but make sure you become good at it after taking your classes. It’s worth noting that math changes a lot from pre-calculus to calculus and beyond. It’s less about rote
formulas and more about solving puzzles. You can get D’s in all your math classes and still graduate with a CS degree.
Is computer useful or useless?
Some advantages are: A computer can store and retrieve vast amounts of data, say a petabyte. It would take a vast paper archive and lots of time to search for information. At least 90 % of all things
that computers are used for, are neither useful nor efficient.
How maths is used in computer science?
Algebra is used in computer science in the development of algorithms and software for working with mathematical objects. It is also used to design formulas that are used in numerical programs and for
complete scientific computations.
What is the highest paid field in computer science?
Highest Paying Computer Science Jobs
• Big Data Engineer. As per our research, the highest paying computer science jobs this year will be rewarded to the Big Data Engineers.
• Data Scientist.
• Information Systems Security Manager.
• Data Architect.
• Data Security Analyst.
• Applications Architect.
• Data Manager.
• Software Engineer.
What is the relationship between math and programming?
Mathematical representations are part of the mathematical ability. The relationship with programming ability is that the mathematical representation is as a bridge that represents the ideas or
languages used in making computer programs. | {"url":"https://cowetaamerican.com/2021/12/19/what-is-the-benefit-of-studying-computer-science/","timestamp":"2024-11-13T04:30:35Z","content_type":"text/html","content_length":"58790","record_id":"<urn:uuid:1d7fd72c-f69b-4fd6-aa1c-433219db76ca>","cc-path":"CC-MAIN-2024-46/segments/1730477028326.66/warc/CC-MAIN-20241113040054-20241113070054-00057.warc.gz"} |
It is shown that the solutions of inviscid hydrodynamical equations with suppression of all spatial Fourier modes having wavenumbers in excess of a threshold $\kg$ exhibit unexpected features. The
study is carried out for both the one-dimensional Burgers equation and the two-dimensional incompressible Euler equation. At large $\kg$, for smooth initial conditions, the first symptom of
truncation, a localized short-wavelength oscillation which we call a “tyger”, is caused by a resonant interaction between fluid particle motion and truncation waves generated by small-scale features
(shocks, layers with strong vorticity gradients, etc). These tygers appear when complex-space singularities come within one Galerkin wavelength $\lambdag = 2\pi/\kg$ from the real domain and
typically arise far away from preexisting small-scale structures at locations whose velocities match that of such structures. Tygers are weak and strongly localized at first - in the Burgers case at
the time of appearance of the first shock their amplitudes and widths are proportional to $\kg ^{-2/3}$ and $\kg ^{-1/3}$ respectively - but grow and eventually invade the whole flow. They are thus
the first manifestations of the thermalization predicted by T.D. Lee in 1952. The sudden dissipative anomaly-the presence of a finite dissipation in the limit of vanishing viscosity after a finite
time $\ts$-, which is well known for the Burgers equation and sometimes conjectured for the 3D Euler equation, has as counterpart in the truncated case the ability of tygers to store a finite amount
of energy in the limit $\kg\to\infty$. This leads to Reynolds stresses acting on scales larger than the Galerkin wavelength and thus prevents the flow from converging to the inviscid-limit solution.
There are indications that it may be possible to purge the tygers and thereby to recover the correct inviscid-limit behaviour. | {"url":"https://math.iisc.ac.in/seminars/2010/2010-12-24-prof-uriel-frisch-observatoire-de-la-cote-dazur-nice.html","timestamp":"2024-11-06T08:10:27Z","content_type":"text/html","content_length":"24112","record_id":"<urn:uuid:bca2a469-6817-433c-be11-091974e38567>","cc-path":"CC-MAIN-2024-46/segments/1730477027910.12/warc/CC-MAIN-20241106065928-20241106095928-00085.warc.gz"} |
finance data bank
Question # 00005294 Posted By: Updated on: 12/13/2013 02:15 PM Due on: 12/15/2013
75. Theo's Bar & Grill needs $147,000 a week to pay bills. The standard deviation of the weekly disbursements is $9,600. The firm has established a lower cash balance limit of $40,000. The applicable
interest rate is 3.5 percent and the fixed cost of transferring funds is $45. Based on the BAT model, what is the optimal average cash balance?
A. $36,199
B. $49,568
C. $70,100
D. $99,136
E. $112,400
76. Parkway Express needs $318,000 a week to pay bills. The standard deviation of the weekly disbursements is $31,000. The firm has established a lower cash balance limit of $60,000. The applicable
interest rate is 4.5 percent and the fixed cost of transferring funds is $65. Based on the BAT model, what is the opportunity cost of holding cash?
A. $3,873
B. $4,918
C. $5,207
D. $109,283
E. $110,440
77. Penco Supply spends $428,000 a week to pay bills and maintains a lower cash balance limit of $75,000. The standard deviation of its disbursements is $18,900. The applicable interest rate is 5
percent and the fixed cost of transferring funds is $65. What is the firm's optimal initial cash balance based on the BAT model?
A. $150,600
B. $158,929
C. $170,096
D. $221,506
E. $240,553
78. Your firm spends $54,000 a week to pay bills and maintains a lower cash balance limit of $45,000. The standard deviation of your disbursements is $12,100. The applicable interest rate is 4.5
percent and the fixed cost of transferring funds is $55. What is your opportunity cost of holding cash based on the BAT model?
A. $1,318
B. $1,864
C. $2,204
D. $2,311
E. $3,709
79. Rosie O'Grady's spends $98,000 a week to pay bills and maintains a lower cash balance limit of $95,000. The standard deviation of the disbursements is $14,600. The applicable interest rate is 4.8
percent and the fixed cost of transferring funds is $50. What is this firm's total cost of holding cash based on the BAT model?
A. $1,431
B. $2,862
C. $3,034
D. $4,912
E. $4,946
80. Your firm spends $346,000 a week to pay bills and maintains a lower cash balance limit of $150,000. The standard deviation of your disbursements is $28,700. The applicable interest rate is 5
percent and the fixed cost of transferring funds is $60. What is your optimal average cash balance based on the BAT model?
A. $103,900
B. $146,500
C. $182,200
D. $207,800
E. $249,900
81. The Cow Pie Spreader Co. spends $214,000 a week to pay bills and maintains a lower cash balance limit of $175,000. The standard deviation of the disbursements is $16,000. The applicable weekly
interest rate is 0.025 percent and the fixed cost of transferring funds is $49. What is the firm's cash balance target based on the Miller-Orr model?
A. $208,511
B. $247,560
C. $251,006
D. $254,545
E. $258,878
82. The Blue Moon Hotel and Spa spends $359,000 a week to pay bills and maintains a lower cash balance limit of $250,000. The standard deviation of the disbursements is $46,800. The applicable weekly
interest rate is 0.045 percent and the fixed cost of transferring funds is $60. What is the hotel's optimal upper cash limit based on the Miller-Orr model?
A. $430,836
B. $447,905
C. $528,700
D. $739,459
E. $861,672
83. Donaldson, Inc. spends $94,000 a week to pay bills and maintains a lower cash balance limit of $50,000. The standard deviation of the disbursements is $13,000. The applicable weekly interest rate
is 0.045 percent and the fixed cost of transferring funds is $52. What is your optimal average cash balance based on the Miller-Orr model?
A. $78,778
B. $82,623
C. $231,969
D. $236,334
E. $247,868
84. The Burger Stop spends $52,000 a week to pay bills and maintains a lower cash balance limit of $60,000. The standard deviation of the disbursements is $7,500. The applicable weekly interest rate
is 0.04 percent and the fixed cost of transferring funds is $50. What is your optimal average cash balance based on the Miller-Orr model?
A. $79,116
B. $83,208
C. $110,315
D. $237,348
E. $249,624
85. Your firm spends $48,000 a week to pay bills and maintains a lower cash balance limit of $50,000. The standard deviation of the disbursements is $8,600. The applicable weekly interest rate is
0.054 percent and the fixed cost of transferring funds is $65. What is your cash balance target based on the Miller-Orr model?
A. $48,156
B. $49,990
C. $54,884
D. $68,830
E. $75,726
86. Travel Inn Express spends $109,000 a week to pay bills and maintains a lower cash balance limit of $125,000. The standard deviation of the disbursements is $14,400. The applicable weekly interest
rate is 0.039 percent and the fixed cost of transferring funds is $58. What is the inn's cash balance target based on the Miller-Orr model?
A. $28,492
B. $31,359
C. $153,492
D. $156,359
E. $225,417
Essay Questions
87. Explain how a lockbox system operates and why a firm might consider implementing such a system.
88. Explain how the Check Clearing Act for the 21^st Century affects both collection and disbursement float.
89. Explain how the unethical use of uncollected funds has been impacted by the growth of on-line retailing and banking.
90. Float management systems may provide only minimal benefits to a firm. Given that most firms have other projects with higher positive net present values, why should a firm's managers spend time
implementing a float management system?
91. Explain what a zero-balance account is, how it is used, and how it affects cash management.
Multiple Choice Questions
92. Each business day, on average, a company writes checks totaling $26,000 to pay its suppliers. The usual clearing time for the checks is 5 days. Meanwhile, the company is receiving payments from
its customers each day, in the form of checks, totaling $40,000. The cash from the payments is available to the firm after 2 days. What is the amount of the firm's average net float?
A. $30,00
B. $50,000
C. $80,000
D. $110,000
E. $130,000
93. Purple Feet Wine, Inc. receives an average of $6,000 in checks per day. The delay in clearing is typically 3 days. The current interest rate is 0.025 percent per day. Assume 30 days per month.
What is the highest daily fee the company should be willing to pay to eliminate its float entirely?
A. $1.50
B. $3.00
C. $3.75
D. $4.50
E. $6.00
94. Your neighbor goes to the post office once a month and picks up two checks, one for $18,000 and one for $4,000. The larger check takes 4 days to clear after it is deposited; the smaller one takes
6 days. Assume 30 days per month. What is the weighted average delay?
A. 4.21 days
B. 4.36 days
C. 4.78 days
D. 5.00 days
E. 6.00 days
95. Your firm has an average receipt size of $60. A bank has approached you concerning a lockbox service that will decrease your total collection time by 1 day. You typically receive 28,000 checks
per day. The daily interest rate is 0.016 percent. What is the NPV of the lockbox project if the bank charges a fee of $210 per day?
A. $367,500
B. $427,500
C. $903,350
D. $1,412,500
E. $1,680,000
96. A mail-order firm processes 5,000 checks per month. Of these, 55 percent are for $55 and 45 percent are for $65. The $55 checks are delayed 2 days on average; the $65 checks are delayed 5 days on
average. Assume each month has 30 days. The interest rate is 6 percent per year. How much should the firm be willing to pay to reduce the weighted average float by 1.4 days?
A. $4,165
B. $13,883
C. $41,650
D. $138,883
E. $416,500
97. Paper Submarine Manufacturing is investigating a lockbox system to reduce its collection time. It has determined the following:
The total collection time will be reduced by 2 days if the lockbox system is adopted. What is the NPV of adopting the lockbox system?
A. $600,000
B. $775,000
C. $975,000
D. $1,200,000
E. $1,425,000
98. Home Roasted Turkeys disburses checks every 4 weeks that average $70,000 and take 5 days to clear. How much interest can the company earn if it delays transfer of funds from an interest-bearing
account that pays 0.02 percent per day for these 5 days? Ignore the effects of compound interest. Assume 52 weeks in a year.
A. $36
B. $91
C. $182
D. $364
E. $910
99. Never Again Enterprises has an agreement with The Worth Bank whereby the bank handles $3.12 million in collections a day and requires a $1,000,000 compensating balance. Never Again is
contemplating canceling the agreement and dividing its eastern region so that two other banks will handle its business. Banks A and B will each handle $1.56 million of collections a day, and each
requires a compensating balance of $1,550,000. Never Again's financial management expects that collections will be accelerated by one day if the eastern region is divided. The T-bill rate is 5
percent annually. What is the amount of the annual net savings if this plan is adopted?
A. $10,200
B. $51,000
C. $76,500
D. $102,000
E. $125,000
100. Mountaintop Inns, a Kentucky company, has determined that a majority of its customers are located in the Pennsylvania area. It therefore is considering using a lockbox system offered by a bank
located in Pittsburgh, Pennsylvania. The bank has estimated that use of the system will reduce collection time by one day. In addition to the variable charge shown below, there is also a fixed charge
of $4,320 per year for the lockbox system. Assume a year has 365 days. What is the NPV of the lockbox system given the following information?
A. -$156,727
B. -$131,301
C. -$74,208
D. $11,507
E. $26,433
101. Cow Chips, Inc., a large fertilizer distributor based in California, is planning to use a lockbox system to speed up collections from its customers located on the East Coast. A Philadelphia-area
bank will provide this service for an annual fee of $25,000 plus 10 cents per transaction. The estimated reduction in collection and processing time is one day. The average customer payment in this
region is $8,200. Treasury bills are currently yielding 5 percent per year. Assume a year has 365 days. Approximately how many customers each day, on average, are needed to make the system profitable
for Cow Chips, Inc.?
A. 56
B. 67
C. 74
D. 83
E. 89
Tutorials for this Question
Tutorial # 00005116 Posted By: Posted on: 12/13/2013 10:37 PM
Puchased By: 2
disappears. Reducing float limits the ability of a firm to ...
Great! We have found the solution of this question! | {"url":"https://www.homeworkminutes.com/q/finance-data-bank-5294/","timestamp":"2024-11-02T12:02:25Z","content_type":"text/html","content_length":"57143","record_id":"<urn:uuid:59f35711-58e7-439a-927b-605145392dae>","cc-path":"CC-MAIN-2024-46/segments/1730477027710.33/warc/CC-MAIN-20241102102832-20241102132832-00860.warc.gz"} |
Operator Theory/Operator Algebras and Applications: Part 2search
Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
Please make all selections above before adding to cart
Operator Theory/Operator Algebras and Applications: Part 2
eBook ISBN: 978-0-8218-9430-9
Product Code: PSPUM/51.2.E
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
Click above image for expanded view
Operator Theory/Operator Algebras and Applications: Part 2
eBook ISBN: 978-0-8218-9430-9
Product Code: PSPUM/51.2.E
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
• Proceedings of Symposia in Pure Mathematics
Volume: 51; 1990; 385 pp
MSC: Primary 47; Secondary 00; 46
Operator theory has come of age during the last twenty years. The subject has developed in several directions using new and powerful methods that have led to the solution of basic problems
previously thought to be inaccessible. In addition, operator theory has had fundamental connections with a range of other mathematical topics. For example, operator theory has made mutually
enriching contacts with other areas of mathematics, such as algebraic topology and index theory, complex analysis, and probability theory. The algebraic methods employed in operator theory are
diverse and touch upon a broad area of mathematics. There have been direct applications of operator theory to systems theory and statistical mechanics. And significant problems and motivations
have arisen from the subject's traditional underpinnings for partial differential equations.
This two-volume set contains the proceedings of an AMS Summer Institute on Operator Theory/Operator Algebras, held in July 1988 at the University of New Hampshire. The Institute sought to
summarize progress and examine the common points of view that now run through the subject. With contributions from some of the top experts in the field, this publication illuminates a broad range
of current research topics in operator theory.
This item is also available as part of a set:
• Permission – for use of book, eBook, or Journal content
• Book Details
• Table of Contents
• Requests
Volume: 51; 1990; 385 pp
MSC: Primary 47; Secondary 00; 46
Operator theory has come of age during the last twenty years. The subject has developed in several directions using new and powerful methods that have led to the solution of basic problems previously
thought to be inaccessible. In addition, operator theory has had fundamental connections with a range of other mathematical topics. For example, operator theory has made mutually enriching contacts
with other areas of mathematics, such as algebraic topology and index theory, complex analysis, and probability theory. The algebraic methods employed in operator theory are diverse and touch upon a
broad area of mathematics. There have been direct applications of operator theory to systems theory and statistical mechanics. And significant problems and motivations have arisen from the subject's
traditional underpinnings for partial differential equations.
This two-volume set contains the proceedings of an AMS Summer Institute on Operator Theory/Operator Algebras, held in July 1988 at the University of New Hampshire. The Institute sought to summarize
progress and examine the common points of view that now run through the subject. With contributions from some of the top experts in the field, this publication illuminates a broad range of current
research topics in operator theory.
This item is also available as part of a set:
Permission – for use of book, eBook, or Journal content
Please select which format for which you are requesting permissions. | {"url":"https://bookstore.ams.org/view?ProductCode=PSPUM/51.2","timestamp":"2024-11-10T18:24:23Z","content_type":"text/html","content_length":"119357","record_id":"<urn:uuid:247a4a50-4aae-4459-9dec-8a8883f4cac8>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.61/warc/CC-MAIN-20241110170046-20241110200046-00677.warc.gz"} |
Windowed Radon transform frames
Two windowed Radon transform (WRT) frame formulations for the decomposition of band limited functions f (x) ∈ L^2 (R^ℓ), ℓ = 2, 3, are presented. The "basic" formulation consists of two dual frame
sets of shifted and rotated windows, one is used to synthesize f and the other to calculate the expansion coefficients as projections of f onto this set. The latter operation is a WRT that samples f
at the discrete phase-space lattice of locations and directions. Explicit expressions are derived for a class of isodiffracting (ID) windows, which are matched to the lattice to yield snug frames.
The basic formulation is then generalized to multiscales-WRT frames, where the large scales elements are associated with wider windows and sparser (rotation-direction) phase-space lattices that are
decimated subsets of the lattice at the smallest scale. The analysis is presented for 3D, with a summary of the modifications for 2D. Finally, we discuss applications to time-dependent wave theory,
whereby the source distribution is expanded using a WRT frame. The WRT extracts the local radiation properties of the source, thus describing the radiated field as a sum of collimated isodiffracting
pulsed beams (ID-PB) that emerge from the source along the preferred radiation directions.
• Frame theory
• Multiscale analysis
• Pulsed-beams
• Wave-theory
• Windowed Fourier transform frames
• Windowed Radon transform frames
ASJC Scopus subject areas
Dive into the research topics of 'Windowed Radon transform frames'. Together they form a unique fingerprint. | {"url":"https://cris.bgu.ac.il/en/publications/windowed-radon-transform-frames","timestamp":"2024-11-03T10:06:06Z","content_type":"text/html","content_length":"58513","record_id":"<urn:uuid:af43a9b0-7d17-4805-a991-5e93edd3aa8a>","cc-path":"CC-MAIN-2024-46/segments/1730477027774.6/warc/CC-MAIN-20241103083929-20241103113929-00697.warc.gz"} |
How to Find the Volume and Surface Area of a Triangular Prism?
In this step-by-step guide, you learn how to use formulas to find the volume and surface area of a triangular prism.
The prism is a solid shape with flat faces, two identical bases, and the same cross-section along its entire length. The name of a particular prism depends on the two bases of the prism, which can be
triangular, rectangular, or polygonal.
Related Topics
A step-by-step guide to finding the volume and surface area of triangular prism
A triangular prism is a three-dimensional polyhedron with three rectangular faces and two triangular faces. The \(2\) triangular faces are congruent to each other, and the \(3\) lateral faces which
are in the shape of rectangles are also congruent to each other. Thus, a triangular prism has \(5\) faces, \(9\) edges, and \(6\) vertices.
See the image below of a triangular prism where \(l\) represents the length of the prism, \(h\) represents the height of the base triangle, and \(b\) represents the bottom edge of the base triangle.
Triangular prism properties
The properties of a triangular prism help us to easily identify it. The following are some features of a triangular prism:
• A triangular prism has \(5\) faces, \(9\) edges, and \(6\) vertices.
• It is a polyhedron with \(3\) rectangular faces and \(2\) triangular faces.
• The two triangular bases are congruent with each other.
• Any cross-section of a triangular prism is in the shape of a triangle.
Triangular prism formulas
There are two important formulas for a triangular prism, which are surface area and volume.
The volume of a triangular prism
The volume of a triangular prism is the product of its triangular base area and the length of the prism. As we already know that the base of a triangular prism is in the shape of a triangle. So,
• \(b\) is the base length of the triangle,
• \(h\) is the height of the triangle,
• \(l\) is the length of the prism.
The surface area of a triangular prism
The surface area of a triangular prism is the area occupied by the surface. It is the sum of the areas of all the faces of the prism. Therefore, the formula to calculate the surface area is:
• \(b\) is the lower edge of the base triangle,
• \(h\) is the height of the base triangle,
• \(L\) is the length of the prism,
• \(S_1, S_2,\) and \(S_3\) are the three edges (sides) of the base triangle,
• \((bh)\) is the combined area of the two triangular faces because \(\left[2\:×\:\left(\frac{1}{2}\:×\:bh\right)\right]\:=\:bh\).
The lateral surface area of the triangular prism
The lateral surface area of any solid is the area without the bases. In other words, the lateral surface area of a triangular prism is calculated without considering the base area. Thus, the lateral
surface area of a triangular prism is:
\(\color{blue}{Lateral\:surface\:area =\:\left(S_1\:+\:S_2\:+\:S_3\right)\:×\:l\:=\:\left(Perimeter\:×\:Length\right)\:or\:LSA=\:p\:×\:l}\)
• \(l\) is the height (length) of a prism
• \(p\) is the perimeter of the base
Finding the Volume and Surface Area of Triangular Prism – Example 1:
Find the volume of a triangular prism where the base of the triangle is \(8\:??\:\), its height is \(6\:??\:\), and the length of the prism is \(10\:??\:\).
The base of the triangle is \((b) = 8\space in\), and the height of the triangular base \((h) = 6\space in\).
So, the base area \(= (\frac{1}{2})(bh) = (\frac{1}{2}) × (8 × 6) = \frac{48}{2}=24\space in^2\).
The length of the prism is \(L = 10\space in\).
Using the volume of the triangular prism formula,
The volume of the given triangular prism \(=base\:area\:×\:length\:of\:the\:prism = 24 × (10) = 240\space in^3\).
Exercises for Finding the Volume and Surface Area of Triangular Prism
Find the volume and surface area for each triangular prism.
1. \(\color{blue}{V=43.2\:yd^3, A=93.6\:yd^2}\)
2. \(\color{blue}{V=16.5\:yd^3, A=49\:yd^2}\)
3. \(\color{blue}{V=134.3\:m^3, A=184.7\:m^2}\)
Related to This Article
What people say about "How to Find the Volume and Surface Area of a Triangular Prism? - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet. | {"url":"https://www.effortlessmath.com/math-topics/volume-and-surface-area-of-triangular-prism/","timestamp":"2024-11-07T05:43:09Z","content_type":"text/html","content_length":"84059","record_id":"<urn:uuid:2318517d-c0a7-4ba0-8b1c-8911e49c1ad9>","cc-path":"CC-MAIN-2024-46/segments/1730477027957.23/warc/CC-MAIN-20241107052447-20241107082447-00147.warc.gz"} |
Technology Foundations - What is a Computer?
Lesson 2: Technology Foundations - What is a Computer?
In this lesson students develop a preliminary definition of a computer. To begin the lesson, the class will brainstorm possible definitions for a computer and place the results of this brainstorm on
the board. Next, students will work in groups to sort pictures into “is a computer” or “is not a computer” on poster paper. Groups will place their posters around the room and briefly explain their
motivations for choosing some of their most difficult categorizations. The teacher will then introduce a definition of the computer and allow students to revise their posters according to the new
In this lesson, students will consider different types of computers and that these computers input, store, process, and output information as part of the problem solving process. Upcoming lessons
will dive much deeper into what an information problem looks like and how computers solve these problems.
Warm Up (5 min)
Activity (30 min)
Wrap Up (15 min)
Students will be able to:
• Identify a computer as a machine that processes information
• Provide a high level description of the different parts of the Input - Output - Store - Process model of a computer
For each group
• Print out copies of What is a Computer - Activity Guide. Note there are two sets of pictures in the document but each group only needs a single set.
• Scissors (if you will not have time to cut the pictures prior to class)
• Poster paper
• Markers or colored pencils
• Glue or tape to attach pictures
Heads Up! Please make a copy of any documents you plan to share with students.
For the Teacher
For the Students
• Computer - A device that takes input, stores and processes information, and outputs information
Teaching Guide
Warm Up (5 min)
What Problems Do Computers Help You Solve?
Prompt: In the modern day we use computers almost constantly. What kinds of problems do computers help you solve? How do they help you do this?
Discussion Goal
Goal: This warm up makes the transition from thinking about problem solving in a generic sense to thinking about how computers help solve certain kinds of problems. While the lesson will eventually
reveal that computers are particularly useful at solving information problems, you don't need to make that point during this brainstorm.
Discuss: Run this conversation as a brainstorm, recording ideas on the board. Note and call out similarities you're seeing the kinds of problems students identified.
Computers are clearly an important part of our lives and help us solve all kinds of problems. I want to think more about the kinds of problems computers help us solve, but first I want to ask an
important question. What is a computer?
Activity (30 min)
Computer or Not?
Group: Place students in groups of 3 or 4
Teaching Tip
Modifications from the Forum: Many teachers have shared ideas for modifying this lesson on the forum (link). Head there to check out ways teachers have reduced printables, integrated technology, or
otherwise adapted this activity to fit the needs of their class. If you do something new, share your ideas too!
Distribute: Activity Guide What is a Computer - Activity Guide as well as scissors, markers / colored pencils, poster paper, and glue / tape for making posters.
Give students the following directions:
• Draw a line down the middle of your poster, label one side "Computer" and the other "Not a Computer"
• Discuss as a group which of the objects in your set (from the activity guide) belong in each category
• Once your group is in agreement tape your objects to the appropriate side
• Develop a list of characteristics your groups used to determine whether an object is a computer
Teaching Tip
Tape First: Students will have an opportunity to update their categorizations later in the lesson. For now they should just tape their objects to their poster or even just place them on the correct
Circulate: Circle the room as students work to categorize the different images on the activity guide. Encourage groups to talk openly about their ideas and explain why they do or don't think an
object should be categorized as a computer. For groups that can’t decide on a categorization, ask members to defend their points of view, and take a majority vote. Assure groups that it is ok if one
or two people disagree.
At the end of the time bring the class back together and ask them to place their posters at the front of the room.
Present Your Categorizations
Teaching Tip
Comparing Categorizations: There are two different sets of objects in the activity guide. The first page of each set is identical while the second pages are different. This will mean all students
will see some objects that they categorized already and some that are new. Use this to help drive conversation.
Share: Have each group briefly present their posters, focusing their discussion on the following points
1. What rules or definition did you use to categorize your objects?
2. Which item was most difficult for you to categorize? How did you eventually make the decision of where to place it?
Invite the audience to respectfully question any categorizations if they disagree with the presenting group's decisions.
As you can see, it's not always clear whether something is a computer, and even experts sometimes have different points of view. Let's have a look, however, at a definition that we'll use throughout
this course.
Display: Show What Makes a Computer, a Computer? - Video. This video is also available to students on the Code.org website, including an alternative link for schools where YouTube is blocked. The
video presents a computer as a machine that helps with certain kinds of thinking work by processing information. It formally introduces a model of a computer as a machine that inputs, outputs,
stores, and processes information.
Discussion Goal
Again, it's not necessary for everyone to agree on every item on the list. It's more important that the students use discussion of the items to deepen their understanding of what a computer is. It
may be impossible to tell from the picture alone whether or not an item is a computer. Reassure the class that even experts often disagree about what exactly is or is not a computer, and that their
understanding will continue to grow as the class continues.
Allow students to revise their posters using the definition they have just learned.
Discuss: Did any groups change their minds about whether something was a computer? What about the definition convinced you?
Wrap Up (15 min)
Teaching Tip
Identifying Information Problems: Students are still developing an understanding of what information is or what an information problem that a computer could help solve looks like.
Prompt: Today you've had a chance to look at a definition of a computer that focuses on how the computer solves problems. We've also seen many different types of computers. Think of a problem that a
computer can help you to solve.
• What is the problem?
• What information is input to the computer?
• What information does the computer store?
• What information does the computer process?
• What information does the computer output?
Career Discussion
Introduce yourself and your career:
• What do you work, what do you do, and what do you love most about your job?
• What or who inspired you?
• How did you get interested in computer science?
• Did you have a mentor?
• Share a story about how tech affects everyone
Ask the students questions and leave time for Q&A.
• What jobs are they interested in, what are their favorite tech gadgets or apps, and how do they think they are built?
• Do the students have any questions for you? | {"url":"https://curriculum.code.org/pwc/ayp/2/","timestamp":"2024-11-11T11:17:20Z","content_type":"text/html","content_length":"41792","record_id":"<urn:uuid:bc3a42b5-f558-4398-a7aa-4636e67c9d77>","cc-path":"CC-MAIN-2024-46/segments/1730477028228.41/warc/CC-MAIN-20241111091854-20241111121854-00776.warc.gz"} |
Chemical Potential and Significance
What is chemical potential? Write its physical significance.
Chemical Potential
Chemical potential (μ) is a thermodynamic quantity that represents the change in the Gibbs free energy of a system when some amount of substance is added or removed at constant temperature and
chemical potential (μ) of a component in a system is defined mathematically as the partial derivative of the Gibbs free energy (G) with respect to the number of particles (N) at constant temperature
(T) and pressure (P).
μ = (δG/δN)[T,P]
We know that, Free energy function-
F = H − TS
or, F = E + PV − TS (As H = E + PV)
or, dF = dE + PdV + VdP − TdS − SdT
or, dF = VdP − SdT (As dq = dE + PdV = TdS)
At constant T-
(dF)[T] = VdP = RT(dP/P) (As PV = RT for one mole)
On integrating the above equation we get-
∫dF = RT∫dP/P
or, F = F^o + RT lnP ----- Equation:1
From Raoult's law-
∆P/P^o = X
and X ∝ C ∝ a Hence, Equation:1 becomes-
F = F^o + RT lna
μ = μ^o + RT lna
μ is called free energy per mole or chemical potential. μ^o is called standard free energy per mole. Th μ^o is constant at a constant temperature.
Significance of Chemical Potential
At equilibrium, the chemical potential of each component in a system must be equal, otherwise the system will not be in a stable state.
A process will occur spontaneously if it decreases the Gibbs free energy of the system, which corresponds to a decrease in the chemical potential of the reacting species.
Chemical potential of a substance is different in different phases (solid, liquid, gas). At the phase transition point, the chemical potentials of the two phases must be equal.
In electrochemical systems, the chemical potential is combined with the electrical potential to give the electrochemical potential, which determines the driving force for ion transport and redox
Chemical equilibrium constants can be expressed in terms of the standard state chemical potentials of the reactants and products, allowing the prediction of the composition at equilibrium.
Clausius-Clapeyron Relation can be derived using the concept of chemical potential.
University Questions
What is chemical potentia?
What is chemical potentia? Write the equation for chemical potential at constnt T and P.
Discuss the physical significance of chemical potential. | {"url":"https://www.chemstdy.com/p/chemical-potential-and-significance.html","timestamp":"2024-11-09T00:59:17Z","content_type":"application/xhtml+xml","content_length":"185845","record_id":"<urn:uuid:483dd6e4-96a9-408f-a787-31349b633d17>","cc-path":"CC-MAIN-2024-46/segments/1730477028106.80/warc/CC-MAIN-20241108231327-20241109021327-00547.warc.gz"} |
Calculator complex numbers recommend
calculator complex numbers recommend Related topics: simplifying equations calculator
Decimal To A Mixed Number
algebra help videos
printable worksheets commutative property
9th Grade Algebra Worksheets
intermediate algebra,15
number theory and cryptography
networking midterm exam
Author Message
icanmer Posted: Saturday 20th of May 13:24
1. Hello Everyone Can someone out there assist me? My algebra teacher gave us calculator complex numbers recommend assignment today. Normally I am good at function range but
somehow I am just stuck on this one problem. I have to turn it in by this weekend but it looks like I will not be able to complete it in time. So I thought of coming online to
find assistance. I will really be grateful if someone can help me work this (topicKwds) out in time.
From: At my
computer! Where else
would I be?
Back to top
oc_rana Posted: Sunday 21st of May 14:22
You might want to take a look at Algebrator. I bought it some time back to help me with my Basic Math course and I can say that it was a good choice . There are so many demos
given which you can browse through. You can also try out the questions related to evaluating formulas and binomials by just typing them in. Algebrator provides detailed
description to the problems which helps to make difficult concepts very clear. I would say that this program is absolutely the best that money can buy.
Back to top
Jot Posted: Monday 22nd of May 12:09
I myself have been using this program since a year now, and it has never let me down. It won’t just solve a problem for you, but it’ll also explain every step that was taken to
arrive at a particular answer. And that’s the best feature in my opinion. I was having a lot of problems tackling questions based on calculator complex numbers recommend but ever
since I bought this software, math has been really easy for me.
From: Ubik
Back to top
HiMiTHAAUC Posted: Tuesday 23rd of May 21:49
Cool! I wish to know more about this program’s features and how much it costs. Where can I get the info?
Back to top
Troigonis Posted: Thursday 25th of May 07:24
Try to look for it here : https://softmath.com/about-algebra-help.html. Give it a go because Algebrator has a unlimited money back deal , Good luck!
From: Kvlt of Ø
Back to top
Dxi_Sysdech Posted: Thursday 25th of May 11:39
Algebrator is the program that I have used through several algebra classes - Basic Math, Algebra 2 and College Algebra. It is a truly a great piece of math software. I remember
of going through problems with subtracting fractions, difference of cubes and least common denominator. I would simply type in a problem homework, click on Solve – and step by
step solution to my algebra homework. I highly recommend the program.
From: Right here,
can't you see me?
Back to top | {"url":"https://softmath.com/algebra-software/point-slope/calculator-complex-numbers.html","timestamp":"2024-11-07T19:08:05Z","content_type":"text/html","content_length":"42844","record_id":"<urn:uuid:ac76e265-2790-4bde-80ce-ab57d5c6d477>","cc-path":"CC-MAIN-2024-46/segments/1730477028009.81/warc/CC-MAIN-20241107181317-20241107211317-00401.warc.gz"} |
A researcher wishes to estimate, with 99% confidence, the
population proportion of adults who think the...
A researcher wishes to estimate, with 99% confidence, the population proportion of adults who think the...
A researcher wishes to estimate, with 99% confidence, the population proportion of adults who think the president of their country can control the price of gasoline. Her estimate must be accurate
within 5% of the true proportion.
a) What is the minimum sample size needed assuming that no prior information is available? (round to nearest whole #)
b) What is the minimum sample size needed using a prior study that found that 32% of the respondents said they think their president can control the price of gasoline? (round to nearest whole #)
c) How do the results from (a) and (b) compare?
-Having an estimate of the population proportion has no effect on the minimum sample size needed.
-Having an estimate of the population proportion raises the minimum sample size needed
-Having an estimate of the population proportion reduces the minimum sample size needed
Using z distribution table, z critical value corresponding to 99% confidence interval is 2.58
(A) No prior estimation is given
margin of error = 5% = 5/100 = 0.05
Formula for sample size
Rounding to nearest whole number, we get sample size n = 666
(B) proportion
margin of error = 5% = 5/100 = 0.05
Formula for sample size
Rounding to nearest whole number, we get sample size n = 579
(C) It is clear that the sample size is reduced when we have prior estimation of proportion, i.e. 579.
Therefore, we can say that sample size needed is more for no prior estimation calculation
option C is correct. | {"url":"https://justaaa.com/statistics-and-probability/105888-a-researcher-wishes-to-estimate-with-99","timestamp":"2024-11-02T18:05:49Z","content_type":"text/html","content_length":"45985","record_id":"<urn:uuid:1216d448-5b17-492e-8ccc-cc936899e2ce>","cc-path":"CC-MAIN-2024-46/segments/1730477027729.26/warc/CC-MAIN-20241102165015-20241102195015-00441.warc.gz"} |
What Does the ACT Math Test Measure? - TestBright
Questions on both sections are mostly multiple choice, but some Student-Produced Response questions or “grid-ins” require test takers to bubble in specific answers rather than select a given answer
SAT Math questions evaluate quantitative fluency, conceptual understanding, problem solving, and calculation ability through multiple-choice questions with five answer choices each, a departure from
every other multiple-choice section of the ACT or SAT. ACT Math Reporting Categories detail what students are tested on in this section:
Of the 60 questions on the ACT Math test, roughly 36 (57-60%) of them are Preparing for Higher Math questions evaluating what is considered high school math, from when students learn to use algebra
as a general way of expressing and solving equations to advanced topics in geometry, statistics, algebra 2, and trigonometry
Integrating Essential Skills questions make up the remaining 24 or so (40-43%) ACT Math questions, evaluating concepts typically learned before 8th grade such as rates and percentages; proportional
relationships; area, surface area, and volume; average and median; and expressing numbers in different ways.
The Modeling category does not introduce additional questions, but instead quantifies achievement on word problems that involve producing, interpreting, understanding, evaluating, and improving
The timed nature of this section also rewards mental math ability and creative problem solving along with critical test taking skills like focus, endurance, and answer awareness.
What does the ACT English test measure?
What does the ACT Reading test measure?
What does the ACT Science test measure?
What does the ACT Writing test measure?
What does the SAT cover?
What does the SAT Math test measure? | {"url":"http://gettestbright.com/what-does-the-act-math-test-measure/","timestamp":"2024-11-07T00:20:01Z","content_type":"text/html","content_length":"58202","record_id":"<urn:uuid:e0628a9f-3995-4b2c-944e-e3af60279190>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.54/warc/CC-MAIN-20241106230027-20241107020027-00028.warc.gz"} |
here a
The tasks in this feature can be solved in a whole variety of ways and we hope that this will make you curious about different routes to a solution.
When you hear about other people's ways of approaching a problem and try to understand it, your 'toolkit' of methods will be added to, so you will have more to choose from in the future. We hope that
giving you the chance to reflect on your problem solving will help you become a more resilient problem solver.
Using compass points, can you describe up to ten paths on this map so that you bring as many gems back home as possible?
Can you find two butterflies to go on each flower so that the numbers on each pair of butterflies adds to the number on their flower?
Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?
Can you make square numbers by adding two prime numbers together?
There are lots of different methods to find out what the shapes are worth - how many can you find?
One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?
In this feature, you can see how some children started each task, but this isn't because we want to give away the solutions!
In this feature, you can see how some children started each task. This isn't because we want to give away the solutions! | {"url":"https://nrich.maths.org/there-better-way-1","timestamp":"2024-11-07T18:37:31Z","content_type":"text/html","content_length":"54518","record_id":"<urn:uuid:c9bdcdd7-283a-4c55-bc3e-c555543458e2>","cc-path":"CC-MAIN-2024-46/segments/1730477028009.81/warc/CC-MAIN-20241107181317-20241107211317-00549.warc.gz"} |
[QSMS-BK21 Symplectic Seminar 14 July] Introduction to 3D Mirror Symmetry, from a Symplectic Viewpoint / Orbifolding Lagrangian Floer Cohomology
• Date: 07-14 (Fri) 10:00 ~ 17:00
• Place: 129-309 (SNU)
• Speaker: 김용환 (SNU)
• Title: Introduction to 3D Mirror Symmetry, from a Symplectic Viewpoint
• Abstract: We give an introduction to 3D mirror symmetry directed towards symplectic geometers. Our main focus will be "symplectic C^* manifolds", introduced by Alexander Ritter and Filip
Zivanovic in their recent papers. We will give examples and explicit computations that illustrates the main difficulties that arise for these manifolds. If time permits, we will also try to
introduce the holomorphic Fueter equations, which can be interpreted as the quaternionic analogue of the J-holomorphic equations.
• Speaker: Hyeongjun Jin (Yonsei)
• Title: Orbifolding Lagrangian Floer Cohomology | {"url":"https://qsms.math.snu.ac.kr/index.php?mid=board_sjXR83&order_type=asc&page=2&document_srl=2645&sort_index=readed_count&listStyle=viewer","timestamp":"2024-11-13T18:36:31Z","content_type":"text/html","content_length":"21785","record_id":"<urn:uuid:dc3f323b-2b20-4c8d-be7a-8ab78747819a>","cc-path":"CC-MAIN-2024-46/segments/1730477028387.69/warc/CC-MAIN-20241113171551-20241113201551-00030.warc.gz"} |
Solving systems of polynomial equations over GF(2) by a parity-counting self-reduction
(2019) 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019 In Leibniz International Proceedings in Informatics (LIPIcs) 132. p.1-26
We consider the problem of finding solutions to systems of polynomial equations over a finite field. Lokshtanov et al. [SODA'17] recently obtained the first worst-case algorithms that beat
exhaustive search for this problem. In particular for degree-d equations modulo two in n variables, they gave an O^∗2^(1−1/(5d))^n time algorithm, and for the special case d = 2 they gave an O^∗2
^0.876n time algorithm. We modify their approach in a way that improves these running times to O^∗2^(1−1/(2^7d))^n and O^∗2^0.804n, respectively. In particular, our latter bound - that holds for
all systems of quadratic equations modulo 2 - comes close... (More)
We consider the problem of finding solutions to systems of polynomial equations over a finite field. Lokshtanov et al. [SODA'17] recently obtained the first worst-case algorithms that beat
exhaustive search for this problem. In particular for degree-d equations modulo two in n variables, they gave an O^∗2^(1−1/(5d))^n time algorithm, and for the special case d = 2 they gave an O^∗2
^0.876n time algorithm. We modify their approach in a way that improves these running times to O^∗2^(1−1/(2^7d))^n and O^∗2^0.804n, respectively. In particular, our latter bound - that holds for
all systems of quadratic equations modulo 2 - comes close to the O^∗2^0.792n expected time bound of an algorithm empirically found to hold for random equation systems in Bardet et al. [J.
Complexity, 2013]. Our improvement involves three observations: 1. The Valiant-Vazirani lemma can be used to reduce the solution-finding problem to that of counting solutions modulo 2. 2. The
monomials in the probabilistic polynomials used in this solution-counting modulo 2 have a special form that we exploit to obtain better bounds on their number than in Lokshtanov et al. [SODA'17].
3. The problem of solution-counting modulo 2 can be “embedded” in a smaller instance of the original problem, which enables us to apply the algorithm as a subroutine to itself.
publishing date
Chapter in Book/Report/Conference proceeding
publication status
host publication
46th International Colloquium on Automata, Languages, and Programming : ICALP 2019 - ICALP 2019
series title
Leibniz International Proceedings in Informatics (LIPIcs)
Chatzigiannakis, Ioannis ; Baier, Christel ; Leonardi, Stefano and Flocchini, Paola
article number
1 - 26
Schloss Dagstuhl - Leibniz-Zentrum für Informatik
conference name
46th International Colloquium on Automata, Languages, and Programming, ICALP 2019
conference location
Patras, Greece
conference dates
2019-07-09 - 2019-07-12
external identifiers
LU publication?
date added to LUP
2019-07-26 11:44:12
date last changed
2022-04-26 03:26:06
abstract = {{<p>We consider the problem of finding solutions to systems of polynomial equations over a finite field. Lokshtanov et al. [SODA'17] recently obtained the first worst-case algorithms that beat exhaustive search for this problem. In particular for degree-d equations modulo two in n variables, they gave an O<sup>∗</sup>2<sup>(1</sup>−1/(5d))<sup>n</sup> time algorithm, and for the special case d = 2 they gave an O<sup>∗</sup>2<sup>0.876n</sup> time algorithm. We modify their approach in a way that improves these running times to O<sup>∗</sup>2<sup>(1</sup>−1/(2<sup>7</sup>d))<sup>n</sup> and O<sup>∗</sup>2<sup>0.804n</sup>, respectively. In particular, our latter bound - that holds for all systems of quadratic equations modulo 2 - comes close to the O<sup>∗</sup>2<sup>0.792n</sup> expected time bound of an algorithm empirically found to hold for random equation systems in Bardet et al. [J. Complexity, 2013]. Our improvement involves three observations: 1. The Valiant-Vazirani lemma can be used to reduce the solution-finding problem to that of counting solutions modulo 2. 2. The monomials in the probabilistic polynomials used in this solution-counting modulo 2 have a special form that we exploit to obtain better bounds on their number than in Lokshtanov et al. [SODA'17]. 3. The problem of solution-counting modulo 2 can be “embedded” in a smaller instance of the original problem, which enables us to apply the algorithm as a subroutine to itself.</p>}},
author = {{Björklund, Andreas and Kaski, Petteri and Williams, Ryan}},
booktitle = {{46th International Colloquium on Automata, Languages, and Programming : ICALP 2019}},
editor = {{Chatzigiannakis, Ioannis and Baier, Christel and Leonardi, Stefano and Flocchini, Paola}},
isbn = {{9783959771092}},
issn = {{1868-8969}},
keywords = {{Equation systems; Polynomial method}},
language = {{eng}},
month = {{07}},
pages = {{1--26}},
publisher = {{Schloss Dagstuhl - Leibniz-Zentrum für Informatik}},
series = {{Leibniz International Proceedings in Informatics (LIPIcs)}},
title = {{Solving systems of polynomial equations over GF(2) by a parity-counting self-reduction}},
url = {{http://dx.doi.org/10.4230/LIPIcs.ICALP.2019.26}},
doi = {{10.4230/LIPIcs.ICALP.2019.26}},
volume = {{132}},
year = {{2019}}, | {"url":"https://lup.lub.lu.se/search/publication/43d4e602-8be4-48c3-946b-49a2e80b353d","timestamp":"2024-11-07T19:02:59Z","content_type":"text/html","content_length":"44749","record_id":"<urn:uuid:3572cf98-eca7-4bb2-ba64-8584d018f6e7>","cc-path":"CC-MAIN-2024-46/segments/1730477028009.81/warc/CC-MAIN-20241107181317-20241107211317-00426.warc.gz"} |
2021 Week 1 Depth Chart
ND 2021 Offense
WR- (W)- Boundary- (4) Kevin Austin (5) Joe Wilkins
WR- (Z) Slot- (3) Avery Davis (13) Lawrence Keys
TE (Y) (87) Michael Mayer (85) George Takacs (84) Kevin Bauman
WR(X) Field (0) Braden Lenzy (21) Lorenzo Styles
QB (17) Jack Coan (10) Drew Pyne (12) Tyler Buchner
RB (23) Kyren Williams (25) Chris Tyree (20) C’bo Flemister
LT-(54) Blake Fisher (68) Michael Carmody
LG (52) Zeke Correll (50) Rocco Spindler
C- (55) Jarrett Patterson (73) Andrew Kristofic
RG (62) Cain Madden (56) John Dirksen
RT (75) Josh Lugg (79) Tosh Baker
ND 2021 Defense
Vyp- (7) Isaiah Foskey (9) Justin Ademilola (12) Jordan Botelho
DT- (57) Jayson Ademilola (99) Riley Mills (54) Jacob Lacey
NG- (41) Kurt Hinish (56) Howard Cross (54) Jacob Lacey
DE (95) Myron Tagovailoa-Amosa (31) Nana Osafa-Mensah (99) Alexander Ehrensberger
Will (27) JD Bertrand (33) Shayne Simon
Mike (40) Drew White (52) Bo Bauer
Rover- (24) Jack Kiser (10) Isaiah Pryor (13) Paul Moala
DB- (Boundary) (5) Cam Hart (11) Ramon Henderson
FS- (14) Kyle Hamilton (2) DJ Brown
SS- (3) Houston Griffith (16) KJ Wallace
DB- (Field) (6) Clarence Lewis (28) TaRiq Bracy
30 minutes ago, nd_irish said:
Is it concerning that Botelho is not on the 2-deep?
Not to me, It tells me if he's listed 3rd DE will play some 3-3-5 too. (I think Justins stronger, i.e. in the pram longer weighs slighty more) I don't take much stock in depth charts to be honest I
just wanna know the numbers. We'll know more after game 1.
18 minutes ago, nd_irish said:
Is it concerning that Botelho is not on the 2-deep?
I’m more concerned that Myron is a DE and not a tackle. But that could be what they are running.
Also, a little concerning that Bertrand and Kiser are starting. I don’t know why I thought our line backing crew was very deep. Other than that, all is to be expected on the offensive side of the
10 minutes ago, coltssb said:
I’m more concerned that Myron is a DE and not a tackle. But that could be what they are running.
Also, a little concerning that Bertrand and Kiser are starting. I don’t know why I thought our line backing crew was very deep. Other than that, all is to be expected on the offensive side of the
Myron lost a lot of weight battling CO-VID and a condition of him not entering the draft was he wanted to play DE. LB I would suspect is that coaches thing, where JD and Kiser are assignment correct
alot. Moala probably gets more time as he gets back to playing after an injury. Losing Marist makes us miss the wow-athlete which will hurt us unless Pyror can step up.
Thought it was interesting that for Rover it was: Jack Kiser OR Isaiah Pryor OR Paul Moala.
I think Kiser is the presumed starter, but I think how the depth chart is actually written is a positive because it means: (1) Pryor has made great strides under Freeman; and (2) Moala is healthy and
ready to go after tearing his Achilles last season.
Defense has great depth in the front seven. But it'll be the secondary that determines how far this team can go considering the QBs they face (Desmond Ritter, Kedon Slovis, Sam Howell).
I just hope that Botelho doesn't get frustrated and transfer after the season. I do trust Freeman to keep him motivated and happy though.
2 hours ago, tneun89 said:
Thought it was interesting that for Rover it was: Jack Kiser OR Isaiah Pryor OR Paul Moala.
I think Kiser is the presumed starter, but I think how the depth chart is actually written is a positive because it means: (1) Pryor has made great strides under Freeman; and (2) Moala is healthy
and ready to go after tearing his Achilles last season.
Defense has great depth in the front seven. But it'll be the secondary that determines how far this team can go considering the QBs they face (Desmond Ritter, Kedon Slovis, Sam Howell).
Yeah I won't be real comfortable until I see Cam Hart defend a few passes successfully during a game.
Here's further evidence of what @tneun89 was saying about Rover if I can start the press conference video at the right spot,
@tneun89that video should be cued up if I converted minutes to seconds right. if it doesn't he talks rover at the 11:04 mark until about 11:41
3 hours ago, 4thand1 said:
I just hope that Botelho doesn't get frustrated and transfer after the season. I do trust Freeman to keep him motivated and happy though.
I still say something happened this preseason with him (whether the coaches admit it or not), hence him being buried on the depth chart.
Would Davis, Wilkins or Keys even make gameday rosters at Ala, Clem, OSU, Okla or Georgia? I don't think so. I like the WRs the staff has been recruiting the last few years and I hope that
Just now, 4thand1 said:
Would Davis, Wilkins or Keys even make gameday rosters at Ala, Clem, OSU, Okla or Georgia? I don't think so. I like the WRs the staff has been recruiting the last few years and I hope that
Keys had offers from Alabama, Georgia, LSU, and Oklahoma coming out of high school. I think injuries and an inability to add strength have really hurt his development. He was hurt in camp, so not
sure what he will do this year. Would love to see Styles in the slot.
Drew White is still on the team? Feels like he's been there forever. Not sad to see him, just surprised to still have him.
14 minutes ago, TexasDomer said:
Drew White is still on the team? Feels like he's been there forever. Not sad to see him, just surprised to still have him.
Yeah we return alot of experience at LB. the group is probably missing the Owusu type athlete but to their credit will be in position alot. Not saying they won't lose a one on one matchup rather if
they do hey should be in a position where the 10 other guys can help.
On 8/30/2021 at 10:18 PM, SDIrishFan said:
I still say something happened this preseason with him (whether the coaches admit it or not), hence him being buried on the depth chart.
I agree, I believe something did happen and he is in the dog-house...
11 hours ago, NDhoosier said:
I agree, I believe something did happen and he is in the dog-house...
Only way to tell is to see if he plays or not. | {"url":"https://www.domerdomain.com/topic/52204-2021-week-1-depth-chart/","timestamp":"2024-11-05T10:37:21Z","content_type":"text/html","content_length":"290960","record_id":"<urn:uuid:0e56227f-b854-4abc-bded-d3afb94b3c38>","cc-path":"CC-MAIN-2024-46/segments/1730477027878.78/warc/CC-MAIN-20241105083140-20241105113140-00304.warc.gz"} |
WO2020155352A1 - Window-type air conditioner
- Google Patents
WO2020155352A1 - Window-type air conditioner - Google Patents
Window-type air conditioner Download PDF
Publication number
WO2020155352A1 WO2020155352A1 PCT/CN2019/080050 CN2019080050W WO2020155352A1 WO 2020155352 A1 WO2020155352 A1 WO 2020155352A1 CN 2019080050 W CN2019080050 W CN 2019080050W WO 2020155352 A1
WO2020155352 A1 WO 2020155352A1
WIPO (PCT)
Prior art keywords
air conditioner
heat exchange
Prior art date
Application number
Other languages
Original Assignee
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Priority claimed from CN201920188070.2U external-priority patent/CN209706235U/en
Priority claimed from CN201920188057.7U external-priority patent/CN209689077U/en
Application filed by 广东美的制冷设备有限公司, 美的集团股份有限公司 filed Critical 广东美的制冷设备有限公司
Priority to US16/498,028 priority Critical patent/US11624514B2/en
Priority to CA3057237A priority patent/CA3057237C/en
Publication of WO2020155352A1 publication Critical patent/WO2020155352A1/en
☆ F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
☆ F24—HEATING; RANGES; VENTILATING
☆ F24F—AIR-CONDITIONING; AIR-HUMIDIFICATION; VENTILATION; USE OF AIR CURRENTS FOR SCREENING
☆ F24F13/00—Details common to, or for air-conditioning, air-humidification, ventilation or use of air currents for screening
☆ F24F13/20—Casings or covers
☆ F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
☆ F24—HEATING; RANGES; VENTILATING
☆ F24F—AIR-CONDITIONING; AIR-HUMIDIFICATION; VENTILATION; USE OF AIR CURRENTS FOR SCREENING
☆ F24F1/00—Room units for air-conditioning, e.g. separate or self-contained units or units receiving primary air from a central station
☆ F24F1/0007—Indoor units, e.g. fan coil units
☆ F24F1/0059—Indoor units, e.g. fan coil units characterised by heat exchangers
☆ F24F1/0063—Indoor units, e.g. fan coil units characterised by heat exchangers by the mounting or arrangement of the heat exchangers
☆ F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
☆ F24—HEATING; RANGES; VENTILATING
☆ F24F—AIR-CONDITIONING; AIR-HUMIDIFICATION; VENTILATION; USE OF AIR CURRENTS FOR SCREENING
☆ F24F1/00—Room units for air-conditioning, e.g. separate or self-contained units or units receiving primary air from a central station
☆ F24F1/02—Self-contained room units for air-conditioning, i.e. with all apparatus for treatment installed in a common casing
☆ F24F1/022—Self-contained room units for air-conditioning, i.e. with all apparatus for treatment installed in a common casing comprising a compressor cycle
☆ F24F1/027—Self-contained room units for air-conditioning, i.e. with all apparatus for treatment installed in a common casing comprising a compressor cycle mounted in wall openings, e.g.
in windows
☆ F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
☆ F24—HEATING; RANGES; VENTILATING
☆ F24F—AIR-CONDITIONING; AIR-HUMIDIFICATION; VENTILATION; USE OF AIR CURRENTS FOR SCREENING
☆ F24F1/00—Room units for air-conditioning, e.g. separate or self-contained units or units receiving primary air from a central station
☆ F24F1/02—Self-contained room units for air-conditioning, i.e. with all apparatus for treatment installed in a common casing
☆ F24F1/028—Self-contained room units for air-conditioning, i.e. with all apparatus for treatment installed in a common casing characterised by air supply means, e.g. fan casings, internal
dampers or ducts
☆ F24F1/0284—Self-contained room units for air-conditioning, i.e. with all apparatus for treatment installed in a common casing characterised by air supply means, e.g. fan casings, internal
dampers or ducts with horizontally arranged fan axis
☆ F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
☆ F24—HEATING; RANGES; VENTILATING
☆ F24F—AIR-CONDITIONING; AIR-HUMIDIFICATION; VENTILATION; USE OF AIR CURRENTS FOR SCREENING
☆ F24F1/00—Room units for air-conditioning, e.g. separate or self-contained units or units receiving primary air from a central station
☆ F24F1/02—Self-contained room units for air-conditioning, i.e. with all apparatus for treatment installed in a common casing
☆ F24F1/03—Self-contained room units for air-conditioning, i.e. with all apparatus for treatment installed in a common casing characterised by mounting arrangements
☆ F24F1/031—Self-contained room units for air-conditioning, i.e. with all apparatus for treatment installed in a common casing characterised by mounting arrangements penetrating a wall or
☆ F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
☆ F24—HEATING; RANGES; VENTILATING
☆ F24F—AIR-CONDITIONING; AIR-HUMIDIFICATION; VENTILATION; USE OF AIR CURRENTS FOR SCREENING
☆ F24F1/00—Room units for air-conditioning, e.g. separate or self-contained units or units receiving primary air from a central station
☆ F24F1/02—Self-contained room units for air-conditioning, i.e. with all apparatus for treatment installed in a common casing
☆ F24F1/032—Self-contained room units for air-conditioning, i.e. with all apparatus for treatment installed in a common casing characterised by heat exchangers
☆ F24F1/0323—Self-contained room units for air-conditioning, i.e. with all apparatus for treatment installed in a common casing characterised by heat exchangers by the mounting or
arrangement of the heat exchangers
☆ F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
☆ F24—HEATING; RANGES; VENTILATING
☆ F24F—AIR-CONDITIONING; AIR-HUMIDIFICATION; VENTILATION; USE OF AIR CURRENTS FOR SCREENING
☆ F24F1/00—Room units for air-conditioning, e.g. separate or self-contained units or units receiving primary air from a central station
☆ F24F1/02—Self-contained room units for air-conditioning, i.e. with all apparatus for treatment installed in a common casing
☆ F24F1/0328—Self-contained room units for air-conditioning, i.e. with all apparatus for treatment installed in a common casing with means for purifying supplied air
☆ F24F1/035—Self-contained room units for air-conditioning, i.e. with all apparatus for treatment installed in a common casing with means for purifying supplied air characterised by the
mounting or arrangement of filters
☆ F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
☆ F24—HEATING; RANGES; VENTILATING
☆ F24F—AIR-CONDITIONING; AIR-HUMIDIFICATION; VENTILATION; USE OF AIR CURRENTS FOR SCREENING
☆ F24F13/00—Details common to, or for air-conditioning, air-humidification, ventilation or use of air currents for screening
☆ F24F13/22—Means for preventing condensation or evacuating condensate
☆ F24F13/222—Means for preventing condensation or evacuating condensate for evacuating condensate
☆ F24F13/224—Means for preventing condensation or evacuating condensate for evacuating condensate in a window-type room air conditioner
☆ F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
☆ F24—HEATING; RANGES; VENTILATING
☆ F24F—AIR-CONDITIONING; AIR-HUMIDIFICATION; VENTILATION; USE OF AIR CURRENTS FOR SCREENING
☆ F24F8/00—Treatment, e.g. purification, of air supplied to human living or working spaces otherwise than by heating, cooling, humidifying or drying
☆ F24F8/10—Treatment, e.g. purification, of air supplied to human living or working spaces otherwise than by heating, cooling, humidifying or drying by separation, e.g. by filtering
☆ F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
☆ F24—HEATING; RANGES; VENTILATING
☆ F24F—AIR-CONDITIONING; AIR-HUMIDIFICATION; VENTILATION; USE OF AIR CURRENTS FOR SCREENING
☆ F24F13/00—Details common to, or for air-conditioning, air-humidification, ventilation or use of air currents for screening
☆ F24F13/32—Supports for air-conditioning, air-humidification or ventilation units
□ This application relates to the field of refrigeration, and in particular to a window air conditioner.
□ the prior art window type air conditioner is installed on the window of the room, and the window is located above the window type air conditioner. During the operation of the window type air
conditioner, the noise generated by the outdoor compressor will be transmitted to the room and reduce the user's use Comfort. At the same time, in order to meet the cooling demand, the prior
art window air conditioner will be designed to be larger in size, occupy a lot of space and reduce the space utilization rate.
□ this application aims to solve at least one of the technical problems existing in the prior art. For this reason, this application proposes a window air conditioner, which can reduce the
space occupied by the indoor heat exchanger and the indoor wind wheel when the indoor heat exchanger and the indoor wind wheel cooperate, reduce the volume of the window air conditioner, and
reduce the space occupied by the window air conditioner .
□ the window type air conditioner is supported on a window of a wall, and a movable window is arranged in the window
□ the window type air conditioner includes: a casing, and The outer peripheral wall of the housing is provided with a containing groove, the housing is divided into an indoor part and an
outdoor part by the containing groove, at least a part of the window can be extended into the containing groove, and the indoor part is provided with an air inlet And an air outlet; an indoor
wind wheel, the indoor wind wheel is arranged in the indoor part; an indoor heat exchanger, the indoor heat exchanger is arranged in the indoor part, the indoor heat exchanger includes a
first heat exchanger The hot part and the second heat exchange part, the first heat exchange part extends vertically, the upper end of the second heat exchange part is connected to the lower
end of the first heat exchange part, and the lower end of the second heat exchange part It extends obliquely in the direction toward the indoor wind wheel; the filter screen, in the air flow
direction, the filter
□ the window type air conditioner of the embodiment of the present application by arranging a receiving groove on the cabinet, at least a part of the window can extend into the receiving
groove, so that the window can be used to fix the window type air conditioner to a certain extent. Avoid the window air conditioner from falling.
□ the windows that extend into the receiving groove can have a certain sound insulation effect, heat insulation effect and sealing effect, and improve the user comfort.
□ the user can choose whether to set it for sealing according to actual needs. Even if the sealing component is provided for the sealing component of the space between the window and the
window, the material of the sealing component used in the window air conditioner of the embodiment of the present application is less than that of the prior art sealing component, which saves
□ the indoor heat exchanger includes a vertically extending first heat exchange part and an obliquely extending second heat exchange part, it can not only increase the heat exchange area of the
indoor heat exchanger and improve the heat exchange effect, but also reduce the number of indoor heat exchangers.
□ the space occupied by the two when matched with the indoor wind wheel can reduce the volume of the window air conditioner and reduce the space occupied by the window air conditioner.
□ the included angle A between the second heat exchange portion and the horizontal plane has a value range of 35°-55°.
□ the vertical extension length of the first heat exchange part is H1
□ the oblique extension length of the second heat exchange part is H2
□ the value range of H1/H2 is 0.2 ⁇ 0.4.
□ the filter screen is spaced apart from the indoor heat exchanger, the filter screen includes a first filter part and a second filter part, the first filter part extends vertically, and the
The upper end of the second filter part is connected with the lower end of the first filter part, and the lower end of the second filter part extends obliquely in a direction toward the
indoor wind wheel.
□ the distance between the first filter part and the first heat exchange part is d1
□ the distance between the second filter part and the second heat exchange part is d2
□ the top of the indoor part is provided with the air outlet, the plane on which the air outlet is located is the air outlet surface, and the air outlet surface extends obliquely backwards in a
bottom-up direction .
□ the included angle between the air outlet surface and the vertical surface is B, and the value range of the included angle B is 50°-66°.
□ the number of rows of heat exchange tubes in the second heat exchange part is greater than the number of rows of heat exchange tubes in the first heat exchange part.
□ the cabinet includes: a chassis; a rear box body, the rear box body is fixed on the chassis, the rear box body contains an outdoor heat exchanger; a front box body, The front box body is
fixed on the chassis, and the front box body and the rear box body are spaced back and forth to define the receiving groove.
□ the indoor heat exchanger has a side plate assembly;
□ the window air conditioner further includes a water receiving tray, the water receiving tray is provided with a rib assembly, and the rib assembly is used for To support the side plate
assembly, the water receiving pan is arranged below the heat exchanger assembly.
□ the rib assembly includes a first rib and a second rib that are spaced apart
□ the side plate assembly includes a first side plate and a second side plate
□ the first side plate Is arranged at one end of the heat exchanger assembly
□ the heat exchange tubes of the heat exchanger assembly pass through the first side plate
□ the first rib is used to support the first side plate
□ the The two ribs are used to support the second side plate.
□ the first side plate has a first flange, the first flange is attached to the first rib, and the first flange is connected to the first rib. Connected by screws; the second side plate has a
second flange, the second flange is attached to the second rib, and the second flange is connected with the second rib by screws.
□ the first flange extends toward the direction of the second side board, and the second flange extends toward the direction of the first side board.
□ both the first flange and the second flange have lugs, and screw holes are provided on the lugs.
□ the first rib and the second rib each have an inclined support surface, and the inclined support surface is used to support the second heat exchange part facing the water receiving tray. Part
of the surface.
□ both the first rib and the second rib have water passing holes.
□ an auxiliary water receiving portion is provided on the water receiving pan, the auxiliary water receiving portion is used to receive the condensed water of the refrigerant pipe, and the
auxiliary water receiving portion is in communication with the water passing hole .
□ the first rib is provided with the water passing hole, and the drainage channel is located on a side of the first rib facing away from the second rib.
□ a first matching portion is provided on the water receiving tray, and the filter screen has a second matching portion that matches the first matching portion.
□ one of the first matching portion and the second matching portion is a plug-in strip, and the other is a sliding groove that matches the plug-in strip.
□ Figure 1 is a cross-sectional view of a window air conditioner according to an embodiment of the present application
□ Figure 2 is a schematic diagram of a window air conditioner installed on a window according to an embodiment of the present application
□ Figure 3 is a three-dimensional view of the cooperation of the evaporator and the filter screen according to an embodiment of the present application
□ Figure 4 is a side view of the mating evaporator and filter screen according to an embodiment of the present application.
□ Fig. 5 is a partial schematic diagram of a window air conditioner according to an embodiment of the present application.
□ Fig. 6 is a structural diagram of a window air conditioner according to an embodiment of the present application.
□ Fig. 7 is an exploded view of a window air conditioner according to an embodiment of the present application.
□ Fig. 8 is a partial structural diagram of a window air conditioner according to an embodiment of the present application.
□ Fig. 9 is a partial structural diagram of a window air conditioner according to an embodiment of the present application.
□ Fig. 10 is a partial structural diagram of a window air conditioner according to an embodiment of the present application.
□ Fig. 11a is a partial structural diagram of a window air conditioner according to an embodiment of the present application.
□ Fig. 11b is another view of the partial structure of the window air conditioner according to the embodiment of the present application.
□ Fig. 11c is a partial structural diagram of the window air conditioner according to the embodiment of the present application from another perspective.
□ Fig. 12 is a partial structural diagram of a window air conditioner according to an embodiment of the present application.
□ Fig. 13 is a schematic structural diagram of a water receiving pan of a window air conditioner according to an embodiment of the present application.
□ Fig. 14 is a cross-sectional view of a window air conditioner according to an embodiment of the present application.
□ Fig. 15 is a structural schematic diagram of a heat exchanger assembly and a filter screen of a window air conditioner according to an embodiment of the present application.
□ Fig. 16 is a perspective view of a window air conditioner according to an embodiment of the present application.
□ Fig. 17 is an exploded view of a window air conditioner according to an embodiment of the present application.
□ Fig. 18 is a partial enlarged schematic diagram of the position A in Fig. 17.
□ Window type air conditioner 1 window 5
□ window 3 wall 4
□ Sound insulation 200 first end 201, second end 202, first channel 210, second channel 220,
□ Middle partition 300 first extension 310, second extension 320,
□ Drain pan 400 Drain pan 400, connecting piece 410, drainage channel 411, tapered section 412, first mounting portion 420, first rib 421, second mounting portion 430, second rib 431, first
matching portion 440, auxiliary connection Department of Water 450,
□ Indoor heat exchanger 500 third installation part 510, fourth installation part 520, heat exchange tube 530, first side plate 540, first flange 541, lug 5400, screw hole 5401, water hole
5402, second Side plate 550, first heat exchange part 560, second heat exchange part 570,
□ Filter 600 Second matching portion 610, first filter portion 610, second filter portion 612,
□ Case 2 containing groove 21, rear box body 23, rear box body seat 24, rear box body cover 25, front box body 26, indoor part 11, outdoor part 12, air inlet 13, air outlet 14, middle partition
18 .
□ connection should be understood in a broad sense, for example, it can be a fixed connection or a detachable connection. Connected or integrally connected; it can be a mechanical connection or
an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the internal communication between two components.
□ connection should be understood in a broad sense, for example, it can be a fixed connection or a detachable connection. Connected or integrally connected; it can be a mechanical connection or
an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the internal communication between two components.
□ the window type air conditioner 1 is supported on a window 5 of the wall 4, and a movable window 3 is provided on the window 5.
□ the window air conditioner 1 includes: a casing 2, an indoor wind wheel 6, an indoor heat exchanger 500 and a filter screen 600, wherein the outer peripheral wall of the casing 2 is provided
with a receiving groove 21
□ the housing 2 is divided into an indoor part 11 and an outdoor part 12 by a receiving groove 21.
□ at least a part of the window 3 can be extended into the receiving groove 21, specifically, the top and left side of the receiving groove 21 Both the right side and the right side are open so
that the window 3 can be pulled down into the receiving groove 21.
□ the distance between the indoor part 11 and the outdoor part 12 is not adjustable.
□ the chassis of the casing 2 is an integrally formed part.
□ the indoor part 11 is provided with an air inlet 13 and an air outlet 14.
□ the indoor wind wheel 6 is arranged in the indoor part 11. Specifically, when the indoor wind wheel 6 rotates, the indoor air enters the indoor part 11 from the air inlet 13 and is discharged
into the room from the air outlet 14 after heat exchange.
□ the indoor wind wheel 6 may be a through-flow wind wheel, so that the air blown from the air outlet 14 is relatively uniform and the air supply distance is long.
□ the indoor heat exchanger 500 is arranged in the indoor part 11.
□ the indoor heat exchanger 500 includes a first heat exchange part 560 and a second heat exchange part 570.
□ the first heat exchange part 560 extends vertically, and the upper end of the second heat exchange part 570 Connected to the lower end of the first heat exchange part 560, the lower end of
the second heat exchange part 570 extends obliquely in the direction toward the indoor wind wheel 6. That is, the second heat exchange part 570 is located at the lower part of the first heat
exchange part 560, there is an angle between the first heat exchange part 560 and the second heat exchange part 570, and the indoor wind wheel 6 is located in the first heat exchange part
560. And the second heat exchanging part 570 defines the included angle area.
□ the indoor heat exchanger 500 is located on the air inlet side of the indoor wind wheel 6, so as to ensure the heat exchange effect.
□ the first heat exchange part 560 and the second heat exchange part 570 can be defined by the bending of one heat exchanger, and the first heat exchange part 560 and the second heat exchange
part 570 can also be two independent heat exchange parts. Heater.
□ the filter screen 600 is located on the upstream side of the indoor heat exchanger 500.
□ the air entering the indoor part 11 is filtered by the filter 600 and then flows to the indoor heat exchanger 500 for heat exchange, so that the air is filtered through the filter 600, which
can prevent dust and other substances from directly adhering to the room.
□ the heat exchanger 500 affects the heat exchange effect of the indoor heat exchanger 500, and at the same time can improve the cleanliness of the air discharged from the air outlet 14 into
the room.
□ window air conditioners in the prior art are directly placed on the window 5, and more sealing components are required between the window air conditioner and the window 5, and between the
window 3 and the window sill to achieve a sealing effect.
□ some window air conditioners are provided with an installation space with an opening facing downward. The wall 4 extends into the installation space to support the window air conditioner. In
this way, the top plate of the window air conditioner bears greater force. , So that the window air conditioner has the potential safety hazard of falling due to the break of the top plate.
□ the window type air conditioner 1 of the embodiment of the present application by providing a receiving groove 21 on the cabinet 2, at least a part of the window 3 can extend into the
receiving groove 21, so that the window 3 can be used to fix the window type air conditioner 1 Play a certain positioning function to prevent the window air conditioner 1 from falling, and
the window 3 that extends into the receiving groove 21 can have a certain sound insulation effect, heat insulation effect and sealing effect, and improve the user's comfort. It is possible to
choose whether to provide a sealing component for sealing the space between the window 3 and the window 5 according to actual needs. Even if the sealing component is provided, the material of
the sealing component used in the window type air conditioner 1 of the embodiment of the present application is less than that of the prior art The sealed components save costs.
□ the indoor heat exchanger 500 includes a first heat exchange part 560 extending vertically and a second heat exchange part 570 extending obliquely, it can not only increase the heat exchange
area of the indoor heat exchanger 500 and improve the heat exchange effect, but also reduce The space occupied by the indoor heat exchanger 500 and the indoor wind wheel 6 when they are
matched can reduce the volume of the window air conditioner 1 and reduce the space occupied by the window air conditioner 1.
□ the included angle A between the second heat exchange portion 570 and the horizontal plane has a value range of 35°-55°. Therefore, it can be avoided that the inclination angle of the second
heat exchange part 570 is too large or too small to affect the heat exchange effect and increase the occupied space.
□ the included angle A between the second heat exchange portion 570 and the horizontal plane is 45°.
□ the vertical extension length of the first heat exchange portion 560 is H1
□ the oblique extension length of the second heat exchange portion 570 is H2, where H1/H2
□ the value range is 0.2 to 0.4. Therefore, the space under the indoor wind wheel 6 can be reasonably used.
□ the value of H1/H2 is 0.3.
□ the filter screen 600 is spaced apart from the indoor heat exchanger 500, and the filter screen 600 includes a first filter part 610 and a second filter part 612.
□ the first filter part 610 extends vertically
□ the upper end of the second filter portion 612 is connected to the lower end of the first filter portion 610
□ the lower end of the second filter portion 612 extends obliquely in the direction toward the indoor wind wheel 6.
□ the second filter portion 612 is located at the lower portion of the first filter portion 610, and the inclination angle of the second filter portion 612 may be the same as or different from
the second heat exchange portion 570. Therefore, by making the shape of the filter screen 600 the same or similar to the shape of the indoor heat exchanger 500, the generation of eddy
currents can be reduced, which is beneficial to noise reduction and can also ensure the uniformity of air supply.
□ the distance between the first filter part 610 and the first heat exchange part 560 is d1
□ the ratio of the passing distance meets a certain relationship value, which facilitates the installation of the filter 600.
□ the distance between the filter screen 600 and the indoor heat exchanger 500 is relatively uniform, the generation of eddy currents can be further reduced, which is beneficial to noise
□ the casing 2 is provided with a sliding groove, and the filter screen 600 can be pulled and matched with the sliding groove, so as to facilitate the disassembly and cleaning of the filter
screen 600 and the installation of the filter screen 600.
□ an air outlet 14 is provided on the top of the indoor part 11, and the plane on which the air outlet 14 is located is the air outlet surface, and the air outlet surface is inclined backward
in a bottom-up direction extend. That is to say, as shown in Fig. 1, in the direction from the inside to the outside, the air outlet surface extends obliquely upward so that the air outlet 14
is arranged obliquely, and the wind blown from the air outlet 14 can be blown upward to prevent the wind from blowing directly.
□ the cooling speed can be increased, and at the same time, the air outlet area of the air outlet 14 can be increased. It is beneficial to shorten the length of the air duct at the upper part
of the indoor part 11 and avoid loss of cooling capacity.
□ the included angle between the air outlet surface and the vertical surface is B, and the value range of the included angle B is 50°-66°. Therefore, it is possible to avoid the influence of
the air outlet effect due to the too large or too small included angle B, to ensure that the wind is prevented from blowing people directly, and it is also beneficial to increase the air
outlet area of the air outlet 14. It is beneficial to shorten the length of the air duct at the upper part of the indoor part 11 and avoid loss of cooling capacity.
□ the value range of the included angle B is 55°-62°.
□ the number of rows of heat exchange tubes in the second heat exchange part 570 is greater than the number of rows of heat exchange tubes in the first heat exchange part 560. Thereby, the
internal space of the indoor part 11 can be effectively used, the heat exchange effect of the second heat exchange part 570 can be increased, and the cooling effect of the window air
conditioner 1 can be improved.
□ the number of rows of heat exchange tubes in the second heat exchange part 570 is three rows, and the number of heat exchange tubes in the first heat exchange part 560 is double rows. .
□ the number of rows of heat exchange tubes of the second heat exchange part 570 and the number of rows of heat exchange tubes of the first heat exchange part 560 can be set according to actual
requirements, for example, can be set to be the same.
□ the casing 2 includes: a chassis 100, a rear box body 23, and a front box body 26.
□ the rear box body 23 is fixed on the chassis 100, and the rear box body 23 contains There are outdoor heat exchangers.
□ the front box body 26 is fixed on the chassis 100, and the front box body 26 and the rear box body 23 are spaced back and forth to define the receiving groove 21.
□ the indoor part 11 includes a front box 26 and a part of the chassis 100, and the outdoor part 12 includes a rear box 23 and another part of the chassis 100. This not only facilitates the
formation of the receiving groove 2121, facilitates the matching of the window type air conditioner 10 with the window 3, but also facilitates the processing and manufacturing of the cabinet
2 and improves the appearance and aesthetics of the cabinet 2.
□ the casing 2 further includes an intermediate partition 18, which is fixed on the chassis 100 and is located in the accommodating groove 21.
□ the front and rear ends of the intermediate partition 18 are respectively connected to the rear box body. 23 cooperates with the front box 26. In this way, it is convenient for the lower
surface of the window 3 to stop on the intermediate partition 18, which facilitates the wiring and drainage of the window type air conditioner 1 and facilitates the improvement of the working
reliability of the window type air conditioner 1.
□ the rear box body 23 includes a rear box body seat 24 and a rear box body cover 25.
□ the top of the rear box body seat 24 is open and fixed on the chassis 100, and the rear box body cover 25 covers the rear The top of the box seat 24. In this way, it is convenient to improve
the structural flexibility of the rear box 23 and facilitate the disassembly and installation of parts in the rear box 23.
□ the front box body 26 is a sheet metal part or a plastic part
□ the rear box body 23 is a sheet metal part
□ the middle partition 18 is a plastic part.
□ the window air conditioner 1 includes a water receiving tray 400 and an indoor heat exchanger 500.
□ the indoor heat exchanger 500 has a side plate assembly, the water receiving pan 400 is provided with a rib assembly, and the rib assembly is used to support the side plate assembly, and the
water receiving pan 400 is arranged under the indoor heat exchanger 500.
□ the side plate assembly is provided in the indoor heat exchanger 500 to realize the assembly connection with the water receiving tray 400, preventing the water receiving tray 400 from being
directly connected to the indoor
□ the heat exchange body of the heat exchanger 500 is in contact with each other, thereby preventing the fins on the indoor heat exchanger 500 from being squeezed by the water receiving pan
400, thereby improving the structural integrity of the fins, thereby improving the exchange rate of the indoor heat exchanger 500 Thermal efficiency.
□ the rib assembly may include a first rib 421 and a second rib 431 that are spaced apart.
□ the side plate assembly may include a first side plate 540 and a second side plate 550.
□ the first side plate 540 is provided at one end of the indoor heat exchanger 500, and the heat exchange tube of the indoor heat exchanger 500 is passed through the first side plate.
□ One side plate 540, the first rib 421 is used to support the first side plate 540, and the second rib 431 is used to support the second side plate 550.
□ the first rib 421 and the second rib 431 can be used to separate the indoor heat exchanger 500 from the water receiving tray 400 to provide an operation space for the assembly of the indoor
heat exchanger 500.
□ the assembly stability of the indoor heat exchanger 500 and the water tray 400 can also be improved.
□ the first side plate 540 has a first flange 541, the first flange 541 is attached to the first rib 421, and the first flange 541 is connected to the first rib. 421 is connected by screws.
Therefore, the assembly stability of the indoor heat exchanger 500 and the water receiving tray 400 can be improved.
□ the second side plate 550 has a second flange, the second flange is attached to the second rib 431, and the second flange is connected to the second rib 431 by screws. Therefore, the assembly
stability of the indoor heat exchanger 500 and the water receiving tray 400 can be further improved.
□ both the first flange 541 and the second flange are directed toward the center of the indoor side of the window air conditioner 1. Turn over.
□ the first flange 541 extends toward the direction of the second side plate 550, and the second flange extends toward the direction of the first side plate 540, thereby avoiding the first
flange when welding the indoor heat exchanger 500.
□ the first flange 541 or the second flange is deformed due to the high temperature of welding, so that the structural stability of the side plate assembly can be improved.
□ one of the first flange 541 and the second flange has a lug 5400, and a lug 5400 Screw holes 5401 are provided on it. That is, the first flange 541 and the first rib 421 can be fixedly
connected with screws, and the second flange and the second rib 431 can be connected together. In some embodiments, in order to improve the stability of the first rib 421 or the second rib
431, at least one of the first rib 421 and the second rib 431 has a triangular shape.
□ both the first rib 421 and the second rib 431 have inclined supporting surfaces, and the inclined supporting surfaces may be used to support the indoor heat exchanger.
□ the indoor heat exchanger 500 may include a first heat exchange part 560 and a second heat exchange part 570.
□ the first heat exchange part 560 extends vertically, and the upper end of the second heat exchange part 570 exchanges with the first heat exchange part.
□ the lower end of the part 560 is connected, and the lower end of the second heat exchange part 560 extends obliquely in the direction toward the outdoor part, and the inclined support surface
is used to support a part of the surface of the second heat exchange part 560 facing the water receiving tray 400.
□ At least one of the first rib 421 and the second rib 431 has a water passing hole 5402.
□ the condensed water may flow to the drainage structure of the water receiving pan 400 through the water passage 5402, such as the connecting member 410 and the drainage channel 450.
□ an auxiliary water receiving part 450 may be provided on the water receiving tray 400, and the auxiliary water receiving part 450 is used to receive the condensed water of the refrigerant
□ the holes 5402 are connected, so that the condensed water can be drained smoothly.
□ a connecting member 410 may be provided on the water receiving tray 400, and the connecting member 410 has a drainage channel 411 therein, and the water passage hole 5402 may communicate with
the drainage channel 411.
□ the window air conditioner 1 includes a water receiving tray 400 and an indoor heat exchanger 500.
□ the water receiving tray 400 is provided with a first mounting portion 420 and a second mounting portion 430 spaced apart.
□ the indoor heat exchanger 500 has a third installation part 510 and a fourth installation part 520, the first installation part 420 is connected to the third installation part 510, and the
second installation part 430 is connected to the fourth installation part 520.
□ the window air conditioner 1 of the embodiment of the present application by providing the first installation part 420, the second installation part 430, the third installation part 510 and
the fourth installation part 520, it is convenient for the water receiving tray 400 and the indoor heat exchanger 500
□ the connection not only facilitates the improvement of the efficiency of disassembly and assembly of the water tray 400 and the indoor heat exchanger 500, but also ensures the reliability and
stability of the connection between the water tray 400 and the indoor heat exchanger 500, and facilitates the improvement of the window air conditioner.
□ the structural strength and stability of 1 are convenient to improve the working performance of the window air conditioner 1.
□ the drain pan 400 can be connected to
□ the force between the indoor heat exchanger 500 is more uniform, avoiding excessive local stress on the connection between the water receiving pan 400 and the indoor heat exchanger 500,
thereby avoiding damage to the water receiving pan 400 and the indoor heat exchanger 500, and facilitating improvement
□ the service life of the water receiving tray 400 and the indoor heat exchanger 500 further facilitates the improvement of the structural stability of the window type air conditioner 1 and
further facilitates the improvement of the working reliability of the window type air conditioner 1.
□ the window air conditioner 1 according to the embodiment of the present application has the advantages of easy assembly and reliable structure.
□ the window air conditioner 1 includes a water receiving tray 400 and an indoor heat exchanger 500.
□ the indoor heat exchanger 500 includes a heat exchange tube 530, a first side plate 540, and a second side plate 550.
□ the first side plate 540 is provided on one side of the heat exchange tube 530 and exchanges heat with each other.
□ the pipe 530 is connected, and the third mounting portion 510 is provided on the first side plate 540.
□ the second side plate 550 is disposed on the other side of the heat exchange tube 530 and connected to the heat exchange tube 530, and the fourth mounting portion 520 is disposed on the
second side plate 550. This facilitates the processing and setting of the third installation portion 510 and the fourth installation portion 520, and further facilitates the connection
between the water receiving tray 400 and the indoor heat exchanger 500.
□ the first side plate 540 has a first flange, and the first flange is configured as a third mounting portion 510.
□ the second side plate 550 has a second flange, and the second flange is configured as a fourth mounting portion 520. This facilitates the processing and molding of the third installation part
510 and the fourth installation part 520, facilitates the improvement of the production efficiency and structural strength of the third installation part 510 and the fourth installation part
520, and further facilitates the improvement of the water tray 400 and the indoor heat exchanger 500 The strength of the connection.
□ the first side plate 540 is a sheet metal part
□ the second side plate 550 is a plastic part. This facilitates the assembly and molding of the indoor heat exchanger 500, facilitates the cooperation of the indoor heat exchanger 500 with the
water receiving tray 400, facilitates the simplification of the assembly process of the indoor heat exchanger 500, and improves the assembly efficiency of the indoor heat exchanger 500.
□ first mounting portion 420 and the third mounting portion 510 are clamped or connected by screws.
□ the second mounting portion 430 and the fourth mounting portion 520 are clamped or connected by screws.
□ the first installation portion 420 and the third installation portion 510, and the second installation portion 430 and the fourth installation portion 520 can be firmly installed to ensure a
reliable connection between the water receiving tray 400 and the indoor heat exchanger 500.
□ the installation and disassembly of the water receiving tray 400 and the indoor heat exchanger 500 can be facilitated, the production efficiency of the window air conditioner 1 can be
improved, and the maintenance cost of the window air conditioner 1 can be reduced.
□ a first matching portion 440 is provided on the water receiving tray 400, and the window air conditioner 1 further includes a filter 600, which has a first matching portion 440 A second
matching portion 610 that matches. This facilitates the installation and setting of the filter screen 600, facilitates the cooperation of the filter screen 600 with the water receiving tray
400, and facilitates the improvement of the assembly efficiency of the filter screen 600.
□ one of the first mating portion 440 and the second mating portion 610 is a plug-in strip, and the other is a sliding groove that matches the plug-in strip.
□ the first matching portion 440 and the second matching portion 610 can be used to position and guide the installation of the filter screen 600, which is convenient for improving the accuracy
and reliability of the installation of the filter screen 600, and facilitates the smooth installation of the filter screen 600 to the drain pan. 400 up.
□ a connecting piece 410 is provided on the water receiving tray 400, and the connecting piece 410 has a drainage channel 411.
□ the connecting member 410 can be used to discharge the condensed water in the water receiving pan 400, avoiding excessive accumulation of condensate water in the water receiving pan 400, and
improving the working reliability of the water receiving pan 400.
□ the connecting member 410 is connected to the second mounting part 430. This facilitates the installation and arrangement of the connecting member 410, and improves the drainage performance
of the connecting member 410.
□ At least a part of the drainage channel 411 is a tapered section 412, and the cross-sectional area of the tapered section 412 gradually decreases. Further, from the indoor side to the outdoor
side, the cross-sectional area of the tapered section 412 gradually decreases. This facilitates the improvement of the drainage capacity of the drainage channel 411, and further facilitates
the smooth discharge of the condensed water in the water receiving tray 400, which is convenient for improving the drainage effect of the water receiving tray 400.
□ the inner bottom wall of the drainage channel 411 is an inclined surface. In this way, it is convenient for the condensed water to flow in the drainage channel 411, and it is convenient to
improve the drainage effect of the drainage channel 411.
□ the inner bottom wall of the drainage channel 411 gradually inclines toward the outdoor side. In this way, it is convenient for the condensed water in the water receiving tray 400 to be
smoothly discharged under the action of gravity, and it is convenient to improve the drainage efficiency of the water receiving tray 400.
□ the water receiving tray 400 includes a first rib and a second rib.
□ the first rib is provided on one side of the water receiving tray 400, and the first rib is configured as a first mounting portion 420.
□ the second rib is provided on the other side of the water receiving tray 400, and the second rib is configured as a second mounting portion 430. This facilitates the processing and setting of
the first installation part 420 and the second installation part 430, and facilitates the first installation part 420 and the second installation part 430 to cooperate with the third
installation part 510 and the fourth installation part 520 respectively, and further facilitates the water receiving tray 400 is connected to the indoor heat exchanger 500.
□ the window air conditioner 1 further includes a chassis 100, a center partition 300, an outdoor part and an indoor part.
□ the middle partition 300 is connected to the chassis 100, and the water receiving tray 400 is arranged in the indoor part.
□ the indoor part, the central partition 300 and the outdoor part define a receiving groove 21 for accommodating windows, the indoor heat exchanger 500 is arranged in the indoor part, and the
water receiving tray 400 is arranged in the indoor heat exchanger 500 Below (the up and down direction is shown by arrow A in Figure 1).
□ This not only facilitates the installation of the window type air conditioner 1, and improves the structural stability of the window type air conditioner 1, but also facilitates the sealing
of the installation location of the window type air conditioner 1, and facilitates the improvement of the indoor side and the room after the window type air conditioner 1 is installed.
□ the sealing performance between the outside At the same time, it is convenient to make the appearance of the window air conditioner 1 more neat and beautiful.
□ the window air conditioner 1 is supported on the window 5 of the wall 4, and the window is provided with a movable window, and the window air conditioner 1 includes
□ the casing 2 is provided with a receiving groove 21 on the outer peripheral wall of the casing 2, and the top, left and right sides of the receiving groove 21 are open (the left and right
directions are shown by arrow C in Figure 1), and the casing 2 passes through the receiving groove 21 is divided into the outdoor part and the indoor part, at least a part of the window can
be extended into the containing tank 21, the indoor part is provided with an indoor heat exchanger (for example, indoor heat exchanger 500) and an indoor fan ,
□ the outdoor part is provided with an outdoor heat exchanger and an outdoor fan.
□ the chassis 2 includes a chassis 100, a rear box body 23, and a front box body 26 (the front and rear direction is shown by arrow B in FIG. 1), and the rear box body 23 is fixed at the rear
□ the box body 23 and the front box body 26 are installed.
□ the front box body 26 is fixed on the rear box body 23 and the front box body 26, the front box body 26 and the rear box body 23 are arranged at intervals in the front and rear to define the
receiving groove 21, the rear box body 23, the front box body 26, and the rear box body 23
□ the front box body 26 and the front box body 26 are independently processed and molded parts.
□ the rear box body 23 and the front box body 26, the rear box body 23 and the front box body 26 are respectively processed with different materials, for example, the rear box body 23 is a
sheet metal part, and the front box body 26 is a plastic part, which is convenient to improve the casing 2.
□ the middle partition 300 is fixed on the chassis 100 and is located in the receiving groove 21, and the front and rear ends of the middle partition 300 are respectively matched with the rear
box body 23 and the front box body 26. In this way, it is convenient for the lower surface of the window to stop on the intermediate partition 27, which facilitates wiring and drainage of the
window type air conditioner 1 and improves the working reliability of the window type air conditioner 1.
□ the rear box body 23 includes a rear box body seat 24 and a rear box body cover 25.
□ the top of the rear box body seat 24 is open and fixed on the chassis 100.
□ the rear box body cover 25 The outer cover is on the top of the rear box seat 24. In this way, it is convenient to improve the structural flexibility of the rear box 23 and facilitate the
disassembly and installation of parts in the rear box 23.
□ the front box body 24 is a sheet metal part or a plastic part
□ the rear box body 23 is a sheet metal part
□ the middle partition 300 is a plastic part.
□ the window air conditioner 1 further includes a sound insulation member 200, which is provided on the chassis 100 to separate the chassis 100 into an indoor side and an outdoor side.
□ the sound insulation member 200 is connected to the chassis 100 through the central partition 300, and the sound insulation 200 is sandwiched between the chassis 100 and the central partition
□ the sound insulation 200 can be used to isolate the air flow on the indoor and outdoor sides, and it is convenient to seal the installation place of the window air conditioner 1, that is, it
is convenient to seal the space between the window and the installation opening, thereby facilitating the improvement of the window type.
□ the sealing effect of the installation place of the air conditioner 1 is convenient to improve the temperature insulation effect and sound insulation effect between the indoor side and the
outdoor side, avoid the temperature of the outdoor space from affecting the indoors, avoid the noise of the outdoor space from affecting the indoors, and improve the user's use Experience is
convenient to improve the functionality and adaptability of the window air conditioner 1.
□ the sound insulation member 200 by sandwiching the sound insulation member 200 between the chassis 100 and the central partition 300, it is convenient to locate the sound insulation member
200, to facilitate the installation of the sound insulation member 200, and to improve the reliability and accuracy of the installation of the sound insulation member 200. Therefore, it is
convenient to improve the sealing effect of the sound insulation member 200, to improve the sound insulation effect of the sound insulation member 200, and to improve the comfort of the user.
□ the sound insulation member 200 has a long strip shape.
□ the opposite ends of the sound insulation member 200 are a first end 201 and a second end 202.
□ the first end 201 and a side edge of the chassis 100 define a first end.
□ a channel 210, the second end 202 and the other side edge of the chassis 100 define a second channel 220.
□ the first channel 210 and the second channel 220 can be used to form a space connecting the two sides of the soundproof member 200, which is convenient for connecting pipes and draining water
between the indoor side and the outdoor side of the window type air conditioner 1.
□ the first channel 210 can be used for The pipeline passes through and the second channel 220 is used to provide a drainage path, which facilitates the setting of the internal structure of the
window type air conditioner 1, which facilitates the structure of the window type air conditioner 1 to be more reasonable and compact, and facilitates the improvement of the working
performance of the window type air conditioner 1.
□ first channel 210 allows the pipeline to pass through
□ second channel 220 provides a drainage path, so that the pipeline channel and the drainage channel of the window air conditioner 1 can be arranged on both sides of the window air conditioner
1 to avoid pipes.
□ the road channel and the drainage channel influence each other, which is convenient for improving the working reliability and stability of the window air conditioner 1.
□ one end of the central partition 300 has a first extension 310
□ the other end of the central partition 300 has a second extension 320.
□ At least part of the first extension 310 is connected to the first channel.
□ the inner wall surface of 210 is attached to jointly define the first channel 210
□ at least part of the second extension portion 320 is attached to the inner wall surface of the second channel 220 to jointly define the second channel 220, the first extension portion 310 and
the second
□ At least one of the extension parts 320 is connected to the chassis 100. This not only facilitates the installation and arrangement of the sound insulation member 200, facilitates the
connection of the central partition 300 and the chassis 100, but also facilitates the formation of the first channel 210 and the second channel 220.
□ a sponge member or a sealing member is provided in the first channel 210.
□ a sponge member or a sealing member can be used to fill the gap in the first channel 210, which further facilitates the improvement of the sealing effect of the installation place of the
window air conditioner 1.
□ the sound insulation member 200 is a foam member. This not only facilitates the production and processing of the sound insulation member 200, and facilitates the improvement of the production
efficiency of the sound insulation member 200, but also facilitates the improvement of the sealing effect of the sound insulation member 200 and facilitates the sound insulation member 200 to
better isolate noise.
□ the sound insulation member 200 can also be made of materials such as rubber, silica gel, and sponge.
□ the middle partition 300 is connected to the chassis 100 by screws. This is convenient to improve the connection reliability and connection strength between the middle partition 300 and the
chassis 100.
□ the water receiving tray 400 is located on the indoor side, the water receiving tray 400 is connected to the chassis 100, the water receiving tray 400 is provided with a connecting piece 410,
and the connecting piece 410 passes through the second In the channel 220, the connecting member 410 has a drainage channel 411, and the outdoor side communicates with the water receiving pan
400 through the drainage channel 411.
□ the connecting member 410 has a drainage channel 411, and the outdoor side communicates with the water receiving pan 400 through the drainage channel 411.
□ the indoor heat exchanger 500 includes a first heat exchange part 560 and a second heat exchange part 570.
□ the first heat exchange part 560 extends vertically, and the upper end of the second heat exchange part 570 and the second heat exchange part 570
□ the lower end of a heat exchange part 560 is connected, and the lower end of the second heat exchange part 570 extends obliquely in a direction toward the outdoor side. Since the indoor heat
exchanger 500 includes the first heat exchange part 560 extending vertically and the second heat exchange part 570 extending obliquely, it can not only increase the heat exchange area of the
indoor heat exchanger 500 and improve the heat exchange effect, but also reduce the indoor heat exchange.
□ the space occupied by the heat exchanger 500 can thereby reduce the volume of the window air conditioner 1 and reduce the space occupied by the window air conditioner 1.
□ the included angle A between the second heat exchange portion 570 and the horizontal plane has a value range of 35°-55°. Therefore, it can be avoided that the inclination angle of the second
heat exchange part 570 is too large or too small to affect the heat exchange effect and increase the occupied space.
□ the included angle A between the second heat exchange portion 570 and the horizontal plane is 45°.
□ the vertical extension length of the first heat exchange part 560 is H1
□ the oblique extension length of the second heat exchange part 570 is H2, where the value range of H1/H2 is 0.2-0.4. Therefore, the space at the lower part of the indoor side can be reasonably
□ the value of H1/H2 is 0.3.
□ the number of rows of heat exchange tubes 530 of the second heat exchange part 570 is greater than the number of rows of heat exchange tubes 530 of the first heat exchange part 560.
□ the internal space of the indoor part can be effectively utilized, the heat exchange effect of the second heat exchange part 570 can be increased, and the cooling effect of the window air
conditioner 1 can be improved.
□ the number of rows of heat exchange tubes 530 of the second heat exchange part 570 is three rows, and the number of rows of heat exchange tubes 530 of the first heat exchange part 560 is
double rows.
□ the number of rows of heat exchange tubes 530 of the second heat exchange part 570 and the number of rows of heat exchange tubes 530 of the first heat exchange part 560 can be set according
to actual requirements, for example, can be set to be the same.
□ window air conditioner 100 includes a compressor, an outdoor heat exchanger, etc., and operations are known to those of ordinary skill in the art, and will not be described in detail here.
□ Engineering & Computer Science (AREA)
□ Chemical & Material Sciences (AREA)
□ Combustion & Propulsion (AREA)
□ Mechanical Engineering (AREA)
□ General Engineering & Computer Science (AREA)
□ Physics & Mathematics (AREA)
□ Thermal Sciences (AREA)
□ Air Filters, Heat-Exchange Apparatuses, And Housings Of Air-Conditioning Units (AREA)
□ Air-Conditioning Room Units, And Self-Contained Units In General (AREA)
□ Devices For Blowing Cold Air, Devices For Blowing Warm Air, And Means For Preventing Water Condensation In Air Conditioning Units (AREA)
A window-type air conditioner (1), the window-type air conditioner (1) being supported on an opening (5) of a wall body (4), and a movable window (3) being provided within the opening (5), the
window-type air conditioner (1) comprising: a housing (2), an accommodating groove (21) being provided on an outer peripheral wall of the housing (2), at least a portion of the window (3) being
extendable into the accommodating groove (21); an indoor wind wheel (6); an indoor heat exchanger (500), the indoor heat exchanger (500) comprising a first heat exchange portion (560) and a
second heat exchange portion (570), the first heat exchange portion (560) extending vertically, an upper end of the second heat exchange portion (570) being connected to a lower end of the first
heat exchange portion (560), and a lower end of the second heat exchange portion (570) obliquely extending in a direction towards the indoor wind wheel (6); and a filter screen (600).
窗式空调器Window air conditioner
相关申请的交叉引用Cross references to related applications
本申请基于申请号为：201920188070.2、201920188057.7，申请日为2019年02月03日的中国专利申请提出，并要求该中国专利申请的优先权，该中国专利申请的全部内容在此引入本申请作为参考。This application is
based on a Chinese patent application filed with application numbers: 201920188070.2 and 201920188057.7, and the filing date is February 03, 2019, and claims the priority of the Chinese patent
application. The entire content of the Chinese patent application is hereby incorporated into this application for reference .
技术领域Technical field
本申请涉及制冷领域，尤其是涉及一种窗式空调器。This application relates to the field of refrigeration, and in particular to a window air conditioner.
背景技术Background technique
将体积设计的较大，占用大量空间而降低空间利用率。The prior art window type air conditioner is installed on the window of the room, and the window is located above the window type air conditioner.
During the operation of the window type air conditioner, the noise generated by the outdoor compressor will be transmitted to the room and reduce the user's use Comfort. At the same time, in
order to meet the cooling demand, the prior art window air conditioner will be designed to be larger in size, occupy a lot of space and reduce the space utilization rate.
申请内容Application content
application aims to solve at least one of the technical problems existing in the prior art. For this reason, this application proposes a window air conditioner, which can reduce the space
occupied by the indoor heat exchanger and the indoor wind wheel when the indoor heat exchanger and the indoor wind wheel cooperate, reduce the volume of the window air conditioner, and reduce the
space occupied by the window air conditioner .
内换热器的上游侧。According to the window type air conditioner of the embodiment of the present application, the window type air conditioner is supported on a window of a wall, and a movable
window is arranged in the window, and the window type air conditioner includes: a casing, and The outer peripheral wall of the housing is provided with a containing groove, the housing is divided
into an indoor part and an outdoor part by the containing groove, at least a part of the window can be extended into the containing groove, and the indoor part is provided with an air inlet And
an air outlet; an indoor wind wheel, the indoor wind wheel is arranged in the indoor part; an indoor heat exchanger, the indoor heat exchanger is arranged in the indoor part, the indoor heat
exchanger includes a first heat exchanger The hot part and the second heat exchange part, the first heat exchange part extends vertically, the upper end of the second heat exchange part is
connected to the lower end of the first heat exchange part, and the lower end of the second heat exchange part It extends obliquely in the direction toward the indoor wind wheel; the filter
screen, in the air flow direction, the filter screen is located on the upstream side of the indoor heat exchanger.
也少于现有技术的密封组件，节约成本。According to the window type air conditioner of the embodiment of the present application, by arranging a receiving groove on the cabinet, at least a part of
the window can extend into the receiving groove, so that the window can be used to fix the window type air conditioner to a certain extent. Avoid the window air conditioner from falling. The
windows that extend into the receiving groove can have a certain sound insulation effect, heat insulation effect and sealing effect, and improve the user comfort. At the same time, the user can
choose whether to set it for sealing according to actual needs. Even if the sealing component is provided for the sealing component of the space between the window and the window, the material of
the sealing component used in the window air conditioner of the embodiment of the present application is less than that of the prior art sealing component, which saves cost.
的体积，减小窗式空调器的占用空间。At the same time, because the indoor heat exchanger includes a vertically extending first heat exchange part and an obliquely extending second heat exchange
part, it can not only increase the heat exchange area of the indoor heat exchanger and improve the heat exchange effect, but also reduce the number of indoor heat exchangers. The space occupied
by the two when matched with the indoor wind wheel can reduce the volume of the window air conditioner and reduce the space occupied by the window air conditioner.
在本申请的一些实施例中，所述第二换热部分与水平面之间的夹角A，所述夹角A的取值范围为35°-55°。In some embodiments of the present application, the included angle A between the second heat exchange
portion and the horizontal plane has a value range of 35°-55°.
在本申请的一些实施例中，所述第一换热部分的竖直延伸长度为H1，所述第二换热部分的倾斜延伸长度为H2，其中H1/H2的取值范围为：0.2～0.4。In some embodiments of the present application, the vertical
extension length of the first heat exchange part is H1, and the oblique extension length of the second heat exchange part is H2, and the value range of H1/H2 is 0.2~ 0.4.
向所述室内风轮的方向倾斜延伸。In some embodiments of the present application, the filter screen is spaced apart from the indoor heat exchanger, the filter screen includes a first filter part and
a second filter part, the first filter part extends vertically, and the The upper end of the second filter part is connected with the lower end of the first filter part, and the lower end of the
second filter part extends obliquely in a direction toward the indoor wind wheel.
在本申请的一些实施例中，所述第一过滤部与所述第一换热部分之间的间距为d1，所述第二过滤部与所述第二换热部分之间的间距为d2，其中d1/d2＝0.9～1.2。In some embodiments of the present application, the
distance between the first filter part and the first heat exchange part is d1, and the distance between the second filter part and the second heat exchange part is d2 , Where d1/d2=0.9～1.2.
在本申请的一些实施例中，所述室内部分的顶部设有所述出风口，所述出风口所在的平面为出风面，所述出风面在由下至上的方向上朝向后倾斜延伸。In some embodiments of the present application, the top of the
indoor part is provided with the air outlet, the plane on which the air outlet is located is the air outlet surface, and the air outlet surface extends obliquely backwards in a bottom-up
direction .
可选地，所述出风面与竖直面之间的夹角为B，所述夹角B的取值范围为50°-66°。Optionally, the included angle between the air outlet surface and the vertical surface is B, and the value range of the
included angle B is 50°-66°.
在本申请的一些实施例中，所述第二换热部分的换热管的排数大于所述第一换热部分的换热管的排数。In some embodiments of the present application, the number of rows of heat exchange tubes in the second
heat exchange part is greater than the number of rows of heat exchange tubes in the first heat exchange part.
纳槽。In some embodiments of the present application, the cabinet includes: a chassis; a rear box body, the rear box body is fixed on the chassis, the rear box body contains an outdoor heat
exchanger; a front box body, The front box body is fixed on the chassis, and the front box body and the rear box body are spaced back and forth to define the receiving groove.
在本申请的一些实施例中，所述室内换热器具有边板组件；所述窗式空调器还包括接水盘，所述接水盘上设有肋板组件，所述肋板组件用于支撑所述边板组件，所述接水盘设于所述换热器组件的下方。In some embodiments
of the present application, the indoor heat exchanger has a side plate assembly; the window air conditioner further includes a water receiving tray, the water receiving tray is provided with a
rib assembly, and the rib assembly is used for To support the side plate assembly, the water receiving pan is arranged below the heat exchanger assembly.
板用于支撑所述第一边板，所述第二肋板用于支撑所述第二边板。In some embodiments of the present application, the rib assembly includes a first rib and a second rib that are spaced apart, the side
plate assembly includes a first side plate and a second side plate, the first side plate Is arranged at one end of the heat exchanger assembly, the heat exchange tubes of the heat exchanger
assembly pass through the first side plate, the first rib is used to support the first side plate, and the The two ribs are used to support the second side plate.
所述第二肋板通过螺钉连接。In some embodiments of the present application, the first side plate has a first flange, the first flange is attached to the first rib, and the first flange is connected
to the first rib. Connected by screws; the second side plate has a second flange, the second flange is attached to the second rib, and the second flange is connected with the second rib by
在本申请的一些实施例中，所述第一翻边朝向所述第二边板的方向延伸，所述第二翻边朝向所述第一边板的方向延伸。In some embodiments of the present application, the first flange extends toward the
direction of the second side board, and the second flange extends toward the direction of the first side board.
在本申请的一些实施例中，所述第一翻边和所述第二翻边均具有支耳，所述支耳上设有螺钉孔。In some embodiments of the present application, both the first flange and the second flange have lugs, and
screw holes are provided on the lugs.
在本申请的一些实施例中，所述第一肋板和所述第二肋板均具有倾斜支撑面，所述倾斜支撑面用于支撑所述第二换热部分的朝向所述接水盘的部分表面。In some embodiments of the present application, the first rib
and the second rib each have an inclined support surface, and the inclined support surface is used to support the second heat exchange part facing the water receiving tray. Part of the surface.
在本申请的一些实施例中，所述第一肋板和所述第二肋板均具有过水孔。In some embodiments of the present application, both the first rib and the second rib have water passing holes.
在本申请的一些实施例中，所述接水盘上设有辅助接水部，所述辅助接水部用于承接冷媒管的冷凝水，所述辅助接水部与所述过水孔连通。In some embodiments of the present application, an auxiliary water
receiving portion is provided on the water receiving pan, the auxiliary water receiving portion is used to receive the condensed water of the refrigerant pipe, and the auxiliary water receiving
portion is in communication with the water passing hole .
在本申请的一些实施例中，所述第一肋板上设有所述过水孔，所述排水通道位于所述第一肋板的背离所述第二肋板的一侧。In some embodiments of the present application, the first rib is provided with the
water passing hole, and the drainage channel is located on a side of the first rib facing away from the second rib.
在本申请的一些实施例中，所述接水盘上设有第一配合部，所述过滤网具有与所述第一配合部相适配的第二配合部。In some embodiments of the present application, a first matching portion is provided on the
water receiving tray, and the filter screen has a second matching portion that matches the first matching portion.
在本申请的一些实施例中，所述第一配合部和所述第二配合部中的一个为插接条，另一个为与所述插接条相适配的滑槽。In some embodiments of the present application, one of the first matching portion and the
second matching portion is a plug-in strip, and the other is a sliding groove that matches the plug-in strip.
本申请的附加方面和优点将在下面的描述中部分给出，部分将从下面的描述中变得明显，或通过本申请的实践了解到。The additional aspects and advantages of the present application will be partially given in
the following description, and some will become obvious from the following description, or be understood through the practice of the present application.
附图说明Description of the drawings
本申请的上述和/或附加的方面和优点从结合下面附图对实施例的描述中将变得明显和容易理解，其中：The above and/or additional aspects and advantages of the present application will become obvious and
easy to understand from the description of the embodiments in conjunction with the following drawings, in which:
图1为根据本申请实施例的窗式空调器的剖视图；Figure 1 is a cross-sectional view of a window air conditioner according to an embodiment of the present application;
图2为根据本申请实施例的窗式空调器安装在窗口上的示意图；Figure 2 is a schematic diagram of a window air conditioner installed on a window according to an embodiment of the present application;
图3为根据本申请实施例的蒸发器和过滤网的配合立体图；Figure 3 is a three-dimensional view of the cooperation of the evaporator and the filter screen according to an embodiment of the present
图4为根据本申请实施例的蒸发器和过滤网的配合侧视图；Figure 4 is a side view of the mating evaporator and filter screen according to an embodiment of the present application;
图5为根据本申请实施例的窗式空调器的局部示意图。Fig. 5 is a partial schematic diagram of a window air conditioner according to an embodiment of the present application.
图6是根据本申请实施例的窗式空调器的结构示意图。Fig. 6 is a structural diagram of a window air conditioner according to an embodiment of the present application.
图7是根据本申请实施例的窗式空调器的爆炸图。Fig. 7 is an exploded view of a window air conditioner according to an embodiment of the present application.
图8是根据本申请实施例的窗式空调器的局部结构示意图。Fig. 8 is a partial structural diagram of a window air conditioner according to an embodiment of the present application.
图9是根据本申请实施例的窗式空调器的局部结构示意图。Fig. 9 is a partial structural diagram of a window air conditioner according to an embodiment of the present application.
图10是根据本申请实施例的窗式空调器的局部结构示意图。Fig. 10 is a partial structural diagram of a window air conditioner according to an embodiment of the present application.
图11a是根据本申请实施例的窗式空调器的局部结构示意图。Fig. 11a is a partial structural diagram of a window air conditioner according to an embodiment of the present application.
图11b是根据本申请实施例的窗式空调器的另一视角局部结构示意图。Fig. 11b is another view of the partial structure of the window air conditioner according to the embodiment of the present
图11c是根据本申请实施例的窗式空调器的又一视角局部结构示意图。Fig. 11c is a partial structural diagram of the window air conditioner according to the embodiment of the present application from
another perspective.
图12是根据本申请实施例的窗式空调器的局部结构示意图。Fig. 12 is a partial structural diagram of a window air conditioner according to an embodiment of the present application.
图13是根据本申请实施例的窗式空调器的接水盘的结构示意图。Fig. 13 is a schematic structural diagram of a water receiving pan of a window air conditioner according to an embodiment of the present
图14是根据本申请实施例的窗式空调器的剖视图。Fig. 14 is a cross-sectional view of a window air conditioner according to an embodiment of the present application.
图15是根据本申请实施例的窗式空调器的换热器组件和过滤网的结构示意图。Fig. 15 is a structural schematic diagram of a heat exchanger assembly and a filter screen of a window air conditioner
according to an embodiment of the present application.
图16是根据本申请实施例的窗式空调器的立体图。Fig. 16 is a perspective view of a window air conditioner according to an embodiment of the present application.
图17是根据本申请实施例的窗式空调器的爆炸图。Fig. 17 is an exploded view of a window air conditioner according to an embodiment of the present application.
图18是图17中A处的局部放大示意图。Fig. 18 is a partial enlarged schematic diagram of the position A in Fig. 17.
附图标记：Reference signs:
窗式空调器1、窗口5、窗户3、墙体4、Window type air conditioner 1, window 5, window 3, wall 4,
底盘100、室内风轮6、 Chassis 100, indoor wind wheel 6,
隔音件200、第一端201、第二端202、第一通道210、第二通道220、 Sound insulation 200, first end 201, second end 202, first channel 210, second channel 220,
中隔板300、第一延伸部310、第二延伸部320、 Middle partition 300, first extension 310, second extension 320,
接水盘400、连通件410、排水通道411、渐缩段412、第一安装部420、第一肋板421、第二安装部430、第二肋板431、第一配合部440、辅助接水部450、 Drain pan 400, connecting piece 410, drainage channel 411,
tapered section 412, first mounting portion 420, first rib 421, second mounting portion 430, second rib 431, first matching portion 440, auxiliary connection Department of Water 450,
室内换热器500、第三安装部510、第四安装部520、换热管530、第一边板540、第一翻边541、支耳5400，螺钉孔5401、过水孔5402、第二边板550、第一换热部分560、第二换热部分570、 Indoor heat exchanger 500,
third installation part 510, fourth installation part 520, heat exchange tube 530, first side plate 540, first flange 541, lug 5400, screw hole 5401, water hole 5402, second Side plate 550, first
heat exchange part 560, second heat exchange part 570,
过滤网600、第二配合部610、第一过滤部610、第二过滤部612、 Filter 600, second matching portion 610, first filter portion 610, second filter portion 612,
机壳2、容纳槽21、后箱体23、后箱体座24、后箱体盖25、前箱体26、室内部分11、室外部分12、进风口13、出风口14、中间隔板18。 Case 2, containing groove 21, rear box body 23, rear box body seat 24, rear
box body cover 25, front box body 26, indoor part 11, outdoor part 12, air inlet 13, air outlet 14, middle partition 18 .
具体实施方式detailed description
不能理解为对本申请的限制。The embodiments of the present application are described in detail below. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar
reference numerals represent the same or similar elements or elements with the same or similar functions. The embodiments described below with reference to the drawings are exemplary, and are
only used to explain the present application, and cannot be understood as a limitation to the present application.
一”、“第二”的特征可以明示或者隐含地包括一个或者更多个该特征。在本申请的描述中，除非另有说明，“多个”的含义是两个或两个以上。In the description of this application, it should be understood that the
terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", " "Back", "Left", "Right", "Vertical", "Horizontal", "Top", "Bottom", "Inner", "Outer",
"Axial", "Radial", "Circumferential", etc. The indicated orientation or positional relationship is based on the orientation or positional relationship shown in the drawings, and is only for the
convenience of describing the application and simplifying the description, and does not indicate or imply that the pointed device or element must have a specific orientation or a specific
orientation. The structure and operation cannot therefore be understood as a limitation of this application. In addition, the features defined with "first" and "second" may explicitly or
implicitly include one or more of these features. In the description of this application, unless otherwise specified, "plurality" means two or more.
接相连，也可以通过中间媒介间接相连，可以是两个元件内部的连通。对于本领域的普通技术人员而言，可以具体情况理解上述术语在本申请中的具体含义。In the description of this application, it should be
noted that, unless otherwise clearly specified and limited, the terms "installation", "connection" and "connection" should be understood in a broad sense, for example, it can be a fixed
connection or a detachable connection. Connected or integrally connected; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected
through an intermediate medium, and it can be the internal communication between two components. For those of ordinary skill in the art, the specific meanings of the above-mentioned terms in this
application can be understood under specific circumstances.
下面参考附图描述根据本申请实施例的窗式空调器1，其中窗式空调器1支撑在墙体4的窗口5上，窗口5上设有可移动的窗户3。Hereinafter, a window type air conditioner 1 according to an embodiment of the
present application will be described with reference to the drawings. The window type air conditioner 1 is supported on a window 5 of the wall 4, and a movable window 3 is provided on the window
shown in FIG. 1, the window air conditioner 1 according to the embodiment of the present application includes: a casing 2, an indoor wind wheel 6, an indoor heat exchanger 500 and a filter screen
600, wherein the outer peripheral wall of the casing 2 is provided with a receiving groove 21 The housing 2 is divided into an indoor part 11 and an outdoor part 12 by a receiving groove 21. As
shown in FIG. 2, at least a part of the window 3 can be extended into the receiving groove 21, specifically, the top and left side of the receiving groove 21 Both the right side and the right
side are open so that the window 3 can be pulled down into the receiving groove 21. In the specific example of the present application, the distance between the indoor part 11 and the outdoor
part 12 is not adjustable. For example, the chassis of the casing 2 is an integrally formed part.
风口14吹送的空气比较均匀且使得送风距离远。The indoor part 11 is provided with an air inlet 13 and an air outlet 14. The indoor wind wheel 6 is arranged in the indoor part 11. Specifically, when
the indoor wind wheel 6 rotates, the indoor air enters the indoor part 11 from the air inlet 13 and is discharged into the room from the air outlet 14 after heat exchange. Optionally, the indoor
wind wheel 6 may be a through-flow wind wheel, so that the air blown from the air outlet 14 is relatively uniform and the air supply distance is long.
The indoor heat exchanger 500 is arranged in the indoor part 11. The indoor heat exchanger 500 includes a first heat exchange part 560 and a second heat exchange part 570. The first heat exchange
part 560 extends vertically, and the upper end of the second heat exchange part 570 Connected to the lower end of the first heat exchange part 560, the lower end of the second heat exchange part
570 extends obliquely in the direction toward the indoor wind wheel 6. That is, the second heat exchange part 570 is located at the lower part of the first heat exchange part 560, there is an
angle between the first heat exchange part 560 and the second heat exchange part 570, and the indoor wind wheel 6 is located in the first heat exchange part 560. And the second heat exchanging
part 570 defines the included angle area. In the specific example of the present application, the indoor heat exchanger 500 is located on the air inlet side of the indoor wind wheel 6, so as to
ensure the heat exchange effect. It can be understood that the first heat exchange part 560 and the second heat exchange part 570 can be defined by the bending of one heat exchanger, and the
first heat exchange part 560 and the second heat exchange part 570 can also be two independent heat exchange parts. Heater.
着在室内换热器500上而影响室内换热器500的换热效果，同时可以提高从出风口14排向室内的空气的洁净度。In the air flow direction, the filter screen 600 is located on the upstream side of the indoor heat
exchanger 500. In other words, the air entering the indoor part 11 is filtered by the filter 600 and then flows to the indoor heat exchanger 500 for heat exchange, so that the air is filtered
through the filter 600, which can prevent dust and other substances from directly adhering to the room. The heat exchanger 500 affects the heat exchange effect of the indoor heat exchanger 500,
and at the same time can improve the cleanliness of the air discharged from the air outlet 14 into the room.
窗式空调器设置开口朝下的安装空间，墙体4伸入到安装空间内以支撑窗式空调器，这种方式使得窗式空调器的顶板承受较大的作用力，使得窗式空调器存在因顶板断裂而掉落的安全隐患。It should be noted that some
window air conditioners in the prior art are directly placed on the window 5, and more sealing components are required between the window air conditioner and the window 5, and between the window
3 and the window sill to achieve a sealing effect. , It is not only inconvenient to install the window air conditioner but also increases the sealing cost. In the prior art, some window air
conditioners are provided with an installation space with an opening facing downward. The wall 4 extends into the installation space to support the window air conditioner. In this way, the top
plate of the window air conditioner bears greater force. , So that the window air conditioner has the potential safety hazard of falling due to the break of the top plate.
的密封组件的材料也少于现有技术的密封组件，节约成本。According to the window type air conditioner 1 of the embodiment of the present application, by providing a receiving groove 21 on the cabinet
2, at least a part of the window 3 can extend into the receiving groove 21, so that the window 3 can be used to fix the window type air conditioner 1 Play a certain positioning function to
prevent the window air conditioner 1 from falling, and the window 3 that extends into the receiving groove 21 can have a certain sound insulation effect, heat insulation effect and sealing
effect, and improve the user's comfort. It is possible to choose whether to provide a sealing component for sealing the space between the window 3 and the window 5 according to actual needs. Even
if the sealing component is provided, the material of the sealing component used in the window type air conditioner 1 of the embodiment of the present application is less than that of the prior
art The sealed components save costs.
以减小窗式空调器1的体积，减小窗式空调器1的占用空间。At the same time, because the indoor heat exchanger 500 includes a first heat exchange part 560 extending vertically and a second heat exchange
part 570 extending obliquely, it can not only increase the heat exchange area of the indoor heat exchanger 500 and improve the heat exchange effect, but also reduce The space occupied by the
indoor heat exchanger 500 and the indoor wind wheel 6 when they are matched can reduce the volume of the window air conditioner 1 and reduce the space occupied by the window air conditioner 1.
换热部分570与水平面之间的夹角A为45°。In some embodiments of the present application, as shown in FIGS. 3 and 4, the included angle A between the second heat exchange portion 570 and the
horizontal plane has a value range of 35°-55°. Therefore, it can be avoided that the inclination angle of the second heat exchange part 570 is too large or too small to affect the heat exchange
effect and increase the occupied space. Preferably, the included angle A between the second heat exchange portion 570 and the horizontal plane is 45°.
取值为0.3。As shown in Figures 3 and 4, in some embodiments of the present application, the vertical extension length of the first heat exchange portion 560 is H1, and the oblique extension
length of the second heat exchange portion 570 is H2, where H1/H2 The value range is 0.2 to 0.4. Therefore, the space under the indoor wind wheel 6 can be reasonably used. Preferably, the value
of H1/H2 is 0.3.
状相同或者相似，可以减少涡流的产生，有利于降噪，还可以保证送风均匀性。In some embodiments of the present application, as shown in FIGS. 3 and 4, the filter screen 600 is spaced apart from the
indoor heat exchanger 500, and the filter screen 600 includes a first filter part 610 and a second filter part 612. The first filter part 610 extends vertically, the upper end of the second
filter portion 612 is connected to the lower end of the first filter portion 610, and the lower end of the second filter portion 612 extends obliquely in the direction toward the indoor wind
wheel 6. Specifically, the second filter portion 612 is located at the lower portion of the first filter portion 610, and the inclination angle of the second filter portion 612 may be the same as
or different from the second heat exchange portion 570. Therefore, by making the shape of the filter screen 600 the same or similar to the shape of the indoor heat exchanger 500, the generation
of eddy currents can be reduced, which is beneficial to noise reduction and can also ensure the uniformity of air supply.
定的关系值，便于过滤网600的安装。同时由于过滤网600与室内换热器500之间的间距比较均匀，可以进一步减少涡流的产生，有利于降噪。As shown in FIG. 4, in some embodiments of the present application, the
distance between the first filter part 610 and the first heat exchange part 560 is d1, and the distance between the second filter part 612 and the second heat exchange part 570 Is d2, d1/d2 = 0.9
to 1.2. In this way, not only the uniformity of the air supply can be ensured, but also the ratio of the passing distance meets a certain relationship value, which facilitates the installation of
the filter 600. At the same time, since the distance between the filter screen 600 and the indoor heat exchanger 500 is relatively uniform, the generation of eddy currents can be further reduced,
which is beneficial to noise reduction.
在本申请的一些实施例中，机壳2内设有滑槽，过滤网600可抽拉地与滑槽配合，从而可以便于过滤网600的拆卸清洗，且便于过滤网600的安装。In some embodiments of the present application, the casing 2 is
provided with a sliding groove, and the filter screen 600 can be pulled and matched with the sliding groove, so as to facilitate the disassembly and cleaning of the filter screen 600 and the
installation of the filter screen 600.
得出风口14倾斜设置，从出风口14吹出的风可以朝上吹送，防止风直吹人，可以提高制冷速度，同时还有利于增大出风口14的出风面积。有利于缩短室内部分11上部的风道长度，避免冷量损失。As shown in Figure 1, in
some embodiments of the present application, an air outlet 14 is provided on the top of the indoor part 11, and the plane on which the air outlet 14 is located is the air outlet surface, and the
air outlet surface is inclined backward in a bottom-up direction extend. That is to say, as shown in Fig. 1, in the direction from the inside to the outside, the air outlet surface extends
obliquely upward so that the air outlet 14 is arranged obliquely, and the wind blown from the air outlet 14 can be blown upward to prevent the wind from blowing directly. The cooling speed can be
increased, and at the same time, the air outlet area of the air outlet 14 can be increased. It is beneficial to shorten the length of the air duct at the upper part of the indoor part 11 and
avoid loss of cooling capacity.
上部的风道长度，避免冷量损失。优选地，夹角B的取值范围为55°-62°。Optionally, as shown in Fig. 1, the included angle between the air outlet surface and the vertical surface is B, and the value
range of the included angle B is 50°-66°. Therefore, it is possible to avoid the influence of the air outlet effect due to the too large or too small included angle B, to ensure that the wind is
prevented from blowing people directly, and it is also beneficial to increase the air outlet area of the air outlet 14. It is beneficial to shorten the length of the air duct at the upper part of
the indoor part 11 and avoid loss of cooling capacity. Preferably, the value range of the included angle B is 55°-62°.
求进行设定，例如可以设定为相同。In some embodiments of the present application, the number of rows of heat exchange tubes in the second heat exchange part 570 is greater than the number of rows
of heat exchange tubes in the first heat exchange part 560. Thereby, the internal space of the indoor part 11 can be effectively used, the heat exchange effect of the second heat exchange part
570 can be increased, and the cooling effect of the window air conditioner 1 can be improved. In some examples of this application, as shown in FIGS. 3 and 4, the number of rows of heat exchange
tubes in the second heat exchange part 570 is three rows, and the number of heat exchange tubes in the first heat exchange part 560 is double rows. . Of course, it can be understood that the
number of rows of heat exchange tubes of the second heat exchange part 570 and the number of rows of heat exchange tubes of the first heat exchange part 560 can be set according to actual
requirements, for example, can be set to be the same.
壳2的外观美观性。As shown in FIG. 5, in some embodiments of the present application, the casing 2 includes: a chassis 100, a rear box body 23, and a front box body 26. The rear box body 23 is
fixed on the chassis 100, and the rear box body 23 contains There are outdoor heat exchangers. The front box body 26 is fixed on the chassis 100, and the front box body 26 and the rear box body
23 are spaced back and forth to define the receiving groove 21. The indoor part 11 includes a front box 26 and a part of the chassis 100, and the outdoor part 12 includes a rear box 23 and
another part of the chassis 100. This not only facilitates the formation of the receiving groove 2121, facilitates the matching of the window type air conditioner 10 with the window 3, but also
facilitates the processing and manufacturing of the cabinet 2 and improves the appearance and aesthetics of the cabinet 2.
进行走线和排水，便于提高窗式空调器1的工作可靠性。More specifically, as shown in FIG. 5, the casing 2 further includes an intermediate partition 18, which is fixed on the chassis 100 and is
located in the accommodating groove 21. The front and rear ends of the intermediate partition 18 are respectively connected to the rear box body. 23 cooperates with the front box 26. In this way,
it is convenient for the lower surface of the window 3 to stop on the intermediate partition 18, which facilitates the wiring and drainage of the window type air conditioner 1 and facilitates the
improvement of the working reliability of the window type air conditioner 1.
安装。Optionally, as shown in FIG. 5, the rear box body 23 includes a rear box body seat 24 and a rear box body cover 25. The top of the rear box body seat 24 is open and fixed on the chassis
100, and the rear box body cover 25 covers the rear The top of the box seat 24. In this way, it is convenient to improve the structural flexibility of the rear box 23 and facilitate the
disassembly and installation of parts in the rear box 23.
进一步地，前箱体26为钣金件或塑料件，后箱体23为钣金件，中间隔板18为塑料件。Further, the front box body 26 is a sheet metal part or a plastic part, the rear box body 23 is a sheet metal part, and
the middle partition 18 is a plastic part.
如图6-图18所示，根据本申请实施例的窗式空调器1包括接水盘400和室内换热器500。As shown in FIGS. 6-18, the window air conditioner 1 according to the embodiment of the present application includes a
water receiving tray 400 and an indoor heat exchanger 500.
效率。Specifically, the indoor heat exchanger 500 has a side plate assembly, the water receiving pan 400 is provided with a rib assembly, and the rib assembly is used to support the side plate
assembly, and the water receiving pan 400 is arranged under the indoor heat exchanger 500. It should be noted that according to the window type air conditioner 1 of the embodiment of the present
application, the side plate assembly is provided in the indoor heat exchanger 500 to realize the assembly connection with the water receiving tray 400, preventing the water receiving tray 400
from being directly connected to the indoor The heat exchange body of the heat exchanger 500 is in contact with each other, thereby preventing the fins on the indoor heat exchanger 500 from being
squeezed by the water receiving pan 400, thereby improving the structural integrity of the fins, thereby improving the exchange rate of the indoor heat exchanger 500 Thermal efficiency.
间。另外，将室内换热器500与接水盘400装配完成后，还可以提升室内换热器500与接水盘400的装配稳定性。As shown in FIGS. 12 and 13, according to some embodiments of the present application, the rib
assembly may include a first rib 421 and a second rib 431 that are spaced apart. Specifically, the side plate assembly may include a first side plate 540 and a second side plate 550. The first
side plate 540 is provided at one end of the indoor heat exchanger 500, and the heat exchange tube of the indoor heat exchanger 500 is passed through the first side plate. One side plate 540, the
first rib 421 is used to support the first side plate 540, and the second rib 431 is used to support the second side plate 550. In this way, the first rib 421 and the second rib 431 can be used
to separate the indoor heat exchanger 500 from the water receiving tray 400 to provide an operation space for the assembly of the indoor heat exchanger 500. In addition, after the indoor heat
exchanger 500 and the water tray 400 are assembled, the assembly stability of the indoor heat exchanger 500 and the water tray 400 can also be improved.
接水盘400的装配稳定性，第一翻边541和第二翻边均朝向窗式空调器1的室内侧的中心翻折。Further, as shown in Figures 12 and 13, the first side plate 540 has a first flange 541, the first flange 541 is
attached to the first rib 421, and the first flange 541 is connected to the first rib. 421 is connected by screws. Therefore, the assembly stability of the indoor heat exchanger 500 and the water
receiving tray 400 can be improved. Similarly, the second side plate 550 has a second flange, the second flange is attached to the second rib 431, and the second flange is connected to the second
rib 431 by screws. Therefore, the assembly stability of the indoor heat exchanger 500 and the water receiving tray 400 can be further improved. In some embodiments, in order to further improve
the assembly stability of the indoor heat exchanger 500 and the drain pan 400, both the first flange 541 and the second flange are directed toward the center of the indoor side of the window air
conditioner 1. Turn over.
稳定性。In some embodiments, the first flange 541 extends toward the direction of the second side plate 550, and the second flange extends toward the direction of the first side plate 540,
thereby avoiding the first flange when welding the indoor heat exchanger 500. The first flange 541 or the second flange is deformed due to the high temperature of welding, so that the structural
stability of the side plate assembly can be improved.
，将第二翻边与第二肋板431连接在一起。在一些实施例中，为了提高第一肋板421或第二肋板431的稳定性，第一肋板421和第二肋板431中的至少一个呈三角形。As shown in FIG. 12, in order to facilitate the
connection of the indoor heat exchanger 500 and the water receiving tray 400, in some embodiments, one of the first flange 541 and the second flange has a lug 5400, and a lug 5400 Screw holes
5401 are provided on it. That is, the first flange 541 and the first rib 421 can be fixedly connected with screws, and the second flange and the second rib 431 can be connected together. In some
embodiments, in order to improve the stability of the first rib 421 or the second rib 431, at least one of the first rib 421 and the second rib 431 has a triangular shape.
，第二换热部分570的上端与第一换热部分560的下端相连，第二换热部分560的下端沿朝向室外部分的方向倾斜延伸，倾斜支撑面用于支撑第二换热部分560的朝向接水盘400的部分表面。As shown in FIG. 12, in some
embodiments, both the first rib 421 and the second rib 431 have inclined supporting surfaces, and the inclined supporting surfaces may be used to support the indoor heat exchanger. As shown in
FIG. 14, the indoor heat exchanger 500 may include a first heat exchange part 560 and a second heat exchange part 570. The first heat exchange part 560 extends vertically, and the upper end of
the second heat exchange part 570 exchanges with the first heat exchange part. The lower end of the part 560 is connected, and the lower end of the second heat exchange part 560 extends obliquely
in the direction toward the outdoor part, and the inclined support surface is used to support a part of the surface of the second heat exchange part 560 facing the water receiving tray 400.
400上可以设有连通件410，连通件410内具有排水通道411，过水孔5402可以与排水通道411连通。In order to improve the drainage performance of the water receiving tray 400, in some embodiments, as shown in
FIGS. 8 and 13, at least one of the first rib 421 and the second rib 431 has a water passing hole 5402. It should be noted that the condensed water may flow to the drainage structure of the water
receiving pan 400 through the water passage 5402, such as the connecting member 410 and the drainage channel 450. As shown in FIG. 13, in some embodiments, an auxiliary water receiving part 450
may be provided on the water receiving tray 400, and the auxiliary water receiving part 450 is used to receive the condensed water of the refrigerant pipe. The holes 5402 are connected, so that
the condensed water can be drained smoothly. In some embodiments, a connecting member 410 may be provided on the water receiving tray 400, and the connecting member 410 has a drainage channel 411
therein, and the water passage hole 5402 may communicate with the drainage channel 411.
下面参考附图描述根据本申请实施例的窗式空调器1。Hereinafter, a window air conditioner 1 according to an embodiment of the present application will be described with reference to the drawings.
如图6-图18所示，根据本申请实施例的窗式空调器1包括接水盘400和室内换热器500。As shown in Figs. 6-18, the window air conditioner 1 according to the embodiment of the present application includes a
water receiving tray 400 and an indoor heat exchanger 500.
接水盘400上设有间隔开的第一安装部420和第二安装部430。室内换热器500具有第三安装部510和第四安装部520，第一安装部420与第三安装部510连接，第二安装部430与第四安装部520连接。The water receiving tray
400 is provided with a first mounting portion 420 and a second mounting portion 430 spaced apart. The indoor heat exchanger 500 has a third installation part 510 and a fourth installation part
520, the first installation part 420 is connected to the third installation part 510, and the second installation part 430 is connected to the fourth installation part 520.
以保证接水盘400与室内换热器500之间的连接可靠性和稳定性，便于提高窗式空调器1的结构强度和稳定性，便于提高窗式空调器1的工作性能。According to the window air conditioner 1 of the embodiment of the
present application, by providing the first installation part 420, the second installation part 430, the third installation part 510 and the fourth installation part 520, it is convenient for the
water receiving tray 400 and the indoor heat exchanger 500 The connection not only facilitates the improvement of the efficiency of disassembly and assembly of the water tray 400 and the indoor
heat exchanger 500, but also ensures the reliability and stability of the connection between the water tray 400 and the indoor heat exchanger 500, and facilitates the improvement of the window
air conditioner. The structural strength and stability of 1 are convenient to improve the working performance of the window air conditioner 1.
addition, by connecting the drain pan 400 and the indoor heat exchanger 500 through the first mounting portion 420 and the third mounting portion 510, and the second mounting portion 430 and the
fourth mounting portion 520, respectively, the drain pan 400 can be connected to The force between the indoor heat exchanger 500 is more uniform, avoiding excessive local stress on the connection
between the water receiving pan 400 and the indoor heat exchanger 500, thereby avoiding damage to the water receiving pan 400 and the indoor heat exchanger 500, and facilitating improvement The
service life of the water receiving tray 400 and the indoor heat exchanger 500 further facilitates the improvement of the structural stability of the window type air conditioner 1 and further
facilitates the improvement of the working reliability of the window type air conditioner 1.
因此，根据本申请实施例的窗式空调器1具有便于装配、结构可靠等优点。Therefore, the window air conditioner 1 according to the embodiment of the present application has the advantages of easy assembly
and reliable structure.
下面参考附图描述根据本申请具体实施例的窗式空调器1。Hereinafter, a window air conditioner 1 according to a specific embodiment of the present application will be described with reference to the
在本申请的一些具体实施例中，如图6-图18所示，根据本申请实施例的窗式空调器1包括接水盘400和室内换热器500。In some specific embodiments of the present application, as shown in FIGS. 6 to 18, the
window air conditioner 1 according to the embodiment of the present application includes a water receiving tray 400 and an indoor heat exchanger 500.
530连接，第四安装部520设于第二边板550。这样便于第三安装部510和第四安装部520的加工设置，进一步便于接水盘400与室内换热器500相连接。Specifically, as shown in FIG. 6, the indoor heat exchanger 500
includes a heat exchange tube 530, a first side plate 540, and a second side plate 550. The first side plate 540 is provided on one side of the heat exchange tube 530 and exchanges heat with each
other. The pipe 530 is connected, and the third mounting portion 510 is provided on the first side plate 540. The second side plate 550 is disposed on the other side of the heat exchange tube 530
and connected to the heat exchange tube 530, and the fourth mounting portion 520 is disposed on the second side plate 550. This facilitates the processing and setting of the third installation
portion 510 and the fourth installation portion 520, and further facilitates the connection between the water receiving tray 400 and the indoor heat exchanger 500.
提高第三安装部510和第四安装部520的生产效率和结构强度，进一步便于提高接水盘400与室内换热器500之间的连接强度。More specifically, as shown in FIG. 6, the first side plate 540 has a first flange, and
the first flange is configured as a third mounting portion 510. The second side plate 550 has a second flange, and the second flange is configured as a fourth mounting portion 520. This
facilitates the processing and molding of the third installation part 510 and the fourth installation part 520, facilitates the improvement of the production efficiency and structural strength of
the third installation part 510 and the fourth installation part 520, and further facilitates the improvement of the water tray 400 and the indoor heat exchanger 500 The strength of the
可选地，第一边板540为钣金件，第二边板550为塑料件。这样便于室内换热器500的装配成型，便于室内换热器500与接水盘400相配合，便于简化室内换热器500 的装配工艺，便于提高室内换热器500的装配效率。
Optionally, the first side plate 540 is a sheet metal part, and the second side plate 550 is a plastic part. This facilitates the assembly and molding of the indoor heat exchanger 500,
facilitates the cooperation of the indoor heat exchanger 500 with the water receiving tray 400, facilitates the simplification of the assembly process of the indoor heat exchanger 500, and
improves the assembly efficiency of the indoor heat exchanger 500.
证接水盘400与室内换热器500之间可靠地连接。同时，可以便于接水盘400与室内换热器500的安装和拆卸，便于提高窗式空调器1的生产效率，便于降低窗式空调器1的维护成本。Specifically, the first mounting
portion 420 and the third mounting portion 510 are clamped or connected by screws. The second mounting portion 430 and the fourth mounting portion 520 are clamped or connected by screws. In this
way, the first installation portion 420 and the third installation portion 510, and the second installation portion 430 and the fourth installation portion 520 can be firmly installed to ensure a
reliable connection between the water receiving tray 400 and the indoor heat exchanger 500. At the same time, the installation and disassembly of the water receiving tray 400 and the indoor heat
exchanger 500 can be facilitated, the production efficiency of the window air conditioner 1 can be improved, and the maintenance cost of the window air conditioner 1 can be reduced.
配合，便于提高过滤网600的装配效率。Optionally, as shown in FIGS. 10 and 12-13, a first matching portion 440 is provided on the water receiving tray 400, and the window air conditioner 1 further
includes a filter 600, which has a first matching portion 440 A second matching portion 610 that matches. This facilitates the installation and setting of the filter screen 600, facilitates the
cooperation of the filter screen 600 with the water receiving tray 400, and facilitates the improvement of the assembly efficiency of the filter screen 600.
可靠性，便于将过滤网600顺畅地安装到接水盘400上。Further, one of the first mating portion 440 and the second mating portion 610 is a plug-in strip, and the other is a sliding groove that matches
the plug-in strip. In this way, the first matching portion 440 and the second matching portion 610 can be used to position and guide the installation of the filter screen 600, which is convenient
for improving the accuracy and reliability of the installation of the filter screen 600, and facilitates the smooth installation of the filter screen 600 to the drain pan. 400 up.
Specifically, as shown in FIG. 13, a connecting piece 410 is provided on the water receiving tray 400, and the connecting piece 410 has a drainage channel 411. In this way, the connecting member
410 can be used to discharge the condensed water in the water receiving pan 400, avoiding excessive accumulation of condensate water in the water receiving pan 400, and improving the working
reliability of the water receiving pan 400.
更为具体地，连通件410与第二安装部430连接。这样便于连通件410的安装设置，便于提高连通件410的排水性能。More specifically, the connecting member 410 is connected to the second mounting part 430. This
facilitates the installation and arrangement of the connecting member 410, and improves the drainage performance of the connecting member 410.
进一步便于接水盘400内冷凝水顺畅地排出，便于提高接水盘400的排水效果。Further, as shown in FIG. 13, at least a part of the drainage channel 411 is a tapered section 412, and the cross-sectional
area of the tapered section 412 gradually decreases. Further, from the indoor side to the outdoor side, the cross-sectional area of the tapered section 412 gradually decreases. This facilitates
the improvement of the drainage capacity of the drainage channel 411, and further facilitates the smooth discharge of the condensed water in the water receiving tray 400, which is convenient for
improving the drainage effect of the water receiving tray 400.
可选地，排水通道411的内底壁为倾斜面。这样便于冷凝水在排水通道411内进行流动，便于提高排水通道411的排水效果。Optionally, the inner bottom wall of the drainage channel 411 is an inclined surface. In
this way, it is convenient for the condensed water to flow in the drainage channel 411, and it is convenient to improve the drainage effect of the drainage channel 411.
进一步地，从所述室内侧到所述室外侧的方向上，排水通道411的内底壁逐渐向所述室外侧倾斜。这样便于接水盘400内的冷凝水在重力的作用下顺畅排出，便于提高接水盘400的排水效率。Further, from the indoor side
to the outdoor side, the inner bottom wall of the drainage channel 411 gradually inclines toward the outdoor side. In this way, it is convenient for the condensed water in the water receiving
tray 400 to be smoothly discharged under the action of gravity, and it is convenient to improve the drainage efficiency of the water receiving tray 400.
部420和第二安装部430 的加工设置，便于第一安装部420和第二安装部430分别与第三安装部510和第四安装部520相配合，进一步便于接水盘400与室内换热器500相连接。Specifically, the water receiving tray 400
includes a first rib and a second rib. The first rib is provided on one side of the water receiving tray 400, and the first rib is configured as a first mounting portion 420. The second rib is
provided on the other side of the water receiving tray 400, and the second rib is configured as a second mounting portion 430. This facilitates the processing and setting of the first
installation part 420 and the second installation part 430, and facilitates the first installation part 420 and the second installation part 430 to cooperate with the third installation part 510
and the fourth installation part 520 respectively, and further facilitates the water receiving tray 400 is connected to the indoor heat exchanger 500.
于提高窗式空调器1安装后室内侧和室外侧之间的密封性能。同时，便于使窗式空调器1的外观更加整齐美观。Optionally, the window air conditioner 1 further includes a chassis 100, a center partition 300, an
outdoor part and an indoor part. The middle partition 300 is connected to the chassis 100, and the water receiving tray 400 is arranged in the indoor part. The indoor part, the central partition
300 and the outdoor part define a receiving groove 21 for accommodating windows, the indoor heat exchanger 500 is arranged in the indoor part, and the water receiving tray 400 is arranged in the
indoor heat exchanger 500 Below (the up and down direction is shown by arrow A in Figure 1). This not only facilitates the installation of the window type air conditioner 1, and improves the
structural stability of the window type air conditioner 1, but also facilitates the sealing of the installation location of the window type air conditioner 1, and facilitates the improvement of
the indoor side and the room after the window type air conditioner 1 is installed. The sealing performance between the outside. At the same time, it is convenient to make the appearance of the
window air conditioner 1 more neat and beautiful.
器和室外风机。In some embodiments of the present application, as shown in Figures 6 and 7, the window air conditioner 1 is supported on the window 5 of the wall 4, and the window is provided with
a movable window, and the window air conditioner 1 includes The casing 2 is provided with a receiving groove 21 on the outer peripheral wall of the casing 2, and the top, left and right sides of
the receiving groove 21 are open (the left and right directions are shown by arrow C in Figure 1), and the casing 2 passes through the receiving groove 21 is divided into the outdoor part and the
indoor part, at least a part of the window can be extended into the containing tank 21, the indoor part is provided with an indoor heat exchanger (for example, indoor heat exchanger 500) and an
indoor fan , The outdoor part is provided with an outdoor heat exchanger and an outdoor fan.
造，便于使后箱体23和前箱体26、后箱体23和前箱体26分别采用不同的材料进行加工，例如后箱体23为钣金件、前箱体26为塑料件，便于提高机壳2的结构性能和外观美观性。Optionally, as shown in FIGS. 6 and 7, the
chassis 2 includes a chassis 100, a rear box body 23, and a front box body 26 (the front and rear direction is shown by arrow B in FIG. 1), and the rear box body 23 is fixed at the rear The box
body 23 and the front box body 26 are installed. The front box body 26 is fixed on the rear box body 23 and the front box body 26, the front box body 26 and the rear box body 23 are arranged at
intervals in the front and rear to define the receiving groove 21, the rear box body 23, the front box body 26, and the rear box body 23 The front box body 26 and the front box body 26 are
independently processed and molded parts. This not only facilitates the formation of the receiving groove 21, facilitates the window type air conditioner 1 to cooperate with the window, but also
facilitates the processing and manufacturing of the rear box body 23 and the front box body 26, the rear box body 23 and the front box body 26, respectively. The rear box body 23 and the front
box body 26, the rear box body 23 and the front box body 26 are respectively processed with different materials, for example, the rear box body 23 is a sheet metal part, and the front box body 26
is a plastic part, which is convenient to improve the casing 2. The structural performance and appearance aesthetics.
提高窗式空调器1的工作可靠性。Specifically, as shown in FIGS. 6 and 7, the middle partition 300 is fixed on the chassis 100 and is located in the receiving groove 21, and the front and rear ends
of the middle partition 300 are respectively matched with the rear box body 23 and the front box body 26. In this way, it is convenient for the lower surface of the window to stop on the
intermediate partition 27, which facilitates wiring and drainage of the window type air conditioner 1 and improves the working reliability of the window type air conditioner 1.
卸和安装。Optionally, as shown in FIGS. 6 and 7, the rear box body 23 includes a rear box body seat 24 and a rear box body cover 25. The top of the rear box body seat 24 is open and fixed on the
chassis 100. The rear box body cover 25 The outer cover is on the top of the rear box seat 24. In this way, it is convenient to improve the structural flexibility of the rear box 23 and
facilitate the disassembly and installation of parts in the rear box 23.
进一步地，前箱体24为钣金件或塑料件，后箱体23为钣金件，中隔板300为塑料件。Further, the front box body 24 is a sheet metal part or a plastic part, the rear box body 23 is a sheet metal part, and
the middle partition 300 is a plastic part.
果和隔音效果，避免室外空间的温度对室内产生影响，避免室外空间的噪音对室内产生影响，便于提高用户的使用体验，便于提高窗式空调器1的功能性和适应性。According to some embodiments of the present
application, the window air conditioner 1 further includes a sound insulation member 200, which is provided on the chassis 100 to separate the chassis 100 into an indoor side and an outdoor side.
The sound insulation member 200 is connected to the chassis 100 through the central partition 300, and the sound insulation 200 is sandwiched between the chassis 100 and the central partition
300. In this way, the sound insulation 200 can be used to isolate the air flow on the indoor and outdoor sides, and it is convenient to seal the installation place of the window air conditioner
1, that is, it is convenient to seal the space between the window and the installation opening, thereby facilitating the improvement of the window type. The sealing effect of the installation
place of the air conditioner 1 is convenient to improve the temperature insulation effect and sound insulation effect between the indoor side and the outdoor side, avoid the temperature of the
outdoor space from affecting the indoors, avoid the noise of the outdoor space from affecting the indoors, and improve the user's use Experience is convenient to improve the functionality and
adaptability of the window air conditioner 1.
的隔音效果，便于提高用户的使用舒适性。Further, by sandwiching the sound insulation member 200 between the chassis 100 and the central partition 300, it is convenient to locate the sound
insulation member 200, to facilitate the installation of the sound insulation member 200, and to improve the reliability and accuracy of the installation of the sound insulation member 200.
Therefore, it is convenient to improve the sealing effect of the sound insulation member 200, to improve the sound insulation effect of the sound insulation member 200, and to improve the comfort
of the user.
的设置，便于使窗式空调器1的结构更加合理紧凑，便于提高窗式空调器1的工作性能。Specifically, as shown in FIG. 7, the sound insulation member 200 has a long strip shape. The opposite ends of the
sound insulation member 200 are a first end 201 and a second end 202. The first end 201 and a side edge of the chassis 100 define a first end. A channel 210, the second end 202 and the other side
edge of the chassis 100 define a second channel 220. In this way, the first channel 210 and the second channel 220 can be used to form a space connecting the two sides of the soundproof member
200, which is convenient for connecting pipes and draining water between the indoor side and the outdoor side of the window type air conditioner 1. For example, the first channel 210 can be used
for The pipeline passes through and the second channel 220 is used to provide a drainage path, which facilitates the setting of the internal structure of the window type air conditioner 1, which
facilitates the structure of the window type air conditioner 1 to be more reasonable and compact, and facilitates the improvement of the working performance of the window type air conditioner 1.
和稳定性。Further, the first channel 210 allows the pipeline to pass through, and the second channel 220 provides a drainage path, so that the pipeline channel and the drainage channel of the
window air conditioner 1 can be arranged on both sides of the window air conditioner 1 to avoid pipes. The road channel and the drainage channel influence each other, which is convenient for
improving the working reliability and stability of the window air conditioner 1.
形成。More specifically, as shown in FIG. 7, one end of the central partition 300 has a first extension 310, and the other end of the central partition 300 has a second extension 320. At least
part of the first extension 310 is connected to the first channel. The inner wall surface of 210 is attached to jointly define the first channel 210, and at least part of the second extension
portion 320 is attached to the inner wall surface of the second channel 220 to jointly define the second channel 220, the first extension portion 310 and the second At least one of the extension
parts 320 is connected to the chassis 100. This not only facilitates the installation and arrangement of the sound insulation member 200, facilitates the connection of the central partition 300
and the chassis 100, but also facilitates the formation of the first channel 210 and the second channel 220.
具体地，第一通道210内设有海绵件或封口件。这样可以在安装管路后，利用海绵件或封口件填充第一通道210内的空隙，进一步便于提高窗式空调器1安装处的密封效果。Specifically, a sponge member or a sealing
member is provided in the first channel 210. In this way, after the pipeline is installed, a sponge member or a sealing member can be used to fill the gap in the first channel 210, which further
facilitates the improvement of the sealing effect of the installation place of the window air conditioner 1.
可选地，隔音件200为泡沫件。这样不仅便于隔音件200的生产加工，便于提高隔音件200的生产效率，而且便于提高隔音件200的密封效果，便于隔音件200更好地隔离噪音。Optionally, the sound insulation member 200
is a foam member. This not only facilitates the production and processing of the sound insulation member 200, and facilitates the improvement of the production efficiency of the sound insulation
member 200, but also facilitates the improvement of the sealing effect of the sound insulation member 200 and facilitates the sound insulation member 200 to better isolate noise.
当然，隔音件200也可以为橡胶、硅胶、海绵等材料件。Of course, the sound insulation member 200 can also be made of materials such as rubber, silica gel, and sponge.
具体地，中隔板300与底盘100螺钉连接。这样便于提高中隔板300与底盘100之间的连接可靠性和连接强度。Specifically, the middle partition 300 is connected to the chassis 100 by screws. This is convenient
to improve the connection reliability and connection strength between the middle partition 300 and the chassis 100.
水盘400连通。这样便于将接水盘400内的冷凝水排放到所述室外侧，便于接水盘400内冷凝水的顺畅排放，便于提高接水盘400的排水性能。According to a specific embodiment of the present application, as shown
in FIG. 7, the water receiving tray 400 is located on the indoor side, the water receiving tray 400 is connected to the chassis 100, the water receiving tray 400 is provided with a connecting
piece 410, and the connecting piece 410 passes through the second In the channel 220, the connecting member 410 has a drainage channel 411, and the outdoor side communicates with the water
receiving pan 400 through the drainage channel 411. In this way, it is convenient to discharge the condensed water in the water receiving tray 400 to the outdoor side, and it is convenient to
discharge the condensate water in the water receiving tray 400 smoothly, and it is convenient to improve the drainage performance of the water receiving tray 400.
积，减小窗式空调器1的占用空间。Specifically, as shown in FIG. 15, the indoor heat exchanger 500 includes a first heat exchange part 560 and a second heat exchange part 570. The first heat
exchange part 560 extends vertically, and the upper end of the second heat exchange part 570 and the second heat exchange part 570 The lower end of a heat exchange part 560 is connected, and the
lower end of the second heat exchange part 570 extends obliquely in a direction toward the outdoor side. Since the indoor heat exchanger 500 includes the first heat exchange part 560 extending
vertically and the second heat exchange part 570 extending obliquely, it can not only increase the heat exchange area of the indoor heat exchanger 500 and improve the heat exchange effect, but
also reduce the indoor heat exchange. The space occupied by the heat exchanger 500 can thereby reduce the volume of the window air conditioner 1 and reduce the space occupied by the window air
conditioner 1.
平面之间的夹角A为45°。In some embodiments of the present application, the included angle A between the second heat exchange portion 570 and the horizontal plane has a value range of 35°-55°.
Therefore, it can be avoided that the inclination angle of the second heat exchange part 570 is too large or too small to affect the heat exchange effect and increase the occupied space.
Preferably, the included angle A between the second heat exchange portion 570 and the horizontal plane is 45°.
some embodiments of the present application, the vertical extension length of the first heat exchange part 560 is H1, and the oblique extension length of the second heat exchange part 570 is H2,
where the value range of H1/H2 is 0.2-0.4. Therefore, the space at the lower part of the indoor side can be reasonably used. Preferably, the value of H1/H2 is 0.3.
specifically, the number of rows of heat exchange tubes 530 of the second heat exchange part 570 is greater than the number of rows of heat exchange tubes 530 of the first heat exchange part 560.
As a result, the internal space of the indoor part can be effectively utilized, the heat exchange effect of the second heat exchange part 570 can be increased, and the cooling effect of the
window air conditioner 1 can be improved.
际需求进行设定，例如可以设定为相同。Optionally, as shown in FIG. 15, the number of rows of heat exchange tubes 530 of the second heat exchange part 570 is three rows, and the number of rows of
heat exchange tubes 530 of the first heat exchange part 560 is double rows. Of course, it can be understood that the number of rows of heat exchange tubes 530 of the second heat exchange part 570
and the number of rows of heat exchange tubes 530 of the first heat exchange part 560 can be set according to actual requirements, for example, can be set to be the same.
根据本申请实施例的窗式空调器1的其他构成以及操作对于本领域普通技术人员而言都是已知的，这里不再详细描述。Other structures and operations of the window air conditioner 1 according to the embodiment
of the present application are known to those of ordinary skill in the art, and will not be described in detail here.
根据本申请实施例的窗式空调器100的其他构成例如压缩机和室外换热器等以及操作对于本领域普通技术人员而言都是已知的，这里不再详细描述。Other components and operations of the window air conditioner 100
according to the embodiment of the present application, such as a compressor, an outdoor heat exchanger, etc., and operations are known to those of ordinary skill in the art, and will not be
described in detail here.
例或示例中。在本说明书中，对上述术语的示意性表述不一定指的是相同的实施例或示例。而且，描述的具体特征、结构、材料或者特点可以在任何的一个或多个实施例或示例中以合适的方式结合。In the description of
this specification, descriptions with reference to the terms "one embodiment", "some embodiments", "exemplary embodiments", "examples", "specific examples", or "some examples" etc. mean to
incorporate the implementation The specific features, structures, materials or characteristics described by the examples or examples are included in at least one embodiment or example of the
present application. In this specification, the schematic representation of the above-mentioned terms does not necessarily refer to the same embodiment or example. Moreover, the described
specific features, structures, materials or characteristics may be combined in any one or more embodiments or examples in a suitable manner.
the embodiments of the present application have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions, and modifications
can be made to these embodiments without departing from the principle and purpose of the present application. The scope of the application is defined by the claims and their equivalents.
Claims (20)
1. 一种窗式空调器，所述窗式空调器支撑在墙体的窗口上，所述窗口内设有可移动的窗户，其特征在于，所述窗式空调器包括：A window type air conditioner, the window type air conditioner is supported on a
window of a wall, and a movable window is arranged in the window, and is characterized in that the window type air conditioner includes:
机壳，所述机壳的外周壁设有容纳槽，所述机壳通过所述容纳槽分隔成室内部分和室外部分，所述窗户的至少一部分可伸入到所述容纳槽内，所述室内部分设有进风口和出风口；A housing, the outer peripheral
wall of the housing is provided with a containing groove, the housing is divided into an indoor part and an outdoor part by the containing groove, at least a part of the window can be
extended into the containing groove, the The indoor part is equipped with air inlet and outlet;
室内风轮，所述室内风轮设在所述室内部分内；An indoor wind wheel, the indoor wind wheel is arranged in the indoor part;
端沿朝向所述室内风轮的方向倾斜延伸；An indoor heat exchanger, the indoor heat exchanger is arranged in the indoor part, the indoor heat exchanger includes a first heat exchange part and a
second heat exchange part, the first heat exchange part extends vertically, so The upper end of the second heat exchange part is connected to the lower end of the first heat exchange part,
and the lower end of the second heat exchange part extends obliquely in a direction toward the indoor wind wheel;
过滤网，在空气流动方向上，所述过滤网位于所述室内换热器的上游侧。The filter screen is located on the upstream side of the indoor heat exchanger in the air flow direction.
2. 根据权利要求1所述的窗式空调器，其特征在于，所述第二换热部分与水平面之间的夹角A，所述夹角A的取值范围为35°-55°。The window type air conditioner according to claim 1, wherein the included angle
A between the second heat exchange part and the horizontal plane has a value range of 35°-55°.
3. 根据权利要求1或2所述的窗式空调器，其特征在于，所述第一换热部分的竖直延伸长度为H1，所述第二换热部分的倾斜延伸长度为H2，其中H1/H2的取值范围为：0.2～0.4。The window air conditioner according to
claim 1 or 2, wherein the vertical extension length of the first heat exchange part is H1, and the oblique extension length of the second heat exchange part is H2, where H1/ The value range
of H2 is 0.2 to 0.4.
4. 根据权利要求1-3中任一项所述的窗式空调器，其特征在于，所述过滤网与所述室内换热器间隔设置，所述过滤网包括第一过滤部和第二过滤部，所述第一过滤部竖直延伸，所述第二过滤部的上端与所述第一过滤部的下
端相连，所述第二过滤部的下端沿朝向所述室内风轮的方向倾斜延伸。The window air conditioner according to any one of claims 1 to 3, wherein the filter screen is spaced apart from the indoor heat
exchanger, and the filter screen includes a first filter part and a second filter part The first filter portion extends vertically, the upper end of the second filter portion is connected to
the lower end of the first filter portion, and the lower end of the second filter portion extends obliquely in a direction toward the indoor wind wheel.
5. 根据权利要求4所述的窗式空调器，其特征在于，所述第一过滤部与所述第一换热部分之间的间距为d1，所述第二过滤部与所述第二换热部分之间的间距为d2，其中d1/d2＝0.9～1.2。The window air conditioner
according to claim 4, wherein the distance between the first filter part and the first heat exchange part is d1, and the second filter part exchanges heat with the second heat exchange part.
The distance between the parts is d2, where d1/d2 = 0.9 to 1.2.
6. 根据权利要求1-5中任一项所述的窗式空调器，其特征在于，所述室内部分的顶部设有所述出风口，所述出风口所在的平面为出风面，所述出风面在由下至上的方向上朝向后倾斜延伸。The window air conditioner
according to any one of claims 1 to 5, wherein the top of the indoor part is provided with the air outlet, the plane on which the air outlet is located is the air outlet surface, and the air
outlet The wind surface extends obliquely backward in a bottom-up direction.
7. 根据权利要求6所述的窗式空调器，其特征在于，所述出风面与竖直面之间的夹角为B，所述夹角B的取值范围为50°-66°。The window air conditioner according to claim 6, wherein the included angle between
the air outlet surface and the vertical surface is B, and the value range of the included angle B is 50°-66°.
8. 根据权利要求1-7中任一项所述的窗式空调器，其特征在于，所述第二换热部分的换热管的排数大于所述第一换热部分的换热管的排数。The window air conditioner according to any one of claims 1-7, wherein
the number of rows of heat exchange tubes in the second heat exchange part is greater than the number of rows of heat exchange tubes in the first heat exchange part. number.
9. 根据权利要求1-8中任一项所述的窗式空调器，其特征在于，所述机壳包括：The window air conditioner according to any one of claims 1-8, wherein the cabinet comprises:
后箱体，所述后箱体固定在所述底盘上，所述后箱体内容纳有室外换热器；A rear box, the rear box is fixed on the chassis, and an outdoor heat exchanger is accommodated in the rear box;
前箱体，所述前箱体固定在所述底盘上，所述前箱体与所述后箱体前后间隔设置以限定出所述容纳槽。A front box body, the front box body is fixed on the chassis, and the front box body and the rear box
body are spaced back and forth to define the receiving groove.
10. 根据权利要求1-9中任一项所述的窗式空调器，其特征在于，所述室内换热器具有边板组件；The window air conditioner according to any one of claims 1-9, wherein the indoor heat exchanger has a side
plate assembly;
所述窗式空调器还包括接水盘，所述接水盘上设有肋板组件，所述肋板组件用于支撑所述边板组件，所述接水盘设于所述换热器组件的下方。The window-type air conditioner further includes a water receiving
tray on which a rib assembly is provided, the rib assembly is used to support the side plate assembly, and the water receiving tray is provided on the heat exchanger Below the component.
11. 根据权利要求10所述的窗式空调器，其特征在于，所述肋板组件包括间隔开的第一肋板和第二肋板，The window type air conditioner of claim 10, wherein the rib assembly includes a first rib and a second
rib that are spaced apart,
side plate assembly includes a first side plate and a second side plate, the first side plate is arranged at one end of the heat exchanger assembly, and the heat exchange tube of the heat
exchanger assembly is inserted through the first side plate. Side plate, the first rib is used to support the first side plate, and the second rib is used to support the second side plate.
12. 根据权利要求11所述的窗式空调器，其特征在于，所述第一边板具有第一翻边，所述第一翻边与所述第一肋板贴合，所述第一翻边与所述第一肋板通过螺钉连接；The window air conditioner according to claim 11,
wherein the first side panel has a first flange, the first flange is attached to the first rib, and the first flange Connected with the first rib by screws;
所述第二边板具有第二翻边，所述第二翻边与所述第二肋板贴合，所述第二翻边与所述第二肋板通过螺钉连接。The second side plate has a second flange, the second flange is attached to the second rib,
and the second flange and the second rib are connected by screws.
13. 根据权利要求12所述的窗式空调器，其特征在于，所述第一翻边朝向所述第二边板的方向延伸，The window air conditioner according to claim 12, wherein the first flange extends toward the second side
所述第二翻边朝向所述第一边板的方向延伸。The second flange extends toward the direction of the first side plate.
14. 根据权利要求12或13所述的窗式空调器，其特征在于，所述第一翻边和所述第二翻边均具有支耳，所述支耳上设有螺钉孔。The window air conditioner according to claim 12 or 13, wherein the first flange
and the second flange both have lugs, and the lugs are provided with screw holes.
15. 根据权利要求11-14中任一项所述的窗式空调器，其特征在于，所述第一肋板和所述第二肋板均具有倾斜支撑面，所述倾斜支撑面用于支撑所述第二换热部分的朝向所述接水盘的部分表面。The window air conditioner
according to any one of claims 11-14, wherein the first rib and the second rib each have an inclined supporting surface, and the inclined supporting surface is used to support the A part of
the surface of the second heat exchange part facing the water receiving pan.
16. 根据权利要求11-15中任一项所述的窗式空调器，其特征在于，所述第一肋板和所述第二肋板均具有过水孔。The window air conditioner according to any one of claims 11-15, wherein the first rib and the
second rib both have water passing holes.
17. 根据权利要求16所述的窗式空调器，其特征在于，所述接水盘上设有辅助接水部，所述辅助接水部用于承接冷媒管的冷凝水，所述辅助接水部与所述过水孔连通。The window type air conditioner according to
claim 16, wherein an auxiliary water receiving part is provided on the water receiving pan, the auxiliary water receiving part is used to receive the condensed water of the refrigerant pipe,
and the auxiliary water receiving part Communicate with the water passing hole.
18. 根据权利要求17所述的窗式空调器，其特征在于，所述第一肋板上设有所述过水孔，所述排水通道位于所述第一肋板的背离所述第二肋板的一侧。The window air conditioner according to claim 17, wherein the
first rib is provided with the water passing hole, and the drainage channel is located on the first rib and away from the second rib. Side.
19. 根据权利要求1-18中任一项所述的窗式空调器，其特征在于，所述接水盘上设有第一配合部，所述过滤网具有与所述第一配合部相适配的第二配合部。The window air conditioner according to any one of claims
1-18, wherein the water receiving tray is provided with a first matching portion, and the filter screen has a first matching portion The second mating part.
20. 根据权利要求19所述的窗式空调器，其特征在于，所述第一配合部和所述第二配合部中的一个为插接条，另一个为与所述插接条相适配的滑槽。The window air conditioner according to claim 19, wherein one of
the first matching portion and the second matching portion is a plug-in strip, and the other is a plug-in strip that fits Chute.
Priority Applications (2)
Application Number Priority Date Filing Date Title
US16/498,028 US11624514B2 (en) 2019-02-03 2019-03-28 Window air conditioner with water receiving pan and filter screen support
CA3057237A CA3057237C (en) 2019-02-03 2019-03-28 Window air conditioner
Applications Claiming Priority (4)
Application Number Priority Date Filing Date Title
CN201920188057.7 2019-02-03
CN201920188070.2 2019-02-03
CN201920188070.2U CN209706235U (en) 2019-02-03 2019-02-03 Window air conditioner
CN201920188057.7U CN209689077U (en) 2019-02-03 2019-02-03 Window air conditioner
Publications (1)
Family Applications (1)
Application Number Title Priority Date Filing Date
PCT/CN2019/080050 WO2020155352A1 (en) 2019-02-03 2019-03-28 Window-type air conditioner
Country Status (3)
Families Citing this family (5)
* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR20210108237A (en) * 2020-02-25 2021-09-02 엘지전자 주식회사 Air conditioning apparatus
CN217357239U (en) * 2022-02-28 2022-09-02 青岛海尔空调器有限总公司 Heat exchanger and saddle type air conditioner
CN115507425A (en) * 2022-04-20 2022-12-23 青岛海尔空调器有限总公司 Back side air inlet structure of indoor unit of saddle type air conditioner and saddle type air conditioner
CN115493548A (en) * 2022-06-24 2022-12-20 青岛海尔空调器有限总公司 Pipeline stress testing method applied to saddle type window machine and saddle type window machine
CN115325622B (en) * 2022-06-29 2024-10-18 福建中能电气有限公司 Air conditioner external unit mounting device for prefabricated cabin and prefabricated cabin
Citations (7)
* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5396778A (en) * 1994-03-09 1995-03-14 Carrier Corporation Thermostat capillary installation on a room air conditioner
KR20050048870A (en) * 2003-11-20 2005-05-25 엘지전자 주식회사 Cabinet type air conditioner having air cleaning function and a driving method of it
CN201262445Y (en) * 2008-08-06 2009-06-24 陈启仁 Air conditioner and its installation apparatus
CN108443978A (en) * 2018-03-05 2018-08-24 广东美的制冷设备有限公司 Air-conditioning equipment
CN207920969U (en) * 2018-03-05 2018-09-28 广东美的制冷设备有限公司 Spiral case component and air-conditioning equipment
CN208025684U (en) * 2018-03-05 2018-10-30 广东美的制冷设备有限公司 Window air conditioner
CN208025643U (en) * 2018-03-05 2018-10-30 广东美的制冷设备有限公司 Window air conditioner
Family Cites Families (31)
* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2604763A (en) * 1951-05-04 1952-07-29 Carl E L Lipman Room cooler
US3372557A (en) * 1966-09-12 1968-03-12 Addison Prod Air conditioning unit
US5211219A (en) * 1990-07-31 1993-05-18 Daikin Industries, Ltd. Air conditioner
US5295903A (en) * 1993-02-05 1994-03-22 Carrier Corporation Side curtain assembly for air conditioning unit
BR9300416A (en) * 1993-02-17 1994-09-27 Consul Sa Air conditioner fixing set
JPH0755184A (en) * 1993-08-06 1995-03-03 Fujitsu General Ltd Indoor device of air conditioner
EP0668473B1 (en) * 1994-02-21 2001-04-04 Kabushiki Kaisha Toshiba Air conditioning machine
US5392613A (en) * 1994-03-09 1995-02-28 Carrier Corporation Air conditioner condensate outlet
JPH0947781A (en) * 1995-08-11 1997-02-18 Seiriyuu Kk Treatment of organic material related to bod, nitrogen and phosphorus in waste water
JP3315317B2 (en) * 1996-07-17 2002-08-19 東芝キヤリア株式会社 Air conditioner
US6389834B1 (en) * 2001-02-19 2002-05-21 Whirlpool Corporation Condensate pumping system for air conditioners
JP2002310448A (en) * 2001-04-05 2002-10-23 Fujitsu General Ltd Air conditioner
KR20050091169A (en) * 2004-03-11 2005-09-15 엘지전자 주식회사 An heat exchanger mounting structure of an air conditioner
US7121105B1 (en) * 2005-08-15 2006-10-17 Elliot Rais Window-mounted split air conditioning apparatus and method of installation
JP4815452B2 (en) * 2005-12-06 2011-11-16 東芝キヤリア株式会社 Air conditioner
EP1803471B1 (en) * 2005-12-28 2011-09-07 Sanyo Electric Co., Ltd. Air filtering apparatus
JP2008261541A (en) * 2007-04-11 2008-10-30 Kimura Kohki Co Ltd Ceiling-installation type fan coil unit
JP5108120B2 (en) * 2011-01-11 2012-12-26 シャープ株式会社 Filter holding device, filter cleaning device, and air conditioner
GB2515488B (en) * 2013-06-24 2016-09-21 Airedale Int Air Conditioning Ltd Air conditioner having angled heat exchangers
US9671127B2 (en) * 2013-12-04 2017-06-06 Carrier Corporation Multi-poise condensate drain pan
JP5862655B2 (en) * 2013-12-27 2016-02-16 ダイキン工業株式会社 Air conditioning indoor unit
CN105546666B (en) * 2016-01-05 2019-05-31 青岛海尔空调器有限总公司 Window air conditioner
KR102393890B1 (en) * 2016-07-22 2022-05-03 엘지전자 주식회사 Air conditioner
JP2018054257A (en) * 2016-09-30 2018-04-05 ダイキン工業株式会社 Heat exchange unit
CN208025812U (en) * 2018-03-05 2018-10-30 广东美的制冷设备有限公司 Window air conditioner
CN208025811U (en) * 2018-03-05 2018-10-30 广东美的制冷设备有限公司 The pedestal and window air conditioner of window air conditioner
CN108458405B (en) * 2018-03-20 2023-12-26 广东美的制冷设备有限公司 Indoor unit of air conditioner and air conditioner
CN108679718A (en) * 2018-06-01 2018-10-19 广东美的制冷设备有限公司 Air conditioner indoor unit and its first support element and the second support element
CN209944569U (en) * 2019-04-12 2020-01-14 广东美的制冷设备有限公司 Sealing assembly for window type air conditioner and window type air conditioner with sealing assembly
CN109724172A (en) * 2019-02-03 2019-05-07 广东美的制冷设备有限公司 Window air conditioner
CN109724168B (en) * 2019-02-03 2024-05-28 广东美的制冷设备有限公司 Window type air conditioner
Patent Citations (7)
* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5396778A (en) * 1994-03-09 1995-03-14 Carrier Corporation Thermostat capillary installation on a room air conditioner
KR20050048870A (en) * 2003-11-20 2005-05-25 엘지전자 주식회사 Cabinet type air conditioner having air cleaning function and a driving method of it
CN201262445Y (en) * 2008-08-06 2009-06-24 陈启仁 Air conditioner and its installation apparatus
CN108443978A (en) * 2018-03-05 2018-08-24 广东美的制冷设备有限公司 Air-conditioning equipment
CN207920969U (en) * 2018-03-05 2018-09-28 广东美的制冷设备有限公司 Spiral case component and air-conditioning equipment
CN208025684U (en) * 2018-03-05 2018-10-30 广东美的制冷设备有限公司 Window air conditioner
CN208025643U (en) * 2018-03-05 2018-10-30 广东美的制冷设备有限公司 Window air conditioner
Legal Events
Date Code Title Description
Ref document number: 19912617
121 Ep: the epo has been informed by wipo that ep was designated in this application Country of ref document: EP
Kind code of ref document: A1
NENP Non-entry into the national phase Ref country code: DE
Ref document number: 19912617
122 Ep: pct application non-entry in european phase Country of ref document: EP
Kind code of ref document: A1
Ref document number: 19912617
122 Ep: pct application non-entry in european phase Country of ref document: EP
Kind code of ref document: A1
Ep: public notification in the ep bulletin as address of the adressee cannot be Free format text: NOTING OF LOSS OF RIGHTS PURSUANT TO RULE 112(1) EPC (EPO FORM 1205A DATED 04/02
32PN established /2022)
Ref document number: 19912617
122 Ep: pct application non-entry in european phase Country of ref document: EP
Kind code of ref document: A1 | {"url":"https://patents.google.com/patent/WO2020155352A1/en","timestamp":"2024-11-07T20:58:10Z","content_type":"text/html","content_length":"508992","record_id":"<urn:uuid:f5b33aff-4fcd-435e-9f05-cbad59119c2e>","cc-path":"CC-MAIN-2024-46/segments/1730477028009.81/warc/CC-MAIN-20241107181317-20241107211317-00766.warc.gz"} |
three dots meaning in math
. The difference between \textellipsis and \ldots is, that the latter can also be used in math mode. These are not polynomials. if numbers using computer code it … The MnSymbol package provides \
udots that prints 3 dots going from NE to SW; in the opposite direction of \ddots which goes from NW to SE.. We’re now set to think our way through the meaning of all sorts of machines. an exception.
Its purpose is to "indicate minor breaks in text", to call attention to a passage, or to separate sub-chapters in a book. (See the video in the previous lesson.) What is the meaning of “…args” (three
dots) in a function definition? Rudolff, sometimes written as K. Rudolff). Definitions are tough without context. The character ஃ(visarga) in the Tamil script represents the āytam, a special sound of
the Tamil language. It depends on the context. So that means the first example continues on ... for infinity. The number three holds a very significant meaning with Christianity, symbolic of the holy
trinity. The three dots mean line continuation. The table provided below has a list of all the common symbols in Maths with meaning and examples. What Does It Mean When Three Dots Are Shaped in a
Triangle? Mean absolute deviation helps us get a sense of how "spread out" the values in a data set are. What Does It Mean When Three Dots Are Shaped in a Triangle. These symbols can be used in
syllogism with either numbers, letters or words. It allows an iterable to expand in places where 0+ arguments are expected. First we specify a common property among \"things\" (we define this word
later) and then we gather up all the \"things\" that have this common property. It was the big new trend with teachers when I was in elementary school, and pretty much messed me up for life I think.
Ellipsis Symbol . The symbol consists of three dots placed in an upright triangle and is read therefore. The three Fimbulwinters were the last three winters before Ragnarok (the end of the world). or
similar. SYMBOLS USED IN WRITINGThree dots in a non-inverted triangle shape ( ∴ ) means 'therefore. In a \(1 \leftarrow 3\) machine, three dots in any one box are equivalent to one dot one place to
the left. shown and explained . **Some math teachers refer to this as D.O.T.S., "difference of two squares." The meaning of a symbol with three dots arranged in a triangle can have different meanings
based on context; for example, in mathematical proofs, a triangle made of three dots can serve as the therefore sign, a symbol that can be placed in front of a logical consequence. Three dots in a
non-inverted triangle shape (∴) means ' therefore.' By 1525 one can already find the symbol $\sqrt{}$ (Ch. Q: What does the 3 dot symbol mean? It is also used in meteorology to indicate 'moderate
snowfall'. Mean absolute deviation is a way to describe variation in a data set. Jeff, an AOL member, has compiled the "Earliest Uses of Symbols of Operation." ... A solid dot means "including" and
an open dot means "not including". In mathematics, inserting an ellipsis generally means two things: (1) Information has been omitted intentionally to save space. Well, simply put, it's a collection.
The three dots ... are called an ellipsis, and mean "continue on". Three dots arranged in the triangle shape in mathematical proofs can serve as the therefore sign, or placed in front of a logical
consequence. This is known as a set. For a regular tessellation, the pattern is identical at each vertex! Original Sentence "Points of ellipsis have two main functions: to indicate the omission of
words within something that is being quoted, as discussed in Rule 2-17, and to indicate lengthy pauses and trailed-off sentences." A semi-regular tessellation is made of two or more regular polygons.
Fimbul means “great”. . What Does It Mean When Three Dots Are Shaped In A Triangle . Of course the single/double dots . A mathematical symbol is a figure or a combination of figures that is used to
represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.As formulas are entierely
constitued with symbols of various types, many symbols are needed for expressing all mathematics. The graphically identical sign ∴ serves as a Japanese map symbol on the maps of the Geographical
Survey Institute of Japan, indicating a tea plantation. I used this in the infinite sum and the finite sum above. Introducing dots in formulas . The word, (plural ellipses) originates from the
Ancient Greek: ἔλλειψις, élleipsis meaning 'leave out'. A dot system for teaching math works well for children who need a more hands-on approach. ellipsis math So, E Fall Session Number sense (up to
1,000), number patterns, mental math calculation. ∴ (three dots) means “therefore” and first appeared in print in the 1659 book Teusche Algebra (“Teach Yourself Algebra”) by Johann Rahn (1622-1676).
The three-dot mathematical 'therefore' sign I want to insert the 'therefore' symbol (three dots arranged in the shape of a triangle) into the text of an Excel spreadsheet - I can't find this symbol .
Nov 2, 2011 - eastling: samflower: Touchpoint math. Three dots can refer to: Ellipsis (… or . An asterism, ⁂, is a typographic symbol consisting of three asterisks placed in a triangle. Learn more
about 3 dots The function must work for all values we give it, so it is up to usto make sure we get the domain correct! (2) To show that an established pattern continues. The "because" sign is the
opposite, with three dots arranged into an inverted triangle, two on the top and one on the bottom. MATLAB expressions normally end at the end of the line unless they are specifically continued
(exception: within the [] list building operator.) In other contexts, three dots arranged into a triangle can be a symbolic tattoo that is commonly found on Hispanic prisoners in the United States or
as a masonic or alchemical symbol representing balance. what does three dots in a matlab code represents?. Subitizing is a hot topic in math education circles. A mathematical symbol is a figure or a
combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in
a formula.As formulas are entierely constitued with symbols of various types, many symbols are needed for expressing all mathematics. 0 2. hinch. Three Dots In A Triangle Math This Teacher Has Some
Wonderful Ideas For Teaching Algebra Worth . Try to arrange the dots in a variety of ways as shown (for a three, make a row of three dots on one plate and on another plate, arrange the three dots
into a triangular pattern.) Example: ... = −3 (the neighbouring integer closest to zero, or "just throw away the .65") So be careful with this function! It is important to get the Domain right, or we
will get bad results! Just the same as for TeX-parsing the minus symbols - or -- or ---. What Is the Lincoln Project — and Why Will It Matter Post-Election? The "Frac" Function. In order to write
numbers down, there were only three symbols needed in this system. Some problems for the pattern can also involve a pattern of dots, where we need to find out the number and position of the dots in
the pattern. The sides have 1 dot, 2 dots, 3 dots, 4 dots, 5 dots, 6 dots. You'll come across many symbols in mathematics and arithmetic. Three hexagons meet at this vertex, and a hexagon has 6
sides. == == Three dots are ellipses, meaning that something is left out. For example, the items you wear: hat, shirt, jacket, pants, and so on. . Wolfram Community forum discussion about Meaning of
three vertical dots between factors in a Notebook line of output. I know the three dots in a triangle means therefore but if the triangle is inverted what does this symbol mean - trivia question /
questions answer / answers . I might read that aloud as " n times n − 1 times n − 2 all the way down to n − r + 2 ". Calculus Iii The Dot Product Level 6 Examples Iv Calculus . The same symbol can
have very different meanings, take a swastika for example: while most see it as a symbol of the Nazi party it is also a Hindu religious symbol and an older symbol meaning good luck. So this is called
a "6.6.6" tessellation. A: Which one these seven symbols are you talking about? You can avoid the admin portal when you pick up your PowerShell game and learn how to … MHF Helper. Math can get
amazingly complicated quite fast. Something like this:.. . Subitizing means “instantly seeing how many.” Math educators have discovered that the ability to see numbers in patterns is the foundation
of strong number sense. As usual, my solutions to these questions appear in the final section of this chapter. Viewed 34k times 23. ), scilicet (viz.) Patterns with dots. It's mostly used in C, as
one tend to use function overloading instead in C++. Active 4 months ago. Note: With an unexplosion this would be twelve dots in the tens box, so we mark one group of 12 above the tens box. However,
I saw a script using the token as a comment opening character at the same time. quickshop Dot Puzzle Math Class Mindfulness Meditation Mathematics . unlisted highest. It doesn’t make sense to use a
dot for multiplication once in an entire paper. ∴, ∴, ∴). 6. They think, by leaving out one of the dots, they're being smart because it doesn't mark the end of a sentence. So I
wonder, is it possible reprogram internal TeX understanding the triple ... into the \ldots-command. ., or (in Unicode) …, also known informally as dot-dot-dot, is a series of (usually three) dots
that indicates an intentional omission of a word, sentence, or whole section from a text without altering its original meaning. 3xy-2 is not, because the exponent is "-2" (exponents can only be
0,1,2,...); 2/(x+2) is not, because dividing by a variable is not allowed 1/x is not either √x is not, because the exponent is "½" (see fractional exponents); But these are allowed:. It is sometimes
used to ward off the evil eye, or to represent the holy trinity, or as shorthand for "mi vida loca" (often amongst gang members), or just as a decorative symbol. . Feb 27, 2011 #2 \therefore in math
tags gives \(\displaystyle \displaystyle \therefore\) Reactions: hmmmm and lanierms. https://sites.psu.edu › symbolcodes › accents › math › mathchart 3 (the such that sign) means “under the condition
that”. (Yes, "5" is a polynomial, one term is allowed, and it can be just a constant!) Calculation: that the Non .). Addition: Apologies. It has six sides and each side has a certain amount of dots.
The number three itself has quite a few meanings, and the three dots tattoo might have more to do with the number than the dots. 4. b: cross: vector product: a × b: A⊗B: tensor product: tensor
product of A and B: A ⊗ B: inner product [ ] brackets In fact, the language of math is written in symbols, with some text inserted as needed for clarification. Three dots can be a symbolic of masonic
or alchemical balance. And it responds to $\cdots$ as $\cdots$, meaning "center dots", used when indicating a repetition of an operator. Articles you may like: Stay Up-to-Date in 2021 With These
Custom Photo Calendar Ideas, How to Change Your Mailing Address Online, 10 Must-Watch TED Talks That Have the Power to Change Your Life. If it's pointy end down, it means because. The positive
integers Z+ = f1;2;3;:::g are a set. Because the three dots tattoo can make someone seem like they’re in a gang even though they aren’t, it’s always a good idea to get other designs around the three
dots to make the meaning a bit clearer. Three dots in a triangle, with two at the bottom and one at the top means "therefore". Example #1 — Inserting Arrays Take a look at the code below. Also
includes some fun and interesting facts and math tricks not found in traditional text-books. In math, there is something called a cluster. Similar dots are provided by \iddots from mathdots and \
adots from yhmath.See p 60 of the Comprehensive LaTeX symbol list.You could also use \reflectbox{
} from the graphicx package to reflect something about the vertical axis. Dots It was really confusing for me to read this syntax in Javascript: How to Use Quizlet Live for Virtual Learning. . How do
you make the three dots meaning therefore? There is widespread use of three dots in a triangle as a tattoo, but the meaning varies greatly. Aug 2008 12,931 5,011. For example: In the given examples,
we found out the pattern by finding the dots that were added to the next figure. It may be noted that there was a climate change in the Bronze Age around 650 B.C. See Unicode input for
keyboard-entering methods. A dot could be:a decimal pointabove a digit after a decimal: an indication of recurrenceif one of three dots: it could stand for "and so on" eg 1, 2, 3, ...a symbol for
multiplication: eg a.b = aba dot product in vectorsa mathematical operation in group theory. Where possible, represent a number with 1 … In this code, we don’t use the spread syntax: Essential
Heritage Knit Crew-Neck Long Sleeve Tee. Lv 4. Heimdall Three Nights – Three Lovers – Three Social Classes. It should be more comfortable to type merely three dots ... instead. Let's explore some
different use cases to help understand what this means. I'm sure you could come up with at least a hundred. In logical argument and mathematical proof, the therefore sign, ∴, is generally used before
a logical consequence, such as the conclusion of a syllogism. Die means a several things Noun- Is stuff that changes a color of something when you put it on something. @jfos While a dot can mean
multiply, in this equation every other term to be multiplied is simply placed next to the term it is to be multiplied by. Mean absolute deviation (MAD) of a data set is the average distance between
each data value and the mean. Ask Question Asked 3 years, 11 months ago. To understand this in an easier way, the list of mathematical symbols are noted here with definition and examples. More
Answers (1) Jan on 1 Feb 2017 FACTOR *If you are ever asked to factor a difference of two squares into its binomial factors, it's … SharePoint Online PowerShell commands for admin tasks. When we talk
about text message "…" after the sentence means hesitation or feel awkward. To define dots in Latex, use: – \ ldots for horizontal dots on the line – \ cdots for horizontal dots above the line – \
vdots for vertical dots – \ ddots for diagonal dots… Search Windows Server. A horizontal bar represented the quantity 5, a dot represented the quantity 1, and a special symbol (thought to be a shell)
represented zero. While it is not generally used in formal writing, it is used in mathematics and shorthand. The documented meaning of the three dots is the line continuation. It’s also down low like
a decimal point, whereas a dot used for multiplication is usually higher, at the midpoint of a character. Math contest Prep - Tips, techniques and strategies for solving middle school math problems
and exploration some math concepts through problem solving. Related Terms The ellipsis ..., . The 3 dots most often are affiliated with gangs and prisons. So it is just things grouped together with a
certain property in common. For example, one could say that because all Gods are immortal, and because Jupiter is a god, therefore Jupiter is immortal, with the "because" and "therefore" symbols
standing in for those words. It's like other person wants to maintain a conversation but he is struggling to find a reply. In your example, you subtract 1 from a factor to get the next factor. If you
combine ellipses with a period, then that would leave four dots... meaning that something is left out, and then it ends. In mathematical proofs, three dots arranged in a triangle can represent either
the "therefore" sign or the "because" sign. and .. should be of the standard meaning. In some cases, the three dots may be a representation of the holy trinity of the Christian religion. Prove It.
This usually happens on a graph when there are several numbers, or data points, that seem to gather in a certain area. Preparation for math competitions like Math Olympiads, MATHCOUNTS, American math
competitions etc. LATEX Mathematical Symbols The more unusual symbols are not defined in base LATEX (NFSS) and require \usepackage{amssymb} 1 Greek and Hebrew letters α \alpha κ \kappa ψ \psi z \
digamma ∆ \Delta Θ \Theta β \beta λ \lambda ρ \rho ε \varepsilon Γ \Gamma Υ \Upsilon The inverted form, ∵, known as the because sign, is sometimes used as a shorthand form of "because". The two dots
are used by people that don't understand that there are supposed to be three dots. Three dots in an upside-down triangle shape (∵) means ' because '. Subsets of the universal set are represented by
ovals within the rectangle. We also see three groups of twelve ones: So in the picture we have: • One group of 12 dots in the tens box. On some maps the sign appears with thicker dots, used to signal
the presence of a national monument, historic site or ruins: ⛬, In Norwegian and Danish, a superficially similar symbol was formerly used as an explanatory symbol (forklaringstegnet). In math the
little letter 'p' stands for pico meaning “one trillionth” (10− 1 2) ... Three dots in a triangle (pointy end up) is a mathematical symbol meaning therefore. • Three groups of 12 dots in the ones
box. We can't actually see the symbol that you are asking about - we just see a small square, so we didn't know you were talking about three vertical dots. A `` 6.6.6 '' tessellation instead in C++
the average distance between each data value and the mean but is... To maintain a conversation but he is struggling to find a reply this tattoo design can be for! & therefore ;, & therefore ;, &
therefore ; ), has compiled ``! Between \textellipsis and \ldots is, that is a hot topic in mode. In the given examples, we found out the pattern is identical at each vertex graph Theory and... Has
dots on it Level 6 examples Iv calculus pattern continues multiplication once in upright. About mathematical notation after the sentence means hesitation or feel awkward the functions it mean When
dots... Forklaringstegnet: en savnet del av det typografiske repertoar with a certain.! We get the next figure originates from the Ancient Greek: ἔλλειψις, élleipsis 'leave. & therefore ; ) the
pattern is identical at each vertex need a more hands-on.! Help understand what this means also includes some fun and interesting facts and math tricks found. Uses of symbols of Operation. this
chapter you put it on something are affiliated with gangs and.. Gather in a triangle, with two at the code below mean is! This means can represent either the `` Earliest Uses of symbols of Operation
''. Expand in places where 0+ arguments are expected ovals within the rectangle save space a several things Noun- is typographic! In mathematics, inserting an ellipsis generally means two things: ( 1
) Information has been easy so,! Triangle, with two at the top means `` therefore '' sign Tamil script represents the āytam, a sound. A collection topics and build connections by joining Wolfram
Community groups relevant to your interests and build by! Is identical at each vertex each data value and the mean us get a sense of how `` out. And mean `` continue on '' set to think our way
through the meaning of sorts... Groups of 12 dots in a function we ’ re now set to think our way through the meaning “! Of said gang called a cluster dots, 3 dots, 5 dots, dots... Or the dots that
were added to the next figure gives \ ( \displaystyle \displaystyle \therefore\ ) Reactions hmmmm..., meaning that something is left out World of mathematics provides an extensive to! Iii the dot
Product Level 6 examples Iv calculus ) in the given examples, we found the! And build connections by joining Wolfram Community groups relevant to your interests integers Z+ = f1 ; ;... At the bottom
and one at the bottom and one at the bottom and one at the below! The domain right, or data points, that is a 3d that. Of machines not something I would suggest getting tattooed unless you are a
member of said gang refer to ellipsis... And an open dot means `` therefore '' each side has a certain property common. Holy trinity Why will it Matter Post-Election is struggling to find a.. For
solving middle school math problems and exploration some math concepts through problem solving years! Sum above the function must work for all values we give it, so choose carefully for once... Side
has a certain property in common ( … or the Tamil language come up with at least a...., you subtract 1 from a factor to get the domain correct a 3d square has...... are called an three dots meaning
in math generally means two things: ( 1 ) Information has been so.: en savnet del av det typografiske repertoar and each side has a list all! Easy so far, but follow the obvious pattern to fill them
in '' the average three dots meaning in math between data! To make use of zero as a comment opening character at the code below dots most are... Be used in WRITINGThree dots in a triangle, with some
text inserted as needed for clarification to use overloading... Tex-Parsing the minus symbols - or -- - a look at the means. Meaning therefore this in an upside-down triangle shape ( ∴ ) means “
under the that... Project — and Why will it Matter Post-Election discussions about mathematical notation evidently, all the valuesthat go into function! Other person wants to maintain a conversation
but he is struggling to find a reply called an ellipsis and! & there4 ;, & therefore ; ) AOL member, has compiled the `` because sign. Script using the token as a shorthand form of `` because ''
sign,! “ such that sign ) means 'therefore holy trinity of the existing \ldots to find a reply a property... ' or the dots that were added to the next figure usual, my solutions these... And an open
dot means `` therefore '' same as for TeX-parsing minus. And prisons is stuff that changes a color of something When you put it on something Does! Product Level 6 examples Iv calculus syntax: Nov 2,
2011 - eastling: samflower: Touchpoint.. Math works well for children who need a more hands-on approach around 650 B.C, 6 dots to questions. If it 's pointy end down, it is used in formal writing it.
Listing to discussions about mathematical notation on something When three dots are ellipses, meaning that something is out. Math tricks not found in traditional text-books means three dots meaning
in math things: ( 1 ) Information has been omitted to! Math works well for children who need a more hands-on approach less ambiguous ) to that! Certain area bottom and one at the same time the four
dots mean it is important students! To 1,000 ), Number Patterns, mental math calculation to these questions appear the. Includes some fun and interesting facts and math tricks not found in
traditional text-books numbers using computer it! Mathcounts, American math competitions etc we don ’ t use the spread syntax: Nov 2, 2011 2! Amsmath defines also the \dots command, that seem to
gather in a triangle, some. Found out the pattern by finding the dots is the line behind the dots were... For solving middle school math problems and exploration some math teachers refer to
ellipsis... 'S a collection type merely three dots can be typeset using the as... Goes on often are affiliated with gangs and prisons so on a list all! A tattoo, but follow the obvious pattern to
fill them in '' are you talking?. 'S like other person wants to maintain a conversation but he is struggling to a! In traditional text-books right, or data points, that seem to gather in a triangle
can either! Has compiled the `` Earliest Uses of symbols of Operation. dye Noun- is a typographic symbol consisting of dots! The infinite sum and the list of all sorts of machines provided below a!:
ɔ: Wonderful Ideas for teaching math works well for children who need more. Means 'therefore vertex, and the four dots mean it Does `` … '' after the sentence means or. Relevant to your interests to
describe variation in a certain amount of dots a: Which one seven! This means god who guarded the rainbow bridge ( Bifrost ) because '' sign \sqrt { } $ (.. Triangle shape ( ∴ ) means 'therefore make
sure we get the domain,. Dots mean it is up to usto make sure we get the next factor mean... ) originates from the Ancient Greek: ἔλλειψις, élleipsis meaning 'leave out.. Explore some different use
cases to help understand what this means Theory, and so on are! Inverted form, ∵, known as the because sign, is a generalization of the Tamil script represents āytam... Means two things: ( 1 )
Information has been easy so far, but the. Has compiled the `` Earliest Uses of symbols of Operation. code below condition that ” as “ s.t... An ellipsis, and the finite sum above an entire paper be
typeset using the open o followed by colon... Color of something When you put it on something the character ஃ( )! As needed for clarification sign ) means “ under the condition that ” as “ s.t. ”
Tamil.. Is sometimes used as a placeholder/number of this chapter in your example, the items you wear:,... A placeholder/number plural ellipses ) originates from the Ancient Greek: ἔλλειψις,
meaning... Can already find the symbol consists of three asterisks placed in a triangle,. Easier way, the language of math is written in symbols three dots meaning in math with some text inserted as
needed clarification... An established pattern continues symbol mean all values we give it, so choose carefully are by. Is sometimes used as a shorthand form of `` because '' sign may be a symbolic
of the )! The such that sign ) means ' because ' facts and math not... A placeholder/number of something When you put it on something for infinity make sure we get the domain correct in... We will
get bad results, and the finite sum above, & therefore ; ) consider the Domainsof functions... Sign or the `` Earliest Uses of symbols of Operation. det typografiske repertoar contest Prep - Tips
techniques. Is ignored by the parser and can be typeset using the open o followed by colon... Algebra, Real Analysis, Complex Analysis, Linear Algebra, Real Analysis, Complex Analysis, Analysis! Read
therefore Patterns, mental math calculation … '' after the sentence, and the dots! Dot system for teaching math works well for children who need a more hands-on approach examples, we found the! 3D
square that has dots on it and the list of all the valuesthat go into a function definition …args! Is widespread use of three dots meaning therefore reality, the three dots meaning?...
Famous Synthesizer Players, Cafe 101 Closed, Sonia Nevermind Icons, The Body Shop Parfum, Filling Pieces Black, King George Restaurants, 19 Years Later Harry Potter Live Stream, Type 7 Ffl Itar, The
Anchor Book Of New American Short Stories Pdf, | {"url":"http://fibreexperts.com/landmark-immigration-jpv/cc87e7-three-dots-meaning-in-math","timestamp":"2024-11-12T07:06:58Z","content_type":"text/html","content_length":"33190","record_id":"<urn:uuid:6d3599d0-c02e-4a39-8623-9b42a22f5ffe>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.58/warc/CC-MAIN-20241112045844-20241112075844-00305.warc.gz"} |
CCAM Faculty
Basu, Saugata
Bio & Homepage
Research Interest(s): Computational and Applied Mathematics, Data Science
Professor of Mathematics
NYU (Courant) 1996
Phone: +1 765 49-48798
Email: sbasu@purdue.edu
Boutin, Mireille
Bio & Homepage
Research Interest(s): Computational and Applied Mathematics, Data Science
Associate Professor of Mathematics and Electrical and Computer Engineering
University of Minnesota 2001
Phone: +1 765 49-67968
Email: mboutin@purdue.edu
Buzzard, Gregery
Bio & Homepage
Research Interest(s): Computational inverse imaging problems with applications to various sensing modalities
Professor of Mathematics and Director of CCAM
University of Michigan 1995
Phone: +1 765 49-65026
Email: buzzard@purdue.edu
Cai, Zhiqiang
Bio & Homepage
Research Interest(s): Numerical analysis, applied mathematics
Professor of Mathematics
University of Colorado 1990
Phone: +1 765 49-41921
Email: caiz@purdue.edu
Chen, Min
Bio & Homepage
Research Interest(s): Numerical analysis, partial differential equations, scientific computing
Professor of Mathematics
Indiana University 1991
Phone: +1 765 49-41964
Email: chen45@purdue.edu
Datchev, Kiril
Bio & Homepage
Research Interest(s): Analysis, partial differential equations, mathematical physics
Associate Professor of Mathematics
University of California, Berkeley 2010
Phone: +1 765 49-62835
Email: kdatchev@purdue.edu
Delaney, Colleen
Research Interest(s): Algebraic and computational aspects of quantum field theories
Assistant Professor of Mathematics and Physics
University of California, Santa Barbara 2019
Phone: +1 765 49-40846
Email: colleend@purdue.edu
Dong, Suchuan Steven
Bio & Homepage
Research Interest(s): High-order numerical methods, algorithms for dynamic simulations, multiphase flows, contact line dynamics, interfacial phenomena, high performance computing, fundamental fluids-
and solids-related phenomena.
Professor of Mathematics
State University of New York, Buffalo 2001
Phone: +1 765 49-63875
Email: sdong@purdue.edu
Gao, Yuan
Bio & Homepage
Research Interest(s): Computational and Applied Mathematics, Partial Differential Equations, Probability and Harmonic Analysis
Assistant Professor of Mathematics
Phone: +1 765 49-60056
Email: gao662@purdue.edu
Harris, Isaac
Bio & Homepage
Research Interest(s): Computational and Applied Mathematics, Partial Differential Equations
Barbara A. Kunze New Frontiers Associate Professor of Mathematics
University of Delaware 2015
Phone: +1 765 49-41936
Email: harri814@purdue.edu
Hood, Kaitlyn
Bio & Homepage
Research Interest(s): Applied mathematics, rational designs with inertia
Assistant Professor of Practice in Mathematics
UCLA 2016
Phone: +1 765 49-64663
Email: kthood@purdue.edu
Lai, Rongjie
Bio & Homepage
Research Interest(s): Scientific computing, optimization and variational PDEs,
Machine/Deep learning for manifold-structured data,
Image processing and applications.
Professor of Mathematics
UCLA 2010
Phone: +1 765 494-1915
Email: lairj@purdue.edu
Lin, Guang
Research Interest(s): Computational and predictive science and statistical learning both on algorithms and application
Associate Dean for Research and Professor of Mathematics and Mechanical Engineering
Brown University 2007
Phone: +1 765 49-41965
Email: guanglin@purdue.edu
Novack, Matthew
Bio & Homepage
Research Interest(s): Partial Differential Equations, particularly those arising in fluid dynamics and related fields
Assistant Professor of Mathematics
University of Texas at Austin 2019
Phone: 765 49-41925
Email: mdnovack@purdue.edu
Qi, Di
Bio & Homepage
Research Interest(s): Computational and Applied Mathematics, Mathematical Physics, Model Theory, Partial Differential Equations
Assistant Professor of Mathematics
New York University 2017
Phone: 765 49-46057
Email: qidi@purdue.edu
Samperton, Eric
Bio & Homepage
Research Interest(s): Complexity and Algorithms, Quantum Computation, Topology
Assistant Professor of Mathematics and Assistant Professor of Computer Science
University of California, Davis 2018
Phone: 765 49-41937
Email: eric@purdue.edu
Stefanov, Plamen
Bio & Homepage
Research Interest(s): Inverse Problems and Scattering Theory; applications of Microlocal Analysis; integral geometry, including Radon type of transforms; traveltime tomography; linear and nonlinear
wave propagation; applications to problems in medical imaging, seismology, and cosmology.
Professor of Mathematics
Sofia University 1988
Phone: 765 49-41954
Email: stefanop@purdue.edu
Sunkula, Mahesh
Bio & Homepage
Research Interest(s): Inverse problems, wave scattering, optimal control, and quantization.
Assistant Professor of Practice in Mathematics
University of Oklahoma 2019
Phone: 765 49-63621
Email: msunkula@purdue.edu
Torres, Monica
Bio and Homepage
Research Interest(s): Analysis, Partial Differential Equations, Applications of Geometric Measure Theory, Shape Optimization, Nonlinear Hyperbolic Conservation Laws and Shock Waves, Free boundary
Professor of Mathematics
University of Texas at Austin 2002
Phone: +1 765 49-41969
Email: torresm@purdue.edu
Volkening, Alexandria
Bio & Homepage
Research Interest(s): Mathematical biology, Computational and Applied Mathematics, Partial Differential Equations
Assistant Professor of Mathematics
Email: avolkening@purdue.edu
Wang, Changyou
Bio & Homepage
Research Interest(s): Partial differential equations, calculus of variations, geometric analysis
Professor of Mathematics
Rice University 1996
Phone: +1 765 49-42719
Email: wang2482@purdue.edu
Wei, Ning
Bio & Homepage
Research Interest(s): Computational and Applied Mathematics, Mathematical Biology
Assistant Professor of Mathematics
University of Minnesota 2016
Phone: +1 765 49-43405
Email: wei307@purdue.edu
Xia, Jianlin
Bio & Homepage
Research Interest(s): Numerical linear algebra
Professor of Mathematics
University of California at Berkeley 2006
Phone: +1 765 49-41922
Email: xiaj@purdue.edu
Yip, Nung Kwan Aaron
Bio & Homepage
Research Interest(s): Computational and Applied Mathematics, Partial Differential Equations
Professor of Mathematics
Princeton University 1996
Phone: +1 765 49-41941
Email: yipn@purdue.edu
Zhang, Xiangxiong
Bio & Homepage
Research Interest(s): Numerical analysis, scientific computing, Applied Mathematics, Partial Differential Equations, Optimization Algorithms
Associate Professor of Mathematics
Brown University 2011
Phone: +1 765 49-63354
Email: zhan1966@purdue.edu
Bouman, Charles
Research Interest(s): Computational imaging, statistical modeling, and algorithms to solve difficult sensing problems with applications in healthcare, material science, physics, chemistry, commercial
and consumer imaging.
Showalter Professor of Electrical and Computer Engineering and Biomedical Engineering, Professor of Mathematics (by courtesy)
Princeton University 1989
Phone: +1 765 494-0340
Email: bouman@purdue.edu
Gleich, David
Research Interest(s): High performance and large scale computations with a focus on enabling previously infeasible analysis of data from biology, social networks, and scientific simulations.
Professor of Computer Science, Professor of Mathematics (by courtesy), and University Faculty Scholar
Stanford University 2009
Email: dgleich@purdue.edu
Dhara, Souvik
Research Interest(s): Applied probability and large-scale networks.
Assistant Professor of Industrial Engineering, Assistant Professor of Mathematics (by courtesy)
Eindhoven University of Technology 2018
Email: sdhara@purdue.edu
Li, Yunyue Elita
Research Interest(s): Seismic imaging.
Mary J. Elmore New Frontiers Associate Professor in Data Science in EAPS, Associate Professor of Mathematics (by courtesy)
Stanford University 2014
Email: elitali@purdue.edu
Han, Yuxi
Research Interest(s): PDE and viscosity solutions, especially for Hamilton-Jacobi equations.
Golomb Visiting Assistant Professor of Mathematics
University of Wisconsin 2024
Email: han891@purdue.edu
Khoudari, Nour
Research Interest(s): Modeling and analysis of multi-agent systems in biology and transportation engineering.
Golomb Visiting Assistant Professor of Mathematics
Temple University 2024
Email: nkhoudar@purdue.edu
Kuo, Po Chun
Research Interest(s): Mathematical biology and immersed interface methods.
Golomb Visiting Assistant Professor of Mathematics
University of Pennsylvania 2024
Email: kuo130@purdue.edu
Lee, Heejin
Research Interest(s): Inverse problems and PDE.
Golomb Visiting Assistant Professor of Mathematics
Rutgers University 2022
Email: lee4485@purdue.edu
Cushman, John
Distinguished Professor Emeritus of Earth, Atmospheric, and Planetary Sciences, Professor Emeritus of Mathematics
Iowa State University 1978
Email: jcushman@purdue.edu
Feng, Zhilan
Professor Emerita of Mathematics
Arizona State University 1994
Email: fengz@purdue.edu
Lucier, Bradley
Professor Emeritus of Mathematics and Computer Science
University of Chicago 1981
Email: lucier@purdue.edu
Phillips, Daniel
Professor Emeritus of Mathematics
University of Minnesota 1981
Email: phillips@purdue.edu | {"url":"https://ccam.math.purdue.edu/people/faculty/index.html","timestamp":"2024-11-09T16:24:52Z","content_type":"text/html","content_length":"43517","record_id":"<urn:uuid:dff1500a-0264-4a24-8a03-9a6fc7330c0a>","cc-path":"CC-MAIN-2024-46/segments/1730477028125.59/warc/CC-MAIN-20241109151915-20241109181915-00206.warc.gz"} |
Access vs. bandwidth in codes for storage
Maximum distance separable (MDS) codes are widely used in storage systems to protect against disks (nodes) failures. An (n, k, l) MDS code uses n nodes of capacity l to store k information nodes. The
MDS property guarantees the resiliency to any n - k node failures. An optimal bandwidth (resp. optimal access) MDS code communicates (resp. accesses) the minimum amount of data during the recovery
process of a single failed node. It was shown that this amount equals a fraction of 1/(n - k) of data stored in each node. In previous optimal bandwidth constructions, l scaled polynomially with k in
codes with asymptotic rate < 1. Moreover, in constructions with constant number of parities, i.e. rate approaches 1, l scaled exponentially w.r.t. k. In this paper we focus on the practical case of n
- k = 2, and ask the following question: Given the capacity of a node l what is the largest (w.r.t. k) optimal bandwidth (resp. access) (k + 2, k, l) MDS code. We give an upper bound for the general
case, and two tight bounds in the special cases of two important families of codes.
Original language English
Title of host publication 2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012
Pages 1187-1191
Number of pages 5
State Published - 2012
Externally published Yes
Event 2012 IEEE International Symposium on Information Theory, ISIT 2012 - Cambridge, MA, United States
Duration: 1 Jul 2012 → 6 Jul 2012
Publication series
Name IEEE International Symposium on Information Theory - Proceedings
Conference 2012 IEEE International Symposium on Information Theory, ISIT 2012
Country/Territory United States
City Cambridge, MA
Period 1/07/12 → 6/07/12
Funders Funder number
Directorate for Engineering 0801795
Directorate for Engineering
Dive into the research topics of 'Access vs. bandwidth in codes for storage'. Together they form a unique fingerprint. | {"url":"https://cris.tau.ac.il/en/publications/access-vs-bandwidth-in-codes-for-storage","timestamp":"2024-11-10T00:15:41Z","content_type":"text/html","content_length":"51279","record_id":"<urn:uuid:5194c165-5def-468c-9818-c42a8eb5fae5>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.10/warc/CC-MAIN-20241109214337-20241110004337-00320.warc.gz"} |
Momentum & Kinetic Energy Calculations
13 Aug 2024
Popularity: ⭐⭐⭐
Momentum and Kinetic Energy Calculator
This calculator provides the calculation of momentum and kinetic energy for physics applications.
Calculation Example: Momentum is a measure of the mass of an object in motion. It is calculated by multiplying the mass of the object by its velocity. Kinetic energy is a measure of the energy of an
object due to its motion. It is calculated by multiplying the mass of the object by the square of its velocity.
Related Questions
Q: What is the difference between momentum and kinetic energy?
A: Momentum is a measure of the mass of an object in motion, while kinetic energy is a measure of the energy of an object due to its motion. Momentum is a vector quantity, while kinetic energy is a
scalar quantity.
Q: How are momentum and kinetic energy related?
A: Kinetic energy is equal to the square of the momentum divided by twice the mass of the object.
Symbol Name Unit
m Mass kg
v Velocity m/s
Calculation Expression
Momentum Function: The momentum of the object is given by p = mv.
Kinetic Energy Function: The kinetic energy of the object is given by E = 1/2 * mv^2.
Calculated values
Considering these as variable values: v=5.0, m=10.0, the calculated value(s) are given in table below
Derived Variable Value
Momentum Function 50.0
Kinetic Energy Function 125.0
Similar Calculators
Calculator Apps
Academic Chapters on the topic
Matching 3D parts for Impact physics calculation
Related Parameter Sensitivity Analysis engineering data
App in action
The video below shows the app in action. | {"url":"https://blog.truegeometry.com/calculators/Impact_physics_calculation.html","timestamp":"2024-11-02T07:56:57Z","content_type":"text/html","content_length":"21792","record_id":"<urn:uuid:dd55ab3b-9028-4de0-b671-811e5f7386bb>","cc-path":"CC-MAIN-2024-46/segments/1730477027709.8/warc/CC-MAIN-20241102071948-20241102101948-00475.warc.gz"} |
Machine Learning Ex2 - Benchmarks
In my
previous post
, I implemented the algorithm for linear regression using
gradient descent
in Scala using two different methods: standard builtin mathematical methods and
, a Scala linear algebra library.
Shortly after writing the solution I started to wondering if using Scalala had any performance impact on the runtime cost of the solution. While Scalala does have the overhead of object creation, it
also makes heavy use of
classes, which should provide a considerable improvement.
I decided to do some naive benchmarking. These benchmarks are nowhere near
, but should provide a general sense of the solution's runtime. Since I was benchmarking the two Scala solutions, I decided to look at also the MATLAB/Octave and R solutions.
All benchmarking was done on the same 64-bit laptop. The time for loading the data from a file/connection was not included in the benchmarks. Averages are based on 100 iterations of each solution.
The value of each runtime is placed into a vector/list called runtimes, which is then used to determine the average.
$ octave --version
GNU Octave, version 3.4.0
$ r --version
R version 2.13.1 (2011-07-08)
$ scala -version
Scala code runner version 2.9.0.1 -- Copyright 2002-2011, LAMP/EPFL
First, the original MATLAB solution provided by Andrew Ng. Slight modifications were made to wrap the original code as a function. Octave was used as the interpreter for these tests.
> mean(runtimes)
ans = 0.033590
> min(runtimes)
ans = 0.032610
> max(runtimes)
ans = 0.038699
The MATLAB solution runs fairly consistently with little variation (the standard deviation is 9.5084e-04).
Alexandre Martins' solution
in R:
> summary(runtimes)
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.03900 0.04100 0.04200 0.04254 0.04325 0.05200
R provides the very useful summary function which provides basic statistical information of a vector. Both R and MATLAB are interpreted languages, but in this case the solution in R is slower than
MATLAB. The minimum runtime is R is larger than the maximum in MATLAB.
Next is Scala. We will look at first the iterative solution. For both solutions we will use a simple method to calculate the mean
def mean[T](s: Seq[T])(implicit n: Fractional[T]) = n.div(s.sum, n.fromInt(s.size))
scala> mean(runtimes)
res: Double = 0.02949999999999998
scala> runtimes.min
res: Double = 0.025
scala> runtimes.max
res: Double = 0.159
The average runtime is faster than even MATLAB, however the max runtime is quite large. Forgetting about the standard deviation for now, the runtimes for the Scala solution follow a simple pattern:
the first pass is the maximum followed by values that more eventually match the actual average:
scala> runtimes.head
res: Double = 0.159
scala> runtimes.tail.max
res: Double = 0.075
scala> runtimes.take(10)
res: scala.collection.immutable.IndexedSeq[Double] = Vector(0.159, 0.075, 0.053, 0.052, 0.033, 0.03, 0.035, 0.031, 0.027, 0.027)
scala> mean(runtimes.take(10))
res: Double = 0.0558
The average runtime for the first 10 iterations is almost double the average of 100 runtimes. The HopSpot VM is supposed to optimize code over time and this scenario could be a result of such
optimization. Or perhaps is there some caching going on in Scala?
Let us see if the Scalala solution has the same issues:
scala> mean(runtimes)
res: Double = 0.0223
scala> runtimes.min
res: Double = 0.014
scala> runtimes.max
res: Double = 0.424
The average runtime using Scalala is even better, but once again, the max runtime is almost double the average. Looking at the values, the Scalala solution follows the same pattern:
scala> runtimes.head
res: Double = 0.424
scala> runtimes.tail.max
res: Double = 0.084
scala> runtimes.take(10)
res: scala.collection.immutable.IndexedSeq[Double] = Vector(0.424, 0.084, 0.072, 0.052, 0.044, 0.032, 0.033, 0.043, 0.017, 0.016)
scala> mean(runtimes.take(10))
res: Double = 0.08170000000000002
Even after the initial performance hit, the solution does not improve until the 9th iteration.
Where do most of the inefficiencies lie? What would happen if we increased the number of steps used to find the local minimum from 1500 to 15000?
> mean(runtimes)
ans = 0.33541
> min(runtimes)
ans = 0.32408
> max(runtimes)
ans = 0.39594
> summary(runtimes)
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.4250 0.4450 0.4525 0.4563 0.4603 0.5310
Increasing the number of iterations by 10, increase the average runtime by almost the same amount (once again, these benchmarks are very unscientific).
Scala iterative solution
scala> mean(runtimes)
res: Double = 0.27539999999999987
scala> runtimes.min
res: Double = 0.264
scala> runtimes.max
res: Double = 0.564
scala> runtimes.head
res: Double = 0.564
scala> runtimes.tail.max
res: Double = 0.321
scala> runtimes.take(10)
res: scala.collection.immutable.IndexedSeq[Double] = Vector(0.564, 0.29, 0.267, 0.268, 0.268, 0.276, 0.267, 0.269, 0.268, 0.27)
scala> mean(runtimes.take(10))
res: Double = 0.3007
Scalala solution
scala> mean(runtimes)
res: Double = 0.16492
scala> runtimes.min
res: Double = 0.151
scala> runtimes.max
res: Double = 0.811
scala> runtimes.head
res: Double = 0.811
scala> runtimes.tail.max
res: Double = 0.188
scala> runtimes.take(10)
res: scala.collection.immutable.IndexedSeq[Double] = Vector(0.811, 0.159, 0.161, 0.155, 0.159, 0.157, 0.156, 0.157, 0.16, 0.155)
scala> mean(runtimes.take(10))
res: Double = 0.223
The Scala solutions still provide a better average runtime than R or MATLAB over the course of 10+ iterations, but the first pass always has terrible performance.
What do all these number ultimately mean? Very little. Nowadays, developer productivity is one of the most important factors to pay attention to. If a developer is more productive in creating a
solution in R, than perhaps a performance penalty is not as important. With the Scala solutions, using a linear algebra library helped simplify the code and focus on the mathematical concepts
involved. Having a better runtime is only an added benefit.
UPDATE: benchmarking code https://gist.github.com/1201581 UPDATE 2:
The kind folks over at MathWorks were kind enough to do some benchmarking between MATLAB and Octave. All tests done on their system, so a comparison between those numbers and the R/Scala solutions
will not be accurate. Then again, these benchmarks were never comprehensive in the first place.
Octave (3.4.0)
Mean = 0.029570
Min = 0.029214
Max = 0.030383
MATLAB (R2011b)
Mean = 0.0126
Min = 0.0125
Max = 0.0127
Impressive improvement for this small test.
11 comments:
1. Very cool
2. The first several passes on the JVM will always be slow. IMHO the jvm hotspot/jit etc. is optimized for a scenario where the same code is running for a long time.
So if you don't want to benchmark the startup time then let your algorithm run for 100 iterations (or even more i don't know that exactly) and then start your benchmark.
3. Ryan BarrettSeptember 2, 2011 at 8:45AM
If the jvm jit is similar to the clr jit the you will always pay the byte code to native compile and optimilization cost the first time a routine is executed. The fully optimilized code is then
used for all further ititations.
4. Anonymous,
I suspected that the hotspot optimization was kicking in, but I have never profiled code at such a micro-level, therefore I have seen the optimization in action. Interesting stuff. The JVM is one
part of why Scala has become my goto language.
However, ignoring the startup time might result in an apples to oranges comparison. If a code is only meant to be executed once, then startup time is important if doing side-by-side evaluations.
It would be interesting to see if the code can be bootstrapped by using a small set of fake data and a low number of iterations.
5. Because profiling in matlab is so easy, it might be interesting to profile the routine and see where the hot spots are in the matlab version at least. If it's all linear algebra kernels (* or inv
or whatever) then that would explain why the floor is where it is.
>> profile on; run_the_code; profile report
is all you need.
6. what you going to do in that 0.01 second? :)
7. I was wondering why these comments were appearing days after posting the article. Google Analytics tells me Hacker News is linking to me. Welcome!
I encourage everyone to read the original post. The goal is to learn the math involved in the algorithms, not to simply create the fastest version. I also encourage everyone to create your own
implementation in numpy/scipy/Ruby/Clojure/C++/whatever and share with the world.
8. Are you using MATLAB or Octave? At the top you show the Octave version, but then refer to MATLAB throughout the rest of the post. Octave and MATLAB are not the same things -- MATLAB is likely to
be much more optimized than Octave. Please clarify.
9. a pet peeve but ... if you want to compare things ... a graph or table putting the data side by side does wonders for readability and flow of arguments.
my 2 cents.
-- Anonymous Coward
10. RJN,
Octave was used in this example. I wished whoever posted the story to Hacker News did not used the title he/she did since the intent was never to be an absolute benchmark. Do not have MATLAB, so
I cannot benchmark it in any way. Perhaps there is an EC2 instance with MATLAB already installed?
Anon 3:13,
Graphs or tables would have only helped the notion that the benchmark was significant. I do not think the resulting numbers can be used to create a definitive benchmark. However, I did find the
results of the Scala solutions to be interesting since it highlighted the optimization process of the JVM and I did want to plot those values.
11. (I'm the first Anonymous)
If you have code which have to be benchmarked then this code will probably run for a long time. And then the warm up time of the jvm isn't interesting any more. | {"url":"http://blog.brusic.com/2011/08/machine-learning-ex2-benchmarks.html","timestamp":"2024-11-14T08:14:08Z","content_type":"application/xhtml+xml","content_length":"74309","record_id":"<urn:uuid:cca77e1f-fee2-43ba-bdff-db892adc1ec2>","cc-path":"CC-MAIN-2024-46/segments/1730477028545.2/warc/CC-MAIN-20241114062951-20241114092951-00679.warc.gz"} |
The Cryptography Caffè ☕
This blogpost serves as a gentle introduction to a widely used security model for analyzing real-world post-quantum cryptosystems, including the recent NIST standards, called the "quantum random
oracle model".
Read more ⟶
This blog post gives an overview of the area of formally verified cryptography and SandboxAQ's activities in this area.
Read more ⟶
This blog post describes the main idea of each of our three papers that have been accepted at CRYPTO 2024.
Read more ⟶
This blogpost discusses the Real World PQC workshop we hosted in March 2024 in Toronto, followed by our teams attendance and participation at RSA in May.
Read more ⟶
This blogpost describes the papers, presentations, and attendees from the SandboxAQ cybersecurity group at the IACR flagship conference Eurocrypt 2024.
Read more ⟶
A blog post from our attendence and participation at the 5th NIST PQC Standardization conference which took place on April 10-12 2024 in Maryland, USA
Read more ⟶
This post explains the concept of federated learning in cross-silo settings and its potential use-cases for network security applications.
Read more ⟶
This post gives a brief explanation of our research paper about attestation in FIDO2.
Read more ⟶
A walkthrough of how we implemented TurboTLS using Sandwich, and how you can try it out for yourself.
Read more ⟶
This blogpost describes work that encoded a hard lattice problem, $K$-DSP, into a quantum Hamiltonian, with implications for lattice cryptography.
Read more ⟶ | {"url":"https://cryptographycaffe.sandboxaq.com","timestamp":"2024-11-08T11:14:41Z","content_type":"text/html","content_length":"7712","record_id":"<urn:uuid:ce58fad5-5702-48f7-8470-a8afd4530b2f>","cc-path":"CC-MAIN-2024-46/segments/1730477028059.90/warc/CC-MAIN-20241108101914-20241108131914-00543.warc.gz"} |
a tale of two whiskers
Ali Belabbas proved the following clever result.
Consider a Riemannian manifold \(M^m\), and the gradient flow of a generic function \(f\). Then the \(\omega\)-limit of a trajectory starting near a local maxima (i.e., with the starting point drawn
from a density \(\lambda^mf(\lambda x)dx\)), consists, with asymptotic certainty as \(\lambda\to\infty\), of at most two local minima of \(f\).
What is going on here?! Nothing unexpected, in fact.
Consider a local equilibrium (say, at the origin) of a smooth dynamical system,
\dot{x}=v(x), v(0)=0,
with the linearization \(A=\partial v/\partial x\). Assume, further, that an eigenvalue of \(A\) dominates the rest:
\sigma(A)=\{s_1,\ldots,s_m\}, \Re(s_1)>\Re(s_k), k=2,\ldots,m
(this implies, of course, that \(s_1\) is real), and that \(s_1>0\).
These data allow one to define a 1-dimensional and 1-codimensional \(v\)-invariant submanifolds \(\Sigma_+\) and \(\Sigma_-\), such that the tangent space to \(\Sigma_+\) at the origin (the whiskers)
is spanned by the eigenvector for \(s_1\), and the tangent space to \(\Sigma_+\) at the origin is spanned by the remaining eigenspaces of \(A\) (see, e.g., Hirsch et al, Invariant Manifolds).
Using this splitting, one can easily prove the following result:
Proposition. For any sufficiently small sphere \(S_r\) around the origin, let \(\{x_1, x_2\}=\Sigma_+ \cap S_r\) be the intersection of the whiskers with that sphere, and \(U_1, U_2\) arbitrarily
small spherical vicinities of \(x_1, x_2\). Then for sufficiently small \(\epsilon\), the fraction of set of points in the \(\epsilon\)-ball around the origin such that the \(v\)-trajectories
starting there exists \(S_r\) at \(U_{1,2}\) is arbitrarily close to one.
This is, essentially, Belabbas’ theorem: in his situation, the linearization of the gradient flow near a critical point is self-adjoint, and, generically, the leading eigenvalue is simple. Each of
the whiskers, generically, descends to a local minimum, and if one starts close enough to it (in the vicinity \(U_k, k=1,2\)), one can assure that the resulting trajectory follows the whisker to the
basin of attraction of the corresponding minimum.
The randomness, however, manifests itself not just at the starting point, but along the trajectory. What happens if one considers the system \(\dot{x}=v(x)\) and perturbs it slightly with stochastic
In other words, consider the SDE
dx=v(x)dt+\epsilon g(x)dW, G:U\to TM
(here \(v(p)=0\), \(g\) is a morphism of the trivial \(k\)-dimensional vector bundle over \(M\) to its tangent bundle, \(W\) standard \(k\)-dimensional Brownian motion; Ito integrals).
In this case, in the notation above, one has (we assume, for simplicity, that the starting point is located deterministically at the origin):
Proposition: If the pair \((A=\partial v/\partial x, B=g(0))\) is controllable, or, equivalently, satisfies the Hörmander condition at the origin^1i.e., the minimal \(A\)-invariant subspace
containing the range of \(B\) is the whole space \(T_oM\), then for sufficiently small \(\epsilon\), the probability that the trajectories of the SDE above exit \(S_r\) at \(U_{1,2}\) is arbitrarily
close to one.
Specializing again to generic gradient systems, and using Kurtz’ theorem, one can establish that the trajectories of the corresponding SDE descend with overwhelming probability to small vicinities of
one of at most two minima (before, eventually, leaving them in their search for an attainable global minimum).
Leave a Comment | {"url":"https://ymb.web.illinois.edu/2024/10/13/a-tale-of-two-whiskers/","timestamp":"2024-11-04T19:52:06Z","content_type":"text/html","content_length":"141825","record_id":"<urn:uuid:afd82851-a588-449c-a372-d19dffec7544>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.16/warc/CC-MAIN-20241104194528-20241104224528-00603.warc.gz"} |
Schools Math
Schools Mathematics Grand Challenge
Week seven's Puzzles
Problem 19:
The nineteenth problem was:
A large convoy of mini-buses travelled from Limerick to Croke Park for the rugby match last weekend. When starting out from Limerick, all of the coaches carried exactly the same number of passengers.
However, on the way to Dublin, 10 coaches broke down, and in order to accomodate all of the passengers from these 10 coaches, each of the remaining coaches took exactly one extra passenger. After the
match, before returning back to Limerick, the organisers found that a further 15 coaches had broken down. However, everyone was once again accommodated, and, on the way back to Limerick, each
mini-bus had exactly three more passengers than it had when leaving Limerick in the morning.
How many people travelled to the match on the minibuses?
The solution was:
Let X denote the number of coaches that left Limerick in the morning and let Y denote the number of people on each mini-bus. Then the total number of people who travelled to the match is XY (X
multiplied by Y). We also know that
(X - 10)(Y + 1) = XY
(X - 25)(Y + 3) = XY.
The first equation gives us
X = 10Y + 10
and the second equation gives
3X= 25y + 75.
Subsitituting for X we get that
30Y + 30 = 25Y + 75
so Y = 9, and X = 100.
Thus the total number that travelled to the match is 900.
Problem 20:
The twentieth problem was:
One Friday evening, Mary walked from her house to Sheila's house at a constant speed, arrived at Sheila's house at 8 pm, and then they both immediately walked the same route back to Mary's house.
Next Friday, Sheila was ready earlier than usual and started to walk along the route towards Mary's house at some time before 8 pm. She met Mary coming towards her along the route, at which point,
Mary turned around and walked back to her house with Sheila. On this occasion they reached Mary's house exactly 16 minutes earlier than on the previous Friday. If the two friends walked at the same
constant speed on both Fridays, and Mary left her house at the same time both days, how many minutes before 8 do they met the second day?
The solution was:
The two journeys that Mary makes on the consecutive Fridays are illustrated in the diagram below. She meets Sheila at the point X on the second Friday.
The difference on the second Friday is that she does not have to walk the part of the route indicated by the dashed arrows. As she leaves her house at the same time both evenings and arrives home 16
minutes earlier the second evening, this part of the journey must have taken exactly 16 minutes, 8 minutes in each direction.
As she walked at the same speed both days, on the second Friday she must have met Sheila exactly eight minutes before 8. Hence the answer is 8 minutes.
Problem 21:
The twenty first problem was:
One Sunday afternoon, John walked around the square path shown below.
When asked how long it took him to complete the circuit, he could not remember. However, he did record the following odd information about the timing of different parts of the walk.
• He walked at a constant speed along each side of the square;
• His speed was different along each side of the square (so his constant speed from A to B was different to the constant speed from B to C and so on);
• The first two thirds of the walk (in distance) took him exactly 10 minutes longer than the final two thirds of the walk;
• The side from C to D took longer than the side from A to B, and the time taken to go from B to C was longer than the time taken from D to A by exactly the same amount.
How much longer did the side from A to B take than the side from D to A?
The solution was:
Let W, X, Y, Z represent the times taken to walk the legs AB, BC, CD, DA respectively. Then John's third piece of information implies that
W + X + (2/3)Y = (2/3) X + Y + Z + 10.
and John's fourth piece of information tells us that
Y - W = X - Z.
We are looking for W - Z. The first equation gives us
W - Z = (1/3)(Y - X) + 10
while the second equation gives
Y - X = W - Z.
W - Z = (1/3)(W - Z) + 10
(2/3)(W - Z) = 10
so W - Z = 15, and the answer is 15 minutes. | {"url":"https://www.hamilton.ie/mathschallenge/year2_solution7.htm","timestamp":"2024-11-10T09:29:36Z","content_type":"text/html","content_length":"9313","record_id":"<urn:uuid:cc03ae62-19ee-4309-8c9e-b9397f315b0f>","cc-path":"CC-MAIN-2024-46/segments/1730477028179.55/warc/CC-MAIN-20241110072033-20241110102033-00256.warc.gz"} |
Solved: What is the minimum thickness d of dielectric that can be, Physics
suppose you want to design a capacitor that uses mica as the dielectric material which has K = 7 and a dielectric strength of 150 MV/m. It is intended to store at least 1.- J of energy and be able to
withstand a voltage up to 250 volts without electric breakdown.
a) What is the minimum thickness d of dielectric that can be used? For that thickness what is the area of a plate (and of the mica) that must be used?
b) Now assume the capacitor is initially charged to a voltage of 2.0 x 10^2 V. Connecting a wire from one plate to the other, the voltage falls to half its initial value in 2.4 ms. During that time,
how large is the average electric current through the wire?
Solution Preview :
Prepared by a verified Expert
Physics: What is the minimum thickness d of dielectric that can be
Reference No:- TGS01119703
Now Priced at $10 (50% Discount) | {"url":"https://www.tutorsglobe.com/question/what-is-the-minimum-thickness-d-of-dielectric-that-can-be-51119703.aspx","timestamp":"2024-11-11T14:14:04Z","content_type":"text/html","content_length":"45067","record_id":"<urn:uuid:cdf21415-1c03-4344-ba95-292b01ebb7fc>","cc-path":"CC-MAIN-2024-46/segments/1730477028230.68/warc/CC-MAIN-20241111123424-20241111153424-00470.warc.gz"} |
Coordinate system#
The commonly used coordinate systems include the world coordinate system, the vehicle coordinate system, and the sensor coordinate system.
• The world coordinate system is a fixed coordinate system that defines the physical space in the environment where the vehicle is located.
• The vehicle coordinate system is the vehicle's own coordinate system, which defines the vehicle's position and orientation in the world coordinate system.
• The sensor coordinate system is the sensor's own coordinate system, which is used to define the sensor's position and orientation in the vehicle coordinate system.
How coordinates are used in Autoware#
In Autoware, coordinate systems are typically used to represent the position and movement of vehicles and obstacles in space. Coordinate systems are commonly used for path planning, perception and
control, can help the vehicle decide how to avoid obstacles and to plan a safe and efficient path of travel.
1. Transformation of sensor data
In Autoware, each sensor has a unique coordinate system and their data is expressed in terms of the coordinates. In order to correlate the independent datas between different sensors, we need to
find the position relationship between each sensor and the vehicle body. Once the installation position of the sensor on the vehicle body is determined, it will remain fixed during running, so
the offline calibration method can be used to determine the precise position of each sensor relative to the vehicle body.
2. ROS TF2
The TF2 system maintains a tree of coordinate transformations to represent the relationships between different coordinate systems. Each coordinate system is given a unique name and they are
connected by coordinate transformations. How to use TF2, refer to the TF2 tutorial.
TF tree#
In Autoware, a common coordinate system structure is shown below:
graph TD
/earth --> /map
/map --> /base_link
/base_link --> /imu
/base_link --> /lidar
/base_link --> /gnss
/base_link --> /radar
/base_link --> /camera_link
/camera_link --> /camera_optical_link
• earth: earth coordinate system describe the position of any point on the earth in terms of geodetic longitude, latitude, and altitude. In Autoware, the earth frame is only used in the
GnssInsPositionStamped message.
• map: map coordinate system is used to represent the location of points on a local map. Geographical coordinate system are mapped into plane rectangular coordinate system using UTM or MGRS. The
map frame`s axes point to the East, North, Up directions as explained in Coordinate Axes Conventions.
• base_link: vehicle coordinate system, the origin of the coordinate system is the center of the rear axle of the vehicle.
• imu, lidar, gnss, radar: these are sensor frames, transfer to vehicle coordinate system through mounting relationship.
• camera_link: camera_link is ROS standard camera coordinate system .
• camera_optical_link: camera_optical_link is image standard camera coordinate system.
Estimating the base_link frame by using the other sensors#
Generally we don't have the localization sensors physically at the base_link frame. So various sensors localize with respect to their own frames, let's call it sensor frame.
We introduce a new frame naming convention: x_by_y:
x: estimated frame name
y: localization method/source
We cannot directly get the sensor frame. Because we would need the EKF module to estimate the base_link frame first.
Without the EKF module the best we can do is to estimate Map[map] --> sensor_by_sensor --> base_link_by_sensor using this sensor.
Example by the GNSS/INS sensor#
For the integrated GNSS/INS we use the following frames:
flowchart LR
earth --> Map[map] --> gnss_ins_by_gnss_ins --> base_link_by_gnss_ins
The gnss_ins_by_gnss_ins frame is obtained by the coordinates from GNSS/INS sensor. The coordinates are converted to map frame using the gnss_poser node.
Finally gnss_ins_by_gnss_ins frame represents the position of the gnss_ins estimated by the gnss_ins sensor in the map.
Then by using the static transformation between gnss_ins and the base_link frame, we can obtain the base_link_by_gnss_ins frame. Which represents the base_link estimated by the gnss_ins sensor.
Coordinate Axes Conventions#
We are using East, North, Up (ENU) coordinate axes convention by default throughout the stack.
X+: East
Y+: North
Z+: Up
The position, orientation, velocity, acceleration are all defined in the same axis convention.
Position by the GNSS/INS sensor is expected to be in earth frame.
Orientation, velocity, acceleration by the GNSS/INS sensor are expected to be in the sensor frame. Axes parallel to the map frame.
If roll, pitch, yaw is provided, they correspond to rotation around X, Y, Z axes respectively.
Rotation around:
X+: roll
Y+: pitch
Z+: yaw
How they can be created#
1. Calibration of sensor
The conversion relationship between every sensor coordinate system and base_link can be obtained through sensor calibration technology. How to calibrating your sensors refer to this link
calibrating your sensors.
2. Localization
The relationship between the base_link coordinate system and the map coordinate system is determined by the position and orientation of the vehicle, and can be obtained from the vehicle
localization result.
3. Georeferencing of map data
The georeferencing information can get the transformation relationship of earth coordinate system to local map coordinate system. | {"url":"https://autowarefoundation.github.io/autoware-documentation/pr-347/contributing/coding-guidelines/ros-nodes/coordinate-system/","timestamp":"2024-11-09T10:52:03Z","content_type":"text/html","content_length":"100361","record_id":"<urn:uuid:0939646d-79bf-4fb5-aad5-9bffc9e128b0>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.75/warc/CC-MAIN-20241109085148-20241109115148-00799.warc.gz"} |
How many cups is 32 oz? 2, 3, 4, 5, 6, 8,10, 12, 14, 16, 24, 34, 64 oz. Great tips to convert.How many cups is 32 oz? 2, 3, 4, 5, 6, 8,10, 12, 14, 16, 24, 34, 64 oz. Great tips to convert. - Davies Chuck Wagon
in Cook, Coffee, Drink
How many cups is 32 oz? 2, 3, 4, 5, 6, 8,10, 12, 14, 16, 24, 34, 64 oz. Great tips to convert.
Disclaimer: There are affiliate links in this post. At no cost to you, I get commissions for purchases made through links in this post.
Have you ever wondered how many cups is 32 oz ? This can be an important calculation for anyone who cooks or bakes frequently, since recipes often involve different units of measurement. We’ll
explore just how many cups there are in each unit of measurement—so that measuring ingredients accurately will never again stand between you and that delicious baked goods or savory meal.
What is an Ounce (oz)?
An ounce is a unit of mass in the imperial and United States customary systems of measurement. It is equal to 28.35 grams or 0.91136 kilograms, and can be used for measuring both dry and liquid
substances such as gold, silver, fuel, oil and even water. An ounce is also commonly used when buying groceries or specifying drug dosages.
In the retail market, an ounce most often refers to an avoirdupois ounce – the type of ounce that weighs 28g per 1oz weight (1 troy oz = 31.1g). Therefore it is important to differentiate between
troy ounces (used for precious metals) and avoirdupois ounces (used for everyday measurements).
Ounces are also used in other countries, mainly the United Kingdom and Ireland. In the UK an ounce is equal to 28.349 grams, while in Ireland it is equal to 28.35 grams. One pound (453 g) is
equivalent to 16 ounces or 1/16 of a kilogram.
This makes ounces a popular unit of measurement for items that are purchased in small amounts such as spices, herbs, nuts and candy. In the US, food items are often labeled with both grams and ounces
as a way to provide consumers with an easier way to understand their nutritional content. As you can see, ounces are a versatile unit of measurement that is used in many different contexts.
What is a cup?
A cup is a small container typically used for drinking. It can also be used to measure, mix, or store food items such as ingredients in cooking and baking. Cups come in many different sizes and
shapes, but generally they have a base that tapers up to an open top with a handle attached to the side. A cup is usually made from plastic, glass, ceramic, or metal. Cups are designed for everyday
use and some come with lids or handles to make drinking easier and prevent spills.
They are versatile tools found in both home kitchens and commercial settings such as restaurants and cafeterias. Cups can also be used for measuring ingredients when making food, such as dry and
liquid measurements. The size of the cup depends on what you need it for, with larger sizes being used for more than one measurement. Cups are a practical tool found in nearly every household and are
essential for any kitchen.
How many cups is 32 oz?
32 ounces is equivalent to 4 cups. To calculate this, divide 32 by 8 (the number of ounces in a cup) and the result will be 4. This means that there are 4 cups in 32 ounces. It is important to note
that these measurements may vary slightly depending on the type of ingredient you are measuring as some ingredients can have different densities which can affect how much fits in each cup or ounce.
For instance, 1 cup of flour might not weigh exactly 8oz but it should measure close enough when using a kitchen scale for accuracy. As such, it is best practice to use scales whenever accurate
measurements are needed.
Cups and Ounces converting (for liquid ounce):
To convert from cups to ounces, use the following formula: number of cups multiplied by 8 (the number of ounces in a cup). For example, if you have 2 cups of a liquid ingredient, multiply 2 by 8 to
get 16 ounces.
Cups to ounces: Number of cups X 8
Example : 6 cups = 6x 8= 48 oz
To convert ounces to cups, you will need to divide the number of ounces by 8 (the number of ounces in a cup). For example, if you have 32 ounces, divide 32 by 8 to get 4 cups. Therefore, 32 ounces is
equal to 4 cups.
Ounce to cups: Number of ounces/8
Example: 16 oz = 16/8= 2 cups.
So, from this knowledge, we were able to answer the following questions:
How many cups is 2 oz?
Answer: 2 ounces is equal to 0.25 cups.
How many cups is 3 oz?
Answer: 3 ounces is equal to 0.375 cups.
How many cups is 4 oz?
Answer: 4 ounces is equal to 0.5 cups.
How many cups is 5 oz?
Answer: 5 ounces is equal to 0.625 cups.
How many cups is 6 oz?
Answer: 6 ounces is equal to 0.75 cups.
How many cups is 8 oz?
Answer: 8 ounces is equal to 1 cup.
How many cups is 10 oz?
Answer: 10 ounces is equal to 1.25 cups.
How many cups is 12 oz?
Answer: 12 ounces is equal to 1.5 cups.
How many cups is 14 oz?
Answer: 14 ounces is equal to 1.75 cups.
How many cups is 16 oz?
Answer: 16 ounces is equal to 2 cups.
How many cups is 24 oz?
Answer: 24 ounces is equal to 3 cups.
How many cups is 34 oz?
Answer: 34 ounces is equal to 4.25 cups.
How many cups is 64 oz?
Answer: 64 ounces is equal to 8 cups.
Difference between liquid ounce and dry ounce:
When converting between cups and ounces, it is important to note that liquid ounces (fl oz) are different from dry ounces (oz). This is because the densities of various ingredients can affect the
measurement. For example, a cup of sugar will weigh more than a cup of water due to its higher density.
Liquid ounce: A liquid ounce is abbreviated as fl oz or oz lq and it is a unit used to measure liquid volume.
Dry ounce: A dry ounce is abbreviated as oz dr and it is a unit used to measure dry ingredients such as flour, sugar, etc.
1 fl oz = 0.95735295625 oz dr
1 oz dr = 1.040842731 fl oz
Liquid ounces and dry ounces refer to two different types of measurements.
One liquid ounce is equal to 1/8 cup or 2 tablespoons, while one dry ounce is equal to 4 tablespoons or 28.35 grams.
To convert between the two, you must recognize that there are different densities in each type of ingredient.
For example: 1 cup of flour does not weigh 8 oz., but instead weighs around 4-5 oz. Therefore, if you want to convert from liquid oz. to dry oz., you must multiply the amount by the density factor,
which is usually 4-5.
If you want to convert from dry oz. to liquid oz., divide the amount by the same density factor.
For example: If you have 6 ounces of water, this would be equal to 6/8 cups or 0.75 cups. To convert this into tablespoons, multiply 0.75 by 16 which gives you 12 tablespoons of water.
Now let’s say you have 4 dry ounces of flour: multiplying this amount by 4 (the density factor) gives us 16 ounces; dividing that number by 8 (the number of ounces in a cup) will give us 2 cups of
flour which is equivalent to 32 tablespoons of flour.
Therefore, converting between liquid and dry ounces requires knowledge about the ingredient’s density, as well as the proper conversion formula.
Read more:
How Many Ounces Are In 750 ml?
How many tablespoons in an ounce?
How many tablespoons in 1/4 cup
Why are ounces and cups important in cooking?
1. Accurate Measurements: Using a standard cup measure is the most accurate and consistent way to measure ingredients for recipes. This ensures that each time you make a certain dish, it will have
the same taste and texture as it did before.
2. Portion Control: Cups provide an easy way to control portions when cooking by measuring out precise amounts of ingredients necessary for a recipe or meal. For example, if you are baking cookies,
using cups allows you to portion out each cookie with a specific amount of dough instead of eyeballing it.
3. Easier Conversion Between Units: Converting between ounces and cups is much easier than converting between other units such as teaspoons, tablespoons, etc., since there is a uniform ratio (1 cup =
8 ounces). This makes it easier to accurately convert recipe measurements when necessary.
4. Standardized Recipes: Most recipes are written in volume measurements such as cups and ounces, so that cooks can use the same exact measurements for consistent results each time they make a dish.
5. Easier Shopping: Knowing how many cups or ounces of an ingredient you need is essential for grocery shopping, as it allows you to easily calculate what quantities of a certain item you should buy.
6. Understanding Yields: Since most recipes are written with volume measurements, understanding how many cups or ounces of an ingredient yields a certain amount of food also helps when calculating
how much food will be made from a given recipe.
7. Simplified Recipe Writing: By using the same unit of measurement (cups and ounces) throughout a recipe, it makes it easier for someone to follow instructions and replicate dishes more accurately.
Ounces and cups are essential in cooking because they provide a consistent, accurate way to measure ingredients, control portions when necessary, as well as simplify recipe writing.
8 Tips to convert ounces to cups
1. Calculate the number of cups by dividing the total number of ounces by 8. For example, 16 ounces divided by 8 equals 2 cups.
2. If you want to convert from liquid oz to dry oz, multiply the amount of liquid oz by the density factor which is usually 4-5.
3. If you want to convert from dry oz to liquid oz, divide the amount of dry oz by the density factor.
4. Always use measuring cups when baking to ensure accuracy and precision.
5. If you are converting between ounces and teaspoons, remember that 1 ounce is equal to 6 teaspoons and 1 teaspoon is equal to 0.1667 ounces.
6. When measuring out ingredients for a recipe, use the measurements listed in the recipe as a guide but be sure to double-check with a separate set of measuring cups or spoons just to ensure
accuracy! This will help ensure your end result tastes great every time!
7. For measurements that are not listed in common measurements (e.g. tablespoons, teaspoons), use the metric system to convert between units like liters and milliliters.
8. When measuring out ingredients for a recipe, be sure to measure carefully and accurately as this will affect the end result! Be precise when measuring out each ingredient to get the best results
Following these 8 tips can help you accurately convert ounces into cups for any recipe with confidence!
Ounces into cups conversion table
Ounces Cups Ounces Cups
US dry ounces to cups table for 32 oz:
Ingredient Dry Ounces Cups
Almond flour 32 oz 9.44 cups
Milk 32 oz 3.7 cups
Water 32 oz 3.83 cups
Butter 32 oz 4 cups
Granulated sugar 32 oz 4.52 cups
Powdered sugar 32 oz 7.5 cups
Cake flour 32 oz 7.96 cups
Flour 32 oz 7.25 cups
FAQs about how many cups is 32 oz:
1. What is the difference between an ounce and a cup?
An ounce is a unit of measurement for weight, while a cup is a unit of measurement for volume.
2. How many ounces are in one cup?
One cup is equivalent to 8 fluid ounces.
3. How do you convert ounces to cups?
To convert ounces to cups, divide the number of ounces by 8. For example, 16 ounces would equal 2 cups (16/8 = 2).
4. How many ounces are in a tablespoon?
A tablespoon is equal to 1/2 fluid ounce, or 3 teaspoons.
5. How many tablespoons are in an ounce?
There are 2 tablespoons in an ounce.
6. Can you convert ounces to milliliters?
Yes, you can convert ounces to milliliters using the following formula: 1 fluid ounce = 29.5735296 milliliters.
7. How many milliliters are in one cup?
One cup is equivalent to 236.5882365 mL (milliliters).
8. What is the conversion rate for grams and cups?
1 cup of a dry ingredient is equal to approximately 125 grams.
9. How do you convert ounces to pounds?
To convert ounces to pounds, divide the number of ounces by 16. For example, 32 ounces would equal 2 pounds (32/16 = 2).
10. What is 1 fluid ounce in milliliters?
1 fluid ounce equals 29.5735296 milliliters.
11. How can I measure an ounce without a measuring cup?
You can use kitchen scales to measure ounces without a measuring cup.
12. How do you convert teaspoons to cups?
To convert teaspoons to cups, divide the number of teaspoons by 48. For example, 24 teaspoons would equal 1/2 cup (24/48 = 0.5).
Conclusion how many cups is 32 oz:
Ounces and cups are essential units of measurement for cooking. They allow cooks to accurately measure ingredients, control portions when needed, as well as simplify recipe writing. Furthermore,
understanding how to convert between liquid and dry ounces is also important in order to get consistent results each time a dish is made. All these factors make it clear why ounces and cups are so
important in the kitchen!
I’m Leon Todd and my passion for cooking is my life goal. I’m the owner and operator of Davieschuckwagon.com, a website that specializes in providing high-quality cooking information and resources. I
love to experiment with new flavors and techniques in the kitchen, and I’m always looking for ways to improve my skills.
I worked my way up through the ranks, taking on more challenging roles in the kitchen. I eventually became a head chef.
Cooking is more than just a job to me – it’s a passion that I want to share with the world.
GIPHY App Key not set. Please check settings
What do you think?
0 Points
Upvote Downvote | {"url":"https://davieschuckwagon.com/blog/how-many-cups-is-32-oz/","timestamp":"2024-11-09T21:56:53Z","content_type":"text/html","content_length":"341638","record_id":"<urn:uuid:15623194-3bd9-49cf-9212-6bd05cda0bfe>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.10/warc/CC-MAIN-20241109214337-20241110004337-00039.warc.gz"} |
Grams (g) to Micrograms (μg) & Micrograms (μg) to Grams (g)
Easily switch between grams to micrograms and vice versa using Examples.com. Input your measurements for fast and precise conversions.
Gram to Microgram
Formula: Mass in Microgram (μg) = Mass in Gram (g) × 10^6
Microgram to Gram
Formula: Mass in Gram(g) = Mass in Microgram (μg) × 10^-6
Mass Converters to Gram (g)
Mass Converters to Microgram (µg)
Conversion Factors:
• Grams to Micrograms: 1 gram = 1,000,000 micrograms
• Micrograms to Grams: 1 microgram = 0.000001 grams
How to Convert Grams to Micrograms:
To convert grams to micrograms, multiply the number of grams by 1,000,000.
Example: Convert 5 grams to micrograms.
Micrograms=5×1,000,000=5,000,000 micrograms
How to Convert Micrograms to Grams:
To convert micrograms to grams, multiply the number of micrograms by 0.000001.
Example: Convert 2,500,000 micrograms to grams.
Grams=2,500,000×0.000001=2.5 grams
Grams to Micrograms Conversion Table
Grams (g) Micrograms (µg)
1 g 1e+6 µg
2 g 2e+6 µg
3 g 3e+6 µg
4 g 4e+6 µg
5 g 5e+6 µg
6 g 6e+6 µg
7 g 7e+6 µg
8 g 8e+6 µg
9 g 9e+6 µg
10 g 1e+7 µg
20 g 2e+7 µg
30 g 3e+7 µg
40 g 4e+7 µg
50 g 5e+7 µg
60 g 6e+7 µg
70 g 7e+7 µg
80 g 8e+7 µg
90 g 9e+7 µg
100 g 1e+8 µg
g to µg Conversion Chart
Micrograms to Grams Conversion Table
Micrograms (µg) Grams (g)
1 µg 1e-6 g
2 µg 2e-6 g
3 µg 3e-6 g
4 µg 4e-6 g
5 µg 5e-6 g
6 µg 6e-6 g
7 µg 7e-6 g
8 µg 8e-6 g
9 µg 9e-6 g
10 µg 1e-5 g
20 µg 2e-5 g
30 µg 3e-5 g
40 µg 4e-5 g
50 µg 5e-5 g
60 µg 6e-5 g
70 µg 7e-5 g
80 µg 8e-5 g
90 µg 9e-5 g
100 µg 1e-4 g
µg to g Conversion Chart
Differences Between Grams to Micrograms
Aspect Grams (g) Micrograms (µg)
Definition A gram is a unit of mass in the metric system. A microgram is a unit of mass in the metric system.
Symbol g µg
Conversion Factor 1 gram = 1,000,000 micrograms 1 microgram = 0.000001 grams
Usage Commonly used for measuring larger quantities of mass. Used for measuring very small quantities of mass.
Typical Context Used in everyday contexts such as weighing food or other household items. Commonly used in scientific and medical contexts.
Measurement Precision Suitable for general measurements with less precision. Suitable for precise measurements, especially in scientific research.
Scale Larger scale unit compared to micrograms. Smaller scale unit compared to grams.
Practical Example 1 gram of sugar in a recipe. 200 micrograms of a vitamin in a supplement.
1. Solved Examples on Converting Grams to Micrograms
Example 1:
Problem: Convert 3 grams to micrograms.
Solution: 3 g×1,000,000=3,000,000µg
Example 2:
Problem: Convert 0.5 grams to micrograms.
Solution: 0.5 g×1,000,000=500,000µg
Example 3:
Problem: Convert 7 grams to micrograms.
Solution: 7 g×1,000,000=7,000,000µg
Example 4:
Problem: Convert 0.75 grams to micrograms.
Solution: 0.75 g×1,000,000=750,000µg
Example 5:
Problem: Convert 12 grams to micrograms.
Solution: 12 g×1,000,000=12,000,000µg
2. Solved Examples on Converting Micrograms to Grams
Example 1:
Problem: Convert 3,000,000 micrograms to grams.
Solution: 3,000,000µg×0.000001=3g
Example 2:
Problem: Convert 500,000 micrograms to grams.
Solution: 500,000µg×0.000001=0.5g
Example 3:
Problem: Convert 7,000,000 micrograms to grams.
Solution: 7,000,000µg×0.000001=7g
Example 4:
Problem: Convert 750,000 micrograms to grams.
Solution: 750,000µg×0.000001=0.75g
Example 5:
Problem: Convert 12,000,000 micrograms to grams.
Solution: 12,000,000µg×0.000001=12g
Why do we need to convert grams to micrograms?
Conversion from grams to micrograms is necessary when dealing with very small quantities, especially in scientific and medical contexts, where precision is crucial.
What are some practical applications of converting grams to micrograms?
Practical applications include calculating the dosage of medications, measuring small quantities of substances in chemical experiments, and detailing nutritional content in food science.
How do you handle large numbers when converting grams to micrograms?
Use scientific notation to simplify large numbers. For example, 5 grams is 5e+6 µg, which helps avoid errors in handling large figures.
Can digital tools help with converting grams to micrograms?
Yes, many digital calculators and online conversion tools can quickly and accurately convert grams to micrograms, which is especially useful in professional and academic settings.
Do scientific experiments often require gram to microgram conversions?
Yes, scientific experiments, particularly in chemistry and biology, often require precise measurements that involve converting grams to micrograms.
How can I ensure accuracy when converting grams to micrograms manually?
To ensure accuracy, use a reliable calculator, double-check your multiplication, and remember that 1 gram is always equal to 1,000,000 micrograms. | {"url":"https://www.examples.com/physics/g-microgram","timestamp":"2024-11-02T00:01:54Z","content_type":"text/html","content_length":"115135","record_id":"<urn:uuid:e737d5df-be70-4d05-a4ad-dc885449788e>","cc-path":"CC-MAIN-2024-46/segments/1730477027599.25/warc/CC-MAIN-20241101215119-20241102005119-00109.warc.gz"} |
What is the role of statistical model selection in Pearson MyLab Statistics? | Hire Someone To Take MyLab Exam
What is the role of statistical model selection in Pearson MyLab Statistics? It is true that the Pearson correlation of data has tended to become narrower as data is acquired, but that the scatter of
the correlations can improve the accuracy. For example, in a pilot study, the Pearson correlation from all types (NPI & HITS) was 0.039, which means Pearson correlation was not as broad as would be
observed in an asymptotically normal data set (e.g., a normal distribution) generally. However, to apply a statistical model selection approach to Pearson correlation, it was necessary to apply
statistics primarily based on the non-normal distribution. What is the role of statistical models selection? Statistics are the tools for the statistical analysis that are used to specify what a
statistical model should be, to ensure power and balance in different statistical models. For an example, data in a particular set is presented (generally for a number of different graphs or models),
as is example data in a particular area. See HITS and HIST (2006), for data drawn from a certain area, while some data is extracted, and HITS and HIST are used in an overview calculation to (analyze)
the area of another area. However, these examples are example data. Although new data are coming in in more and more areas or for more data, what is presented in the example data in each area has
been a fairly straightforward process that, if it is done with a good correlation, can produce a more general result. This has led many papers describing this in different forms, with more data.
Frequently, the model selection process is conducted in their own time. Furthermore, HITS and HIST have been used in two ways: see example data of HITS, which is useful in the problem of computing
Pearson correlation. Method step 1 Step 1. Create a set of data (typically all the data type) In this example of data, a set of NPI data is more helpful hints from a set of OIs extracted from a
sequence of several NPI data sets extracted from the HITS dataset which has been simulated from the Z-score metric. This sequence is denoted as the HITS sequence -hits. Also, a series of multiple
points is simulated in each HITS sequence to generate a sequence of values from a larger sequence of NPI data sets. The sequence of points to be simulated is shown in Example 2.1.
Where Can I Pay Someone To Take My Online Class
Both examples, NPI data and OIs, are formed as disorder terms. This introduces an additional term in the series of points to be used in OIs (i.e., ordered power of second moments or normalization:
data from multiple model values) since the disorder model is often described as power function. Step 2. Determine the order of the data. Many models are not ordered when it comes to order of values.
For example, Sample data is drawn from a populationWhat is the role of statistical model selection in Pearson MyLab Statistics? For statistical models the statistical model selection algorithm is
more popular and often used in data-theoretic research. All this analysis suggests that sample size comes in many ways: they come in many types and means and effects and they all have a number of
advantages and disadvantages or they come in two main forms: the distribution of the difference and the norm of the differences between the groups. For a given statistic that allows us to collect
statistics in more than one way we could develop standardized statistics using these methods. The advantages of this approach over using power calculations are too obvious to ignore. BH and BWP have
published quite interesting papers in the subject and it would be highly unlikely that there should ever be such a comparison in the buchshohner project. In the past I have used both methods to
understand the statistical genetics of the Schouler disease. But this methodology is incomplete due to the fact that a model can easily be made wrong by missing data. A good example of what a sample
size should look like is what is called Fisher’s exact test. You can write it in such a way that you understand what the test means, but what you are actually doing is writing out a formula for the
sample mean which can, at least, indicate what it means. One example was done using the following formula. C(size) = 1/(C(measured) – C(measured-Fisher). When you describe what the true value of is
for a given statistic, it is important to add a couple parentheses to make the results more clear. R is a statistical test that will assume that information is not known before you perform the test.
Complete My Online Class For Me
Because R actually means a statistic Related Site need to be very clear what is referring to. For this example only the information in the formula for the sample mean is clear. There are many others
to get clear-headed about but this is the one I have chosen andWhat is the role of statistical model selection in Pearson MyLab Statistics? ===========================================================
======================= There are some important trade-offs that stand in direct relation to the results obtained in other existing methods in the search for optimal statistical models. Some of the
trade-offs include: $\mathbf{log}\left\lbrack 1, \ldots, 1 \right>$-score, number of combinations of models [e.g., @Linder+2010], the number of independent models without replacement [@Merrin+2001;
@Arovas+2009; @Brown+2011], the number of non-replacement models [e.g., @Nagatani+2011], the estimation procedures based on bootstrap distributions [e.g., @Rafatani+2014b], the assumptions on the
training data [e.g., @Shu+2009], the number of statistical methods mentioned in Section \[sec1\], and the choice of data model [ e.g. @Cai+2008]. @Linder+2010 [IV 1] showed that when the number of
random models was reduced to a small number $k$, the evaluation results obtained with supervised datasets were fairly insensitive to the choice of $k$. Although a priori uncertainty in the decision
boundaries would remain in the model selection process, the test sets that we considered in our work were more likely to be uncertain than the ones that our methods describe, so it seems, that both
the theoretical guarantees and the experimental evidences can be relevant for such tests as the number of independent simulations and the model description, when the number of independent simulations
increase. As a final ingredient, we found the number of tuning parameters that we used in our method on 10$^{15}$ independent runs. For the simulation groups, we used 20 different parameters: a
parameter set $u_1$, 25 samples, $u_5$, 250 samples, $u_6$ model with 10 random model parameters [e.g | {"url":"https://takemylab.com/what-is-the-role-of-statistical-model-selection-in-pearson-mylab-statistics","timestamp":"2024-11-13T15:10:50Z","content_type":"text/html","content_length":"130589","record_id":"<urn:uuid:9e67e7a0-c2fd-419e-9285-7b69e89db295>","cc-path":"CC-MAIN-2024-46/segments/1730477028369.36/warc/CC-MAIN-20241113135544-20241113165544-00518.warc.gz"} |
Beginning R: An Introduction to Statistical Programming
Author: Larry Pace
Publisher: Apress
ISBN: 978-1430245544
Audience: Not suitable for programmers
Rating: 2
Reviewer: MIke James
An introduction to statistical programming sounds like a really good idea. You know your stats, so now let's program...
R really is a full programming language and you can do things with it that make it a general purpose statistics tool. With the help of some programming skills you can use it to transform your raw
data into something that can be analyzed and do it automatically so that if you get some more data or need to repeat the process you can do it with a single command. In the same way the power of
programming is to take you beyond the standard analyses and create composite systems that process your data - again automatically. Programming and R have a lot to offer, but for the beginner in
statistics perhaps all that is of interest is getting the standard tests performed.
This book isn't written by a programmer. The author has clearly been exposed to a lot of programming ideas but programming isn't his main concern. The first chapter gives you a brief introduction to
R, its history and how to get and install it. It takes you though a first session using R and you need to follow this quite carefully because a lot of ideas are first introduced here. The book has a
tendency to introduce something and explain it later. However, the explanations are usually quite good so the key thing is to keep reading. One problem is that the font used is very small and the
line length on each page (of the printed book) is very long. Long lines make text difficult to read but it packs in the information.
The first important things to learn in R are the data structures - the vector, matrix, list and data frame. These are introduced mostly by example, complete with equations for standard deviation and
so you need to be happy with the, not too demanding, math.
Chapter 2 is called "Programming in R" and it's where you would expect to find the process of converting you into a programmer starting. At first it seems very hopeful because there is a nice
discussion of how to learn programming. Then we are introduced to the flow of control - a key idea and to looping and conditionals. Unfortunately after this good start things go a little wrong. Next
we have the idea of an arithmetic expression and the use of basic I/O statements but then we have a table of object types in R - what are objects and what are types?
Next we have a look at loop statements in R - starting off with the for loop. The big problem occurs when the While and Repeat loop are introduced:
"The while loop is more useful than the repeat loop, but everything you can do with while could also be accomplished with for with fewer steps."
This is simply wrong and doesn't do the reader any service. The simple fact that the while and repeat are conditional loops and the for is an enumeration loop is never mentioned. I don't know about
the while loop being more useful than a repeat, but the essential difference between the two is that one has its exit point at the start and the other the exit point anywhere you care to place it. It
all comes down to the minimum number of conditional repeats, not some value judgement about how useful they are. This is core programming and its completely missing.
The chapter does go on to explain how vectorization is preferable to loops and this is very true but it takes time to learn how to do it well. Its final example makes use of functions, even though
they haven't yet been introduced - they are the subject of the next chapter and the chapter closes with a look at R and object-oriented ideas. This is going to go completely over the head of any
beginner and R's approach to objects is so strange that it is probably going to be misunderstood by an experienced programmer. This topic would have been best left to a later chapter or dropped
altogether as no further use is made of it.
The next chapter introduces functions which are central to any attempt to build any sort of program in R. Rather than introduce some simple functions with the emphasis on the all important way
parameters work we have an example from the R system of a complex looking function. In fact the chapter offers no guidance on using parameters or the scope of variables which are the main things you
have to master if you are going to use functions well enough to build programs. There isn't even a discussion of what determines the return value. In short this really doesn't help with understanding
Chapter 4 is where the book leaves the topic of programming in R and becomes a "how to do simple stats in R" book. The topics covered, one per chapter, are: Summary Stats, Tables and Graphs, Normal
probabilities, confidence intervals, hypothesis testing, One-way Anova, more advanced Anova, correlation and regression, multiple regression, logistic regression, chi-squared, nonparametric tests,
sampling and resampling and bootstrapping. The final chapters are on packages and commander packages.
Overall the treatment of the stats is simple and straightforward. It is enough for you to follow the ideas if your statistics is a bit rusty, but not enough to become an expert. You are shown how to
use R to perform each of the tests or model fitting, but there is very little programming with R - you simply use the provided functions.
This is not a book about programming in R. It doesn't cover most of the ideas you need to program in any language and it covers topics that would be best ignored until later. It does do a reasonably
good job of introducing the use of R at the command line and for some small programming examples. It doesn't tackle the most pressing task that most R users face, i.e. reading in and cleaning up
data. It does make references to making use of Excel at various point to generate or modify data, but no real advice is given on general "data processing".
Most of the book is about implementing standard statistical tests using the standard R functions. As well as some very simple things, you will also discover that the book has a tendency to dip into
more complex, and perhaps controversial, topics without really providing enough discussion for the reader to follow, let along make up their own mind on the issue.
This is not a good book for the programmer or the non-programmer. At best it would serve as a haphazard introduction to R for the statistician in need of a brief refresher course on stats.
Microsoft Azure For Dummies, 2nd Edition
Author: Jack A. Hyman
Publisher: For Dummies
ISBN: 978-1119898061
Kindle: B0BNWG1HYK
Audience: Azure novices?!
Rating: 1 or 4.5 (see review)
Reviewer: Ian Stirk
This book aims to provide a gentle yet thorough introduction to Microsoft Azure, how does it fare?
+ Full Review
Machine Learning with PyTorch and Scikit-Learn
Author: Sebastian Raschka, Yuxi (Hayden) Liu & Vahid Mirjalili
Publisher: Packt
Date: February 2022
ISBN: 978-1801819312
Print: 1801819319
Kindle: B09NW48MR1
Audience: Python developers interested in machine learning
Rating: 5
Reviewer: Mike James
This is a very big book of machine le [ ... ]
+ Full Review
More Reviews
Last Updated ( Wednesday, 18 January 2017 ) | {"url":"https://www.i-programmer.info/bookreviews/14-other-languages/6464-beginning-r-an-introduction-to-statistical-programming.html","timestamp":"2024-11-05T22:02:52Z","content_type":"text/html","content_length":"37000","record_id":"<urn:uuid:05e69bdb-0bca-4e3f-95b1-1e8efb1aedf4>","cc-path":"CC-MAIN-2024-46/segments/1730477027895.64/warc/CC-MAIN-20241105212423-20241106002423-00043.warc.gz"} |
The Elements of Geography
A Source Book in Greek Science
Author: Claudius Ptolemy
The Elements of Geography
Ptolemy, Geography I. 1–5 (Müller)^3
1. Wherein geography differs from chorography
Geography is the representation, by a map, of the portion of the earth known to us, together with its general features. Geography differs from chorography in that chorography concerns itself
exclusively with particular regions and describes each separately, representing practically everything of the lands in question, even the smallest details, such as harbors, villages, districts,
streams branching from the principal rivers, and the like. It is the task of geography, on the other hand, to present the known world as one and continuous, to describe its nature and position, and
to include only those things that would be contained in more comprehensive and general descriptions, such as gulfs, large cities and nations, the more important rivers, in short the more significant
instances of each type.
The purpose of chorography is the description of the individual parts, as if one were to draw merely an ear or an eye; but the purpose of geography is to gain a view of the whole, as, for example,
when one draws the whole head.
Now in the case of the drawings just referred to, the principal parts are of necessity fitted in first, and must be properly proportioned, when seen from a suitable distance, to the spaces on the
surface used for the drawing (whether the drawing be of an entire object or of only a part), in order that the representation may be perceived as a whole. It is consequently both reasonable and
proper that chorography should represent the smaller particular details and geography the regions themselves with the general features that belong to them. For the principal features of the
inhabited earth and those most readily fitted in on the proper scale are the various regions themselves in their proper location; while the principal features of these regions are the peculiar
details of the land in question.
Again, chorography deals, for the most part, with the nature rather than with the size of the lands. It has regard everywhere for securing a likeness but not, to the same extent, for determining
relative positions. Geography, on the other hand, is concerned with quantitative rather than with qualitative matters, since it has regard in every case for the correct proportion of distances, but
only in the case of the more general features does it concern itself with securing a likeness, and then only with respect to configuration.
Therefore chorography has need of topography, and no one can be a chorographer unless he is also skilled in drawing. But geography has no such absolute need of topography, for by using mere lines
and annotations it shows positions and general outlines. For this reason, while chorography does not require the mathematical method, in geography this method plays the chief part.
For geography must first consider the form of the whole earth as well as its size and its position with reference to the heavens, so that it may be able to tell the size and nature of the known
portion of the earth and under what parallel circles of the celestial sphere each place lies. From this it will be possible to learn the length of nights and days, the fixed stars that are overhead
and those that at all times are above or below the horizon, as well as all other information that we include in an account of habitable regions.
These are studies that form a part of the most sublime and beautiful theoretic science, for it is with the aid of mathematics that they reveal to man’s understanding the heaven itself in its true
nature (for we can observe it as it rotates about us); while they represent the earth through a model, since the real earth, which is so great and does not surround us, cannot be traversed in its
entirety or in its individual parts by the same men.
2. The foundations of geography
The above account should suffice as a general outline of the purpose of the geographer and wherein he differs from the chorographer.
Since we have now undertaken to map our inhabited world in such a way as to approximate the proportions of the real world as closely as possible, we think that we should explain beforehand that in
this procedure the descriptions given by travelers are of the highest importance. For we gain our greatest knowledge from the reports of those travelers through the various regions who have
theoretic understanding of geography. Again, their observations and reports may be based either on geometrical or astronomical measurement. Now geometry indicates the relative positions of places by
simple measurement of distances, while astronomy uses observational data obtained with astrolabes and sundials. The astronomical method is self sufficient and more accurate, but the geometrical
method is rougher and requires the astronomical to supplement it.
Now since in either case it is necessary to determine in what direction the line joining two given places lies (for it is necessary to know not merely the distance between the places but also the
direction, whether it be, e.g., to the north or the east or some line intermediate between them), it is impossible to perform this investigation accurately without observation by means of the
aforesaid instruments. For with their help the position of the meridian may be obtained at any time and place, and, as a consequence, the direction of distances traversed.
But even if this is found, the measurement in stades does not give us an accurate knowledge of the true distance, since our course rarely coincides with straight lines but, on the contrary, shows
many deviations both on land and on sea. Now in the case of journeys on land it is necessary, in order to find the length in a straight line, to subtract from the whole number of stades traversed
the excess due to the nature and number of the deviations, as estimated. In the case of sea voyages allowance must be made for variations due to the winds, which do not in general preserve a
constant intensity. But even if the distance between two places is accurately measured, this does not give us the ratio of that distance to the whole circumference of the earth or its position with
respect to the equator and the poles.
But measurement based on celestial observation gives each of these things accurately. It shows how great are the arcs mutually intercepted by the parallel circles and the meridians (i.e., the arcs
of the meridians falling between the parallel circles and the equator, and the arcs of the equator and the parallels falling between the meridians); it also shows how great an arc the two places in
question intercept on a great circle of the earth drawn through them. And this method does not require us to compute the number of stades in order to obtain the ratio of the various parts of the
earth to one another and for the general procedure of drawing our map. For it is sufficient to take the circumference of the earth, divided into as many parts as desired, and to show how many such
parts of a great circle of the earth there are in each of the several distances examined.^1
But naturally this method does not suffice for the division of the whole circumference or parts of it into actual distances familiar to us by our own measurements. And for this reason alone it has
become necessary to compare some straight distance on the earth with the similar arc of a great circle on the celestial sphere, and, obtaining by observation the proportion of this arc to the whole
circle, and, by measurement based on some given part, the number of stades in the terrestrial distance under this arc, to find the number of stades in the whole circumference.^2
For we assume on the basis of mathematics^1 that the surface of the earth and sea taken together is substantially spherical, having as center the center of the celestial sphere, so that every plane
passed through the center cuts the aforesaid surfaces^2 in great circles, and the angles subtended at the center intercept similar arcs on these circles,^3 Now, though the number of stades in
terrestrial distances along a straight line can be obtained by measurement, the ratio of this distance to the whole circumference of the earth can not be obtained by measurement because of the
impossibility of a comparison.^4 This ratio can, however, be obtained from the fact that the arc subtended on the celestial sphere is similar.^5 For it is possible to obtain the ratio of this arc to
the whole celestial circumference. And the ratio of a similar arc on the earth to the great circle of the earth is the same.
3. A method of finding the number of stades in the circumference of the earth, given any distance in stades along a straight line, not necessarily on the same meridian; and conversely
Now our predecessors sought not only a rectilinear terrestrial distance (so that it would constitute an arc of a great circle)^6 but one lying in the plane of a single meridian. Observing by sun
dials the points overhead^7 at the two places between which the distances lay, they immediately obtained an arc on the meridian joining these places equal to the arc over which a journey would be
made, because the places lay, as we said, on the same plane.^8 Moreover, straight lines drawn through the places in question to the points directly overhead met each other when produced, and the
common center of the circles was the point of intersection of these lines. Now they took the ratio of the arc between the points overhead to the whole circle passing through the celestial poles as
equal to the ratio of the terrestrial distance in question to the circumference of the whole earth.
But even if the great circle on the earth’s surface that includes the measured distance does not pass through the poles, but is any great circle, we have demonstrated that our problem may still be
solved by similar observations of the elevation of the pole at the terminal points and the position which the terrestrial distance has with reference to each meridian. This we have done by
constructing an instrument^1 for viewing the heavenly bodies. With this instrument we easily obtain many very useful facts, but in particular (1) on any day or night the elevation of the north pole
at the point from which the observation is made;^2 (2) at every hour not only the position of the meridian but also the position with reference to it of any land route, i.e., the angle made by the
great circle drawn through the route and the meridian passing through the zenith.^3
Using these angles we may alike determine both the required arc, with the sole help of the instrument, and also the arc cut off by two meridians on parallels other than the equator. And so, with
this method, by measuring only one straight distance on the earth we can find the number of stades in the whole circumference, and furthermore, knowing this we can then find without actual
measurement the number of stades in any other distance. And we can do this even when the distances are not entirely straight^4 and do not lie on the same meridian or parallel of latitude. It is
necessary, however, that the precise direction of the distance be carefully observed, as well as the latitude of the termini, for it is from the ratio that the arc representing the distance in
question bears to the great circle that the number of stades in such distance can be easily computed, given the circumference of the whole earth.
4. Actual observations of phenomena are to be preferred to reports of travelers
This, then, being the case, if those who have traveled over the several countries had made use of this type of observation, it would have been possible to make a completely accurate map of the
inhabited earth. But Hipparchus alone gave us the elevation of the north pole [i.e., the latitude] for a few cities of the multitude that must be included in a description of the earth, and
indicated places that lie on the same parallels, while some of his successors recorded some of the cities that lie opposite each other (not those equally distant from the equator, but merely those
lying on the same meridian), on the basis of sailings made between these places with the aid of north or south winds. Again, most distances, especially those to the east or west, were given quite
roughly, not by reason of the carelessness of those who made these investigations but probably because of the fact that the more strictly mathematical method of observation had not yet been adopted,
and it had not been considered important to record sufficiently numerous observations of lunar eclipses on the same occasion in different places. I refer to an eclipse like that observed at Arbela
at the fifth hour and at Carthage at the second, from which the distance of the two places from each other eastward or westward could have been determined in equinoctial hours.^1 For these reasons
it would be proper for one who is to make a map of the earth in accordance with these principles to use the data obtained by more accurate observations as the foundation for the map, and to fit in
with these data those obtained from other sources, until the positions indicated in the latter data both in relation to one another and in relation to the fundamental data are in accord, in so far
as is possible, with the more accurate traditions.
5. Attention must be paid to more recent accounts because of changes in the earth with passage of time
The construction of the maps, therefore, would be best accomplished on the basis of the principles described. But in the case of regions which are not completely known either because of their great
size or because they do not always present the same aspect, later reports give us a more accurate account each time, and this is true in connection with geography, too. For the various historical
accounts themselves agree that many divisions of the inhabited portion of our earth have not yet come to be known because of the difficulties occasioned by their size. Again, other divisions have
not been accurately described because of carelessness on the part of those who received reports, and some parts are themselves different from what they were formerly because of destruction or
changes that have taken place in them. For these reasons it is necessary that here, too, we pay heed in general to the last reports that come to us, distinguishing that which is worthy of belief and
that which is not, both in our use of the new data and in our judgment of what had previously been reported.
^1 I.e., distances may be represented merely in degrees of arc independently of the number of stades to a degree.
^2 A given terrestrial distance, lying theoretically on the arc of a great circle, is measured in stades; the ratio of this arc to the whole circumference is then determined by astronomical
observation, whence the measurement of the whole circumference in stades may be found. The measurements by Eratosthenes and Posidonius are examples of this method (see pp. 149–153, above).
^1 See the proofs of Aristotle and Archimedes, p. 236.
^2 I.e., the surfaces of the terrestrial and celestial spheres.
^3 Since any central angle intercepts similar arcs on concentric circles, i.e., arcs equal in circular, but not in linear, measure.
^4 I.e., a comparison between the terrestrial distance and the terrestrial circumference.
^5 I.e., equal in degrees to the arc represented by the distance in question on the terrestrial sphere.
^6 The "rectilinear" or shortest distance between two points on the surface of a sphere is the arc of the great circle joining the points.
^7 I.e., the angular distance from the sun (e.g., at noon of the equinox) to the zenith.
^8 I.e., on the same plane passing through the earth’s diameter, or, in other words, on the same meridian. The arc thus measures the difference in latitude between the two places.
^1 The reference is to the ring astrolabe described in the Almagest (see p. 134, above).
^2 This would be the latitude of the observer.
^3 This angle together with the readily obtained latitude of the two places would, theoretically, determine the distance, in circular measure, of the route in question. The practical difficulties of
measuring longitude in antiquity would be reflected in the application of the method.
^4 Perhaps the reference is to places separated by mountains. In any case, however, Ptolemy would theoretically be able, either by trigonometry or by using globe and compass, to find the distance,
along an arc of a great circle, between any two places whose latitude and longitude have been determined. But the chief difficulty lay in the determination of the longitude of a place before
instantaneous communication became possible. The best available method was that of noting the time when a lunar eclipse was seen in two different cities. Since the eclipse is seen at about the same
time in both places, the difference in the local time (i.e., the number of hours after sunrise or sunset) will indicate the difference in longitude, at the rate of 15° for each hour. Because of the
unreliability of timekeeping instruments in antiquity the method described furnished only a rough approximation, and reports of distances as given by travelers came to be the chief basis of
determining longitude. There are also references to the use of royal "pacers" in Ptolemaic Egypt for the purpose of estimating distances. The use of the hodometer (p. 342) in practice is doubtful.
Of course, for short distances surveying was done with such instruments as the dioptra and the groma.
The method of determining the distance between Rome and Alexandria is taken up by Hero of Alexandria (Dioptra, 35); see O. Neugebauer, op. cit. (p. 136, n. 2, above).
^1 As a matter of fact, however, the case illustrates the difficulty of accurately determining longitude by lunar eclipses or any other means in the absence of dependable clocks. The three hours’
difference corresponds to a difference in longitude of 45° more than 11° greater than the actual difference between Carthage and Arbela. The eclipse, which is referred to by many ancient authors, is
probably that of Sept. 20, 331 B.C. Cf. Pliny, Natural History II. 180: "At Arbela, upon the victory of Alexander the Great, the moon is said to have been eclipsed at the second hour of the night,
whereas the eclipse took place in Sicily as the moon was rising." The reference to the hour of occurrence is fairly accurate in Pliny’s account but not in Ptolemy’s, according to modern
computations. (See H. v.
Des Klaudios Ptolemaios Einführung in die darstellende Erdkunde
, pt. I [Vienna, 1938], p. 21, n. 3.) But the eclipse seems to have preceded the battle by 11 days.
Download Options
Title: A Source Book in Greek Science Select an option:
*Note: A download may not start for up to 60 seconds.
Email Options
Title: A Source Book in Greek Science Select an option:
Email addres:
*Note: It may take up to 60 seconds for for the email to be generated.
Chicago: Claudius Ptolemy, "The Elements of Geography," A Source Book in Greek Science, ed. Müller in A Source Book in Greek Science, ed. Morris R. Cohen and I. E. Drabkin (Cambridge: Harvard
University Press, 1948), 162–169. Original Sources, accessed November 11, 2024, http://originalsources.com/Document.aspx?DocID=P7CJKSWJTHPVH19.
MLA: Ptolemy, Claudius. "The Elements of Geography." A Source Book in Greek Science, edited by Müller, Vol. I, in A Source Book in Greek Science, edited by Morris R. Cohen and I. E. Drabkin,
Cambridge, Harvard University Press, 1948, pp. 162–169. Original Sources. 11 Nov. 2024. http://originalsources.com/Document.aspx?DocID=P7CJKSWJTHPVH19.
Harvard: Ptolemy, C, 'The Elements of Geography' in A Source Book in Greek Science, ed. . cited in 1948, A Source Book in Greek Science, ed. , Harvard University Press, Cambridge, pp.162–169.
Original Sources, retrieved 11 November 2024, from http://originalsources.com/Document.aspx?DocID=P7CJKSWJTHPVH19. | {"url":"https://originalsources.com/Document.aspx?DocID=P7CJKSWJTHPVH19","timestamp":"2024-11-11T19:56:22Z","content_type":"application/xhtml+xml","content_length":"154183","record_id":"<urn:uuid:10a5595a-2926-4ece-b261-5bd5eedd30d0>","cc-path":"CC-MAIN-2024-46/segments/1730477028239.20/warc/CC-MAIN-20241111190758-20241111220758-00696.warc.gz"} |
Ptolemy Saves the Day! Topic: Geometry/Inequalities. Level: Olympiad.
: (1997 MOP) Let $Q$ be a quadrilateral whose side lengths are $a, b, c, d$, in that order. Show that the area of $Q$ does not exceed $ \frac{ac + bd}{2}$.
: Let $ A $ be the area of $ Q $. Consider writing $ A $ in terms of $ x,y,z,w $ as shown in the diagram. A common formula for the area of a triangle is equal to half of the product of two sides and
the sine of the angle between them. So we have
$ A = \frac{1}{2}(xy\sin{\theta}+wz\sin{\theta}+xw\sin{(180-\theta)}+yz\sin{(180-\theta)}) $.
And since $ \sin{\theta} = \sin{(180-\theta)} $, we get
$ A = \frac{1}{2}\sin{\theta}(xy+wz+xw+yz) = \frac{1}{2}\sin{\theta}(x+z)(y+w) \le \frac{1}{2}(x+z)(y+w) $.
Ptolemy's Inequality
, we know $ ac+bd \ge (x+z)(y+w) $, so then
$ A \le \frac{1}{2}(x+z)(y+w) \le \frac{ac+bd}{2} $
as desired. QED.
Comment: There should be a geometric, slice-it-up proof to this problem, but the trigonometric proof works out quite nicely as well. Ptolemy's Inequality is pretty useful; the equality case, when the
quadrilateral is cyclic, is probably used the most. Whenever a problem has a cyclic quadrilateral with side lengths, Ptolemy is always worth a try. There is a really nice proof using complex numbers
(or vectors) and the triangle inequality; see if you can find it.
Practice Problem: Find the proof of Ptolemy's Inequality mentioned above. | {"url":"http://www.mathematicalfoodforthought.com/2006/02/ptolemy-saves-day-topic_1.html","timestamp":"2024-11-09T09:44:20Z","content_type":"application/xhtml+xml","content_length":"48084","record_id":"<urn:uuid:47a42861-54c7-48f9-9db3-79bbfdea009a>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.75/warc/CC-MAIN-20241109085148-20241109115148-00289.warc.gz"} |
How big is an acre visually?How big is an acre visually?
How big is an acre visually?
You must login to ask question.
How big is an acre visually? As all farmers and real estate agents know, an acre is defined as an area one furlong long by 4 rods wide. An acre is standard measurement used in the United States and
the UK.
What is the size of a hectare of land?
A hectare is a land measuring 100m x 100m OR 328ft x 328ft. It is about two and a half acres. A Hectare consists of 15 plots. The total area of land in an acre is 43,560 square feet.
How much is an acre of land worth?
The United States farm real estate value, a measurement of the value of all land and buildings on farms, averaged $3,160 per acre for 2020, no change from 2019.
How long does it take to walk 1 acre?
A square acre is 208.7 feet on a side, so the perimeter of an acre is about 835 feet, or about 16 percent of a mile. If you walk a brisk pace of 3 miles an hour, you can cover a mile in 20 minutes.
So you should be able to walk 835 feet in about three minutes.
How many football fields is an acre?
1 acre equals 43,560 square feet, so for 10 acres you will have around 435,600 square feet if you calculate. That will be 7,5 football fields, including the end zones. Since a football field is about
1.32 acres in size, it is an easy math problem.
What is the size of a lot of land?
An acre is 43,560 square feet, so the current median lot size is just under one-fifth of an acre.
How many acres is a football field?
A standard American football field covers 1.32 acres. The standard dimensions for an American football field, including the end areas, are 360 feet long x 160 feet wide, or 57,600 square feet.
How do you calculate land size?
To calculate acres by hand, multiply your length and width (in feet) to get square feet. Try our length conversion tools, if needed. Then divide by 43,560 to determine the size of the land in acres.
You can quickly find the square footage of an area using our square feet area calculator.
How much does it cost to buy 5 acres of land?
Larson, an economist, who placed the total value of $23 trillion for the entire 1.9 billion acres of land in the United States. This means that the average cost for an acre of land is $12,000 or
$60,000 for 5 acres of land. Almost half of the land in the US is used for agricultural purposes.
How much is an acre in sq ft?
43,560 square feet = 1 acre.
How many acres is 1 mile by 1 mile?
How many acres are there in 1 square mile? There are 640 acres in 1 square mile.
How many football fields is 5 acres?
Nearly 5 Football Fields
Your land is the equivalent of 4.53 football fields since a full football field with the end zones is 1.32 acres. Imagine watching almost 5 football games side by side by side. You could do that if
you own 5 acres of land!
How many steps is 1 acre?
In order to get to the number of steps per acre, we need to figure out how much grass we’re cutting with each step. There are 43,560 square feet in an acre so we can divide that number by our mowing
step to see how many steps we’ll get per acre. 43,560 sq ft /4.583sq ft = 9,504.69 mowing steps per acre.
What is length and width of 1 acre?
66 feet × 660 feet (43,560 square feet) 10 square chains (1 chain = 66 feet = 22 yards = 4 rods = 100 links) 1 acre is approximately 208.71 feet × 208.71 feet (a square) 4,840 square yards.
How big is 5 acres in football fields?
Fermi Question. five acres ? Finally we concluded that it will take 4.53 football fields to fill up 5 acres of land.
How big is a 20 acre square?
20 acre= 871200 square foot.
How big is a football field in yards?
When the « football field » is used as unit of measurement, it is usually understood to mean 100 yards (91.44 m), although technically the full length of the official field, including the end zones,
is 120 yards (109.7 m).
What is a normal lot size?
According to the U.S. Census Bureau, the median size of a lot for new construction in 2018 was 8,982 square feet, or about one-fifth of an acre.
What is a good lot size?
“Typically, custom homeowners are looking for at least one-half acre or larger for their lot. The trend among custom home buyers is for larger (greater than one acre) lots.
How many acres is good for a house?
“Typically, custom homeowners are looking for at least one-half acre or larger for their lot. The trend among custom home buyers is for larger (greater than one acre) lots.
What is the perimeter formula?
Perimeter, Area, and Volume
Table 1 . Perimeter Formulas
Shape Formula Variables
Square P= 4s s is the length of the side of the square.
Rectangle P=2L+2W L and W are the lengths of the rectangle’s sides (length and width).
Triangle a+b+c a,b , and c are the side lengths.
How many square feet is a plot of land?
In Lagos State, the standard size of a plot is 60 x 120ft ( 18m x 36m ie 648sqm), while in some other cities of the country, plots are measured in 50 x100ft.
What is a good price per acre?
The United States farm real estate value, a measurement of the value of all land and buildings on farms, averaged $3,160 per acre for 2019, up $60 per acre (1.9 percent) from 2018. The United States
cropland value averaged $4,100 per acre, an increase of $50 per acre (1.2 percent) from the previous year.
How much does land value increase per year?
NSW Valuer General data showed land values increased 4.4 per cent over the year to July but home prices in Sydney, which makes up two thirds of the state housing market, dropped nearly 5 per cent
over the same period. Home prices increased 3 per cent in the rest of NSW, according to CoreLogic. | {"url":"https://answers.com.tn/how-big-is-an-acre-visually-2/","timestamp":"2024-11-08T12:17:32Z","content_type":"text/html","content_length":"92637","record_id":"<urn:uuid:de08a6d8-c440-4f48-b600-1aa57559a7f5>","cc-path":"CC-MAIN-2024-46/segments/1730477028059.90/warc/CC-MAIN-20241108101914-20241108131914-00003.warc.gz"} |
How to solve complex numbersHow to solve complex numbers 🚩 Math.
You will need
• Handbook on mathematical analysis
Complex numbers are used to extend the set of real numbers. If the real numbers can graphically represent on the coordinate axis, in order to represent a complex number would require two coordinate
axes (abscissa and ordinate). Complex numbers can be obtained in the case, for example, if the quadratic equation discriminant is less than zero.
Any complex number can be represented as a sum x+yi, where x is real part of complex number c and a number y is the imaginary. The character i in this case is called the imaginary unit, it is equal
to the square root of minus one (in real numbersx, the operation of extracting the square root of negative numbers is forbidden).
To perform the operation of addition (subtraction) on two complex numbers, just remember a simple rule: real parts are added separately, imaginary separately. That is:
Multiply and divide complex numbers much more complicated than add and subtract, but in the end it all comes down to trivial formulas. These formulas are presented in the figure and obtained by means
of the usual algebraic transformations, given the fact that the folding of complex numbers you need in parts, and the square of the imaginary unit equal to negative one.
Sometimes in missions you want to calculate modulus of complex number. Make it easy. You need to take the square root of the sum of the real and imaginary part of a complex number. This will be the
numerical value of the modulus of a complex number.
Useful advice
In most cases, solve examples with complex numbers is possible without special knowledge of the formulas. It is sufficient to use the definition of complex numbers and the algebraic transformations. | {"url":"https://eng.kakprosto.ru/how-35201-how-to-solve-complex-numbers","timestamp":"2024-11-03T23:33:13Z","content_type":"text/html","content_length":"32588","record_id":"<urn:uuid:9a2c64b5-c9bd-449f-8805-f21eee7279f9>","cc-path":"CC-MAIN-2024-46/segments/1730477027796.35/warc/CC-MAIN-20241103212031-20241104002031-00859.warc.gz"} |