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http://www.ams.org/books/conm/321/
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math
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Trends in Banach Spaces and Operator Theory
About this Title
Anna Kamińska, Editor
This volume contains proceedings of the conference on Trends in Banach Spaces and Operator Theory, which was devoted to recent advances in theories of Banach spaces and linear operators.
Included in the volume are 25 papers, some of which are expository, while others present new results. The articles address the following topics: history of the famous James' theorem on reflexivity, projective tensor products, construction of noncommutative $L_p$-spaces via interpolation, Banach spaces with abundance of nontrivial operators, Banach spaces with small spaces of operators, convex geometry of Coxeter-invariant polyhedra, uniqueness of unconditional bases in quasi-Banach spaces, dynamics of cohyponormal operators, and Fourier algebras for locally compact groupoids.
The book is suitable for graduate students and research mathematicians interested in Banach spaces and operator theory and their applications.
Graduate students and research mathematicians interested in Banach spaces and operator theory and their applications.
Table of Contents
- María D. Acosta, Julio Becerra Guerrero and Manuel Ruiz Galán – Characterizations of the reflexive spaces in the spirit of James’ Theorem [MR 1978803]
- Fernando Albiac, Nigel J. Kalton and Camino Leránoz – Uniqueness of unconditional bases in quasi-Banach spaces [MR 1978804]
- George Androulakis – A note on the method of minimal vectors [MR 1978805]
- Joe Diestel, Jan Fourie and Johan Swart – The projective tensor product. I [MR 1978806]
- S. J. Dilworth and Vladimir G. Troitsky – Spectrum of a weakly hypercyclic operator meets the unit circle [MR 1978807]
- Nathan S. Feldman – The dynamics of cohyponormal operators [MR 1978808]
- Eva A. Gallardo-Gutiérrez and María J. González – Hilbert-Schmidt composition operators on Dirichlet spaces [MR 1978809]
- N. J. Kalton – A remark on sectorial operators with an $H^\infty $-calculus [MR 1978810]
- Jun Kawabe – Borel injective tensor product and convolution of vector measures and their weak convergence [MR 1978811]
- V. A. Khatskevich and V. S. Shulman – On linear operator pencils and inclusions of images of balls [MR 1978812]
- Denny H. Leung and Wee-Kee Tang – Ordinal indices and $l^1$-spreading models [MR 1978813]
- Julián López-Gómez and Carlos Mora-Corral – Characterizing the existence of local Smith forms for $\scr C^\infty $ families of matrix operators [MR 1978814]
- Nicholas McCarthy, David Ogilvie, Nahum Zobin and Veronica Zobin – Convex geometry of Coxeter-invariant polyhedra [MR 1978815]
- Jie Miao – Commutators on bounded symmetric domains in $\Bbb C^n$ [MR 1978816]
- T. L. Miller, V. G. Miller and M. M. Neumann – Growth conditions and decomposable extensions [MR 1978817]
- Jennifer Moorhouse and Carl Toews – Differences of composition operators [MR 1978818]
- Gustavo A. Muñoz – Complex vs real variables for real 3-homogeneous polynomials on $l_1^2$: a counterexample [MR 1978819]
- Alan L. T. Paterson – The Fourier-Stieltjes and Fourier algebras for locally compact groupoids [MR 1978820]
- Gabriel T. Prǎjiturǎ – Preserving the commutant under functional calculus [MR 1978821]
- Yves Raynaud – $L_p$-spaces associated with a von Neumann algebra without trace: a gentle introduction via complex interpolation [MR 1978822]
- Haskell P. Rosenthal – Banach and operator space structure of $C^*$-algebras [MR 1978823]
- Th. Schlumprecht – How many operators exist on a Banach space? [MR 1978824]
- Geoffrey V. Wood – Maximal algebra norms [MR 1978825]
- András Zsák – On Banach spaces with small spaces of operators [MR 1978826]
- Artem Zvavitch – A remark on $p$-summing norms of operators [MR 1978827]
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CC-MAIN-2022-27
| 3,789 | 33 |
https://www.teacherspayteachers.com/Product/Back-to-School-6th-Grade-Math-1960438
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math
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This “Back to School” resource reviews various concepts taught in 5th grade math.
The 8 student pages include:
1. Evaluate expressions with grouping symbols.
2. Use exponents to denote powers of 10.
3. Compare two decimals to thousandths.
4. Round decimals to any place.
5. Multiply and divide whole numbers.
6. Add, subtract, multiply and divide decimals to hundredths.
7. Add, subtract, multiply and divide fractions.
8. Find the volume of rectangular prisms.
9. Plot points in the first quadrant.
10. Classify two dimensional figures.
Common Core Standards:
5.NBT.2, 3, 4, 5, 6, 7
5.NF.1, 4, 7
You may choose to use the entire resource at the beginning of school, or you may use the pages separately to review before you teach a related concept in 6th grade math. There are eight student pages in the resource.
Click on a title below for additional 6th grade math resources.
Math Board Games Bundle - 6th Grade - (6.RP) (6.NS) (6.EE) (6.G) (6.SP)
Common Core Math 6th Grade Geometry 6.G.1 Area Parallelogram Triangle Activities
Common Core Math 6th Grade Geometry 6.G.4 Surface Area Prisms
Common Core Math 6th Grade Expressions (6.EE.2a,b,c) with I Have-Who Has Game
Common Core Math 6th Grade Equivalent Expressions (6.EE.3,4) with I Have-Who Has
Common Core Math 6th Grade Equations/Inequalities Write Expressions (6.EE.5.6)
Common Core Math 6th Grade - Solve Equations - Graph Inequalities (6.EE.7,8)
Common Core Math Activities 6th Grade (6.EE.9) Tables, Graphs, Equations
Common Core Math 6th Grade Ratios and Proportional Relationships 6.RP.1.2.3ab
Common Core Math 6th Grade Ratios and Proportional Relationships 6.RP.3cd
6th Grade Math - Ratios, Rational Numbers, Expressions, Statistics
Common Core Math 6th Grade - Statistics and Probability - CCSS 6.SP
Thanks for viewing!
Created by Hilda Ratliff
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| 1,816 | 31 |
https://nrich.maths.org/public/leg.php?code=31&cl=2&cldcmpid=1889
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math
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Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
This is an adding game for two players.
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Choose a symbol to put into the number sentence.
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
If you have only four weights, where could you place them in order to balance this equaliser?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
This challenge extends the Plants investigation so now four or more children are involved.
You have 5 darts and your target score is 44. How many different ways could you score 44?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?
Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
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?
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
Find the sum of all three-digit numbers each of whose digits is odd.
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.
Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.
Ben has five coins in his pocket. How much money might he have?
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
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?
Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?
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!
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
Can you substitute numbers for the letters in these sums?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
These two group activities use mathematical reasoning - one is numerical, one geometric.
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Try out this number trick. What happens with different starting numbers? What do you notice?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
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.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
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| 6,604 | 50 |
https://realitypanel.com/list-of-ordinary-top-numbers/
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math
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A prime quantity chart is a chart that shows a listing of top numbers in an arranged order. It should be stated that all top numbers are odd numbers beside the range 2 which is a fair range. Interestingly, 2 is the simplest prime number this is even. This method that the listing of strange numbers may be continued beginning from 3 because the remaining top numbers are abnormal. For instance, 3, five, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, forty seven, 53, fifty nine, 61, sixty seven, seventy one, 73, seventy nine, 83, 89, And so are odd high numbers. Click here https://caresclub.com/
Records Of Top Numbers
Prime numbers have aroused human interest when you consider that historic instances. Even these days, mathematicians are searching for high numbers with mysterious homes. Euclid proposed the theory of top numbers – there are infinitely many high numbers.
Get to know more about various subjects 70 inches in cm
Do you understand all the high numbers from 1 to a hundred? Did you check if each number is divisible through the smaller numbers? Eratosthenes changed into one of the greatest scientists who lived a few a long time after Euclid. He devised a smart way to decide all of the top numbers as much as a given variety. This approach is called the Sieve of Eratosthenes. Let us study the Sieve of Eratosthenes in the following section.
Sieve Of Eratosthenes
The Sieve of Eratosthenes is an ancient set of rules used to discover high numbers up to any range. The following discern suggests the high numbers as much as 100 which can be observed using the Sieve of Eratosthenes. The numbers without crosses in the figure constitute the top numbers that can be left after using the Sieve of Eratosthenes.
Suppose we need to find the top numbers as much as ‘n’, so we can list all of the numbers from 2 to n. The following steps show the way to find all top numbers as much as 100 the usage of the Sieve of Eratosthenes.
- Step 1: First make a list of numbers from 2 to a hundred as shown above. We leave out the number 1 because all top numbers are extra than 1.
- Step 2: We start with the primary number 2 inside the listing. We cut out every variety that may be more than one of 2 besides 2. For instance, we round as many as a hundred as four, 6, eight, 10, 12, 14, sixteen, and so forth.
- Step 3: Then, circulate directly to the following uncrossed number that’s 3. Cut off each range that may be a couple of 3 except 3. This will consist of some of the multiples which can be already crossed out. So we traverse the rest. For example, 9, 15, 21, and so on until 100.
- Step 4: Then, we circulate on to the next unsorted number in the listing after three which is 5. Truncate every range that’s more than one of five besides 5. This will consist of some multiples which can be already crossed out. So we traverse the rest. For example, 25, 35, 55, and so on till one hundred.
- Step five: Next in the listing after 7, five is the unnumbered variety. Therefore, truncate every wide variety that is more than one of seven besides 7. This will include a few multiples which might be already crossed out. So we traverse the rest. For instance, 49. After this step, we will be left with the best high numbers. In different words, the Sieve of Eratosthenes filters out all numbers, and only primes are left in the back. In the Sieve of Eratosthenes above, take a look at the numbers that are crossed out and those that are left as primes.
Smallest High Number
The smallest top variety is two. Interestingly, it’s miles the simplest even wide variety that could be a high quantity. It must be noted that 1 is neither a top nor a composite number because it has only 1 aspect which is 1, therefore, it’s far a uniquely wide variety.
Even Top Quantity
The handiest prime number which is a fair quantity is 2. This approach that everyone even numbers are composite numbers. 2 is a prime wide variety because it has the most effective 2 elements 1 and the wide variety itself 2.
Best High Number
The biggest top range cannot be indexed because the numbers are endless and the largest top cannot be decided.
Important Tips On Prime Numbers
The best even top number is two.
The first five top numbers are 2, three, five, 7, and eleven.
Not all top numbers are extraordinary. This is because 2 is a fair number and additionally a high range. In reality, 2 is the most effective even with high variety.
1 is neither a high variety nor a composite number.
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CC-MAIN-2023-14
| 4,478 | 24 |
https://cvgmt.sns.it/paper/4001/
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math
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Inserted: 10 aug 2018
Last Updated: 10 aug 2018
Journal: Journal of Convex Analysis
In this paper we analyze the concentration phenomena which occur in thin rods, solving the following optimization problem: a given fraction of elastic material must be distributed into a cylindrical design region with infinitesimal cross section in an optimal way, so that it maximizes the resistance to a given external load. For small volume fractions, the optimal configuration of material is described by a measure which concentrates on 2-rectifiable sets. For some choices of the external charging, the concentration phenomena turn out to be related to some new variants of the Cheeger problem of the cross section of the rod. The same study has already been carried out in the particular case of pure torsion regime in G. Bouchitté, I. Fragalà, I. Lucardesi, P. Seppecher: Optimal thin torsion rods and Cheeger sets, SIAM J. Math. Anal. 44 (2012). Here we extend those results by enlarging the class of admissible loads.
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CC-MAIN-2024-10
| 1,012 | 4 |
http://slideplayer.com/slide/4336937/
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math
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Presentation on theme: "Statistics Measures of Regression and Prediction Intervals."— Presentation transcript:
Statistics Measures of Regression and Prediction Intervals
Warm-up What value of “r” below best describes the scatterplot below? a) 0.9 b) -0.9 c) 0.3 d) -0.3 e) 0
Warm-up A least squares regression equation was created from last year’s students data to predict Exam 3 scores based on Exam 1 scores. The equation was: a) 69.70 b) 79.89 c) 85.53 d) 89.33 e) 90.53 Predict the score on Exam 3 for a student that scored an 80 on Exam 1.
Objectives Interpret the three types of variation about a regression line Find and interpret the coefficient of determination Find and interpret the standard error of the estimate for a regression line
Variation About a Regression Line Three types of variation about a regression line Total variation Explained variation Unexplained variation To find the total variation, you must first calculate The total deviation The explained deviation The unexplained deviation
Variation About a Regression Line (x i, ŷ i ) x y (x i, y i ) Unexplained deviation Total deviation Explained deviation Total Deviation = Explained Deviation = Unexplained Deviation =
Total variation The sum of the squares of the differences between the y-value of each ordered pair and the mean of y. Explained variation The sum of the squares of the differences between each predicted y-value and the mean of y. Variation About a Regression Line Total variation = Explained variation =
Unexplained variation The sum of the squares of the differences between the y-value of each ordered pair and each corresponding predicted y-value. Variation About a Regression Line Unexplained variation = The sum of the explained and unexplained variation is equal to the total variation. Total variation = Explained variation + Unexplained variation
Coefficient of Determination Coefficient of determination The ratio of the explained variation to the total variation. Denoted by r 2
Example: Coefficient of Determination About 83.4% of the variation in the company sales can be explained by the variation in the advertising expenditures. About 16.9% of the variation is unexplained. The correlation coefficient for the advertising expenses and company sales data as calculated is r ≈ 0.913. Find the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation? Solution :
The Standard Error of Estimate Standard error of estimate The standard deviation of the observed y i -values about the predicted ŷ-value for a given x i -value. Denoted by s e. The closer the observed y-values are to the predicted y- values, the smaller the standard error of estimate will be. n is the number of ordered pairs in the data set
The Standard Error of Estimate 1.Make a table that includes the column heading shown. 2.Use the regression equation to calculate the predicted y-values. 3.Calculate the sum of the squares of the differences between each observed y-value and the corresponding predicted y-value. 4.Find the standard error of estimate. In WordsIn Symbols
Example: Standard Error of Estimate The regression equation for the advertising expenses and company sales data is ŷ = 50.729x + 104.061 Find the standard error of estimate. Solution: Use a table to calculate the sum of the squared differences of each observed y-value and the corresponding predicted y-value.
Standard error of Estimate Related to unexplained variation (residuals) It is a measurement of the variation of the points about the regression line. s e = 0, r = 1 or -1, a perfect relation exists. The larger the s e, the more variability exists and the lower the quality of the relationship.
Solution: Standard Error of Estimate n = 8, Σ(y i – ŷ i ) 2 = 635.3463 The standard error of estimate of the company sales for a specific advertising expense is about $10.29.
Summary Interpreted the three types of variation about a regression line Found and interpreted the coefficient of determination Found and interpreted the standard error of the estimate for a regression line
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CC-MAIN-2018-26
| 4,215 | 18 |
https://forums.catholic.com/t/if-you-could-5-questions-to-answer/609109
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math
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1.)Go one place where would it be?
2.)Do one thing what would it be?
3.)Gain one thing what would it be?
4.) Meet one person who would that be?
5.)Possess one thing what would it be?
1.)Heaven for sure, Bora Bora (Thanks adam—Switzerland as well) 2.)Swim with dolphins or sky dive 3.)wisdom 4.)God 5.)an indoor in ground swimming pool
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CC-MAIN-2020-50
| 336 | 6 |
http://www.chegg.com/homework-help/questions-and-answers/use-tables-transforms-properties-find-ft-s-following-signals-problems-understanding-evalua-q3262744
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math
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Question: Use the tables of transforms and properties to fin...
Use the tables of transforms and properties to find the FT's of the
following signals: I am having problems understanding how to
evaluate this. Please be thorough when possible, I am having
problems knowing why its 5-w/pi for pi
No answer yet. Submit this question to the community.
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s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738663308.86/warc/CC-MAIN-20160924173743-00054-ip-10-143-35-109.ec2.internal.warc.gz
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CC-MAIN-2016-40
| 346 | 6 |
https://www.nystceexampracticetests.com/nystce-chemistry/
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math
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The NYSTCE Chemistry test measures your knowledge according to the New York State Academic Standards. Success on this test indicates that you are qualified to teach chemistry in the New York State public school system. The test content is drawn from these subareas: Foundations of Scientific Inquiry (19% of the exam); Matter and Atomic Structure (16%); Energy, Chemical Bonds, and Molecular Structure (16%); Chemical Reactions (16%); Stoichiometry and Solutions (13%); Interactions of Chemistry and the Environment (10%); and a Foundations of Scientific Inquiry constructed-response question (10%). The test consists of approximately 90 multiple-choice questions and one constructed-response question.
NYSTCE Chemistry Practice Questions
1. How many bonding pairs of electrons are there in Cl2?
2. What are the columns in the Periodic Table called?
3. What kind of spin do unpaired electrons in degenerate orbitals have?
4. What is the SI unit of energy?
5. Which of the following colors is composed of waves with the longest wavelengths?
1. A. A bonding electron has an orbit that extends around the entire molecule.
2. C. Each group in the Periodic Table is composed of elements with similar attributes.
3. D. Degenerate orbitals have the same energy level.
4. B. A joule is the amount of energy that is expended (equal to the work that is performed) when a one-newton force acts over a distance of one meter.
5. B. The basic spectrum in order of descending wavelength is red, orange, yellow, green, blue, indigo, and violet.
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CC-MAIN-2018-47
| 1,528 | 12 |
https://xenforo.com/community/threads/why-is-it-called-xenforo-anyway.982/
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math
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Thanks DSF, So is that the Xen which they mean (virtual-machine monitor)? or they mean something else? I just can't get the full meaning in XenForo that XF team intended to have it in the name of this forum.
And what does the prefix 'xeno' or 'xenos' mean?
Does it mean: foreign, stranger as it stated HERE?
If so, then the meaning of XenForo is something like: "Unique Forum", "Out Standing Forum" Or "Alien Forum ", right?
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CC-MAIN-2018-51
| 424 | 4 |
https://howto.org/how-to-calculate-the-internal-rate-of-return/
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math
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For learning how to compute IRR, we will take an example. Let’s assume initial investment is $5000, and return for first year be $500, second year be $750, third year be $1000, fourth year be $1750, fifth year be $2500.
How to calculate IRR:
- Make a sheet in Excel, where Value corresponding to CF0 (Initial Cash Flow) will be the value of investment, CF1 will be the returns at the end of 1st year, CF2 will be the returns at the end of 2nd year and so on. By inputting these values you will get something like this:
Note:- Initial investment is to be negative because of the fact that initially there was an outflow of Cash instead of an inflow.
- Now we have to use IRR formula to compute the IRR. We will use the following formula:-
- By applying this formula we will get our IRR. In the example we have taken IRR is 7%.
- In case of loss/Negative result in any year, we will input cash flow for that year with a negative sign (-).
- Negative IRR means that a company is unable to recover its cost over the period of time.
- In case profitability of any asset is to be computed, then residual value of asset is to be added in last year’s profit only. For example In the above example asset from whom such returns were generated is sold for $500, then we will add this value in CF5. In case you mentioned that amount in next cell, whole answer will change and Formula will assume such cash flow from year 6.
What is the formula for calculating internal rate of return?
It is calculated by taking the difference between the current or expected future value and the original beginning value, divided by the original value and multiplied by 100.
How do you calculate IRR quickly?
So the rule of thumb is that, for “double your money” scenarios, you take 100%, divide by the # of years, and then estimate the IRR as about 75-80% of that value. For example, if you double your money in 3 years, 100% / 3 = 33%. 75% of 33% is about 25%, which is the approximate IRR in this case.
How do you calculate IRR and NPV?
The IRR Formula
Broken down, each period’s after-tax cash flow at time t is discounted by some rate, r. The sum of all these discounted cash flows is then offset by the initial investment, which equals the current NPV. To find the IRR, you would need to “reverse engineer” what r is required so that the NPV equals zero.
What is IRR with example?
IRR is the rate of interest that makes the sum of all cash flows zero, and is useful to compare one investment to another. In the above example, if we replace 8% with 13.92%, NPV will become zero, and that’s your IRR. Therefore, IRR is defined as the discount rate at which the NPV of a project becomes zero.
What are the rules of IRR?
The internal rate of return (IRR) rule states that a project or investment should be pursued if its IRR is greater than the minimum required rate of return, also known as the hurdle rate. The IRR Rule helps companies decide whether or not to proceed with a project.
What is a good IRR percentage?
If you were basing your decision on IRR, you might favor the 20% IRR project. But that would be a mistake. You’re better off getting an IRR of 13% for 10 years than 20% for one year if your corporate hurdle rate is 10% during that period.
Is NPV or IRR better?
In other words, long projects with fluctuating cash flows and additional investments of capital may have multiple distinct IRR values. If a discount rate is not known, or cannot be applied to a specific project for whatever reason, the IRR is of limited value. In cases like this, the NPV method is superior.
Is ROI the same as IRR?
ROI indicates total growth, start to finish, of an investment, while IRR identifies the annual growth rate. While the two numbers will be roughly the same over the course of one year, they will not be the same for longer periods.
Can IRR be more than 100%?
There’s nothing special about 100%. For one thing, it depends on the time horizon. 100% is a day is a very high IRR, 100% in a century is very low. Or over a year, for example, if a $1 investment returns $2 at the end, that’s 100%; but it’s not significantly different from an investment that returns $1.99 or $2.01.
What does a 100% IRR mean?
If you invest 1 dollar and get 2 dollars in return, the IRR will be 100%, which sounds incredible. In reality, your profit isn’t big. So, a high IRR doesn’t mean a certain investment will make you rich. However, it does make a project more attractive to look into.
What are the problems with IRR?
A disadvantage of using the IRR method is that it does not account for the project size when comparing projects. Cash flows are simply compared to the amount of capital outlay generating those cash flows.
What if IRR is greater than NPV?
Level 1 CFA Exam Takeaways For NPV and IRR
NPV equals the sum of present values of all cash flows in a project (both inflows and outflows). If the NPV is greater than zero, the project is profitable. If the IRR is higher than the required return, you should invest in the project.
Why does IRR set NPV to zero?
As we can see, the IRR is in effect the discounted cash flow (DFC) return that makes the NPV zero. This is because both implicitly assume reinvestment of returns at their own rates (i.e., r% for NPV and IRR% for IRR).
What is the conflict between IRR and NPV?
In capital budgeting, NPV and IRR conflict refers to a situation in which the NPV method ranks projects differently from the IRR method. In event of such a difference, a company should accept project(s) with higher NPV.
What is difference between NPV and IRR?
What Are NPV and IRR? Net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time. By contrast, the internal rate of return (IRR) is a calculation used to estimate the profitability of potential investments.
How does reinvestment affect both NPV and IRR?
The NPV has no reinvestment rate assumption; therefore, the reinvestment rate will not change the outcome of the project. The IRR has a reinvestment rate assumption that assumes that the company will reinvest cash inflows at the IRR’s rate of return for the lifetime of the project.
What is IRR NPV calculator?
IRR is independent of the Discount Rate. To calculate NPV, enter a discount rate which may be your cost of borrowing rate. Discount Cash Flow Rate of Return Analysis is a very useful tool to help you analyze your investment projects.
Can IRR be positive if NPV negative?
Nope, you can‘t get a positive return on a money losing project. If, for example, there are some tax benefits to be gained from write offs and such, you should be incorporating those into the NPV, which may then become positive, then calculating a positive IRR.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474653.81/warc/CC-MAIN-20240226062606-20240226092606-00568.warc.gz
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CC-MAIN-2024-10
| 6,768 | 47 |
http://www.e-booksdirectory.com/details.php?ebook=8263
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math
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Notes on Symmetric Spaces
by Jonathan Holland, Bogdan Ion
Publisher: arXiv 2012
Number of pages: 109
Contents: Affine connections and transformations; Symmetric spaces; Orthogonal symmetric Lie algebras; Examples; Noncompact symmetric spaces; Compact semisimple Lie groups; Hermitian symmetric spaces; Classification of real simple Lie algebras.
Home page url
Download or read it online for free here:
by Gerhard Knieper, Norbert Peyerimhoff - arXiv
We provide a survey on recent results on noncompact simply connected harmonic manifolds, and we also prove many new results, both for general noncompact harmonic manifolds and for noncompact harmonic manifolds with purely exponential volume growth.
by Paul Bracken (ed.) - InTech
Differential geometry is a very active field of research and has many applications to areas such as physics and gravity, for example. The papers in this book cover a number of subjects which will be of interest to workers in these areas.
by M. Kuranishi - Tata Institute of Fundamental Research
Contents: Parametrization of sets of integral submanifolds (Regular linear maps, Germs of submanifolds of a manifold); Exterior differential systems (Differential systems with independent variables); Prolongation of Exterior Differential Systems.
by Paul Loya - Binghamton University
This is a lecture-based class on the Atiyah-Singer index theorem, proved in the 60's by Sir Michael Atiyah and Isadore Singer. Their work on this theorem lead to a joint Abel prize in 2004. Requirements: Knowledge of topology and manifolds.
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CC-MAIN-2019-51
| 1,549 | 15 |
https://advancesindifferenceequations.springeropen.com/articles/10.1155/2010/103065
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math
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- Research Article
- Open Access
Oscillation of Second-Order Sublinear Dynamic Equations with Damping on Isolated Time Scales
© Q. Lin and B. Jia. 2010
- Received: 8 October 2010
- Accepted: 27 December 2010
- Published: 30 December 2010
This paper concerns the oscillation of solutions to the second sublinear dynamic equation with damping , on an isolated time scale which is unbounded above. In , α is the quotient of odd positive integers. As an application, we get the difference equation , where , , and is any real number, is oscillatory.
- Dynamic Equation
- Difference Equation
- Jump Operator
- Part Formula
- Closed Nonempty Subset
During the past years, there has been an increasing interest in studying the oscillation of solution of second-order damped dynamic equations on time scale which attempts to harmonize the oscillation theory for continuousness and discreteness, to include them in one comprehensive theory, and to eliminate obscurity from both. We refer the readers to the papers [1–4] and the references cited therein.
In , under the assumption of being an isolated time scale, we prove that, when is allowed to take on negative values, is sufficient for the oscillation of the dynamic equation (1.3). As an application, we get that, when is allowed to take on negative values, is sufficient for the oscillation of the dynamic equation (1.4), which improves a result of Hooker and Patula [7, Theorem 4.1] and Mingarelli .
where , , , and is any real number, is oscillatory.
Note that if , then the delta derivative is just the standard derivative, and when the delta derivative is just the forward difference operator. Hence, our results contain the discrete and continuous cases as special cases and generalize these results to arbitrary time scales (e.g., the time scale which is very important in quantum theory ).
We will need the following second mean value theorem (see [10, Theorem 5.45]).
Lemmas 2.2 and 2.4 give two lower bounds of definite integrals on time scale, respectively.
It is easy to know that, when , and, when , .
Assume that , where . Suppose that
(i)there exists a real number such that , for all ;
Then, (1.1) is oscillatory.
Since , we get , for large , which is a contradiction. Thus, (1.1) is oscillatory.
is sufficient for the oscillation of the difference equation (1.4).
then (1.4) is oscillatory.
where . It is easy to get the following.
Then, the differential equation (3.16) is oscillatory.
where , , , and is any real number.
for large . That means . It is easy to get that and is nonincreasing for large . So from Theorem 3.1, (3.18) is oscillatory.
and is nonincreasing. So from Theorem 3.1, (3.21) is oscillatory.
where , , , and is any real number.
So from Theorem 3.3, (3.23) is oscillatory.
This work was supported by the National Natural Science Foundation of China (no. 10971232).
- Bohner M, Saker SH: Oscillation of damped second order nonlinear delay differential equations of Emden-Fowler type. Advances in Dynamical Systems and Applications 2006,1(2):163-182.MATHMathSciNetGoogle Scholar
- Han Z, Chen W, Sun S, Li T: Oscillation behavior of a class of second-order dynamic equations with damping on time scales. Discrete Dynamics in Nature and Society 2010, 2010:-15.Google Scholar
- Erbe L, Hassan TS, Peterson A: Oscillation criteria for nonlinear damped dynamic equations on time scales. Applied Mathematics and Computation 2008,203(1):343-357. 10.1016/j.amc.2008.04.038MATHMathSciNetView ArticleGoogle Scholar
- Saker SH, Agarwal RP, O'Regan D: Oscillation of second-order damped dynamic equations on time scales. Journal of Mathematical Analysis and Applications 2007,330(2):1317-1337. 10.1016/j.jmaa.2006.06.103MATHMathSciNetView ArticleGoogle Scholar
- Bohner M, Erbe L, Peterson A: Oscillation for nonlinear second order dynamic equations on a time scale. Journal of Mathematical Analysis and Applications 2005,301(2):491-507. 10.1016/j.jmaa.2004.07.038MATHMathSciNetView ArticleGoogle Scholar
- Erbe L, Baoguo J, Peterson A: Belohorec-type oscillation theorem for second ordersuperlinear dynamic equation on time scales. Mathematische Nachrichten. In pressGoogle Scholar
- Hooker JW, Patula WT: A second-order nonlinear difference equation: oscillation and asymptotic behavior. Journal of Mathematical Analysis and Applications 1983,91(1):9-29. 10.1016/0022-247X(83)90088-4MATHMathSciNetView ArticleGoogle Scholar
- Mingarelli AB: Volterra-Stieltjes integral equations and generalized differential equations, Ph.D. thesis. University of Toronto; 1983.Google Scholar
- Bohner M, Peterson A: Dynamic Equation on Time Scales: An Introduction with Applications. Birkhäuser, Boston, Mass, USA; 2001:x+358.View ArticleGoogle Scholar
- Bohner M, Peterson A (Eds): Advances in Dynamic Equations on Time Scales. Birkhäuser, Boston, Mass, USA; 2003:xii+348.MATHGoogle Scholar
- Kac V, Cheung P: Quantum Calculus. Springer, New York, NY, USA; 2002:x+112.MATHView ArticleGoogle Scholar
- Baoguo J, Erbe L, Peterson A: Oscillation of sublinear Emden-Fowler dynamic equations on time scales. Journal of Difference Equations and Applications 2010,16(2-3):217-226. 10.1080/10236190802631881MATHMathSciNetView ArticleGoogle Scholar
This article is published under license to BioMed Central Ltd. 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.
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CC-MAIN-2019-18
| 5,481 | 47 |
https://myweb4ed.symbaloo.com/mix/systemsofequations10
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math
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IXL - Solve a system of equa... Elimination method Systems of Inequalit Solve systems of equ Systems of Linear Equations:...Solving by Elimination IXL - Is (x, y) a solution? IXL - Solve a system of equa... Substitution method Systems of linear in Solve a system by Substituti... Solving by Graphing Graphing Equations Using Alg...
Systems of Equations
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s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362891.54/warc/CC-MAIN-20211203151849-20211203181849-00065.warc.gz
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CC-MAIN-2021-49
| 352 | 2 |
https://ems.press/journals/pm/articles/12080
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math
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This paper is concerned with the existence of solutions to the class of nonlocal boundary value problems of the type
where is a smooth bounded domain of and is a positive continuous function. By assuming that is a Carathéodory function which growths at most , , and under a suitable growth condition on , one proves an existence result by applying the Leray–Schauder fixed point theorem.
Cite this article
Anderson L.A. de Araujo, Another approach on an elliptic equation of Kirchhoff type. Port. Math. 70 (2013), no. 1, pp. 11–22DOI 10.4171/PM/1923
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CC-MAIN-2023-50
| 554 | 4 |
https://imj.ut.ac.ir/article_20362.html?lang=en
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math
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This paper presents a combination of Data Envelopment Analysis (DEA) and Principal Component Analysis (PCA) to reduce the dimensionality of data set. DEA is known as effective tool for assessment and benchmarking. The weak point of DEA, it is that the number of efficient DMUs relies on the number of variables (inputs and outputs). For solving this, first, we do principal component analysis (PCA) on the ratios of a single output to a single input. In order to reduce the dimensionality of data set, the required principal components have been selected from the generated ones according to the given choice principle. Then a linear monotone increasing data transformation is made to the chosen principal components to avoid being negative. Finally, the transformed principal components are treated as outputs into data envelopment analysis (DEA) models. One of the main differences of this model versus previous models is that this one's multi objective model. We used this approach to rank the bank branches of Tehran.
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CC-MAIN-2024-10
| 1,021 | 1 |
https://detmagazine.ru/7-step-problem-solving-model-373.html
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math
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b) When things keep going wrong no matter how hard everyone tries.c) When everyone believes that there is a problem to solve.Not all decisions need to be made by teams nor do all problems need to be solved by groups.Tags: Bibliography In Research PaperI Need Help With My Math HomeworkQuarterly Essay George PellWriting A Literature Review OutlineRental House Application Cover LetterHow To Write A Memoir Essay ExamplesEnglish As A Medium Of Instruction In Pakistan Essay
These ten steps are effective with most of the problems the team will encounter.
Each step is discussed here, and end products for step completion are specified as check points for team progress.
Often the PFD can dramatically help define the problem.
After the problem is well defined, Step 2 helps the team measure the extent of the problem.
The Problem Solving Model provides you a road map to continuous improvement.
As its name implies, this model is the road map to follow to solve problems. a) When the process isn't doing what it is supposed to and people don't know why.
The first step in the model is to define the problem; it does not matter if it is late shipments, stock outs, computer downtime, typos, lost messages, or an agreed upon "red bead" that everyone keeps running into.
Before you can solve the problem, you must truly understand what it is.
Before we begin a discussion about the steps of the problem-solving model, we should talk a little about the philosophy that good problem solvers have about problems.
Here are a number of ideas that are part of the philosophy.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988763.83/warc/CC-MAIN-20210506205251-20210506235251-00419.warc.gz
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CC-MAIN-2021-21
| 1,565 | 11 |
http://www.emra-net.eu/download-pdf-illustrated-hawaiian-dictionary-book-by-bess-press.pdf
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math
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Serves as a useful resource for beginning speakers and students of the Hawaiian language and for those interested in Hawaiian language, history, and culture. This dictionary contains features that include: over 5, 000 entries in Hawaiian and English; an additional 2, 500 synonyms and related words and phrases; grammar notes; and more.[a#39;Ehia mele Hawaia#39;i i himeni a#39;ia ma ka a#39;aha mele a#39;o Kanikapila? How many Hawaiian songs were sung at the Kanikapila concert?] conclusion ... 2. pohihihi. congratulate hoa#39;omaikaa#39;i. congratulations hoa#39;omaikaa#39;i. ... pau ka a#39;ike, kauhola; regain consciousness = pohala, ao) consent a#39;ae (also means to agree, allow, say yes to).
|Title||:||Illustrated Hawaiian Dictionary|
|Publisher||:||Bess Press - 2005-01|
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s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988720475.79/warc/CC-MAIN-20161020183840-00158-ip-10-171-6-4.ec2.internal.warc.gz
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CC-MAIN-2016-44
| 784 | 3 |
https://macdownload.informer.com/Tg/equation-copier/
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math
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Log in / Sign up
Edit an equation in Equation Editor. If you used Equation Editor to insert an equation...
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http://quellish.blogspot.com/2002/11/argh.html
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math
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Friday, November 29, 2002
Argh. Seems my powerbook's hinge is fubar after Ethan decided to play tug of war with it last night before we put it back safely in the car. Hopefully I can get it to stay intact till I can get to it with a Torx.
[ 11/29/2002 12:07:00 PM ] [
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| 270 | 3 |
https://kunduz.com/questions/what-volume-of-hydrogen-gas-at-standard-conditions-stp-can-be-liberated-by-the-reaction-of-sulfuric-acid-with-0067-g-mg-write-a-balanced-equation-for-the-reaction-determine-the-volume-of-h-liberated-in-a-different-64475/
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math
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What volume of hydrogen gas, at standard conditions (STP),
Last updated: 8/7/2022
What volume of hydrogen gas, at standard conditions (STP), can be liberated by the reaction of sulfuric acid with 0.067 g Mg? Write a balanced equation for the reaction? Determine the volume of H₂ liberated? In a different trial but same experiment, calculate the mass of magnesium metal that should be used to generate 50.0 mL of H₂ at standard conditions.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499899.9/warc/CC-MAIN-20230201013650-20230201043650-00275.warc.gz
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CC-MAIN-2023-06
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https://arbital.greaterwrong.com/p/bayes_rule_elimination?l=1y6
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math
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Belief revision as probability elimination
One way of understanding the reasoning behind Bayes’ rule is that the process of updating \(\mathbb P\) in the face of new evidence can be interpreted as the elimination of probability mass from \(\mathbb P\) (namely, all the probability mass inconsistent with the evidence).
You are screening a set of patients for a disease, which we’ll call Diseasitis. You expect that around 20% of the patients in the screening population start out with Diseasitis. You are testing for the presence of the disease using a tongue depressor with a sensitive chemical strip. Among patients with Diseasitis, 90% turn the tongue depressor black. However, 30% of the patients without Diseasitis will also turn the tongue depressor black. One of your patients comes into the office, takes your test, and turns the tongue depressor black. Given only that information, what is the probability that they have Diseasitis? <div>
In the situation with a single, individual patient, before observing any evidence, there are four possible worlds we could be in:
To observe that the patient gets a positive result, is to eliminate from further consideration the possible worlds where the patient gets a negative result, and vice versa:
So Bayes’ rule says: to update your beliefs in the face of evidence, simply throw away the probability mass that was inconsistent with the evidence.
Example: Socks-dresser problem
Realizing that observing evidence corresponds to eliminating probability mass and concerning ourselves only with the probability mass that remains, is the key to solving the sock-dresser search problem:
You left your socks somewhere in your room. You think there’s a 4⁄5 chance that they’ve been tossed into some random drawer of your dresser, so you start looking through your dresser’s 8 drawers. After checking 6 drawers at random, you haven’t found your socks yet. What is the probability you will find your socks in the next drawer you check?
(You can optionally try to solve this problem yourself before continuing.)
We initially have 20% of the probability mass in “Socks outside the dresser”, and 80% of the probability mass for “Socks inside the dresser”. This corresponds to 10% probability mass for each of the 8 drawers (because each of the 8 drawers is equally likely to contain the socks).
After eliminating the probability mass in 6 of the drawers, we have 40% of the original mass remaining, 20% for “Socks outside the dresser” and 10% each for the remaining 2 drawers.
Since this remaining 40% probability mass is now our whole world, the effect on our probability distribution is like amplifying the 40% until it expands back up to 100%, aka renormalizing the probability distribution. Within the remaining prior probability mass of 40%, the “outside the dresser” hypothesis has half of it (prior 20%), and the two drawers have a quarter each (prior 10% each).
So the probability of finding our socks in the next drawer is 25%.
For some more flavorful examples of this method of using Bayes’ rule, see The ups and downs of the hope function in a fruitless search.
Extension to subjective probability
On the Bayesian paradigm, this idiom of belief revision as conditioning aon evidence works both in cases where there are statistical populations with objective frequencies corresponding to the probabilities, and in cases where our uncertainty is subjective.
For example, imagine being a king thinking about a uniquely weird person who seems around 20% likely to be an assassin. This doesn’t mean that there’s a population of similar people of whom 20% are assassins; it means that you weighed up your uncertainty and guesses and decided that you would bet at odds of 1 : 4 that they’re an assassin.
You then estimate that, if this person is an assassin, they’re 90% likely to own a dagger — so far as your subjective uncertainty goes; if you imagine them being an assassin, you think that 9 : 1 would be good betting odds for that. If this particular person is not an assassin, you feel like the probability that she ought to own a dagger is around 30%.
When you have your guards search her, and they find a dagger, then (according to students of Bayes’ rule) you should update your beliefs in the same way you update your belief in the Diseasitis setting — where there is a large population with an objective frequency of sickness — despite the fact that this maybe-assassin is a unique case. According to a Bayesian, your brain can track the probabilities of different possibilities regardless, even when there are no large populations and objective frequencies anywhere to be found, and when you update your beliefs using evidence, you’re not “eliminating people from consideration,” you’re eliminating probability mass from certain possible worlds represented in your own subjective belief state.
- Bayes' rule
Bayes’ rule is the core theorem of probability theory saying how to revise our beliefs when we make a new observation.
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https://books.google.co.ve/books?id=DPo2AAAAMAAJ&pg=PA201&vq=%22line+drawn+through+the+centre,+and+terminated+both+ways+by+the+circumference.+A%22&dq=related:ISBN8474916712&lr=&output=html_text
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math
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« AnteriorContinuar »
multiply the sum by the height, and the product again by 1.5708 for the folidity.
RULE 2. From the folidity of the whole sphere, fubtract the folidity of the segments ABC and DEF; the remainder is the folidity of the zone.
RULE 3. Add into one fum twice the square of the sphere's diameter, and the square of the diameter of the zone's base ; divide this sum by 3.8197, and multiply the quotient by the zone's height; the product is the soliditý.
By RULE I.
Ex. 2. Required the solidity of a zone, whose greater diameter is 2 feet, the less 1 foot 4 inches, and the height į foot 8 inches.
inf. 10723.328 inches. Ex. 3. What is the solid content of a zone, whose height is 30, and end diameters 60 and 40 inches?
Anf. 75398.4 cubic inches. Ex. 4. What is the solidity of a zone, whose height is 8 inches, and diameter of the ends 12 inches ?
Anf. 1172 864 cubic inches.
PROBLEM XVI. Fig. 96.
To find the area of a circular Spindle.
Multiply the length of the spindle by the radius of the revolving arch; again multiply the distance between the centre of the revolving arch and the centre of the spindle Iby the length
of the revolving arch ; subtract this last product from the former, and multiply the remainder by 6.2832 for the superficies.
EXAMPLE. Required the area of a circular spindle, whose length is 40 and thickness 30 inches.
AD2+BD- = AB the chord of the arch ABC; that is,
400+225 = 25
=DH and DH+BD=FB rad. also FB-BD=DF cent. dift.
=26.6 and 26.6+16=20.83 rad. also 20.83–15=5.83=DF 15
Then fay, As 360°: 147° 2 :: 3.1416 X 41.6:53.58 leng. of arch,
Or thus :
53.3 the arch nearly.
Ex. 2. Required the number of square inches which will cover a circular spindle, whose length is 80 and thickness 16 inches ?
Anf. 2747.3166 336. Ex. 3. Required the area of a circular spindle, whose length is 12, and thicknefs y inches.
Anf. 294.3621 sq. inches.
To find the solidity of a circular spindle.
Multiply the area of the revolving segment by the distance between the centres of the arch and spindle, subtract the prcduct from the cube of half the length of the spindle, then multiply the remainder by 4, and this product again by 3.1416 for the solidity. See the last figure.
Required the area of a circular spindle, whose length is 60 and diameter 4). Dd
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https://lonacyv.web.app/62324/58500.html
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math
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OH = cos 270° = cos (3 /2) = 0: A trecentosessanta gradi e' come a zero gradi ed avremo che il coseno vale uno OH = cos 360° = cos 0° = 1: Riassumendo il valore del coseno parte dal valore 1 a 0° diminuisce fino a raggiungere il valore 0 a 90
The following example uses Cos to evaluate certain trigonometric identities for selected angles. // Example for the trigonometric Math.Sin( double ) // and Math.Cos( double ) methods. using namespace System; // Evaluate trigonometric identities with a given Apr 15, 2019 · The value of ∫ sin^3x/sin x + cos x ,x ∈[0, π/2] dx is : asked May 19, 2019 in Mathematics by Jagan (21.1k points) jee mains 2019 +1 vote. 1 answer.
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Thus, you are obtaining the value of (cosπ)/2=(−1)/2=−0.5. Nov 29, 2017 0 pi in degree form =180 =cos(180/2) =cos(90) =0. May 19, 2016 cos(π2)=0. Explanation: For an angle in standard position cos(θ)=xr (definition). From the images below, we can see that as θ→π2. XXXx→0. Oct 26, 2020 Compute cos(pi/2) with the unit circleIf you enjoyed this video please consider liking, sharing, and subscribing.Udemy 0:00 / 1:07.
Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.
cos ( π 6) = cos ( π 6) = 3 2. cos ( π 4) = cos ( π 4) = 2 2. cos ( π 3) = cos ( π 3) = 1 2.
pi/2*x-1=cos^-1 (0) This is asking you what angle has a cos value of 0 on the interval from 0 to pi, which is the domain of inverse cosine. pi/2 is the angle, so. pi/2*x-1=pi/2 Do some algebra to solve for x. pi/2*x= (pi/2)+1. pi/2*x= (pi/2)+2/2. (pi/2)x= (pi+2)/2.
Evaluate : ∫π/2 0 (sin^2 x)/(sinx+cosx)dx Aug 04, 2011 · cot(pi/2) = 1/tan(pi/2) = 1/undefined =/= 0 I don't see how the two are equal, and ya I think I may be getting some things mixed up as I haven't dealt with basic trig in several years lolz Aug 4, 2011 Feb 13, 2020 · Ex 3.3, 6 Prove that: cos (π/4−𝑥) cos (π/4−𝑦) – sin (π/4−𝑥) sin (π/4−𝑦) = sin(𝑥 + 𝑦) Taking L.H.S We know that cos (A + B) = cos A cos B – sin A sin B The equation given in Question is of this form Where A = (𝜋/4 −𝑥) B = (𝜋/4 −𝑦) Hence cos (π/4−𝑥) cos (π/4−𝑦) – sin (π Mar 01, 2018 · We observe that our cosine graph has amplitude `13.892` and it has been shifted to the right by `0.528` radians, which is consistent with the expression we obtained: 13.892 cos (θ − 0.528) 2. Express 2.348 sin θ − 1.251 cos θ in the form −R cos ( θ + α) , where 0 ≤ α < π/2. Find sin(u-pi), cos(u-pi), sin(u-pi/2), cos(u-pi/2) I tried solving this question but I could not get the right answer. Here are the step I tried for solving this problem.
8. 9. 9.. ÷.
Besides The cos of -pi/2 radians is 0, the same as cos of -pi/2 radians in degrees. Jul 15, 2020 cos2(0)+cos2(π6)+cos2(π3)+cos2(π2). check-circle. Answer. Step by step solution by experts to help you in doubt clearance & scoring Answer to Consider the folowing. lim x → 0+ [cos(pi/2-x)]^x Solved: simplify cos(pi/2-X) - Slader. MARKDOWN and KATEX.
By the definition of the functions of trigonometry, the sine of pi/2 is equal to the y-coordinate of the point with polar coordinates (r,theta)=(1,pi/2), giving sin(pi/2)=1. Similarly, cos(pi/2)=0, since it is the x-coordinate of this point. Filling out the other trigonometric functions then gives cos(pi/2) = 0 (1) cot(pi/2) = 0 (2) csc(pi/2) = 1 (3) sec(pi/2) = infty (4) sin(pi/2) = 1 (5) tan Definite Integrals - Integral of cos^2x / ( cos^2x + 4 sin^2x)`int _0^(pi/2) cos^2x/(cos^2x+4sin^2x) dx``int _0^(pi/2) cos^2x/(cos^2x+4sin^2x) dx`integral 0 24/10/2015 Click here👆to get an answer to your question ️ For 0 < ϕ < pi/2 if x = ∑n = 0^∞cos ^2nϕ, y = ∑n = 0^∞sin ^2nϕ, z = ∑n = 0^∞cos ^2nϕsin^2nϕ , then 14/01/2016 Question: In HW Item #5, The Final Answer Involves Cos(pi/2) = 0 O Cos(pi/2) = 1 O Sin(pi/2) = 0 Express In Terms Of Sine, Cosine, Or Tangent Of One Angle. Then Find The Exact Value. Зл TT Зл TT TT 5л TT 5л 5. COS COS + Sin Sin 6.
How do I get this value to revert to 0, which is the true value? Is sin always related to the y axis? I'm confused because if we look at angle theta + pi/2, why is it that sin doesn't have the opposite/hypotenuse definition Aug 1, 2019 Hi! While trying out some stuff in Julia, I came across the fact that cos(pi/2) does not give exact 0, but some type dependent output (6e-17 for limit as h->0 when [cos(pi/2+h)]/h when I sub in zeroI get 0/0so I have to use L' hopital's rule So I take the derivative of the numberator and cos(pi/2_=x/r=0/|y|= cos(3pi/2)=x/r=0/|y|. The trigonometric functional values of angles coterminal with 0, π/2 , π, and 3π/2 are the same as those above, and the Cos -Pi/2: All about cos minus Pi/2 radians, incl. the trigonometric identities.
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π 2 represents a quarter of a circle (90 ∘) wich corresponds to (0, 1) on the unit circle, i.e.
using namespace System; // Evaluate trigonometric identities with a given Apr 15, 2019 · The value of ∫ sin^3x/sin x + cos x ,x ∈[0, π/2] dx is : asked May 19, 2019 in Mathematics by Jagan (21.1k points) jee mains 2019 +1 vote.
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https://articles.cbseguess.com/others-2/techniques-to-use-in-solving-gmat-math-questions
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math
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Techniques To Use In Solving GMAT Math Questions
GMAT Math questions are given to test your understanding of the mathematical concepts than to test your ability to actually carry out quantitative procedures correctly. These questions are simple but test-writers often complicate these problems by altering the sentences and concealing its structure and intent, while preserving its behavior. They usually do this to deceive the testers. Be careful in making assumptions that you are not supposed to make. It is impossible to overstate the importance of careful reading.
There are techniques that can be used to solve these problems and can also be found on GMAT preparation guides. One of which is by reading the question several times might help understand the question. Try to put it into your own words if not, break them into parts until you get the correct thought. Be careful with traps. Some numbers or words are usually added to confuse the reader.
Another technique is back solving. This is done by substituting the answer choices to the given equation. For numerical answers, it is best to start with the middle choice then just go up or down based on the attempted result. Assume that the answer does not contain a variable and ensure that the numbers you chose don’t work on multiple equations.
Avoid unnecessary calculation. This will only waste precious time. You will go in circles, or worst, prompt you to the wrong answer. Do not solve for more than what is necessary. Know what is given and what is asked in the question. Do estimations if necessary. Some questions require lengthy g calculations. This is applicable if the answers are not close in value. The bottom line is that you need to be very careful when reading GMAT problems. Moreover, you must be precise and thoughtful when labeling your variables.
In problem solving questions, there are answers that can be eliminated right away. If you are running out of time, this is the best way to do it. Eliminate the obviously wrong answers and guess. Never leave a blank space. Your choice might be correct. Often, by simply determining the sign of the answer, whether it is positive or negative and the rough value of the answer, you can rule out an answer or two and improve your odds of guessing the correct answer.
The more time you spend practicing solving Math questions, the better able you will be to internalize the techniques given above. You will also become very comfortable with the type of questions. You will realize that there are many math areas where you need to master your skills. When the time comes that you will take the examination for the GMAT, you will already know what to do to perform well during the exam. Also, there are many GMAT study guide that are currently available to help you prepare for the examination.
About The Author
About The GMAT Bootcamp
The GMAT Bootcamp is a gmat preparation service based in Los Angeles. They serve students from a variety of industries and backgrounds and seek to provide the best GMAT preparation resources available. For additional articles and GMAT study material, visit www.thegmatbootcamp.com
The author invites you to visit: http://www.thegmatbootcamp.com
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https://www.chucks.com/items/incredible-seafood-cake-dinner
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math
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Back To Menu
"Incredible" Seafood Cake Dinner
Topped with our special chipotle aioli - 3 count.
(Select 1) Sides:Roasted Garlic Smashed Potato Baked Idaho Potato French Fries Baked Sweet Potato Broccoli/Herb Butter Vegetable of the Day Loaded Baked Potato +$3Loaded Mashed Potato +$3Loaded Cheesy Parmesan Fries +$3Sweet Potato Fries +$31/2 Order Grilled Zucchini and summer squash +$3
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https://lists.isc.org/pipermail/inn-bugs/2002-March/000855.html
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math
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[2.3.2] makehistory segfaults due to cnfs problems
Katsuhiro_Kondou at isc.org
Tue Mar 12 15:52:44 UTC 2002
In article <87it8s13e7.fsf at myrkr.in-berlin.de>,
Torsten Hilbrich <email at myrkr.in-berlin.de> wrote;
} I run "makehistory -O -F" and soon run into a segfault. Using a debug
} version of makehistory I noticed that the error occured in free, called
} from cnfs.c line 1523 (function cnfs_next):
It looks like the code is correct.
} By commenting out the DISPOSE line I was able to rebuild both the history
} file and the overview database.
It may work, but memory would be leaked. How about
setting true for articlemmap in inn.conf?
More information about the inn-bugs
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https://m.atlib.info/en/calc/pressure-transfer
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math
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Pressure converting calculator in bars per MPa, kgf and psi
Pressure is a quantity that is equal to the force acting strictly perpendicular to the unit surface area. Calculated by the formula: P = F/S. The international system of calculation assumes the measurement of such a value in pascals (1 Pa is equal to a force of 1 newton per area of 1 square meter, N / m2). But since this is a fairly small pressure, measurements are more often indicated in kPa or MPa. In various industries, it is customary to use their own numbering systems; in automotive, pressure can be measured: in bars, atmospheres, kilograms of force per cm² (technical atmosphere), mega pascals or pounds per square inch (psi).
To quickly convert units of measurement, you should focus on this relationship of values to each other:
1 MPa = 10 bar;
100 kPa = 1 bar;
1 bar ≈ 1 atm;
3 atm = 44 psi;
1 PSI ≈ 0.07 kgf/cm²;
1 kgf/cm² = 1 at.
|Pressure Ratio Table|
|1 atm (physical atmosphere)||0,10133||1,0133||1||1,0333||14,696||1.033227|
|1 at (technical atmosphere)||0.098066||0.980665||0.96784||1||14.223||1|
Why pressure unit conversion calculator is needed
The online calculator allows you to quickly and accurately convert values from one pressure measurement unit to another. Such a conversion can be useful for car owners when measuring compression in the engine, when checking the pressure in the fuel line, pumping tires to the required value (very often you have to convert PSI to atmosphere or MPa to bar when checking pressure), filling the air conditioner with freon. Since the scale on the gauge can be in one system of calculation, and in the instruction in a completely different one, there is often a need to convert bars to kilograms, megapascals, kilograms of force per square centimeter, technical or physical atmospheres. Or, if you need a result in the English system of calculation, then the pound-force per square inch (lbf • in²), in order to exactly comply with the required instructions.
How to use online calculator
In order to use sudden converting of one pressure value to another and find out how much a bar will be in MPa, kgf/cm², atm or psi:
- In the left list, select the unit with which you want to perform the conversion;
- In the right list, set the unit to which the conversion will be performed;
- Immediately after entering the number in any of the two fields appears «result». So you can convert from one value to another or vice versa.
For example, in the first field, the number 25 was entered, then, depending on the unit chosen, you calculate how many bars, atmospheres, megapascals, kilograms of force produced per cm² or pounds-force per square inch. When this same value was put in another (right) field, the calculator will say the inverse ratio of the selected physical pressure values.
1 bar how many atmospheres?
To get an approximate result of how many atmospheres there are in one bar, divide the pressure value by a factor of 1.013. That is, 1 bar is 0.98 atm. Therefore, when converting one unit of measurement of a small pressure (up to 10 bar) to another, it is customary to assume that 1 bar ≈ 1 atm. This ratio will give an error in calculations not exceeding 2%.
How many bars is 1 MPa?
To find out how many bars are in one megapascal, it is sufficient to multiply the pressure value expressed in MPa by 10. That is, 1 MPa = 10 bar.
1 MPa is how many kgf cm2?
To convert one Megapascal into a pressure value expressed in kilogram-force per square centimeter, it is sufficient to multiply the MPa value by 10.197. Thus 1 MPa = 10.197 kgf/m².
Kgf how many atmospheres?
When converting kgf/cm2 to atm you need to divide the pressure value expressed in kgf cm2 by 1.033. Using this ratio, you can convert any pressure value expressed in kilograms of force to atmospheres.
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https://pdfwale.com/pdf/vedic-mathematics-book
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math
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Vedic Mathematics Book PDF , Vedic Mathematics Book PDF Download , Vedic Mathematics Book PDF Download for free using the direct download link given at the bottom of this article. Vedic Mathematics Book PDF Details.Here in this article, we have brought for you Vedic Mathematics Book PDF. Vedic Mathematics is a book written by Indian monk Bharati Krishna Tirtha, and first published in 1965. It contains a list of mathematical techniques, which the author derived from the Vedas and is believed to contain all mathematical knowledge. These statements have since been rejected outright. Krishna Teerth failed to produce sources, and scholars unanimously consider it to be the speed of early mathematical calculations without overlap with historical mathematical developments during the Vedic period. To raise only considered a collection of moves. However, there has been a proliferation of publications in this area and several attempts by right-wing Hindu nationalist governments to integrate the subject into mainstream education.Here you can free download Vedic Mathematics Book PDF by clicking the link given below. Vedic Mathematics Book PDF Download Link..
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| 1,163 | 1 |
https://pennstate.pure.elsevier.com/en/publications/lattice-gas-generalization-of-the-hard-hexagon-model-ii-the-local
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math
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In a previous paper we considered an extension of the hard hexagon model to a solvable two-dimensional lattice gas with at most two particles per pair of adjacent sites. Here we use various mathematical identities (in particular Gordon's generalization of the Rogers-Ramanujan relations) to express the local densities in terms of elliptic functions. The critical behavior is then readily obtained.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
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https://www.physicsforums.com/threads/uniform-continuity.272755/
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math
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1. The problem statement, all variables and given/known data If f and g are uniformly continuous on X, give an example showing f*g may not be uniformly continuous. 3. The attempt at a solution i think if the functions are unbounded the product will not uniformly continuous. Is there a specific example of this function..?
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CC-MAIN-2018-43
| 322 | 1 |
https://www.mysanantonio.com/food/restaurants/article/Celebrate-Pi-Day-with-San-Antonio-s-best-pizzas-6889061.php
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math
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This is a carousel. Use Next and Previous buttons to navigate
For all the math geeks out there, it's Pi Day!
March 14 — 3/14 — celebrates the mathematical symbol Π, which is 3.14159 ... and it goes on like that. (Here's Pi to a million places if you'd like to memorize that. Who knows? It could impress somebody.)
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https://attic.city/item/Jdwj/danish-rosewood-extendable-dining-table-320-085-/by-design-modern
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math
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Danish Rosewood Extendable Dining Table - (320-085)
Danish rosewood extendable dining table circa 1960's. Table expands with two half circle drop down removable leaves and one central leaf turning it into an ...
$$$$$ · Indexed on January 21, 2022
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https://cs.nyu.edu/pipermail/fom/2000-May/003997.html
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math
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Robert.Black at nottingham.ac.uk
Mon May 29 16:49:33 EDT 2000
>I am a formalist, in that I believe: 1) it is essential to modern
>mathematics that it can be formalized, and 2) for much of modern
>mathematics the only meaningful notion of truth (if it is a notion of
>truth at all) is provability in some formal system.
I don't think anyone on this list is likely to quarrel with (1), but if one
starts pressing (2) (and disregards the let-out 'much of') I think it
starts to fall apart. Bourbaki says something closely related (_Theorie des
Ensembles_ I,22) when he says that the claim that some sentence is not a
theorem of a formal system 'can have no sense *in mathematics*' (Bourbaki's
When we prove a sentence S in a formal system, if all we take ourselves to
be really doing is announcing that it is so provable, then we are always
announcing a sigma_1 result, whatever the logical complexity of S, and our
proof of that result is of course constructive; we have exhibited the
(Goedel numer of the) array of dried ink which is a proof of S. So this is
really the view that all mathematical knowledge consists of constructively
proved sigma_1 results.
Consider now a pi_1 claim like 'PA is consistent'. What is the 'formalist'
going to say about this claim? He can of course announce that it's
provable, in, say, ZF (a sigma_1 fact), or that it's disprovable in, say,
PA+not-Con(PA) (another sigma_1 fact), but what about the claim itself's
being true or false?
There seem to be two options:
Either: You say it's not the sort of thing that could be true. I find this
pretty zany, particularly because it could (for all we know) be false! Do
you really want to go down this road? Is the claim meaningless though its
negation is meaningful? Or do it and its negation suddenly become
meaningful only if the negation turns out to be true? Or is it meaningful
but couldn't be true though it could be false???
Or: You say that it probably is true, but the claim that it's true is not
*mathematical*. (Is this Bourbaki's let-out?) But then what on earth is the
name of the branch of human intellectual endeavour to which that claim
*does* belong? Perhaps universities should open up some departments for
this new subject!
Dept of Philosophy
University of Nottingham
Nottingham NG7 2RD
tel. 0115-951 5845
More information about the FOM
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https://bpackindustries.in/determine-their-length-x-because-the-crow-flies/
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math
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a 2 = c dos ? q 2 + b 2 ? 2bq + q dos = c 2 + b 2 ? 2bq
Addititionally there is an important relationships within three sides off a standard triangle in addition to cosine of 1 of the bases
Figure 30 reveals the trail out of a ship you to definitely sailed 30 kilometres due east, following turned into as a result of 120° and you will sailed a deeper 40 kilometres.
Among indoor basics away from a good triangle is actually 120°. In case your sides adjacent to so it position is actually off length 4 yards and you can 5 meters, make use of the cosine signal to discover the length of the medial side reverse brand new offered perspective.
cuatro.2 Trigonometric identities
A large amount of applicable mathematics can be involved that have equations. It’s generally the case these equations are only genuine in the event the parameters they consist of deal with certain specific beliefs; including, 4x = cuatro is only true whenever x = 1. not, we sometimes take note of equations that are genuine for everybody opinions of your variables, for example (x + 1) 2 = x 2 + 2x + step one. Equations on the second variety of, we.e. of those which might be genuine no matter this thinking of your variables they contain, was properly titled identities. i
You can find a great many trigonometric identities, we.elizabeth. relationships ranging from trigonometric attributes which might be in addition to the specific viewpoints of the parameters they include. They have certain applications and it is beneficial to enjoys an effective listing of her or him for simple resource. 1st are provided below – you have got already met the original eight (inside the slightly different forms) before on the module while some exists during the certain products throughout the FLAP. Observe that ? and you can ? may represent any amounts or angular beliefs, unless the viewpoints is minimal from the significance of the functions alarmed.
Brand new abbreviations asin, acos and you may atan or alternatively sin ?step one , cos ?1 and you can tan ?step one , are sometimes employed for the latest inverse trigonometric qualities.
Pythagorass theorem states that square of the hypotenuse into the a good right–angled triangle is equivalent to the entire squares of the other a couple corners.
The latest angles 180° and you can 90° match a rotation by way of 50 % of and another–one-fourth out-of a group, respectively. A perspective off 90° is named a right direction. A column at 90° to a given line (otherwise surface) is considered become perpendicular otherwise regular into unique line (or epidermis).
Once the 2? = six.2832 (to help you four decimal cities) they uses that step one radian = °, given that stated earlier. Desk step 1 brings certain basics measured inside the degrees and radians. As you can tell from this table, of a lot are not–put bases are simple portions otherwise multiples of ? radians, but note that basics shown in the radians commonly usually indicated with regards to ?. Don’t make prominent mistake off thinking that ? try some sort of angular tool; it is simply several.
not, the space of large square can also be found of the incorporating the room of your own faster square, h 2 , to the regions of the newest five spot triangles. For every triangle has actually a location xy/2 (each is 50 % of good rectangle out-of corners x and you can y) so the the main large square is
The research off correct–angled triangles is called trigonometry, plus the around three collection of rates away from sets of edges is along referred to as trigonometric rates. He is known as sine, cosine and you can tangent of your own position ? – abbreviated so you’re able to sin, cos and tan, respectively we – and you will defined as employs:
One of the several good reason why trigonometric rates we is actually of attention so you can physicists is they assist to influence the new lengths of all dominican cupid log in of the edges off a right–angled triangle regarding a knowledge of a single side length and you can one indoor angle (aside from the best direction).
The newest proportion meanings of sine, cosine and tangent (we.age. Equations 5, six and you may eight) merely seem sensible having bases on the variety 0 in order to ?/dos radians, simply because they cover the new sides regarding the right–tilted triangle. Within subsection we are going to describe about three trigonometric attributes, also known as sine, cosine and tangent, and denoted sin(?), cos(?) and you can bronze(?), correspondingly. we Such services commonly enable us to attach a meaning so you can the newest sine and you may cosine of any direction, and also to new tangent of every angle that’s not an strange numerous ?/dos. For instance the trigonometric percentages which they generalize, this type of trigonometric services is of good pros from inside the physics.
However, not only is it the signs of this new trigonometric services one changes due to the fact ? develops otherwise reduces and you may P moves within circle in Contour 16. The values out of x and you may y, and therefore out of sin(?), cos(?) and you may bronze(?) together with will vary.
On the best such as for instance activity, simple harmonic actions, the latest altering updates x out of a size oscillating with the end from a springtime is generally represented by x = Acos(?t + ?). Even with appearances none of one’s quantity when you look at the bracket is an angle (even if they can be offered angular interpretations); t is the time that is mentioned inside mere seconds, ? is a steady known as the angular frequency that’s related to the brand new functions of the bulk and spring which can be measured from inside the hertz (1 Hz = step 1 s ?1 ), and you may ?, the fresh stage lingering, is actually a number, usually regarding the diversity 0 to help you 2?.
Clearly, including a positive ongoing, ?/dos, into conflict of your own means has got the effect of progressing brand new chart left from the ?/2. From inside the crude terms, this new addition has actually raised the dispute and helps make what you happen prior to (we.age. further left).
In the event that cos(?) = x, in which 0 ? ? ? ? and you will ?step one ? x ?step 1 upcoming arccos(x) = ? (Eqn 26b)
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CC-MAIN-2024-18
| 6,283 | 19 |
https://ir.canterbury.ac.nz/handle/10092/10163
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math
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A MATLAB implementation of elliptic curve cryptography
Degree GrantorUniversity of Canterbury
Degree NameBachelor of Science with Honours
The ultimate purpose of this project has been the implementation in MATLAB of an Elliptic Curve Cryptography (ECC) system, primarily the Elliptic Curve Diffie-Hellman (ECDH) key exchange. We first introduce the fundamentals of Elliptic Curves, over both the real numbers and the integers modulo p where p is prime. Then the theoretical underpinnings of the ECDH system are covered, including a brief look at how this system is broken. Next we develop the individual elements that will be needed in the implementation of ECDH, such as functions for calculating modular square roots and the addition of points on an EC. We then bring these elements together to create a working ECDH program, and discuss the limitations of the MATLAB environment in which it was created. Finally we look at the real world application of ECC and its future in the realm of cryptography.
SubjectsField of Research::01 - Mathematical Sciences::0101 - Pure Mathematics::010102 - Algebraic and Differential Geometry
- Engineering: Reports
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s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232259327.59/warc/CC-MAIN-20190526165427-20190526191427-00248.warc.gz
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CC-MAIN-2019-22
| 1,152 | 6 |
http://fastestballchallenge--sjmc.blogspot.com/p/pre-camp-research.html
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math
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In terms of vector, the angle of inclination is:
Conservation of Energy
Work is defined to be the amount of energy transferred to another system by a force acting through a distance.
The law of conservation of energy states that energy cannot be created or destroyed; it can only be transformed from one state to another.
Therefore, in this project, the ball has gravitational potential energy transformed to kinetic potential energy.
Upon doing the experiment, we have to find the initial and final energy of the ball and track.
m - Mass of the ball,
g - acceleration due to gravity, (g= 9.81ms^-2 ) tri h is the change of vertical displacement.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267864482.90/warc/CC-MAIN-20180622123642-20180622143642-00509.warc.gz
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CC-MAIN-2018-26
| 646 | 8 |
https://books.google.gr/books?id=pZFJAAAAIAAJ&dq=editions:UOMDLPabq7928_0001_001&hl=el&output=html_text&lr=
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math
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Τι λένε οι χρήστες - Σύνταξη κριτικής
Δεν εντοπίσαμε κριτικές στις συνήθεις τοποθεσίες.
Άλλες εκδόσεις - Προβολή όλων
12 inches 20 inches 9 inches ABCD adjacent altitude angles formed base base angle called centimeters chord circle whose radius circumference Cloth coincide common Compare Construct contains cube cubic diagonal diameter difference distance divided Draw drawn edge equal sides equilateral triangle exterior angle extremities faces feet figure Find the area Find the length Find the perimeter Find the ratio four Give given greater hexagon History Illustrate inches long inches longer inscribed interior isosceles triangle Join kind larger less measure meters middle point millimeters NotE opposite parallel parallelogram perpendicular Place polygon PRINCIPLE prolonging proportion QUERY Quote radii rectangle regular hexagon represent rhomboid rhombus right angle right triangle rods sector segment shorter similar smaller solid square inches straight line SUGGESTION supplement surface tangent trapezium trapezoid triangle ABC twice vertex wide width
Σελίδα 82 - If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal.
Σελίδα 173 - The square of the sum of two numbers is equal to the square of the first, plus twice the product of the first and the second, plus the square of the second.
Σελίδα 177 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Σελίδα 101 - Hence, the area of a trapezoid is equal to the product of its altitude by the line connecting the middle points of the sides which are not parallel.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703519784.35/warc/CC-MAIN-20210119201033-20210119231033-00209.warc.gz
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CC-MAIN-2021-04
| 1,877 | 8 |
https://appleseedscenter.com/2020/11/22/question-what-type-of-data-is-gender/
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math
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- What are 3 types of variables?
- Is GPA nominal or ordinal?
- Is salary an ordinal variable?
- What are the 2 types of variables?
- What type of variable is age?
- Is gender nominal or ordinal?
- What type of variable is gender?
- Is gender a nominal data?
- What type of data is gender in SPSS?
- Is age an ordinal variable?
- What are the 5 types of variables?
- Is age a covariate?
- What are variables in data?
- What is the difference between nominal and ordinal data?
- Is age nominal for years?
- Is name a categorical variable?
- Is age categorical or numerical?
- Are salaries nominal or ordinal?
- Is ordinal data qualitative or quantitative?
- What type of data is age in SPSS?
- How do you separate gender in SPSS?
What are 3 types of variables?
A variable is any factor, trait, or condition that can exist in differing amounts or types.
An experiment usually has three kinds of variables: independent, dependent, and controlled.
The independent variable is the one that is changed by the scientist..
Is GPA nominal or ordinal?
1. Mathematically or statistically, there is a problem with the concept of a Grade Point Average. In a technical sense, letter grades are Ordinal (rather than Interval) numbers — meaning, the distance between two letter grades is not the same.
Is salary an ordinal variable?
Interval/ratio can be re-formatted to become ordinal or nominal, ordinal can become nominal. Example: salary data for is often recorded as interval data (i.e. just a number). operations such as finding the average salary.
What are the 2 types of variables?
Frequently asked questions about variables You can think of independent and dependent variables in terms of cause and effect: an independent variable is the variable you think is the cause, while a dependent variable is the effect.
What type of variable is age?
Mondal suggests that age can be viewed as a discrete variable because it is commonly expressed as an integer in units of years with no decimal to indicate days and presumably, hours, minutes, and seconds.
Is gender nominal or ordinal?
There are two types of categorical variable, nominal and ordinal. A nominal variable has no intrinsic ordering to its categories. For example, gender is a categorical variable having two categories (male and female) with no intrinsic ordering to the categories. An ordinal variable has a clear ordering.
What type of variable is gender?
A categorical variable (sometimes called a nominal variable) is one that has two or more categories, but there is no intrinsic ordering to the categories. For example, gender is a categorical variable having two categories (male and female) and there is no intrinsic ordering to the categories.
Is gender a nominal data?
A good example of a nominal variable is sex (or gender). Information in a data set on sex is usually coded as 0 or 1, 1 indicating male and 0 indicating female (or the other way around–0 for male, 1 for female).
What type of data is gender in SPSS?
Measure in SPSS A Nominal (sometimes also called categorical) variable is one whose values vary in categories. It is not possible to rank the categories created. e.g. Gender varies in that an individual is either categorised as “male” or “female”.
Is age an ordinal variable?
Age can be both nominal and ordinal data depending on the question types. I.e “How old are you” is a used to collect nominal data while “Are you the first born or What position are you in your family” is used to collect ordinal data. Age becomes ordinal data when there’s some sort of order to it.
What are the 5 types of variables?
There are six common variable types:DEPENDENT VARIABLES.INDEPENDENT VARIABLES.INTERVENING VARIABLES.MODERATOR VARIABLES.CONTROL VARIABLES.EXTRANEOUS VARIABLES.
Is age a covariate?
You can add age as a continuous covariate, but keep in mind that, e.g. ~age + … implies that gene expression will have multiplicative increases with each unit of age.
What are variables in data?
In statistics, a variable has two defining characteristics: A variable is an attribute that describes a person, place, thing, or idea. The value of the variable can “vary” from one entity to another.
What is the difference between nominal and ordinal data?
Nominal and ordinal are two of the four levels of measurement. Nominal level data can only be classified, while ordinal level data can be classified and ordered.
Is age nominal for years?
There is no order associated with values on nominal variables. [Ratio] Age is at the ratio level of measurement because it has an absolute zero value and the difference between values is meaningful. For example, a person who is 20 years old has lived (since birth) half as long as a person who is 40 years old.
Is name a categorical variable?
Categorical variables take on values that are names or labels. The color of a ball (e.g., red, green, blue) or the breed of a dog (e.g., collie, shepherd, terrier) would be examples of categorical variables.
Is age categorical or numerical?
In our medical example, age is an example of a quantitative variable because it can take on multiple numerical values. It also makes sense to think about it in numerical form; that is, a person can be 18 years old or 80 years old.
Are salaries nominal or ordinal?
Nominal (Unordered categories) of Data For example, salary can be turned into a nominal variable by defining “high salary” as an annual salary of more than $200,000, “moderate salary” as less than or equal to $200,000 and more than $75,000, and “low salary” as less than or equal to $75,000.
Is ordinal data qualitative or quantitative?
Data at the ordinal level of measurement are quantitative or qualitative. They can be arranged in order (ranked), but differences between entries are not meaningful. Data at the interval level of measurement are quantitative. They can be ordered, and meaningful differences between data entries can be calculated.
What type of data is age in SPSS?
An additional practice example is suggested at the end of this guide. The example assumes you have already opened the data file in SPSS. Age is a key demographic variable, frequently recorded in survey data as part of a broader set of demographic variables such as education, income, race, ethnicity, and gender.
How do you separate gender in SPSS?
To split the data in a way that separates the output for each group:Click Data > Split File.Select the option Organize output by groups.Double-click the variable Gender to move it to the Groups Based on field.When you are finished, click OK.
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CC-MAIN-2021-25
| 6,570 | 65 |
http://en.wiktionary.org/wiki/extrapolation
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math
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Definition from Wiktionary, the free dictionary
- Rhymes: -eɪʃən
extrapolation (plural extrapolations)
- (mathematics) A calculation of an estimate of the value of some function outside the range of known values.
- An inference about some hypothetical situation based on known facts.
calculation of an estimate
Related terms
extrapolation f (plural extrapolations)
- an extrapolation; inference of a hypothetical situation.
Declension of extrapolation
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s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368700168711/warc/CC-MAIN-20130516102928-00079-ip-10-60-113-184.ec2.internal.warc.gz
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CC-MAIN-2013-20
| 455 | 10 |
https://www.surveytool.org/knowledge-base/4-1-what-is-skipping/
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math
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4.1 What is skipping?
Skipping is the feature to redirect respondents to a specific question based on a previous given answers. Skipping is available with the question type Multiple choice, 1 answer possible. The respondent can be redirected to any question futher in the survey or directly to the end of the survey.
This is schematic example of skipping in a survey.
This example is being used in this survey: Example survey skipping
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s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337723.23/warc/CC-MAIN-20221006025949-20221006055949-00128.warc.gz
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CC-MAIN-2022-40
| 434 | 4 |
https://www.chalapathiphysics4you.com/2017/12/why-are-spokes-provided-in-bicycle-wheel.html?showComment=1608982065938
|
math
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WHY ARE SPOKES PROVIDED IN A BICYCLE WHEEL?
QUESTION: Why are spokes provided in a bicycle wheel?
The spokes of cycle wheel increases its moment of inertia. If it is a disc some mass will be very near to axis of rotation. Due to spokes maximum mass for rim leads to more moment of inertia, greater is the opposition to any change in uniform rotational motion. As a result the cycle runs smoother and steadier. if the cycle wheel had no spokes, the cycle would be driven in jerks and hence unsafe.
- Is it necessary that a mass should be present at the center of mass of any system?
No. It is not necessary to have some mass at center of mass of the system.
Eg: For bangle or ring center of mass is at its center but there is no mass particle at center of mass.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780055601.25/warc/CC-MAIN-20210917055515-20210917085515-00022.warc.gz
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CC-MAIN-2021-39
| 760 | 6 |
http://udpaperzwjv.agorisme.info/a-study-on-the-coefficient-of-expansion-on-heating-solids.html
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math
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A study on the coefficient of expansion on heating solids
Any help would really be helpful because this problem would really help me study if alpha represents a linear expansion coefficient you are heating. What is coefficient of thermal expansion (cte) thermal expansion of solids heating or cooling affects all the dimensions of a body of material,. The thermal expansion coefficient is a a good way to determine the elements of the tensor is to study the expansion by then heating it.
Custom courses are courses that you create from studycom heating up a jar lid increases the size of the gaps thermal expansion & heat transfer related study. Heat experiment by for an object with initial lengthli,we can define α, the average coefficient of linear expansion heating/cooling controller volume expansion. 01 thermal expansion 1 liquids also expand on heating just like solids success study circle 8 to bend on heating their coefficient of linear expansion. Thermal properties 4 expansion coefficient, specific heat, differential thermal analysis, and viscoelasticity, by heating rate of temperature.
1 phonons, nature of bonding and their relation to anomalous thermal expansion behavior of m 2 o (m=au, ag, cu) m k gupta, r mittal and s l chaplot. Variation of density of solids and liquids with temperature solid or a liquid decreases on heating is its coefficient of cubical expansion, then v. Negative thermal expansion: a review and opens the door to composites with a coefficient of thermal expansion solids expand upon heating,. The heat transfer module can be used to study the three types of heat transfer in thermal expansion is very common currents and heat transfer in solids,. Thermal effects on materials may be used advantageously polycrystalline solids) • thermal properties: density, thermal expansion coefficient,.Today, we study heat transfer in deformed solids in an example, we take into account the thermoelastic effects of the material when physics are coupled. Determination of coefficient of expansion of air to what has been noticed in the case of solids and water, this was indirect heating of the. How can one find the coefficient of thermal expansion of during heating as well as melting, certain expansion will the average expansion coefficient for. Full-text paper (pdf): density, viscosity and coefficient of thermal expansion of clear grape juice at different soluble solid concentrations and temperatures. A study of enhancement of the properties of expansion coefficient of the mixture and he found a study of enhancement of the properties of lubricant oil. Physics notes class 11 chapter 11 thermal properties of matter of solids 2 expansion of γ is a coefficient of cubical expansion coefficient of. Définitions de coefficient_of_thermal_expansion, thermal expansion coefficient for solids elements of the tensor is to study the expansion by powder.
Overview in this white paper machining equipment, where thermal expansion may affect the dimensional stability convection coefficient, also known as a film. In the present study: thermal expansion coefficient thermal expansion of solids is experimental studies on coefficient of linear thermal expansion for. The effects of heat on matter heating, causing a possible the increase in length the coefficient of linear expansion for the material needs to be known. Transient thermal expansion of solids during inert heating, phase change, and surface gasification.
Thermodynamic and mechanical heat transfer is calculated with the heat transfer coefficient, and heating a bed, or the study the radiant heat transfer by. Sir, why does solid expand on heating the answer to this question given in my book is “the potential energy curve is asymmetric about the. Volumetric thermal expansion coefficient as a function of temperature has been reported by - expansion of solids is very important for heating rate between. Learn topics like thermal expansion in solids and coefficient of thermal expansion, linear expansion of solids and coefficient of linear expansion.
The objective of this study was to obtain information on with two heating sections, the heat transfer coefficients. Coefficient of linear expansion solids expand in response to heating and this is equivalent to the expansion coefficient multiplied by the change in. The coefficient of linear expansion is the in order to compare the abilities of different solids to expand on heating the coefficient is.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267160454.88/warc/CC-MAIN-20180924125835-20180924150235-00113.warc.gz
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CC-MAIN-2018-39
| 4,460 | 7 |
https://www.mittag-leffler.se/seminar/workshop-title-tba-10/
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math
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Jörg Schmeling, Lund University
Protentials with logarithmic singularities occur in many situations. They are natural in systems with a zero or a pole of the derivative. They also occur in some number theoretical problems or in the study of diffraction measures of substitutions. In this talk I will give a survey of the recent development as well as some open problems. Most of the talk is based on joint work with A. Fan, W. Shen; Ph. Gohlke and G. Lamprinakis.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474523.8/warc/CC-MAIN-20240224044749-20240224074749-00372.warc.gz
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CC-MAIN-2024-10
| 464 | 2 |
https://www.excelforum.com/excel-programming-vba-macros/828748-attendance-tracker.html
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math
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I have attached a sample tracker - where i have 2 tabs one is attendance tracker and another one is production tracker.
Now i am looking out for a formula which counts attendance based on there production numbers for that respective day.
Here is what is am looking:
If an employee has done production more than "0" than his attendance should reflect as "Present".
If an employee has done production less than or equal to "0", than his attendance should reflect as "Absent".
Can anyone please help me out to solve this.
Re: Attendance Tracker
Try the following formula in cell B3 on your Attendance Tracker sheet.
Then copy and paste.
=IF(SUMPRODUCT(--('Production Tracker'!$A$3:$A$17=B$1)*('Production Tracker'!$B$3:$B$17=$A3)*('Production Tracker'!$C$3:$C$17))>0,"Present","Absent")
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Search Engine Friendly URLs by vBSEO 3.6.0 RC 1
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710900.9/warc/CC-MAIN-20221202082526-20221202112526-00816.warc.gz
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CC-MAIN-2022-49
| 933 | 13 |
https://rd.springer.com/article/10.1007/s10589-011-9407-1
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math
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A numerical algorithm for finding solutions of a generalized Nash equilibrium problem
- 311 Downloads
A family of nonempty closed convex sets is built by using the data of the Generalized Nash equilibrium problem (GNEP). The sets are selected iteratively such that the intersection of the selected sets contains solutions of the GNEP. The algorithm introduced by Iusem-Sosa (Optimization 52:301–316, 2003) is adapted to obtain solutions of the GNEP. Finally some numerical experiments are given to illustrate the numerical behavior of the algorithm.
KeywordsConvex feasibility problem Generalized Nash equilibrium problem Projection methods
Unable to display preview. Download preview PDF.
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CC-MAIN-2018-34
| 691 | 5 |
https://electronics.stackexchange.com/questions/56991/eagle-pcb-design-libraries/276785
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math
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I am doing my first Eagle PCB design. It's been going smoothly so far, however, I just hit a road bump. I am using a TC1269 Regulator, but cannot find the CAD library for it. I have looked into tutorials to creating custom parts, but I was hoping that instead I would be able to find a premade one since the TC1269 employs a 8 pin MSOP package, which is common enough that there should be some CAD equivalents already out there.
Does anyone know perhaps another equivalent part that employs the same package that I can use in place of the TC1269 or perhaps a library with the 8 pin MSOP package?
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817674.12/warc/CC-MAIN-20240420184033-20240420214033-00128.warc.gz
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CC-MAIN-2024-18
| 595 | 2 |
https://statisticscalculators.net/statistics/median-calculator/
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math
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Take the help of free Median Calculator to calculate the median for given list of data set quickly. Just enter data set list in the input box and hit the calculate button to get the result with detailed explanation.
What is the Median?
In mathematics, the median is defined as the middle value of the sorted list of numbers. The numbers are arranged in the ascending order. After the arranging numbers in the order the middle value is called the median of the given data set.
The formula of median for the odd number of observations is Median = [(n+1)/2]th term
The median formula for the even number of observations is Median = Average of [n/2]th term and [(n+2)/2]th term
n is the set of numbers
Steps to Find Median for Given Data
The following are the steps to calculate the median for the given data set of numbers easily. Check out those rules and instructions to get the result.
- Consider a set of numbers.
- Arrange the numbers in the data set from least to greatest i.e ascending order.
- Count the numbers in the given data set.
- For a data set with odd number of values, middle value from the sorted set is the median.
- For a data set with even number of values, the mean of two middle values is the median.
Calculate the medain of 15, 21, 18, 10, 7, 16, 20, 63, 36.
Given set of numbers are 15, 21, 18, 10, 7, 16, 20, 63, 36
Arrange the given numbers in the ascending order.
7, 10, 15, 16, 18, 20, 21, 36, 63
The total numbers in the adat set are 9.
Median formula is Median = (n+1)/2
= 10/2 = 5th term
Therefore, median of 15, 21, 18, 10, 7, 16, 20, 63, 36 is 7.
statisticscalculators.net is an ultimate website with all free statistics concepts calculators for assisting the students and every single person out there in maths basic and advanced concepts.
Median Example Calculations
Frequently Asked Question's on Median Calculator
1. How to find the median on a calculator?
To calculate the median of a data set, you have to enter data set in the specified input box and press on the calculate button to avail the exact answer i.e median with detailed explanation.
2. What is meant by median?
In statistics, median is defined as the middle value in the set of numbers of data. The middle number is found by ordering the numbers.
3. What is the formula to get median of numbers?
The simple formulas to find median of odd number of observations is [(n+1)/2] and even number of observations is n/2.
4. What is the median of 15?
The number of items in the data set n = 15
The formula to calculate median = (n+1)/2
= (15+1)/2 = 16/2
Median = 8
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CC-MAIN-2023-40
| 2,557 | 35 |
https://www.semanticscholar.org/paper/Abelian-Tensors-Landsberg-Micha%C5%82ek/73a231c6103ecf486555c1ed4239d6f9d9062278
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math
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Irreversibility of Structure Tensors of Modules
- Computer ScienceCollectanea Mathematica
It is shown that it is impossible to prove ω = 2 by starting with structure tensors of modules of fixed degree and using arbitrary restrictions, and it implies that the same is impossible byStarting with 1A-generic non-diagonal tensor of fixed size with minimal border rank.
The Hitchhiker Guide to: Secant Varieties and Tensor Decomposition
We consider here the problem, which is quite classical in Algebraic geometry, of studying the secant varieties of a projective variety X. The case we concentrate on is when X is a Veronese variety, a…
Bounds on complexity of matrix multiplication away from CW tensors
Three families of minimal border rank tensors are presented: they come from highest weight vectors, smoothable algebras, or monomial algebraes; they also explain how in certain monomial cases using the laser method directly is less profitable than first degenerating.
Hermitian K-theory via oriented Gorenstein algebras
We show that hermitian K-theory is universal among generalized motivic cohomology theories with transfers along finite Gorenstein morphisms with trivialized dualizing sheaf. As an application, we…
A geometric study of Strassen's asymptotic rank conjecture and its variants
Surprisingly, this dimension equals the dimension of the set of oblique tensors, a less restrictive class of tensors that Strassen identified as useful for his laser method.
Geometric conditions for strict submultiplicativity of rank and border rank
The X -rank of a point p in projective space is the minimal number of points of an algebraic variety X whose linear span contains p . This notion is naturally submultiplicative under tensor product.…
On Comon’s and Strassen’s Conjectures
Comon’s conjecture on the equality of the rank and the symmetric rank of a symmetric tensor, and Strassen’s conjecture on the additivity of the rank of tensors are two of the most challenging and…
On Degeneration of Tensors and Algebras
- Mathematics, Computer ScienceMFCS
This work describes the smoothable algebra associated to the Coppersmith-Winograd tensor and proves a lower bound for the border rank of the tensor used in the "easy construction" of Coppermith and Winograd.
Towards a geometric approach to Strassen’s asymptotic rank conjecture
- MathematicsCollectanea Mathematica
A first geometric study of three varieties in C m, including the Zariski closure of the set of tight tensors, the tensors with continuous regular symmetry, to develop a geometric framework for Strassen’s asymptotic rank conjecture that the asymptic rank of any tight tensor is minimal.
SHOWING 1-10 OF 57 REFERENCES
Typical Tensorial Rank
The typical rank R(f) of a format f is the rank of Zariski almost all tensors of that format. Following Strassen and Lickteig we determine the asymptotic growth of the function R and…
Stratification of the fourth secant variety of Veronese varieties via the symmetric rank
Abstract. If is a projective non-degenerate variety, the X-rank of a point is defined to be the minimum integer r such that P belongs to the span of r points of X. We describe the complete…
Toward a Salmon Conjecture
- MathematicsExp. Math.
Methods from numerical algebraic geometry are applied in combination with techniques from classical representation theory to show that the variety of 3×3×4 tensors of border rank 4 is cut out by polynomials of degree 6 and 9, furnishing a computational solution of an open problem in algebraic statistics.
On the Ranks and Border Ranks of Symmetric Tensors
- Mathematics, Computer ScienceFound. Comput. Math.
Improved lower bounds for the rank of a symmetric tensor are provided by considering the singularities of the hypersurface defined by the polynomial.
Varieties of reductions for $gl\_n$
We study the varieties of reductions associated to the variety of rank one matrices in $\fgl\_n$. These varieties are defined as natural compactifications of the different ways to write the identity…
Generalizations of Strassen's Equations for Secant Varieties of Segre Varieties
We define many new examples of modules of equations for secant varieties of Segre varieties that generalize Strassen's commutation equations (Strassen, 1988). Our modules of equations are obtained by…
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| 4,330 | 36 |
https://cafedoing.com/karmic-number-worksheet-worksheets-numerology/
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math
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Karmic Number Worksheet Worksheets Numerology
Karmic Number Worksheet Worksheets Numerology.
Differential truth table worksheet instrument name reviewed by date instrument flag instrument differential table classify the differential flags into one the the four categories and total each column table calculate the following parameters tn x x number of x number of total x Truth tables worksheet name boolean connectors truth tables only consider the two columns connected by the boolean connector, cover up the rest of the columns mentally or physically use connector meaning or hint words to evaluate statement as true or truth table shows all possible truth values.
tautologies in logic, a tautology is a compound sentence that is always true, no matter what truth values are assigned to the simple sentences within the compound sentence. for example, let us study the truth value of p q p v q by building a truth table.
Point slope form worksheet doc equation puzzles riddles poi writing linear equations. Education. Interpreting periodic table activity page teaching chemistry worksheets. Karmic number worksheet worksheets numerology. Word search fisherman wife worksheets early learning summer reading program hidden words. Maths questions algebra math. Propositional logic brilliant math science wiki physics mathematics worksheets.
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http://demonstrations.wolfram.com/search.html?query=symbols:BellB%20OR%20BernoulliB%20OR%20Binomial%20OR%20CatalanNumber%20OR%20EulerE%20OR%20Factorial%20OR%20Factorial2%20OR%20Fibonacci%20OR%20HarmonicNumber%20OR%20LerchPhi%20OR%20LucasL%20OR%20MatrixExp%20OR%20NorlundB%20OR%20PolyGamma%20OR%20PolyLog%20OR%20RSolve%20OR%20StirlingS1%20OR%20StirlingS2%20OR%20Sum%20OR%20Zeta&start=1101&limit=20
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Demonstrations 1101 - 1116 of 1116
Spectra of the D-Lines of Alkali Vapors
Conservative Hex Drift Machine
Fractional Graphs and Flowers
Keyboard and Composer
Forces in a Power Tower Truss
Geometric Interpretation of Perrin and Padovan Numbers
Mutualism and Evolutionary Multiplayer Games: Revisiting the Red King Effect
A Discrete Green's Theorem
Simulating the IRR
The Duty to Settle
Effect of High Expense Charges on an Investment's Net Return
Extended Discrete Green's Theorem
Enclosing the Spectrum by Gershgorin-Type Sets
Phonon Modes for 2D Lattice Vibrations
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http://www.slideshare.net/bweldon/7-4-multiply-to-eliminate-day-1
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math
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1. Solve Linear Systems by Multiplying First Section 7.4 P. 451
2. Steps1. Arrange the equations with like terms in columns.2. Multiply one or both of the the equations by a number to obtain coefficients that are opposites for one of the variables.3. Add /Subt the equations and one term/variable will be eliminated. Solve for the other.4. Substitute the value in Step 3 into either of the original equations. Solve for other variable.5. Check solution in each of the original equations.
3. 6x + 5y = 192x + 3y = 5 Multiply by: ?
4. • Sometimes you need to use a “multiple” of one equation to get terms eliminated. This means multiplying each term by the same number. (Equivalent equations)• Solve 3x = -6y + 12 -x + 3y = 6
5. EXAMPLE 2 Multiply both equations, then subtract Solve the linear system: 4x + 5y = 35 Equation 1 2y = 3x – 9 Equation 2 SOLUTION STEP 1 Arrange: the equations so that like terms are in columns. 4x + 5y = 35 Write Equation 1. –3x + 2y = –9 Rewrite Equation 2.
6. EXAMPLE 2 Multiply both equations, then subtract STEP 2 Multiply: Equation 1 by 2 and Equation 2 by 5 so that the coefficient of y in each equation is the least common multiple of 5 and 2, or 10. 4x + 5y = 35 8x + 10y = 70 –3x + 2y = –9 –15x +10y = –45 STEP 3 Subtract: the equations. 23x = 115 STEP 4 Solve: for x. x=5
7. EXAMPLE 2 Multiply both equations, then subtract STEP 5Substitute: 5 for x in either of the original equationsand solve for y. 4x + 5y = 35 Write Equation 1. 4(5) + 5y = 35 Substitute 5 for x. y=3 Solve for y. ANSWER The solution is (5, 3).
8. • Solve: 2x = 4y + 8 3y = 5x - 13
9. Do P. 454 3-12Show original equation and then newequation (s) through multiplication.Show solution in ordered pair (x, y)
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| 1,739 | 9 |
http://www.gallery.ca/cybermuse/teachers/plans/chrono_e.jsp?lessonid=324
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math
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Teachers Lesson Plans
Seeing Math in Art
25000 BCE Early geometric designs used and found in archaeological references
5000 BCE Egyptians use decimals and geometry for surveying, engineering, agriculture
3400 BCE Symbols used for number, although only straight lines, in Egypt
2000 BCE Babylonians correctly solve problems with rectangular right prisms and right cylinders.
1850 BCE Babylonians document what is known as Pythagorean Theorem.
700 BCE Indian Sulbasutras created indicating extensive geometric and astronomical understanding used to construct altars for the Veda people
575 BCE Thales brings Babylonian mathematics to Greece - using geometry to calculate the height of pyramids, distance of ships
530 BCE Pythagoras teaches and creates a society of learning and religious secrecy, probably the first person to prove Pythagorean Theorem.
300 BCE Euclid presents systematic development of geometry in The Elements.
250 BCE Archimedes presents formulae for calculating volume of sphere and cylinder, with an approximation of π.
Brahmagupta uses zero and negative numbers in written work
Al-Khwarizmi writes work using arithmetic, geography, and astronomy and first work is the source of the word algebra (from al-jabr).
Fibonacci writes work that introduces famous sequence of numbers called Fibonacci sequence.
Zhu Shijie indicates Chinese understanding of what is now known as Pascal's Triangles and sum of sequences.
First mathematics book Euclid's Elements printed.
Copernicus publishes work that the Sun, not the Earth, is the centre of the Universe
Galileo publishes discoveries made with telescopes.
Kepler uses elliptical orbits to document conic sections, beginning early introduction to Calculus
First use of trigonometric abbreviations (sin, tan, cos) in writing by Girard.
Descartes formally applies algebra to geometry, beginning branch now called Cartesian Geometry.
Fermat and Pascal exchange letters to work out formal laws for chance and probability.
Leibniz demonstrates a calculating machine which can multiply, divide, and extract roots.
Newton presents theories of motion, gravity, and mechanics.
The Greek letter π used to represent the ratio of circumference to its diameter.
Bernoulli publishes work documenting probability models and exponential series.
Bayes presents new ideas about chance, now considered Bayesian Theory of Probability.
Babbage begins construction of a large machine (engine), to calculate logarithmic and trigonometric functions.
M÷bius presents a strip of paper with only one side and edge - now known as the M÷bius strip.
Venn diagrams presented as visual in group theory.
Hilbert poses famous problem list as a challenge to the next century.
Einstein offers General Theory of Relativity.
Sierpinski works on Set Theory and presents closed curve leading to fractals.
Turing describes theoretical machine (Turing machine) leading to the modern computer.
Mandelbrot describes the theory of fractals, more fully described in 1982.
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https://hodelyvecanuxiwej.frecklesandhoney.com/integral-and-functional-differential-equations-book-15880aa.php
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math
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3 edition of Integral and Functional Differential Equations (Pure and Applied Mathematics (Marcel Dekker)) found in the catalog.
May 1, 1981
Written in English
|The Physical Object|
|Number of Pages||296|
Elementary Differential Equations with Boundary Value Problems is written for students in science, en-gineering,and mathematics whohave completed calculus throughpartialdifferentiation. Ifyoursyllabus includes Chapter 10 (Linear Systems of Differential Equations), your students should have some prepa-ration inlinear algebra. The text also presents general optimal control problems, optimal control of ordinary differential equations, and different types of functional-integral equations. The book discusses control problems defined by equations in Banach spaces, the convex cost functionals, and the weak necessary conditions for an original Edition: 1.
Ulam Stability of Operators presents a modern, unified, and systematic approach to the field. Focusing on the stability of functional equations across single variable, difference equations, differential equations, and integral equations, the book collects, compares, unifies, complements, generalizes, and updates key results. Definitely the best intro book on ODEs that I've read is Ordinary Differential Equations by Tenebaum and Pollard. Dover books has a reprint of the book for maybe dollars on Amazon, and considering it has answers to most of the problems found.
The book deals with linear integral equations, that is, equations involving an unknown function which appears under the integral sign and contains topics such as Abel's integral equation, Volterra integral equations, Fredholm integral integral equations, singular and nonlinear integral equations, orthogonal systems of functions, Green's. The book can be used as a database of test problems for numerical and approximate methods for solving linear and nonlinear integral equations. Discover the world's research 17+ million members.
The clockmaker, or, The sayings and doings of Samuel Slick of Slickville
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Unemployment, health and social policy.
Samuel Taylor Darling.
Years of liberalism and fascism
childrens Blue bird
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Interpretation of motor fuel survey data
Introduction to the Early Childhood Environment Rating Scale (Viewers Guide&Training Workbook)
Sediments and microfauna off the coasts of Mississippi and adjacent states
Integral and Functional Differential Equations (Lecture Notes in Pure and Applied Mathematics) 1st Edition by H. Stech (Author) ISBN ISBN Why is ISBN important. ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book.
Cited by: 7. Theory of Functionals and of Integral and Integro-Differential Equations (Dover Books on Mathematics) Hardcover – Janu by Vito Volterra (Author) › Visit Amazon's Vito Volterra Page. Find all the books, read about the author, and more.
See search results for this author Cited by: This is the first comprehensive introduction to collocation methods for the numerical solution of initial-value problems for ordinary differential equations, Volterra integral and integro-differential equations, and various classes of more general functional equations.
Its principal aims are to guide the reader from basic ideas to the current state of the art, to describe important problems and directions Format: Hardcover. Techniques of Functional Analysis for Differential and Integral Equations describes a variety of powerful and modern tools from mathematical analysis, for graduate study and further research in ordinary differential equations, integral equations and partial differential equations.
Knowledge of these techniques is particularly useful as preparation for graduate courses and PhD research in differential equations Format: Paperback. Book Description. The purpose of this book is threefold: to be used for graduate courses on integral equations; to be a reference for researchers; and to describe methods of application of the theory.
The author emphasizes the role of Volterra equations as a unifying tool in the study of functional equations, and investigates the relation between abstract Volterra equations and other types of functional-differential by: This book seeks to present Volterra integral and functional differential equations in that same framwork, allowing the readers to parlay their knowledge of ordinary differential equations into theory and application of the more general problems.
Differential and Integral Inequalities: Functional Partial, Abstract and Complex Differential Equations v. 2: Theory and Applications: Functional | Lakshmikantham | download | B–OK.
Download books for free. Find books. Description Techniques of Functional Analysis for Differential and Integral Equations describes a variety of powerful and modern tools from mathematical analysis, for graduate study and further research in ordinary differential equations, integral equations and partial differential equations.
Theory of functionals and of integral and integro-differential equations Vito Volterra A general theory of the functions depending on a continuous set of values of another function, this volume is based on the author's fundamental notion of the transition from a finite number of.
SOME REMARKS AND NOTATION 1. In Chapters 1–11 in the original integral equations, the independent variable is denoted by x, the integration variable by t, and the unknown function by y = y(x).
For a function of one variable f = f(x), we use the following notation for the derivatives: f. Book description Collocation based on piecewise polynomial approximation represents a powerful class of methods for the numerical solution of initial-value problems for functional differential and integral equations arising in a wide spectrum of applications, including biological and physical by: functional equations but Sm`ıtal presents beautifully the topic of iterations and functional equations of one variable2.
Similarly, Small’s book is a very enjoyable, well written book and focuses on the most essential aspects of functional equations. Once the reader. This book explains the following topics: First Order Equations, Numerical Methods, Applications of First Order Equations1em, Linear Second Order Equations, Applcations of Linear Second Order Equations, Series Solutions of Linear Second Order Equations, Laplace Transforms, Linear Higher Order Equations, Linear Systems of Differential Equations, Boundary Value Problems and Fourier.
"The Conference on Integral and Functional Differential Equations was held June, at West Virginia University in Morgantown, West Virginia"--Preface. Description: x, pages ; 26 cm. Series Title: Lecture notes in pure and applied mathematics, v.
Responsibility: edited by Terry L. Herdman and Harlan W. Stech and Samuel M. The theorems for regular integral equations may easily be carried over to cases in which fewer assumptions are made about the kernel. The definitions of regular and singular integral equations used here follow those in Ph.
Frank and R. Mises: Differential-and Integralgleichungen der Mechanik and Physik, 2nd ed., Vol. 1, p. Brunswick Collocation methods for Volterra integral and related functional differential equations Brunner H. This is the first comprehensive introduction to collocation methods for the numerical solution of initial-value problems for ordinary differential equations, Volterra integral and integro-differential equations, and various classes of more general.
ordinary differential equations, partial differential equations, Laplace transforms, Fourier transforms, Hilbert transforms, analytic functions of complex variables and contour integrations are expected on the part of the reader. The book deals with linear integral equations, that is, equations involving an.
Most mathematicians, engineers, and many other scientists are well-acquainted with theory and application of ordinary differential equations. This book seeks to present Volterra integral and functional differential equations in that same framework, allowing the readers to parlay their knowledge of ordinary differential equations into theory and application of the more general p.
The present book builds upon an earlier work of J. Hale, "Theory of Func tional Differential Equations" published in We have tried to maintain the spirit of that book and have retained approximately one-third of the material intact.
This book is an introduction to partial differential equations (PDEs) and the relevant functional analysis tools which PDEs require. This material is intended for second year graduate students of mathematics and is based on a course taught at Michigan State University for a number of years.
About this book This classic work is now available in an unabridged paperback edition. Hochstatdt's concise treatment of integral equations represents the best compromise between the detailed classical approach and the faster functional analytic approach, while .Linear and Nonlinear Integral Equations - Books.
EqWorld.Collocation Methods for Volterra Integral and Related Functional Differential Equations, Cambridge University Press, Cochran, J. A., The Analysis of Linear Integral Equations, McGraw-Hill Book Co., New York, That is, a functional differential equation is an equation that contains some function and some of its derivatives to different argument values.
Functional differential equations find use in mathematical models that assume a specified behavior or phenomenon depends on the present as well as the past state of a system.
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http://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.106224.html
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math
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You can put this solution on YOUR website!
d=st d=distance, s=speed, t=time
d=200 miles, s=Steve's speed in mph, t= his time in hrs
The distance of both trips is the same. So,:
s*200/s+10*200/s-s-10=200 plug 200/s for every t in the above equation.
-s^2-10s+2000=0 multiply both sides by s to eliminate the fraction.
s^2+10s-2000=0 multiply both sides times -1
s can't be a negative number.
at 40 mph it takes 5 hrs to go 200 mi
at 50 mph it takes 1 hr less
you had the right answer all the time and didn't know it!
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https://www.hackmath.net/en/math-problem/908
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math
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Sum of series
Determine the 6-th member and the sum of a geometric series:
Did you find an error or inaccuracy? Feel free to write us. Thank you!
Thank you for submitting an example text correction or rephasing. We will review the example in a short time and work on the publish it.
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Need help to calculate sum, simplify or multiply fractions? Try our fraction calculator.
You need to know the following knowledge to solve this word math problem:
Related math problems and questions:
- Saving per cents
The first day I save 1 cent and every next day cent more. How many I saved per year (365 days)?
- Infinite decimal
Imagine the infinite decimal number 0.99999999 .. ... ... ... That is a decimal and her endless series of nines. Determine how much this number is less than the number 1. Thank you in advance.
- Probably member
Look at the series 2,6,25,96,285, ? What number should come next?
- Geometric sequence 5
About members of geometric sequence we know: 3 a5:a3 = 27:25 7 a3 +5 a7 = 1 : 564 Calculate a1 (first member) and q (common ratio or q-coefficient)
- Hot air balloon
Hot air balloon ascends 25 meters up for a minute after launch. Every minute ascends 75 percent of the height, which climbed in the previous minute. a) how many meters ascend six minutes after takeoff? b) what is the overall height 10 minutes after launch
- Series and sequences
Find a fraction equivalent to the recurring decimal? 0.435643564356
- Geometric sequence
In the geometric sequence is a4 = 20 a9 = -160. Calculate the first member a1 and quotient q.
- Decimal to fraction
Write decimal number 8.638333333 as a fraction A/B in the basic form. Given decimal has infinite repeating figures.
Fraction frac(0, overline(38))(0,38) write as fraction a/b, a, b is integers numerator/denominator.
- AP - basics
Determine first member and differentiate of the the following sequence: a3-a5=24 a4-2a5=61
- Sum of GP members
Determine the sum of the GP 30, 6, 1.2, to 5 terms. What is the sum of all terms (to infinity)?
- To the cinema
Jane at 8 am got message that all 1093 school pupils will go to the cinema. Within 20 min she said it to the three friends. Each of them again for 20 minutes said to the other three. In this way the message spread further. At what time all the children in
- Infinite sum of areas
Above the height of the equilateral triangle ABC is constructed an equilateral triangle A1, B1, C1, of the height of the equilateral triangle built A2, B2, C2, and so on. The procedure is repeated continuously. What is the total sum of the areas of all tr
- Recursion squares
In the square, ABCD has inscribed a square so that its vertices lie at the centers of the sides of the square ABCD. The procedure of inscribing the square is repeated this way. The side length of the square ABCD is a = 22 cm. Calculate: a) the sum of peri
- Population growth
How many people will be on Earth from two people for 5,000 years, if every couple has always 4 children, (2 boys and 2 girls) at the age of 25-35, and every man will live 75 years?
- Find next member
Find x if the numbers from a GP 7, 49, x.
-12, 60, -300,1500 need next 2 numbers of pattern
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https://thesportsdb.com/team/140621?cutout=2
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math
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|03 Jul 22||12 de|| ||1 - 3|| ||General Caballero|
|25 Jun 22||General Caballero|| ||2 - 1|| ||Resistencia|
|21 Jun 22||Cerro Porteño|| ||3 - 1|| ||General Caballero|
|17 Jun 22||General Caballero|| ||1 - 1|| ||Sol de|
|12 Jun 22||Guaireña FC|| ||1 - 2|| ||General Caballero|
General Caballero Club is a soccer club from Paraguay, from the city of Dr. Juan León Mallorquín (formerly Ka'arendy) in the Alto Paraná department. It was founded on June 21, 1962, being one of the founding clubs of the Ka'arendy Soccer League. In 2018 it achieved its promotion to the Second Division of Paraguay, in which it will be in the military since 2019. It is popularly identified as General Caballero JLM to differentiate it from other clubs with the same denomination in the different divisions of the Paraguayan Soccer Association.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710931.81/warc/CC-MAIN-20221203111902-20221203141902-00116.warc.gz
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CC-MAIN-2022-49
| 835 | 6 |
https://www.ninetyeast.net/maths/grade-9-10-gcse-hsc/algebra/introduction-to-equations-variables-and-formulas
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math
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Introduction to Equations, Variables and Formulas
This is a Maths tutorial aimed at Grade 9/10 students, discussing what equations, variables and formulas are. The video tutorial is still to come.
What are Equations?
An equation is a shorthand way of describing two things as being equal. For example, the below equation tells us that one metric kilo of apples is equivalent in mass to 2.2 imperial pounds of apples.
1 kilogram of apples = 2.2 pounds of apples
The above equation can be rewritten using variables.
What are variables?
A variable is a symbol used to represent a number, either in an equation or in text. These symbols are usually letters of an alphabet; most commonly from either the English (e.g. a, b, c) or Greek (e.g. alpha (α), beta (β), gamma (γ)) alphabets. For example, G is the symbol used to represent the gravitational constant (6.67408 × 10-11 m3/kg1·s2). Similarly, the small letter g is used to represent acceleration due to gravity.
Unknown vs Known Variables
Variables can be classified as being either known or unknown. Other terms are real and apparent; and bound and unbound respectively.
Known, Real, Bound Variables
A known, real or bound variable is one where the value is a set number which does not change; this is also known as a constant number. G, the gravitational constant is a constant number, and thus can be called a known, real or bound variable.
Unknown, Apparent, Unbound Variables
An unknown, apparent or unbound variable is one which can change i.e. it is not constant. Acceleration due to gravity varies depending on the masses of the different bodies involved. For example, the value of g is approximately six times greater on earth than it is on the moon.
This variability in g makes it an apparent variable, but only until the subjects involved (e.g. earth, moon, pluto etc.) are defined - then it becomes a known variable. This is important: variables can switch between being known or unknown.
What are Formulas?
Formulas are a special type of equation that includes multiple unknown variables. At the beginning of this tutorial we said that the first equation (1 kilogram of apples = 2.2 pounds of apples) could be rewritten using variables. Below is one way of doing this. Have a look at it and decide if you think it can be classified as a formula or not.
y = 2.2 x
~ y is mass (of anything, including apples) in kilograms; and
~ x is mass (of anything, including apples) in pounds.
So what did you think? Can it be classified as a formula?
If you answered yes, then you're correct. In this equation, 2.2 is a known variable and BOTH y and x are unknown variables. Two unknown variables in an equation makes it a formula.
In this tutorial we've learned what equations, variables and formulae# are. The next tutorial will discuss why formulae are useful.
#NB: The words formulae and formulas are both the plural of formula.
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https://www.eetimes.com/document.asp?doc_id=1147665&piddl_msgorder=asc
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math
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HANCOCK, N.H. Renewed scrutiny of a statistical technique used by British intelligence to decode German military communications during World War II has opened new avenues in statistical prediction that researchers say could improve machine-learning software.
Today's spell checkers, data retrieval methods and speech recognition systems use variations of the Good-Turing estimator, named for British mathematicians I.J. Good and Alan M. Turing. The technique, representing an intuitive breakthrough in the modeling of probability distributions behind data streams, was credited with shortening the war by several years. But while Good published a mathematical justification of the method after the war, statisticians remained unsure why the estimator worked so well.
Only within the past few years has an outside group come up with a method for quantifying the success of the Good-Turing algorithm. Now that work, by Alon Orlitsky and his colleagues at the University of California-San Diego's Department of Electrical Engineering, has yielded a statistical estimator that the researchers say is more accurate than Good-Turing over time. The innovation is asymptotic, meaning that it will eventually outperform Good-Turing predictions on given sequences. But the rate of convergence is a practical issue that needs more work, Orlitsky said.
As Orlitsky's team tried to measure the performance of Good-Turing, it discovered a definite limit on how well the method performs. A precise mathematical formulation of that limit led to insights into creating a limitless estimator.
The estimation problem is commonly encountered in applications of probability theory: Given a random data stream, infer the probability distribution that generates it. For example, observations of a long string of binary digits generated by repeated coin tosses would quickly reveal that the occurrence of each digit is equally likely. Even if an observer doesn't know how the string of bits is generated, the frequency patterns will give clues to its generation. As the data stream lengthens, the frequencies will converge to equal outcomes for each digit-and in general, the longer the sequence, the better the estimation technique becomes.
"If the number of possible outcomes is small, the problem is easy. But with a large set of outcomes, the optimal distribution begins to disappear into noise," Orlitsky said. In addition, it is necessary to include all possible outcomes in the estimation of a probability distribution even if they do not occur-the so-called "hidden outcome" problem.
Orlitsky uses the example of a safari drive that yields sightings of three giraffes, one zebra and two elephants. Based on that experience, one might naturally assign probabilities of 1/2 for encountering giraffes, 1/6 for zebras and 1/3 for elephants. But that assumption fails to recognize that the next animal encountered might be a lion. To avoid a nasty surprise, the good estimator would take the entire set of known species in the area of the game drive into account and assign a probability to all species in the set.
That was the problem faced by British cryptologists during the World War II. The German Enigma encryption machine used a huge number of decryption keys, making it almost impossible to crack the code. British intelligence had gained possession of Enigma machines, had determined how they worked and had even obtained a copy of the full book of keys. Some messages had been decrypted and the keys used recorded, so that the code breakers had a small sample from a very large set of keys. But it was unlikely the Germans would continue to use the same keys, so some method of assigning a probability distribution to the keys not yet used was needed.
Instead of quantifying the occurrence of keys, Good and Turing decided to quantify the frequencies at which keys occurred. It seems intuitive that if a key has been seen frequently already, it is less likely to occur in the future, while one that has not yet occurred or has been seen only once will have a higher probability of appearing.
Turing assumed that the frequencies would follow a standard binomial distribution. Taking the frequency of known keys as empirical data, he assigned probabilities to the entire set of keys.
It was a promising approach, but the method suffered from noise problems. Good introduced smoothing algorithms on the data to eliminate the noise. That was the genesis of the Good-Turing estimator.
The data-smoothing aspect is key to getting the method to work effectively, and a lot of work over the years has gone into devising better smoothing techniques. Depending on how data is smoothed, different versions of the Good-Turing estimator have been created for different applications. By coming up with a means of quantifying the success of these different estimators, Orlitsky found that they all have a hard limit on their effectiveness.
Orlitsky was able to discover this limit by quantifying the problem in terms of the positive integers. The nature of the sample set is actually irrelevant to the probabilistic algorithm. What matters is the order in which outcomes appear and how often they appear. So a sample sequence such as giraffe, giraffe, elephant, giraffe, zebra would be encoded in numbers as 1,1,2,1,3. Every time a new item appears, it is assigned the next-highest number, so that this mathematical model, according to its creators, can capture the worst possible problem-one in which there is an infinite number of hidden data items.
Using numbers as the sample set also makes it possible to consider the asymptotic behavior of estimators as the length of sampled data increases indefinitely.
A given method for estimating the probability of a sequence of numbers is compared with the maximum probability assigned to the sequence by all possible probability distributions. Specifically, Orlitsky defines the attenuation of an estimator as the ratio of the maximum value resulting from the application of all possible probability distributions to the value assigned by the estimator. Since an estimator uses some probability distribution, its value will always be lower than the maximum value, so this measure is always greater than 1. Thus, a figure of merit would be how close the attenuation of an estimator approaches 1.
"That type of definition has been used before on problems where the sample set is small and known, but we have extended it to large, even infinite sample sets," Orlitsky said. By looking at how attenuation varies as the length of a data stream increases, Orlitsky and his colleagues were able to discover the ultimate limits of a given estimation technique.
A common technique known as the add-constant estimator, which was first suggested by Pierre-Simon Laplace, the inventor of probability theory, turns out to be very poor. As the data stream lengthens, the estimates actually diverge away from 1; thus add-constant estimators have infinite attenuation. That was a surprising finding, because add-constant estimators have always been a simple and effective approach on small-sample-set problems.
Good-Turing estimators always stay within a factor of 2 of the optimum probability, but Orlitsky discovered that they have a lower limit as well. He was able to show that an estimator with one of the simplest smoothing algorithms could not get below a factor of 1.39 of the best possible estimation for a string of data. Estimators with more complex smoothing algorithms were difficult to analyze, but simulations indicated that they too had a lower limit on their attenuation.
"Theoretically we can show that it is possible to create estimators that attenuate to 1, but the practical aspect is how fast they converge," Orlitsky said. "That is a problem we are working on now-and we have some new results that we are not ready to talk about at this time."
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s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948512208.1/warc/CC-MAIN-20171211052406-20171211072406-00165.warc.gz
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CC-MAIN-2017-51
| 7,871 | 19 |
http://mgoblog.com/content/2008-usa-today-preseason-poll?page=19%2C1%2C1%2C0%2C0%2C0%2C1
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math
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"This is really important to be here," Lewan said. "I'm here to give back and help out my teammate."
2008 USA Today Preseason Poll
August 1st, 2008 at 10:51 AM#952
That is surprising...
about both Michigan and Utah. I would have guessed their places would be reversed. Also, Duke didn't receive any votes this year. Did Spurrier actually cave? Notre Dame got 5 votes. Do you think they got 5 votes at 25th or did Weis rank them at 20th?
August 1st, 2008 at 10:56 AM#953
Wow, 24? Really? I sort of
Wow, 24? Really? I sort of would have liked to be further down.
August 1st, 2008 at 10:58 AM#954
I think that they alot votes
I think that they alot votes by mass, hence Charlies counted 5 times.
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s3://commoncrawl/crawl-data/CC-MAIN-2015-27/segments/1435375093899.18/warc/CC-MAIN-20150627031813-00015-ip-10-179-60-89.ec2.internal.warc.gz
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CC-MAIN-2015-27
| 692 | 11 |
http://rfteststation.com/physics-lecture-notes-phys-395-electronics-book/150/
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math
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CHAPTER 7. DIGITAL CIRCUITS148At any time only one gate may drive information onto the bus line but several gates mayreceive it. In general, information may flow on the bus wires in both directions. This typeof bus is referred to as a bidirectional data bus.7.8Two-State Storage ElementsAnalog voltage storage times are limited since the charge on a capacitor will eventually leakaway. The problem of discrete storage reduces to the need to store a large number of two-state variables. The four commonly used methods are: 1) magnetic domain orientation, 2)presence or absence of charge (not amount of charge) on a capacitor, 3) presence or absenceof an electrical connection and 4) the DC current path through the latches and flip-flops ofa digital circuit. We will discuss only the latter.7.9Latches and Un-Clocked Flip-FlopsIt is possible using basic logic gates to build a circuit that remembers its present condition.It is also possible to build counting circuits. The basic counting unit is the flip-flop (FF).7.9.1LatchesAll latches have two inputs: data and enable/disable. And typically Q and Q outputs. Aones-catching latch can be built as shown in figure 7.17.When the control input C is false, the output Q follows the input D, but when the con-trol input goes true, the output latches true as soon as D goes true and then stays thereindependent of further changes in D.One of the most useful latches is known as the transparent latch or D-type latch. Thetransparent latch is like the ones-catching latch but the input D is frozen when the latch isdisabled. The operation of this latch is the same as that of the statically triggered D flip-flopdiscussed below.7.9.2RS and RS Flip-FlopsThe RS flip-flop (RSFF) is the result of cross-connecting two NOR gates as shown in fig-ure 7.18. The RS inputs are referred to as active ones.The ideal flip-flop has only two rest states, set and reset, defined by QQ = 10 and QQ = 01,respectively.A very similar flip-flop can be constructed using two NAND gates as shown in figure 7.19.The RS inputs are now active zeros.These FFs are often referred to as the set/reset type and are un-clocked.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257648000.93/warc/CC-MAIN-20180322190333-20180322210333-00314.warc.gz
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CC-MAIN-2018-13
| 2,159 | 1 |
http://eyassignmenttdnt.getfiredband.us/mat-116-assignment-functions-and-their.html
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math
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Mat 116 mathematics for life 3 cr emphasis on functions and their graphs and lab assignments prereq: placement or mat 221 with a grade. Mat 116 assignment functions and their graphsdoc mat 116 assignment solving inequalities and graphing equationsdoc mat 116 assignment systems of.
Mat 116 week 6 exercise: day 4 [assignments section] post your 50-word response to the following: assignment: functions and their graphs resource: appendix e. Nonlinear functions, sequences, and series use logarithmic functions use arithmetic and geometric sequences and series use composite functions. Mat 116 complete class to purchase this visit here: contact us assignment: functions and their graphs. Comprehensive course tutorials for mat 116 the tutorials offered include all assignments, week tutorials, all dqs, quizzes, and final exam.
In my math lab, assignment:function and graphs(quiz) week6 mat/116 - answered by a verified math tutor or teacher. Mat 116 uop course tutorial / mat116dotcom mat 116 assignment: functions and their graphs mat 116 assignment: expressions and equations. Free essays on mat 116 week 6 assignment for students use our papers to help you with yours 1 - 30. Mat 116-college algebra section 05 crn 20627 mat 116, section 05 meets t r you are encouraged to complete all homework assignments and problems.
Description this course is intended for the non-mathematics student who needs an enhanced foundation in algebra and trigonometry the topics include algebraic and trigonometric functions and their graphs. This pack includes mat 116 assignment functions and their graphs resource: appendix e, mymathlab® due date: day 7 [individual forum and mymathlab®]. Mat 116 week one dq 1 what are the steps of the order of operations mat 116 week 6 assignment functions and their graphs appendix e mat 116 week 6 dq 1. Mat 116 week 6 assignment: functions and their graphs (appendix e) -complete appendix e to apply the skills learned in ch 7 to a real-life situation.
Assignment: functions and their graphs • resource: appendix e mat 116 week 6 exercise: week six concept check • due date: day 4 [assignments section]. Some typical files mat 116 assignment expressions and equationsdoc mat 116 assignment functions and their graphsdoc mat 116 assignment solving inequalities. Thank you mat 116 application assignment #3 let's go for the distance traveled by the anthropologist as a function of time t is given as.
Mat 116 -mat 116 algebra 1a version 5 12/15/07 mat 116 algebra 1a course syllabus mat 116 program council assignment: functions and their graphs. Mat 116 – college algebra course assignments otherwise a exponential functions and their applications b logarithmic functions and their applications. Describe a real-life situation that could be modeled by a function mat 116 week 6 assignment functions and their graphs appendix e.Download
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s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267160400.74/warc/CC-MAIN-20180924110050-20180924130450-00173.warc.gz
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CC-MAIN-2018-39
| 2,870 | 6 |
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math
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s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571147.84/warc/CC-MAIN-20220810040253-20220810070253-00595.warc.gz
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http://tcisiah79.blogspot.com/2017/07/sir-isaac-newton.html
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math
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Sir Isaac Newton is known for his theory about the 3 laws of motion which his first law is the law of inertia, Meaning an object will remain stationary or in motion unless an unbalanced force is acted upon it for example A ball will stay stationary unless a force (foot) is acted on it, e.g your foot kicking the ball,
His second law of motion is the law of acceleration meaning the greater the mass the more force needed to accelerate it e.g if their were two balls with an unequal mass then for one ball you will have to apply more force than the other, with the equation F= M x A.
Newtons third and final law is the law of action and reaction meaning with every action there is an equal an opposite reaction an example is if you jump on a trampoline the action is you jumping and the equal and opposite reaction is the trampoline pushing you up.
The game inertia ball demonstrated the three laws of motion, The first law of inertia was shown in the game when we had to throw the smaller balls at the big ball, It was shown when the force of the thrown ball hit the staple big ball causing in to move. The second law (law of acceleration) was shown when we threw the basketball with the basketball having a greater mass the force had a stronger impact then the tennis ball did.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376826715.45/warc/CC-MAIN-20181215035757-20181215061757-00082.warc.gz
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https://ridto.com/travel-average-speed-calculator/
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math
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Certainly, the Travel Average Speed Calculator is a tool that helps users determine the average speed at which they've travelled given the distance covered and the time taken. Here's how the calculator works and how to use it:
Step 1: Input Values
Distance: Enter the distance you've travelled. This can be in miles, meters, kilometres, or yards, depending on the options available in the drop-down menu.
Time: Specify the time it took you to cover the given distance. Input the hours, minutes, and seconds separately.
Step 2: Calculate Results
After providing the necessary input values, click the "Calculate" button or similar action provided by the calculator.
Step 3: Review Results
The calculator will provide you with the following information:
Average Speed in Miles per Hour (mph): The calculated average speed is based on the provided distance and time.
Average Speed in Kilometres per Hour (km/h): The average speed converted to kilometres per hour.
Average Speed in Metres per Second (meters/sec): The average speed converted to meters per second.
Average Speed in Feet per Minute (feet/minute): The average speed converted to feet per minute.
Step 4: Understand the Results
Review the calculated results in the table to understand your average speed in different units of measurement.
Step 5: Interpretation
You can use the calculated average speeds to understand how fast you were travelling relative to different units of measurement. For instance, if you travel at a certain speed in miles per hour, you can see how that speed translates to kilometres per hour, meters per second, and feet per minute.
This Travel Average Speed Calculator is useful for those who want to know their average speed during a journey, whether it's a road trip, a run, or any other form of travel. It's a handy tool to have, especially when you need to convert your average speed between different units for better comprehension or comparison.
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CC-MAIN-2024-10
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math
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Originally Posted by ratherunique
right now i'd say my thief of thieves #1 comicspro variant
still cant understand how this book is not more valuable. the regular #1 sells for about $50 there is like 15,000 of those. the comics pro sells for like $150 and i have heard there is only 500 or less. if priced according to scarcity this book should be selling for like $1500 lol but i think it should at least be a $500 book min.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917125881.93/warc/CC-MAIN-20170423031205-00199-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 425 | 3 |
https://asving.com/category/group-cohomology/
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math
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It is quite often of interest to study the properties of some variety . However, it is generally much easier to study varieties over algebraically closed fields and so we need some way of translating a property of to . This idea is known as descent and in this post, I would like to say a little bit about the simplest example of descent – over vector spaces.
Let be an extension of fields and a vector space over . Consider . The Galois Group acts on through the second factor (not by linear actions but by semi-linear ones – see below). One can consider the -vector space . This is the vector space fixed by .
Theorem 1 (Descent of Vector Spaces) The natural map is an isomorphism. In particular, if is finite dimensional, then .
It is not hard to prove this theorem directly (Theorem 2.14 in these notes of K. Conrad) but I would like to relate it to another theorem. This is also well known and is a generalization of the famous Hilbert’s Theorem 90. Let be the group of invertible -dimensional matrices over and consider the cohomology . This is not a group unless since is non-commutative in general. However, it is a pointed set and we have the following theorem:
Theorem 2 (Hilbert’s 90)
Hilbert stated the above theorem (in a disguised form) for and a finite cyclic extension. Noether generalized the theorem to arbitrary extensions. I do not know who is responsible for the generalization to general linear groups but I saw this theorem first in Serre’s “Galois Cohomology”.
In this post, I will show that the above theorems are equivalent in the following sense:
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s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572174.8/warc/CC-MAIN-20220815115129-20220815145129-00628.warc.gz
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CC-MAIN-2022-33
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http://bcassignmenthhgv.strompreisevergleichen.info/mathematics-homework-help.html
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math
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Homework help find homework resources for k-12 students online and at all our libraries: history, language arts, math, science and more jump to. A writing lab provides help within 24 hours of submitting your work online and a test center for the sat, discovery math homework help - resources to help. Get mathematics help at studypool post your mathematics homework questions and get answers from qualified tutors thousands of online mathematics tutors.
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CC-MAIN-2018-43
| 3,483 | 7 |
http://www.ravelry.com/patterns/library/pullover-sweater-2
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math
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Instructions are given for x-small, larger sizes are given in square brackets.
Where only one figure is given, this applies to all sizes. Where the figure 0 appears, no sts, rows or times are worked for this size.
Materials Needed: 50g balls Pure Merino DK Shade WM2 Soft Pink
x-small = 7
small = 8
medium = 9
large = 10
x-large = 11
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917123484.45/warc/CC-MAIN-20170423031203-00154-ip-10-145-167-34.ec2.internal.warc.gz
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| 333 | 8 |
http://qgessayruym.bethanyspringretreats.us/limiting-reagents-and-percentage-yield-worksheet.html
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math
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Stoichiometry worksheet: mole-mole problems 32 stoichiometry worksheet: mass-mass problems 34 limiting reactant and percent yield worksheet 36. Module six – limiting reagents, theoretical yields and percent yields introduction to module six the introduction to module 4 includes the following balanced.
What is a limiting reagent limiting reagents and percent yield please turn in c7/c10 worksheet objectives: determine the limiting reagent in a.
Practice problems: limiting reagents (answer key) take the reaction: 716 g c6h5br b if the actual yield of c6h5br is 636 g, what is the percent yield. What is the percent yield of a reaction in which 415 g of solid tungsten(vi) oxide a limiting reagent is the reactant that is completely used up in a reaction. Ii) what percentage yield of iodine was produced 2 zinc and sulphur react to form a) which chemical is the limiting reactant b) how many grams of zns will .
1 limiting reactant and percent yield practice name________________________________________ 1) consider the following reaction: nh4no3 +.
Limiting reagents and percentage yield worksheet answersdoc - free download as word doc (doc), pdf file (pdf), text file (txt) or read online for free. The limiting reagent (or limiting reactant, lr) in a chemical reaction is the substance that is the limiting reagent must be identified in order to calculate the percentage yield of a reaction, since the theoretical yield is defined as the amount of product obtained when the limiting reagent reacts completely given the balanced.
How to determine the limiting reagent, and using stoichiometry to calculate the theoretical and percent yield. Stoichiometric calculations - limiting reagents and percentage yield find the limiting reactant, if any, and calculate the theoretical yield, (in moles) of water solution: stoichiometry limiting reagents and % yield calculations worksheet.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039746800.89/warc/CC-MAIN-20181120211528-20181120232536-00002.warc.gz
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CC-MAIN-2018-47
| 1,888 | 6 |
https://www.black-holes.org/explore/glossary/41-p/85-pi
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math
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or π (Pronounced as "pie".) An important number in geometry. This is defined to be the ratio of the circumference of a circle to the diameter of that circle, in flat space. π is an irrational number, which means that its exact value cannot be written down, though it can be calculated as precisely as necessary. Its value is approximately 3.14159265358979323...
Come, you lost Atoms, to your Centre draw,
And be the Eternal Mirror that you saw:
Rays that have wander'd into Darkness wide,
Return and back into your Sun subside.
From Farid al-Din Attar's
The Conference of the Birds
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https://gazzarra.org/2020/04/06/achieving-success-through-used-mathematics/
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math
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Developments in applied mathematics are currently impacting different areas of the world of today. The newest techniques of mathematics’ effect is running a finance and operation. Z teachers can help students mba application essay prepare for business careers by delivering their application in real life scenarios along with educational opportunities for problem solving.
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CC-MAIN-2021-25
| 4,129 | 12 |
https://allisonbrookephotography.com/which-linear-inequality-is-represented-by-the-graph-y-gt-2x-2-y-x-1-y-gt-2x-1-y-x-2/
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math
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You deserve to see the y = x + 2 line, and the shaded area is where y is less than or same to x + 2
A straight Inequality is like a straight Equation (such as y = 2x+1) ...
You are watching: Which linear inequality is represented by the graph? y > 2x + 2 y ≥ x + 1 y > 2x + 1 y ≥ x + 2
... However it will have actually an Inequality choose , ≤, or ≥ rather of an =.
How to Graph a straight Inequality
First, graph the "equals" line, then the shade in the exactly area.
See more: Kyou Kara Ore Wa Loli No Himo!
There space three steps:Rearrange the equation so "y" is ~ above the left and everything rather on the right.Plot the "y=" heat (make that a hard line for y≤ or y≥, and also a dashed line because that y)Shade over the line because that a "greater than" (y> or y≥) or below the line because that a "less than" (y
Let us try some examples:
1. The inequality already has "y" top top the left and also everything rather on the right, therefore no have to rearrange
2. Plot y=2x-1 (as a heavy line due to the fact that y≤ includes equal to)
3. The shade the area listed below (because y is less than or equal to)
1. Us will need to rearrange this one for this reason "y" is on its own on the left:
2. Currently plot y = 2x − 4 (as a dashed line because y> walk not include equals to)
3. The shade the area above (because y is greater than)
The dashed line shows that the inequality walk not include the heat y=2x-4.
Two one-of-a-kind Cases
You could likewise have a horizontal or vertical line:
|This reflects where y is much less than 4 (from, however not including, the line y=4 on down)Notice that we have actually a dashed line to display that it does not encompass where y=4||This one doesn"t even have y in it!It has the heat x=1, and is shaded because that all worths of x better than (or equal to) 1|
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s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103922377.50/warc/CC-MAIN-20220701064920-20220701094920-00345.warc.gz
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CC-MAIN-2022-27
| 1,832 | 19 |
http://mathhelpforum.com/algebra/109001-work-problem.html
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math
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Workers A and B can do a certain task together in 12/7 hours. If A starts early and works for 1 hour only, B takes 8/3 hours to finish the rest of the task. How long does it take each worker to do the task alone?
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s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560284376.37/warc/CC-MAIN-20170116095124-00426-ip-10-171-10-70.ec2.internal.warc.gz
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CC-MAIN-2017-04
| 274 | 3 |
http://mathhelpforum.com/trigonometry/3508-tis-question-so-confusing-hu-can-solve.html
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math
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(a)The arc lamp to the shadow, and the man's head to the shadow form two similar triangles.Originally Posted by xiaoz
The ratio of height to base for the man's triangle is
The ratio of height to base for the arc-lamp triangle is
Because the triangles are similar, the two ratios are equal...
Which means the height of the arc-lamp triangle is 9m.
(b) This is an interesting question. Imagine the man on a co-ordinate plane with the arc-lamp in the center. He is on point (10,0) and walks to point (10,20).
We need to first find the distance between him and the lamp. The distance formula is...
Just to make it easy to write, we'll say the distance between the man and the lamp is
Now we know the heights of both triangles, we know they're similar, so we remake our ratios...
and solve from there.
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s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698543030.95/warc/CC-MAIN-20161202170903-00409-ip-10-31-129-80.ec2.internal.warc.gz
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CC-MAIN-2016-50
| 796 | 10 |
https://www.hackmath.net/en/math-problem/40491
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math
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Jacobs mom bought two whole pizzas. He ate 2/10 of the pizza and his dad ate 1 1/5. How much is left.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178374391.90/warc/CC-MAIN-20210306035529-20210306065529-00401.warc.gz
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CC-MAIN-2021-10
| 2,455 | 37 |
https://books.google.com.jm/books?id=uCMAAAAAYAAJ&vq=%22have+an+angle+of+the+one+equal+to+an+angle+of+the+other,%22&dq=editions:UOM39015063898350&lr=&output=html_text&source=gbs_navlinks_s
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math
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Other editions - View all
allel altitude apothegm Axiom Bisect the angles Book chord circle circumference coincide cone construction convex surface diagonal diameter diedral divided draw drawn equal Theo equal to half equally distant equilateral triangle equivalent exterior angle figure frustum Geometry given angle given line given point given straight line half the product Hence hexagon homologous sides hypotenuse hypothesis inscribed inscribed angle intersection isosceles Let ABC measured by half mutually equiangular number of equal number of sides parallel parallelogram parallelopiped pendicular perimeter perpendicular plane polyedron prism Prove pyramid quadrilateral Ques radii radius ratio rectangle regular polygon respectively equal right angles right-angled triangle secant segment slant height sphere square tangent tetraedron THEOREM THEOREM XI third trapezoid trian triangles ABC triedral vertex
Page 104 - If from a point without a circle, a tangent and a secant be drawn, the tangent will be a mean proportional between the secant and its external segment.
Page 54 - The circumference of every circle is supposed to' be divided into 360 equal parts, called degrees ; each degree into 60 minutes, and each minute into 60 seconds. Degrees, minutes, and seconds are designated by the characters °, ', ". Thus 23° 14' 35" is read 23 degrees, 14 minutes, and 35 seconds.
Page 42 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Page 107 - The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R
Page 147 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 140 - A cone is a solid figure described by the revolution of a right-angled triangle about one of the sides containing the right angle, which side remains fixed.
Page 50 - The area of a regular polygon is equal to half the product of its apothem and perimeter.
Page 141 - The altitude of a pyramid or cone is the perpendicular distance from the ve~rtex to the base.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296818067.32/warc/CC-MAIN-20240421225303-20240422015303-00400.warc.gz
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CC-MAIN-2024-18
| 2,219 | 10 |
https://www.arxiv-vanity.com/papers/1803.08215/
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math
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Implementing Tidal and Gravitational Wave Energy Losses in Few-body Codes: A Fast and Easy Drag Force Model
We present a drag force model for evolving chaotic few-body interactions with the inclusion of orbital energy losses, such as tidal dissipation and gravitational wave (GW) emission. The main effect from such losses is the formation of two-body captures, that for compact objects result in GW mergers, and for stars lead to either compact binaries, mergers or disruptions. Studying the inclusion of energy loss terms in few-body interactions is therefore likely to be important for modeling and understanding the variety of transients that soon will be observed by current and upcoming surveys. However, including especially tides in few-body codes has been shown to be technically difficult and computationally heavy, which has lead to very few systematic tidal studies. In this paper we derive a drag force term that can be used to model the effects from tidal, as well as other, energy losses in few-body interactions, if the two-body orbit averaged energy loss is known a priori. This drag force model is very fast to evolve, and gives results in agreement with other approaches, including the impulsive and affine tide approximations.
keywords:gravitation – methods: numerical – stars: black holes – stars: kinematics and dynamics
Transient events, including gravitational wave (GW) mergers (2016PhRvL.116f1102A; 2016PhRvL.116x1103A; 2016PhRvX...6d1015A; 2017PhRvL.118v1101A; 2017PhRvL.119n1101A; 2017PhRvL.119p1101A), stellar mergers (e.g. 2011A&A...528A.114T), and stellar tidal disruptions (e.g., 2016ApJ...823..113P, and references therein), are often the product of a two-body or a dynamical few-body system loosing orbital energy through one or more dissipative mechanisms. The most important of such mechanisms include energy dissipation through the the emission of GWs (e.g. Peters:1964bc; Hansen:1972il; 1977ApJ...216..610T), and orbital energy losses through tidal excitations (e.g. 1977ApJ...213..183P; 1986ApJ...310..176L) and dissipation (e.g. 2014ARA&A..52..171O, and references therein). In the isolated binary problem, these effects will lead to a merger between the two objects within a finite time, and depending on the stellar types the final binary evolution will either be dominated by GWs (e.g. Peters:1964bc) (if both objects are compact), tides (2014ARA&A..52..171O) (if at least one object is a star), or common envelope evolution (e.g. 1976IAUS...73...75P; 1993PASP..105.1373I; 2000ARA&A..38..113T; 2018arXiv180303261M) (if one of the objects evolves to indulge the other).
During chaotic interactions involving three or more objects, the loss or dissipation of orbital energy often results in the formation of eccentric two-body captures (e.g. 1992ApJ...385..604K; 2014ApJ...784...71S; 2016ApJ...823..113P; 2017ApJ...846...36S). A capture refers here to a scenario involving a very close approach between two objects with such a small pericenter distance that the energy loss over one orbit is large enough for the two objects to quickly inspiral and detach from the rest of the -body system. Such captures are well known and studied in the single-single case (e.g. Hansen:1972il; 1975MNRAS.172P..15F; 1977ApJ...213..183P; 1985AcA....35..401G; 1985AcA....35..119G; 1986AcA....36..181G; 1986ApJ...310..176L; 1993ApJ...418..147L). Their outcome could have interesting observational consequences, from the formation of transients (e.g. 2016ApJ...823..113P), to compact mass transferring binaries (e.g. 1975MNRAS.172P..15F; 1975ApJ...199L.143C). Interestingly, recent studies indicate that such captures form at a higher rate during few-body interactions, compared to single-single interactions. For example, it was recently shown by 2014ApJ...784...71S, that the rate of eccentric binary black hole (BBH) mergers forming through captures mediated by gravitational wave emission likely is dominated by three-body interactions, and not single-single interactions. Similar eccentric mergers can also form through tidal captures in three-body interactions, as shown by 2008MNRAS.384..376G; 2010MNRAS.402..105G; 2017ApJ...846...36S. The point here is that the majority of such eccentric capture mergers are likely to form in dense stellar systems, compared to say the field, and any observation of such eccentric sources will therefore be an indirect probe of the dynamical channel for BBH and other mergers and the importance of dense stellar environments. Despite their possible importance, energy loss terms are often not included in the -body equations-of-motion (EOM) (e.g. Fregeau2004). For this reason how energy losses during strong few-body encounters, including GWs and tides, affect not only the host cluster dynamics, but also the range of relevant observables, is not yet well understood.
Energy dissipation from GW emission is not difficult to include in -body codes thanks to the development of the post-Newtonian (PN) formalism (e.g. 2014LRR....17....2B), and aspects of such corrections have therefore been studied. For example, using full -body simulations 2006MNRAS.371L..45K showed how large BHs can form in a GW capture run-away. Similarly, 2014ApJ...784...71S; 2017ApJ...840L..14S; 2017arXiv171107452S; 2018ApJ...853..140S performed isolated three-body scatterings which lead them to conclude that the GW captures forming during the interactions are likely to dominate the rate of eccentric BBH mergers forming in globular clusters (GCs) observable by the ‘Laser Interferometer Gravitational-Wave Observatory’ (LIGO). A monte-carlo (MC) approach for studying the evolution of GCs including scatterings up to binary-binary interactions with PN terms was recently presented by 2017arXiv171204937R, along with a similar study by 2017arXiv171206186S, who both confirmed that GW emission in the -body EOM is crucial for probing the population of eccentric BBH mergers forming in clusters (2017arXiv171107452S).
Including tides is significantly more difficult than gravitational wave emission. This is due not only to our limited understanding of stellar structure and the mechanism(s) via which tides are excited and subsequently dissipated, but also because tidal effects are extremely time consuming to computationally evolve in an -body code. Some few-body studies have been done using full hydro dynamics (e.g. 2010MNRAS.402..105G), but doing large systematic studies are not yet possible due to computational limits. Other methods for studying the effects from dynamical tides include the impulsive approximation, where tidal energy and angular momentum losses are included by simply correcting the velocity vectors at pericenter ‘by hand’ every time two of the objects pass very close to each other (e.g. 2006MNRAS.372..467B). A similar approach was also used by Mardling:2001dl, and does indeed work. But, making such discontinuous corrections to the -body system often lead to poor performance and complicated decision making. Finally, other approaches include only solving for the evolution of a subset of the tidal modes, which can be done in both linear tidal theory (Mardling:1995hx) using the Press and Teukolsky (PT) approach (1977ApJ...213..183P), and non-linearly using the so-called affine model (1985MNRAS.212...23C; Luminet:1986cha; 1992ApJ...385..604K; 1992MNRAS.258..715K; 1993ApJS...88..205L; 1993ApJ...406L..63L; 1994ApJ...420..811L; 1994ApJ...423..344L; 1995ApJ...443..705L; 1995MNRAS.275..498D; 1996PThPh..96..901O; 2001ApJ...549..467I; 2003MNRAS.338..147I; 2017ApJ...846...36S); a model we will apply later in this paper. However, such prescriptions are still too computationally expensive for say parameter space studies and derivations of tidal capture cross sections (2017ApJ...846...36S); other strategies are therefore needed.
In this paper we propose to include energy loss effects in few-body codes through a simple drag force term in the equations-of-motion. Many few-body codes have already been optimized to include drag forces, e.g., the 2.5 PN term that accounts for energy dissipation through the emission of GWs is no more than a simple drag force. Our ansatz in this paper is therefore to derive a general drag force that can be used to model any energy loss effects, and again, with tides as the main motivation. The only input our drag force model requires is an estimate for the amount of orbital energy lost if two of the objects undergo a near parabolic encounter. This has been calculated in several studies for tides (1977ApJ...213..183P; 1986ApJ...310..176L), and fitting formulae have also been provided to speed up these calculations (e.g. 1985AcA....35..401G; 1993A&A...280..174P).
As illustrated in this paper, the use of such fitting formulae together with our proposed drag force model allows one to quickly evolve few-body systems with both energy losses from tides and GW emission. We note here that our model does not give any new insight into the two-body tidal problem, but it will be able to provide insight into how especially tides affect the evolution of chaotic few-body interactions. For that reason, our model has the same limitations as the two-body tidal problem, e.g., we are not able to predict what happens after a tidal capture; do the two objects merge or do they form a stable binary? However, what we are able to accurately probe and resolve the number of tidal captures forming in chaotic few-body interactions. We illustrate this in a few examples, by performing controlled two-body and three-body experiments with different tidal implementations, including our proposed drag force model. In the near future we plan to include this model into the MOCCA (MOnte Carlo Cluster simulAtor) code (Hypki2013; Giersz2013), which will allow us to perform systematic studies of how tidal energy losses in chaotic interactions could affect observables and feedback in to the underlying host cluster dynamics. These are key questions that have to be addressed, as new searches for transient phenomena will soon be monitoring the sky, including LSST (2009arXiv0912.0201L), JWST (2006SSRv..123..485G), and WFIRST (2013arXiv1305.5422S).
The paper is organized as follows. In Section 2 we present our drag force model, and describe how to normalize it for different energy loss mechanisms. We especially discuss how to apply it for describing tidal energy losses, which is the main motivator for this paper. A short step-by-step description of how to implement the model in an -body code is also given. In Section 2 we numerically evolve a few two-body and three-body scattering experiments involving tidal and compact objects with the inclusion of our proposed drag force model. We especially compare our drag force results with other tidal prescriptions, including the impulsive and affine tidal approximations. Conclusions are given in Section LABEL:sec:conclusions.
2 Drag Force Model
In this section we describe and derive our proposed tidal drag force model, that in principle can be used to dynamically evolve chaotic few-body systems with the inclusion of any type of energy loss mechanism; however, our main motivation is how tidal effects impact the evolution. In short, our approach is to model orbital energy losses by introducing a drag force that acts against the relative motion between any pair of objects in the few-body system. For deriving the drag force, we assume that the largest energy loss occurs during close pairwise encounters, and that these encounters can be considered as isolated two-body systems during the period where most of the energy is lost (see Figure 1). This is an excellent assumption, as basically all of the relevant energy loss mechanisms depend steeply on the relative distance between the objects, implying that most of the energy loss in few-body systems do indeed take place during close pairwise encounters (e.g. 2017ApJ...846...36S). The amount of energy that is lost over a single close passage for an isolated two-body system has been studied extensively in the literature, both for GWs (Peters:1964bc; Hansen:1972il; 1977ApJ...216..610T) and tides (1977ApJ...213..183P; 1985AcA....35..401G; 1985AcA....35..119G). Following our assumption that every object pair in the few-body interaction can be treated as an isolated binary when modeling the energy loss, this allows us to derive the normalization of the drag force, a computation has to be done at each time step.
The functional form of the drag force that controls how energy is lost over a given orbit has to be such that most of the loss takes place near the pericenter of the two considered objects. This emulates how the energy is actually lost in many mechanisms, and it naturally makes the assumption of pairwise two-body isolation a good approximation for the purpose of modeling energy losses. We note that with such a drag force the pairwise energy loss will be close to that found from the impulsive approach, where the individual velocity vectors are ‘corrected by hand’ at each pericenter passage (e.g. 2006MNRAS.372..467B). However, the loss of energy due to the drag force will happen continuously over the orbit, which makes our approach both more realistic and easy to implement in modern few-body codes. In fact, besides the implementation of the drag force into the few-body code described in 2017ApJ...846...36S that we will use in this paper, we have already successfully implemented it in the regularized code used in (e.g. 2016ApJ...831...61T)
In the sections below we illustrate how a drag force with the properties described above can be constructed. We also discuss its limitations, and what can be improved.
2.1 Drag Force Functional Form
We consider two objects on a Kepler orbit, bound or unbound, with an initial semi-major (SMA) and eccentricity . For this system we now consider a drag force with magnitude that acts against the orbital motion of the two objects, as further described and illustrated in Figure 1. In this picture, the two-body system will loose an amount of orbital energy per differential line element integrated along the orbit. Assuming that the change in orbital angular momentum per orbit is negligible, one can in all relevant cases approximate the total energy loss over one orbit, denoted by , by the following integral (see 1977ApJ...216..610T for a similar procedure applied to GW energy losses),
where is the differential change in time, is the true anomaly, and for a bound orbit and for an unbound orbit (see Figure 1). The term is simply the relative velocity between the two interacting objects, denoted by , which can be written as,
where is the total mass of the two interacting objects, referred to as and , and is their relative distance. The term can be derived from Kepler’s relation , from which it follows,
To proceed we now have to chose a functional form for the drag force, . As described, the form should both be simple to implement in a few-body code, possibly similar to the 2.5 PN drag force that has been successfully implemented in many recent few-body codes, while ensuring that most of the energy loss happens at pericenter. A first proposed form could be a force that is , where is some power; however, in this case one finds that the integral in Equation \eqrefeq:intDE does not have an analytical solution for any , including . This ‘problem’ relates to the fact that the circumference of an ellipse cannot be written out in a closed form. This is why ‘elliptical’ integrals always have to be solved numerically. However, if we instead choose a force that is , then the integral in Equation \eqrefeq:intDE can be written out in closed form for any , which allows us to analytically estimate the drag force normalization, or coefficient. This leads to a very fast derivation of the drag force per time step. In this paper we therefore choose to work with the following drag force,
where is a normalization factor that to leading order depends on the orbital parameters for the two-body system and the considered energy loss mechanism. Although this choice of drag force could seem arbitrary, we note that the 2.5 PN drag force is exactly of this type with . Therefore, a code that is optimized to run with PN terms, should have no problem in evolving the system with our proposed drag force. Below we illustrate how to estimate the drag force coefficient .
2.2 Drag Force Normalization Coefficient
The coefficient of the drag force introduced in the above Equation \eqrefeq:DF_eq, can be estimated using Equation \eqrefeq:intDE assuming that is known a priori for the considered two-body system. After some algebraic manipulations we find from solving equation \eqrefeq:intDE with our proposed drag force from Equation \eqrefeq:DF_eq that,
where is the solution to the following integral
This factor can be written out in closed form for any value of . In this paper we will study the performance for two different values of , namely for and . For these two cases evaluates to,
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s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057524.58/warc/CC-MAIN-20210924110455-20210924140455-00398.warc.gz
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CC-MAIN-2021-39
| 17,007 | 24 |
https://ipht.cea.fr/Phocea/Vie_des_labos/Seminaires/index.php?id_type=1&type=1&id=992728
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math
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Liouville theory with a central charge less than one
Lundi 15/12/2014, 11:00
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
We argue that for any value $c leq 1$ of the central charge there exists a consistent CFT whose spectrum is the same as in Liouville theory. This extends the definition and consistency of Liouville theory to all complex values of $c$. On the other hand there is no consistent ``timelike Liouville theory''. Our claims are backed by numerical tests of crossing symmetry of the four-point function.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296818337.62/warc/CC-MAIN-20240422175900-20240422205900-00201.warc.gz
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CC-MAIN-2024-18
| 526 | 4 |
https://www.commonsense.org/education/website/khan-academy-7th-grade-math
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math
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Teachers are best off using Khan Academy's 7th Grade Math content to support their own instructional practices. Before assigning students a lesson on a specific topic, it would be good to check out some of the practice exercises and videos first. The lessons here can work well as a preview to a given unit in class -- students can build context for what they're about to learn. Alternatively, teachers can assign students specific content as part of the 7th Grade Mission.
For whole-class use, some videos (like those covering the number system) will be very helpful to students. However, some of the more specific videos (like those in the probability lessons) offer some procedural examples but might not offer as much help to kids who are stuck. Whether using the 7th Grade Mission or the tutorials, some of the conversational vocabulary in the videos might go beyond what kids at this age are used to hearing and reading. By trying out the content and watching the accompanying videos beforehand, teachers can better prepare their own mini-lessons, using the site as a nice complement to classroom instruction.
Full Disclosure: Khan Academy and Common Sense Education share funders; however, those relationships do not impact Common Sense Education's editorial independence and this learning rating.
Key Standards Supported
Expressions And Equations
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”
Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
Ratios And Proportional Relationships
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
Recognize and represent proportional relationships between quantities.
Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
Statistics And Probability
Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.
Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.
Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?
Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?
Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.
The Number System
Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.
Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
Apply properties of operations as strategies to add and subtract rational numbers.
Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real- world contexts.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304287.0/warc/CC-MAIN-20220123141754-20220123171754-00604.warc.gz
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CC-MAIN-2022-05
| 9,847 | 38 |
http://hubpages.com/education/How-to-Solve-Systems-of-Equations-in-Seven-Steps
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math
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How to Solve Systems of Equations in Seven Steps
Solving systems of linear equations is really hard for many students because it's simply not taught in a way that students can understand. The average curriculum teaches a few "methods" for how solve these systems, but these methods can't really be applied to more complicated systems. Moreover, these "methods" are really cookie-cutter in nature, and require perfectly-formulated examples to work well. Instead of following the "traditional" method of teaching this subject, we have a much easier way to solve this stuff.
Step 1: Get Both Equations in Slope-Intercept Form
This method requires that both of your equations be written in slope-intercept form, which looks something like y = mx + b. Many of your problems and exercises will give you equations in other formats, like the standard form that looks like Ax + Bx = C. Before you can solve a system of equations, however, you must check to make sure that the lines in question aren't parallel (which means there are no solutions) and that they aren't actually the same line (which means there are infinite solutions). To do this, we need the equations in the slope-intercept form.
Step 2: Compare the Slopes and Y-Intercepts
If the slopes of the two equations are different, then there is exactly one solution to the system of equations. If the slopes are the same, then there will not be exactly one solution.
When you have slopes that are the same, you have to look at the y-intercepts of each equation to see if there are zero or infinite solutions. If the y-intercepts are the same, then the two equations are the same (which should be obvious), and there are infinite solutions. Otherwise, there will be no solutions because the lines are parallel.
This much should have been a review for most students. Now that we've verified that there is one solution, it's time to find that solution with a simple method!
How Many Solutions?
Step 3: Set the Equations Equal to Each Other
If your equations were y = 3x + 4 and y = -2x + 1, then you can have 3x + 4 = -2x + 1 because both of these expressions are equal to y. This is a very basic type of substitution that's really easy to perform once you have the equations in slope-intercept form.
The point here is that normally you're taught to use "elimination", "substitution", or "graphing" to solve systems of equations. The problem is that "elimination" is very difficult to use unless the problems are hand-picked, and "graphing" is very difficult to do unless nice, even numbers are used. In the real world, you need a substitution method that's easy to do and is resistant to mistakes. Since you have to put the equations in slope-intercept form anyway, this method will always be available, and will always be very simple to follow.
Step 4: Solve for X
We had y = 3x + 4 and y = -2x + 1 in our previous example, and that gave us 3x + 4 = -2x + 1. What we're left with here is just a simple linear equation of a type that that we've solved over and over again. For example, we could have the following:
3x + 4 = -2x + 1
5x + 4 = 1
5x = -3
x = -3/5
And we have solved for x in just a few simple steps. Doesn't this beat the more "traditional" methods?!
Step 5: Solve for Y
We said that we found x = -3/5 in step 4, so now we'll just need to substitute that into one of our starting equations to find a value for y. We have y = 3x + 4, so here we go:
y = 3(-3/5) + 4
y = -9/5 + 4
y = -9/5 + 20/5
y = 11/5
And that took all of maybe a minute to do if you're familiar with how to handle the fractions, which you should be at this point in learning Algebra 1.
Step 6: Check Your Answer
Take the x and y coordinate that you get as a solution for this problem and plug it into each of the equations, making sure that it works. It's not enough to know how to get *an* answer, but you want to be able to make sure that you have *the* answer by knowing ways to quickly and easily check yourself. Taking a moment to check your answers using easy methods like substituting your answer into the original equations will give your grade a dramatic boost.
Step 7: Laugh at Your Classmates
Now that you have the answer, and you're sure that it's the right answer, it's time to sit back and watch everyone else work really hard and get confused over a problem that you just finished with ease!
More About Solving Linear Equations
- Algebra 1 Help.org - Algebra 1 Made Easy
This website shows the easy ways to do everything you'll need to learn how to do in Algebra 1. There are step by step tutorials that show the really easy ways to do everything instead of blindly following some old textbook.
- Linear Systems Summary | Algebra 1 Help.org
This is a set of Algebra 1 tutorials that help you with everything you need to know about solving systems of linear equations. This covers all ways of solving systems of equations, and everything you need to know to pass your tests with good grades.
More by this Author
So here's the deal. Subtracting integers gives a lot of people a really hard time. For some reason, this is a topic that isn't covered very well by most Algebra 1 instructors because it's taken for granted as a skill....
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https://pure.psu.edu/en/publications/hyperbolic-measures-and-commuting-maps-in-low-dimension
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math
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We study invariant measures with non-vanishing Lyapunov characteristic exponents for commuting diffeomorphisms of compact manifolds. In particular we show that for k = 2, 3 no faithful ℤk real-analytic action on a k-dimensional manifold preserves a hyperbolic measure. In the smooth case similar statements hold for actions faithful on the support of the measure. Generalizations to higher dimension are proved under certain non-degeneracy conditions for the Lyapunov exponents.
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Applied Mathematics
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https://mathtuition88.com/2013/12/05/mathematics-is-not-a-spectator-sport-how-to-study-maths-for-humanities-students/
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math
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Studying Mathematics is totally different from studying Humanities, this is the reason why humanities students often don’t do well in maths. But with the right studying techniques (i.e. practising doing mathematics), humanities students can be very good at maths. Together with their creativity and good memory, humanities students have the potential to achieve the top grades in maths exams.
I have taught Pure Literature students and found that they definitely have the potential to do well in Maths once they learn the correct method of mathematical studying and thinking, and how to approach solving Maths questions.
One of the top mathematical physicists, Edward Witten, majored in history and minored in linguistics! (http://en.wikipedia.org/wiki/Edward_Witten)
Mathematics is not a spectator sport
Even if you understand every word in lecture and in the textbook, the only way to really learn mathematics is by doing mathematics. Sometimes this means doing even more than the assigned problems. (See “time committment” above.) This is how to avoid the common pitfall of “understanding everything in class but blanking out on the exams.”
I realize this isn’t welcome advice, and I admit that I haven’t always followed it myself. But in years of teaching (and 20+ years of learning) mathematics I haven’t found any shortcut.
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https://studdy.ai/shared-solution/b1dc2412-0d78-4b96-9c80-e457a74be608
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math
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Assumptions1. We are dividing a mixed number by a fraction. . The mixed number is . 3. The fraction is .
First, we need to convert the mixed number into an improper fraction. The formula to convert a mixed number to an improper fraction is
Now, plug in the given values for the whole number, denominator, and numerator to convert the mixed number into an improper fraction.
Calculate the improper fraction. So, is equivalent to .
Now that we have the mixed number as an improper fraction, we can proceed with the division. In fraction division, we multiply the first fraction by the reciprocal of the second fraction.
Now, we multiply the numerators together and the denominators together.
Calculate the multiplication. So, .
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http://jxpaperxdvq.refleksija.me/write-numbers-in-standard-form.html
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math
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Name _____ place value and expanded notation a write each number in standard form 80 + 4 = 300 + 20 + 9 = 900 + 2 = 1,000 + 50 + 6. Expanded form worksheets and word form worksheets for converting numbers learn and practice how to write numbers in expanded form and in word form answers keys. Basic maths - how to write numbers in standard form - (for key stage 2 + 3, gcses, and beginners) - duration: 6:01 careervidz 3,820 views. In this worksheet, students write numbers in standard index form.
Standard form refers to the regular way you write out a number, such as 4,300, as opposed to scientific notation, which is 43 x 10^3, or in expanded form, such as. Can someone show me how to write complex numbers in standard form i missed a few days of class and do not have the text book answering a simple question like the. Write numbers in expanded form write it in expanded form and in standard form 1 300 9 309 2 1,000 200 60 1 1,261 8 3,000 + 7 3,007 9 900 + 10 + 3 913. 2 number and operations in base ten write the number in standard form write each number in the forms named use base ten blocks to build each number. Number level 8: pupils will be able to write any ordinary number in standard formchange a number written in standard form back into an ordinary number.
A full powerpoint lesson on standard form using real life data about planets this lesson has an introduction with examples and questions which is suitable to be. Math worksheets for write expanded form numbers in standard form. Expanded form calculator to write numbers in expanded form given decimal place value converter for expanded numbers form, expanded factors form, exponential form and.
Standard notation calculator converts number word this is the typical way to write numbers since words converting from number word form to standard. Standard index form standard index form is also known as standard form it is very useful when writing very big or very small numbers in standard form, a number is. Standard form is a way of writing down very large or very small numbers easily 10 3 = 1000, so 4 × 10 3 = 4000 so 4000 can be written as 4 × 10³.
The standard form of a decimal number places the decimal point after the first digit and then reflects the true size of the number by multiplying it by the. 24 complex numbers two complex numbers in standard form can write this number in standard form. Converting forms worksheets has 15 problems writing a number based on the tens converting from a calculator scientific notation to standard form. Students are asked to write numbers involving decimals in both standard form (as base ten numerals) and expanded form.
Learn to write six hundred forty-five million, five hundred eighty-four thousand, four hundred sixty-two with numbers. Students will read numbers up to hundred millions and write them in standard form. Number forms there are generally four word forms that help students to understand place value in large numbers those are standard form (the way we usually write. Writing numbers in standard form free video and text lesson explaining all three forms of writing numbers. After completing this tutorial, you should be able to: take the principle square root of a negative number write a complex number in standard form.
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https://www.hackmath.net/en/math-problem/31081
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math
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Ace or king
What is the probability that we will choose an ace or a king when choosing from a deck of sevens cards?
Did you find an error or inaccuracy? Feel free to write us. Thank you!
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You need to know the following knowledge to solve this word math problem:
Related math problems and questions:
From complete sets of playing cards (32 cards), we pulled out one card. What is the probability of pulling the ace?
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What is the probability that when we roll three dice, we roll the numbers 1,2,3?
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From 32 playing cards containing 8 red cards, we choose 4 cards. What is the probability that just 2 will be red?
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The player gets 8 cards of 32. What is the probability that it gets a) all 4 aces b) at least 1 ace
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When drawing numbers from a hat from 1 to 35, we select random given numbers. What is the probability that the drawn numbers will be divisible by 8 and 2?
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What is the probability that two dice throw twice in a row will result the sum of 10?
From the bag with numbered balls (numbers 1,2,3,. ..20) we pick one ball. What is the probability of choosing a number containing 1?
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What is the probability of events that if we throw a dice is rolled less than 6?
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What is the probability that when choosing 3 carats from seven carats, all 3 reds will be red?
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We throw two dice. What is the probability that max one three falls?
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From a 32 card box we randomly pick 1 card and then 2 more cards. What is the probability that last two drawn cards are aces?
- Prime number
Jan wrote any number from 1 to 20. What is the probability that he wrote the prime number?
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https://www.jiskha.com/display.cgi?id=1330799966
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math
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posted by Muhammad .
I Have an assignment that requires me to design, write and carry out an analysis and a report of survey from beginning to end however, the confusing part it that it has to be done without any actual data i don't know how to start that. Please help topic is Cancer related to occupational health
I think I would either have data, or research before I make any analysis, argument or conclusion.
Why are there no watches with iridescent dials? http://en.wikipedia.org/wiki/Radium_Girls
Why can't pregnant xray technicians do their job in the first three months of pregnancy?
Why has asbestos been eliminated from steam pipes?
Why has tobacco usage been discouraged at businesses?
Why has the production of vinyl chlorides been greatly reduced?
Why are dioxin byproducts being eliminated in workplaces?
I see what is if i try to assume data results, based on prior knowledge is that possible if so how would i do that can you please point me in the right direction. Thank you very much appreciate it.
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https://help.geogebra.org/topic/locus-of-a-list-with-circles-and-a-line-very-unstable
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math
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Locus of a list with circles and a line: very unstable
The attached GeoGebra file implements the inversion of a páck of circles using a rectangle with circles and a straight line. But it has several instabilities in its operation. Please, see the animation here:
If I ask to GeoGebra animate the point P after the construction is loaded, P walks over all elements of the list. But, if I change the value of n, the animation of P occurs only on the top circles.
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https://betterlesson.com/lesson/433113/understanding-rates-and-unit-rates-stations-activity
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math
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I will be using a warm up worksheet called Math Maze (Math Investigations, Fisher). This problem has the students looking for patterns to move through the numbers, start to finish. They must find the rule and continue the rule through all the numbers they pass. (SMP 7)There are 3 possible rules the student can find: multiplies of 7, multiples of 3, and two digit odd numbers.(MP 2 and 4)
The Stations during this lesson will be an independent work station, a teacher work station, and a computer station.
Teacher: The student will be working on a formative assessment. I will give them all the same question and they will answer it independently on white boards. I will randomly choose students to explain their reasoning. I will purposefully choose students that used different strategies so that students can see there is more than one way to solve a problem. During this assessment, students will be using the following practices in the following ways.
SMP 1: Students will need to make sense of the problem
SMP2: Students will need to know what the numbers represent
SMP3: Students will need to support their answers with mathematical reasoning
SMP 4: Students will be modeling their math by writing ratios.
In the formative assessment questions, #6 asks the students to find both unit rates. Remind students that this mean they will be finding the per hour and per mile rate. Students will be assessed on both unit rates, according to the CCSS, so it is important that they continue to have exposure to it.
Resource: Formative Assessment Questions
Computer: The students will be working on a web site that focuses the learning on unit rates. Students can work independently or in pairs based on the amount of computers you have available. (SMP 1)
Independent: the students will be working on a problem called Snail pace from illustrative math. This problem takes them through several problems using the same information. I’ve included the question and answer key. I like to put the answer key nearby so the students can check their work and make corrections if needed. (SMP 1 and 4)
For the wrap up, I want students to use a Venn Diagram to make a comparing/contrasting rates and unit rates. I chose this for the wrap up because students will be asked to find a rate or a unit rate and they need to know the difference. Also, sutdents may be asked to use a unit rate to find a rate. Again, they will need to know what each means and does.
If students don't know how to use a Venn Diagram, explain to them that the overlap is the way rates and unit rates are the same. The other part of the circle is how they are different.
Allow students time to complete and then let them share with their tablemates.
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https://www.physicsforums.com/threads/mirage-refraction-or-reflection.7285/
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math
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So what is it?
This is not a homework question. But I anticipate a good discussion.
Mostly refraction, but there might be some reflection in it. It's mostly a refraction of light from the sky, which looks like it's coming from the ground ahead, and is taken for a lake or something of the sort.
We had a thread on the optical technicalities a while back. Does anyone know where it is?
Mirages - A Reflection effect!!! - a consequence of Refraction
U see, the air does not get heated uniformly. Instead, it gets heated in layers. Thus the optical properties of the diff layers of air will be diff. The light from a distant object rises up, and moves from an optically denser layer to an optically lighter layer and if the angle of incidence is such that the critical angle is achieved, TOTAL INTERNAL REFLECTION occurs. This causes an image of the object to be created on the surface at diff location which we observe as the mirage...
Hope u understood...
Just out of curiosity, how does "light rise up"??
So i't is reflexion, Right. But how about this?
So is he right or is he wrong?
In the mean time I found that other thread about mirages:
but it is not really adressing the question "refraction or reflection?", so we can continue.
Why the or? A mirage is a reflection produced by refaction. The point is that a reflection is not a mechanism it is a result. When you see a refletion in a mirror there is a different mechanism (free electron mobility) which produces that reflection.
Refraction is the apparent bending of light rays due to light passing an interface to a material with a different index of refaction.
As far as I know reflection is not a carefully defined term.
I wanted to say that.
The physics of a mirage is understood. Light bends due to a gradient in the refractive index. The rest is semantics. I like sridhar_n's sig. It's a distinction some of my kids' teachers don't appreciate.
My vote is that the bending of light is caused by semantics.
Semantics? I don't think so. I think that sridhar_n is about right. As far as the input and output of a Mirage producing system is concerned I think it is 100% reflection and 0,0% refraction. Not even a little refraction as net result.
Once again, refraction is the MECHANISM which produces a REFLECTION.
There we are, this is the essential flaw in my humble opinion.
Edit made a thinking error here. There is refraction going on but most certainly there are limits to refractions.
Why is it that none of these pages explaining mirages do not substantiate it with Snellius law? Because it doesn't work.
I knew we would have a good discussion
Perhaps this failure to explain is because you are not reading a real Optics text. I have scanned a few pages from an old text I have, Optics by Rossi.
Warning for the bandwidth challenged this is a 2Meg PDF file.
edit: spell check
Perhaps not that relevant, but we use a nice experiment at my school to show refraction of light.
A long thin tank has extremely saturated salt solution in the bottom, to a depth of about an inch. Tap water is then slowly put on top of this (with a U shaped tube), to a depth of several inches. and allowed to stand for a few hours.
A laser beam is then placed at the side of the tank, about midway up, and if you've done it right, the beam takes a beautiful curved path, dipping down to the bottom.
Simple to do and VERY impressive.
I have done this, only used a sugar solution. If you get the laser beam the correct distance from the bottom of the dish it will be totally reflected from the bottom and mirror its entry path on exit.
Well, impressive text book, Integral but did you notice that there is always a division by sin(phi). Sinusses can be zero.
Let's look at Snellius law. R1*sin(phi-in)=R2*sin(phi-out). In which Ri is the refractive index of the medium and phi-in and phi-out obviously the angle of the light before and after refraction. We want to investigate what happens to the light direction after refraction. Therefore we have to reshuffle that law as
(angles in relation to the vertical plane)
Now, weren't there some complications for an arcsine? The factor under the brackets must be less than or equal to one. Otherwise there is no solution. So let us take a closer look at that expression.
R1 is the refractive index for the incoming light in the heavier colder air and since R2 is a smaller index for lighter warm air, the R1/R2 term is always more than one. Hence sin(Phi-in) must always be less than one or concequently Phi-in must be less than 90 degrees.
Also, this means that there is a critical angle for Phi-in beyond which refraction is not possible. The formula also indicated that the maximum angle for the refracted light is 90 degrees. So if a light ray is refracted in another material with a horizontal surface, it will never exceed the horizontal, so obviously there is no such thing as refracting back. Yet we see things at and beyond the horizon apparently refracted.
Ever been swimming underwater? When you look up you only see a circle of light directly above you. The more distant water surface around you is dark. Why? Because the critical angle has been exceeded and the light coming in too shallow is not refracting but either absorbed or reflected. Beyond that angle only the dark bottom under the water is reflected.
Now look at this impressive picture of a superior (on top) mirage.
It's with an inverted mirage, due to very cold air on the surfaces, think the cold inversion being water instead of cold air, with the higher refractive index. The Light at the horizon cannot be refracted due to the critical angle. Instead, you see the bottom reflected and in this case that's the mountains. No wonder that they are upside down. Reflection has that mirroring habit.
So this mirage is just the same as happens under water, reflection at the water surface , but now there is a critical layer somewhere where the reflection takes place.
How about a regular mirage in the desert or on the road on a sunny day? Apart from turning the scenario upside down, it's exactly the same.
Here several examples of inferior (Desert warm type) and superior (artic cold type) mirages:
So the ultimate trick is real reflection, just like sridhar_n indicated.
Now how come that after ages of Snellius law and know mirages, we have always assumed a wrong explanation? Time to rewrite some textbooks.
It is still not clear to me where the incorrect explanation is. Seems to work to me.
The angle at which total internal reflection occurs is called the Brewster angle, are you attempting to say that this is incorrectly handled? I think it is correctly handled.
Perhaps you are reading different books then I am. You tone seems to indicate that you have read them all. Is this possible? Or are you making some assumptions?
Rereading your post, and my text, it occurs to me that while you are impressed with it, you are ignoring it. Please read, and make an effort to understand the development. If you are unable to understand the approach, then please do not continue your criticisms of the general understanding, when it is YOU who is having the trouble.
No I admit that I did not study it intensely and I will do it on your recommandation but the only thing that I tried to state that the limit of refraction is 90o as can be seen in the law of Snellius. The refraction of light grazing at the critical angle is exactly at 90o. Beyond the critical angle there is no refraction, just total internal reflection. You can read that in any textbook as well:
Now the mirage object is always in the heavier cooler air, the more dense medium, regardless of an inferior or superior mirage. It approaches the warmer air, the less dense medium, either from aloft or below. So the first condition has most certainly been met.
The mirage is always an image of something close to the horizon where the angle of incidence is closing in on the limit of 90o. So for a mirage this conditions looks plausible.
Now please look at the first figure in the same link with the example of refraction at the critical angle (left) and total internal reflection (right) at the water surface from below. Now replace "water" with "denser colder air" and you've got yourself a superior mirage. Total internal reflection beyond the critical angle of probably something like 89,9o. Now turn the figure upside down and you're looking at the normal inferior mirage, famous for deserts.
For a inferior mirage you could argue that the curvature of the Earth would bring the horizontal refracted light into cooler regions again causing it to refract up again, but that does not work for superior mirages where the curvature of the Earth opposes refraction.
edit after studying:
Integral, does your textbook actually say something else? I see equations 2-6 and the final one on chapter 2-2 of the example. Now try and use those in practice to see if you can get refraction beyond 0o or 90o depending upon the definition of phi. Notice that the textbook does not indicate that it has proved the bending back up with refraction.
Sometimes theory may need revisiting.
I do have some problems with this. Would this be the sole reason why it takes a generation before a correct paradigm shift can take place. I think that general understanding should be questioned at all times if not the Earth would still have been flat. Arent those forums to discuss those things. OK most challenges will be plain wrong. Please explain where I am wrong.
You're not totally wrong, but I think that you're not considering the appropriate situation. This business with the critical angle and total internal reflection if for a stark boundary between two distinct media. Mirages and the like are phenomena that occur in continuous media (no boundaries, but gradients). You are correct in that total internal reflection occurs when the angle of incidence is greater than the critical angle (by DEFINITION), but you are not correct to assume that the phenomenon of a mirage is a total internal reflection, as there is no distinct medium to which it is internal.
Refraction at a boundary can be considered strictly using trigonometry in the ray theory of optics, but you mustn't forget that this is based on Hyugen's principle. When you shift your consideration to a continuous medium (gradients vs. boundaries), the intamacy to the principle is greatly amplified. You should take a step back and consider the light in terms of wavefronts rather than rays. The rays are like the vectors and the wavefronts are like the 1-forms. You can consider them as identical objects in a uniform medium and then only worry about them at a boundary (and thus use the ray theory), but, in a non-uniform medium, it becomes a bit more tricky.
Separate names with a comma.
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http://www.barnesandnoble.com/w/numerical-methods-for-engineers-steven-c-chapra/1101918145?ean=9780072431933
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math
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Numerical Methods for Engineers: With Software and Programming Applications / Edition 4by Steven C. Chapra, Raymond Canale, Raymond P. Canale, Raymond Canale
Pub. Date: 08/01/2001
Publisher: McGraw-Hill Companies, The
The Fourth Edition of Numerical Methods for Engineers continues the tradition of excellence it established as the winner of the ASEE Meriam/Wiley award for BestTextbook. Instructors love it because it is a comprehensive text that is easy to teach from. Students love it because it is written for themwith great pedagogy and clear explanations and examples throughout. This edition features an even broader array of applications, including all engineering disciplines. The revision retains the successful pedagogy of the prior editions. Chapra and Canale's unique approach opens each part of the text with sections called Motivation, Mathematical Background, and Orientation, preparing the student for what is to come in a motivating and engaging manner. Each part closes with an Epilogue containing sections called Trade-Offs, Important Relationships and Formulas, and Advanced Methods and Additional References. Much more than a summary, the Epilogue deepens understanding of what has been learned and provides a peek into more advanced methods. What's new in this edition? A shift in orientation toward more use of software packages, specifically MATLAB and Excel with VBA. This includes material on developing MATLAB m-files and VBA macros. In addition, the text has been updated to reflect improvements in MATLAB and Excel since the last edition. Also, many more, and more challenging problems are included. The expanded breadth of engineering disciplines covered is especially evident in the problems, which now cover such areas as biotechnology and biomedical engineering.
Table of ContentsPart 1 Modeling, Computers, and Error Analysis1 Mathematical Modeling and Engineering Problem Solving 2 Programming and Software 3 Approximations and Round-Off Errors 4 Truncation Errors and the Taylor Series Part 2 Roots of Equations 5 Bracketing Methods 6 Open Methods 8 Engineering Applications: Roots of Equations Part 3 Linear Algebraic Equations 9 Gauss Elimination 10 LU Decomposition and Matrix Inversion 11 Special Matrices and Gauss-Seidel 12 Engineering Applications: Linear Algebraic Equations Part 4 Optimization 13 One-Dimensional Unconstrained Optimization 14 Multidimensional Unconstrained Optimization 15 Constrained Optimization 16 Engineering Applications: Optimization Part 5 Curve Fitting 17 Least-Squares Regression 18 Interpolation 19 Fourier Approximation 20 Engineering Applications: Curve Fitting Part 6 Numerical Differentiation and Integration 21 Newton-Cotes Integration Formulas 22 Integration of Equations 23 Numerical Differentiation (and more...)
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https://classroom20.com/profiles/blogs/first-post-for-new-ideas
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math
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Well, this is my first post and the first thing I wanted to do was to give a little informatioin about myself. I am a mathematics teach at a vocational/technical school. I have recently been starting to get more involved min the technology resource scene thanks to the help of my collegues and my Masters classes.
Recently i have been working a lot with Camtasia, starting to make videos of math problems, normally the example problems from class, to give students a way to review the material from class. So far it is working out great and i feel that when the videos are fully underway in usage, i will be seeing great returns and saving myself a lot of hassle as well. My question to you is, what other ways have you been incorporating technology into your classroom, and possibly more specifically, into a math classroom
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https://www.arxiv-vanity.com/papers/1111.2321/
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math
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Disparity in Selmer ranks of quadratic twists of elliptic curves
We study the parity of -Selmer ranks in the family of quadratic twists of an arbitrary elliptic curve over an arbitrary number field . We prove that the fraction of twists (of a given elliptic curve over a fixed number field) having even -Selmer rank exists as a stable limit over the family of twists, and we compute this fraction as an explicit product of local factors. We give an example of an elliptic curve such that as varies, these fractions are dense in . More generally, our results also apply to -Selmer ranks of twists of -dimensional self-dual -representations of the absolute Galois group of by characters of order .
2010 Mathematics Subject Classification:Primary: 11G05, Secondary: 11G40
The type of question that we consider in this paper has its roots in a conjecture of Goldfeld [6, Conjecture B] on the distribution of Mordell-Weil ranks in the family of quadratic twists of an arbitrary elliptic curve over , and a result of Heath-Brown [7, Theorem 2] on the distribution of -Selmer ranks in the family of quadratic twists over of the elliptic curve .
We study here the distribution of the parities of -Selmer ranks in the family of quadratic twists of an arbitrary elliptic curve over an arbitrary number field . For example, let be the fraction of quadratic twists of that have odd -Selmer rank. Precisely, for real numbers let
It follows from a result of Monsky [16, Theorem 1.5] along with root number calculations that for every elliptic curve . It had already been noticed (see ) that this is not true when is replaced by an arbitrary number field , because there are examples with for which , and others with . Our main theorem (see Theorem 7.6) evaluates .
Suppose is an elliptic curve defined over a number field . Then for all sufficiently large we have
where is given by an explicit finite product of local factors (see Definition 7.4).
We call the “disparity” in the distribution of -Selmer ranks of twists of . If has a real embedding then so (see Corollary 7.10). On the other hand, Example 7.11 exhibits a particular elliptic curve such that as varies, the set is dense in , so is dense in .
The finiteness of the -part of the Shafarevich-Tate group would imply that the parity of the -Selmer rank is the same as the parity of the Mordell-Weil rank. Thus one would expect that Theorem A holds with -Selmer rank replaced by Mordell-Weil rank. Further, Theorem A suggests a natural generalization of Goldfeld’s conjecture (see Conjecture 7.12).
In a forthcoming paper , we will use the methods of this paper to make a finer study of the distribution of -Selmer ranks, inspired by the work of Heath-Brown , Swinnerton-Dyer , and Kane .
Our methods begin with those of and . Namely, we view all of the Selmer groups as subspaces of , defined by local conditions that vary with . In this way we can attach a Selmer group to a collection of local quadratic characters. The question of which collections of local characters arise from global characters is an exercise in class field theory (see §6).
To prove Theorem A, we show that the parity of depends only on the restrictions of to the decomposition groups at places dividing , where is the discriminant of some model of (see Proposition 7.2). (This is consistent with the behavior of the global root numbers of twists of .) In particular the map that sends a character to the parity of factors through the finite quotient . Using this fact we are able to deduce Theorem A.
There is another important ingredient in the proof of Theorem A. We make essential use of a recent observation of Poonen and Rains that the local conditions that define the -Selmer groups we are studying are maximal isotropic subspaces for a natural quadratic form on the local cohomology groups . We use this in a crucial way in the proof of Theorem 3.9, which extends a result from to include the case . Theorem 3.9 is a key ingredient in the proof of Theorem A.
Our methods apply much more generally than to -Selmer groups of elliptic curves, and throughout this paper we work in this fuller generality. Namely, suppose is any prime, and is a -dimensional -vector space with
an action of the absolute Galois group ,
a nondegenerate -equivariant alternating -valued pairing, and
a “global metabolic structure” (see Definition 3.3).
We also assume we are given “twisting data” (Definition 4.4) that allows us to define a family of Selmer groups as runs through characters of of order . We have analogues of Theorem A describing the distribution of in this setting.
For example, if is an elliptic curve over , then , the kernel of multiplication by on , comes equipped with all the structure we require. When the Selmer groups are not Selmer groups of elliptic curves, but they are Selmer groups of -dimensional abelian varieties over that are twists of in the sense of . See §5, and see Theorem 8.2 for the analogue of Theorem A in this setting.
The layout of the paper is as follows. Let be a Galois module as above. In §2 we derive some elementary properties of Lagrangian subspaces in quadratic vector spaces that we will need in the sequel. In §3 we define metabolic structures and Selmer groups in the generality we will need them. The key result is Theorem 3.9, which shows how the parity of the Selmer rank changes when we change some of the defining local conditions. In §4 we define the Selmer groups associated to twists of , and in §5 we show how these Selmer groups reduce to classical Selmer groups of twists when for an elliptic curve .
Fix a number field and a rational prime . Let denote a fixed algebraic closure of , and . Let denote the group of -th roots of unity in .
Throughout this paper will denote a two-dimensional -vector space with a continuous action of , and with a nondegenerate -equivariant alternating pairing corresponding to an isomorphism
We will use (resp., ) for a place (resp., nonarchimedean place, or prime ideal) of . If is a place of , we let denote the completion of at , and its maximal unramified extension. We say that is unramified at if the inertia subgroup of acts trivially on , and in that case we define the unramified subgroup by
If and is a place of , we will often abbreviate for the localization of in .
We also fix a finite set of places of , containing all places where is ramified, all primes above , and all archimedean places.
2. Metabolic spaces
Fix for this section a finite dimensional -vector space .
A quadratic form on is a function such that
for every and ,
the map is a bilinear form.
If , we denote by the orthogonal complement of in under the pairing . We say that is a metabolic space if is nondegenerate and has a subspace such that and . Such a subspace is called a Lagrangian subspace of .
For this section, if is an -vector space we let .
Suppose is a metabolic space, is a Lagrangian subspace, and is a subspace of such that . Then is a Lagrangian subspace of .
Exercise. See for example [17, Remark 2.4]. ∎
Suppose is a metabolic space and , , and are Lagrangian subspaces of . Then
Suppose . Write and with and , and define
Note that and are well-defined modulo , so does not depend on the choice of or . Thus is a well-defined bilinear pairing on .
By definition we have
Since , , and are Lagrangian, and , we have , so for every , i.e., is alternating (and therefore also skew-symmetric).
If then we can take in (2.1), so for every . Using the skew-symmetry we deduce that is in the (left and right) kernel of the pairing . Similarly , and hence , is in the kernel.
Conversely, if is in the kernel of this pairing, then (still writing with and )
for every and . Applying Lemma 2.2 with , we see that
Thus, modifying and by an element of , we may assume that , and then as well, so .
This completes the proof that the pairing (2.1) is alternating and nondegenerate on . A standard argument now shows that the dimension is even, and the lemma follows. ∎
Suppose is a metabolic space and , , and are Lagrangian subspaces of . Then
Suppose is a metabolic space and , , and are Lagrangian subspaces of . Then
This follows directly from Proposition 2.4. ∎
3. Metabolic structures and Selmer structures
In this section we define what we mean by a global metabolic structure on , and by a Selmer group for and . The main result is Theorem 3.9, which shows how the parity of the Selmer rank changes when we change the defining local conditions.
The cup product and the pairing (1.1) induce a pairing
If is a place of and is the completion of at , then applying the same construction over the field gives local pairings
For every there is a canonical inclusion that is an isomorphism unless either , or and . The local Tate pairing is the composition
The Tate pairings satisfy the following well-known properties.
For every , the pairing is symmetric and nondegenerate.
If then is equal to its own orthogonal complement under .
If , then for almost all and .
For (i) and (ii), see for example [15, Corollary I.2.3 and Theorem I.2.6]. The first part of (iii) follows from (ii), and the second from the fact that the sum of the local invariants of an element of the global Brauer group is zero. ∎
Suppose is a place of . We say that is a Tate quadratic form on if the bilinear form induced by (Definition 2.1) is . If , then we say that is unramified if for all .
Suppose is as above. A global metabolic structure on consists of a Tate quadratic form on for every place , such that
is a metabolic space for every ,
if then is unramified,
if then .
Note that if then for almost all , so the sum in Definition 3.3(iii) is finite.
If then there is a unique Tate quadratic form on for every , and a unique global metabolic structure on .
Suppose and is a global metabolic structure on . If is such that for every , then for every we can define a new Tate quadratic form on by
It is straightforward to check (using Theorem 3.1) that is again a global metabolic structure on , and if then .
Suppose is a place of and is a quadratic form on . Let
Suppose and is a Tate quadratic form on . Let . Then:
every has dimension ,
if and is unramified, then .
shows that . This proves (i) and (ii).
Assertion (iii) follows from a calculation of Poonen and Rains [17, Proposition 2.6(b,e)]. ∎
Suppose is as above and is a global metabolic structure on . A Selmer structure for (or simply for , if is understood) consists of
a finite set of places of , containing ,
for every , a Lagrangian subspace .
If is a Selmer structure, we set if , and we define the Selmer group by
i.e., the subgroup of such that for every .
Suppose and are two Selmer structures for . Then
Let . Define , so is a metabolic space. Let denote the product of the localization maps. Define three subspaces of
is the image under of .
The spaces and are Lagrangian by definition of Selmer structure. That is also Lagrangian can be seen as follows. We have by Poitou-Tate global duality (see for example [15, Theorem I.4.10], [24, Theorem 3.1], or [19, Theorem 1.7.3]). If , then with satisfying for every . Then if by Definition 3.3(ii), so
by Definition 3.3(iii). Thus is Lagrangian.
Note that from the definitions we have exact sequences
where the kernel in both sequences is
Thus by Proposition 2.4 we have
Since , this completes the proof of the theorem. ∎
4. Twisted Selmer groups
Given as above (and some additional “twisting data”, see Definition 4.4), in this section we show how to attach to every character a Selmer group . More generally, we attach a Selmer group to every collection of local characters with for in some finite set containing . Our main result is Theorem 4.11, which uses Theorem 3.9 to show how the parity of the Selmer rank changes when we change some of the .
If is a field, define
(throughout this paper, “” will always mean continuous homomorphisms). If is a local field, we let denote the subset of ramified characters. In this case local class field theory identifies with , and is then the subset of characters nontrivial on the local units . Let denote the trivial character.
There is a natural action of on , and we let . Then is naturally identified with the set of cyclic extensions of of degree dividing , via the correspondence that sends to the fixed field of in . If is a local field, then denotes the set of ramified extensions in .
and . Define the width of a prime of , , by if .
Let denote the field of definition of the elements of , i.e., the fixed field in of .
Suppose is a prime of , , and let be a Frobenius element for some choice of prime above . Then
if and only if ,
if and only if has order exactly ,
if and only if .
In particular has positive density in the set of all primes of , and has positive density if and only if .
Fix an -basis of so that we can view . Then by (1.1)
Since , is unramified at , so , the subspace of fixed by . We have if and only if , and if , then if and only if has order . This proves the lemma. ∎
Suppose , are as above, and is a global metabolic structure on . By twisting data we mean
for every , a (set) map
for every , a bijection
Note that if then the first equality by local class field theory (since by definition and ) and the second by Lemma 3.7(iii).
If and is a place of , we let denote the restriction of to .
and if let (resp., ) be the product of all primes dividing that lie in (resp., ), so . For every , define the width of by
Define a finite set
and let and denote the natural maps
Note that is a group, and is not a group but it is closed under multiplication by unramified characters. Since is the fiber over of the map that sends to the part of its conductor supported on , we have .
Given , , and twisting data as in Definition 4.4, we define a Selmer structure for every and as follows.
If then let .
If , let be the unique element of .
If , let .
If we will also write , and if then we define
It is clear from the definition that depends only on the extension of cut out by , i.e., for all . However, when we later count the twists with certain properties, it will be convenient to deal with rather than because is a group. In any case the natural map is -to-one except for the single fiber consisting of the trivial character, so it is simple to go from counting results for to results for . In particular, when the natural map is a bijection.
Remark 4.9 (Remarks about twisting data).
Our definition of twisting data is designed to ensure that for , all subspaces occur with equal frequency as we run over characters that are ramified at . That fact is all we require to prove our results in sections 7 and 8 about the rank statistics of . In particular, the conclusions of Theorems 7.6 and 8.2 below do not depend on the choice of twisting data for .
We will see in §5 that when is an elliptic curve over , is a rational prime, and , then there is natural global metabolic structure on and natural twisting data such that for every , is a classical Selmer group of a twist of (an abelian variety twist, when ). An analogous statement should hold for more general (self-dual) motives and their Bloch-Kato -Selmer groups, so our results below should also apply to Bloch-Kato Selmer groups in families of twists.
If and , define
Suppose , , and . Then
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https://www.statstutor.net/downloads/question-2015505-other-economics-problems/
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math
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Question: A very simple economy consists of two sectors: agriculture and milling. To produce one unit of agriculture products requires 1/3 of a unit of agricultural products and 1/4 of a unit of milled products. To produce one unit of milled products requires 3/4 of a unit of agricultural products and no units of milled products. Determine the production levels needed to satisfy an external demand for 300 units of agricultural and 500 units of milled products.
Deliverables: Word Document
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https://mathshistory.st-andrews.ac.uk/Biographies/Zehfuss/
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math
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Johann Georg Zehfuss
Darmstadt-Bessungen, Darmstadt, Grand Duchy of Hesse, now Germany
Frankfurt am Main, Germany
BiographyGeorg Zehfuss was the son of Johann Heinrich Zehfuss, Court Chamber-Registrar, and Susanne Magdalene Noack. He attended the Höhere Gewerbeschule Darmstadt, the higher trade school which was founded in 1836. Günter Kern writes :-
As Zehfuss himself admits, in his youth he showed more interest in languages and history than mathematics. At the age of fifteen, he entered the Polytechnic in Darmstadt, where he devoted himself to the study of mathematics, mechanics, physics and chemistry, encouraged by his teacher Strecker, but continued to attend classes in Latin, French as well as German history and literature.The Polytechnic which Kern mentions in this quote is actually the Höhere Gewerbeschule Darmstadt which was renamed the Polytechnic School in 1868, many years after Zehfuss had completed his studies there. At the Gewerbeschule, Zehfuss took classes in mathematics, technical drawing, physics and chemistry. He would also have learned practical skills required for the study of engineering topics. Among his teachers at this school we mention Edmund Külp (1800-1862) who had been inspired to study mathematics by Adolphe Quetelet at the Athenaeum in Brussels. Külp had studied at the University of Heidelberg and was awarded a doctorate by the University of Giessen in 1824. In his first years at the school Zehfuss was taught chemistry by Adolph Strecker (1822-1871) but Strecker left in 1846 to take up an appointment at the University of Giessen. Another of Zehfuss's teachers was Ludwig Christian Wiener who was appointed to the Höhere Gewerbeschule in 1848 and taught physics, mechanics, hydraulics and descriptive geometry. Zehfuss graduated "summa cum laude" from the Höhere Gewerbeschule Darmstadt in 1850 and began his studies of mathematics at the Justus Liebig University of Giessen.
At the University of Giessen his main interest was the finite difference calculus, the results of which he summarised in the papers Einige Punkte über die Bestimmung der Constanten, welche bei Integration der endlichen Differenzengleichungen eingehen Ⓣ (1856) and Über die Auflösung der linearen endlichen Differenzengleichungen mit variabeln Coefficienten Ⓣ (1858).
For a list of Zehfuss's publications, see THIS LINK.
Zehfuss completed his studies in Giessen on 31 January 1853 when he obtained a doctorate and qualified to teach in a Gymnasium. Although he performed well at Giessen, he did not find the university mathematically stimulating. After graduating, he obtained a temporary teaching position at the Gewerbeschule Darmstadt where he assisted his former teacher Edmund Külp teaching mathematics and physics from 1853 to 1858.
In 1857 Zehfuss habilitated in mathematics and physics at the Ruprecht-Karls University of Heidelberg when he submitted his dissertation Abhandlung über einige mathematische Gegenstände. Inauguralschrift Ⓣ. This dissertation was examined by Otto Hesse and Gustav Kirchhoff; Hesse evaluated the three mathematical parts of the dissertation while Kirchhoff evaluated the one part related to physics. Hesse wrote in his report that the dissertation dealt :-
... with difficult parts of the subject that are only accessible to the more advanced mathematicians.Kirchhoff also praised the physics section which was on the theory of thermodynamics.
Otto Hesse had been appointed to the chair of mathematics in University of Heidelberg in 1856. He had made investigations into the theory of determinants while undertaking research on invariant theory and he inspired Zehfuss to work on determinant theory. Zehfuss published his first work on this topic in 1858 with three papers appearing in that year, namely: Über die Zeichen der einzelnen Glieder einer Determinanten Ⓣ; Über eine gewisse Determinante Ⓣ; and Kommentar des Buches von Richard Baltzer "Theorie und Anwendungen der Determinanten mit Beziehung auf die Orginalquellen" Ⓣ.
In the first of these papers Zehfuss proves a rule stated by Gabriel Cramer about the change in the signs of determinants. In the second of the papers he proves a rule about the tensor product of square matrices. Some authors believe that the tensor product, often called the Kronecker product, should be called the 'Zehfuss product'. Note that we have made a subtle change from 'determinant' to 'matrix'. Early work on matrices was given in terms of determinants. See below for quotes about the 'Zehfuss product'. In the third of the papers he gives a detailed analysis of the book by Richard Baltzer. This book contains many illustrative references to the original sources of determinant theory and their applications.
Zehfuss worked as a docent at the University of Heidelberg for four years between 1857 and 1861. During these years he taught arithmetic, algebra and geometry, differential calculus, theory of definite integrals, elliptic functions, theory of higher equations, analytical geometry of the plane and of 3-space, and analytical mechanics. On 11 July 1861 Zehfuss married Louise Stein (1838-1911).
In November 1861 Richard Dedekind left the Polytechnikum in Zürich after three years there and took up a position in the Brunswick Polytechnikum. Zehfuss applied for the vacant position in Zürich but it was offered to Rudolf Lipschitz. He, however, turned down the position and it was then offered to Elwin Christoffel. Zehfuss, unable to find a permanent position in Germany, accepted the post of high school professor of mathematics and physics in Reval (now Tallinn in Estonia) in September 1860. He taught at the Cathedral School in Reval and while there his son Gustav Heinrich Julius Wilhelm Zehfuss was born on 20 August 1862. However, Zehfuss was not very happy at the Cathedral School in Reval since he did not feel that this offered him the environment to reach his full potential as a researcher.
In February 1862 Zehfuss applied for a position as a professor in mathematics or physics at the Polytechnic of Riga in Latvia. His application included recommendations from many mathematicians including Ludwig Christian Wiener, Ferdinand Minding, Osip Ivanovich Somov, Oskar Schlömilch, Otto Hesse, Gustav Kirchhoff and Richard Dedekind. Zehfuss was appointed and took up the position as professor of higher mathematics at the Polytechnic of Riga on 9 January 1863. This was a new institution and initially it struggled to establish itself. Zehfuss decided to return to Germany when offered a position at the Gewerbeschule in Frankfurt am Main. He took up the position in 1864. At this school he taught algebraic analysis, trigonometry, the theory of higher degree equations, two dimensional analytic geometry, mechanics, differential and integral calculus, and three dimensional analytic geometry. His second child, a daughter Cornelia Charlotte Marie Auguste Mathilde Victoria Zehfuss, was born in Darmstadt on 16 September 1864. Zehfuss continued in his position at the Gewerbeschule in Frankfurt am Main for the rest of his career.
Zehfuss died in Frankfurt am Main on 5 May 1901. He was buried in Heidelberg in the mountain cemetery of Heidelberg-Südstadt. Also buried there are his wife Luisa, his daughter Cornelia (1864-1949), and his daughter's husband Georg Anton Karch (1856-1937).
Today the name of Zehfuss is not known by many but those who are aware of his contributions almost certainly know him through his contribution to the tensor product of matrices. Without offering a definite opinion as to whether the 'Kronecker product' should be called the 'Zehfuss product' let us simply quote from a number of sources.
Amy N Langville and William J Stewart write :-
The operation defined by the symbol was first used by Johann Georg Zehfuss in 1858. It has since been called by various names, including the Zehfuss product, the Producttransformation, the conjunction, the tensor product, the direct product and the Kronecker product. In the end, the Kronecker product stuck as the name for the symbol and operation, .H Zhang and F Ding write :-
The Kronecker product, named after German mathematician Leopold Kronecker, is very important in the areas of linear algebra and signal processing. In fact, the Kronecker product should be called the Zehfuss product because Johann Georg Zehfuss published a paper in 1858 which contained the well-known determinant conclusion, for square matrices and with order and .Roger A Horn and Charles R Johnson write :-
Some historians of mathematics have questioned the association of the ⊗ product with Kronecker's name on the grounds that there is no known evidence in the literature for Kronecker's priority in its discovery or use. Indeed, Sir Thomas Muir's authoritative history calls the 'Zehfuss determinant' of A and B because the determinant identityappears first in an 1858 paper of Johann Georg Zehfuss ("Über eine gewisse Determinante Ⓣ, Zeitschrift für Mathematik und Physik 3 (1858), 298-301"). Following Muir's lead, a few later authors have called A ⊗ B the 'Zehfuss matrix' of A and B, for example "D E Rutherford, On the Condition that two Zehfuss matrices be equal, Bull. Amer. Math. Soc. 39 (1933), 801-808", and "A C Aitken, The normal form of compound and induced matrices, Proc. London Math. Soc 38 (2) (1935), 354-376". However, a series of influential texts at and after the turn of the century permanently associated Kronecker's name with the ⊗ product, and this terminology is nearly universal today. For further discussion (including claims by others to independent discovery of the determinant result) and numerous references, see "H V Henderson, F Pukelsheim and S R Searle, On the history of the Kronecker product, Linear and Multilinear Algebra 14 (2) (1983), 113-120".
Harold V Henderson, Friedrich Pukelsheim and Shayle R Searle write :-
Our story begins with one Johann Georg Zehfuss (1832-1901) at the University of Heidelberg who, according to biographical notes by Poggendorf (1863, 1898), published papers on determinants until at least 1868 before moving to studies in astronomy. In particular, Zehfuss (1858) contains the determinant resultAlthough Zehfuss is best known for his contributions to determinants, he made other contributions to mathematics in difference equations, differential and integral calculus and combinatorics. Later in his career, however, his attention turned more towards physics and astronomy. He actively participated in the annual meetings of the Gesellschaft Deutscher Naturforscher und Ärzte Ⓣ, especially when the meetings were in Frankfurt am Main or in the vicinity of the city. He also participated in meetings of the Wetterauischen Naturforschenden Gesellschaft zu Hanau Ⓣ. He lectured to these societies on determinants, but also showed a model of a Riemann surface and gave a lecture "On a Possible Cause of the Delay of Earth Rotation." In this lecture he showed (see ):-for square matrices A and B of order a and b, respectively. Zehfuss wrote in terms of determinants rather than matrices, following the then customary practice of employing the term 'determinant' both for what we now call a square matrix as well as for its determinant. ... Unfortunately, the Zehfuss (1858) determinant result seems to have been overlooked for more than fifty years, until its rediscovery by Muir (1911, reprinted in ) who claims it for Zehfuss and accordingly calls the Zehfuss determinant of A and B. Others, notably Rutherford (1933), and Aitken (1935) and his student Ledermann (1936), following Muir's lead, have gone further and called A B the Zehfuss matrix of A and B. Aitken's adoption of this name is of interest in light of Ledermann's later (1968) comment that Aitken "was particularly fond of stressing the claims of lesser known mathematicians of former times for discoveries erroneously attributed to their more famous contemporaries. Many of his historical references were gleaned from Sir Thomas Muir's monumental work on determinants, for which Aitken had a profound admiration."
... that magnetic forces which the heavenly bodies mutually exert cannot effect this delay, whereas the constant magnetic field in which the planets move can cause a change in precession which could lead to an explanation of the observation.Other lectures related to astronomy included "On meteorites" delivered in 1870 and "Some explanations of the appearance of the Northern Lights" in 1871.
He wrote the book Die Pneumatische Canalisation beleuchtet mit Rücksicht auf Gesundheitspflege, Land- und Volkswirthschaft Ⓣ which was translated into English by D Coar of Philadelphia, Pennsylvania, USA and appeared as The Pneumatic Sewage System treated with reference to Public Health, Agriculture and National Economy published by Wilhelm Hassel in Cologne in 1869. The book commences with an historical introduction in which Zehfuss refers to sewage systems mentioned in the Bible, those constructed by the Hindus, the ancient Egyptians, the Babylonians, and the Romans in 600 B.C. A patent was sought in the United States for the sewage system Zehfuss describes in the book and he received a letter of patent from the United States Patent Office in 1870 (letter of patent No. 100,347).
Finally, let us note that prior to the appearance of , few biographical details concerning Zehfuss were readily available. Much of the biographical information in our biography above comes from Walter Strobl's paper.
- R A Horn and C R Johnson, Topics in Matrix Analysis (Cambridge University Press, Cambridge, 1994).
- G Kern, Die Entwicklung des Faches Mathematik an der Universität Heidelberg 1835-1914 (Universitätsbibliothek, Heidelberg, 1992). http://www.ub.uni-heidelberg.de/archiv/14583
- T Muir, The Theory of Determinants in the Historical Order of Development (5 Volumes) (London, 1960).
- G Zehfuss, The Pneumatic Sewage System Treated with Reference to Public Health, Agriculture and National Economy, Part 1 (Hassel, 1869).
- H V Henderson, F Pukelsheim and S R Searle, On the history of the Kronecker product, Linear and Multilinear Algebra 14 (2) (1983), 113-120.
- A N Langville and W J Stewart, The Kronecker product and stochastic automata networks, Journal of Computational and Applied Mathematics 167 (2004) 429-447.
- W Strobl, Georg Zehfuss: Sein Leben und seine Werke. http://www.ub.uni-heidelberg.de/archiv/24214
- H Zhang and F Ding, On the Kronecker Products and Their Applications, Journal of Applied Mathematics 2013 (2013). http://dx.doi.org/10.1155/2013/296185
Additional Resources (show)
Other pages about Georg Zehfuss:
Written by J J O'Connor and E F Robertson
Last Update May 2018
Last Update May 2018
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http://essaywriting.club/essay-checklist/solving-simple-trigonometric-problems.php
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math
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Skip to main content. Basic Trigonometry involves the ratios of the sides of right triangles.
So now I can do the trig; namely, solving those two resulting trigonometric equations, using what I've memorized about the cosine wave. Finding a Formula for trjgonometric Trigonometric Graph.
It plays an important role in surveying, navigation, engineering, astronomy and many other branches of physical science.
Trigonometric Ratios in the Four Quadrants.
2. • Use standard algebraic techniques to solve trigonometric equations. • Solve trigonometric equations of quadratic type. • Solve trigonometric equations involving multiple angles. • Use inverse trigonometric functions to solve trigonometric equations. What You Should Learn.– Bruce, Anaheim, CA
Sometimes it will be that we want for the solution and sometimes we will want both (or neither) of the listed angles. Therefore, since there isn't anything in this problem (contrast this with the next problem) to tell us which is the correct solution we will need to list ALL possible solutions. This is very easy to do. Recall from the.– Kimberly, Corpus Christi, TX
SOLVING TRIGONOMETRIC EQUATIONS. This sections illustrates the process of solving trigonometric equations of various forms. It also shows you how to check your answer three different ways: algebraically, graphically, and using the concept of essaywriting.club following table is a partial lists of typical equations. Solve.– Sandra, Lexington, KY
Find Unknown Sides of Right Angles. Find Height of Object using Trigonometry. Trigonometry Word Problems Videos. Angle of Elevation and Depression.
Area of Triangle using the Sine Function. Law of Sines or Sine Rule. Law of Cosines or Cosine Rule. Angles at Standard Position and Coterminal Angles. Trigonometric Ratios in the Four Quadrants.
Finding the Quadrant in Which an Angle Lies. Trigonometric Functions in so,ving Cartesian Plane. Evaluating Trigonometric Functions at Important Angles.
Transformation of Trigonometric Graphs.
Graphing Sine and Cosine with Different Coefficients. Amplitude, Period, Vertical and Horizontal Shifts. Tangent, Cotangent, Secant, Cosecant Graphs.
Finding a Formula for a Trigonometric Graph. Solving simple trigonometric problems Trigonometric Identities to Simplify Expressions. Sum and Difference Identities. Double-Angle and Half-Angle Formulas.
Simplifying Trigonometric Expressions Involving Fractions. Putting these the two solution sets together, I get the solution for the original equation as being:. This equation is "a quadratic in sine"; that is, the form of the equation is the quadratic-equation format:.
Since this is quadratic in form, I can apply some quadratic-equation methods. In the case of this equation, I can factor the quadratic:. But the sine is never more than 1so this solving simple trigonometric problems is not solvable; it has no solution. So my complete solution is:. I can use a double-angle identity on the right-hand side, and rearrange and simplify; then I'll factor:.
So the complete solution is:. I'm really not seeing anything here. It sure would have been nice if one of these trig expressions were squared From the last line above, either sine is zero or else top creative writing programs in florida is zero, so my solution appears to be:.
However and this is important! If you square something, you can't just square-root to get back to what you'd started with, because the squaring may have changed a sign somewhere.
So, to be sure of my results, I need to check my answers in the original equation, to make sure that I didn't accidentally create solutions that don't actually count. Plugging back in, I see:. It's a good thing that I checked my solutions, because two of them don't actually work. They were created by the process of squaring. The answer would have been the same, but I would have needed to account for the solution interval:.
After doing the necessary check because of the squaring and discarding the extraneous solutions, my final answer would have been the same as previously. The squaring trick in the last example above doesn't solving simple trigonometric problems up often, but if nothing else is working, it might be worth a try.
Keep it in mind for the solving simple trigonometric problems test. Page 1 Page 2. Skip to main content. Purplemath Solving trig equations use both the reference angles and trigonometric identities that you've memorized, together with a lot of the algebra solving simple trigonometric problems learned. Just as with linear equationsI'll first isolate the variable-containing term:
This is particularly useful for a performance or restaurant review. Causal Analysis: This measures the effect on the audience.Read more
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https://andik4physics.blogspot.com/2013/09/storm-in-ice-cube.html
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math
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IceCube is a neutrino detector located right at the South Pole. Most of what they see are atmospheric neutrinos produced when cosmic rays hit Earth's atmosphere. Obviously, nobody would be freezing his off in the Antarctica for that. The goal of IceCube was always to catch neutrinos of astrophysical origin, thus inaugurating neutrino astronomy. Finally, last year they announced the detection of 2 neutrino cascade events, both with the same (within experimental uncertainty) 1 PeV = 1000 TeV energy. This is interesting not only because these are the highest energy neutrinos ever detected. The main point is that the atmospheric neutrino spectrum is expected to drop off quickly at large energies, and is very unlikely (at about 3 sigma or so) to produce as much as two PeV events. The more recent development is that there is in fact more than just two events. There appears to be a broad excess (quantified at 4.3 sigma) of 28 events above 30 TeV where only about 10 are expected from atmospheric neutrinos alone. The flavor composition in that range is consistent with 1:1:1 ratio of the 3 neutrino species, as expected for faraway sources because of neutrino oscillations along the way.
All these more detailed statements are at this point not very significant statistically, but if they persist after future updates things will get even more interesting. Indeed, sharp spectral features are more tricky to explain in terms of known astrophysical phenomena, which are rather expected to produce a smooth power-law spectrum (typically assumed as 1/Energy^2). For particle physicists the natural question is whether these neutrinos could be the signal of annihilation or decay of dark matter in our galaxy. Dark matter would have to be made of PeV mass particles - more than is typically considered. But why not: any mass between sub-eV and Planck scale is equally plausible at this point.
Of course, theorists have models for every occasion up their sleeves. On interesting proposal is that the two PeV events can be interpreted as a monochromatic neutrino line. This could arise if dark matter decays into a 2-body final state containing at least one neutrino (dark matter annihilation with a large enough cross section is difficult to realize for such a heavy mass). To explain the observation of 2 events in IceCube, the life-time of dark matter should be about 10^28 seconds or 10^21 years - much longer than the age of the Universe and compatible with all existing constraints. The presence of the continuum excess around 100 TeV makes the picture more complicated... but not necessarily unrealistic. It is perfectly conceivable that dark matter has more than one decay channels, for example 10% branching fraction into 2 neutrinos, and the remaining 90% into quarks. The former would be responsible for the PeV events, and the latter would produce neutrinos with smaller energies from the hadronic cascades, which would explain the broad feature near 100 TeV. This paper shows that a general scenario of this type can fit the data very well, somewhat better than the smooth 1/E^2 spectrum.
So, as usual, the possibilities are endless, and we badly need more experimental input. The dataset analyzed so far corresponds to the 2010-2012 period, so there should be 50% more events already waiting in the pipeline. Most likely, it will turn out that these ultra-high energy neutrinos are produced by some boring astrophysical processes (although I admit that the boring astrophysics producing PeV monster neutrinos must be less boring than typical boring astrophysics). But, well, who knows, maybe this time they will hit the jackpot?
For more details and naked photos of Bert and Ernie, see this talk.
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https://www.accountingnotes.net/financial-management/cost-of-capital/5-major-problems-in-the-determination-of-cost-of-capital/7775
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math
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This article throws light upon the five major problems in determination of cost of capital. The problems are: 1. Conceptual Controversies Regarding the Relationship between the Cost of Capital and the Capital Structure 2. Historic Cost and Future Cost 3. Problems in Computation of Cost of Equity 4. Problems in Computation of Cost of Retained Earnings 5. Problems in Assigning Weights.
Determination of Cost of Capital:
- Conceptual Controversies Regarding the Relationship between the Cost of Capital and the Capital Structure
- Historic Cost and Future Cost
- Problems in Computation of Cost of Equity
- Problems in Computation of Cost of Retained Earnings
- Problems in Assigning Weights
Problem # 1. Conceptual Controversies Regarding the Relationship between the Cost of Capital and the Capital Structure:
Different theories have been propounded by different authors explaining the relationship between capital structure, cost of capital and the value of the firm.
This has resulted into various conceptual difficulties. According to the Net Income Approach and the traditional theories both the cost of capital as well the value of the firm have a direct relationship with the method and level of financing. In their opinion, a firm can minimise the weighted average cost of capital and increase the value of the firm by using debt financing.
On the other hand, Net Operating Income and Modigliani and Miller Approach prove that the cost of capital is not affected by changes in the capital structure or say that debt equity mix is irrelevant in determination of cost of capital and the value of a firm.
However, the M and M approach is based upon certain unrealistic assumptions such as, there is a perfect market or the expected earnings of all the firms have identical risk characteristic, etc.
Problem # 2. Historic Cost and Future Cost:
Another problem in the determination of cost of capital arises on account of the difference of opinion as regards the concept of cost itself. It is argued that historic costs are book costs which are related to the past and are irrelevant in the decision-making process.
In their opinion, future estimated costs are more relevant for decision-making. In the same manner, arguments are given in favour of specific cost and composite cost as well as explicit cost and implicit cost and the marginal cost.
Problem # 3. Problems in Computation of Cost of Equity:
The computation of cost of equity capital depends upon the expected rate of return by its investors. But the quantification of the expectations of equity shareholders is a very difficult task because there are many factors which influence their valuation about a firm.
Problem # 4. Problems in Computation of Cost of Retained Earnings:
It is sometimes argued that retained earnings do not involve any cost. But in reality, it is the opportunity cost of dividends foregone by its shareholders. Since different shareholders may have different opportunities for investing their dividends, it becomes very difficult to compute the cost of retained earnings.
Problem # 5. Problems in Assigning Weights:
For determining the weighted average cost of capital, weights have to be assigned to the specific cost of individual sources of finance. The choice of using the book value of the source or the market value of the source poses another problem in the determination of cost of capital.
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https://www.open.edu.au/subjects/curtin-university-mathematical-modelling-in-business-cur-pa530?year=2021
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math
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Mathematical Modelling in Business
Solve economical issues with the power of mathematics. You’ll cover linear models, matrix algebra, general function models, integral calculus and more. Become a practical mathematician.
Enrolments for this year have closed. Keep exploring subjects.
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At the completion of this subject students will be able to:
- translate economic issues into mathematical programming
- analyse mathematical models to examine economic issues
- evaluate mathematical models in terms of their relevance to particular economic issues
- analyse economic issues using appropriate mathematical models and translate the results into meaningful economic interpretations.
- Elements in Matrix Algebra
- Determinants and Inverse
- System of Equations
- Linear Dependence
- Eigenvalues and Eigenvectors
- Differential Calculus
- Optimization I
- Optimization II
- Optimization III
- Integral Calculus
- Differential Equations
In order to enrol in this subject, you must be accepted into one of the following degrees:
No additional requirements
This subject covers linear models and matrix algebra, differentiation and comparative static analysis, general function models, exponential and logarithmic functions, optimisation, economic dynamics and integral calculus, differential and difference equations.
Please Note: If it’s your first time studying a Curtin University subject you’ll need to complete their compulsory ‘Academic Integrity Program’. It only takes two hours to complete online, and provides you with vital information about studying with Curtin University. The Academic Integrity Program is compulsory, so if it’s not completed your subject grades will be withheld.
Find out more about the Academic Integrity module.
- Economic Analysis (20%)
- Critical Evaluation (30%)
- Modelling Project (50%)
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| 1,882 | 29 |
https://www.mcqlearn.com/grade8/math/math-applications.php?page=6
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math
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Math Applications Multiple Choice Questions and Answers 6 PDF Download
Math applications multiple choice questions, learn grade 8 math online test prep 6 for elementary school online courses, distance learning for exam prep. Practice profit and loss percentage multiple choice questions (MCQs), math applications quiz questions and answers for math class for 8th grade online math for students.
Study elementary school math multiple choice questions (MCQs): harry bought 50kg of potatoes for resale on his retailer store whereas he paid $2/kg. he expects that 5% potatoes will be rotten. if 95% profit on cost is to be obtained then selling price is, for free online courses with choices $6.20, $4.10, $5.80, and $7.30, profit and loss percentage quiz with online job interview questions and answers for formative assessment in competitive exams. Free math study guide for online learning profit and loss percentage quiz questions to attempt multiple choice questions based test.
MCQs on Math Applications Worksheets 6 Quiz PDF Download
MCQ: Harry bought 50kg of potatoes for resale on his retailer store whereas he paid $2/kg. he expects that 5% potatoes will be rotten. If 95% profit on cost is to be obtained then selling price is
MCQ: John invested $8000 at 6.5% per annum compound interest which is compounded daily. amount at end of fifth year is
MCQ: Income tax imposed on first $90000 of income is $4000 and next $20000 is 7%. If chargeable income is $100,000 then tax payable by tax payers is
MCQ: If a book is sold for $250 at 15% loss on cost then cost price of book is
MCQ: Shopkeeper paid $80 each for two pair of shoes. He sell first pair of shoes making profit of 35% of cost price. He sell second pair of shoes at loss of 18% of cost price. selling price of each pair of shoes respectively is
- $125, $60.7
- $123, $69.7
- $108, $65.6
- $110, $68.6
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| 1,864 | 13 |
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