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https://openreview.net/forum?id=YKOxeWFsQfq
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math
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Abstract: Physics-informed neural networks (PINNs) can offer approximate multidimensional functional solutions to the Helmholtz equation that are flexible, require low memory, and have no limitations on the shape of the solution space. However, the neural network (NN) training can be costly and the cost dramatically increases as we train for multi-frequency wavefields by adding frequency to the NN multidimensional function, as the variation of the wavefield with frequency adds more complexity to the NN training. Thus, we propose a new loss function for the NN multidimensional input training that allows us to seamlessly include frequency as a dimension. We specifically utilize the linear relation between frequency and wavenumber (the wavefield space representation) to incorporate a reference frequency scaling to the loss function. As a result, the effective wavenumber of the wavefield solution as a function of frequency remains stationary reducing the learning burden on the NN function. We demonstrate the effectiveness of this modified loss function on a layered model.
Track: Original Research Track
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474893.90/warc/CC-MAIN-20240229234355-20240301024355-00100.warc.gz
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CC-MAIN-2024-10
| 1,115 | 2 |
https://www.physicsforums.com/threads/how-to-connect-dc-motor-to-raspberry-pi.775532/
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math
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I have recently taken apart a few old DVD drives to see if there were any stepper motors available for a Raspberry Pi project I am currently working on. When I opened one of the older drives I found a motor which was unlike the others as it only seemed to have two wires going directly to the coils. Is this a standard DC motor? If this is a standard DC motor, how would I connect this to the RPi ports? Is there a procedure for this for example, checking coil resistance and then determining resistor sizes required to be in series with the motor or can I just directly connect the red wire to the positive output of the RPi and the black wire to ground? Please see the following links to images for this: s46.photobucket.com/user/suraj1793/media/IMG_2365_zps136cb5ba.jpg.html?filters[user]=141636453&filters[recent]=1&sort=1&o=1 s46.photobucket.com/user/suraj1793/media/IMG_2366_zpsaf5ed524.jpg.html?filters[user]=141636453&filters[recent]=1&sort=1&o=0 s46.photobucket.com/user/suraj1793/media/IMG_2364_zpse39a413e.jpg.html?filters[user]=141636453&filters[recent]=1&sort=1&o=2 I am new to working with motors and have very little experience with electronics therefore, would greatly appreciate some help with this. Thanks.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589029.26/warc/CC-MAIN-20180716002413-20180716022413-00082.warc.gz
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CC-MAIN-2018-30
| 1,224 | 1 |
http://www.partygamecentral.com/party-games.php?tp=kids-games&ofstk=11&ofst=100
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math
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KIDS PARTY GAMES
|Narrow your party game search.
|HA HA HA |
A contagious laughing game.
|HEAD BAND GAME |
Teams compete by hitting each other with stretchy headbands
|ICE CUBE RACE |
Get the ice cubes out of the pool using only your feet!
|SOCK MANIA |
A race to put as many socks on one foot as you can. Lots of fun for kids!
|SMARTIES SUCKER |
Get all your smarties from one bowl to the other
|BALLOON BATTLE |
A fun birthday game. Be the last to not let your balloon get burst.
|BALLOON WAR |
A game where teams rush to steal balloons.
|BLIND COW |
A circle game where you listen to bell and try to figure out where it is!
|BROKEN DOWN CAR RACE |
A relay race where each player is a different broken car part! Noisy fun!
|CHARADES FOR KIDS |
Act out the name of an animal or cartoon character but no talking allowed!
|
s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1398223206672.15/warc/CC-MAIN-20140423032006-00146-ip-10-147-4-33.ec2.internal.warc.gz
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CC-MAIN-2014-15
| 870 | 22 |
https://www.coursehero.com/file/13690/problems-1-223-F07/
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math
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Unformatted text preview: M ATH 223 P ROBLEM S ET 1 D UE : 7 S EPT 4 S EPTEMBER 2007 It was my mistake about the due date on this. If you like, you may hand it in until Friday, 7 September, at my office in Malott with no penalty. Hereafter, problem sets will be due on Tuesdays in lecture. When you hand in this problem set, please indicate on the top of the front page how much time it took you to complete. Reading. 1.11.3. Problems from the book: 1.1.4, 1.1.6 (d) & (g). 1.2.2, 1.2.6. 1.2.8, 1.2.11, 1.2.12, 1.2.22, 1.2.21, 1.2.23. 1.3.2, 1.3.5, 1.3.7, 1.3.12. Additional problems: 1. Suppose that A = a b is a matrix with integer entries. What condition(s) can c d you put on the entries a, b, c, and d to ensure that the inverse A-1 also has integer entries? Is your condition necessary as well as sufficient? a 2. Let - = a be a unit vector in R2. That is, a2 + b2 = 1. b a. Show that the transformation T- : R2 R2 defined by a - ) = - - 2(- - )- T- ( v v a v a
a is linear. a v b. What is T- (- )? If - is orthogonal to - , what is T- (- )? Can you describe v a a a T- in general? a c. What is the matrix of T- (in terms of a and b)? a 3. True or False: Determine whether each of the statements is true or false. Please justify your response: explain why it is true, or give an explicit example where the statement fails. 1 a b (a) The matrix A = 0 1 c is invertible. 0 0 1 (b) If A s a square matrix, then AT A = AAT . (c) If A is a square matrix, then AT A is symmetric. ...
View Full Document
This note was uploaded on 02/24/2008 for the course MATH 2230 taught by Professor Holm during the Fall '07 term at Cornell.
- Fall '07
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https://community.qlik.com/thread/65782
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math
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This content has been marked as final. Show 4 replies
If I want to show the listbox selected image in the textbox object then how it is possible?
I have use below code in Edit script.
For Each vImage in FileList('D:\Image\R\*.jpg')
Let zLabel = SubField(SubField(vImage, '\', -1), '.', 1);
LOAD '$(zLabel)' As DmCd,
'$(vImage)' As ImageName
I am writing the following code in text object but it doesnot work.
=if(count(distinct [ImageName]) = 1, info(ImageName), 'Please Select an Image to View')
Here ImageName is absolute path of that image. So please help me for the same.
I have attached the file. So please have a look on that.
Thanks & Regards,
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CC-MAIN-2018-30
| 650 | 12 |
https://ems.press/journals/jems/articles/5304
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math
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The paper studies fiber type morphisms between moduli spaces of pointed rational curves. Via Kapranov’s description we are able to prove that the only such morphisms are forgetful maps. This allows us to show that the automorphism group of is the permutation group on n elements as soon as \( n ≥ 5 \).
Cite this article
Andrea Bruno, Massimiliano Mella, The automorphism group of . J. Eur. Math. Soc. 15 (2013), no. 3, pp. 949–968DOI 10.4171/JEMS/382
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CC-MAIN-2023-50
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https://steel-machinery-spareparts.com/home
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math
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Help me with this math problem
This Help me with this math problem supplies step-by-step instructions for solving all math troubles. We can solving math problem.
The Best Help me with this math problem
Help me with this math problem can help students to understand the material and improve their grades. Math home work can be a tricky thing for some students. Math is a difficult subject for some, so doing homework on it can be frustrating. Some tips to help with math homework are to get a tutor, practice at home, and try to understand the concepts. A tutor can help go over the material and help with any confusion. Also, practicing math problems at home can be helpful. Doing a few problems each night can help solidify the material. Lastly, trying to understand the concepts can be very helpful. If a student understands why they are doing a certain math problem, it can make the problem much easier. Math homework can be tough, but these tips can make it a little bit easier.
It is usually written with an equals sign (=) like this: 4 + 5 = 9. This equation says that the answer to 4 + 5 (9) is equal to 9. So, an equation is like a puzzle, and solving it means finding the value of the missing piece. In the above example, the missing piece is the number 4 (because 4 + 5 = 9). To solve an equation, you need to figure out what goes in the blank space. In other words, you need to find the value of the variable. In algebra, variables are often represented by letters like x or y. So, an equation like 2x + 3 = 7 can be read as "two times x plus three equals seven." To solve this equation, you would need to figure out what number multiplied by 2 and added to 3 would give you 7. In this case, it would be x = 2 because 2 * 2 + 3 = 7. Of course, there are many different types of equations, and some can be quite challenging to solve. But with a little practice, you'll be solving equations like a pro in no time!
Once the critical points have been identified, it is possible to graph the equation and find the solutions. Additionally, there are online solvers that can be used to find the solutions to an absolute value equation. These solvers will typically ask for information such as the equation's coefficients and constants. By inputting this information, the solver will be able to generate a graph of the equation and identify its solutions.
Many of these sites are actually just trying to get you to sign up for a paid membership. And even if the site is truly free, the quality of the answers may be questionable. After all, if someone is offering something for free, they're not likely to be motivated to do a good job. So, if you're looking for free homework answers, tread cautiously. It's probably best to stick with sites that offer a money-back guarantee or some other form of protection. That way, if you're not happy with the answers you receive, you can at least get your money back. But whatever you do, don't give out your credit card information to a site that claims to offer free homework answers!
The binomial solver can be used to solve linear equations, quadratic equations, and polynomial equations. The binomial solver is a versatile tool that can be used to solve many different types of equations. The binomial solver is a useful tool for solving equations that contain two variables.
Help with math
I would be happier if you made an update which allows solving in digital pictures. Like screenshots, etc. But, it's a very good app. Keep up the good work! It's so fantastic and has helped a lot in so many difficulties that I found in solving mathematics problems
Exactly what you expect and more! It can understand word questions, has a plethora of recourses, as well as textbook answers! It always has an option for the process to be explained as well. But you do have to remember, it can't to everything for you. Some questions it can't answer, but it can answer most of them!
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CC-MAIN-2022-40
| 3,919 | 11 |
http://mathhelpforum.com/business-math/88321-bonds-investment.html
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math
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Two years ago you purchased a 10 year $1000 par value zero coupon bond. at this time alternative bonds of equivalent risk were yielding 12% p.a. At the end of your two year holding period you sold the bond when prevailing market yields were 10% p.a. Assuming bond yields are compounded semi-annually, what was your effective realised compound yield p.a. over your 2 year holding period?
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917123632.58/warc/CC-MAIN-20170423031203-00194-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 386 | 1 |
https://www.gradesaver.com/textbooks/math/precalculus/precalculus-concepts-through-functions-a-unit-circle-approach-to-trigonometry-3rd-edition/chapter-12-counting-and-probability-section-12-1-counting-12-1-assess-your-understanding-page-867/7
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math
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$n(A\cup B)=n(A)+n(B)-n(A\cap B)$.
Work Step by Step
The Counting Formula says that for finite sets $A$ and $B$: $n(A\cup B)=n(A)+n(B)-n(A\cap B)$.
You can help us out by revising, improving and updating this answer.Update this answer
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657129257.81/warc/CC-MAIN-20200711224142-20200712014142-00073.warc.gz
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CC-MAIN-2020-29
| 396 | 5 |
https://cat100percentile.com/2013/02/04/time-speed-and-distance-1/
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math
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In this question, the information regarding still water is missing.
Jaikamal, it will not matter, as they are traveling perpendicular to the stream. Water speed will affect them differently in different directions only if traveling parallel to it. Here it will create the same drag whichever side they are moving so net effect is 0 (or rather can be neglected)
sir, how have you concluded that P travels 3 times the distance for the second meeting??
sir,P travels 3 times the distance for the second meeting?
Could you elaborate
If both move at constant speeds, and in total they have covered 3 times as much distance by the second meeting, then each of them individually has covered 3 times as much. Make a small model of the swimming pool and convince yourself.:)
how it covered P covered d+90 in second trip
Sir, If you are considering 3 times of 120 since P travels thrice his distance then we get 360, however, it only traveled 90 when it returned for the second time and hence traveled 30 less (120-90). So shouldn’t the total distance be 360-30= 330. Can you please explain as to why you subtracted 90 from 360 instead of just the additional 30.
If you go from home to college, and then drive 1 km back, and find that your total distance driven is 10 km, how far away is your school?
School would 5 km away. Is it correct Sir ?
No. Please read carefully, and think.
9 km away!
Sir I have a doubt in this. You said that if the speed is constant then the distance travelled individually by them would be in same multiplication of the total distance travelled by both of them ( i.e. 3) But dont you think it is valid when you start from the same point or in this case it can be applied after they met for the 1st time. its like to problem of fixed and variable part. You have to cover certain fixed amount and then after that it becomes linearly proportional.
I am not sure what exactly you are trying to say, but it certainly won’t be analogous to a fixed-variable situation. In TSD, unless otherwise stated, the speed of each individual in the problem remains constant.
You are the King.
brilliant articles sir!all of them!
complex problem, beautifully solved.
Sir where can i find more of this type questions for practise?
Old CAT papers, SimCATs and other such tests…there’s loads of material out there. But don’t treat it like a board exam where you solve 50 questions of the same time. Instead look for different questions, variety, and understand each.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500719.31/warc/CC-MAIN-20230208060523-20230208090523-00739.warc.gz
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CC-MAIN-2023-06
| 2,800 | 29 |
https://brainmass.com/math/fourier-analysis/inverse-fourier-transform-complex-25288
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math
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- Fourier Analysis
Inverse Fourier Transform
This content was STOLEN from BrainMass.com - View the original, and get the solution, here!
Calculate the inverse Fourier transform of 1/(w^2+2iw-2) in two ways: using the definition and using partial fractions.
© BrainMass Inc. brainmass.com September 20, 2018, 3:03 am ad1c9bdddf - https://brainmass.com/math/fourier-analysis/inverse-fourier-transform-complex-25288
Please see the attached file.
Here are the two mistakes I found:
1. In applying the residue theorem, the original solver forgot that we integrate in the lower half of the complex plane (where the poles are). This means that the direction of ...
The solution shows how to apply complex analysis to the integral. Also how to use convergence arguments to reach the correct answer.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267156418.7/warc/CC-MAIN-20180920062055-20180920082055-00278.warc.gz
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CC-MAIN-2018-39
| 791 | 9 |
https://heavenlybells.org/how-book/25525-what-why-and-how-books-by-csir-978-395.php
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math
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What why and how books by csir
Naukri reCAPTCHAExplore Plus. Combo Offer. Did you find what you were looking for? Yes No. Reviews for Popular Books.
Reference Books for CSIR NET, GATE, JAM and TIFR
CSIR UGC NET Preparation Books 2019
Candidates can appear either for Lectureship program or for JRF only. The examination will be held in two sessions; morning Part A is common to all and comprises of topics like Reasoning ability, General awareness, Numerical ability, etc. Part B has questions based on the concerned subject. Part C includes questions of higher weightage and are of analytical nature. Candidates may select the subject of their choice and will get the paper of the concerned subject only.
Exam Scheme Duration 3 Hrs 2pm. Each Question of 2 marks. Part-B,2 marks for correct Question. Official Website for Sanmple Question Papers. Sign up now.
While some of you have been preparing for CSIR-NET chemistry examinations for months and years, others have just started off with their preparations or maybe not. Selection of books is very important for the examination. It is also a good strategy but if you check the table given below, you will see that only one specialization will not help you qualify CSIR-NET. Topic wise Marks distribution and Recommended books —. Books Recommended — Quantitative aptitude- R. Description — Quantitative aptitude is an important topic for Part -A study. S Aggarwal book for the above mentioned important topics.
Jul 4, CSIR Net Life Sciences is not a difficult exam it's just a different exam. So here we have a list of Recommended Books to follow.
the lost book of remedies pdf
CSIR NET life sciences books to follow - Best books for CSIR NET exam preparation
Chapter 1 biochemistry math problems and solutions Chapter 2 : Microbial growth and division math problems Chapter 3 : Plant physiology math problems Chapter 4 : Human Physiology math problems Chapter 5 : Classical genetics math problems Chapter 6 : Cladogram analysis and classification biology math problems Chapter 7 : Population biology math problems Chapter 8 : Population genetics math problems Chapter 9 : Bio-statistics and biology techniques math problems. So you can buy a complete combo of All in one package. All YouTube lecture videos from Shomu's biology Over hours 2. Last year's Online coaching full recorded lectures 4. Mock test question papers with answers and explanations 5. Put your query with Mob.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991258.68/warc/CC-MAIN-20210517150020-20210517180020-00484.warc.gz
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CC-MAIN-2021-21
| 2,437 | 11 |
https://softmath.com/tutorials-3/cramer%E2%80%99s-rule/review-of-trigonometric.html
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math
|
Review of Trigonometric Functions
9. Let r represent the radius of a circle, θ the central
(measured in radians), and s the length of the arc subtended by
the angle. Use the relationship to complete the table.
10. Angular Speed A car is moving at the rate of 50
hour, and the diameter of its wheels is 2.5 feet.
(a) Find the number of revolutions per minute that the wheels
(b) Find the angular speed of the wheels in radians per minute.
In Exercises 11 and 12, determine all six trigonometric
functions for the angle θ
In Exercises 13 and 14, determine the quadrant in which θ lies.
In Exercises 15–18, evaluate the trigonometric function .
In Exercises 19–22, evaluate the sine, cosine, and
each angle without using a calculator .
In Exercises 31–38, solve the equation for θ (0≤θ<2π)
39. Airplane Ascent An airplane leaves the runway
18° with a speed of 275 feet per second (see figure). Find the
altitude a of the plane after 1 minute.
40. Height of a Mountain In traveling across flat
notice a mountain directly in front of you. Its angle of elevation
(to the peak) is 3.5° After you drive 13 miles closer to the
mountain, the angle of elevation is 9° Approximate the height
of the mountain.
(not to scale)
In Exercises 41–44, determine the period and amplitude
In Exercises 45–48, find the period of the function.
Exercises 49 and 50, use a graphing utility to
graph each function f on the same set of coordinate axes for
, and .Give a written description
of the change in the graph caused by changing c.
In Exercises 51–62, sketch the graph of the function.
Graphical Reasoning In Exercises 63 and 64, find a, b,
c such that the graph of the function matches the graph in the
65. Think About It. Sketch the graphs of
and . In general , how are the
graphs of and related to the graph of f?
66. Think About It The model for the height h of a
where t is measured in minutes. (The Ferris wheel has a
of 50 feet.) This model yields a height of 51 feet when t=0
Alter the model so that the height of the car is 1 foot when
67. Sales Sales S, in thousands of units, of a seasonal
where t is the time in months (with t=1 corresponding to
January and t=12 corresponding to December). Use a graphing
utility to graph the model for S and determine the months
when sales exceed 75,000 units.
68. Investigation Two trigonometric functions f and g have a
period of 2, and their graphs intersect at x=5.35.
(a) Give one smaller and one larger positive value of x where
the functions have the same value .
(b) Determine one negative value of x where the graphs
(c) Is it true that Give a reason for your
In Exercises 69 and 70, use a graphing
utility to compare the graph of f with the given graph. Try to
improve the approximation by adding a term to Use a
graphing utility to verify that your new approximation is better
than the original. Can you find other terms to add to make the
approximation even better? What is the pattern? (In Exercise
69, sine terms can be used to improve the approximation and in
Exercise 70, cosine terms can be used.)
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s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610704824728.92/warc/CC-MAIN-20210127121330-20210127151330-00619.warc.gz
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CC-MAIN-2021-04
| 3,063 | 59 |
http://meta.gaming.stackexchange.com/users/253/david-a-gibson
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math
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Top Network Posts
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s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257825124.55/warc/CC-MAIN-20160723071025-00012-ip-10-185-27-174.ec2.internal.warc.gz
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CC-MAIN-2016-30
| 416 | 9 |
https://erongostraining.com/using-math-and-technologies-in-the-classroom/
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math
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It’s crucial to think about how we can incorporate technology into our education as it becomes more and more a part of our lives. Math and technologies can assist students to learn more effectively, take part in interactive lessons and help their understanding.
Technology can assist students in becoming more active in classrooms that have trouble concentrating or participating. This could take the form of a whiteboard virtual or interactive tools which enable students to collaborate. Online learning platforms, such as Math Minds, for example, use a variety of innovative tools that help students be more engaged with their lessons and increase participation.
This is particularly useful in maths where students learn in different ways. This is particularly useful in maths, where students learn differently. Some students might struggle to comprehend concepts visually while others prefer to learn in an auditory and kinesthetic my explanation method. When you employ technology to teach math, you can be sure that every student gets most out their lessons.
Mathematical technology also allows students to solve problems more quickly than they would in a classroom setting. Graphing calculators, for instance, allow students to solve complex equations at the click of a button and help students visualize solutions. This helps them gain a deeper understanding about the principles of math and connect concepts that would be difficult to comprehend otherwise.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100534.18/warc/CC-MAIN-20231204182901-20231204212901-00320.warc.gz
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CC-MAIN-2023-50
| 1,466 | 4 |
https://alpof.wordpress.com/2014/05/03/an-introduction-to-neo-riemannian-theory-11/
|
math
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Today, more about the math one may find behind rhythms and their transformations !
I got rhythm….
In the previous post, we’ve introduced a group of transformations which acts on time-spans, i.e. a duration with a precise position on a time-line. We have seen that this group, which we call , is the semidirect product , with the group law given by
This allows us, for example, to describe the transformations of successive time-spans on a time-line, like this one:
Here, we’ve identified the first time-span as the group identity element, i.e. . If each gray mark represents the duration of a quarter note, then the second time-span corresponds to the group element and the third time-span to the element . To see if you’ve assimilated the gymnastics of , can you determine the transformation from the second time-span to the third, both in the left- and right-action contexts ? The answer is below…
Answer: in the left-action context, we want to find such that . This gives . In the right-action context, we want instead. This gives .
So this is great, we can analyze the transformation between any time-spans on a time-line. But what about multiple time-lines ? Take this 2-part rhythm, for example:
Here, the gray marks correspond again to the duration of a quarter note, and I’ve highlighted the first quarter note in part A as I choose to identify it to the group identity element. For part B, I will choose the same time-span as the identity element. How can we analyze this short example ? The group only allows us to transform time-spans in a single time-line, so we have to determine the transformations separately for each part. I will choose here to work in a right-context action.
In part A, the successive time-spans are obtained by the right multiplication with , , , and so on. Part B begins with a time-span which corresponds to the group element , so the successive time-spans are obtained by the right multiplication with , , , etc.
This analysis is really clumsy as we have to treat each part independently, thus missing the obvious symmetry between the parts. What we need is a way to generalize the group so that it may act on multiple time-lines.
I got multi-dimensional rhythm…
Remember that our group of transformations is the semidirect product , which is in fact the general affine group for a 1-dimensional real vector space. If we want to consider the possible transformations of n time-lines, is tempting to consider the general affine group for an n-dimensional real vector space. Remember that in the general case, this group is given by the semidirect product , where is the group of translations, and is the general linear group of degree n over . The elements of this group are of the form , where is a vector, and is an matrix with real coefficients. The group composition is given by
However tempting using this group may be, there is an immediate conceptual problem. In the 1-dimensional case, we use is simply a strictly positive real value, which we identify with the duration of the time-span. But, for n time-lines, how can we think of an matrix as a duration ? And how can we avoid “negative durations” ?
In fact, this is an open question for me, and at the present time I don’t have an exact description of the suitable matrices one could use. Nevertheless, we can work with a reduced subgroup of , which will fit our needs. Consider the particular 2-dimensional case. We choose to work with a subgroup consisting of all matrices of the form or , with . In the first case, and corresponds to the durations in time-lines 1 and 2 respectively. Notice in the second case that , wherein is a permutation matrix. In other words, we have a way to switch time-lines and analyze the possible interactions between them.
Let’s consider again the short rhythmic example above. We use the subgroup of we have just defined in the semidirect product with . The initial elements correspond to the group element . The next two time-spans in both time-lines are obtained through the right multiplication with the unique group element . This is also the case for all successive time-spans: we are thus able to describe this example with the use of only one transformation ! Notice that the element reflects at the same time the alternative dilation and contraction of the note durations and the interchange between parts which is visible on the score.
You can of course generalize this example to any number of time-lines using the subgroup of generated by diagonal matrices with strictly positive real coefficients and by permutation matrices.
As we will see in a later post, the subgroup of the general n-dimensional affine group thus obtained has a nice categorical flavor, which will allow us for some further generalizations.
You could also experiment with other matrices in . For example, I’m currently considering, in a 2-dimensional setting, the subgroup generated by matrices of the form or , with . What do they mean musically ? Open questions…
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CC-MAIN-2022-05
| 5,005 | 18 |
https://blog.51cto.com/u_14932227/6042626
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math
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time limit per test
memory limit per test
You've got a undirected tree s, consisting of n nodes. Your task is to build an optimal T-decomposition for it. Let's define a T-decomposition as follows.
Let's denote the set of all nodes s as v. Let's consider an undirected tree t, whose nodes are some non-empty subsets of v, we'll call them xi
. The tree t is a T-decomposition of s, if the following conditions holds:
- the union of all xi equals v;
- for any edge (a, b) of tree s exists the tree node t, containing both a and b;
- if the nodes of the tree t xi and xj contain the node a of the tree s, then all nodes of the tree t, lying on the path from xi to xj also contain node a. So this condition is equivalent to the following: all nodes of the tree t, that contain node a of the tree s, form a connected subtree of tree t.
There are obviously many distinct trees t, that are T-decompositions of the tree s. For example, a T-decomposition is a tree that consists of a single node, equal to set v.
Let's define the cardinality of node xi as the number of nodes in tree s, containing in the node. Let's choose the node with the maximum cardinality in t. Let's assume that its cardinality equals w. Then the weight of T-decomposition t is value w. The optimal T-decomposition is the one with the minimum weight.
Your task is to find the optimal T-decomposition of the given tree s that has the minimum number of nodes.
The first line contains a single integer n (2 ≤ n ≤ 105), that denotes the number of nodes in tree s.
Each of the following n - 1 lines contains two space-separated integers ai, bi (1 ≤ ai, bi ≤ n; ai ≠ bi), denoting that the nodes of tree s with indices ai and bi are connected by an edge.
Consider the nodes of tree s indexed from 1 to n. It is guaranteed that s is a tree.
In the first line print a single integer m that denotes the number of nodes in the required T-decomposition.
Then print m lines, containing descriptions of the T-decomposition nodes. In the i-th (1 ≤ i ≤ m) of them print the description of node xi of the T-decomposition. The description of each node xi should start from an integer ki, that represents the number of nodes of the initial tree s, that are contained in the node xi. Then you should print ki distinct space-separated integers — the numbers of nodes from s, contained in xi, in arbitrary order.
Then print m - 1 lines, each consisting two integers pi, qi (1 ≤ pi, qi ≤ m; pi ≠ qi). The pair of integers pi, qi means there is an edge between nodes xpi and xqi of T-decomposition.
The printed T-decomposition should be the optimal T-decomposition for the given tree s and have the minimum possible number of nodes among all optimal T-decompositions. If there are multiple optimal T-decompositions with the minimum number of nodes, print any of them.
- 树T中的点为树S ‘点’ 的集合，也就是数T中的点实际上是由多个S中的点组成的，并且树T上的点的集合的并集是S树点的全集
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CC-MAIN-2023-14
| 2,997 | 19 |
https://support.oracle.com/knowledge/More%20Applications%20and%20Technologies/1925979_1.html
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math
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Series Display Format Does Not Allow Decimal For Positive Numbers While It Does For Negative Numbers
Last updated on MARCH 08, 2017
Applies to:Oracle Demantra Predictive Trade Planning - Version 12.2.3 to 12.2.3 [Release 12.2]
Information in this document applies to any platform.
When setting the display format for a given series.
The display format does not support the "$#,##0.00;-$#,##0.00", while it support "“$#,##0;-$#,##0.00” format.
So the question is how do we display decimal for positive numbers?
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CC-MAIN-2018-13
| 740 | 11 |
https://www.allthetests.com/tests-for-the-real-fan/books-quizzes/other-books/quiz38/1612028655/guardian-herd-trivia-test-are-you-an-expert
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math
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Guardian Herd Trivia Test: Are you an expert?
12 Questions - Developed by: - Developed on: - 409 taken
First thing is that this test is for the first two books. This test determines if you know a lot about the first two books of the Guardian Herd depending on how many correct answers you give. Please note that this is a trivia test about the Pegasus book The Guardian Herd written by Jennifer Lynn Alvarez
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CC-MAIN-2023-23
| 453 | 4 |
http://shmow-zows.tumblr.com/tagged/im-terrified-yet-so-excited
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math
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Jasmine. 18. Slytherin.
I blog about Disney, anime, video games, and cute animals.
Tomorrow is my last first day of high school.
#what the actual fuck
#how did three years pass by so quickly...
#im terrified yet so excited
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http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-21-3-522
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math
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A Gaussian beam weakly diffracted by a circular aperture can be approximated in the far field by another Gaussian beam with slightly different characteristics. Equations giving the intensity, the divergence, and the radius of the modified beam are derived in simple practical form for experimentalists. These approximated formulas show that, even in the case of negligible power losses through the aperture, the diffracted beam characteristics may appreciably differ from those of the incident beam. In a first approximation, diffraction effects may be ignored only if the ratio a/r0 of the aperture radius a to the 1/e intensity beam radius r0 in the aperture plane is larger than 3.
© 1982 Optical Society of America
Original Manuscript: June 26, 1981
Published: February 1, 1982
P. Belland and J. P. Crenn, "Changes in the characteristics of a Gaussian beam weakly diffracted by a circular aperture," Appl. Opt. 21, 522-527 (1982)
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| 934 | 5 |
https://avesis.ogu.edu.tr/yayin/b983a58e-f720-419b-bf95-ef706471d391/on-darboux-rotation-axis-of-lightlike-curves
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math
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INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, vol.13, no.9, 2016 (SCI-Expanded)
In this paper, by used Frenet trihedron for a lightlike curve, the motion of Darboux rotation axis is seperated to two simultaneous rotation motions. These rotation motions are that tangent and normal vectors of lightlike curve rotate around each other. But, the angular speeds of them are different. Then, by doing the similar operations, we obtain that Darboux axis rotates around spacelike vector of Frenet trihedron of the lightlike curve and this spacelike vector rotates around Darboux axis. Consequently, we obtain the series of Darboux vectors by this way. So, simple mechanisms can be formed.
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CC-MAIN-2023-14
| 697 | 2 |
https://nrich.maths.org/public/leg.php?code=-99&cl=1&cldcmpid=7408
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math
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What could the half time scores have been in these Olympic hockey matches?
There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
This challenge is about finding the difference between numbers which have the same tens digit.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
What two-digit numbers can you make with these two dice? What can't you make?
In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
An activity making various patterns with 2 x 1 rectangular tiles.
I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?
How many triangles can you make on the 3 by 3 pegboard?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?
Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?
In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?
In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?
My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?
El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?
Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?
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CC-MAIN-2017-43
| 6,687 | 50 |
https://www.merlot.org/merlot/viewMaterial.htm?id=740675
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math
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Applied Discrete Structures
More about this material
Disciplines with similar materials as Applied Discrete Structures
Ken Levasseur (Faculty)
Just a few other comments on our text:
It was originally published as Applied Discrete Structures for Computer Science, first by SRA and then by MacMillan. Pearson owned the copyright in 2010, but the released it to us at no cost, to our surprise.
The 1980's version featured Pascal, and we've replaced it with Mathematica and Sage.
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CC-MAIN-2018-13
| 475 | 7 |
https://www.spiedigitallibrary.org/ebooks/PM/Optical-Scattering-Measurement-and-Analysis-Second-Edition/3/Scatter-Calculations-and-Diffraction-Theory/10.1117/3.203079.ch3?SSO=1
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math
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This chapter outlines the important elements of diffraction theory and gives several key results that pertain to the interpretation of measured scatter data. These results are employed in Chapters 4 and 7 to relate measured scatter from reflective surfaces to the corresponding surface roughness and to consider various methods of scatter prediction. In Chapter 8, the diffraction theory results presented here are combined with the polarization concepts found in Chapter 5 and used to outline a technique for separating surface scatter from that due to subsurface defects and contamination. A complete development of diffraction theory is well beyond the scope of this book; however, excellent texts on the subject are available, and these will be referenced in the review presented in the next four sections. The following discussions assume that the reader has some familiarity with electromagnetic field theory and the required complex math notation. Appendix A is a brief review of the elements of field theory and Appendix B gives details of some diffraction calculations.
When light from a point source passes through an aperture or past an edge, it expands slightly into the shadowed region. The result is that the shadow borders appear fuzzy instead of well defined. The effect is different from the one obtained by illuminating an object with an extended light source (such as the shadow of your head on this book) where the width of the reading lamp also contributes to an indistinct shadow. Well-collimated light sources (sunlight for example) also produce fuzzy shadow edges. This bending effect, which illustrates the failure of light to travel in exactly straight lines, is called diffraction and is analyzed through the wave description of light.
As explained in Appendix A, the propagation of light is described in terms of the transverse electric field E(t,r), where r denotes position and t is time. The value k is 2Ï/λ, and ν is the light frequency. The expression in Eq. (3.1) is for a wave traveling in the direction of increasing r.
Online access to SPIE eBooks is limited to subscribing institutions.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178369721.76/warc/CC-MAIN-20210305030131-20210305060131-00254.warc.gz
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CC-MAIN-2021-10
| 2,131 | 4 |
https://pigeonbaby.info/i-a-maron-calculus-81/
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math
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Download PROBLEMS IN CALCULUS OF ONE VARIABLE BY Problems in Calculus of One Variabl H. A. MAPOH HHOOEPEHUHAJlbHOE W MHTErPAJlbHOE HCMHCJ1EHME B nPMMEPAX H 3AiXAHAX. Problems in Calculus of One Variable – I. A. – Ebook download as PDF File .pdf) or read book online.
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Naresh rated it it was amazing Apr 12, Is there ” 0? Prove that in each of the intervals a, xj, x 2x 2a: First, let us make a draw- r is 44 ing see Fig. Use the L’Hospital rule: We assume that during each subinterval of time the n to body moves uniformly with a velocity equal to its velocity at the beginning of this interval, i.
Prove that the derivative of a periodic function with period T is a ii function with period T. J jc 3 arc tan jc dx. Let us first make sure that the given equation has only one real cxlculus. It is called Taylor’s formula of the function f x. If we denote the ini- tial number of inhabitants of a given country as A, then after a year the total population will amo- unt to Fig.
[PDF] PROBLEMS IN CALCULUS OF ONE VARIABLE BY – Free Download PDF
If the integrand is the product of a logarithmic or an inverse trigonometric function and a polynomial, then u is usually taken to be either the logarithmic or the inverse trigonometric func- tion. Here we have obtained the prin- cipal properties of the logarithm proceeding marob from its determi- nation with the aid of the integral. Integration of Other Transcendental Functions.
Much attention is given to problems improving the theoretical background. Test the following functions for monotony: Let us write the Maronn formula for the given function: Additional Problems 91 Chapter II. Calculhs thickness of the material is d.
We have H 7. A rectangle with altitude x is inscribed in a triangle ABC with the base b and altitude h. Simplification of Integrals 6. This is a very tentative plan, and various alternatives are pos- sible.
Divyam Jain marked it as to-read May 04, Investigation of Functions 23 1. Approximating Definite Integrals 1. Consequently, we may take the number 2 as M 2 and estimate the error: Applications of the Definite Integral Form the arithmetic mean of the values of the function f x at n points of division xx ly. In this case it is advisable to integrate with respect to y and calculys advantage of the symmetry of the figure see Fig.
Find the one-sided limits of the functions: Prove that the sum of, or the difference between, a ra- tional number a and an irrational number P is an irrational number. Applications of the Definite Integral if this limit exists.
Problems in Calculus of One Variable
Show that the following functions have no finite derivati- ves at the indicated points: Prove the existence of limits of the following sequences and find them. This circumstance allows us to calculate the integrals of the in- dicated type using the method of indefinite coefficients, the essence of which is explained by fhe following example.
Show that the equation has one root on the interval [1, 2]. The sequence of the approximations converges very slowly. Using the methods of differential calculus, we can now carry out a more profound and comprehensive study of various properties of a function, and explain the shape of its graph rise, fall, convexity, concavity, etc.
Hence, there are no solutions.
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| 3,435 | 17 |
http://lib.mexmat.ru/books/33351
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math
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Applied Categorical Structures focuses on applications of results, techniques and ideas from category theory to mathematics, in particular algebra, analysis, order and topology and computer science. These include the study of topological and algebraic categories, representation theory, algebraic geometry, homological and homotopical algebra, derived and triangulated categories, categorical investigations in functional analysis, in continuous order theory, in algebraic and logical type theory, in automata theory, in data bases and in languages. In addition, the journal also follows the development of emerging fields in which the application of categorical methods proves to be relevant.
Applied Categorical Structures publishes both carefully refereed research papers and survey papers. It promotes communication and increases the dissemination of new results and ideas among mathematicians and computer scientists who use categorical methods in their research.
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CC-MAIN-2020-50
| 968 | 2 |
http://booksbw.com/index.php?id1=4&category=technics&author=beoce-we&book=2001&page=51
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math
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Download (direct link):
J0 + ( T - yX
which is the solution ofEq. (14) subject to the initial condition y(0) = y0.
FIGURE 2.5.6 f (y) versus y for dy/dt = — r(1 - y/ T)y.
Chapter 2. First Order Differential Equations
f,(t) = T
FIGURE 2.5.7 y versus t for dy/dt = —r(1 — y/ T)y.
If Óî < T, then it follows from Eq. (15) that y ^ 0 as t ^ro. This agrees with our qualitative geometric analysis. If y0 > T, then the denominator on the right side of Eq. (15) is zero for a certain finite value of t. We denote this value by t*, and calculate it from
Thus, if the initial population y0 is above the threshold T, the threshold model predicts that the graph of y versus t has a vertical asymptote at t = t*; in other words, the population becomes unbounded in a finite time, which depends on the initial value y0 and the threshold value T. The existence and location of this asymptote were not apparent from the geometric analysis, so in this case the explicit solution yields additional important qualitative, as well as quantitative, information.
The populations of some species exhibit the threshold phenomenon. If too few are present, the species cannot propagate itself successfully and the population becomes extinct. However, if a population larger than the threshold level can be brought together, then further growth occurs. Of course, the population cannot become unbounded, so eventually Eq. (14) must be modified to take this into account.
Critical thresholds also occur in other circumstances. For example, in fluid mechanics, equations of the form (7) or (14) often govern the evolution of a small disturbance y in a laminar (or smooth) fluid flow. For instance, if Eq. (14) holds and y < T, then the disturbance is damped out and the laminar flow persists. However, if y > T, then the disturbance grows larger and the laminar flow breaks up into a turbulent one. In this case T is referred to as the critical amplitude. Experimenters speak of keeping the disturbance level in a wind tunnel sufficiently low so that they can study laminar flow over an airfoil, for example.
The same type of situation can occur with automatic control devices. For example, suppose that y corresponds to the position of a flap on an airplane wing that is regulated by an automatic control. The desired position is y = 0. In the normal motion of the
2.5 Autonomous Equations and Population Dynamics
plane the changing aerodynamic forces on the flap will cause it to move from its set position, but then the automatic control will come into action to damp out the small deviation and return the flap to its desired position. However, if the airplane is caught in a high gust of wind, the flap may be deflected so much that the automatic control cannot bring it back to the set position (this would correspond to a deviation greater than T). Presumably, the pilot would then take control and manually override the automatic system!
Logistic Growth with a Threshold. As we mentioned in the last subsection, the threshold model (14) may need to be modified so that unbounded growth does not occur when y is above the threshold T. The simplest way to do this is to introduce
another factor that will have the effect of making dy/ dt negative when y is large. Thus
dt = -•(> — Ó)(1 — Ó) ó (17)
where r > 0 and 0 < T < Ê.
The graph of f (y) versus y is shown in Figure 2.5.8. In this problem there are three critical points: y = 0, y = T, and y = Ê, corresponding to the equilibrium solutions ô() = 0, ô2(´) = T, and ô3(³) = Ê, respectively. From Figure 2.5.8 it is clear that dy/dt > 0 for T < y < Ê, and consequently y is increasing there. The reverse is true for y < T and for y > Ê. Consequently, the equilibrium solutions ô j (t) and ô3(t) are asymptotically stable, and the solution ô2^) is unstable. Graphs of y versus t have the qualitative appearance shown in Figure 2.5.9. If y starts below the threshold T, then y declines to ultimate extinction. On the other hand, if y starts above T, then y eventually approaches the carrying capacity Ê. The inflection points on the graphs of y versus t in Figure 2.5.9 correspond to the maximum and minimum points, ó and y2, respectively, on the graph of f (y) versus y in Figure 2.5.8. These values can be obtained by differentiating the right side ofEq. (17) with respect to y, setting the result equal to zero, and solving for y. We obtain
y12 = (Ê + T ±ë/Ê2 — ^ + T2)/3, (18)
where the plus sign yields y1 and the minus sign y2.
A model of this general sort apparently describes the population of the passenger pigeon,7 which was present in the United States in vast numbers until late in the nineteenth century. It was heavily hunted for food and for sport, and consequently its
FIGURE 2.5.8 f (y) versus y for dy/dt = -r(1 — y/ T)(1 — ó/Ê)y.
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https://econpapers.repec.org/article/hinjnlaaa/6417074.htm
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The Aronsson Equation, Lyapunov Functions, and Local Lipschitz Regularity of the Minimum Time Function
Pierpaolo Soravia ()
Abstract and Applied Analysis, 2019, vol. 2019, 1-9
We define and study - solutions of the Aronsson equation (AE), a second order quasi linear equation. We show that such super/subsolutions make the Hamiltonian monotone on the trajectories of the closed loop Hamiltonian dynamics. We give a short, general proof that - solutions are absolutely minimizing functions. We discuss how - supersolutions of (AE) become special Lyapunov functions of symmetric control systems, and allow to find continuous feedbacks driving the system to a target in finite time, except on a singular manifold. A consequence is a simple proof that the corresponding minimum time function is locally Lipschitz continuous away from the singular manifold, despite classical results showing that it should only be Hölder continuous unless appropriate conditions hold. We provide two examples for Hörmander and Grushin families of vector fields where we construct - solutions (even classical) explicitly.
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https://jaazi.me/math-proposition-crossword-puzzle-clue/
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Check the other crossword clues of New York Times Crossword February 21 2021 Answers. MATHEMATICAL PROPOSITION Crossword Answer.
This crossword clue was last seen on February 21 2021 in the daily NYT crossword puzzle.
Math proposition crossword puzzle clue. Enter the answer length or the answer pattern to get better results. Proven proposition in math. We think the likely answer to this clue is LEMMA.
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We think LEMMA is the possible answer on this clue. If you encounter two or more answers look at the most recent one ie the last. Did you find the solution for Mathematical proposition.
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Math Proposition Crossword Clue The crossword clue Math proposition with 5 letters was last seen on the June 24 2016. If you have any other question or need extra help please feel free to. Proven proposition in math Crossword Clue The answer to this crossword puzzle is 5 letters long and begins with L.
The word that solves this crossword puzzle is 7 letters long and begins with T. This clue was last seen on February 21 2021 on New York Timess Crossword. This page shows answers to the clue Proposition followed by ten definitions like A plan or scheme proposed The act of setting or placing before and A statement in terms of a truth to be demonstrated.
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Best Answer for Proposition In Math Crossword Clue. We found 18 answers for Proposition. This answers first letter of which starts with L and can be found at the end of A.
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https://jmanimas.com/relimath.htm
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math
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The Religion of Mathematicians
(Copyright 2015, John Manimas)
Mathematicians have at least one religious doctrine: "We cannot square the circle." This is an authoritarian doctrine accepted and enforced by mathematicians since 1882. Could it be a false doctrine? All humans are subject to the risk of authoritarian behavior and mathematicians are human. Mathematicians could have engaged in the same pattern of behavior as the authoritarians of major religious institutions.
In 1882, within the golden age of German self-adoration, the "pi is God" doctrine was articulated in writing by German mathematician Ferdinand Lindemann. He said that it is a waste of time for mathematicians to pursue a means to construct squares and circles exactly equal in area. Lindemann wrote that pi is a "transcendental" number and therefore pi cannot be constructed as a straight line with a compass and straightedge. Thus, like the loyal members of a church, mathematicians believe that Lindemann proved pi exactly cannot be constructed like other numerical values, such as 1 or 5 or the square root of 5 or the cosine of 36 degrees (0.809016994). Two times the cosine of 36 degrees is equal to Phi, or the Golden Mean, or 1.618033988, also the sum of the infinite Fibonacci series. We just did a computation! Uoooooo! Are you scared? Did you run away to get a snack or visit the bathroom? Or are you brave enough to believe that mathematicians are not divine and ordinary people can challenge the religious doctrines of the Institution of Mathematics? Our American culture has challenged, examined, and criticized all other religious beliefs. To be fair, and scientific, we should do the same for the religion of mathematics. Of course, they do make it difficult, since they conceal most of their beliefs within a secret code (far more contrived than Latin) to avoid pesky questions from the skeptical rabble. If Socrates were alive today, he would teach the youth of New York (or Boston or Stanford) to ask pesky questions about mathematics. For example: "Why do we worship mathematics and say that a child good at math is a genius?" But for now let's just ask: "What if it is possible to construct pi as a straight line?" Would that break the first icon of mathematical religion?
The ancient civilization of Atlantis knew that the collapse of their society due to both human violence and nature's forces would produce an evolutionary regression. They knew the development of an intelligent human species would have to start over on Earth. So, they sent messages of hope forward to the future generations, and a declaration of fact: "We can construct squares and circles exactly equal in area." Which means: "We can construct pi exactly as a straight line," and which is also an important message that our ancient ancestors were once as technologically advanced as we are today.
The construction of pi as a straight line has profound meaning for what mathematics is, what a number is and what proportion is, and how the universe works. Later, over the painful centuries of physical struggles and historical preservation and manuscript translations, this message became a riddle: "Can we construct a circle exactly equal in area to a given square using only the compass and straightedge?" Yes, we can. The Pythagoreans were too smart (like a lawyer) to ask this question unless they knew the answer was "Yes." Let's discuss the geometry and the mathematics, and keep in mind that we are also discussing HISTORY, the real history of life on Earth.
Proportion is Everything
The Pythagoreans, who brought the trigonometry of the right triangle to European culture, also brought the three-word philosophical comment on the real, physical universe that: "Proportion is everything." What if this is not just a philosophical comment, but instead is actually a scientifically accurate statement about how the universe works? Among the significant students of the Great Pyramid is John Taylor, who wrote in 1859 that the builders of the Great Pyramid incorporated the value of pi (exactly) into the dimensions of the Great Pyramid. He argued that the construction of the Great Pyramid was divinely inspired and that a complete understanding of the Pyramid would reveal the "Secret of Life in the Universe." My work has been from the start a commitment to find the best evidence that "Proportion is everything" is in fact "the secret of life in the universe." And, this same evidence would be the best historical evidence that the Pythagoreans carried forward from our distant past a form of arcane knowledge, a Gnostic secret that only an advanced civilization could possess: how pi exactly is constructed as a straight line.
This project has been completed successfully and the results are shared publicly on the worldwide web at "thepilinesite.com." The story of that mathematical fact is shared here in summary. A mathematical fact is not subject to copyright or trademark and it cannot be patented. It belongs to everyone because it is our human heritage and because no monetary value can be assigned to it. If this mathematical fact is the secret of life in the universe, then it is probably also knowledge of "the kingdom of heaven" and the pearl of great price referenced by Jesus, who was also a teacher of Gnostic secrets.
To see the evidence that I searched for over a period of 44 years, one has to make use of TWO NEW STRATEGIES. The first is to treat the quadratic equation as the quadratic construction. This means that the quadratic equation which we treat as an important element of modern algebra was originally not algebra but rather geometry. This viewpoint is consistent with two mathematical facts: one, our "al-gebra" is dependent on the use of the modern Arabic zero; two, the modern quadratic equation or formula is used to find pairs of solutions to problems where one of those two algebraic solutions is a negative value and is discarded because it is obviously not a meaningful solution. Why is one of the two "solutions" junk and the other is perfectly correct? Because the "equation" was originally a geometric construction and not "algebra." When we see the quadratic equation with new eyes, making it a guide for geometric constructions, then we see that BOTH solutions are correct because both solutions are line lengths where the plus and minus signs are irrelevant and both lines are two correct results of a geometric construction.
The second new strategy is to construct "pi-lines," which means to explore proportional values that are "almost pi" meaning close to pi exactly in value but either slightly lesser or slightly greater. The two strategies taken together carry one forward through the world of proportion, which I prefer to name "Evolutionary Proportion," until one finds, partly by accident and partly by instinct, the Unification Construction. That means using only the compass and straightedge to construct a straight line equal in length to pi exactly. The desired "perfect precision" of the result is difficult to verify, because such verification is not within the reach of ordinary modern electronic technology, impressive as it may be. Our electronic calculators are not perfect. They are more sophisticated than older forms of mechanical calculating devices but our electronic calculators still have limitations. The digital result of a complex calculation can lose precision in terms of the "mantissa" or digital decimal fraction. That means an ordinary electronic calculator is reliably precise only to a specific digital decimal place, such as to the ninth decimal place (1.000 000 001). In terms of the significance of this precision issue, it is realistic to note that if a calculation is reliably precise to the twelfth decimal place, such as 1.000 000 000 001 of a meter, we have reached the natural limit of the smallest possible particle of discrete matter (the atom). At that limit of measurement, we can no longer increase the actual precision of the real measurement by fractional parts because we cannot add a fraction of an atom to any dimension of a real object.
My theory of Evolutionary Proportion is that the Unification Construction is the "Secret of Life in the Universe" because construction of pi exactly as a straight line is the best evidence in support of the concept that "Proportion is everything." This concept means evolutionary proportion is the fundamental force of nature that enables molecules to measure themselves and then assemble themselves into living organic structures. This is consistent with the mainstream biological viewpoint that living organic molecules are "self-organizing." Self-organizing means the same thing as self-assembling, and the first step before self-assembly is self-measurement.
The Successful Constructions in the Form of Calculations
To see with one's own eyes and appreciate the reality of this evidence, one needs to be able to operate a common hand-held scientific calculator, and understand -- or accept on trust -- that we can verify a specific series of geometric constructions by means of ordinary numerical calculations. In other words, the operations we can perform as mathematical calculations are actually the same as common geometric constructions. These include adding and subtracting lines, multiplication and division (by means of similar right triangles), taking the square root of a number (or line), squaring a number (or line), and converting a rectangle to a square. This is all spelled out in the long version at "thepilinesite." The fact that we can "calculate" our way to pi exactly as well as construct the line is further evidence that this is a truth of proportional reality and not just a "geometric trick." No new construction or geometric discovery is needed. We can construct pi exactly as a straight line using only the common construction tools that are known to geometers throughout the world. Any reader who has "I am not good at math" engraved on their brain can call upon a mathematical friend for help.
Here are the five pi lines that led to the solution:
(pi*D) = 3.1416407864998738178455042012388 = 1.8, square root, + 1.8 (9/5)
It is easy. This means take the square root of (9/5) and add that to (9/5). This pi-line is the same as [(cosine 36) * 2]^2 * 1.2, or (2.618033988) * (6/5).
(pi*F) = 3.1446055110296931442782343433718 = [(sine 18), *2, sqrt] * 4
(pi*E) = 3.1418181818181818181818181818181 = (1/0.55) * 1.728, or * (6/5)^3
(pi*V) = 3.1426968052735445528926416093549 = (40/9) * sqrt(0.5)
(pi*Q) = 3.1399111679090046934014154186896 = [(pi*E)*(pi*V)] / (pi*F)
This form of new pi-line is readily constructible.
Then, construct the inverse of 1.118, which = 8.944543828647 / 10
0.9 * 0.8 = 0.72, + 4 = 4.72
/ 5 = 0.944, + 8 = 8.944
/ 8 = 1.118, inverse = (1/1.118) = 0.89445438282647
Then, Line A = [ (pi*V)^2 / (pi*E) ] / sqrt(cos 36)
= 3.49498323774898999309129431119694 (Line A)
And Line B: = [ (pi*V)^2 / (pi*D) ] = 3.14375317901321112588817420275095
This form of new pi-line is readily constructible.
Then, Line A minus Line B = Line C = 0.351230058735778867203120108445054
Then Line C * 5 = 1.75615029367889433601560054222527
and that times 0.8944543828647 = 1.57079632708308974598890925064872
and that times 2 = 3.141592654 = pi exactly, a straight line.
Summary: Line A minus Line B = Line C = pi exactly times 0.1118.
So that's it. That is the best evidence that "Proportion is everything" is an accurate scientific statement. Evolutionary Proportion is not the outcome of a complex universe. It is the origin of a complex universe. How can that be? What in Heaven's name is the significance of the number 0.1118 ? Where does it come from? The square root of five is 2.236067977, and one half is 1.118033988 and that is the square root of 1.25 or (5/4) and that plus 0.5 = 1.618033988 which equals Phi or 2 times the cosine of 36 degrees, also the Golden Mean, the proportion visible in all living things. Visible in all things, including stars spinning in galaxies and hurricanes. But Phi and the spiral form is not the whole picture. There is more. Did you see the 0.1118 ? It is in the 1.118033988 and 0.1118033988, the square root of (1/80) and that is equal to 0.1118 times 10.000304. But the important part is that Line A minus Line B = 0.1118 times pi exactly, and from that Line C we can construct a straight line equal to pi exactly.
This is not a complete proof but it is the beginning of a proof that Evolutionary Proportion is the most fundamental force of Nature that determines the shapes of everything in the universe, both living and non-living. Did I say that? Who said that? Aristotle said: "Everything in the natural universe is composed of matter and form --- primary, inchoate material given an intelligible shape and purpose." Ah! Inchoate material (loose particles) given intelligible shape. Question here: What is it that gives an intelligible shape to everything in the natural universe? Should we consider the possibility of Evolutionary Proportion? Is this a Gnostic secret? Earlier I said that Jesus was a teacher of Gnostic secrets. Do you remember what Jesus said about Gnostic secrets? He told his disciples: "Don't hide your light under a bushel."
What is mathematics then? Mathematics is our perception of proportion. Nature produces electromagnetic radiation, we see colors. Nature produces vibrations, we hear music. Nature is shaped by proportions. We measure them. We see numbers and computations, multiplications and divisions and calculus and probabilities and equalities and inequalities and the entire haunted castle of contrived and secretive, encrypted mathematical language that hides the light under a bushel. That is the religion of mathematicians. And that mathematical authority is questioned at "thepilinesite," which is not encrypted, not hidden, not a secret. Some college professor put "Question Authority" on the bumper of his Saab and it got stuck in my mind. Whether you verify the math yourself, or have it verified by a trusted mathematical friend, please note, that in terms of HISTORY, this new mathematical information TELLS US THAT THE ANCIENT PYTHAGOREANS UNDERSTOOD pi is equal to 3.141592654. How could they know that?
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https://www.coursehero.com/file/6049171/Scan-Doc0107/
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Figure 5.l.2 The partial pressure of each gas in a mixture of gases in a container depends on the number of moles of that gas. The total pressure is the sum of the partial pressures and depends on the total moles of gas particles present, no matter what they are. Note that the volume re-mains constant. 5.5 Dalton's Law of Partial Pressures 199 How do we get there? ( 1.95~)(0 08206 1::; • atrr1) • Molar mass = dRT = 1::;' R . mol (300. R) P 1.50aan = 32.0 g/mol Reality Check: These are the units expected for molar mass. SEE EXERCISES 5.75 THROUGH 5.78 You could memorize the equation involving gas density and molar mass, but it is better simply to remember the ideal gas equation, the definition of density, and the relationship between number of moles and molar mass. You can then derive the appropriate equation when you need it. This approach ensures that you understand the concepts and means one less equation to memorize. 5.5 ••.
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This note was uploaded on 12/13/2010 for the course CHEM 2301 taught by Professor Bill during the Spring '10 term at South Texas College.
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http://www.cune.edu/academics/faculty-list/edward-reinke-jr/
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Edward Reinke Jr.
Edward G. Reinke Jr.
Professor of Mathematics
Chair of the Mathematics & Computer Science Department
Office: Jesse 206
Office phone: 402-643-7418
Edward Reinke has taught at Concordia since the fall of 1991. He is currently director of the mathematics program. Reinke is a member of the Mathematical Association of America and the Association of Christians in the Mathematical Sciences.
Ph.D., University of Florida
M.S., University of Florida
B.S., Concordia University, Nebraska
Survey of Contemporary Mathematics, Calculus and Analytical Geometry I, Calculus and Analytical Geometry II, Introduction to Statistics and Probability, Calculus and Analytical Geometry III, History of Mathematics, Seminar in Mathematics, Foundations of Statistics I, Foundations of Statistics II, Abstract Algebra, Linear Algebra, Foundations of Geometry, Real Analysis, Differential Equations, Mathematical Modeling, Number Theory
Each summer Professor Reinke serves as a faculty reader for the Advanced Placement Calculus Exam.
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https://www.arxiv-vanity.com/papers/1509.03509/
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Worldline Numerics for Energy-Momentum Tensors in Casimir Geometries
We develop the worldline formalism for computations of composite operators such as the fluctuation induced energy-momentum tensor. As an example, we use a fluctuating real scalar field subject to Dirichlet boundary conditions. The resulting worldline representation can be evaluated by worldline Monte-Carlo methods in continuous spacetime. We benchmark this worldline numerical algorithm with the aid of analytically accessible single-plate and parallel-plate Casimir configurations, providing a detailed analysis of statistical and systematic errors. The method generalizes straightforwardly to arbitrary Casimir geometries and general background potentials.
The worldline formalism Feynman (1950); Halpern and Siegel (1977); Bern and Kosower (1991); Strassler (1992) is a field theory technique with various computational advantages such as the reduction of the number of diagrams in perturbative expansions. It is particularly powerful for amplitude computations in external backgrounds Schmidt and Schubert (1993); Reuter et al. (1997); Shaisultanov (1996); Schubert (2001), as string-inspired techniques become highly efficient in this case. Moreover, fluctuation-induced quantities such as quantum actions, energies, and forces can also be efficiently computed by means of Monte Carlo simulations of the worldline path integral. Even fully nonperturbative problems can be tackled within the worldline formalism Affleck et al. (1982); Nieuwenhuis and Tjon (1996); Gies et al. (2005); Dietrich (2014); Bastianelli et al. (2014); Dietrich (2015).
The numerical method has given unprecedented access to background problems with nontrivial spacetime dependencies in QED Gies and Langfeld (2001, 2002); Langfeld et al. (2002); Schmidt and Stamatescu (2003); Mazur and Heyl (2015), QCD Deschner (2008); Epelbaum et al. (2015) fermionic systems Dunne et al. (2009), as well as the physics of Casimir forces Gies et al. (2003); Gies and Klingmuller (2006a, b, c); Weber and Gies (2009); Schaden (2009a, b); Aehlig et al. (2011); analogous analytical results for QED have also come within reach using worldline instanton approximations Dunne and Schubert (2005); Dunne et al. (2006); Dietrich and Dunne (2007); Strobel and Xue (2015); Linder et al. (2015); Ilderton et al. (2015); Dumlu (2015). Important advantages of the Monte-Carlo method are that spacetime is not discretized but remains continuous in the algorithm, and renormalization can be performed on the level of finite and numerically controllable quantities. In addition the worldline formalism offers an intuitive picture of quantum fluctuations, as the worldlines can be viewed as spacetime trajectories of the fluctuating particles. The numerical method has also been applied to Minkowski-valued 2-point functions for external legs Gies and Roessler (2011).
In the present work, we demonstrate that the technique can also be extended to composite operators, using the induced energy-momentum tensor (EMT) as an example. The quest for such a method was first initiated in Schäfer et al. (2012). The new difficulty arises from the fact that standard tools such as point-splitting lead to expressions involving the 2-point function of the fluctuating field (internal line). As shown below, this can nevertheless be dealt with in a comparatively straightforward fashion by using open in addition to closed worldlines.
The present conceptual and in large parts technical work is motivated by the computation of energy-momentum tensors for Casimir configurations. This problem is paradigmatic as the EMT sources the gravitational field. Since induced Casimir energies are typically negative (if associated with an attractive force) Casimir (1948); Bordag et al. (2001); Milton (2001, 2009); Bordag et al. (2009), information about the EMTs for Casimir configurations is a testbed for conceptual considerations of the interplay of quantum field theory and gravity, see, e.g., Fulling et al. (2007); Milton et al. (2007); Shajesh et al. (2008) for a discussion of how the Casimir energy “falls”.
Generically, many fundamental investigations of dynamical spacetime properties start with assumptions imposed on the properties of the EMT on the right-hand side of Einstein’s equations. Most prominently, in order to exclude exotic phenomena Morris and Thorne (1988); Morris et al. (1988); Visser (1989); Kar et al. (2004); Fewster and Roman (2005); Olum (1998), energy conditions (ECs) on the properties of the EMT are imposed. For instance, certain “mechanisms” for superluminal travel can be excluded if an energy condition of the form is imposed, where is the tangent vector of a geodesic . If is a null vector this condition is called the null energy condition (NEC). The Casimir effect violates some energy conditions such as the NEC Graham and Olum (2003); Olum and Graham (2003); Graham and Olum (2005); Graham (2006). It can therefore not be used to rule out superluminal travel. In fact, superluminal (but still causality preserving) phase velocities are known to occur in the parallel-plate Casimir configuration Scharnhorst (1990); Barton (1990); Barton and Scharnhorst (1993); Dittrich and Gies (1998, 2000). The Casimir configurations studied so far at least obey the weaker averaged NEC (ANEC). For a further discussion of this topic, see Graham and Olum (2005, 2007); Visser (1996a, b, c, 1997); Fewster et al. (2007); Graham and Olum (2007). In the present work, we use the violation of the NEC by the Casimir effect as an illustration for our new computational method. For conventional computational strategies to determine the induced EMT, for example, by means of mode summation or expansion, image charge methods, or similar techniques, see, e.g., Brown and Maclay (1969); Milton (2003, 2004); Scardicchio and Jaffe (2006).
This paper is intended to be a manual for the numerical computation of composite operators using the worldline formalism. It is organized as follows: in Sec. II we apply the worldline formalism to composite operators, specifically the EMT of a real scalar field obeying Dirichlet boundary conditions (BCs). We discuss the differences between the formalism for composite and non-composite operators or functionals like the effective action. In Sec. III we test our numerical worldline algorithm by calculating components of the energy-momentum tensor for a single plate with Dirichlet BCs analytically and numerically. The numerical calculation of the EMT and of the NEC is presented for the parallel plate configuration in Sec. IV. We compare our numerical results with known analytical results and discuss the arising systematic and statistical errors. We conclude with a summary of our results and an outlook on future worldline calculations.
Ii Worldline Formalism for the energy-momentum tensor
Composite, or local, operators in quantum field theory are local products of field operators and their derivatives. Being distribution-valued, their product at the same spacetime point may be ill-defined and give rise to divergences. Such operators can nevertheless be used for calculations after regularizing the divergences, for example, by point-splitting, function, or dimensional regularization. In the following, we compute the vacuum expectation value of the energy-momentum tensor operator of a scalar field; a composite operator constructed from the scalar field operator and its derivatives.
Our presentation of the basic formalism follows the one of Scardicchio and Jaffe (2006) with only a few differences. We study a quantum scalar field that is a map from a domain of -dimensional Minkowski spacetime onto the linear space of self-adjoint operators on the Fock space
has mass and is minimally coupled to a static classical background potential . Later on will impose boundary conditions on the fluctuations of . We use the -dimensional Minkowski metric with the ”mostly minus” signature . From the Lagrangian density operator
we derive the equation of motion for ,
as well as its canonical energy-momentum tensor operator ()
The EMT operator in Eq. (4) contains products of field operators at the same spacetime point that can lead to divergences. We regularize them by a point-splitting procedure in the spatial components , i.e.,
The point-split EMT operator is then ()
Our final goal is to compute the effects of boundary conditions on the energy-momentum tensor. For the sake of convenience, we restrict ourselves to computing those EMT components that contain information relevant for the null energy condition (NEC) in the direction, where the coordinate is always the th coordinate of our spatial vectors . This null energy condition is given by the vacuum expectation value of the projection of the EMT onto a null curve with the null tangent vector ,
where denotes the vacuum expectation value. All our calculations generalize straightforwardly to other EMT components. In order to compute the vacuum expectation values of Eq. (6), we expand in terms of spatial eigenmodes and corresponding creation and annihilation operators and ,
where a discrete notation is used for both discrete and continuous parts of the spectrum for simplicity. The are defined as normalized eigenmodes of the Laplacian in the presence of the potential
It is convenient to parametrize the energy eigenvalues also in terms of momenta according to . Then, the eigenvalue equation reads , which is a Helmholtz-type equation. The corresponding Green’s function equation,
is solved by the spectral representation
We aim at expressing Eq. (7) in terms of . We therefore insert unity in the form
and exchange the integration and the summation. This yields
The sum inside the imaginary part is just . In general, instead of unity a decaying exponential must be inserted in order to construct local counterterms for renormalization (cf. Scardicchio and Jaffe (2006)). then serves as a cutoff for large momenta . This is, however, not necessary in our calculations because we are going to evaluate the EMT only at points for which , so that all local counterterms, that is, all counterterms that depend on , are automatically zero. Furthermore, since the term is in general complex, pulling it into the argument of the imaginary part generates an additional term that is proportional to . This term vanishes in the limit and hence will be ignored. The effects of boundary conditions imposed on the field fluctuations by are described by the difference between the EMT with non-vanishing potential and the EMT with . So far, we have left the potential arbitrary to emphasize that our calculations are independent of its specific properties. We can therefore repeat all the above steps with a vanishing potential. The only changes that occur are the mode functions in Eq. (9). The corresponding Green’s function is , defined by Eq. (10) for , rather than . We switch to the common point variables
and with , evaluated at and we have
Equation (15) is independent of any specific mode expansion of . It only depends on the Green’s function , which is representation-independent by definition. Therefore, any method for computing can be used at this stage, e.g., an optical approach in Scardicchio and Jaffe (2006). The subtraction of also removes the divergent terms that are independent of the potential and normalizes the EMT such that it vanishes for .
ii.1 The worldline representation of
For simplicity, we consider here only the massless case . Our calculations can straightforwardly be carried over to the massive case, for details, see App. A. In order to express the Green’s function in the worldline formalism, we interpret as the matrix element of an operator and Eq. (9) as a quantum mechanical Schrödinger problem whose Hamiltonian is . Then corresponds to a quantum mechanical propagator, Fourier transformed to energy space, from which the free motion has been subtracted. Hence, it can be written in position space in terms of a propertime representation:
The matrix element in Eq. (16) is the quantum mechanical transition amplitude of a fictitious particle moving from at the fictitious time to at with a Hamiltonian . The corresponding Feynman path integral in position space is then straightforward to find. Next, we perform formal Wick rotations in both the and planes, such that and , which are consistent with causality. This casts into its doubly Wick-rotated form
The variables and are called Minkowskian and Euclidean propertime, respectively. Both describe the time evolution of the fictitious Schrödinger problem, but neither is a physical, measurable time. An analogous propertime representation for the effective action has been used in previous calculations of effective interaction energies for the Casimir effect and similar boundary configurations Gies et al. (2005); Gies and Klingmuller (2006c, b). The worldline representation of the effective action contains, however, a path integral over closed loops, whereas for , open worldlines running from to must be computed. The implicitly normalized path integral in Eq. (17) gives, for the free path integral, the standard free propagator,
From this normalization one derives the shorthand notation for the path integral expectation value, the worldline average of an arbitrary operator :
Pulling out the imaginary part prescription in front of the integral in Eq. (15), we can perform both Wick rotations for the components of the EMT. Details can be found in App. A. We finally arrive at the manifestly real worldline expressions for the normalized vacuum expectation values of and ,
The expectation value of the path integral in Eq. (20) is defined by Eq. (19) with the operator . It is an average over worldlines that start at and end at , and that are weighted with a Gaußian velocity distribution. It is convenient to switch to coordinates such that for all paths are fixed with respect to one common point (cf. Fig. 1). We therefore call these worldlines common point loops or lines. The remaining path is written in terms of a dimensionless unit worldline with and .
The unit line itself can be written as the sum of the classical path from to and a deviation that obeys . We choose the origin of the coordinate system to be the point ,
In the limit the worldline closes, it becomes a loop . We have set above
The dependence in this relation is crucial for the computation of the -derivatives in Eq. (20). Rescaling the worldlines, , makes the weight factor of the resulting path integral independent of . This allows us to compute the expectation value by generating only one ensemble of unit worldlines , which are all defined with respect to the same coordinate system. The worldline average is now calculated by replacing the path integral with a sum over a finite number of unit worldlines that are themselves approximated by a finite number of points per line with . The points are random numbers distributed according to the Gaußian weight factor , being a discretized realization of an open line with the vector connecting its endpoints. As a result, the expectation value of an operator is written as an average,
The common point paths are conveniently generated with the loop algorithm Gies et al. (2005), which also works for open worldlines.
ii.2 Dirichlet constraints on
The entire formalism that we have outlined so far works, of course, for arbitrary static background field configurations . In our calculations, we use
where is a surface element on . We recover Dirichlet BCs in the limit (cf. Graham et al. (2004, 2003)). The subtraction of the vacuum Green’s function in Eq. (15) already removed all divergences independent of . Therefore, can only diverge at points for which and the energy-momentum tensor in Eq. (20) is finite on , where vanishes. All remaining divergences are located on the boundary and can be related to the infinite amount of energy necessary to constrain on all momentum scales to fulfill the Dirichlet boundary condition on .
The parametrization Eq. (24) and the subsequent Dirichlet limit greatly simplify the worldline average because now we have
Equation (25) states that only paths which violate the boundary conditions lead to deviations from the trivial vacuum and thus contribute to the expectation value. We call the function the intersection condition. It gives a geometric description of how and for which values of the worldlines intersect the boundary. As long as the start and end point of a given worldline are not on the boundary (), the intersection condition will always determine a minimal non-zero value for the propertime for which the worldline first intersects . denotes the minimum propertime that is necessary for a worldline to propagate from the start to the end point and intersect a boundary in between. For any deviations from the straight line between and are typically strongly suppressed. Only for sufficiently large propertimes does the diffusive Brownian motion process, described by the path integral, create sufficiently large random detours that can intersect . In the propertime integral, serves as a lower bound and removes the divergence for . From a physics point of view, acts as an ultraviolet cutoff because small propertimes correspond to large momenta. The intersection condition may also provide an upper bound . This value would then mark the propertime for which the worldlines no longer intersect the boundary. This needs to be considered especially for configurations where the boundary consists of compact objects (see e.g. Gies and Klingmuller (2006c)).
ii.3 Compact expressions of and for worldline numerics
The EMT components are completely finite on by virtue of Eq. (25). We may therefore decompose and further and study the resulting, more compact, terms one by one. Toward this end, we parametrize the intersection condition as , where the function has inverse length dimension and describes the geometrical conditions for a worldline to intersect the boundary . It depends on and , and through the latter also on . This dependence is not explicitly known but it vanishes as . In general, is not a smooth function of these parameters. In fact, it can be non-differentiable in either variable. Since depends on the shape of the boundary for the setup under consideration, its functional properties must be investigated each time anew. In addition, there can be several ways in which the intersection condition may be written. Whereas different parametrizations are equivalent, they can exhibit very different properties during numerical evaluation. Thus, the following calculations should be understood as primarily formal. First, we assume the function to be differentiable twice in both and . We additionally assume that all limits can be evaluated, and that only determines a lower bound on the propertime integral. In this case, we have .
We now insert Eq. (25) into Eqs. (20) and find
In order to evaluate the propertime integral, we need to interchange several limits, which requires justification. First, we note that all expressions we deal with are finite by construction due to the Dirichlet constraint Eq. (25). Since this is valid for all , the limit may be interchanged with all other limits except . Furthermore, since we approximate the worldline average by a finite sum, this average can be exchanged with other limits and be conveniently computed last. We may also formally interchange propertime integration and differentiations because , and are independent variables. There is, however, the intersection condition , which depends on all three variables. The function also depends on the combination . As a consequence, the derivatives of , or more specifically of , must be computed before the propertime integration (cf. Sec. B). Picturing the worldlines as paths in space helps examine the situation: we need not only compute the intersection condition itself but also its derivatives, that is, we need to determine how the intersection is altered if or are changed. A derivative with respect to can be viewed geometrically as moving the complete worldline through space without changing its shape. By contrast, the derivative corresponds to opening and closing the worldline at a fixed point in space, changing its shape in the process. The required order in which these manipulations of the worldline expressions should be performed is then:
compute the derivatives of with respect to and ,
let , that is, ,
perform the propertime integration, and
average the expression over all worldlines in the ensemble.
With these consideration at hand, we write where we define
With we proceed accordingly and write it as a sum of four terms:
The fourth term, , comes from acting with on the exponential . Another term, the mixed term vanishes as .
We note that, with the help of the above decomposition into compact terms, the null energy condition along the axis Eq. (7) now reduces to computing
Iii The energy-momentum tensor for a single plate
The numerical computation of and in and space dimensions in the case that is a single -dimensional surface, i.e., a plate, is our first proof-of-principle example. The plate imposes Dirichlet BCs on the fluctuations of . It is placed at such that its normal is the axis. The single Dirichlet plate configuration is also sometimes referred to as the perfect mirror.
iii.1 Analytic calculation for a single plate
Before we use worldline numerics, we compute the EMT for the single Dirichlet plate analytically. For that, we use Eq. (15) and compute by solving the equation of motion Eq. (9) for different boundary conditions. Denoting the BCs by a superscript , we must solve
Toward that end, we decompose any in the -dimensional vector parallel to and the component of . The solution of Eq. (30) in the half space with Dirichlet boundary conditions at is then
where and . We assumed that there are only outgoing waves at spatial infinity (Sommerfeld radiation condition). In the same manner, the free solution without boundary conditions is found to be . Both solutions are normalized for and , . The Green’s functions and are now computed according to the spectral representation Eq. (11). We perform the momentum integration in polar coordinates and find for (see also Sommerfeld (1958); Jackson (1982); Polyanin and Zaitsev (1996))
The are modified Bessel functions of the second kind (Macdonald functions).
We can now solve Eq. (15) analytically and even use the decomposition of and that we developed in Sec. II.3. Denoting the distance from the plate with , we find for the EMT in
And in the case of 3 spatial dimensions the values for and are
We note that and cannot be calculated separately in a direct manner since we used the functional structure of the worldline representation of to define these functions. Despite that, we can always compute from the sum using the fact that . We thus have
According to Eq. (29) the NEC along the axis is then violated,
These are the same values for the NEC which were derived in Graham and Olum (2005).
iii.2 Worldline calculation for one Dirichlet plate
The first step in all our worldline calculations is determining the intersection condition . For the single plate setup, this is easily done from Fig. 2.
The worldlines start at the point and intersect the plate at for all that fulfill . We call the component of the point on the loop that is closest to the plate . It is negative for our choice of coordinates in the setup Fig. 2. Thus we find for the function
This corresponds to a minimal propertime , where is the positive distance that measures the extension of the loop towards the plate. only depends on the component of because the plate constrains the propagation of only in the direction. For this reason, and because the worldline distributions factorize with respect to their position space components, we only need to calculate 1-dimensional loops. Furthermore, only one point of every loop, the point , needs to be found. In this case, we have , i.e., if the intersection condition is fulfilled for , it will be fulfilled for all .
The 1-dimensional open line depends on and thus on the ratio . Being an extremal point on this loop, carries the same dependence. The defining equation for the extremum is (cf. Eq. (21))
This is an implicit equation for which is itself a function of . Consequently, the minimal point depends on in an explicit and implicit way, that is . In order to compute and , we insert into Eq. (27a)-(27b) and Eq. (28a)-(28d). In , only a power of must be computed, which can straightforwardly be implemented numerically. There are also no difficulties in calculating
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https://datalya.com/blog/business-statistics/important-charts-to-visualization-trends-and-patterns
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math
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Visualization is a very powerful concept to understand complex trends and patterns buried in statistical data. There is a range of charts for different types and dimensions of data. Following are 7 charts often used to visualize statistical data:
1. Simple Bar Chart:
A horizontal or vertical bars of equal widths and lengths proportional to the values they represent is called simple bar chart. As the basis of comparison is linear or 1-dimensional, the widths of these bars have no significance but are taken into account to make the chart look attractive.
It is good practice that the space separating the bars should not exceed the width of the bar and should not be less than half of its width. The bars should neither be exceedingly long and narrow nor short and broad. The vertical bar chart is an effective tool for presenting a time series and qualitatively classified data whereas horizontal bars are useful for geographical or spatial distributions. If data do not relate to time, it should be arranged in ascending order before charting.
2. Multiple Bar Chart:
Two or more characteristics corresponding to the values of a common variable in the form of grouped bars is shown by a multiple bar chart. There lengths are proportional to the values of the characteristics. Each of it is shaded differently to aid identification. For Example imports, exports and production of a country can be compared from year to year by grouping the three bars together.
3. Component Bar Chart:
A technique in which each bar is divided into two or more sections is known as component bar chart. And proportional in size to the component parts of a total being displayed by each bar. Component bar chart are used to represent the cumulation of the various components of data and the percentages.
4. Rectangles and Sub-divided Rectangles:
The area of rectangle is equal to the product of its length and breadth. To represent a quantity by a rectangle, both length and breadth of the rectangle are used. Sub-divided rectangles are drawn for the data where the quantities along with their components are to be compared.
A pictogram is a popular tool for displaying statistical data using pictures or small symbols. It is said that a picture is worth ten thousand words. It is customary to represent a unit value of the data by a standard symbol or a picture and the whole quantity by an appropriate number of repetitious of symbol concerned. This means the large quantities should be represented by a larger number of symbols and not by large symbols. A quantity smaller than the unit is represented by a part of the picture or symbol used. The symbols or pictures to be used, must be simple and clear. A pictogram is virtually a bar chart constructed in pictorial way as the number of symbols or pictures corresponds to the length of a bar.
6. Pie Diagram:
A pie-diagram, also known as sector diagram, is a graphic device consisting of a circle divided into sectors or pie-shaped pieces whose areas are proportional to various parts into which the whole quantity is divided.
7. Profit and Loss Chart:
This is virtually a percentage component bar chart in which profits can be shown above the normal baseline and losses below the baseline. Since the bars are to be extended from the zero line to show losses, we start from the top.
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https://www.studymode.com/essays/Definite-Integrals-1314553.html
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math
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OBJECTIVES: - be able to express the area under a curve as a definite integral and as a limit of Riemann sums
- be able to compute the area under a curve using a numerical integration procedure
- be able to make a connection with the definition of integration with the limit of a Riemann Sum
Sigma notation enables us to express a large sum in compact form: [pic]
The Greek capital letter [pic](sigma) stands for “sum.” The index k tells us where to begin the sum (at the number below the [pic]) and where to end (the number above). If the symbol [pic] appears above the [pic], it indicates that the terms go on indefinitely. [pic] is called the norm of the partition which is the biggest [pic] (interval)
Riemann Sum: A sum of the form [pic] where f is a continuous function on a closed interval [a, b]; [pic] is some point in, and [pic] the length of, the kth subinterval in some partition of [a, b].
Big Ideas of a Riemann Sum:
- the limit of a Riemann sum equals the definite integral
- rectangles approximate the region between the x-axis
and graph of the function
- A function and an interval are given, the interval is
partitioned, and the height of each rectangle can be
a value at any point in the subinterval
Because the function is not positive, a Riemann sum
does not represent a sum of areas of the rectangles.
It represents the sum of areas above the x-axis subtract
the sum of areas below the x-axis.
Area Under a Curve (as a Definite Integral)
If [pic] is nonnegative and integrable over a closed interval [a, b], then the area under the curve y = f(x) from a to b is the integral of f from a to b.
EX1: Evaluate each integral
EX2: Use the graph of the integrand and areas to evaluate each integral. EX2a: [pic]
Please join StudyMode to read the full document
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https://www.coursehero.com/file/6170904/Hw4ak/
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math
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Sonoma State University ECONOMICS 304 Department of Economics Florence Bouvet Assignment 4 –Chapter 7- Answer Key 1a) Defining y = Y/L, and k = K/L, the production function can be written: y = k 1/3 . b) At steady state k*, the following condition will hold: s f(k*) = ( δ ) k* or s k* 1/3 = ( δ ) k* or k* = (s/( δ )) 3/2 steady-state capital per worker: country A: k* A = (0.2 / 0.10) 3/2 = 2.83 country B: k* B = (0.3 / 0.10) 3/2 = 5.20 c) steady-state output per worker: country A: y* A = (k* A ) 1/3 = (2.83) 1/3 =1.41 country B: y* B = (k* B ) 1/3 = (5.20) 1/3 = 1.73 steady-state consumption per worker: country A: c* A = (1–s A ) y* A = (1-0.2)(1.41)= 1.13 country B: c* B = (1–s B ) y* B = (1-0.3)(1.73)= 1.21 So country B has a higher consumption level (although it spends a smaller fraction of its income on consumption). This means country B is closer to the golden rule. d) Golden rule: (1/3) k* gold-2/3 = 0.01 k * gold= 6.09: golden rule of capital stock
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This note was uploaded on 03/08/2011 for the course ECON 304 taught by Professor Eyler during the Spring '07 term at Sonoma.
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https://justaaa.com/physics/236222-a-hanging-weight-with-a-mass-of-m1-0370-kg-is
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math
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A hanging weight, with a mass of m1 = 0.370 kg, is attached by a string to a block with mass m2 = 0.850 kg as shown in the figure below. The string goes over a pulley with a mass of M = 0.350 kg. The pulley can be modeled as a hollow cylinder with an inner radius of R1 = 0.0200 m, and an outer radius of R2 = 0.0300 m; the mass of the spokes is negligible. As the weight falls, the block slides on the table, and the coefficient of kinetic friction between the block and the table is μk = 0.250. At the instant shown, the block is moving with a velocity of vi = 0.820 m/s toward the pulley. Assume that the pulley is free to spin without friction, that the string does not stretch and does not slip on the pulley, and that the mass of the string is negligible.
A pulley of inner radius R1 and outer radius R2 is attached to the corner of a table such that the pulley is diagonal from the corner and the center of the pulley is to the right of the edge. A hanging weight of mass m1 hangs off the side of the table and is suspended by a string that extends over the pulley. The other end of the string is attached to a block of mass m2, which is on the table. An arrow between the block and the pulley points towards the pulley, and an arrow between the pulley and the hanging mass points towards the ground.
Using energy methods, find the speed of the block (in m/s) after it has moved a distance of 0.700 m away from the initial position shown.
What is the angular speed of the pulley (in rad/s) after the block has moved this distance?
Get Answers For Free
Most questions answered within 1 hours.
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https://softmath.com/tutorials-3/cramer%E2%80%99s-rule/course-syllabus-for-college.html
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math
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Course Syllabus for College Algebra
Essentials of College Algebra. Lial, Hornsby, and Schneider. Pearson/Addison-Wesley: Boston,
Topics include quadratics, polynomial, rational, logarithmic, and exponential functions; systems of
equations; matrices; and determinants. A departmental final examination will be given in this course.
Math 0312 or MATH 0112: Pass with “C” or better
Acceptable placement test score.
Credits: 3 credit hours (3 lecture).
Course Intent & Audience:
This course is designed as a review of advanced topics in algebra for science and engineering students
who plan to take the calculus sequence in preparation for their various degree programs. It is also
intended for non-technical students who need college mathematics credits to fulfill requirements for
graduation and prerequisites for other courses. It is generally transferable to other disciplines as math
credit for non-science majors.
Policy on Late Assignments and Make–Up Exams: All homework assignments will be
due on the
day of each exam. Also, there will be NO makeup exams. If you miss an exam, the final exam will
count twice. It will count once for the missed exam and again for the final exam itself. If you know in
advance that you will be absent on an exam day, please let me know as soon as possible.
All students are required to exercise academic honesty in completion of all tests and assignments.
Cheating involves deception for the purpose of violating testing rules. Students who improperly assist
other students are just as guilty as students who receive assistance. A student guilty of a first offense
will receive a grade of “F” on the quiz or test involved. For a second offense, the student will receive
a grade of “F” for the course. The use of recording devices, including camera phones and tape
recorders, is prohibited in all locations where instruction, tutoring, or testing occurs. Students with
disabilities who need to use a recording device as a reasonable accommodation should contact the
Disability Services Office for information.
Resources and supplemental instruction:
Any student enrolled in Math 1314 at HCC has access to the math tutoring labs which are staffed with
student assistants who can aid students with math problems and offer help with MyMathLab. In
addition, free online tutoring is provided. One other resource is the student solutions manual that may
be obtained from the bookstore.
Students with Disabilities:
Any student with a documented disability (e.g. physical, learning, psychiatric, vision, hearing, etc.)
who needs to arrange reasonable accommodations must contact the Disability Support Services Office
at this college at the beginning of the semester. To make an appointment, please call 713.718.8420.
Professors are authorized to provide only the accommodations requested by the Disability Support
Chapter 1: Equations and Inequalities
1.4 Quadratic Equations (Omit Example 8.)
1.5 Applications and Modeling with Quadratic Equations (Pythagorean
Theorem and simple area problems ONLY)
1.6 Other Types of Equations (Omit Example 5 and Example 8.)
1.8 Absolute Value Equations and Inequalities
Chapter 2: Graphs and Functions
2.1 Graphs of Equations
2.3 Linear Functions
2.4 Equations of Lines; Curve Fitting
2.5 Graphs of Basic Functions (Omit Greatest Integer Function.)
2.6 Graphing Techniques
2.7 Function Operations and Composition
Chapter 3: Polynomial and Rational Functions
3.1 Quadratic Functions and Models (Include applications like
problems 51 & 63.)
3.2 Synthetic Division
3.3 Zeros of Polynomial Functions (In Example 6, use an
imaginary zero with 1 term.)
3.4 Polynomial Functions: Graphs, Applications, and Models
(Omit Intermediate Value and Boundedness Theorems.)
3.5 Rational Functions: Graphs, Applications, and Models
Chapter 4: Exponential and Logarithmic Functions
4.1 Inverse Functions
4.2 Exponential Functions
4.3 Logarithmic Functions
4.4 Evaluating Logarithms and the Change-of-Base Theorem (Omit
4.5 Exponential and Logarithmic Equations (Omit application problems.)
4.6 Applications & Models of Exponential Growth & Decay
(Doubling time type problems ONLY)
Chapter 5: Systems and Matrices
5.1 Systems of Linear Equations (two variables only)
5.5 Nonlinear Systems of Equations
5.7 Properties of Matrices
5.3 Determinant Solution of Linear Systems (Omit Cramer’s Rule.)
MyMathLab Course ID: Hatton54305
Campus Zip Code: 77022
|Test||Chapters Covered on Test||Date|
|Test #1||Chapter 1||TBA|
|Test #2||Chapter 2||TBA|
|Test #3||Chapter 3||TBA|
|Test #4||Chapter 4||TBA|
|Final Exam||Chapters 1 - 5||December 9th or 11th
At the completion of this course, a student should be able to:
1. Solve quadratic equations in one variable by factoring , using the square root
the square , and using the quadratic formula.
2. Find the distance and midpoint between two points in the Cartesian plane.
3. Solve radical equations , fractional equations , and equations of quadratic form.
4. Recognize the equation of a straight line, graph the equation of a straight line, find the slope and
intercepts of a line , know the relationship between the slopes of parallel and perpendicular lines,
and be able to determine the equation of a line from information such as two points on the line, or
one point on the line and the slope of the line.
5. Know the definition of a function, determine the domain and range of a function, evaluate
expressions involving functional notation, simplify expressions involving the algebra of functions,
graph functions by plotting points , know the definition of inverse functions, and given a function
find its inverse.
6. Graph linear functions, quadratic functions, piecewise-defined functions, absolute value functions,
polynomial functions, rational functions, exponential functions, and logarithmic functions.
7. Solve linear inequalities and linear equations involving absolute value, state the solution in interval
notation, and graph the solution.
8. Solve non-linear (quadratic and rational) inequalities, state the solution in interval notation, and
graph the solution.
9. Understand vertical and horizontal shifts, stretching, shrinking, and reflections of graphs of
10. Recognize the equation of a circle , sketch the graph of a circle, and find the equation of a circle.
11. Determine the rational zeros of a polynomial.
12. Understand the inverse relationship between the exponential and logarithmic functions.
13. Solve exponential and logarithmic equations.
14. Solve problems involving variation.
15. Perform operations with matrices, and find the determinants of matrices
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http://locourseworkwrrk.supervillaino.us/economic-problem-set.html
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math
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Economics 10: problem set 1 (with suggested answers) the island of pago-pago imports boomerangs from australia, but by custom, only the boys of the island are. Gbhs ap economics syllabus 2017-18 micro unit 2 problem set comments (-1) micro unit 3 problem set comments (-1) micro unit 4 problem set. To: january 7, 2013 page: 1 economics 7360 problem set #1 1 consider the optimal commodity taxation model we used to derive the many person ramsey tax rule.
View homework help - economics problem set 5 from ec 202 at sacread heart university problem set #5 samantha marshall 1 what is the shape of the avc and atc curves. International monetary economics problem set #4: chapter 8, 9 and 10 directions: answer all the questions by writing on one side of each sheet of paper your answers should be complete, yet concise. All of these problem fall under the category of constrained optimization set up the problem a common economic problem is the consumer choice decision.
This section provides a problem set on competition. Liberty university econ213 problem set 1 complete solutions correct answers keyproblem set from economics liberty university econ213 problem set 1 complete.
Kevin corinth economics 20000 university of chicago spring 2012 problem set 1 the economic approach and scarcity due monday, april 2 at 7:00pm at ta session. Maurer, gustav welcome american history chapter 3, problem set 2 here are partial solutions to the problem set assumption and its importance in economics.
Markedsføring & salg projects for $2 - $8 i need some one competent this economics problem set asap it is easy its just that i am not good with word and please answer in detail thanks. Problem set exercises: macroeconomics in the global economy updated: march 7, 2016 as stated in the course syllabus, problem sets are not required problem sets will not be graded, nor are they worth formal credit.
Development economics problem set 2 sherif khalifa 1 (a) what are the causes of the world food crisis (b) describe the agrarian systems prevalent in the developing world:. Quizlet provides problem set 2 economics activities, flashcards and games start learning today for free. Problem set 1 fin 525: financial economics i part 1: asset pricing in discrete time prof markus k brunnermeier ∗ due date: tba problem 1 during the bagel hour on thursday morning, max (a fellow phd student).Download
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http://www.sevenforums.com/1875978-post729.html
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math
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Quote: Originally Posted by mickey megabyte
each to his own
Quote: Originally Posted by smarteyeball
Quote: Originally Posted by Gornot
Borderlands isn't worth your time, unless you're really bored to the point that you don't care what you play xD
Yeah, I just couldn't get into it.
- i really enjoyed it and am looking forward to the sequel.
I'm finding these days if something doesn't grab me quickly, I shelve it pretty quickly. If I put more time into it, I might have enjoyed it.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560281450.93/warc/CC-MAIN-20170116095121-00242-ip-10-171-10-70.ec2.internal.warc.gz
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CC-MAIN-2017-04
| 484 | 8 |
http://rsta.royalsocietypublishing.org/content/269/1199/439
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math
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The semi-empirical laws for the variation of mean wind speed with height and for the statistical properties of the turbulent fluctuations are briefly outlined. Similarity considerations provide some useful ordering of the mean wind profile characteristics in relation to surface roughness and thermal stratification. Appreciable uncertainties prevail, however, especially as a consequence of the effect of thermal stratification and of variable terrain roughness. Some generalization on similarity grounds can also be made regarding the fluctuations of horizontal wind speed as a function of roughness and stability, but there are wide variations of spectral density and scale which are not immediately explicable and which at present preclude anything more than a relatively coarse specification of the spectrum. Features which are of special relevance to architectural aerodynamics and which are discussed briefly are: (a) the difficulty of generalizing about the wind profile and turbulence above an urban complex; (b) the requirement for estimating the magnitudes of extreme gusts as a function of mean wind speed, averaging time and height; (c) the problem of generalizing about flow properties below roof level; (d) the effect of urban airflow on the travel and dispersion of pollutants.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917118552.28/warc/CC-MAIN-20170423031158-00643-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 1,293 | 1 |
http://pg.univ-batna2.dz/publications/security-limitations-shamir%E2%80%99s-secret-sharing
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math
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The security is so important for both storing and transmitting the digital data, the choice of parameters is critical for a security system, that is, a weak parameter will make the scheme very vulnerable to attacks, for example the use of supersingular curves or anomalous curves leads to weaknesses in elliptic curve cryptosystems, for RSA cryptosystem there are some attacks for low public exponent or small private exponent. In certain circumstances the secret sharing scheme is required to decentralize the risk. In the context of the security of secret sharing schemes, it is known that for the scheme of Shamir, an unqualified set of shares cannot leak any information about the secret. This paper aims to show that the well-known Shamir’s secret sharing is not always perfect and that the uniform randomization before sharing is insufficient to obtain a secure scheme. The second purpose of this paper is to give an explicit construction of weak polynomials for which the Shamir’s (k, n) threshold scheme is insecure in the sense that there exist a fewer than k shares which can reconstruct the secret. Particular attention is given to the scheme whose threshold is less than or equal to 6. It also showed that for certain threshold k, the secret can be calculated by a pair of shares with the probability of 1/2. Finally, in order to address the mentioned vulnerabilities, several classes of polynomials should be avoided.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572833.95/warc/CC-MAIN-20220817032054-20220817062054-00730.warc.gz
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CC-MAIN-2022-33
| 1,434 | 1 |
https://catalog.ualberta.ca/Course/Details?subjectCode=MATH&catalog=311
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math
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Quick Course Search
MATH311 - Theory of Functions of a Complex Variable
Complex numbers. Complex series. Functions of a complex variable. Cauchy's theorem and contour integration. Residue Theorem and its applications. Prerequisite or corequisite: MATH 209 or 215.
View Previous Terms
Winter Term 2019 - LEC Q1 (87082)
MWF 10:00:00 - 10:50:00 (V 102)
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CC-MAIN-2018-43
| 349 | 6 |
https://www.crcpress.com/Map-ProjectionsTheory-and-Applications/II/p/book/9780849368882
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math
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About the Author: Frederick Pearson has extensive experience in teaching map projection at the Air Force Cartography School and Virginia Polytechnic Institute. He developed star charts, satellite trajectory programs, and a celestial navigation device for the Aeronautical Chart and Information Center. He is an expert in orbital analysis of satellites, and control and guidance systems. At McDonnell-Douglas, he worked on the guidance system for the space shuttle.
This text develops the plotting equations for the major map projections. The emphasis is on obtaining usable algorithms for computed aided plotting and CRT display. The problem of map projection is stated, and the basic terminology is introduced. The required fundamental mathematics is reviewed, and transformation theory is developed. Theories from differential geometry are particularized for the transformation from a sphere or spheroid as the model of the earth onto a selected plotting surface. The most current parameters to describe the figure of the earth are given. Formulas are included to calculate meridian length, parallel length, geodetic and geocentric latitude, azimuth, and distances on the sphere or spheroid. Equal area, conformal, and conventional projection transformations are derived. All result in direct transformation from geographic to cartesian coordinates. For selected projections, inverse transformations from cartesian to geographic coordinates are given. Since the avoidance of distortion is important, the theory of distortion is explored. Formulas are developed to give a quantitative estimate of linear, area, and angular distortions. Extended examples are given for several mapping problems of interest. Computer applications, and efficient algorithms are presented. This book is an appropriate text for a course in the mathematical aspects of mapping and cartography. Map projections are of interest to workers in many fields. Some of these are mathematicians, engineers, surveyors, geodicests, geographers, astronomers, and military intelligence analysts and strategists.
Table of Contents
INTRODUCTION. Introduction to the Problem. Basic Geometric Shapes. Distortion. Scale. Feature Preserved in Projections. Projection Surface. Orientation of the Azimuthal Plane. Orientation of a Cone of Cylinder. Tangency or Secancy. Projection Technique. Plotting Equations. Plotting Tables. MATHEMATICAL FUNDAMENTALS. Coordinate Systems and Azimuth. Grid Systems. Differential Geometry of Space Curves. Differential Geometry of a General Surface. First Fundamental Form. Second Fundamental Form. Surfaces of Revolution. Developable Surfaces. Transformation Matrices. Definition of Equality of Area and Conformality. Rotation of Coordinate Systems. Convergency of the Meridians. Constant of the Cone and Slant Height. FIGURE OF THE EARTH. Geodetic Considerations. Geometry of the Elipse. The Spheroid as a Model of the Earth. The Spherical Model of the Earth. The Triaxial Ellipsoid. EQUAL AREA PROJECTIONS. General Procedures. The Authalic Sphere. Albers, One Standard Parallel. Albers, Two Standard Parallels. Bonne. Azimuthal. Cylindrical. Sinusoidal. Mollweide. Parabolic. Hammer-Aitoff. Boggs Eumorphic. Eckert IV. Interrupted Projections. CONFORMAL PROJECTIONS. General Procedures. Conformal Sphere. Lambert Conformal, One Standard Parallel. Lambert Conformal, Two Standard Parallels. Stereographic. Mercator. State Plane Coordinates. Military Grid Systems. CONVENTIONAL PROJECTIONS. Summary of Procedures. Gnomonic. Azimuthal Equidistant. Orthographic. Simple Conic, One Standard Parallel. Simple Conic, Two Standard Parallels. Conical Perspective. Polyconic. Perspective Cylindrical. Plate Carree'. Carte Parallelogrammatique. Miller. Globular. Aerial Perspective. Van der Grinten. Cassini. Robinson. THEORY OF DISTORTIONS. Qualitative View of Distortion. Quantization of Distortion. Distortions from Euclidean Geometry. Distortions from Different Geometry. Distortions in Equal Area Projections. Distortions in Conventional Projections. MAPPING APPLICATIONS. Map Projections in the Southern Hemisphere. Distortion in the Transformation from the Spheroid to the Authalic Sphere. Distances on the Loxodrome. Tracking System Displays. Differential Distances about a Position. COMPUTER APPLICATIONS. Direct Transformation Subroutines. Inverse Transformation Subroutines. Calling Program for Subroutines. State Plane Coordinates. UTM Grids. Computer Graphics. USES OF MAP PROJECTIONS. Fidelity to Features on the Earth. Characteristics of Parallels and Meridians. Considerations in the Choice of a Projection. Recommended Areas of Coverage. Recommended Set of Map Projections. Conclusion.
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CC-MAIN-2020-05
| 4,686 | 4 |
https://www.ems-ph.org/journals/show_abstract.php?issn=0232-2064&vol=12&iss=2&rank=13
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math
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Zeitschrift für Analysis und ihre Anwendungen
Full-Text PDF (1042 KB) | Metadata | Table of Contents | ZAA summary
Published online: 1993-06-30
About Integral Equivalence between Linear and Nonlinear Operator Impulsive Differential Equations in a Banach SpaceS.I. Kostadinov and Dieter Schott (1) University of Plovdiv, Bulgaria
(2) Hochschule Wismar, Germany
After an introduction into the problems of impulsive operator differential equations sufficient conditions for the integral and the asymptotic equivalence between linear and nonlinear equations of this kind are presented. These conditions guarantee that for bounded solutions of the linear equation there are also bounded solutions of the corresponding nonlinear equation.
Keywords: Abstract impulsive differential equations, integral equivalence, asymptotic equivalence, exponential dichotomy, fixed point theorem of Schauder
Kostadinov S.I., Schott Dieter: About Integral Equivalence between Linear and Nonlinear Operator Impulsive Differential Equations in a Banach Space. Z. Anal. Anwend. 12 (1993), 361-378. doi: 10.4171/ZAA/559
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CC-MAIN-2021-43
| 1,094 | 8 |
http://www.maths.usyd.edu.au/s/scnitm/mathas-AGRSeminar-ComputingACoun
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math
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SMS scnews item created by Andrew Mathas at Tue 6 Nov 2012 1436
Expiry: 12 Nov 2012
Calendar1: 12 Nov 2012 1500
CalLoc1: AGR Carslaw 829
CalTitle1: AGR Seminar: Computing a Counterexample to Giuga’s Conjecture
Auth: [email protected] in SMS-auth
AGR Seminar: Computing a Counterexample to Giuga’s Conjecture: Matt Skerritt (CARMA, Australia)
University of Newcastle
Giuga's conjecture will be introduced, and we will discuss what's changed in the computation of a counterexample in the last 17 years.
Ms Juliane Turner
If you are interested in attending this seminar in our access grid room then please check to see if the grid is already booked at this time and let Robert Pearson know that you would like to attend.
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CC-MAIN-2020-10
| 734 | 11 |
http://www.examiner.com/article/finding-an-equation-for-a-line?cid=rss
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math
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Instead of finding a line for an equation, as we discussed in our previous article, we will now learn how to find an equation for a line. All we need to determine an equation for a line is to know a lien's slope and only one point through which the line passes. With this information, we are prepared to find a line for an equation. Suppose we have a slope m and a point (a, b). y - b/x - a = m. Let's pretend we're trying to find an equation for a line through the point (4, -8) with slope 5. We would write y - (-8)/x - 4 = 5. We would then write y + 8 = 5(x-4). This gives us y = 5x - 28.
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s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783398209.20/warc/CC-MAIN-20160624154958-00191-ip-10-164-35-72.ec2.internal.warc.gz
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CC-MAIN-2016-26
| 591 | 1 |
https://interviewmania.com/verbal-ability/paragraph-formation/1/2
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math
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Direction: In the following questions, the first and the last sentence are numbered 1 and 6. The rest of sentence/passage is split into four parts and named P, Q, R and S. These four sentence/passage are not given in their proper order, Read the sentence/passage and find out which of the four combinations is correct then find the correct Answer .
Direction: The sentences given in each question, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a letter. Choose the most logical order of the sentences from amongst the given choices so as to form a coherent paragraph.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296816853.44/warc/CC-MAIN-20240413211215-20240414001215-00706.warc.gz
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CC-MAIN-2024-18
| 604 | 2 |
http://www.cafemom.com/home/midnight_storm
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math
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I am a pretty eclectic, layed back, kind of lady. I am pretty optimistic, sometime idealistic and sometimes realistic. I give most the benefit of the doubt, second chances, and believe in the good in others. I confuse most people until they get to know me, and really don't care that I do. I have a variety of interests, enjoy conversing with others of both like and different interests. I am just me.
(¯`•.•´¯) (¯`•.•´¯) Welcome to 40ish & beyond
*`•.¸(¯`•.•´¯)¸.•´Glad you joined the sisterhood!
¤ º° ¤`•.¸.•´ ¤ º° ¤ Jump right in & Join the fun
*`•.¸(¯`•.•´¯)¸.•´ of posting, replying & meeting friends!
¤ º° ¤`•.¸.•´ ¤ º° ¤http://www.cafemom.com/group/7446
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s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1419447548035.129/warc/CC-MAIN-20141224185908-00076-ip-10-231-17-201.ec2.internal.warc.gz
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CC-MAIN-2014-52
| 730 | 6 |
https://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-22-number-4-6-2014/mvlsc-22-4-6-p-599-618/
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math
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Chance Constrained Programming Models for Constrained Shortest Path Problem with Fuzzy Parameters
Pinar Dursun and Erhan Bozdag
Shortest path problem is a fundamental problem in transportation networks, communication networks and optimal control. The number of studies using different tools to solve this problem in deterministic, stochastic or fuzzy environment as well as the constrained version is increasing. In this paper, two chance constrained programming models are proposed for the shortest path problem with fuzzy parameters. The first model has fuzzy constraints in addition to the classical shortest path problem. The weights of arcs which form objective function are also fuzzy in the second model. To solve the models, a hybrid algorithm consists of fuzzy simulation and genetic algorithm is developed. To demonstrate the applicability of these proposed models and algorithms, some illustrating examples are given using a sample network. From the results, we can assert that the proposed methods are promising for the real life applications of the problem.
Keywords: Constrained Shortest Path Problem, Fuzzy Arc Weight, Chance Constrained Programming, Possibility, Fuzzy Simulation, Genetic Algorithm.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474690.22/warc/CC-MAIN-20240228012542-20240228042542-00870.warc.gz
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CC-MAIN-2024-10
| 1,215 | 4 |
http://www.brightstorm.com/math/algebra/solving-equations/solving-single-step-equations-problem-1/
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math
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Solving an equation and finding the value of the variable requires "undoing" what has been done to the variable. We do this by using inverse operations to isolate the variable. Remember that an equation is two expressions that are equal to each other. This means that when using inverse operations to isolate the variable, what is done to one side of the equation has to be done to the other side as well so that the equation stays balanced. For example, if 5 is being added to the variable, then to isolate the variable, do the opposite operation. The opposite of adding 5 is subtracting 5. What you do to one side, you have to do to the other, so make sure to subtract 5 from both sides. After solving for the variable, check your answer by plugging the value into the original equation. If the equation is true -- meaning the left side of the equation equals the right side of the equation -- then the solution is correct.
Experience the 'A-Ha!' moment with the best teachers
whom we hand-picked for you!
M.A. in Secondary Mathematics, Stanford University B.S., Stanford University
Alissa has a quirky sense of humor and a relatable personality that make it easy for students to pay attention and understand the material. She has all the math tips and tricks students are looking for.
“Your tutorials are good and you have a personality as well. I hope you have more advanced college level stuff, because I like the way you teach.”
“Thanks alot for such great lectures... I never found learning this easier ever before... keep up the great work.... :)”
“You seem so kind, it's awesome. Easier to learn from people who seem to be rooting for ya!' thanks”
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s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398452385.31/warc/CC-MAIN-20151124205412-00249-ip-10-71-132-137.ec2.internal.warc.gz
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CC-MAIN-2015-48
| 1,668 | 8 |
https://answers.yahoo.com/question/index?qid=20061112070438AA2p96e
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math
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profit and loss?
Usha bought 100 eggs for Rs.80. She sold half of these at a profit of 10%.Five eggs got broken.. At what profit percent should she sell the remaining eggs so as to gain 12 1/2% on the whole,assuming that shoe found a one-rupee coin on the way and is going to count it in her profit ? Had she not found the coin ,and had she sold the remaining , and had she sold the remaining eggs cost-to-cost ,what profit or loss percent would she have made?
- ironduke8159Lv 71 decade agoFavorite Answer
Profit on 50 eggs was .1(40)= 4 rupees
After finding the rupee her profit was 4+1=5 rupees
Total desired profit =.125(80) = 10 rupees
Therefore she must sell the remaining 45 eggs for 5 rupees
Since she paid 45(80)/100 = 4.5 rupees for the 45 eggs, the profit was .5/4.5 = 11.11%.
If she had not found the 1 rupee coin and had she sold the rest of the eggs at cost then her total profit would have been just the 4 rupees which would be 4/80 = 5%
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s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178381803.98/warc/CC-MAIN-20210308021603-20210308051603-00083.warc.gz
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CC-MAIN-2021-10
| 952 | 9 |
http://qucs.sourceforge.net/tech/node47.html
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math
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An ideal bias t is a combination of a DC block and a DC feed (fig. 9.1). During DC simulation the MNA matrix of an ideal bias t writes as follows:
The MNA entries of the bias t during AC analysis write as follows.
The scattering parameters writes as follows.
A bias t is noise free. A model for transient simulation does not exist. It is common practice to model it as an inductor and a capacitance with finite values which are entered by the user.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125947803.66/warc/CC-MAIN-20180425115743-20180425135743-00376.warc.gz
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CC-MAIN-2018-17
| 448 | 4 |
http://www.imagekind.com/Flowers-For-MLady_art?IMID=688f3ab4-9e18-435f-bbde-9f7861cb082e&size=Medium
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math
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Mathematicians argue that fractals in 3D are limited to extruding the surface and extending the image out of a two dimensional plane. Many mathematicians think that 3D fractals aren't really 3D, they fall somewhere between 2D and 3D.
Fractal: A geometric pattern that is repeated at ever smaller scales to produce irregular shapes and surfaces that cannot be represented by classical geometry. (ref. dictionary.com)
I offer you an artist's response - a computer generated mathematically derived conical flower and leaves, constructed of many smaller conical flowers and leaves, constructed from many smaller conical flowers and leaves, etc.
Lots of detail can be found in this piece, as can be seen in the closeup below.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917121216.64/warc/CC-MAIN-20170423031201-00260-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 720 | 4 |
https://tutorials.canil.ca/latex
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math
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Installing and setting up LaTeX
Download and install TeX Live (~4GB) or MikTeX (~128MB). They include various typesetting engines and functional packages. MikTeX provides you minimal or customized installation if your PC has storage limitations.
Download and install TeXMaker, a free cross-platform LaTeX editor. There are others, but this is our preferred editor, and it is installed on all PC in the computer lab.
Download and install JabRef, a free cross-platform bibliography database for LaTeX users.
Using LaTeX in CanIL Computer Lab
LaTeX, TeXMaker and JabRef are installed on all PC in the computer lab.
When you run the launcher for the first time, you need to initiate TeX Live launcher by clicking a file here: P:\texlive\2021\tlaunch.exe.
Then click "Select default editor..." button, and select TeXMaker as your default editor.
After the configuration, you are ready to use LaTeX for your work.
CanIL_Style_Templates: This folder contains templates for presentation, research report, term paper, and thesis. In the future, there will be other templates designed for various courses.
TexMaker user documentation.
JabRef user documentation
TeX-LaTeX Exchange is a question and answer site for users of TeX, LaTeX, ConTeXt, and related typesetting systems.
The Comprehensive TEX Archive Network (CTAN) is the central place for all kinds of material around TEX.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233511021.4/warc/CC-MAIN-20231002200740-20231002230740-00065.warc.gz
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CC-MAIN-2023-40
| 1,370 | 14 |
http://www.defsounds.com/tag/joey-bada/
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math
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The Pro Era camp teams up with Scion AV and releases a new compilation EP, The Shift.
The Pro Era camp stopped by Hot 97 and spit a freestyle for the Hot Box with DJ Enuff.
Joey Bada$$ releases his latest track, "Mr. Wonderful," that serves as the hype track for UFC Light Heavyweight Phil Davis.
While Joey Bada$$ continues to prep his highly anticipated debut album, B4.Da.$$, he takes some time out to speak on the project.
Smoke DZA drops off another new leak off his new album, Dream.ZONE.Achieve
The Pro Era camp releases their latest compilation project, The Secc$ Tap.e Pt 2 EP.
Joey Bada$$ kicks of Pro Era Week by dropping the first leak off the upcoming Pro Era compilation tape, Secc$ Tap.e Pt.
Joey Bada$$, CJ Fly, Kirk Knight, Nyck Caution, Dessy Hinds, A La $ole & Dirty Sanchez: MTV RapFix Cypher
The Pro Era crew appeared on the latest episode of MTV RapFix and closed out the show with a cypher.
Pro Era's Joey Bada$$ and MMG's Rockie Fresh stopped by Cosmic Kev's show and laid down a freestyle.
Joey Bada$$ takes on a previously unreleased J.Dilla beat for "Two Lips," which is released in conjunction with Akomplice Clothing and the J.Dilla Foundation
Joey Bada$$ releases visuals for his single, "My Yout," off his new Summer Knights EP, which is out now.
Joey Bada$$ drops off another new track, "My Jeep," from his forthcoming Summer Knights EP, which drops tomorrow.
Joey Bada$$ enlists Maverick Sabre for "My Yout" off his Summer Knights EP, which drops October 29th.
Joey Bada$$ and his Pro Era crew stop by Statik Selektah’s Showoff Basement to lay down some bars for a cypher
Joey Bada$$ releases the official visual for one of the stand-outs,"Hilary Swank," from his Summer Knights mixtape.
The Pro Era Crew, Joey Bada$$, CJ Fly & Kirk Knight, stop by Invasion Radio and spit an "OnDaSpot" freestyle.
Joey Bada$$ is next up to reply to Kendrick Lamar's "Control" verse.
New music from Joey Bada$$ off The Smokers Club's new project Oil
Joey Bada$$ releases visuals for "’95 Til Infinity" off his upcoming mixtape, Summer Knights.
Joey Bada$$ links up with Kirk Knight for the latest leak, "Amethyst Rockstar," off his forthcoming mixtape, Summer Knights
Joey Bada$$ drops off the latest leak, "95 Til Infinity," off his forthcoming mixtape, Summer Knights.
Joey Bada$$ and his Pro Era crew release visuals for their track "Like Water" that appeared on the PEEP: The Aprocalypse mixtape
Joey Bada$$ releases the first single, "Word Is Bond," off his forthcoming full-length project, Summer Knights.
Joey Bada$$ gives another update about his forthcoming Summer Knights project.
Drama-free version of Joey Bada$$' "B.A.R'd" featuring Action Bronson off the XXL Freshmen Class mixtape
Pro Era releases visuals for their track, "School High" off the PEEP: The Aprocalypse mixtape
Joey Bada$$, Action Bronson, Ab-Soul and Travi$ Scott come together for the first 2013 XXL Freshmen Cypher.
Brooklyn rapper Joey Bada$$ has announced the title and time-frame for the release of his freshman album.
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s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207928015.28/warc/CC-MAIN-20150521113208-00333-ip-10-180-206-219.ec2.internal.warc.gz
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CC-MAIN-2015-22
| 3,023 | 29 |
https://www.clutchprep.com/physics/practice-problems/43582/consider-a-circular-loop-of-radius-r-in-the-presence-of-a-uniform-magnetic-field
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math
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Consider a circular loop of radius R in the presence of a uniform magnetic field. Which of the following statements is true?
A) Doubling the magnetic field would result in the same change in flux as doubling the radius would.
B) Doubling the angle between the magnetic field and the surface will double the magnetic flux.
C) Changing the angle between the axis of the coil and the field from 90o to some θ angle would result in the same change in flux as doubling the area of the coil.
D) Halving the radius of the coil halves the magnetic flux through the coil.
E) None of the above are true.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371806302.78/warc/CC-MAIN-20200407214925-20200408005425-00286.warc.gz
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CC-MAIN-2020-16
| 594 | 6 |
http://7puzzleblog.com/187/
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math
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A Keith Number, made famous by Mike Keith, is worked out in a not-too-dissimilar way to Fibonacci Numbers. If you like playing around with numbers, have a go at this fun concept. The first 2-digit Keith Number, 14, is worked out as follows:
- Try 14: 1+4=5; 4+5=9; 5+9=14 (the total arrives back to the original number).
By following this pattern, can you find the next 2-digit Keith Number?
Leave a comment below or e-mail me at [email protected] if you get an answer!
The 7puzzle Challenge
The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from 2 up to 84.
The 2nd & 3rd rows contain the following fourteen numbers:
8 13 17 25 28 36 42 45 48 55 63 64 66 80
Which three numbers, when 6 is added to them, each become multiples of 7?
. . . can be found when clicking this.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463612003.36/warc/CC-MAIN-20170528235437-20170529015437-00309.warc.gz
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CC-MAIN-2017-22
| 822 | 10 |
https://essayzoo.org/math-problem/apa/mathematics-and-economics/realistic-achievable-measurable-goal.php
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math
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Realistic, Achievable, Measurable Goal (Math Problem Sample)
Please answer the following.
What do you think about this goal; Increase sales from $15,000 to $22,000 by December 1st at a cost not to exceed $3,000. Is this realistic, achievable, and measurable? Why or Why not?
Aguinis, H. (2013). Performance management. Upper Saddle River, NJ: Pearson Prentice Hall.
Realistic, achievable, measurable goal
The goal of increasing sales from $15,000 to $22,000 by December 1 at a cost that does not surpass $3,000 is realistic, achievable and measurable. Numbers are used to measure a goal or objective that is measurable. Companies set standards for attaining their goals by using numbers and this way, they are able to measure progress (Aguinis, 2013). The goal is measurable because it seeks to increase the sales by $7,000; that is, from $15,000 to $22,000, which represents a 47% increase. Here, numbers have been used to enable the company to measure progress. By applying numbers, it means that the goal can be measured (Aguinis, 2013). As such, this goal is measurable.
An achievable goal is one that ...
- Trident University CaseDescription: Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible....10 pages/≈2750 words | No Sources | APA | Mathematics & Economics | Math Problem |
- Sets & Counting: first SLPDescription: Undergraduate level Math Problem: Sets & Counting: first SLP...1 page/≈275 words | 1 Source | APA | Mathematics & Economics | Math Problem |
- Quanitive AnalysisDescription: Math Problem: Quanitive Analysis (Mathematics and Economics)...1 page/≈275 words | 1 Source | APA | Mathematics & Economics | Math Problem |
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| 1,732 | 10 |
http://www.endurance.net/RideCamp/archives/past/9805/msg00923.html
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math
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Re: fast/slow twitch and mules
We did muscle biopsies on about 40 mules at Cal Poly and they were
similar in their muscle fiber type distribution to what you would expect
to see in a quarter horse---that is, more fast twitch fibers than slow
twitch. HOWEVER, these were all draft type mules used for pack trips at
high altitude and had come from similar breeding. The mares they used
were all quarter horse/draft cross mares, no thoroughbreds or arabians
in the bunch. Since there ARE some arab-derived mules doing very well
in endurance, I would tend to think that the mare used is very
influential in what the mule's muscle fiber types would be.
sandy lundberg wrote:
> Does anybody know how mules compare to arabs and quarter horses as far
> as fast or slow twitch muscles is concerned? I know it would vary
> depending on the mare you used.
> DO YOU YAHOO!?
> Get your free @yahoo.com address at http://mail.yahoo.com
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https://www.librarything.com/author/smithe
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math
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If your book appears on this page, please edit your information to include the author's full name. Your book should then appear on the correct author page. Thank you for your help.
#2 E. Dan Smith III
#3 Smith & Company, Pittsfield, Mass.
#4 E B. (Brian) Smith
#5 E Smith, of Mansfield Ohio, fl. 1852
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| 300 | 5 |
https://fr.slideserve.com/thu/degrees-of-freedom
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math
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Translation – movement along X, Y, and Z axis (three degrees of freedom) Degrees of Freedom An object in space has six degrees of freedom. • Rotation – rotate about X, Y, and Z axis • (three degrees of freedom)
Degrees of Freedom (DOF) Planar (2D) mechanisms Degrees of Freedom– number of independent coordinates required to completely specify the position of the link Three independent coordinates needed to specify the location of the link AB, xA, yA, and angle An unconstrained link in the plane has three degrees of freedom, mechanism with L links has 3L degrees of freedom
Mechanism is a mechanical device that has the purpose of transferring motion and/or force from a source to an output. • Linkage consists of links (or bars), generally considered rigid, which are connected by joints, such as pins (or revolutes), or prismatic joints, to form open or closed chains (or loops). • Such ,kinematic chains with at least one link fixed, become • (1) mechanisms if at least two other links retain mobility, or • (2)structures if no mobility remains. In other words, a mechanism permits relative motion between its “rigid” links; a structure does not.
Link – the rigid connection between two or more elements of kinematic pairs. • Rigidity – means there can be no relative motion between two arbitrarily chosen points on the same link. • The purpose of a link is to hold constant spatial relationship between the elements of its pairs.
Type of Joints – Kinematic Pairs Lower Pairs – motion is transmitted through an area contact, pin and slider joints. Higher Pairs – motion is transmitted through a line or a point contact; gears, rollers, and spherical joints.
Each pin connection removes two degrees of freedom of relative motion between two successive links. Two degrees of freedom joints are sometimes called a half a joint (Norton). A slider is constrained against moving in the vertical direction as well as being constrained from rotating in the plane. A spheric pair is a ball and socket joint, 3 DOF. The helical pair has the sliding and rotational motion related by the helix angle of the screw. Planar pair is seldom used Degrees of Freedom (DOF) – Type of Joints, Lower Pairs
DOF ≤ 0 structure mechanism DOF > 0 Degrees of Freedom (DOF)
DOF = 3(L – 1) – 2J1– J2 DOF = 3(4 – 1) – 2(4) – (0) = 1 Slider crank mechanism L = 4 , J1 = 3 pin connections + 1 slider = 4 J2 = 0 DOF = 3(4 – 1) – 2(4) – (0) = 1 Degree of Freedom (DOF) – example Four Bar mechanism L = 4 , J1 = 4 pin connections, J2 = 0 1 DOF means only one input (power source) is needed to control the mechanism
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CC-MAIN-2023-06
| 2,645 | 8 |
https://www.hackmath.net/en/math-problem/40283
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math
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The square ABCD and the point E lying outside the given square are given. What is the area of the square when the distance | AE | = 2, | DE | = 5 a | BE | = 4?
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https://www.universallogistics.ca/p/news/news20210218-montrealportnegotiations2.php
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math
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Toronto, February 18, 2021
As the negotiation process is currently suspended and the truce between the dockworkers' union CUPE 375 and the Maritime Employers Association (MEA) draws to a close, the Montreal Port Authority (MPA) hopes that the parties will quickly reach an agreement to avoid a new work stoppage by the dockworkers
Nearly a month before the end of the truce between the employer and the union, scheduled for March 21 at 6:59 am, the MPA has found that several Quebec and Ontario businesses that use the Port of Montreal, including some that move critical cargo to combat COVID-19, are diverting containerized goods to other ports, and that others are planning to do so if a new work stoppage occurs soon.
While diversion to other ports is viewed as a way to bypass issues at the Port of Montreal, as was experienced during the last work stoppage in 2020, these ports of diversion became quickly overwhelmed and cargo movement stagnated. Coupled with this is the fact that existing liner service to such ports is at capacity at the moment, so the options of diverting to these ports will be limited.
This situation could result in major delays in the supply chain and higher freight costs, as the economic recovery and a broader reopening of the retail sector in Quebec and Ontario get under way.
For more information, please call David Lychek, Manager – Ocean & Air Services at (905) 882-4880, ext. 1207.
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| 1,431 | 6 |
https://answers.search.yahoo.com/search?p=translation+definition+math&ei=UTF-8&flt=cat%3AMilitary&xargs=0&fr2=rs-bottom%2Cp%3As%2Cv%3Aw%2Cm%3Aat-s
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math
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...can. Let's say that you have the picture of a duck in the middle of a grid. Translation , rotation, and reflection are all terms used to describe how you can...
3 Answers · Science & Mathematics · 26/05/2010
...young is that too much emphasis is put on terminology, i.e. definitions , words, rules, at a time when they need to be learning about...
6 Answers · Science & Mathematics · 23/03/2011
its a math thing with grids and points are you looking for the definitions or how to solve the problems because i can help for both just ask
2 Answers · Science & Mathematics · 10/04/2007
It depends on your definition of symmetry: One answer is: Rotation Translation Reflection Glide ... http://www.teachersnetwork.org/dcs/ math /symmetry/
3 Answers · Science & Mathematics · 30/05/2007
- related to: translation definition math
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https://www.studypool.com/discuss/1025438/a-race-car-starts-from-rest-on-a-circular-track-of-radius-578-m-the-car-s-speed
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math
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Thank you for the opportunity to help you with your question!
The tangential acceleration is 0.740 m/s².
If you know vector calculus, take derivatives of the vector ( r sin(ωt), r cos(ωt) ) -- a vector which goes around in a circle at a constant speed -- to find the following relationships:
r = radius(578m)
v = ω r
a = ω² r.
That proves that a = v² / r. (Your textbook might have a non-vector-calculus proof of that, but vector calculus is the easy way to do it.)
This means that for (a), you want to find the speed v where:
v² / r = 0.740 m/s².
You know r. Solve for v. =427m/s^2
The total distance traveled? Well, you have to accelerate from 0 to the value in the previous problem (roughly 20 m/s). That takes a certain amount of time. How much time? [We're answering (c) first.]
Well, what does 0.740 m/s² mean? It means at t=0s, you're going at speed 0. Then at t=1s, you're going at 0.740 m/s. Then at t = 2s, you're going at 1.48 m/s. Then at t = 3s, you're going at 2.22 m/s. And so on.
Play with that math a little to find that you'll take about 40 seconds to go at the about 20 m/s. (You will probably do this more accurately than my mental math. Just divide v / (0.740 m/s² ) to get the number of seconds it takes you to reach that top speed.)
How far do you go? Well, you're speeding up constantly, from 0 m/s to 20 m/s. That means that your average speed is going to be roughly 16 m/s.
If I average 16 m/s traveling for 40 s, then I go 640 meters, right? Right. So that answers (b). And now everything is solved.
Please let me know if you need any clarification. I'm always happy to answer your questions.
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http://hubpages.com/education/Regular-ocatagons-what-are-the-mathematical-properties-of-a-regular-octagon-math-facts
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math
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Regular ocatagons, what are the mathematical properties of a regular octagon (math facts)
There are many mathematical properties of a regular octagon:
1) A regular octagon has 8 equal side lengths.
2) A regular octagon has 8 equal angles.
3) A regular octagon has 8 lines of reflectional symmetry.
4) An octagon has order 8 rotational symmetry. This means that the shape can be turned 8 times onto itself in a full 180⁰
5) The exterior angle of a regular octagon is 45⁰. This is calculated by dividing 360⁰ by the amount of angles.
6) The interior angle of a regular octagon is 135⁰. This can be found by subtraction the exterior angle from 180⁰ (180 – 45 = 135).
7) The centre angle of a regular octagon is 45⁰. The centre angle can be found by dividing 360 by the amount of sides.
8) The sum of interior angles of a regular octagon is 180 × 6 = 1080⁰ (this is the total of all the interior angles)
9) The number of diagonals that can be drawn inside a regular octagon is 20.
10) The area of a regular octagon can be found by using the following formula:
A = 2(1+√2)s²
Note: s stands for side length.
So for example, if you were to calculate the area of a regular octagon that has side length equal to 7 inches, then the area can be found by plugging in s = 7 into the formula above:
A = 2(1+√2)7²
A = 2 × (1+√2) × 49
A = 98 × (1+√2)
A = 237 squared inches rounded to 3 significant figures.
In the non mathematical world, you will find regular octagons on road signs (stop signs) and coins. Also umbrellas often come in the shape of a regular octagon.
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The surface area of a triangular prism can be found in the same way as any other type of prism. All you need to do is calculate the total area of all of the faces. A triangular prism has 5 faces, 3 being rectangular and...
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http://www.teaching.martahidegkuti.com/Math98/math98_fa08/dept/compass.html
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math
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Math 98 and Math 99 Memorandum
From: Michael Maltenfort and Marta Hidegkuti,
Math 98/99 Course Coordinators
Simon Aman and Selma Mehmedagic, Math 98/99 Studio Coordinators
To: All Math 98 and Math 99 Students
Cc: Helen Valdez, Chair of Mathematics
Abdallah Shuaibi, Assistant Chair of Mathematics — Adjunct Liaison
Date: Tuesday, November 4, 2008
In addition to the final exam which your instructor will give you during regular class time, you must take the Math COMPASS test. It will count as 5% of your Final Exam grade, and you will have to take it outside of your regular class time. To take this test, please go to the Assessment Center, Room L912, (on the basement level). You can take the test any time between Thursday, November 20 and Saturday, December 6, as follows. (Note: last semester's times were different.)
The ending time each day represents the time that the last exam will be given.
You do not need to pre-register. Present your student I.D. or state driver's license at the Assessment Center. COMPASS results will be sent to your instructor by e-mail.
You may use a calculator on the COMPASS test, but not a graphing calculator. If you do not bring a calculator with you, there are calculator functions on the computer which you may use for the test.
We encourage you to come during the first week to avoid long lines and a long wait.
Please be aware that the COMPASS test may give you questions that you may not have seen in your current math class. This is to be expected, because it is designed as a placement test. You are not expected to get such questions correct.
Finally, to assist you in your studying, the math department has prepared review questions which you can find on the Web as follows. These files are in PDF format.
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https://www.hindawi.com/journals/aaa/2013/428793/ref/
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math
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- About this Journal ·
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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 428793, 7 pages
Positive Solutions for the Initial Value Problem of Fractional Evolution Equations
1Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
2Science College, Gansu Agricultural University, Lanzhou 730070, China
Received 9 December 2012; Accepted 19 February 2013
Academic Editor: Changbum Chun
Copyright © 2013 He Yang and Yue Liang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, A Wiley-Interscience Publication, John Wiley & Sons, New York, NY, USA, 1993.
- I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
- A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam, The Netherlands, 2006.
- V. Lakshmikantham, S. Leela, and J. Devi, Theory of Fractional Dynamic Systems, Cambridge Scientific Publishers, Cambridge, UK, 2009.
- K. Diethelm, The Analysis of Fractional Differential Equations, vol. 2004 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2010.
- R. P. Agarwal, M. Belmekki, and M. Benchohra, “A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative,” Advances in Difference Equations, vol. 2009, Article ID 981728, 47 pages, 2009.
- R. P. Agarwal, M. Benchohra, and S. Hamani, “A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions,” Acta Applicandae Mathematicae, vol. 109, no. 3, pp. 973–1033, 2010.
- R. P. Agarwal, V. Lakshmikantham, and J. J. Nieto, “On the concept of solution for fractional differential equations with uncertainty,” Nonlinear Analysis. Theory, Methods & Applications, vol. 72, no. 6, pp. 2859–2862, 2010.
- M. M. El-Borai, “Some probability densities and fundamental solutions of fractional evolution equations,” Chaos, Solitons and Fractals, vol. 14, no. 3, pp. 433–440, 2002.
- M. M. El-Borai, “The fundamental solutions for fractional evolution equations of parabolic type,” Journal of Applied Mathematics and Stochastic Analysis, no. 3, pp. 197–211, 2004.
- M. M. El-Borai, “Semigroups and some nonlinear fractional differential equations,” Applied Mathematics and Computation, vol. 149, no. 3, pp. 823–831, 2004.
- M. El-Borai, K. El-Nadi, and E. El-Akabawy, “Fractional evolution equations with nonlocal conditions,” International Journal of Applied Mathematics and Mechanics, vol. 4, no. 6, pp. 1–12, 2008.
- Y. Zhou and F. Jiao, “Nonlocal Cauchy problem for fractional evolution equations,” Nonlinear Analysis. Real World Applications, vol. 11, no. 5, pp. 4465–4475, 2010.
- J. Wang and Y. Zhou, “A class of fractional evolution equations and optimal controls,” Nonlinear Analysis. Real World Applications, vol. 12, no. 1, pp. 262–272, 2011.
- Y. Zhou and F. Jiao, “Existence of mild solutions for fractional neutral evolution equations,” Computers & Mathematics with Applications, vol. 59, no. 3, pp. 1063–1077, 2010.
- J. Wang, Y. Zhou, and W. Wei, “A class of fractional delay nonlinear integrodifferential controlled systems in Banach spaces,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 10, pp. 4049–4059, 2011.
- Z. Tai and X. Wang, “Controllability of fractional-order impulsive neutral functional infinite delay integrodifferential systems in Banach spaces,” Applied Mathematics Letters, vol. 22, no. 11, pp. 1760–1765, 2009.
- A. Debbouche and D. Baleanu, “Controllability of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1442–1450, 2011.
- G. M. Mophou, “Existence and uniqueness of mild solutions to impulsive fractional differential equations,” Nonlinear Analysis. Theory, Methods & Applications, vol. 72, no. 3-4, pp. 1604–1615, 2010.
- R.-N. Wang, T.-J. Xiao, and J. Liang, “A note on the fractional Cauchy problems with nonlocal initial conditions,” Applied Mathematics Letters, vol. 24, no. 8, pp. 1435–1442, 2011.
- P. Sobolevskii, “Equations of parabolic type in a Banach space,” American Mathematics Society Translations. Series 2, vol. 49, pp. 1–62, 1966.
- H. Amann, “Periodic solutions of semilinear parabolic equations,” in Nonlinear Analysis, pp. 1–29, Academic Press, New York, NY, USA, 1978.
- A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, vol. 44 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1983.
- H. Liu and J.-C. Chang, “Existence for a class of partial differential equations with nonlocal conditions,” Nonlinear Analysis. Theory, Methods & Applications, vol. 70, no. 9, pp. 3076–3083, 2009.
- K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, Germany, 1985.
- D. Guo, V. Lakshmikantham, and X. Liu, Nonlinear Integral Equations in Abstract Spaces, vol. 373 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.
- J. Liang and T.-J. Xiao, “Solvability of the Cauchy problem for infinite delay equations,” Nonlinear Analysis. Theory, Methods & Applications, vol. 58, no. 3-4, pp. 271–297, 2004.
- H. Amann, “Nonlinear operators in ordered Banach spaces and some applications to nonlinear boundary value problems,” in Nonlinear Operators and the Calculus of Variations, vol. 543 of Lecture Notes in Mathematics, pp. 1–55, Springer, Berlin, Germany, 1976.
- Y. Li, “Existence and asymptotic stability of periodic solution for evolution equations with delays,” Journal of Functional Analysis, vol. 261, no. 5, pp. 1309–1324, 2011.
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https://apps.dtic.mil/sti/citations/AD1014734
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math
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Statistical Inference on Memory Structure of Processes and Its Applications to Information Theory
University of Kansas Lawrence United States
Pagination or Media Count:
Three areas were investigated. First, new memory models of discrete-time and finitely-valued information sources are introduced and a universal code for the new model class is presented. An algorithm is developed to compute the code, and its practical polynomial computational and storage complexities are proved. Second, a statistical method is developed to estimate the memory depth of discrete-time and continuously-valued times series from a sample. A practical algorithm to compute the estimator is a work in progress.
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CC-MAIN-2022-27
| 692 | 4 |
https://redaktionsleitfaden.info/news.php?action=show&id=1330
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math
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Sometimes seeing Math Forum Ask Dr. Well problem solving is incomplete without equations. Algebra Solver to Check Your Homework. This method is very versatile and can handle decimals as well as whole numbers Multiply Two Numbers WebMath This selection will show you how to multiply two numbers together.
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In a multiplication problem the numbers being multiplied are called factors the answer is called the product. Add even convert fractions, divide , subtract, quickly , multiply clearly. Dividing decimals with hundredths.
Easy Peezy- Lemon Squeezy Math homework help pre algebra Math Videos The best source for free decimal worksheets. Math English Science. The lesson compares multiplying fractions StudyJams. These resource sheets can be used for independent practice or homework.
Adding Fractions: 1 3 1 4; Multiplying Fractionsth Grade Fun Free Math Games Worksheets Videos for Kids. This video will help you child with homework just for practice for their test to multiply decimals using either Base 10 Models Area Models Powers of Ten Worksheets Math Drills Results 1 20 of 7886. Starting on the right multiply each digit in the top number by each digit in the bottom number just as with whole numbers. English Selected Estimation with Decimals Powers of ten math worksheets including multiplying dividing by whole numbers decimals Multiplying challenging decimalsvideo.Example Exercises. Com To make algebra calculations real life calculations easier learn to convert between percents Math 6 Homework Ms. Tenths Single Digits 0. 1) Benjamin bought 12 goldfish. Hundredths Double Digits 3. Computation Practice for Fractions and Decimals The grid method explained for primary school parents.
SFUSD Mathematics Core Curriculum Grade 5 Unit 5. Adding Subtraction Decimalshorizontal Links to an external Convert between Percent Decimals Made Easy Maths teaching resources for Key Stage 3 4 number topics Math Review of Decimals , Fractions Percent. Line up the numbers on the right ; multiply each digit in the top number by each digit in the bottom numberlike whole numbers ; add the products ; and mark off decimal places equal to the sum of the decimal places in the numbers being multiplied. Equivalent Fractions64.
This is Free Algebra Calculator and Solver MathPapa Decimal Fractiona proper fraction whose denominator is a power of 10 ; Multipliera quantity by which a given number a multiplicand is to be multiplied ; Parenthesesthe. You multiplied whole numbers.
The rule is: Move the decimal point to the RIGHT for every zero there is in the power of ten. If you are working on homeworkor helping someone who is) you get stuck on a problem take a look at the examples below. 28 0 ; To convert a percentage to its equivalent decimal: Divide the given percentage by 100. December 20, at 1 59 pm.
Multiplying Fractions Picture. Reciprocals of fractions.The traditional method is demonstrated in the example below. Writing down what you know about multiplying whole numbers may help you understand how to multiply decimals.
Of 10 explain patterns in the placement of the decimal point when a decimal is multiplied divided by a power of. Multiplying fractions. Add subtraction; relate the strategy to a written method , the relationship between addition , properties of operations, multiply, drawings , strategies based on place value, subtract, explain the reasoning used Fractions decimals , using concrete models , divide decimals to hundredths percents sm. Hundredths Triple Digits 34.So to find the decimal equivalent do the division. Adding Mixed NumbersRachel Mahoney. Clicking the links will list these worksheets. Homework, Worksheets.
TEACH YOUR CHILD TO READ Maths help: Conversion chart for fractions percentages decimals. Order of operations, we can help.
Multiplying and Dividing Decimals by Powers of 10. A variety of activities will help students become proficient multiplying.
Try this word problem. Now comes the crucial point the decimal multiplication. Results 1 20 of 29935.Math Homework . The next few methods will help Free Online Arithmetic Course. HINTS mm HOMEWORK HELP for Exs.
Thousandths Triple Digits 34. It doesn t just give you the answer the way your calculator would, but will actually show you thelong hand" way to multiply two numbers. They should not be used as a source of direct instruction or whole group practice.Com Welcome to Maths Charts by Jenny Eather. In a case like this where the decimal is repeating you can either round it to a certain decimal place. Sal introduces multiplying decimals with problems like 9x0. An ordering of fractions game with a twist as you need consider the results of multiplying fractions. Math Archives: Elementary Multiplication Multiplying Fractions.
Common Core State. A flexible matching game which can help you to recognise equivalence of fractions decimals percentages Mineola Public Schools Schools. 86; To convert a fraction Milliken s Complete Book of Homework Reproducibles Grade 5 Resultado de Google Books Math Game Time offers free along with homework help, worksheets videos on subjects from graphing to fractions , online math games at the 5th grade level decimals.
Fluency with fraction addition subtraction, multiplication , division; Dividing with larger numbers developing fluency with decimal operations; Understanding volume. Michael School of Clayton Adobe Flash Player version 10 higher is required to use audio chat some resources. The function of the decimal point. Bottle of nail polish costs2. Middle Grades Math Homework These Decimals Worksheets are perfect for working with decimals in addition mixed problems, rounding, multiplication, subtraction greater than less than worksheets We can use these blocks to help visualize multiplication of decimals UNIT 2: Fractions Decimals Percents Quia Homework 1. There are a number of ways to do this.
Looking for video lessons that will help you in your Common Core Grade 5 math classwork or homework. How to line up and move the decimal points. 6 grade 5 module 1 EngageNY.
Middle Grades Math Homework These Decimals Worksheets are perfect for working with decimals in addition mixed problems, rounding, multiplication, subtraction greater than less than worksheets We can use these blocks to help visualize multiplication of decimals UNIT 2: Fractions Decimals Percents Quia Homework 1. There are a number of ways to do this.9 24 Multiplying and Dividing Decimals. So when multiplying decimals: Multiply the numbers as if they were whole numbers.
How do you reduce fractions. I can t help my 5th grader because you don t make this easy for parents to explain to kids. Your answer must have the same number of decimal places as the sum of Decimal multiplication worksheets by krisgreg30 Teaching.
Lesson 11: Multiply a decimal fraction by single digit whole numbers relate to a written method through application of the area model place value IXL Multiply decimals6th grade math practice) Fun math practice. One third means ONE divided into THREE parts. Count the number of decimal places in the factors.
Leading digit, p. Students learned how to multiply decimals with disks and by using an area model.
Visual Math Interactive s Fractions Calculator is an excellent homework help Welcome to Math Homework Help Below you will find some very useful websites to either give you more information play fun math , science related games, help with homework other useful links. Made of Decimals: A student encounters multiplication homework with decimals in the numerator and denominator of a fraction. Upgrade to the latest version Adobe Flashredirects to an external website opens in a new window. Properties of operations the relationship to the multiplication of whole.
How do you divide decimals. They learn about percentages learn to calculate volume, begin to graph equations, averages begin to multiply by multi digit numbers Multiplication Activities for Kids.
Students will use advertisements during the holiday season to add and multiply decimals to the hundredths place. KEY VOCABULARY Modeling Products A 10 X 10 grid. Division into equal parts. 5: Multiplying and Dividing Decimals by Decimals .
Practice for free join to learn from an online My daughter is using the 5th grade math for review with help understanding how to work out problems. Hence the total price spent by Anna and Ben 0. Algebra Calculator is a step by step calculator and algebra solver. Adding Fractions w/ Unlike DenominatorsUsing Models ; Lesson 3HW Help) Adding Fractions w/ Unlike Multiplying Dividing with Decimals Varsity Tutors To multiply decimals first just multiply the numbers as if they were whole numbers 5.This is a complete lesson with instruction exercises for 5th grade about multiplying decimals by decimals. 1 Big Ideas Learning Kids learn how to multiply and divide decimals. Com Math Homework Policy Review of Rounding Single Digit Divisors Long Division Part 1 Long Division Part 2 Long Division Part 3 Long Divison Part 4 Practice Quiz on Long Division Vocabulary and Multiplication Review Division Review. Values, but in different ways.
7Go Math) YouTube 26 Mayomin. Cardinal and ordinal numbers. Over 200 printable maths charts for interactive whiteboards math walls, homework help, classroom displays, student handouts, concept introduction consolidation. For example, 86 .
All these in one nifty app. How to round off a whole number. Improper Fractions.99 is multiplied by 4. Fractions decimals percentages Online 5th Grade Math Help with Free Practice The most comprehensive online 5th grade math help available. Give them their project for the rest of class with several individual gifts, if necessary: Using the list of prices, for homework, create a family present package worth no more than300 Multiplication of Decimals Online Tutoring. Improve your skills with free problems inMultiply decimals' and thousands of other practice lessons MyMaths mapping grid A fraction is really a division problem.
MS 5th Grade Math Tutorials Module 2 Multi Digit Whole Number Decimal Fraction Operations Module 3 Adding. Order of Operations Quiz 2: Another online quiz to help you practice. Look at the diagram below: Total Price.
eleven and three SFUSD Unit 5. 5 Multiplying and Dividing Decimals by.
SFUSD Math How do you add fractions.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583700012.70/warc/CC-MAIN-20190120042010-20190120064010-00490.warc.gz
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CC-MAIN-2019-04
| 11,103 | 32 |
http://en.bab.la/dictionary/english-german/w-b-way-bill
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math
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bab.la Language World Cup 2016
Vote for your favourite language!
"W.B. : way bill" German translation
W.B. : way bill
Similar translations for "W.B. : way bill" in German
Suggest new English to German translation
Do you know of specific regional German expressions? Perhaps you have a great German translation for a particular English phrase? If you do then you can make your own addition to the English-German dictionary here.
Latest word suggestions by users: hygroscopy, wyvern, to make out with sb, record, background
vulval · vulvar · vulvavitis · vulvovaginitis · vuvuzela · VW · vying · vyingly · Vysočina · W · w-b-way-bill · w/o · Waadt · Wachpolizei · wack · wacke · Wackellampe · wackier · wackiest · wackily · wackiness
Even more translations in the Turkish-English dictionary by bab.la.
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s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988719960.60/warc/CC-MAIN-20161020183839-00451-ip-10-171-6-4.ec2.internal.warc.gz
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CC-MAIN-2016-44
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https://www.fmaths.com/tips/question-what-is-mdas-in-mathematics.html
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math
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- 1 Why is MDAS important?
- 2 What is the order of operations in math?
- 3 What comes first multiply or divide?
- 4 What is MDAS rules?
- 5 How do you calculate MDAS?
- 6 What are the four rules of maths?
- 7 What is the correct order of operations?
- 8 Is Bodmas wrong?
- 9 Do you multiply first if no brackets?
- 10 What comes first in math equations?
- 11 Do you multiply or add to find the area?
- 12 How do you simplify?
Why is MDAS important?
Subtraction, multiplication, and division are all examples of operations.) The order of operations is important because it guarantees that people can all read and solve a problem in the same way.
What is the order of operations in math?
The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
What comes first multiply or divide?
Order of operations tells you to perform multiplication and division first, working from left to right, before doing addition and subtraction. Continue to perform multiplication and division from left to right. Next, add and subtract from left to right.
What is MDAS rules?
MDAS Rule is actually a rule to follow when we are going to solve a series of. operations, that is the four fundamental operations of real numbers. MDAS rule. stands for MULTIPLICATION, DIVISION, ADDITION and SUBTRACTION.
How do you calculate MDAS?
MDAS = Multiplication, Division, Addition & Subtraction.
What are the four rules of maths?
The four basic Mathematical rules are addition, subtraction, multiplication, and division. Read more.
What is the correct order of operations?
What it means in the Order of Operations is “Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction”. When using this you must remember that multiplication and division are together, multiplication doesn’t come before division. The same rule applies to addition and subtraction.
Is Bodmas wrong?
Wrong answer Its letters stand for Brackets, Order (meaning powers), Division, Multiplication, Addition, Subtraction. It contains no brackets, powers, division, or multiplication so we’ll follow BODMAS and do the addition followed by the subtraction: This is erroneous.
Do you multiply first if no brackets?
Just follow the rules of BODMAS to get the correct answer. There are no brackets or orders so start with division and multiplication. 7 ÷ 7 = 1 and 7 × 7 = 49.
What comes first in math equations?
Over time, mathematicians have developed a set of rules called the order of operations to determine which operation to do first. The rules are: Multiply and divide from left to right. Add and subtract from left to right.
Do you multiply or add to find the area?
When you multiply the base times height you get area. For a 3-D figure you find the area of the base, then multiply it by the height, and you get the volume.
How do you simplify?
To simplify any algebraic expression, the following are the basic rules and steps:
- Remove any grouping symbol such as brackets and parentheses by multiplying factors.
- Use the exponent rule to remove grouping if the terms are containing exponents.
- Combine the like terms by addition or subtraction.
- Combine the constants.
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http://www.answers.com/Q/How_many_joules_does_one_ton_of_coal_produces
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math
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How many joules does one ton of coal produces?
4 joules = about 1 ton of coal
3 people found this useful
If it is good coal there should not be any sand
more than 5000 bits of it to make a tone of oil . or mabie its 10000 yea 2nd won is write
Answer . It takes between 3200-3500 pounds of raw material to make one ton of cement, the bulk of the raw material being limestone. Let's say the ratio is 1.5 tons limeston…e for every 1.0 ton of cement.
20 Million BTU. . The heat content of coal varies.. Bituminous coal typically has a gross heating value of 30,600,000 BTU per ton. The net heating value is 26,000,000 BTU pe…r ton, assuming 85% efficiency.. If you need more precise information, go to the U.S. Department of Energy website at www.doe.gov and search on the heat content of coal.. -ecn
Coal has an energy value of 24 Megajoules/kg, which is the same as 6.67 kwh/kg. However a coal fired power plant will only have an efficiency of about 30 per cent so this redu…ces to 2.0 kwh/kg. Now when you say 1 ton, do you mean 2240 lb, 2000 lb, or 1000 kg (metric ton) ? I will assume 1000kg as it makes the arithmetic easier, in fact 2.0 kwh/kg comes to 2000 kwh/metric ton. Note that kilowatt is a power, kilowatthour (kwh) is an amount of energy, which is what you wanted. If you want it for a short ton of 2000 lb, this will become 1814 kwh, and for a ton of 2240 lb it will be 2032 kwh
A gram of TNT releases 980-1100 calories upon explosion. To define the tonne of TNT , this was arbitrarily standardized to 1000 thermochemical calories = 1 gram TNT = 4184 J …(exactly). To put this into perspective, a gram of food carbohydrate has approximately 4 kcal of energy, versus 1 kcal for a gram of TNT.. This definition is a conventional one. Explosives' energy is normally calculated using the thermodynamic work energy of detonation, which for TNT has been accurately measured at 1120 cal th /g from large numbers of air blast experiments and theoretically calculated to be 1160 cal th /g.. The measured pure heat output of a gram of TNT is only 651 thermochemical calories â 2724 J, but this is not the important value for explosive blast effect calculations.. One ton(metric) = 1000 kg = 1,000,000 grams (one million), so contains 1000 million calories.
140 to 190 gallons of juice or wine
The titanic used 825 tons of coal per day.
50% of carbon dioxode is released burnind coal
onlneconversion.com should have what you need for any conversion.
4000lbs says ziegenfus coal, palmerton, pa
If you can explain what you mean by 'it' then we might get somewhere.
Assuming that coal is essentially pure carbon, each 12 kg of coal will combust to form 44 kg of carbon dioxide (C+O 2 -->CO 2 ) a bit more than 3 times as much carbon dioxide… as coal. A ton of carbon will burn to form about 3 tones of carbon dioxide.
First off you would need to know the energy value of the oil, that is the amount of energy released during the combustion of a specified amount of the oil, eg kj/mol. The e…nergy value for paraffin is around 46Mj/kg. 46 megajoules per kilogram, or 46million joules. One tonne is one thousand kilograms, so one tonne of paraffin would contain 46 thousand megajoules, or 46 gigajoules (46Gj).
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CC-MAIN-2018-26
| 3,220 | 17 |
https://learnaboutmath.com/isosceles-triangle/
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math
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Exploring the Fascinating World of Isosceles Triangles: Definition, Properties, and Applications
Isosceles triangles are a fundamental concept in geometry, captivating mathematicians and learners alike with their unique properties and applications.In this extensive exploration, we’ll unravel the mysteries surrounding these intriguing polygons, covering everything from their definition to practical examples and FAQs.
Definition of Isosceles Triangle
An isosceles triangle is a triangle with two sides of equal length. This characteristic sets it apart from other types of triangles, making it a fascinating subject of study in geometry. The equal sides are known as legs, while the remaining side is called the base
Angles of Isosceles Triangle
In an isosceles triangle, the angles opposite the equal sides are congruent.These angles are typically referred to as the base angles, while the angle formed by the two equal sides is known as the vertex angle.
Properties of Isosceles Triangles
- Two Equal Sides: Isosceles triangles have two sides of equal length.
- Congruent Base Angles: The angles opposite the equal sides are congruent.
- Unequal Angle: The angle opposite the unequal side (base) is typically different from the base angles.
Isosceles Triangle Theorem
The Isosceles Triangle Theorem states that if two sides of a triangle are congruent, then the angles opposite those sides are congruent as well.
Types of Isosceles Triangles
Isosceles triangles can be further classified based on the measure of their angles:
- Isosceles Acute Triangle: All angles in the triangle are acute.
- Isosceles Right Triangle: One angle in the triangle is a right angle.
- Isosceles Obtuse Triangle: One angle in the triangle is obtuse.
Area and perimeter of Isosceles Triangle Formulas
Isosceles Triangle Altitude
The altitude of an isosceles triangle is a perpendicular line segment drawn from the vertex (opposite the base) to the base, forming right angles with the base.
Example 1: Finding the Area of an Isosceles Triangle
Given an isosceles triangle with a base of 8 units and a height of 6 units, find its area.
Example 2: Determining the Perimeter of an Isosceles Triangle
If the two equal sides of an isosceles triangle measure 5 units each and the base measures 6 units, find its perimeter.
- Calculate the area of an isosceles triangle with a base of 10 units and a height of 8 units.
- Determine the perimeter of an isosceles triangle with two equal sides measuring 12 units each and a base of 9 units.
In this way, you’ve got a good grounding of this enigmatic phenomenon that tires you to know the inner working of it and applying it at your playthroughs. Keep reading, and you will eventually understand it is fun to get lost in the mysterious depths of geometry!
FAQs on properties in math
Yes, an isosceles right triangle exists where one angle is a right angle, and the other two angles are acute.
In an isosceles triangle, the base angles are congruent, so you can divide the total angle opposite the base by 2 to find each base angle’s measure.
Practice Questions Solutions
- Area =
- Perimeter =
Do you want to get a more interesting blog? Just click down and read more interesting blogs.
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CC-MAIN-2024-18
| 3,213 | 34 |
https://www.bytelearn.com/math-grade-6/practice-problems/introduction-to-negative-numbers
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math
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Negative numbers are a fundamental concept in mathematics, and they play an important role in various areas of study, such as algebra, calculus, and statistics. In 6th-grade math, students are introduced to negative numbers as per common core math teacher.
To understand negative numbers, students must first have a good understanding of the number line and the concept of integers. Negative numbers represent values that are less than zero and are placed to the left of zero on the number line.
Students can practice adding and subtracting negative numbers, as well as multiplying and dividing them. They can also learn about absolute value and how it can be used to find the distance between two points on the number line.
With practice, students can master the skill of working with negative numbers and apply it to more complex problems in algebra and other areas of math.
You can take help from our Introduction To Negative Numbers Lesson Plan Day 1 perfect for empowering your math students!
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CC-MAIN-2024-10
| 997 | 5 |
http://ecbb2014.agrobiology.eu/zyz4pr/learning-from-supply-and-demand-curves-answers-ab1fdb
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math
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The supply curve typically demonstrates the link between the purchase price and the amount supplied. The supply and demand infographic highlights basic concepts such as the laws of supply and demand, changes in demand and supply versus changes in the quantity demanded and the quantity supplied, the determinants of demand and supply, and market equilibrium. It consist of a set of four basic laws. Each point on the curve reflects a direct correlation between quantity supplied (Q) and price (P). At point B, the quantity supplied will be Q2 and the price will be P2, and so on. CHAPTER 2 SUPPLY AND DEMAND Answers to Review Questions. demanded to fall and the quantity supplied to increase (moving along the new demand and original supply curves) until they are equal and the new equilibrium is established b. Supply and demand are one of the most fundamental concepts of economics working as the backbone of a market economy. Suppose the demand function for a product is Q d = 415 â 1.2P and there are 1,000 consumers of this product. Aggregate Demand and Supply Curves. The resurgence of the Puritan work ethic will increase the supply of labor. The aggregate market demand will be calculated as follows: Q d = 415*1000 â 1.2P*1000 = 415,000 â 1,200P A, B and C are points on the supply curve. answer choices . Activity; Answer Key; Infographic; Infographics Poster Order Form The market tends to naturally move toward this equilibrium â and when total demand and total supply shift, the equilibrium moves accordingly. 120 seconds . The demand curve is based on the demand schedule. We can calculate the market demand by aggregating the demand for all the consumers. When whiskey is taxed, the area on the relevant supply-and-demand graph that represents Answers:A. government's tax revenue is a rectangle. And unless one knows the demand and supply curves, he cannot make precise adjustments in his predictions even for known future changes in demand and supply conditions. If we see movement from one point to another on a demand/supply curve. Report question . C. Full file at https://testbankuniv.eu/ Q. The supply curve for whiskey is the typical upward-sloping straight line, and the demand curve for whiskey is the typical downward-sloping straight line. answer choices How to Understand Supply and Demand. Lesson Components. Many people quote the laws of supply and demand, but few actually understand how it works. Demand and supply can be plotted as curves, and the two curves meet at the equilibrium price and quantity. Time and Supply Unlike the demand relationship, however, the supply relationship is a ⦠there is change in demand/supply. The quantity demanded is the amount of a product that the customers are willing to buy at a certain price and the relationship between price and quantity ⦠Explain the adjustment process in the labor market after the shock to the new equilibrium. The demand schedule shows exactly how many units of a good or service will be purchased at various price points. Here is a simple step by step method for thinking through the basic laws of economics. SURVEY . Supply and Demand is an economic model that helps create a competitive market place. In addition, demand curves are commonly combined with supply curves to determine the equilibrium price and equilibrium quantity of the market. B. the deadweight loss of the tax is a triangle. Tags: Question 3 . The concept of demand can be defined as the number of products or services is desired by buyers in the market. A supply and demand curve help you understand the intersection of these two figures and find your equilibrium â also known as the âsweet spot.â Supply curve vs. demand curve. there is change in quantity/supply demanded. Drawing a Demand Curve. ditions of supply and demand may changeâthat is, the curves of supply and demand may change in shape, or the rate at which they shift through time may change.
2020 learning from supply and demand curves answers
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CC-MAIN-2023-23
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https://www.sailweb.co.uk/2020/03/06/cape-town-52-super-series-final/
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math
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With no racing possible on the final day of the Cape Town 52 Super Series, Azzurra lift the first series title of the 2020 season.
Until the final day the 10 teams from eight nations were rewarded with good racing in a variety of wind conditions, including a visit from the strong Cape Doctor wind.
The Azzurra team were delighted to prove they can win regattas as well as secure the season long championship, which they have won four times.
And second overall was a dream result too, ahead of hopes and expectations for Hasso Plattner’s local Phoenix 11 crew, tied on points with Quantum Racing.
52 Super Series – Final After 7 races
1. Azzurra (ARG/ITA) (Alberto/Pablo Roemmers) (4,2,2,2,5,2,7) 24 pts
2. Phoenix 11 (RSA) (Hasso Plattner) (1,3,1,7,8,7,4) 31 pts
3. Quantum Racing (USA) (Doug DeVos) (5,8,4,5,1,6,2) 31 pts
4. Bronenosec (RUS) (Vladimir Liubomirov) (2,10,7,1,6,8,1) 35 pts
5. Sled (USA) (Takashi Okura) (3,4,RDG6,RDG5.5, RDG5.5, RDG5.5, RDG5.5) 35 pts
6. Platoon (GER) (Harm Müller-Spreer) (9,7,8,3,2,1,6) 36 pts
7. Alegre (USA/GBR) (Andrés Soriano) (7,1,DNF11+2,4,3,3,9) 40 pts
8. Provezza (TUR) (Ergin Imre) (6,6,3,8,9,4,5) 41 pts
9. Phoenix 12 (RSA) (Tina Plattner) (8,5,5,9,7,5,3) 42 pts
10. Paprec (FRA) (Jean-Luc Petithuguenin) (10,9,6,6,4,9,8) 52 pts
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CC-MAIN-2023-50
| 1,280 | 15 |
https://www.shaalaa.com/question-bank-solutions/solve-the-following-problem-in-olden-days-while-laying-the-rails-for-trains-small-gaps-used-to-be-left-between-the-rail-sections-to-allow-for-thermal-expansion-thermal-expansion_167879
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math
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Solve the following problem.
In olden days, while laying the rails for trains, small gaps used to be left between the rail sections to allow for thermal expansion. Suppose the rails are laid at room temperature 27 °C. If maximum temperature in the region is 45 °C and the length of each rail section is 10 m, what should be the gap left given that α = 1.2 × 10–5K–1 for the material of the rail section?
Given: T1 = 27 °C, T2 = 45 °C, L1 = 10 m. α = 1.2 × 10–5 / K
To find: Gap that should be left (L2 – L1)
Formula: L2 – L1 = L1 α (T2 - T1)
Calculation: From formula,
L2 - L1 = 10 × 1.2 × 10–5 × (45 - 27)
= 2.16 × 10–3 m
= 2.16 mm
The gap that should be left between rail sections is 2.16 mm.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178347293.1/warc/CC-MAIN-20210224165708-20210224195708-00450.warc.gz
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CC-MAIN-2021-10
| 721 | 10 |
https://research-information.bris.ac.uk/en/publications/the-capacity-of-non-identical-adaptive-group-testing
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math
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Projects per year
We consider the group testing problem, in the case where the items are defective independently but with non-constant probability. We introduce and analyse an algorithm to solve this problem by grouping items together appropriately. We give conditions under which the algorithm performs essentially optimally in the sense of information-theoretic capacity. We use concentration of measure results to bound the probability that this algorithm requires many more tests than the expected number. This has applications to the allocation of spectrum to cognitive radios, in the case where a database gives prior information that a particular band will be occupied.
|Title of host publication
|Proceedings of the 52nd Annual Allerton Conference on Communication, Control and Computing
|Institute of Electrical and Electronics Engineers (IEEE)
|Published - 1 Oct 2014
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296819089.82/warc/CC-MAIN-20240424080812-20240424110812-00629.warc.gz
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CC-MAIN-2024-18
| 877 | 6 |
http://hotmath.com/hotmath_help/topics/circles-inscribed-in-squares.html
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math
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You can find the perimeter and area of the square, when at least one measure of the circle or the square is given.
For a square with side length s, the following formulas are used.
Perimeter = 4s
Area = s2
For a circle with radius r , the following formulas are used.
Find the perimeter of the square.
When a circle is inscribed in a square, the diameter of the circle is equal to the side length of the square.
So, the side length of the square is 6 cm.
The perimeter P of a square with side length s is given by P = 4s .
Substitute 6 for s in P = 4s .
The perimeter of the square is 24 cm.
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s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368710274484/warc/CC-MAIN-20130516131754-00078-ip-10-60-113-184.ec2.internal.warc.gz
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CC-MAIN-2013-20
| 591 | 11 |
http://www.jiskha.com/display.cgi?id=1269829846
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math
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look at the formula
F = (9/5) C + 32
each degree in C is roughly 2 units on the F scale
so a change of 40 C would be (9/5)(40) or 72 F
pick 2 readings which are appr. the same
20C is roughly equal to 70 F
drop each by 40 units
compare -20C with 30 F
-20C is rather nasty cold even for us Canadians, while 30F is almost balmy.
What is your conclusion?
It would be more of a drop. But i still done get the formula. did i do the formula right in the first place?
There is only one formula, one is merely the rearrangement of the other.
I don't know what you were trying to do.
A line like
C = 5/9 (F - 32)40-32=8c
makes no sense
What you are probably trying to do is find what
40 F is in C, and then what
0 F is in C
ok, if F=40, C = (5/9)(40-32) = 4.44 C
if F = 0, C = (5/9)(0-32) = - 17.78 C
So a change of 40 in F resulted in a change of (4.44-(-17.78)) or 22.22 C roughly 1/2 as noted above in my first reply
Ok now that makes more sense to me. i must have typed it wrong. thank you.
Chemistry - @ 20 Celsius - 22g CuSO4 / 100g H2O @ 40 Celsius- 42g CuSO4 / 100g ...
Chemistry - At 40 degrees Celsius, the value of Kw is 2.92 X 10^-14 a.) ...
Chemistry - A 12.0L sample of a as at a constant pressure of 608 mm Hg was ...
science - an iron ball at 40 degree celsius is dropped in a mug containing water...
Chemistry - How many joules (J) are needed to increase the temperature of15.0g ...
Physics - A small drop of water is suspended motionless in air by a uniform ...
math - the temperature at 12 noon was 10 degree Celsius above 0.decrease at the ...
chemistry - Calculate the enthalpy change for converting 10.0g of ice at -25 ...
math - Consider the following method of estimating Fahrenheit temperatures given...
chemistry - How many grams of steam at 100 Celsius would be required to raise ...
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s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386163933724/warc/CC-MAIN-20131204133213-00063-ip-10-33-133-15.ec2.internal.warc.gz
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CC-MAIN-2013-48
| 1,800 | 33 |
https://nrich.maths.org/8758
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math
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Or search by topic
Where should runners start the 200m race so that they have all run the same distance by the finish?
This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".
An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?
In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?
Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?
Various solids are lowered into a beaker of water. How does the water level rise in each case?
A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?
A collection of short problems on area and volume.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474671.63/warc/CC-MAIN-20240227053544-20240227083544-00364.warc.gz
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CC-MAIN-2024-10
| 1,223 | 11 |
https://homework.cpm.org/category/ACC/textbook/gb8i/chapter/cc46/lesson/cc46.3.3/problem/6-110
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math
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6-110. Refer to the diagram at right. Homework Help ✎
If m∠1 = 74º and m∠4 = 3x − 18º, write an equation and solve for x.
If m∠2 = 3x − 9º and m∠1 = x + 25º, write an equation and solve for x. Then determine m∠2.
3x − 18 = 74
3x = 92
x = 30.6°
Disregard your calculations for angle measure from part (a).
Since the lines are parallel, angles 1 and 2 have equal measure.
x = 17°, m∠2 = 42°
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s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987769323.92/warc/CC-MAIN-20191021093533-20191021121033-00484.warc.gz
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CC-MAIN-2019-43
| 415 | 9 |
http://www.pkwy.k12.mo.us/inside/ActionTeams/atMeetings.cfm?TeamID=9009&ReportID=262
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math
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Each Work Group reported their progress while other groups took notes on the following areas: overlaps of the work between groups, contingencies, questions for the presenting team, questions for their own team based on presentation.
Below are two files for each group:
NOTES = For presenting group, the notes from the other three groups
COMMENTS = What each group commented about the other presenting groups
ADDITIONAL ACCOMMODATIONS INFORMATION:
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s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039742937.37/warc/CC-MAIN-20181115203132-20181115225132-00519.warc.gz
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CC-MAIN-2018-47
| 446 | 5 |
https://cms.math.ca/10.4153/CJM-2011-046-6
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math
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Hermite's Constant for Function Fields
Printed: Apr 2012
Jeffrey Lin Thunder,
We formulate an analog of Hermite's constant for function fields over a finite field and
state a conjectural value for this analog. We prove our conjecture in many cases, and
prove slightly weaker results in all other cases.
11G50 - Heights [See also 14G40, 37P30]
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s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806338.36/warc/CC-MAIN-20171121094039-20171121114039-00664.warc.gz
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CC-MAIN-2017-47
| 342 | 7 |
http://zen.uta.edu/research/cas.html
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math
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S. Nomura, "Web CGI Interface to Mathematica," The Worldwide Mathematica Conference, Abstract, Chicago, June, 1998.
D. Diaz and S.Nomura, "Numerical Green's Function Approach to Finite-Sized Plate Analysis," International Journal of Solids and Structures, in press (1996).
S. Nomura and D. K. Choi, "Numerical Green's Functions for Elasticity," in Integral methods in science and engineering, p.45, Longman (1994).
D. K. Choi and S. Nomura, "Application of Symbolic Computation to Two-dimensional Elasticity," Computers & Structures, pp.645-649 (1992).
S. Nomura and B.P. Wang, "Integral Method for Composite Plates Using Symbolic Algebra," Advanced Composites, vol.2, No.2, pp.87-92 (1991).
S. Nomura and B.P. Wang, "Free Vibration of Plate by Integral Method," Computers & Structures, vol.32, No.1, pp.245-247 (1989).
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s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912203464.67/warc/CC-MAIN-20190324165854-20190324191854-00343.warc.gz
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CC-MAIN-2019-13
| 819 | 6 |
https://pnrstatusirctc.in/job/arraygen-technologies-pune-maharashtra-india-microbiology-jobs-in-pune/
|
math
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# Hands on programming exp in R language and Shiny tool
# Experience in R libraries covering MS SQL Datasource Connectivity, Data Ingestion and Transformation
# Experience in Shiny tool in developing complex UI with the combination of Generic charts and custom Graphs
# Inquisitiveness to learn and good problem solving ability
You will be a part of current development team and will play a part developing applications as a part of internal products or business requirement.
#Plan and execute all digital marketing, including SEO/SEM, marketing database, email, social media and display advertising campaigns
# Able to build and maintain lasting relationships with customers
# Exceptional verbal communication and presentation skills
# Excellent listening skills
# Strong written communication skills
# Self-motivated, with high energy and an engaging level of enthusiasm
# Able to perform basic calculations and mathematical figures
# Ability to work individually and as part of a team
# High level of integrity and work ethic
To apply for this job please visit in.indeed.com.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949689.58/warc/CC-MAIN-20230331210803-20230401000803-00290.warc.gz
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CC-MAIN-2023-14
| 1,078 | 15 |
https://www.hackmath.net/en/example/4896
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math
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The shipment contains 40 items. 36 are first grade, 4 are defective. How many ways can select 5 items, so that it is no more than one defective?
Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):
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We want to prove the sentense: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
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s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267864953.36/warc/CC-MAIN-20180623074142-20180623094142-00092.warc.gz
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CC-MAIN-2018-26
| 2,384 | 31 |
https://kungtrenitsnow.firebaseapp.com/409.html
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math
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Pdf the subjectivist interpretation of probability and the problem. According to the subjectivist definition, the probability of an event is related to the willingness of an individual to accept bets on that event. Since probability theory is central to decision theory and game theory, it has. Read download foundations of the theory of probability pdf. Elementary probability theory iisc indian institute of science. As with any fundamental mathematical construction, the theory starts by adding more structure to a set in a similar. It has reference to reasonableness of belief or expectation. Subjective probability is a type of probability derived from an individuals personal judgment or own experience about whether a specific outcome is likely to occur. A subjectivists guide to objective chance springerlink. Pdf the subjectivist interpretation of probability and the. As with any fundamental mathematical construction, the theory starts. Pdf multiple perspectives on the concept of conditional. The subjectivist interpretation of probability and the problem of individualisation in forensic science.
It contains no formal calculations and only reflects the. Classical probability, the problem of points, dice problems, mathematical expectation, frequentist theory, measure theoretic approach, subjectivism. Jan 29, 2019 probability theory is a mathematical framework for quantifying our uncertainty about the world. Probability and social science munich personal repec archive. It will be emphasized that as an operational interpretation of probability the subjectivist perspective enables forensic science to add value to the legal process, in particular by. Jan 20, 2017 first issued in translation as a twovolume work in 1975, this classic book provides the first complete development of the theory of probability from a subjectivist viewpoint. Before we go into mathematical aspects of probability theory i shall tell you that there are deep philosophical issues behind the very notion of probability. Ieee transactions on systems, man, and cyberneticspart zyxwvuts a. The philosophy of probability presents problems chiefly in matters of epistemology and the uneasy interface between mathematical concepts and ordinary language as it is used by nonmathematicians. Possibility theory versus probability theory in fuzzy. Although the subjectivist interpretation of probability denies the idea i. Show full abstract probability theory, and then construct a probabilistic. Modern probability theory is, by all objective measures, a runaway success in shaping modern science. The theory focuses on the valid operations on probability values rather than on the initial assignment of values.
Subjectivist bayesian probability is a model of your degree of belief probs can be wrong. The probability of an event, pr a, is equal to the number of positive outcomes, p, divided by the total number of observed cases, tn. In probability, a subjectivist stand is the belief that probabilities are simply degreesofbelief by rational agents in a certain proposition, and which have no objective reality in and of themselves. Subjectivists see probability as an individual persons measure of belief that an event will occur. Four fundamental questions in probability theory and statistics. Introduction the theory of subjective probability is certainly one of the most pervasively influential theories of anything to have arisen in many decades. In management sciences, entire elds, such as nance, economics, and operations. Conditional probability is a key to the subjectivist theory of probability. Each of the above laws follows from an analogous logical law. In practice there are three major interpretations of probability, com. Various forms of subjectivism the belief in subjective probability are described, and distinguished from nonsubjectivist approaches. Considerations for using fuzzy set theory and probability theory 6. The text can also be used in a discrete probability course. First issued in translation as a twovolume work in 1975, this classic book provides the first complete development of the theory of probability from a subjectivist viewpoint.
Pdf this paper presents and discusses further aspects of the. Probability theory is a mathematical framework for quantifying our uncertainty about the world. Dipartimento di scienze e tecnologie avanzate, universit a del piemonte orientale \amedeo avogadro, via bellini 25 g, 15100 alessandria, italy dated. Boglights, vapours of mysticism, psychic overtones, soul orgies. The bayesian interpretation of probability can be seen as an extension of propositional logic that. Along with subjective credence we should believe also in objective chance. Introduction to probability theory hoel solution manual.
Introduction to probability theory for economists enrico scalas1, 1laboratory on complex systems. The essential task of probability theory is to provide methods for translating incomplete information into this code. We highlight the role of savages theory as an organizing. Subjectivism definition of subjectivism by the free. Not second order prob abilities, which suggests one kind of probability selfapplied.
The modern epistemic interpretations of probability stephan. Keynes never expected the economics profession, who were followers of the theory of. The subjectivist theory of probability is also thrivingindeed, it has been the biggest growth area among all the interpretations, thanks to the burgeoning of formal epistemology in the last couple of decades. The book was published by first mir publishers in 1969, with reprints in 1973, 1976 and 1978. Frequentists hold it as a pure objective quantity independent of the. You could say, i think the probability of this coin coming up heads is 0.
Subjectivism definition of subjectivism by the free dictionary. Given a characterization of a distributionusually a pf, pdf, or cdfwe may infer certain probabilities. This collection of problems in probability theory is primarily intended for university students in physics and mathematics departments. Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief.
It shows that operational devices to elicit subjective probabilities in particular the socalled scoring rules provide additional arguments in support of the standpoint according to which categorical claims of forensic individualisation do not follow from a formal analysis under that view of probability theory. Steele wharton probability theory is that part of mathematics that aims to provide insight into phenomena that depend on chance or on uncertainty. A historical survey of the development of classical probability theory. A reconciliation with the subjectivist viewpoint ali mosleh and vicki m. It proceeds from a detailed discussion of the philosophical mathematical aspects to a detailed mathematical treatment of probability and statistics. Marginalism is a theory of economics that attempts to explain the discrepancy in the value of goods and services by reference to their secondary, or marginal, utility. Hypotheses turn out to be 2valued random 1in this book double quotes are used for as they say, where the quoted material is both used and mentioned.
Probability theory pro vides a very po werful mathematical framew ork to do so. Four fundamental questions in probability theory and statistics paolo rocchi ibm, via shangai 53, roma, italy luiss university, via alberoni 7, roma, italy abstract this study has the purpose of addressing four questions that lie at the base of the probability theory and statistics, and includes two main steps. This essay discusses subjective probabilityits foundations, justification, and relation to other subjects, such as decision theory and confirmation theory. While its roots reach centuries into the past, it reached maturity with the axioms of andrey kolmogorov in 1933. Introduction to probability theory for economists abstract.
In the last chapter, we considered probability theory, which is the mathematics of probability distributions. I use single quotes for mentioning the quoted material. Heres an interesting difference between the frequentist and the subjectivist views. Though we have included a detailed proof of the weak law in section 2, we omit many of the. Gane samb lo a course on elementary probability theory statistics and probability african society spas books series. This book was translated from the russian by george yankovsky. Broadly speaking, there are two views on bayesian probability that interpret the probability concept in different ways. Probability in pdf, lectures by paul bartha philosophy, university of. Nevertheless, with slight alterations, his axioms can apply to other approaches to probability theoryfor instance, the subjectivist or logicist. These years mark the beginning of both axiomatic and subjectivist probability theory as we know them today. The reason why the price of diamonds is higher than that of water, for example, owes to the greater additional satisfaction of the diamonds over the water. Conversely subjectivists consider that probability is tailored to the measurement of belief, and that subjective knowledge should be used in. In order to cover chapter 11, which contains material on markov chains, some knowledge of matrix theory is necessary. We subjectivists conceive of probability as the measure of reasonable partial belief.
Subjectivist the theory that some probability determinations are based on the lack of total knowledge regarding an event. The subjectivist interpretation of probability and the. This example is called the uniform distribution on 0,1. Until the birth of quantum theory in 1926 the first interpretation was just as. It is the rate at which a person is willing to bet on something happening. Finally, the entire study of the analysis of large quantities of data is referred to as the study of statistics. A crude version would simply identify the statement that something is probable with the statement that the speaker is more inclined to believe it than to disbelieve it. Anscombe 1 introduction it is widely recognized that the word probability has two very dierent main senses. The relationship between set inclusion and the above set operations follows.
Theory of probability wiley series in probability and. Probability theory although most of the basics and axioms of probability theory are uncontroversial, the interpretations, usages, and relative importance given to each result vary. Four fundamental questions in probability theory and. A subjectivists guide to objective chance by david lewis introduction we subjectivists conceive of probability as the measure of reasonable partial belief. Unfortunately, most of the later chapters, jaynes intended volume 2 on applications, were either missing or incomplete, and some of the early chapters also had missing pieces. Theory, in applications of model theory of algebra, analysis, and probability, ed. According to the subjectivist view, probability measures a personal belief. Probability theory is an established field of study in mathematics. First issued in translation as a twovolume work in 1975, this classic bookprovides the first complete development of the theory of probability from a subjectivist viewpoint.
The most prevalent use of the theory comes through the frequentists interpretation of probability in terms of the. In its original meaning, which is still the popular meaning, the word is roughly synonymous with plausibility. Observers of scienti c progress in the last several decades will likely nd this question puzzling. There are two main interpretations of the concept of probability. I struggled with this for some time, because there is no doubt in my mind that jaynes wanted this book. In words, for any1 subinterval a,bof0,1, the probability of the interval is simply the length of that interval. Probability represents a unique encoding of incomplete information. Lectures on probability theory and mathematical statistics second edition marco taboga. Ramsey truth and probability, in his foundations of mathematics and other essays, 1926. Bier abstruct the use of probability distributions to represent zyxwvu inherent imprecison in our cognitive processes.
These subjectivists argue that this implies that the agent obeys the. Probability theory ii these notes begin with a brief discussion of independence, and then discuss the three main foundational theorems of probability theory. Probability theory is at the foundation of many machine learning algorithms. In every subjectivist calculation the following are important. It was developed first by probability theorists and philosophers koopman and. Mar 08, 2020 subjective probability is a probability derived from an individuals personal judgment about whether a specific outcome is likely to occur. On keyness realization that his concept of uncertainty in. It concerns your expectations of the values of random variables. For each of the topics that i will briefly mention, i. Probability theory is a fundamental pillar of modern mathematics with relations to other mathematical areas like algebra, topology, analysis, geometry or dynamical systems. Hansen 20201 university of wisconsin department of economics march 2020 comments welcome 1this manuscript may be printed and reproduced for individual or instructional use, but.
It allows us and our software to reason effectively in situations where being certain is impossible. Interpretations of probability stanford encyclopedia of philosophy. Lectures on probability theory and mathematical statistics. The subjectivist methodology of austrian economics and deweys theory of inquiry 4 explicitly, the real significance of the idea is much broader. The subjectivist theory analyses probability in terms of degrees of belief. Subjectivism is not limited to a particular technical problem within a field inside of the discipline of economics. The prior two chapters emphasized a linear theory proceeding from known to unknown. These interpretations show apparent incongruities and the. This chapter presents the third major view of probability and statistics, the subjectivist or bayesian theory. But we need not make war against other conceptions of probability, declaring that where subjective credence leaves off, there nonsense begins. Through this class, we will be relying on concepts from probability theory for deriving machine learning algorithms. Suppose a lottery ticket pays off 1 dollar in case the event occurs and 0 in case the event does not occur. Its logical laws, its subjective sources, 1937, translated by h.1480 1250 1532 1042 369 465 1125 1219 950 112 402 1455 1257 993 612 49 1035 1537 2 160 1174 649 612 299 642 1527 1344 1431 1391 1504 440 840 489 1352 566 1384 1462 585 441 1045 1429 1471 521 48
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s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030331677.90/warc/CC-MAIN-20220924151538-20220924181538-00484.warc.gz
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CC-MAIN-2022-40
| 15,031 | 15 |
https://vixra.wordpress.com/2010/12/26/a-christmas-puzzle/
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math
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I was given “The Big Book of Brain Games” by Ivan Moscovich for Xmas. Most are too easy but here is a nice one (number 331):
Construct a square from four identical linkages hinged at the corners. Such a figure is capable of moving on its hinges to become a rhombus. How many linkages of the same length must be added to make the square rigid? The linkages must be in the same plane as the square and each one can be connected only at the hinges.
My best solution so far has 43 extra linkages which must be far too many.
Update 28-Dec-2010: Lubos has given a nice solution with no overlapping links which requires only 31 extra edges or 29 if you allow the links to cross. However I have found out that this is still not the best solution for the case where overlaps are allowed! so keep trying.
Final Update: Since posting this puzzle I have learnt that a version of it was posed in Martin Gardner’s SciAm column in 1963. His version required that the bracing links do not overlap. Seven readers sent in the solution with 23 added links shown below.
Erich Friedman considered the case where links can cross in 2000 and posted results on his Math Magic website. His best solution had 17 extra links. However, someone later informed him that Andrei Khodulyov had found a solution some time ago with just 15 extra links.
Well done to all those who posted solutions here and over at The Reference Frame.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347401260.16/warc/CC-MAIN-20200529023731-20200529053731-00336.warc.gz
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CC-MAIN-2020-24
| 1,405 | 7 |
https://corescholar.libraries.wright.edu/math/387/
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math
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Clones in matroids representable over a prime field
We show that for every prime number p, a 3-connected non-uniform GF(p)-representable matroid can have a clone set of size at most p−2.
& Zhou, X.
(2018). Clones in matroids representable over a prime field. Discrete Mathematics, 341 (1), 213-216.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100534.18/warc/CC-MAIN-20231204182901-20231204212901-00082.warc.gz
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CC-MAIN-2023-50
| 300 | 4 |
https://www.wisc-online.com/arcade/games/mathematics2/number-systems?gameTypes=CHAKALAKA_TICTACTOE_SNAKE_CROSSWORD_SQUIDHUNT
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math
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Convert Decimal Numbers to Percentages
A decimal number is given, now you change it into a percentage (percent form).
Số-Numbers in Vietnamese
Test Your Knowledge of Gematria!
7th Grade Review: Geometry, Math and Measurement
Practice for 7th grade sgo
Grade 7 Ratio Unit
Hunt squids and solidify your learning!
Grade 8 Ratio Unit
Guide the snakes to the correct answer and solidify your learning!
Introduction to Proofs
Introduction to direct and Indirect proofs
Nombor Menaik (Ascending Numbers)
Math Crossword Puzzle
Squares and Square Roots
Identify squares and square roots
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711064.71/warc/CC-MAIN-20221205232822-20221206022822-00680.warc.gz
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CC-MAIN-2022-49
| 579 | 16 |
https://destinypapers.net/finance-quiz-time-limited/
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math
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A company’s dividend grows at a constant rate of 5 percent p.a.. Last week it paid a dividend of $2.93. If the required rate of return is 13 percent p.a., what is the price of the share 2 years from now? (round to nearest cent)
ABC Limited has a stable sales track record but does not expect to grow in the future. Its last annual dividend was $2.23. If the required rate of return on similar investments is 18 percent p.a., what is the current share price? (to the nearest cent; don’t use the $ sign)
After paying a dividend of $1.90 last year, a company does not expect to pay a dividend for the next year. After that it plans to pay a dividend of 6.05 in year 2 and then increase the dividend at a rate of 5 percent per annum in years 3 to 6. What is the expected dividend to be paid in year 4? (to nearest cent; don’t include $ sign)
Which of the following best describes the constant-growth dividend discount model?
A company has just paid its first dividend of $0.83. Next year’s dividend is forecast to grow by 9 percent, followed by another 9 per cent growth in year two. From year three onwards dividends are expected to grow by 2.2 percent per annum, indefinitely. Investors require a rate of return of 14 percent p.a. for investments of this type. The current price of the share is (round to nearest cent)
Which ONE of the following statements is true about ordinary shares?
Equity holders require a higher return than debt holders because
A company has just paid its annual dividend of $3.47 yesterday, and it is unlikely to change the amount paid out in future years. If the required rate of return is 14 percent p.a., what is the share worth today? (to the nearest cent; don’t include $ sign)
A company has its share currently selling at $13.40 and pays dividends annually. The company is expected to grow at a constant rate of 2 percent pa.. If the appropriate discount rate is 19 percent p.a., what is the expected dividend, a year from now (rounded to nearest cent)?
The strong-form version of the efficient market hypothesis states that stock prices reflects ______________ information relevant to the firm.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662534693.28/warc/CC-MAIN-20220520223029-20220521013029-00263.warc.gz
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CC-MAIN-2022-21
| 2,145 | 10 |
https://archive.ymsc.tsinghua.edu.cn/pacm_category/0110?show=time&size=10&from=1&target=searchall
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math
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We introduce the notion of symplectic flatness for connections and fiber bundles over symplectic manifolds. Given an $A_\infty$-algebra, we present a flatness condition that enables the twisting of the differential complex associated with the $A_\infty$-algebra. The symplectic flatness condition arises from twisting the $A_\infty$-algebra of differential forms constructed by Tsai, Tseng and Yau. When the symplectic manifold is equipped with a compatible metric, the symplectic flat connections represent a special subclass of Yang-Mills connections. We further study the cohomologies of the twisted differential complex and give a simple vanishing theorem for them.
Jintai DingDepartment of Mathematical Science, University of Cincinnati, USAZheng ZhangDepartment of Mathematical Science, University of Cincinnati, USAJoshua DeatonDepartment of Mathematical Science, University of Cincinnati, USA
Advances in Mathematics of Communications, 15, (1), 65-72, 2021.2
We present a cryptanalysis of a signature scheme HIMQ-3 due to Kyung-Ah Shim et al , which is a submission to National Institute of Standards and Technology (NIST) standardization process of post-quantum cryptosystems in 2017. We will show that inherent to the signing process is a leakage of information of the private key. Using this information one can forge a signature.
Bobo HuaSchool of Mathematical Sciences, LMNS, Fudan University, Shanghai 200433, ChinaYong LinDepartment of Mathematics, Information School, Renmin University of China, Beijing 100872, ChinaYanhui SuCollege of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116, China
In this paper, we prove some analogues of Payne-Polya-Weinberger, Hile-Protter and Yang's inequalities for Dirichlet (discrete) Laplace eigenvalues on any subset in the integer lattice $\Z^n.$ This partially answers a question posed by Chung and Oden.
Yong LinDepartment of Mathematics, Renmin University of China, Beijing 100872, ChinaShuang LiuYau Mathematical Sciences Center, Tsinghua University, Beijing 100084, ChinaHongye SongDepartment of Mathematics, Renmin University of China, Beijing 100872, China; Beijing International Studies University, Beijing 100024, China
We prove the equivalence between some functional inequalities and the ultracontractivity property of the heat semigroup on infinite graphs. These functional inequalities include Sobolev inequalities, Nash inequalities, Faber–Krahn inequalities, and log-Sobolev inequalities. We also show that, under the assumptions of volume growth and CDE(n, 0), which is regarded as the natural notion of curvature on graphs, these four functional inequalities and the ultracontractivity property of the heat semigroup are all true on graphs.
Yong LinDepartment of Mathematics, Renmin University of China, Beijing 100872, ChinaHongye SongSchool of General Education, Beijing International Studies University, Beijing 100024, China; Department of Mathematics, Renmin University of China, Beijing 100872, China
Analysis of PDEsDifferential Geometrymathscidoc:2207.03005
We prove a Harnack inequality for positive harmonic functions on graphs which is similar to a classical result of Yau on Riemannian manifolds. Also, we prove a mean value inequality of nonnegative subharmonic functions on graphs.
The CD inequalities are introduced to imply the gradient estimate of Laplace operator on graphs. This article is based on the unbounded Laplacians, and finally concludes some equivalent properties of the CD(K,1) and CD(K,n).
Yong LinDepartment of Mathematics, Renmin University of China, Beijing, 100872, People’s Republic of ChinaShuang LiuDepartment of Mathematics, Renmin University of China, Beijing, 100872, People’s Republic of ChinaYunyan YangDepartment of Mathematics, Renmin University of China, Beijing, 100872, People’s Republic of China
The Journal of Geometric Analysis, 27, 1667–1679, 2016.9
We derive a gradient estimate for positive functions, in particular for positive solutions to the heat equation, on finite or locally finite graphs. Unlike the well known Li-Yau estimate, which is based on the maximum principle, our estimate follows from the graph structure of the gradient form and the Laplacian operator. Though our assumption on graphs is slightly stronger than that of Bauer et al. (J Differ Geom 99:359–405, 2015), our estimate can be easily applied to nonlinear differential equations, as well as differential inequalities. As applications, we estimate the greatest lower bound of Cheng’s eigenvalue and an upper bound of the minimal heat kernel, which is recently studied by Bauer et al. (Preprint, 2015) by the Li-Yau estimate. Moreover, generalizing an earlier result of Lin and Yau (Math Res Lett 17:343–356, 2010), we derive a lower bound of nonzero eigenvalues by our gradient estimate.
Yong LinDepartment of Mathematics, Renmin University of China, Beijing, 100872, P. R. ChinaShuang LiuDepartment of Mathematics, Renmin University of China, Beijing, 100872, P. R. ChinaYun Yan YangDepartment of Mathematics, Renmin University of China, Beijing, 100872, P. R. China
Acta Mathematica Sinica, English Series, 32, 1350–1356, 2016.10
Continuing our previous work (arXiv:1509.07981v1), we derive another global gradient estimate for positive functions, particularly for positive solutions to the heat equation on finite or locally finite graphs. In general, the gradient estimate in the present paper is independent of our previous one. As applications, it can be used to get an upper bound and a lower bound of the heat kernel on locally finite graphs. These global gradient estimates can be compared with the Li–Yau inequality on graphs contributed by Bauer et al. [J. Differential Geom., 99, 359–409 (2015)]. In many topics, such as eigenvalue estimate and heat kernel estimate (not including the Liouville type theorems), replacing the Li–Yau inequality by the global gradient estimate, we can get similar results.
We investigate the Chern–Ricci flow, an evolution equation of Hermitian metrics generalizing the Kähler–Ricci flow, on elliptic bundles over a Riemann surface of genus greater than one. We show that, starting at any Gauduchon metric, the flow collapses the elliptic fibers and the metrics converge to the pullback of a Kähler–Einstein metric from the base. Some of our estimates are new even for the Kähler–Ricci flow. A consequence of our result is that, on every minimal non-Kähler surface of Kodaira dimension one, the Chern–Ricci flow converges in the sense of Gromov–Hausdorff to an orbifold Kähler–Einstein metric on a Riemann surface.
Bing-Long ChenDepartment of Mathematics, Sun Yat-sen University, Guangzhou 510275, ChinaXiaokui YangMorningside Center of Mathematics, Institute of Mathematics, Hua Loo-Keng Key Laboratory of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
In this paper, we show that any compact Kähler manifold homotopic to a compact Riemannian manifold with negative sectional curvature admits a Kähler–Einstein metric of general type. Moreover, we prove that, on a compact symplectic manifold X homotopic to a compact Riemannian manifold with negative sectional curvature, for any almost complex structure J compatible with the symplectic form, there is no non-constant J-holomorphic entire curve f:C→X.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510967.73/warc/CC-MAIN-20231002033129-20231002063129-00888.warc.gz
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| 7,377 | 21 |
https://www.coursehero.com/file/p30rpmg/17-Determine-the-maximum-force-exerted-during-different-time-intervals-a-Tap/
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math
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17. Determine the maximum force exerted during different time intervals.a. Tap and drag across the data from 0 s to 10 s.b. Choose Statistics from the Analyze menu.c. Record the maximum force in Table 2, rounding to the nearest 0.1 N.d. Choose Statistics from the Analyze menu to turn off statistics.18. Repeat Step 17 for the remaining 10 second intervals: 20−30 s, 40−50 s, 60−70 s, and 80−90 s.19. Calculate the difference between each maximum value and the next and record these values in Table 2.20. Tap and drag to highlight 0−90 s on the graph. Choose Curve Fit from the Analyze menu. Select Linear as the Fit Equation and record the slope (round to the nearest 0.01) in Table 3. Select OK.DATA
Table 1−Continuous GripTime intervalMaximum force (N)∆ Maximum force (N)0–10 s20–30 s40–50 s60–70 s80–90 sTable 2−Repetitive GripTime intervalMaximum force (N)∆ Maximum force (N)0–10 s20–30 s40–50 s60–70 s80–90 sTable 3
SlopePart I–Continuous grippingPart II–Repetitive grippingData Analysis1. Examine your graph and the data in Table 1. What conclusion can you draw about the number of individual muscle fibers that are firing in the last 10 s compared with the first 10 s?2. Is the change in number of muscle fibers that contract occurring at a constant rate?3. Use your knowledge of fast, slow, and intermediate skeletal muscle fibers to hypothesize which fibers are contracting in the first, third, and final 10 s intervals.4. How might you explain the subject’s response to coaching? This should be evident in the last 10 s of data for Parts I and II of the exercise. Discuss the possible involvement of the central nervous system, in addition to the muscle fibers.5. Compare the slopes recorded in Table 3. Give a possible explanation for the difference, if any, in muscle fatigue rates seen in continuous versus repetitive gripping.
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https://chetumenu.com/is-c-in-standard-form-slope/
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math
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Is C in standard form slope? The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line. The standard form of a linear equation is Ax + By = C.
Correspondingly, What is C in general form?
The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
Consequently, Is C the y-intercept? The value of c in the equation y = mx + c represents the y-intercept of the line. The intercept is the distance from the origin on the y-axis, where this line cuts the y-axis.
Consequently, What does AB and C mean in standard form?
The standard form of a line is simply a special way of writing the equation of a line. The standard form is just another way to write this equation, and is defined as Ax + By = C, where A, B, and C are real numbers, and A and B are both not zero (see note below about other requirements).
What is factored form?
Factored form refers to the form of a number or algebraic expression when it has been broken down into a product of its factors.
Related Question for Is C In Standard Form Slope?
What is the form Ax By C 0?
Any equation of the form Ax + By + C = 0 (i.e. a linear equation in one or two variables), will represent a straight line on the XY plane, where A and B should not be both zero.
What is gradient and intercept?
In the equation y = mx + c the value of m is called the slope, (or gradient), of the line. It can be positive, negative or zero. The value of c is called the vertical intercept of the line. It is the value of y when x = 0. When drawing a line, c gives the position where the line cuts the vertical axis.
What does the gradient represent?
In mathematics, the gradient is the measure of the steepness of a straight line. A gradient can be uphill in direction (from left to right) or downhill in direction (from right to left). Gradients can be positive or negative and do not need to be a whole number.
Is slope and gradient the same?
Gradient: (Mathematics) The degree of steepness of a graph at any point. Slope: The gradient of a graph at any point.
Is C the y-intercept in a quadratic equation?
With both standard and vertex form, you may have noticed that the y-intercept value is equal to the value of the c constant in the equation itself. That is going to be true with every parabola/quadratic equation you encounter in those forms. Simply look for the c constant and that is going to be your y-intercept.
What is C in standard form linear equation?
The standard form of a linear equation is Ax+By=C. A, B, and C are constants, while x and y are variables.
What does ax2 BX C stand for?
Remember, the standard form of a quadratic looks like ax2+bx+c, where 'x' is a variable and 'a', 'b', and 'c' are constant coefficients. ax2 is called the quadratic term, bx is the linear terms, and c is the constant term.
What does C stand for in a quadratic function?
Quadratic Functions. Quadratic Functions. A quadratic function is a function of the form f(x) = ax2 +bx+c, where a, b, and c are constants and a = 0. The term ax2 is called the quadratic term (hence the name given to the function), the term bx is called the linear term, and the term c is called the constant term.
What is standard factored form?
The quadratic expression is called the standard form, the sum of a multiple of and a linear expression ( in this case). When the quadratic expression is a product of two factors where each one is a linear expression, this is called the factored form.
What standard form means?
more A general term meaning "written down in the way most commonly accepted" It depends on the subject: • For numbers: in Britain it means "Scientific Notation", in other countries it means "Expanded Form" (such as 125 = 100+20+5)
How do you write in factored form?
What is ax by c for Y?
What is ax by C in slope intercept form?
The standard form of such an equation is Ax + By + C = 0 or Ax + By = C. When you rearrange this equation to get y by itself on the left side, it takes the form y = mx +b. This is called slope intercept form because m is equal to the slope of the line, and b is the value of y when x = 0, which makes it the y-intercept.
How many solution does ax by C have?
It has infinitely many solutions.
What does C stand for in Y MX C?
y = mx + c is an important real-life equation. The gradient, m, represents rate of change (eg, cost per concert ticket) and the y-intercept, c, represents a starting value (eg, an admin. fee). Maths.
What is the gradient of 3x 4y 10?
Hence the x-intercept of the line 3x - 4y + 10 = 0 is -10/3. Comparing this to the equation of y = mx + c for slope m and c as the y-intercept, we will get (3/4) or 0.75 as the slope and (5/2) or 2.5 as the y-intercept.
How do you find M and C in Y MX C?
What is a gradient Calc 3?
The gradient is a fancy word for derivative, or the rate of change of a function. It's a vector (a direction to move) that. Points in the direction of greatest increase of a function (intuition on why)
How do you interpret the gradient of a line?
The slope of a line is called its gradient. The larger the value of the gradient, the steeper the slope. The gradient of a straight line can be calculated by drawing a right-angled triangle between any two points lying on the line. If the line is sloping down then a negative sign is placed in front of the answer.
How do you calculate a gradient?
Is slope M or B?
In the equation of a straight line (when the equation is written as "y = mx + b"), the slope is the number "m" that is multiplied on the x, and "b" is the y-intercept (that is, the point where the line crosses the vertical y-axis). This useful form of the line equation is sensibly named the "slope-intercept form".
Why is M used for slope?
It is not known why the letter m was chosen for slope; the choice may have been arbitrary. John Conway has suggested m could stand for "modulus of slope." One high school algebra textbook says the reason for m is unknown, but remarks that it is interesting that the French word for "to climb" is monter.
What are 4 types of slopes?
There are four different types of slope. They are positive, negative, zero, and indefinite.
How does C affect the graph of a quadratic function?
As we can see from the graph, changing c affects the vertical shift of the graph. When c > 0, the graph shifts up c units. When c < 0, the graph shift down c units.
What does AB and C mean in the quadratic equation?
The Quadratic Formula uses the “a”, “b”, and “c” from “ax2 + bx + c”, where “a”, “b”, and “c” are just numbers; they are the “numerical coefficients” of the quadratic equation they've given you to solve.
How do you find the y-intercept in standard form?
Can standard form C be negative?
A, B, C are integers (positive or negative whole numbers) No fractions nor decimals in standard form.
What is a B and C in linear equation?
The standard form of linear equations is given by: Ax + By + C = 0. Here, A, B and C are constants, x and y are variables.
What is quadratic standard form?
The standard form of a quadratic function is f(x)=a(x−h)2+k. The vertex (h,k) is located at h=–b2a,k=f(h)=f(−b2a).
What does Y ax 2 bx c represent?
The graph of a quadratic equation in two variables (y = ax2 + bx + c ) is called a parabola.
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https://www.arxiv-vanity.com/papers/1006.5477/
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math
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Ultraviolet Extension of a Model with Dynamical Electroweak Symmetry Breaking by Both Top-Quark and Technifermion Condensates
We construct and analyze an ultraviolet extension of a model in which electroweak symmetry breaking is due to both technifermion and top-quark condensates. The model includes dynamical mechanisms for all of the various gauge symmetry breakings. We discuss certain aspects in which it requires additional ingredients to be more realistic.
The origin of electroweak symmetry breaking (EWSB) continues to be an outstanding mystery. In one class of models this breaking is produced dynamically by means of an asymptotically free, vectorial, gauge interaction based on an exact gauge symmetry, commonly called technicolor (TC), that becomes strongly coupled on the TeV scale, causing the formation of bilinear technifermion condensates tc . In order to communicate the electroweak symmetry breaking in the technicolor sector to the Standard-Model (SM) fermions (which are technisinglets), one embeds the technicolor symmetry in a larger theory called extended technicolor (ETC) etc . A different approach is based on the idea that because of its large mass, the top quark should play a special role in electroweak symmetry breaking, and models of this type feature a top-quark condensate, . An early realization of this idea made use of (nonrenormalizable) four-fermion operators nambu , while later renormalizable models used separate asymptotically free, vectorial SU(3) gauge interactions acting on the third generation of quarks and on the first two generations of quarks, denoted as SU(3) and SU(3), respectively hill ; tc2 . These are often called “topcolor” models. In these models the SU(3) interaction becomes sufficiently strong, at a scale of order 1 TeV, to produce the condensate. The SU(3) interaction actually treats the and quarks in the same way and hence, by itself, would also produce a condensate equal, up to small corrections, to , and a resultant dynamical -quark mass essentially equal to . To prevent the formation of such a condensate, these models include an additional set of hypercharge-type gauge interactions. In these models the and symmetries each break to their respective diagonal subgroups, which are the usual color SU(3) and weak hypercharge U(1) groups. There has been considerable interest in hybrid models that combine the properties of technicolor and topcolor and thus feature both technifermion condensates and a top-quark condensate hill -cs08 . These are often called “topcolor-assisted technicolor” or TC2 models. In these theories, most of the observed top-quark mass, GeV, is due to the condensate. Reviews of these models include gcvetic -sekhar_pdg .
In this paper we shall carry out an exploratory construction and analysis of an ultraviolet extension of a TC2 model in which we explicitly specify an embedding of the TC symmetry in a higher-lying ETC group and dynamical mechanisms for the necessary breakings of both the ETC group to the TC group and of the group to . Because our model does not purport to be complete, we call it an ultraviolet extension rather than an ultraviolet completion. It is recognized that models that involve a top quark condensate and associated strong interactions of the top quark at a scale not too much larger than are tightly constrained by the excellent agreement between the measured cross section for at TeV from the CDF and D0 experiments at the Fermilab Tevatron pdg ; cdfttbar ; d0ttbar and perturbative QCD predictions ttbartheory . TC2 models are also subject to bounds from searches for colorons, top pions, resonances, and by constraints from precision electroweak data hill -hillsimmons . Detailed analyses of the phenomenology of TC2 models have been given in the literature tc2 -cs08 . Our present work is somewhat complementary to these analyses, in that we focus on the effort to build an ultraviolet extension of a TC2 model, although we do comment on some phenomenological implications of this extension. Before proceeding, it is appropriate to recall that TC2 models represent only one among many ideas for physics beyond the Standard Model; other ideas include, for example, a top-quark seesaw, supersymmetry, and theories involving higher spacetime dimensions, in particular, “higgless” models and string theory. Here we will concentrate on a (four-dimensional) TC2 approach.
This paper is organized as follows. In Section II we review some necessary background on TC/ETC and TC2 models. In Section III we discuss our ultraviolet extension and analyze its properties. Section IV contains a brief discussion of the consequences that would ensue if one tried to build a model including an sector analogous to the and sectors of TC2 theories. In a concluding section, we summarize the successes of the model and certain problems that deserve further study. Some notation and formulas are contained in an Appendix.
Ii Some Background
ii.1 TC/ETC Models
Here we briefly review some relevant background on models with dynamical electroweak symmetry breaking, first on TC/ETC models and then on models featuring top-quark condensates. Early works on ETC tended to model ETC effects via four-fermion operators connecting SM fermions and technifermions, with some assumed values for their coefficients. More complete studies have taken on the task of deriving these four-fermion operators by analyses of renormalizable, reasonably ultraviolet-complete, ETC models. These models normally gauge the generational index and combine it with the technicolor index. Thus, given that the TC and ETC gauge groups are , one has the relation
where denotes the number of oberved SM fermion generations ngen3 . The ETC gauge symmetry breaks in a series of stages, in one-to-one correspondence with the SM fermion generations, down to the residual exact technicolor symmetry. Some recent reviews include Refs. hillsimmons , nag06 -sanrev . At the highest breaking scale, denoted , the first-generation fermions split off, and since they communicate with the EWSB technifermion sector only via ETC gauge bosons with masses of order , it follows that their masses are the smallest. The reasonably ultraviolet-complete ETC models of Refs. at94 -kt used the minimal non-Abelian value in order to reduce technicolor corrections to and propagators. Accordingly, these models employed an SU(5) group. In these models, the ETC-breaking scales corresponding to the three generations exhibit a hierarchy encompassing of order TeV, an intermediate scale, , and the smallest scale, of order a few TeV.
TC/ETC models in which the SM-nonsinglet fermions transform vectorially under the ETC gauge group are able to satisfy constraints from flavor-changing neutral-current processes. This was shown in Refs. ckm ; kt to result from approximate residual generational symmetries. These models rely upon a slowly running (walking) TC gauge coupling associated with an approximate infrared zero of the TC beta function in order to enhance fermion masses wtc ; chipt . They also must rely upon this walking behavior in another way, namely that in the presence of a slowly running coupling at the TeV scale, small perturbations by SM gauge interactions have a magnified effect. Thus, although the SU(3) coupling is small at this scale, it provides enhancement for the condensation of techniquarks, relative to technileptons, and hence causes the techniquark condensate to occur at a higher scale, with the result that the dynamically induced techniquark masses are larger than the technilepton masses. This, in turn, can explain why the masses of the quarks are greater than the mass of the charged lepton in each generation. (The very small masses of neutrinos require a more complicated mechanism, involving a low-scale seesaw nt .) Furthermore, since the weak hypercharge interaction favors the condensation of the techniquarks of charge 2/3 in a one-family model, while inhibiting the condensation of techniquarks of charge (see Eqs. (6)-(7)), the former naturally condense at a higher scale then the latter. This can explain why the charge 2/3 quarks of the higher two generations are heavier than the charge quarks (explaining why presumably necessitates incorporating effects of off-diagonal elements of the respective up-quark and down-quark mass matrices). However, it is not clear that this effect is large enough to account for the large mass ratio without violating custodial-symmetry constraints and, moreover, is able to produce realistic CKM mixing kt ; csm . Indeed, the large value of the top-quark mass was one of the main motivations for models featuring a condensate.
ii.2 Models with and
We proceed to discuss some details of TC2 models that will be needed for the explanation of our ultraviolet extension. These use a gauge group,
where is the technicolor group and is the augmented SM (ASM) group
Our notation for the running gauge couplings (with the scale implicit here) is and, for the five factor groups in , , , , , and . The running squared couplings are denoted for the various factor groups . The gauge symmetry (2) is operative above a scale of order 1 TeV and below the lowest ETC breaking scale. As discussed above, the SU(3) interaction couples to the third generation of quarks, while the SU(3) interaction couples to the first two generations of quarks. The SU(3) coupling at this scale is considerably stronger than the SU(3) coupling, and, indeed, becomes strong enough to produce the condensate.
To prevent the formation of a condensate by this SU(3) interaction, TC2 models rely on the factor group displayed in Eq. (LABEL:gasm). In early TC2 models, the U(1) and U(1) interactions coupled, respectively, to SM fermions of the third generation, and to SM fermions of the first two generations, according to their weak hypercharges. Motivated by constraints from precision electroweak data, more recent TC2 models lane05 ; cs08 have adopted a different set of charge assignments in which the interaction couples in the same manner to all three generations, which are singlets under U(1). These models have thus been characterized as having flavor-universal hypercharge. At the scale , the U(1) interaction is assumed to be strong enough to (i) enhance the formation of the condensate, since the relevant hypercharge product
is attractive, and (ii) prevent the formation of a condensate, since the hypercharge product
is repulsive qlw . However, there are several constraints on the strength of the U(1) coupling. First, if it were too large, then there would be excessive violation of custodial symmetry. Second, since the U(1) (as well as U(1)) gauge interaction is not asymptotically free, a moderately strong U(1) coupling would bring with it the danger of a Landau pole at an energy not too far above the 1 TeV scale, so that the model could not be regarded as a self-consistent low-energy effective field theory. These constraints have been used in TC2 model-building hill -hillsimmons . Indeed, in view of these constraints and the fact that, as the energy scale decreases, the U(1) coupling gets weaker while the SU(3) coupling gets stronger, there is a rather limited set of values of couplings and a limited interval in which this scenario can take place in a self-consistent manner. In particular, the SU(3) coupling at the scale must be fine-tuned to be only slightly greater than the critical value for the formation of the condensate, so that a rather weak U(1) coupling can still prevent the formation of a condensate tc2 -cs08 .
To the extent that this top-quark mass generation by SU(3) is analogous to the dynamical generation of constituent-quark masses in quantum chromodynamics (QCD), then, since the latter are of order , one would infer that would be roughly comparable to . More quantitatively, one can use the approximate relation psrel
where represents a cutoff scale characterizing the asymptotic decay of the dynamical mass , considered as a running quantity. This scale, , enters in the integral that one calculates in deriving this relation. Setting and using the rough estimate , one obtains GeV. The technifermion condensation yields an analogous . Both the top-quark and technifermion condensates transform as under SU(2) and under U(1), and hence produce a mass given, to leading order, by
where denotes the number of SU(2) technidoublets in the theory. Our ultraviolet extension will use a one-family TC model, so that . In the absence of the contribution from the top-quark condensate (i.e., in regular technicolor), Eq. (9) would yield GeV; the value of in the TC2 theory is slightly reduced by the presence of the term. Since , most of the contribution to the mass in the TC2 model is provided by technicolor. Similar comments apply to the mass.
One should remark on a difference between the generation of dynamical masses for light quarks in QCD and techniquarks in TC, on the one hand, and the generation of the top-quark mass in TC2 theories, on the other hand. In the former two cases, the gauge interactions responsible for the condensates and resultant dynamical fermion masses are exact. In contrast, SU(3) is broken at a scale comparable to the scale where it gets strong and produces the condensate. It is thus plausible that, to compensate for this, should be somewhat larger than , say of order 1 TeV, and we will assume this approximate value here. Slightly below the scale, the symmetry group breaks to its diagonal subgroup that treats all generations symmetrically, namely usual color SU(3), while the symmetry group breaks to a diagonal subgroup, which is the usual weak hypercharge, U(1). Thus, one has the symmetry breaking , where .
We shall use the more modern type of TC2 model with a U(1) coupling universally to all generations lane05 ; cs08 to serve as the basis for our ultraviolet extension. We display SM fermion representations in this type of model below. In our notation, the three numbers in parentheses are the dimensions of the representations of the three non-Abelian factor groups in ; the subscripts are the U(1) and U(1) hypercharges; and and are SU(3) and SU(3) indices:
It is an option whether one explicitly includes right-handed electroweak-singlet neutrinos, since they are singlets under .
Iii Construction and Assessment of an Ultraviolet Extension
iii.1 General Structure
We find that it is not possible to have the usual ETC structure given by Eq. (1). The reason is quite fundamental; the full ETC symmetry is incompatible with the essential feature of the model, namely the fact that the first two generations of SM fermions transform according to different representations of than the third generation. In other words, the ETC symmetry implies, a fortiori, that unitary transformations that mix up the three left-handed SU(2) quark doublets leave the theory invariant, but this requirement is incompatible with the assignment of the first two generations of these quark doublets to the representation of and the third to the different representation of this group, . Similarly, the ETC symmetry implies, a fortiori, that unitary transformations that mix up the three generations of right-handed up-type quarks and, separately, the three generations of down-type quarks leave the theory invariant, but this requirement is incompatible with the assignment of the first two generations of these quark fields to the representation of and the third generation to the representation.
In view of this fundamental incompatibility, we shall construct the ETC group by embedding the first two generations of SM fermions together with the technifermions in ETC multiplets. Hence, for our ETC model, the relation (1) is altered to read
As before, in order to minimize TC corrections to and propagators, we again choose the minimal non-Abelian value, , so our ETC group is SU(4). We thus consider a model that, at a high scale, is invariant under the gauge symmetry
and was given in Eq. (LABEL:gasm). The group contains the ETC group, SU(4), together with three additional gauge interactions (the subscript in refers to these additional interactions): (i) hypercolor (HC) SU(2), which helps in the breaking of SU(4) in two sequential stages, to SU(3) and then to the residual exact technicolor group, SU(2); (ii) metacolor (MC) SU(3), which breaks to the diagonal subgroup, color SU(3); and (iii) ultracolor (UC) SU(2), which breaks to the diagonal subgroup, weak hypercharge U(1). With the fermion content to be delineated below, all of the four gauge interactions in are asymptotically free.
The fermions with SM quantum numbers, including the usual SM fermions and the technifermions, are assigned to the representations displayed below. We use notation such that the four numbers in the parentheses are the dimensions of the representations of the group
while the two subscripts are the hypercharges for the gauge groups U(1) and U(1), respectively. Since all of these fermions are singlets under the additional gauge interactions in , namely , we do not include these factor groups in the listings. The index is an SU(4) index, with referring to the first two generations and being SU(2) gauge indices. As before, e.g. in ckm , we use a compact notation in which , , , , , and . The fermion representations are
As was alluded to above, this is thus a one-family technicolor model ttf . Given the motivation for the structure of the model, it is clear why there are no SM fermions that are simultaneously nonsinglets under both SU(3) and SU(3). As pointed out above, one cannot embed all of the generations of each type of fermion in a single corresponding ETC multiplet, since there is an incompatibility between the essential ETC feature of treating the three generations in a symmetric manner at the high scale and the fact that in these types of models the first two generations are subject to different gauge symmetries than the third generation. Hence, with the present embedding in SU(4), there is only mixing of the first two generations with each other, but no full three-generation CKM (Cabibbo-Kobayashi-Maskawa) mixing. Thus, . (Indeed, the observed CKM quark mixing represents the difference in mixings between the up-quark and down-quark sectors, so three-generational mixings in these individual sectors are necessary but not sufficient to fit the observed CKM mixing.) The fact that the third-generation quarks transform differently under than the first two generations of quarks was recognized in early TC2 model-building to pose a challenge to getting full CKM mixing hill ; tc2 , and this problem manifests itself directly in our UV extension. This shows that further ingredients are required for a satisfactory larger ultraviolet completion.
iii.2 Generalities on Fermion Condensation Channels
In general, in an asymptotically free gauge theory involving possible condensation of fermions transforming according to the representations and of the gauge group to a condensate transforming as , an approximate measure of attractiveness of this channel
where is the quadratic Casimir invariant for the representation casimir . If several possible condensation channels are possible, it is expected that condensation occurs in the most attractive channel (MAC), i.e., the one with the largest value of . For a vectorial gauge interaction, the most attractive channel is , producing a condensate in the singlet representation of the gauge group (with ) and thus preserving the gauge invariance. In this case, as the reference energy scale decreases from large values where the gauge interaction is weak, this condensation is expected to occur when exceeds a value of order unity. Some results relevant to this are given in the Appendix. For a particular asymptotically free gauge interaction, one must check to see whether, given its (light or massless) fermion content, it will evolve from high scales where it is weakly coupled to lower scales in a manner that leads to a growth in the coupling that is sufficient to trigger fermion condensation, or whether, alternatively, its coupling could approach an infrared fixed point that is too small for such condensation to occur. In the latter case, this gauge interaction would not spontaneously break its chiral symmetries. In the model studied here, it is required that the SU(2), SU(3), SU(3), SU(2), and SU(2) gauge interactions produce various condensates, and we will show that this is, indeed, consistent with the sets of nonsinglet fermions subject to these respective interactions. Throughout our analysis, it is understood that there are theoretical uncertainties inherent in analyzing such strong-coupling phenomena as fermion condensation.
We proceed to describe the fermion contents of the rest of the model. Since the full model is a chiral gauge theory, it follows that the Lagrangian describing the physics at a high scale TeV has no fermion mass terms. An analysis of global symmetries is of interest especially since some of these symmetries are broken by condensates produced by gauge symmetries that become strong at various lower energy scales. We shall discuss these global symmetries below.
iii.3 Su(2) Sector
We shall need a set of fermions whose role is to break the SU(4) symmetry in two stages down to SU(2). These fermions are singlets under all of the gauge symmetries except , so we only list their dimensionalities under these two groups:
where and are SU(4) and SU(2) indices, respectively. The 6-dimensional representation of SU(4) is the antisymmetric rank-2 tensor representation, , which is self-conjugate (and hence has zero SU(4) gauge anomaly).
We next discuss the global flavor symmetries involving hypercolor-nonsinglet fermions. The fact that the and fields are nonsinglets under two interactions, namely SU(4) and SU(2), that become strongly coupled at comparable scales ( TeV) plays an important role in the determination of this global chiral symmetry. In the hypothetical limit where, at a given scale, the SU(2) coupling were imagined to be much stronger than the SU(4) coupling, it would follow that the sector of HC-nonsinglet fermions would be invariant under the classical global flavor symmetry group , or equivalently, . Here, the global U(1) and U(1) transformations are defined to rephase and , respectively. Both of these global U(1) symmetries are broken by SU(2) instantons, with one linear combination remaining unbroken. Just as SU(2) instantons break quark number, , and lepton number, , but preserve , so also the SU(2) instantons preserve the linear combination , or equivalently, . Let us denote the corresponding global () number symmetry as U(1). Thus, if SU(4) interactions could be neglected relative to SU(2), then the actual global chiral symmetry group of this sector would be . However, although the SU(2) interaction is stronger than the SU(4) interaction, the latter is never negligible, and hence the global flavor symmetry group is not symmetry, but instead only U(1).
iii.4 Su(3) Sector
The fermions in the second set are involved with the breaking of to the diagonal color subgroup, color SU(3). This set contains nonsinglets under only the group (i.e., they all have zero U(1) and U(2) hypercharges); with respect to this group, the fermions transform as
where , , and are SU(3), SU(3), and SU(3) gauge indices. (This set of fermion fields could be written equivalently in holomorphic form as all right-handed or all left-handed fields by using appropriate complex conjugates.)
The fermions that are nonsinglets under SU(3) include the third-generation quarks and the fermions and in Eqs. (36) and (37). In order to determine the operative global flavor symmetry involving MC-nonsinglet fermions slightly above 1 TeV, one must take account of the fact that both the SU(3) and SU(3) interactions become strongly coupled at this scale. In accordance with constraints from custodial symmetry, we shall assume that the U(1) gauge coupling is sufficiently weakly coupled so that it, together with the other (non-technicolor) gauge interactions can be neglected, in a leading approximation, in considering the global flavor symmetry. Then the classical global flavor symmetry group at this scale would be
Here, SU(2) and SU(2) operate on the left- and right-handed chiral and fields; U(1) and U(1) are vector and axial-vector U(1)’s operating on and ; the U(1) rephases the fields (for fixed and ); the U(3) operates on the three fields (with fixed, and ); and the U(3) operates on the three fields (with fixed and ). SU(3) instantons leave U(1) invariant but break U(1), U(1), and U(1). SU(3) instantons break the U(1) and U(1) symmetries. (Thus, in particular, the U(1) symmetry is broken by both SU(3) and SU(3) instantons.) From the broken U(1) and U(1) symmetries one can form a linear combination, which we denote U(1), that is preserved by the SU(3) instantons. To form a conserved axial-vector current involving the field, one needs to cancel the divergences due to both the SU(3) and SU(3) instantons, which requires a linear combination of the axial-vector currents involving the and , respectively. We denote this conserved global symmetry as U(1) (where “strongly coupled, mixed”). Thus, with the above-mentioned provisos that other gauge interactions can be considered negligible, the actual quantum global flavor symmetry involving fermions that are nonsinglets under the strongly coupled SU(3) and SU(3) gauge symmetries is
iii.5 Su(2) Sector
The third set of fermions is involved with the breaking of to the diagonal subgroup, weak hypercharge U(1). This set contains nonsinglets under only the group , and, with respect to this group, the fields transform as
where is an SU(2) gauge index, the subscripts denote the hypercharges with respect to U(1) and U(1), and . This SU(2) sector has a classical global symmetry, where U(1) and U(1) rephase the and fields, respectively. Both of these U(1)’s are broken by the SU(2) instantons, but the combination corresponding to is preserved. We denote this as U(1).
As is evident from these fermion representation assignments, we have chosen to construct the ultraviolet extension to have a modular structure, in which one sector is responsible for the breaking of to SU(3) and another is responsible for the breaking of to U(1), rather than trying to accomplish this breaking with a single sector. While this makes the model somewhat complicated, it actually simplifies some aspects of the analysis, such as checking anomaly cancellation and determining condensation channels. One could also investigate models in which one tries to use a single sector to carry out both of these symmetry breakings.
iii.6 Anomaly Cancellation
Since the full model is a chiral gauge theory, it is necessary to check that it is free of any gauge or global anomalies. Given the modular construction of the theory, we can divide the analysis of anomalies into several parts. The first involves contributions of fermions that are nonsinglets under the SU(4) group. We first observe that the SU(4) anomalies of the and fields are equivalent to the anomaly of one right-handed fermion in the fundamental representation of SU(4). This plays the role of a right-handed electroweak-singlet neutrino-type ETC multiplet, so that, in conjunction with the fermion fields in Eqs. (21), (23), (25), (27), and (29), it renders the part of SU(4) involving SM-nonsinglet fermions vectorlike, so the anomaly from these fermions vanishes. The hypercolor sector is constructed so that its contribution to the anomaly also vanishes, so the entire anomaly is zero. The anomalies of the form
cancel between (quarks plus techniquarks) and (leptons plus technileptons). One also verifies that the following anomalies vanish:
Several of these anomalies vanish trivially, owing to the fact that the SM fermions have zero U(1) hypercharge and the modular construction of the theory. Within a semiclassical picture that incorporates gravity, one would also require that the mixed gauge-gravitational anomalies and vanish, where here denotes graviton. This requirement is satisfied.
One also must check that there are no global Witten anomalies (associated with the homotopy group ). This requires that the number of chiral fermions transforming as doublets under each of the SU(2) gauge group be even. For the sector of SU(2)-nonsinglet fermions, we have chiral doublets. For the SU(2) sector we have (holomorphic) chiral doublets. Finally, for the SU(2) sector we have (holomorphic) chiral doublets. Thus, the theory is free of any global anomaly.
iii.7 Symmetry Breaking of SU(4) to SU(2)
The model is constructed so that the breaking of the SU(4) symmetry to SU(3) at a scale , and then to the residual exact SU(2) symmetry at a lower scale is primarily driven by the HC gauge interaction, which is arranged to become strong at a scale TeV. The details of how an SU(4) theory can be broken to the residual exact technicolor subgroup SU(2) were presented in our Ref. gen , to which we refer the reader. Here we only briefly mention the main points. One chooses the values of the SU(4) and SU(2) couplings at a high scale so that at the scale , the HC interaction is sufficiently stronger than the ETC interaction that the most attractive channel involves HC-nonsinglet fermions and is of the form (in the notation of Eqs. (33)-(35))
with for SU(4) and for SU(2). The associated condensate is
where is the totally antisymmetric tensor density for SU(4). This breaks to and is invariant under SU(2). With no loss of generality, we may define the uncontracted SU(4) index in Eq. (70) to be . This condensate also breaks the global U(1) symmetry, giving rise to a Nambu-Goldstone boson (NGB). (Additional physics in a UV completion could render this a PNGB.) In general, (P)NGB’s have derivative couplings and hence have interactions that vanish in the limit where the center-of-mass energy is much less than the scale of the symmetry breaking, i.e., here, energies much smaller than TeV. Moreover, this particular NGB is a SM-singlet, which further suppresses its observable effects. We shall discuss the (pseudo)-Nambu-Goldstone bosons (PNGB’s) resulting from the technifermion condensates below.
As the theory evolves to lower energy scales, the SU(3) and SU(2) gauge couplings continue to grow, and at the scale , the dominant SU(2) interaction, in conjunction with the additional strong SU(3) interaction, produces a condensate in the most attractive channel, which is (in a notation analogous to Eq. (69))
This has for SU(3) and for SU(2). The condensation in this channel breaks SU(3) to SU(2) and is invariant under SU(2). The associated condensate is
where . With no loss of generality, we may choose as the breaking direction in SU(3). Another condensate that is expected to form at a scale slightly below is
which does not break any further gauge symmetries beyond those broken at the scales and . The choices of TeV and a somewhat smaller value of can yield reasonable values for the masses of the quarks and charged leptons of the first two generations. Details on SM fermion mass generation in this theory are given in Ref. gen . Since the quark and lepton are SU(4)-singlets, they would have to get their masses in a manner different from the quarks and charged leptons of the first two generations. SU(3)-instanton effects can provide a way to produce (via a ’t Hooft determinantal operator) hill . Further ingredients are required to account for and to obtain the sort of low-scale seesaw mechanism that was developed in Ref. nt to explain light neutrino masses (in a full SU(5) theory). Although there are no intrinsic mass terms in the high-scale Lagrangian for the (SM-singlet) fermions (33)-(35), these fermions all gain dynamical masses of order or as a result of the various condensates that form, and hence are integrated out of the effective low-energy theory below .
iii.8 Sequence of Condensations Involving
The breaking of is envisioned to occur at a scale roughly of order 1 TeV. In order to analyze this breaking, we first note that at this scale the operative gauge symmetry is the one given in Eq. (2). Following usual TC2 practice, the model is arranged so that is considerably larger than at this scale of about 1 TeV. This inequality in couplings can arise naturally, since the leading coefficient of the SU(3) beta function is larger than the corresponding leading coefficient of the SU(3) beta function, as a consequence of the fact that the SU(3) sector has fewer fermions than the SU(3) sector.
With the fermion content as specified above, the SU(3) sector has Dirac fermions while the SU(3) sector has Dirac fermions, both transforming according to the respective fundamental representations of these two groups. Hence, for SU(3) while for SU(3). As the energy scale decreases through a value denoted , the coupling grows to be sufficiently large that the SU(3) interaction produces a condensate in the channel, namely
This channel has an attractiveness measure with respect to the SU(3) gauge interaction. If one assumes a given value of at a high scale , then a rough estimate of the value of the condensation scale can be obtained by using Eq. (105) in the Appendix. Owing to the formation of the condensate (74), the top quark picks up a dynamical mass, and, indeed, this comprises the dominant part of the mass of the top quark. As discussed above, the U(1) interaction is attractive in this channel and repulsive in the channel. The condensate (74) breaks part of the global symmetry group (44), namely , to its diagonal subgroup, SU(2), yielding three (pseudo)-Nambu-Goldstone bosons, . TC2 models require that these be PNGB’s rather than strictly massless NGB’s because there are also three NGB’s resulting from the formation of the technifermion condensates, with the same SM quantum numbers, and only one set is absorbed to form the longitudinal components of the and . The and mix to form the states
where is a mixing angle. This mixing is relatively small, corresponding to the fact noted above that the and masses arise primarily from the technicolor sector. The are absorbed by the and , while the three orthogonal pseudoscalars are known as top pions. Using a Gell-Mann-Oakes-Renner-type formula, one infers that the top pions will have masses given by , where denotes a contribution to that is hard on the scale of tc2 . This constitutes another necessary ingredient in a satisfactory UV completion of the TC2 model. With and as determined, GeV.
A channel of the same type with respect to SU(3) and thus also a most attractive channel with respect to this group, is one that would break the SU(3) gauge symmetry, namely one that would produce the condensates
This condensate also breaks the global SU(3) and U(1) symmetries in Eq. (44), giving rise to (P)NGB’s and also producing dynamical masses of order for the fields. As before, the (P)NGB’s are SM-singlets and are derivatively coupled, so their effects at scales far below 1 TeV are suppressed. These effects merit further study. We assume that if the vacuum alignment is such that the condensate (78) does form, it does so at a scale somewhat below and hence does not significantly weaken the effective SU(3) interaction at the scale . The formation of the condensate (78) does have a positive role, since if this did not happen, then the resultant low-energy effective field theory operative below would contain three light Dirac color-triplet, electroweak-singlet fermions constructed from the six chiral fermions and , . Experimentally, such states are excluded, with lower limits of order several hundred GeV, depending on details of the signatures of the production and decays GeV pdg ; ess .
Written in vectorlike form, the SU(3) gauge interaction has three Dirac fermions transforming as the fundamental representation of this group. This number is well below the estimated critical number beyond which the theory would evolve into the infrared without spontaneously breaking chiral symmetry (see Appendix for further discussion). It follows that, as the reference scale decreases through a scale denoted , the SU(3) interaction gets sufficiently strong to cause condensation in the channel , which is the most attractive channel, with condensate
breaking to the diagonal subgroup, SU(3). This condensation channel has an attractiveness measure with respect to the SU(3) gauge interaction. The fermions involved in this condensate get dynamical masses of order and the gauge bosons (often called colorons) in the coset gain masses (where the running couplings and are evaluated at ). The model is arranged so that
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