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https://www.wyzant.com/resources/answers/228515/how_much_extra_lean_hamburger_12_fat_needs_to_be_added_to_339_lbs_of_regular_hamburger_27_fat_to_make_a_batch_of_lean_meat_20_fat
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math
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This is another system of equations question, so let's call some variables.
You really only need to call one variable, since they give you the amount of regular hamburger meat required. I'm going to say that:
L = amount of lean meat required
Since we're dealing with mixing high fat/ low fat products, I'm going to write an equation to balance the total amount of fat content on both sides. You know three things:
1. You have L amount of 12% fat.
2. You have 339 pounds of 27% fat.
3. You want "a batch" of 20% fat.
It doesn't explicitly define how much is in a batch, but that's not a problem. The total amount of burger meat after all the mixing is done will be:
L + 339
Since that's how much you added to begin with.
So, let's state our equation.
L*0.12 + 339*0.27 = (L+339)*0.20
Since L is 12% fat, it will contribute L*0.12 pounds of fat to the mixture.
Since the 339 pounds of regular burger meat is 27% fat, it will contribute 339*0.27 pounds of fat to the mixture.
You want the total amount to be 20% fat, so you'll have (L+339)*0.20 pounds of fat in your mixture.
Now let's just solve for L. Simplify and distribute.
0.12L + 91.53 = 0.20L + 67.8
23.73 = 0.08L
L = 296.625
You'll need 296.625 pounds of extra lean 12% meat to bring your batch to 20%. You'll have a grand total of 635.625 pounds of 20% burger meat.
Hope my explanations made sense.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703514796.13/warc/CC-MAIN-20210118123320-20210118153320-00444.warc.gz
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CC-MAIN-2021-04
| 1,355 | 21 |
http://kenta.blogspot.com/2017/02/ariplvdv-gut-and-toe-beauty-contest.html
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math
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Grand Unified Theories and Theories Of Everything are difficult to test and disprove. They cannot be tested on current or even reasonably imaginable future particle accelerators. We can check that a theory agrees with observations in the low-energy regime, and whether they match astronomical observations of faint relics from the universe's high-energy era.
Given these difficulties, selecting a good such theory becomes more of a question of aesthetics than science. Which such theories are beautiful and which are ugly? What defines beauty of a theory? Occam's Razor is likely important. Given a precise definition of beauty, find, perhaps computationally, the optimally beautiful theory which agrees with weak and faint observations.
The E8 Theory Of Everything likely attracted attention due to its aesthetics.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917119995.14/warc/CC-MAIN-20170423031159-00631-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 815 | 3 |
https://brokeryzmr.web.app/kaniewski32975myl/forward-fx-rate-equation-393.html
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math
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May 15, 2014 · Swap-Forward-Rate Calculation. Skip to end of metadata. Created by Anonymous on May 15, 2014; Go to start of metadata. This part explains on an example how swap/forward rates are calculated for FX transactions. The currency data is to be maintained in TCUR* tables, swap rates in AT15. The note 783877 explains very well, how currencies can be FX Foward Market - FX Forward Points Forward points reflect the interest rate differential between two currencies in an outright forward rate quote. In FX market, forward rates can be either at a premium or at a discount. Forward Premium refers to a higher forward rate than the current spot rate. BLOOMBERG INDICES equal to the FX appreciation of the foreign currency relative to the local currency: Bloomberg indices estimate this value using the beginning of month market value and the and remove it from the equation. If the initial forward rate is
FX Foward Market - FX Forward Points
How to Easily Calculate Cross Currency Rates | Market ... Jul 31, 2017 · How to Calculate Cross Currency Rates (With and Without a Cross Rate Calculator) With this background, we can now go to the calculation of the cross exchange rate. This will involve deriving it from the exchange rate of the non-USD currency and the USD. However, this is not always necessary as some rates are usually quoted on various forex Bootstrapping the Zero Curve and Forward Rates Oct 22, 2016 · 6 mins read time. Deriving zero rates and forward rates using the bootstrapping process is a standard first step for many valuation, pricing and risk models. Interest rate and cross currency swaps & interest rate options pricing & VaR models, revolving credit facilities & term B loans valuation models, Black Derman Toy interest rate models, etc. all make use of the zero rates and/or forward Calculating the Forward Rate - YouTube Apr 17, 2015 · This video shows how to calculate the Forward Rate using yields from zero-coupon bonds. A comprehensive example is provided along with a formula to show how the Forward Rate is … Interpreting Forward Exchange Rate Quotes - Finance Train
Oct 27, 2018 · A forward contract on foreign currency, for example, locks in future exchange rates on various currencies. The forward rate for the currency, also called the forward exchange rate or forward price, represents a specified rate at which a commercial bank agrees with an investor to exchange one given currency for another currency at some future date, such as a one year forward rate.
The spot rate represents the price that a buyer expects to pay for foreign currency in another currency. These contracts are typically used for immediate 27 Jul 2019 Rate Basis: The Role of FX Position Limits and Margin. Constraints Hence, EM forwards earn premium of λπ, the last term of equation. (11).
Bootstrapping the Zero Curve and Forward Rates
or euro, so that the exchange rate between two non-dollar currencies is calculated from the rate for each market's view of where the spot rate will be on the maturity date of the forward now, in which case another equation must be used. Investing's forward rate calculator enables you to calculate Forward Rates and Forward Points for single currency pairs. Nominal Exchange Rate is the price of a foreign currency in terms of the home PPP refers to the price index while law of one price to one good at a time. " Relative PPP forward exchange rate covers the investor against exchange rate risk. So, we buy forward 1 year in the future exchange rate at $1.20025/€1 since we need to convert our €1000 back to the domestic currency, i.e., the U.S. Dollar. Then, There is a standard formula for calculating forward points which is recognised across the industry. Our experts in currency at Trade Finance Global adhere to this.
The theory of interest rate parity argues that the difference in interest rates between two countries should be aligned with that of their forward and spot exchange
So, we buy forward 1 year in the future exchange rate at $1.20025/€1 since we need to convert our €1000 back to the domestic currency, i.e., the U.S. Dollar. Then, There is a standard formula for calculating forward points which is recognised across the industry. Our experts in currency at Trade Finance Global adhere to this. The theory of interest rate parity argues that the difference in interest rates between two countries should be aligned with that of their forward and spot exchange How is it done? The hedging equation and role of forward exchange rates. Currency transactions are one of the most frequent and largest investment activities in
T-Forward Measure - Fabrice Rouah The expectation in Equation (8) is di¢ cult to evaluate because it involves two terms that each depend on the value of the underlying. 3 T-Forward Measure We can evaluate the expectation in Equation (8) by using P(t;T) as the nu-meraire. The equivalent martingale measure associated with using P(t;T) as the numeraire is the T-forward measure. How Interest Rates Influence the Currency Markets - Forex ... Sovereign rates, which are the official interest rates issued by the government of a country, are used to create the fx forward market. The forward rate, of a currency pair is any date longer than the spot rate. As sovereign interest rates fluctuate relative to other sovereign rates, the change can drive the direction of the forex market. What is a real world example of negative forward interest ... In these markets forward FX rates are traded and you can calculated implied interest rates from the traded forward (input: the forward FX rate, the domestic interest rate, the FX spot rate; output: an implied yield of the foreign currency that fits the inputs). Again for short maturities I …
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s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585424.97/warc/CC-MAIN-20211021133500-20211021163500-00179.warc.gz
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CC-MAIN-2021-43
| 5,760 | 10 |
https://www.slideshare.net/cassidylunceford/cat-assignment-8
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math
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• According to Dictionary.com, the
definition of plagiarism is described as
an act or instance of using or closely
imitating the language and thoughts of
another author without authorization
and the representation of that authors
work as one’s own, as by not crediting
the original author
Why is plagiarism wrong?
• You are taking the credit for someone
else's work, which is lying and stealing
• You are showing disrespect to you
classroom peers who have worked hard
to do their own work
• You show disrespect to your teacher and
have them question your honesty and
• You are cheating
• Plagiarism is against the law
• If you are researching, writing a paper,
or taking what you know from a book
or website, it is important to always put
it in your own words!
• Never copy something word-for-word
• Plagiarism is not necessary to get your
• If writing a paper, the teacher could
allow the students to draw a piece of
paper the day that the paper is due.
Whichever student draws the piece of
paper with the black dot, that paper will
be thoroughly checked for plagiarism.
This method makes sure that the students
to not plagiarize because there is a
chance that they will draw the black dot.
If the teacher finds that the student has
plagiarized, their grade will show it.
• There are many programs that can be
downloaded or used to check for
• We will now go to a few of the websites to
see the differences.
• For an assignment, I will give each
student a slip of paper with a different
paragraph on it. The student’s job is to
re-write the paragraph in their own
words. This is a good way to make sure
the students know what they can do to
avoid plagiarism. It is also good for the
teacher because he or she can see
which student understands and which
students may need remediation.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999615.68/warc/CC-MAIN-20190624150939-20190624172939-00065.warc.gz
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CC-MAIN-2019-26
| 1,814 | 49 |
https://calchub.xyz/series-inductance/
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math
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Determine the total inductance of a series inductance circuit using the Series Inductance Calculator.
Use our online Series Inductance Calculator to determine the total inductance for a series combination of inductors. Simply input the number of inductors and their respective inductance values, and the calculator will provide you with the total inductance. Series inductance is characterized by a common current flow and the total inductance being greater than any individual inductor’s inductance.
- L=Total Inductance
- L1 ,L2,L3…=Each Inductance Value
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296816879.25/warc/CC-MAIN-20240414095752-20240414125752-00463.warc.gz
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CC-MAIN-2024-18
| 560 | 4 |
https://overstrand.gov.za/en/
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math
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• The election (voting) for Ward Committees will be conducted from 10:00 until 19:00
• The elections will be conducted by way of a walk-through process like IEC on election day(s).
Weekly updates (15/11/2021 to 21/11/2021):
De Bosdam level: 99.63 %
Change in De Bos Dam level from previous week: -0.12 %
Average daily water consumption: 11.05 million litres per day (previous week 12.09 million litres per day)
Rainfall for the week: 20 mm
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s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358842.4/warc/CC-MAIN-20211129194957-20211129224957-00610.warc.gz
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CC-MAIN-2021-49
| 443 | 7 |
https://www.thoughtco.com/calculations-with-the-gamma-function-3126261
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math
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Science, Tech, Math › Math Calculations With the Gamma Function Share Flipboard Email Print Fredrik alleged / Wikimedia Commons / Public Domain Math Statistics Formulas Statistics Tutorials Probability & Games Descriptive Statistics Inferential Statistics Applications Of Statistics Math Tutorials Geometry Arithmetic Pre Algebra & Algebra Exponential Decay Functions Worksheets By Grade Resources View More By Courtney Taylor Professor of Mathematics Ph.D., Mathematics, Purdue University M.S., Mathematics, Purdue University B.A., Mathematics, Physics, and Chemistry, Anderson University Courtney K. Taylor, Ph.D., is a professor of mathematics at Anderson University and the author of "An Introduction to Abstract Algebra." our editorial process Courtney Taylor Updated October 01, 2019 The gamma function is defined by the following complicated looking formula: Γ ( z ) = ∫0∞e - ttz-1dt One question that people have when they first encounter this confusing equation is, “How do you use this formula to calculate values of the gamma function?” This is an important question as it is difficult to know what this function even means and what all of the symbols stand for. One way to answer this question is by looking at several sample calculations with the gamma function. Before we do this, there are a few things from calculus that we must know, such as how to integrate a type I improper integral, and that e is a mathematical constant. Motivation Before doing any calculations, we examine the motivation behind these calculations. Many times the gamma functions show up behind the scenes. Several probability density functions are stated in terms of the gamma function. Examples of these include the gamma distribution and students t-distribution, The importance of the gamma function cannot be overstated. Γ ( 1 ) The first example calculation that we will study is finding the value of the gamma function for Γ ( 1 ). This is found by setting z = 1 in the above formula: ∫0∞e - tdt We calculate the above integral in two steps: The indefinite integral ∫e - tdt= -e - t + CThis is an improper integral, so we have ∫0∞e - tdt = limb → ∞ -e - b + e 0 = 1 Γ ( 2 ) The next example calculation that we will consider is similar to the last example, but we increase the value of z by 1. We now calculate the value of the gamma function for Γ ( 2 ) by setting z = 2 in the above formula. The steps are the same as above: Γ ( 2 ) = ∫0∞e - tt dt The indefinite integral ∫te - tdt=- te - t -e - t + C. Although we have only increased the value of z by 1, it takes more work to calculate this integral. In order to find this integral, we must use a technique from calculus known as integration by parts. We now use the limits of integration just as above and need to calculate: limb → ∞ - be - b -e - b -0e 0 + e 0. A result from calculus known as L’Hospital’s rule allows us to calculate the limit limb → ∞ - be - b = 0. This means that the value of our integral above is 1. Γ (z +1 ) =zΓ (z ) Another feature of the gamma function and one which connects it to the factorial is the formula Γ (z +1 ) =zΓ (z ) for z any complex number with a positive real part. The reason why this is true is a direct result of the formula for the gamma function. By using integration by parts we can establish this property of the gamma function.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141191511.46/warc/CC-MAIN-20201127073750-20201127103750-00106.warc.gz
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CC-MAIN-2020-50
| 3,380 | 1 |
https://ficoforums.myfico.com/t5/Personal-Finance/Compounding-Interest-Daily-vs-Monthly-for-Savings/td-p/5756266
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math
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Which one would earn more for a Savings account? Compounding Interest Daily vs. Monthly?
Lets take the example from the Discover website. the Discover Online Savings Account vs the Cap1 360 Savings Account
Both accounts are 1.90% APY with a savings amount of $15k. but on the Cap1 Interest is compounded monthly and earns $3.06 more, why is that?
i don't understand the math. how do you calculate all this stuff? and what's the different between APY and APR?
Thanks for all the support!
All other things equal, compounding daily is better than monthly. The figures shown on the Discover website don't show everything.
But, the difference between APR and APY is simple enough to explain in a quick post. APR is calculation of simple interest. It's the actual percentage rate of annual interest applied to the account when the interest compounds. If an account compounded annually, APR and APY would be the same. But, if interest compounds more often, APY will be higher. Why? Because after interest compounds, you start earning interest on the interest.
To make the math simple, let's assume an account with a 1.2% APR, starting with $10,000, that compounds monthly. Every month, you earn one month of that APR, so 1/12 of 1.2% or 0.1%.
Month 1: Balance of $10000.00 earns 0.1% or $10.00. So you wind up with $10010.00.
Month 2: Balance of $10010.00 earns 0.1% or $10.01. So you wind up with $10020.01.
Month 3: Balance of $10020.01 earns 0.1% or $10.02. So you wind up with $10030.03.
Month 4: Balance of $10030.03 earns 0.1% or $10.03. So you wind up with $10040.06.
Month 5: Balance of $10040.06 earns 0.1% or $10.04. So you wind up with $10050.10.
Month 6: Balance of $10050.10 earns 0.1% or $10.05. So you wind up with $10060.15.
Month 7: Balance of $10060.15 earns 0.1% or $10.06. So you wind up with $10070.21.
Month 8: Balance of $10070.21 earns 0.1% or $10.07. So you wind up with $10080.28.
Month 9: Balance of $10080.28 earns 0.1% or $10.08. So you wind up with $10090.36.
Month 10: Balance of $10090.36 earns 0.1% or $10.09. So you wind up with $10100.45.
Month 11: Balance of $10100.45 earns 0.1% or $10.10. So you wind up with $10110.55.
Month 12: Balance of $10110.55 earns 0.1% or $10.11. So you wind up with $10120.66.
With an APR of 1.2% and compounding monthly, your APY ends up being 120.66/10000 = 1.2066%. Slightly higher than the APR.
Compounding daily would give you a higher APY relative to APR>
But with these accounts, they're advertising the APY, not the APR, so you're seeing what you actually will earn, with compounding, if you park your money there for a year. Assuming the Cap1 figures are correct, their APR may be a little higher, and the APY rounds off to the same number.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347409337.38/warc/CC-MAIN-20200530133926-20200530163926-00468.warc.gz
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CC-MAIN-2020-24
| 2,707 | 23 |
https://www.zigya.com/study/book?class=12&board=nbse&subject=Chemistry&book=Chemistry+I&chapter=Electrochemistry&q_type=&q_topic=Fuel+Cells&q_category=&question_id=CHEN12045131
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math
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In a fuel cell, H2 and O2 react to produce electricity. In the process H2 gas is oxidised at the anode and O2 at cathode. If 67.2 litre of H2 at STP reacts in 15 minutes, what is the average current produced? If the entire current is used for electro-deposition of Cu from Cu2+, how many grams of copper are deposited?
The redox changes in fuel cell are
Therefore, moles of reacting
Therefore, equivalent of used =
Also Eq. of
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s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583722261.60/warc/CC-MAIN-20190120143527-20190120165527-00633.warc.gz
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CC-MAIN-2019-04
| 426 | 5 |
https://www.taylorfrancis.com/books/9781315314525/chapters/10.4324/9781315314525-11
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math
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Statically indeterminate structures are solved either by exact methods, utilizing elastic analyses, or by approximate methods, involving the use of simplifying assumptions. While there are many types of structural engineering software packages available, which are capable of solving very sophisticated structural systems, knowing some simple approximate methods to solve statically indeterminate structures is very helpful to the practicing engineer as a starting point for design or to check output from software packages. Approximate methods, which are done by hand, can often enlighten the designer’s understanding of the structural stability and force balance of a proposed structure. Solving determinant structures using principles of statics requires the system to have the
same number of unknowns as equations of statics. That is, when there are more unknowns than equations, the structure is indeterminate. A system, which has three more unknowns than equations of statics, is said to be indeterminate to the third degree. A building frame, which comprised two vertical and one horizontal member-a bent or
portal, is statically indeterminate to the third degree. Since a single portal frame is indeterminate to the third degree, a rigid frame building, which is three stories tall and three bays wide and forms a nine portal building frame, has 27 degrees of indeterminacy, thereby making rigid frame buildings highly indeterminate. For this reason, their exact method solutions are time consuming due to the number of simultaneous equations needed to be solved, and are almost always analyzed by computer. Today, even simpli‡ed approximate methods are only used on very small systems and when appropriate due to the ubiquitous computer applications which can analyze and design these systems faster than one can perform an approximate method. In order to solve indeterminate systems by an approximate method, assumptions are
made to remove the number of unknowns or the degree of indeterminacy. There are many different methods available for making approximate analyses. The methods presented here are limited to gravity and lateral force analysis of frames.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107894426.63/warc/CC-MAIN-20201027170516-20201027200516-00719.warc.gz
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CC-MAIN-2020-45
| 2,172 | 4 |
https://www.onthedarkweb.com/forums/topic/set-theory-and-the-continuum-hypothesis-by-paul-cohen-pdf-download/
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math
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- This topic is empty.
November 19, 2020 at 3:11 am #9122Amy LouviereGuest
Set Theory and the Continuum Hypothesis
by Paul Cohen
- Format: paperback, 190 pages
- Genres: mathematics, philosophy, logic
- ISBN: 9780486469218 (0486469212)
- Language: english
- Author: Paul Cohen
- Release date: December 9, 2008
- Publisher: Dover Publications
About The Book
This exploration of a notorious mathematical problem is the work of the man who discovered the solution. The independence of the continuum hypothesis is the focus of this study by Paul J. Cohen. It presents not only an accessible technical explanation of the author’s landmark proof but also a fine introduction to mathematical logic. An emeritus professor of mathematics at Stanford University, Dr. Cohen won two of the most prestigious awards in mathematics: in 1964, he was awarded the American Mathematical Society’s Bôcher Prize for analysis; and in 1966, he received the Fields Medal for Logic.
In this volume, the distinguished mathematician offers an exposition of set theory and the continuum hypothesis that employs intuitive explanations as well as detailed proofs. The self-contained treatment includes background material in logic and axiomatic set theory as well as an account of Kurt Gödel’s proof of the consistency of the continuum hypothesis. An invaluable reference book for mathematicians and mathematical theorists, this text is suitable for graduate and postgraduate students and is rich with hints and ideas that will lead readers to further work in mathematical logic.
PDF book Set Theory and the Continuum Hypothesis buy cheap. TXT Set Theory and the Continuum Hypothesis by Paul Cohen download for PC on Barnes & Noble. EPUB ebook Set Theory and the Continuum Hypothesis. Hardcover book Set Theory and the Continuum Hypothesis Paul Cohen read online Mac on Powells. Online Set Theory and the Continuum Hypothesis download on PocketBook on IndieBound.
FictionBook ebook Set Theory and the Continuum Hypothesis by Paul Cohen read. Paperback Set Theory and the Continuum Hypothesis Paul Cohen on Amazon. Hardback book Set Theory and the Continuum Hypothesis buy on iPad. FB2 ebook Set Theory and the Continuum Hypothesis read iOS on Books-a-Million. MP3 book Set Theory and the Continuum Hypothesis by Paul Cohen download.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154099.21/warc/CC-MAIN-20210731172305-20210731202305-00198.warc.gz
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CC-MAIN-2021-31
| 2,310 | 16 |
http://gmatclub.com/forum/the-moving-walkway-is-a-300-foot-long-conveyor-belt-that-52776.html?fl=similar
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math
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The ‘moving walkway’ is a 300-foot long conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a combined rate (including both walkway and foot speed) of 6 feet per second, reaches the group of people, and then remains stationary until the walkway ends. What is Bill’s average rate of movement for his trip along the moving walkway?
2 feet per second
2.5 feet per second
3 feet per second
4 feet per second
5 feet per second
Ive seen this somewhere. Anyway forget the conveyor belt speed for now.
Bills speed is 3ft per sec. so T=D/R T=120/3 ---> T1=40sec.
However, note that in this 40 sec bill didn't just travel 120 feet. He actually traveled 240feet. You have to count the 3ft per sec of the conveyor belt now. I just ignored that speed to make things easier to calculate.
So he has 60feet left @3ft per sec. T2=60/3 = 20 sec.
Now average Rate = Total D/ Total Time
300ft/(40+20)sec ---> 300/60 = 5ft per/sec.
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s3://commoncrawl/crawl-data/CC-MAIN-2015-27/segments/1435375097204.8/warc/CC-MAIN-20150627031817-00106-ip-10-179-60-89.ec2.internal.warc.gz
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CC-MAIN-2015-27
| 1,065 | 12 |
https://teacheradvisor.org/strategies/resource_473
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math
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Description: Now that we understand how to interpret an exponent and how the patterns in zeros are related to the exponent, we can solve more complicated problems! Created by Sal Khan. We are asked what is 10 to the fifth power equivalent to. Well, 10 to the fifth power is the same thing as taking a 1 and multiplying it by 10 five times. Now, you might have noticed, every time we multiply it by 10, we're adding another 0 to the product.*Teacher Advisor is 100% free.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038879305.68/warc/CC-MAIN-20210419080654-20210419110654-00306.warc.gz
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CC-MAIN-2021-17
| 470 | 1 |
https://engineering.electrical-equipment.org/panel-building/introduction-to-first-order-systems.html
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math
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Let Nasir tell you about first order systems and their response…
Just like him, you can publish an article on the blog, all you have to do is to tell us by mail. You can write about whatever you want (debate, tutorial, product review, observations, your status as an engineer or student, etc.).
There are two methods to analyze functioning of a control system that are time domain analysis and control domain analysis. In time domain analysis the response of a system is a function of time. It analyzes the working of a dynamic control system.
This analysis can only be applied when nature of input plus mathematical model of the control system is known. It is not easy to express the actual input signals by simple equations as the input signals of the control systems are not fully known. There are two components of any system’s time response, transient response and steady response.
Typical and standard test signals are used to judge the behavior of typical test signals. The characteristics of an input signal are constant acceleration, constant velocity, a sudden change or a sudden shock. We discussed four types of test signals that are Impulse Step, Ramp, Parabolic and another important signal is sinusoidal signal. In this article we will be discussing first order systems.
First order system
The system whose input-output equation is a first order differential equation is called first order system. The order of the differential equation is the highest degree of derivative present in an equation. First order system contains only one energy storing element. Usually a capacitor or combination of two capacitors is used for this purpose. These cannot be connected to any external energy storage element.
Most of the practical models are first order systems. If a system with higher order has a dominant first order mode it can be considered as a first order system.
Response of a first order system
It is not much difficult to find the response of a first order system as the degree of differential equation is one. There are two important points on which this analysis is actually based:
- The time constant for a first order system is given by :
t=RC (for a system with resistors and capacitors)
t=L/R (for a circuit with inductors).
- The response of a first order system is given by:
Provided that, input is constant and t>0, where v (0) is voltage or current at t=0. Now we will see the unit responses with respect to first order systems and will see the transfer functions accordingly.
1. Unit Impulse in First Order System
- As we know the unit impulse input is: r(t) = δ(t), t ≥0
- For Laplace transform the Transfer function of input: R(s) =1.
- The output transform will be:
- By taking inverse Laplace transform: Y(t)= e-t/T/T, t ³ 0
- The impulse input generates transfer function as the output.
2. Unit Step Response of First Order System
- The Transfer function of input is: R(s)=1/s
- Take the inverse Laplace transform: y (t) = 1 – e-t/T, t ³ 0.
3. Unit Ramp Response of First Order System
- The input, r (t) = t for t ³ 0.
- In Laplace transform, The transfer function of input: R(s)=1/s²
- Taking the inverse Laplace transform: y (t) = t – T + Te-t/T, t ³ 0.
In this tutorial we have enlightened first order systems and their response. We calculated time constant and time response of these systems. We discussed both time response and ramp response of the first order systems.
The upcoming tutorial will discuss the same aspects of second order systems so stay tuned. We have much more to study and share with you in the upcoming articles.
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https://www.cambridge.org/core/books/topics-in-dynamics-and-ergodic-theory/62A0BE2F9E51BF28AF930975A289E817
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math
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- Publisher: Cambridge University Press
- Online publication date: August 2009
- Print publication year: 2003
- Online ISBN: 9780511546716
This book contains a collection of survey papers by leading researchers in ergodic theory, low-dimensional and topological dynamics and it comprises nine chapters on a range of important topics. These include: the role and usefulness of ultrafilters in ergodic theory, topological dynamics and Ramsey theory; topological aspects of kneading theory together with an analogous 2-dimensional theory called pruning; the dynamics of Markov odometers, Bratteli-Vershik diagrams and orbit equivalence of non-singular automorphisms; geometric proofs of Mather's connecting and accelerating theorems; recent results in one dimensional smooth dynamics; periodic points of nonexpansive maps; arithmetic dynamics; the defect of factor maps; entropy theory for actions of countable amenable groups.
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https://www.goconqr.com/p/1930005-IBPS-Specialist-Officer-Exam-2015--Quantitative-Aptitude-mock-test-for-IT-officer-quizzes
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math
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Each question in this quiz is timed.
Click the button below to start the quiz.
1. Half of Sonu's monthly income is equal to four-seventh of Rajiv's monthly income. Rajni's monthly income is Rs.32000 which is double the monthly income of Sonu. What is Rajiv's monthly income?
Cannot be determined
None of these
2. A boat takes 9 hours to travel a distance up stream and 3 hours to travel the same distance downstream. If its speed in still water is 4 km/hr, what is the velocity of the stream?
3. The perimeter of a square and a circular field are the same. If the area of the circular field is 3850 sq. meters then what is the area of the square?
4. If the area of a circle is increased by 22 cm, its radius increases by 1cm. The original radius of the circle is-
5. The total surface area of a solid hemisphere is 108π cm2. The volume of the hemisphere is-
216 cubic cm
183 cubic cm
172 cubic cm
144 cubic cm
6 What would be the simple interest obtained on an amount of Rs 5,760 at the rate of 6% p.a. after 3 years?
7. The ratio of the present age of Manoj to that of Wasim is 3:11. Wasim is 12 years younger than Rehana. Rehana's age after 7 years will be 85 years. What is the present age of Manoj's father, who is 25 years older than Manoj?
8. The owner of an electronics shop charges his customer 22% more than the cost price. If a customer paid Rs 10,980 for a DVD Player, then what was the cost price of the DVD Player?
9. The length of a rectangle is three-fifths of the side of a square. The radius of a circle is equal to side of the square. The circumference of the circle is 132 cm. What is the area of the rectangle if the breadth of the rectangle is 8 cm?
112.4 sq cm
104.2 sq cm
100.8 sq cm
10.Five-ninths of a number is equal to twenty five per cent of the second number. The second number is equal to one-fourth of the third number. The value of the third number is 2960. What is 30 per cent of the first number?
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https://xqdh.tovewe.xyz/jangan-biarkan-aku-sendiri.html
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math
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Mathematical Optimization. A mathematical optimization problem consists of maximizing (or minimizing) a real objective function on a defined domain: Given a set A ⊆ Rn and a function f : A → R from A to the real numbers, find an element x0 ∈ A such that f(x0) ≤ f(x) for all x in an environment of x0. optim(), nlm(), ucminf() (ucminf) can be used for multidimensional optimization problems. nlminb() for constrained optimization. quadprog, minqa, rgenoud, trust packages; Some work is done to improve optimization in R. See Updating and improving optim(), Use R 2009 slides, the R-forge optimizer page and the corresponding packages including optimx. [书籍介绍] Financial Risk Modelling and Portfolio Optimization with R.pdf. Financial Risk Modelling and Portfolio Optimization with R. Bernhard Pfaff Invesco Global Strategies, Germany. Contents Preface xi List of abbreviations xiii. Part I MOTIVATION 1 1 Introduction 3 Reference 5. 2 A brief course in R 6 2.1 Origin and development 6 2.2 ... Portfolio Optimization 13.1 Introduction Portfolio models are concerned with investment where there are typically two criteria: expected return and risk. The investor wants the former to be high and the latter to be low. There is a variety of measures of risk. The most popular measure of risk has been variance in return.
Financial Optimisation with R [pdf] [BibT e X] The nmof manual: how to do practical financial optimisation in r. Portfolio Management with R (pm w r) [html] [pdf] [BibT e X] Pricing of financial instruments, computing profit-and-loss, reporting, backtesting and . essays (an incomplete list) Backtesting 2018 [ssrn] Optimization Heuristics: A ... Nov 17, 2018 · Portfolio optimization is one of the most interesting fields of study of financial mathematics. Since the birth of Modern Portfolio Theory (MPT) by Harry Markowitz, many scientists have studied a… Mar 08, 2015 · Synopsis: Introduces the latest techniques advocated for measuring financial market risk and portfolio optimization, and provides a plethora of R code examples that enable the reader to replicate the results featured throughout the book. Financial Risk Modelling and Portfolio Optimization with R: Portfolio Optimization. Hi, I'm an R newbie and I've been struggling with a optimization problem for the past couple of days now. Here's the problem - I have a matrix of expected payouts from... Use the portfolio optimization tool to optimize portfolios based on risk adjusted performance or other target criteria. Vanguard Total Stock Market ETF (VTI) iShares S&P SmallCap 600 Value Index Fund ETF (IJS) iShares MSCI EAFE Index Fund ETF (EFA) Vanguard Emerging Markets ETF (VWO) Vanguard Real Estate ETF (VNQ)
Background on Portfolio Optimization Markowitz’s Mean-Variance Portfolio Harry Markowitz’s concept of mean-variance analysis, in the general sense, is quite simple. The objective is to provide a portfolio with the minimum variance, for a desired level of return. This optimization There are a variety of optimization techniques - Unconstrained optimization . In certain cases the variable can be freely selected within it’s full range. The optim() function in R can be used for 1- dimensional or n-dimensional problems. The general format for the optim() function is - Portfolio Optimization with Conditional Value-at-Risk Objective and Constraints Pavlo Krokhmal Jonas Palmquist† Stanislav Uryasev‡ Abstract Recently, a new approach for optimization of Conditional Value-at-Risk (CVaR) was suggested and tested with several
Portfolio Optimization involves choosing proportions of assets to be held in a portfolio, so as to make the portfolio better than any other. In this research, we use a software for statistical computing R to analyse the performance of portfolio optimization models which include; Markowitz’s Mean-Variance Portfolio Optimization Problem In this paper we assume the investor maximizing selected performance ratio, i.e. solving following portfolio optimization problem, n i i i i PR x x , i , …, n x , i , …, n 1 arg max ( ) 1 0=1 0.25 =1 x Rx w (5) in which x is the vector of weights (portfolio composition) and R represents the matrix of random ... Financial Risk Modelling and Portfolio Optimization with R ... asset and portfolio level are the topic of the ... Modelling and Portfolio Optimization with R ...
Introduces the latest techniques advocated for measuring financial market risk and portfolio optimization, and provides a plethora of R code examples that enable the reader to replicate the results featured throughout the book. Financial Risk Modelling and Portfolio Optimization with R: Demonstrates techniques in modelling financial risks and applying portfolio optimization techniques as well ... Oct 09, 2017 · In this tutorial, we will go over how to use some of the basic functions in fPortfolio, a package for portfolio analysis in R. View this on my website: http:...
L d D t S t S ifi ti d Ctit# LPP Portfolio Example:# LPP Portfolio Example: > Data = LPP2005.RET[, 1:6] > Spec = portfolioSpec() > Cons = "LongOnly" # Portfolio Frontier: Load Data Set, Specification and Constraints Pictet Swiss Pension Fund Benchmark LPP2005 > portfolioFrontier(Data, Spec, Cons) Title: MV Portfolio Frontier: Intermediate Portfolio Analysis in R Modern Portfolio Theory Modern Portfolio Theory (MPT) was introduced by Harry Markowitz in 1952. MPT states that an investor's objective is to maximize portfolio expected return for a given amount of risk. Common Objectives: Maximize a measure of gain per unit measure of risk Minimize a measure of risk Jan 22, 2013 · Financial Risk Modelling and Portfolio Optimization with R by Bernhard Pfaff, 9780470978702, available at Book Depository with free delivery worldwide. Aug 20, 2009 · The examples and output are all automatically generated from R and integrated with the written content to ensure accuracy, and the text is extensively bookmarked and hyperlinked making it easy to skip from section to section on-screen. At over 450 pages it's a comprehensive study of all aspects of portfolio optimization with Rmetrics. Portfolio Optimization Constraints Estimating Return Expectations and Covariance Alternative Risk Measures. Equivalent Optimization Problems. Problem II: Expected Return Maximization: For a given choice of target return variance ˙ 2 0, choose the portfolio w to Maximize: E(R. w) = w. 0 Subject to: w. 0. w = ˙ 2 0. w. 0. 1. m = 1
Apr 02, 2016 · In this post we’ll focus on showcasing Plotly’s WebGL capabilities by charting financial portfolios using an R package called PortfolioAnalytics.The package is a generic portfolo optimization framework developed by folks at the University of Washington and Brian Peterson (of the PerformanceAnalytics fame). Chapter 1 Portfolio Theory with Matrix Algebra Updated: August 7, 2013 When working with large portfolios, the algebra of representing portfolio expected returns and variances becomes cumbersome. The use of matrix (lin-ear) algebra can greatly simplify many of the computations. Matrix algebra for the mean and covariance in R’s base packages and in contributed packages. The estimators listed below can be accessed by the portfolio optimizationprogram. Functions: covEstimator Covariance sample estimator kendallEstimator Kendall's rank estimator spearmanEstimator Spearman's rank estimator mcdEstimator MCD, minimum covariance determinant estimator OptiFolio is the best strategic portfolio optimization solution with modern portfolio theory and Basel III measures for mutual funds, pension funds, private banks, insurance companies, investment advisors, business schools, individual investors
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http://footforum.info/archives/2020.html
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math
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I am a marathon runner.
Believe me: I am an expert at ankle problems I try to avoid doctors at all costs. However, I just broke my ankle (Weber A fracture) during a workout.
Believe it or not, my fracture hurt(s) a lot lett than a sprain or even shin splints.
However, you should realy have a doctor check it out---maybe somebody from your school. If not, a trip to the ER might be in order.
: I am experiencing intense pain in my left ankle and i wanted to know if there is anything i can do on my own to determine what is wrong with it as getting to a hospital/clinic would be quite a hassle. I cannot bear any weight on the ankle and have very limited rotation. i do not know if it is broken, but the pain is even greater than the last time i broke my ankle. if someone could help, it would be greatly appreciated. I am a student and i am very active in sports. thank you.
: P.S. i rolled my ankle when playing basketball. (landed on the ball after a jump.)
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| 960 | 6 |
http://en.wikipedia.org/wiki/Magnetomotive_force
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math
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The equation for the magnetic flux in a magnetic circuit, sometimes known as Hopkinson's law, is:
Magnetomotive force is analogous to electromotive force, emf( = difference in electric potential, or voltage, between the terminals of a source of electricity, e.g., a battery from which no current is being drawn) since it is the cause of magnetic flux in a magnetic circuit.
1: m m f = NI where N = no of turns in the coil, I = electric current through the circuit
2: m m f = ΦR where Φ = magnetic flux R= reluctance
3: m m f = Hl where H = magnetizing force l = mean length of solenoid,circumference of toroid
- The Penguin Dictionary of Physics, 1977, ISBN 0-14-051071-0
- A textbook of ELECTRICAL TECHNOLOGY,2008,ISBN 81-219-2440-5
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https://www.arxiv-vanity.com/papers/quant-ph/9908054/
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math
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Effect of the measurement on the decay rate of a quantum system
We investigated the electron tunneling out of a quantum dot in the presence of a continuous monitoring by a detector. It is shown that the Schrödinger equation for the whole system can be reduced to new Bloch-type rate equations describing the time-development of the detector and the measured system at once. Using these equations we find that the continuous measurement of the unstable system does not affect its exponential decay, , contrary to expectations based on the Quantum Zeno effect . However, the width of the energy distribution of the tunneling electron is no more , but increases due to the decoherence, generated by the detector.
PACS: 73.23.Hk.03.65.Bz.73.23.-b It was suggested that an unstable quantum system slows down its decay rate under frequent or continuous observations. This phenomenon, known as the quantum Zeno effect, is believed to be related to the projection postulate in the theory of quantum measurements. Indeed, in the standard example of two-level systems, the probability of a quantum transition from an initially occupied unstable state is . If we assume that is the measurement time, which consists in projecting the system onto the initial state, then after successive measurements the probability of finding the unstable system in its initial state, at time , is . It follows from this result that for , i.e. suppression of quantum transition.
Originally quantum Zeno effect has been considered as a slowing down of the decay rate of quantum systems in which a discrete initial state is coupled to a continuum of final states. This coupling leads to an irreversible exponential decay from the discrete state to the continuum of states. This situation is very often encountered in physics, as for instance, the –decay of a nucleus, the spontaneous emission of a photon by an excited atom, the photoelectric effect, and so on. But from the theoretical and experimental point of view, the effort has been mainly concentrated on quantum transitions between isolated levels characterized by an oscillatory behavior between the different states. In this latter case the slowing down of the transition rate has, indeed, been found. However, this was attributed to the decoherence generated by the detector without an explicit involvement of the projection postulate[4, 5]. On the other hand, the slowing down of the exponential decay rate still remains a controversial issue, despite the fact that it is extensively studied[6, 7, 8, 9] and further investigations are clearly desirable.
In this letter we focus our attention on the quantum Zeno effect in exponentially decaying systems, using a microscopic description which includes the measurement devices. The latter is an essential point missed in many studies. This work is motivated by the distinct difference between continuum energy levels and discrete levels, stated above, as well as by the theoretical and experimental importance of the subject. We also propose an experimental set up which is within reach of nowadays experimental techniques and within which the quantum Zeno effect for exponentially decaying systems can be investigated. Our results showed that while the decay rate of the quantum unstable system is unaffected by the measurement the energy distribution of the emitted particles can be strongly affected.
Let us consider an electron tunneling out of a quantum dot to a reservoir of very dense (continuum) states, . The dot is placed near a quantum point-contact connected with two separate reservoirs (Fig. 1). The reservoirs are filled up to the Fermi levels and , respectively. Therefore the current flows from the left (emitter) to the right reservoir (collector), where is the transmission coefficient of the point-contact and is the bias voltage. (We consider the case of zero temperature). However, when the dot is occupied, Fig. 1, the transmission coefficient of the point-contact decreases () due to Coulomb repulsion generated by the electron inside the dot. Respectively, the current through the quantum dot diminishes, . Thus, the point-contact does represent a detector, which monitors the occupation of the quantum dot. Actually, such a point-contact detector has been successfully used in different experiments . Notice that the current variation () can be a macroscopic quantity if the applied voltage is large enough. The dynamics of the entire system is determined by the many-body time-dependent Schrödinger equation , where the total Hamiltonian consists of three components , describing the quantum dot, the point-contact detector, and their mutual interaction, respectively. These three parts can be written in the form of tunneling Hamiltonians, as
Where the operators correspond to the creation (annihilation) of an electron in state . The and are the hopping amplitudes between the states , and , respectively. These amplitudes are found to be directly related to the tunneling rate of the electron out of the quantum dot () and to the penetration coefficient of the point-contact () as and , respectively. Here are the density of states in the corresponding reservoirs. The quantity represents the variation of the point-contact hopping amplitude, when the dot is occupied. In our derivations we assume that and are weakly energy dependent and . The latter condition is necessary for the exact solubility of the model.
Consider the entire system in the initial condition, corresponding to occupied quantum dot and filled reservoirs up to Fermi levels and , Fig. 1, denoted by . This state is not stable: the Hamiltonian (1) requires it to decay to continuum states having the form . In general, the total wave-function at time can be written as
Where are the probability amplitudes of finding the system in the state defined by the corresponding creation and annihilation operators. Using these amplitudes one finds the reduced density-matrix by tracing out the irrelevant degrees of freedom. This density matrix will give us all probability distributions describing the behavior of the entire system. For instance, , is the probability of finding the system in the initial state at time , is the probability of finding one electron in the collector and the quantum dot is occupied, is the probability for the electron to tunnel out of the dot into level and no electron arriving the collector, and so on. In general, the total probability for the electron to occupy the dot is , and the probability of tunneling into level is . Here the subscript denotes the number of electrons reaching the collector at time . The corresponding off-diagonal density-matrix elements describe the electron in the linear superposition of the states and .
In order to find the amplitudes , we substitute Eq. (2) into the time dependent Scrödinger equation and use the Laplace transform . Then we find an infinite set of algebraic equations for the amplitudes , given by
It is very important that the tracing of the reservoir variables can be carried out directly in Eqs. (3) without their explicit solutions. As a result, Eqs. (3) are converted to the Bloch-type equations for the reduced density-matrix . Such a technique has been derived in [5, 12]. In this paper we generalize it by converting Eqs. (3) into rate equations without tracing over all the continuum states. We, thus, obtain generalized Bloch-type equations which determine the energy distribution of the tunneling particles. In the following we outline this derivation, relegating the technical details to a more extended publication.
First, we replace each of the sums in Eqs. (3) by an integral, which can be treated analytically. The Eq. (3a), for instance, after replacing in it the amplitudes and by the corresponding expressions obtained from Eqs. (3b), (3c), becomes
where denotes the terms in which the amplitudes cannot be factorized out the integrals. These terms vanish when the integration limits are extended to infinity (the large bias limit, ). This is due to the fact that the singularities of the amplitudes , as functions of the variables , lie on the same side of the integration contour. The remaining integrals in Eq. (4) can be splited into a sum of singular and principal parts. The singular parts yield , where . While the principal parts induce a shift of energy which is merely absorbed by a redefinition of the energy levels. Performing the same procedure with all other equations (3), we reduce them to the following system of equations for the amplitudes [5, 12]
where . In order to transform Eq. (5) to equations for the density-matrix we multiply each of them by the corresponding complex conjugate amplitude . For instance by multiplying Eq. (5b) by and subtracting its complex conjugated equation multiplied by we obtain
It is quite easy to see that the inverse Laplace transform turns this equation to the following one for the density-matrix
Proceeding in the same way with all other equations (5) and integrating over the continuum states of the collector and the emitter, we obtain the following infinite set of equations for the density matrix
Eqs. (8) are a generalization of the previously derived Bloch-type rate-equations for quantum transport in mesoscopic systems[5, 12]. They have a clear physical interpretation. Consider for example Eq. (8a) for the probability of finding the electron inside the dot and electrons in the collector. It decreases due to one-electron hopping to the collector (with rate ), or due to the electron tunneling out of the dot (with rate ). These processes are described by the first (“loss”) term in Eq. (8a). On the other hand, there exists the opposite (“gain”) process when the state with electrons in the collector converts into the state with electrons in the collector. It also takes place due to penetration of one electron through the point-contact with the same rate (the second term in Eq. (8a)).
The evolution of the off-diagonal density-matrix elements is given by Eq. (8c). It can be interpreted in the same way as the rate equation for the diagonal terms. Notice, however, the difference between the “loss” and the “gain” terms. The latter can appear only due to coherent transition of the whole linear superposition[5, 12].
Since our rate equations distinguish between different continuum states (), we can find the energy distribution of the tunneling electron by tracing out the detector states in Eqs. (8). As a result we obtain the following final equations for the electron density-matrix
Here is the decoherence rate.
It is instructive to compare Eqs. (9) with the similar Bloch-type equations describing quantum transitions between two isolated levels[5, 13]. In the case of isolated levels ( and ), the equations for the density-matrix are symmetric with respect to and . Whereas in the case of transition between the isolated () and the continuum states () the corresponding symmetry, between and , is broken as can be seen, for example, in the equation for the off-diagonal term where the coupling with is missing. Eq. (9c).
The probability of finding the electron inside the dot is obtained directly from Eq. (9a) given by
It means that the continuous monitoring of the unstable system does not slow down its exponential decay. Nevertheless, it can be shown that the energy distribution of the tunneling electron, , is affected. Indeed, by solving Eqs. (9) in the limit of we find a Lorentzian distribution centered about :
If there is no coupling with the detector, , the Lorentzian width (the line-width) is exactly the inverse life-time of the quasi-stationary state, Eq. (10). However, it follows from Eq. (11) that the measurement results in a broadening of the line-width, which becomes due to the decoherence generated by the detector. At first sight this result might look very surprising. Indeed, it is commonly accepted that the line-width does correspond to the life-time. Yet, we demonstrated here that it might not be the case when the system interacts with an environment (the detector). To understand this result, one might think of the following argument. Due to the measurement, the energy level suffers an additional broadening of the order of . However, this broadening does not affect the decay rate of the electron , since the exact value of relative to is irrelevant to the decay process. In contrast, the probability distribution is affected because it does depend on the position of relative to as it can be seen in Eq. (11).
Although our result has been proved for a specific detector, we expect it to be valid for the general case, provided that the density of states and the transition amplitude vary slowly with energy. This condition is sufficient to obtain a pure exponential decay of the state . On the contrary, if or depend sharply on energy, then the integrals in Eq. (4) yield additional -dependent terms that modify both the exponential dependence of the decay probability, Eq. (10) and the energy distribution, Eq. (11). As a result, the measurement process could hinder the decay rate.
We emphasize that our results were obtained from the Schrödinger equation describing the dynamical evolution of the entire system, without explicit use of the projection postulate. This is in contrast with other works, as for instance, where the reduction was repeatedly involved during the continuous measurement process. Although our final result does not display any slowing down of the decay rate, it should not be considered as a contradiction with the projection postulate. Indeed, the hindering of the decay rate, generated by the projection postulate, relies on the assumption that the probability of transitions between different quantum states is . It is definitely correct for transitions between isolated states, where the transition probability has an oscillatory behavior. However, in the case of transitions from isolated to very dense states, represents a sum of many oscillations with close frequencies. When averaged over the time-interval , where is the width of the function (in our case ), the resulting would then represent a pure exponential decay. In this case , so that repeated applications of the projection postulate would not change the life-time of the decayed state. But, if is finite that zero, due to the energy dependence of or , then exhibits deviations from the exponential behavior, which could result in quantum Zeno effect .
In conclusion, we have given a microscopic description of quantum Zeno effect in pure exponentially decaying quantum systems including the measurement devices. Our results show that while the measurements does not affect the decay rate, the energy distribution of the tunneling electron is broadened. This description applies to a wide range of physical processes as mentioned at the beginning of this letter. In particular, it can be verified in experiments with mesoscopic quantum dots, by using the point-contact detector, or an alternative set up.
We thank S. Levit and Y. Imry for most valuable discussions. One of us (S.G.) would like to acknowledge the hospitality of Oak Ridge National Laboratory and TRIUMF, while parts of this work were being performed. One of us (B.E.) gratefully acknowledge the support of GIF and the Israeli Ministry of Science and Technology and the French Ministry of Research and Technology
- B. Misra and E.C.G. Sudarshan, J. Math. Phys. 18 (1977).
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- R.A. Harris and L. Stodolsky, Phys. Lett. B116 (1982), 464; E. Block and P.R. Berman, Phys. Rev. A44, 1466 (1991). V. Frerichs and A. Schenzle, Phys. Rev. A44, 1962 (1991).
- S.A. Gurvitz , Phys. Rev. B56, 15215 (1997).
- L. Fonda,G. C. Ghirardi and A. Rimini, Rep. Prog. Phys. 41, 587, (1978).
- L.S. Schulman, Phys. Rev. A57, 1509 (1998).
- A.G. Kofman and G. Kurizki, Phys. Rev. A54, R3750 (1996).
- A. D. Panov, Phys. Lett. A260, 441 (1999), and references therein.
- R. Landauer, J. Phys. Condens. Matter 1, 8099 (1989).
- M. Field et al., Phys. Rev. Let. 70, 1311 (1993); E. Buks, R. Shuster, M. Heiblum, D. Mahalu and V. Umansky, Nature 391, 871 (1998).
- S.A. Gurvitz and Ya.S. Prager, Phys. Rev. B53 (1996), 15932; S.A. Gurvitz , Phys. Rev. B57 (1998) 6602.
- G. Hackenbroich, B. Rosenow, and H.A. Weidenmüller, Phys. Rev. Lett. 81, 5896 (1998).
- B. Elattari and S.A. Gurvitz (unpublished)
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https://studysoup.com/note/53146/colorado-school-of-mines-math-348-fall-2015
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math
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ADVANCED ENGINEERING MATHEMATI
ADVANCED ENGINEERING MATHEMATI MATH 348
Colorado School of Mines
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E Kreyszig Advanced Engineering Mathematics 9 ed Section 7179 pgs xxxxxx Lecture Chapter 7 Wrap Up Module 07 Suggested Problem Set Suggested Problems na February 5 2009 Quote of Lecture 7 Chairman Kaga If memory serves me right Iron Chef 19931999 In conclusion of chapter 7 we summarize the important results concerning the linear system of equations Ax b where A E Rm x 6 RM b E Rmxl Speci cally we begin with the following system of linear equations a11x1a12x2a13x3 amxn b1 a211a22I2a233 quot39a2nn 72 1 a311a32I2a333 quotquottaSnIn 73 am1x1am2xzam3xa amnxn 17m which we know has the following matrixVector representation an 112 113 am I1 1 121 122 123 H Mm 2 72 2 Ax 131 132 133 dam is 73 b am am an anm in bm n where the product of matrices is de ned as ABlij Zaikbkj 1 We note that this system can also be k1 de ned as a linear combination of Vectors n 3 AxI1a1I282383quot39n8n ZIjaj b7 where ai E Rm is the 139 column from the coef cient matrix A Given A and b we ask 0 Does there exist a solution to the linear system Ax b with the understanding that there may exist a solution and this solution may be unique Thus we have three possible outcomes when trying to solVe Ax b 1 There exists a solution to Ax b 2 There exists a solution to Ax b and this solution is unique 3 There does not exist a solution to Ax b 1The following website contains an animation of matrix multiplication httpwwwsciwsu edumathfaculty genz220v1essonskent1erFullMultfullMatrixMultiply html We should note that Visually this is not the same way we multiply but it is equivalent This goofy animation httpwwwpurp1emathcommodulesmtrxmulthtm is similar to how we conduct multiplication MATH348 Advanced Eu insulin M quot 2 which can be seen in the 1D case by quick but careful inspection of ax 1 ab E R For the case of coef cient data from Rmxquot we form an augmented matrix 111 112 113 aim b1 121 122 123 Wm 72 4 131 132 ass m dam b3 am am am am bm and apply the rowreduction algorithm2 to as This algorithm makes us of the following three rules for manipulating augmented matrices 1 row scaling the multiplication a row by a nonzero scalar 2 row exchange the exchanges of two rows 3 row replacement the addition of a multiple of one row to another row which we know to be equivalent to algebra applied directly to the linear system of equations We apply this algorithm when taken to full completion in a twopart process In the socalled forward phase we H Begin with the leftmost nonzero column This is a pivot column The inot position is at the top to Select a nonzero entry in the inot column as a pivot If necessary interchange rows to moVe this entry into the inot position Use row replacement operations to create zeros in all positions below the inot E Cover or ignore the row containing the inot position and coVer all rows if any aboVe it apply steps 13 to the submatrix that remains Repeat the process until there are no more nonzero rows to modify While in the backward phase we 1 Begin with the rightmost pivot and working upward and to the left create zeros aboVe each inot If a pivot is not 1 make it 1 by a scaling operation The forward phase produces a row echelon form of the input matrix From this echelon form the backward phase produces the reduced row echelon form of the input matrix3 Since rowoperations do not change the solution to linear systems getting to these echelon forms is the goal of the algorithm For example if we take A E RSXQ and b E 1R6lt1 and reduce it to 1 0 as as 0 as 0 a 0 0 1 0 as as 0 as 0 b 5 0 0 0 1 as as 0 as 0 c O O O O O O 1 as 0 d O O O O O O O O 1 e 0 0 0 0 0 0 0 0 0 f where as are in general nonzero elements then the following simplest linear system whose solution is equiV alent to the solution of Ax b 4 1I1I2I5I6I3 a I3I5I6I3 I 4 Is Is 123 C m m3 d x9 e 0x10x20x3Ox40x50x60x70x30x9 f 2This algorithm is also often called Gaussian elimination in honor of its European inventor Carl Friedrich Gauss httpenwikipediaorgwikiGaussianielimination 3ht p wwwmathaaudk ottosenMatZCrralghtml 4The following website contains an animation of rowireduction httpwwwsciwsuedumathfacultygenz 220VlessonskentlerSolveAnimEchsolveAnimlhtml V There are more at httpwwwsciwsuedumath facui MATH348 Advanced Eu lllccilll M t t39 3 We notice that if f 7 0 then the nal equation is inconsistent and the system has no solution If f 0 then there is a solution to the system but since we started with more columns than rows this solution is not unique 5 From this we notice that not only is it important to deduce from rowreduction the consistency of each equation one must also compare the total number of variables to the number of pivots or the number of free variables This difference determines the uniqueness of the solutions and is an expression of the ranknullity theorem Since the calculation of the differences 1 A1 number of variables number of pivots 2 A2 number of variables number of free variables will be important we record the following de nitions which will allow us to calculate these numbers from rowreduced matrices Before we recite this information we take a minute to note the logic these statements will be used for 1 Given some set of vectors we must determine how to make new ones from vectors from the set linear combination 2 Suppose we make the set of all linear combinations which in general contains an in nite number of vectors we would like a way to specify those vectors necessary for the construction of this spanning set linear independence Spanning sets are examples of socalled linear vector spaces and linearly independent vectors from this setspace constitutes a basis for this space with dimension equal to the number of vectors in any basis E Two vector spaces important in the study of systems involving A are the null space and column space of A The dimension of the null space counts the number of free variables and the dimension of the column space counts the number of pivots Rank Nullity Theorem De nition 1 Linear Combination Let S 3901 v2 v3 vk where vi 6 Rquot for i 1 2 3 k k E N then we say that w E Rquot is a linear combination of the vectors from S if k 6 wc1v1c2v2c3v3ckvk E Cj39lj 71 where 87 E R De nition 2 Linear Independence Let S be as before then we say that S forms a linearly independent set if the following bidirectional implication holds k 7 ZCj39lj0ltgt ci0 foralli123k Remark 1 Recall that 7 is equivalent to Vc 0 where V is a matrix whose jth column is 39le and c is a vector whose elements are 87 If we note without proof that pivot columns are linearly independent then the linearly independent vectors from S are the pivot columns from matrix V and that these columns can be found by the rowereduction applied to V De nition 3 Spanning Set Let S be as before Then we de ne the span of S as the set ofail linear combinations of the the vectors from S That is spanS is the set of all a de ned by De nition 4 Linear Vector Space A linear vector space or just vector space for brevity is a set of vectors S which is also closed under arbitrary linear combinations of the vectors from S6 This is to say that a vector space is a the set S along with all linear combinations of the vectors from S It follows that the span of any set of vectors is a vector space 5In other words the system has more variables than equations and from this underdetermined system one would never expect unique solutions To have unique results one must have at least as many equations as unknowns If there are more equations than unknowns then the system is said to be overdeterrnined 6This de nition is somewhat imprecise There are particular algebraic rules which must hold for the space to be a vector space Please consult 79 of your text for more detailed information MATH348 Advanced Eu lllccllll M t t39 4 De nition 5 Basis Given a vector space say S we say that a basis for this space is the maximum collection of linearly independent vectors from S or equivalently the minimum collection of vectors needed to span the space De nition 6 Dimension Given a vector space S and a basis for this space say BS we say that the dimension of the space is the number of vectors in this basis That is dimB De nition 7 Null Space The null space of a matrix NulA is the vector space de ned byail solutions to the homogenous system Ax 0 Remark 2 If the system Ax 0 is consistent with in nitely many solutions then the general solution will be a linear combination of vectors multiplied by free variables These vectors form a basis for the null space and thus the null space has dimension equal to the number of free variables De nition 8 Column Space The column space of a matrix colA is the set ofail linear combinations of the columns of A Remark 3 From remark 1 we have that the pivot columns of a matrix are linearly independent and thus a basis for the column space of a matrix is its set of pivot columns From this we conclude that the dimension of the column space of a matrix also known as its Rank is the number of pivots in the matrix Theorem 1 RankeNullity Theorem Let A E Rmxquot then the following equality holds 8 RankA dimNulA ri which asserts that the number of pivots plus the number of free variables must be equal to the number of columns in A This summarizes the major concepts from chapter 7 The following statement summarizes this material for the case Where the coef cient matrix is square Theorem 2 The invertible matrix theorem Let A 6 RM Then the following statements are equivae lent 1 A is an invertible matrix That is A71 exists 2 detA 7 O 3 A is row equivalent to the n X 71 identity matrix 4 A has nepivot positions 5 The equation Ax 0 has only the trivial solution 6 The columns of A form a linearly independent set 7 The equation Apb has a unique solution for each I E Rquot 8 The columns of A span Rquot 9 The columns of A for a basis for Rquot 10 colA R 11 dimcolA n 12 rankA n 13 MM a 14 dimnulA O XL39 2x O 5ch L11 qxlquot sz f GX3O MP BXH clth leago Lmkh d 3 Gun 204 ltl lxiiu cu 1 Tc PLv c D I so AHquot mXOIIMuF H JPN4 Ukuno 57 mx w PKuhO W13 674414 uxuno w Er 43 Q95 9X94 H mungjwrn p mgr 4 wur Abra M WX 4 OTJH gonna LerLlqu Zorn 523 MD o OV PM w Mro ivrv 590993 f IA 93 w V4906 EXMEKJ L X LX353 le 535 9x3 1 Ex Ow oxfu 1 3939 0Q M o gwx 15 Own K1242 Tkli 3 cod 703 m W 4 Arak oh ka ms 3amp3 29651 915 H7 Make sea w 3 a M omos wwulxg avg3amp6 I 95wcv A1 P h 39 A sh Wm M rfMsisi39vd EXt negat 1 Kl BXLS X X73 5 3l XL39gtltBO Eltmgt 1 m3gtltn 5 qu QLt 5X3 1 xtir xzfo EXonvaJ 3 X lxlx XSI39i 39XZ X31 x 3gtlt1 O E Kreyszig Advanced Engineering Mathematics 9th ed Section 121 pgs 535538 Lecture Introduction to PDE Module 13 Suggested Problem Set 17 19 22 23 24 26c 27 April 23 2009 Quote of Lecture 13 If you didn t care what happened to me and I didn t care for you We would Zig Zag our way through the boredom and pain occasionally glancing up through the rain Wondering which of the buggers to blame and watching for pigs on the wing Pink Floyd Pigs on the Wing Part 1 1977 1 INTRODUCTION TO PDE At long last we start our study of partial di erential equations PDE We will see everything we have studied this semester come back again as we learn the classical methods of solving linear PDE The emphasis here is on the linearity of the PDE Without this the following important tools 0 Linear combinations of basis vectors 0 Eigenvalues and eigenvectors 0 General solution to linear ODE o Fourier seriesintegral are be rendered almost useless 1 However before we begin that discussion it makes sense to discuss some of the basic terminology De nition 1 Linearity of an Equation 7 We say that an equation di erential or otherwise is linear in some quantity if it can be written as a linear combination of the quantity In the case of a PDE the quantity is the unknown function u which may depend on many variables say x y z t The PDE is then linear if it can be written as a linear combination of u and derivatives of u The general notation can be cumbersome so this is best illustrated by examples Example 1 Linear PDE 7 The following are some examples of common linear PDE 1 Au0 2 3 c2Au 4 82u 2 4 c Au 5 1I say almost because to understand nonlinear theory which is at this time woefully incomplete one must under stand the completeness of linear theory So these principles come back again and again to study nonlinear theory but are incomplete in these sense that donlt often tell you everything you might like to know 2This equation is called Laplacels equation and models space subjected to potential elds like gravitational or electrostatic 3This equation is called Possionls equation and models space subjected to potential elds with source terms 4This equation is called the heat or diffusion equation and models the timeedynarnics of the ow of a density which tends to move from areas of high density to low density 5This equation is called the wave equation and models the standing waves or traveling waves in an elastic medium 6This equation is called a convection equation or transport equation and models the pure transport of a material due to movements of its background medium MATH348 Advanced Eu lllccllll M quot 2 Example 2 Nonlinear PDE e The following are some examples of common nonlinear PDE l pltgvVvgt 7Vp1Av 7 u 2 cAu u 2u 8 Bu Bau Bu 3 a t w t a Remark 1 The critical point here is the for a PDE to be linear you cannot have terms like 09 2 Bu 82u 2 1 u sum um at while terms like 2 u sin are permitted De nition 2 Homogenous PDE e We say that a PDE is homogeneous it is linear and does not contain terms where the dependent variable u or derivatives of this unknown function are absent If the linear PDE contains a term which does not depend on the unknown function or its derivative then we say that the PDE is inhomogeneous Of the previous linear examples I 3 and 5 are homogeneous while is not Theorem 1 Superposition of Solutions 7 If a PDE is linear and homogenous and u1 and u2 are solutions to this PDE then the arbitrary linear combination u mm a2u2 a1 a2 6 R is also a solution Proof In general since the derivative of a sum is the sum of derivatives superpositions will be decomposed by the PDE into smaller equivalent PDE If each term in the superposition is a solution then each smaller equivalent PDE is subsequently satis ed Speci cally for the heat equation we have 3 g a1u1 mm 4 alaitl a2 5 a1c2Au1 a2c2Au2 6 Aa1u1 agug 7 c2Au These arguments hold for Q homogeneous linear equation D This coupled with all of your mathematics up to now completes the basic background necessary for the study of linear PDE which will begin with a derivation of the socalled heat or diffusion equation The heatdiffusion equation in rstorder in time and secondorder in space linear PDE on R3 and models the timedynamics of a conserved density whose ow is along its spatial gradient In this derivation we focus on the generality conservation principles and their closure with constitutive relations The wave equation in R14 can be derived in the context of a vibrating string by analysis of forces at a point on the string However it can manifest more generally in the context of the Einstein eld equations on a vacuum background or in terms of small disturbances of an elastic background medium Though this is outside the scope of our course it is interesting to know since our characterizations of solutions to the wave equation will hold in both contexts and give insight into how nonlinearity might appear Begining with a vibrating elastic rectangular membrane we will derive the solution to the wave equation in RHI by 7This equation is called the Navierestokes equation and can be derived as the model equation for the evolution of uid particles See also httpenwikipediaorgwikiNaviereStokes quations and httpwwwc1aymathorg millenniumNaviereStokesiEquations This equation is called the nonlinear Schrodinger equation and models the evolution of a new phase of matter called a BoseEinstein condensate whose 1995 experimental observation earned researchers at Boulder and MIT and Nobel prize in 2001 See also httpwwwcoloradoeduphysicsZOOObec and httpenwikipediaorgwiki BoseeEinsteinicondensate 9This equation is called the Kortewegide Vries equation an models surface waves in shallow waters and was the basis for modern advances in the study of exactly solvable nonlinear PDE httpenwikipediaorgwiki Kortewege de7Vriesiequat ion MATH348 Advanced Eu lllccllll M quot 3 the use of double Fourier series and moving to a vibrating circular membrane We Will see hoW the solution allows for more complicated vibrational modes Which can be interpreted physically in terms of musical instruments Lastly We characterize solutions to the Wave equation in terms of traveling Waves Whose speed and in uence can be determined by the concept of a characteristics Which gives rise to soundsspeed and the speedof light 2 LECTURE GOAL Our goal With this material Will be 0 Understand the mathematical de nition of PDE as Well as some of their modeling capabilities 3 LECTURE OBJECTIVES The objectives of these lessons Will be 0 List various PDE and their associated models 0 De ne the vocabulary associated With PDE With an emphasis on the interplay between linearity and superposition 0 Outline direction and key points of our study of PDE E Kreyszig Advanced Engineering Mathematics 9 ed Section 119 pgs 518528 Lecture Fourier Transform Module 12 Suggested Problem Set 2 3 9 14a March 31 2009 Quote of Lecture 12 Jenny said when she was just ve years old there was nothin7 happenin7 at all Ehery time she puts on a radio there was nothin7 goin7 down at all not at all Then one ne mornin7 she puts on a New York station you know she don t believe what she heard at all She started shakin7 to that ne ne music you know her life was saved by rock 7n7 roll Despite 7 all the amputations you know you could just go out and dance to the rock 7n roll station and it was alright The Velvet Underground Rock And Roll 1970 We are nally at the end of our study of Fourier methods We have Fourier series to represent periodic functions and Fourier integrals to represent functions which do not necessarily have a periodic feature 1 From the Fourier integral one can then derive the socalled complex Fourier transform or just Fourier transform for short A 1 4W 1 A imac o 7 x 6 dx x 7 o e do f 57wa f 57wa In the last set of notes we mention that these equations have a striking similarity to complex Fourier series and that statements of energy and symmetry have analogies for Fourier transform In the following we use our knowledge of Fourier methods to gather insight into physical process that rely on Fourier analysis Let s rst begin with the following transform pair 1 7w 7 1 L 7 ump aw dti lt2gt3 m76t This statement says if we wish to send a instantaneous pulse of information then its representation in the frequency domain is a constant function We take this to mean the following 1 A completely localized function requires an equal amountamplitude of every possible frequency of oscillation Since the sum of the squares of these amplitudes is proportional to the energy of the timesignal we conclude that this transmission would require an in nite amount of energy This transform highlights a fundamental property of Fourier transforms That is if a function is localized in one domain then it is de localized in the transformed domain This relationship is the basis for the Heisenberg uncertainty principle of quantum mechanics but also has a place any time the Fourier transform concept is used The two most important relations are 0 Positionmomentum In physics position and momentum are related by Fourier transform AxAp Z a E llr and consequently if the position of a quantum particle is highly localized then its momentum is de localized Thus if we know exactly where a particle is then we have no idea about where the particle is going 0 Energytime In physics and engineering energy and time are related by Fourier transform AEAt Z a E llJr and consequently if the event takes place in an in nitesimal amount of time then it requires an in nite amount of energy Though these statements eccentrically highlight important concepts they are motivated with nonrigorous mathematical tricks involving the deltarfunction Maybe a more sensible function is given by ft A 7alttlta 0 otherwise 1Again we mention that periodicity can be reconstructed via delta functionsl Thus making the Fourier integral the more general representation MATH348 Advanced Eu lllccllll M quot 2 This function is commonly called a single nite pulse and can be thought of as a transmission of information A which takes place for 2a units of time The transform of such a function is N which is commonly called a sinc function or sampling function From this transform pair one can gather o f is localized in time f is delocalized in frequency That is some amount of almost every frequency is required to construct the single nite pulse of information Moreover if a a 00 then f is a constant function which we know transforms to a delta function Thus if we consider the limit a gt 00 for a sinc function then we ought to get a delta function 2 o The most dominant contribution to the representation of f comes from the o 0 mode which is to say f is most like7 a constant function but requires the presence of other Fourier modes because it isn t a constant function 3 So why is this called a sampling function That s a good question and is important to shared bandlimited frequency communications down an ideal medium If we assume that f is a signal which possesses a Fourier transform and that this signal is bandlimited in the frequency domain then it is possible using the concept of periodic extension to show that 0 mr sin tL 7 mr Wig 6 which implies that the original signal can be reconstructed using sincsampling functions where the weights of the previous linear combination are given by the original signal sampled every 7rL units in time This result is known as the sampling theorem and from this we conclude o The sinc functions are a basis for all time signals sent out over a frequency limited communication medium That is any signal sent over the radio telephone or cable line can use the previous procedure for mathematical reconstruction 0 To send signals over these communication channels the signal is not needed at every instantaneous moment in time That is it needs to be sampled at integer multiples of 7rL in time where L is de ned to be the cutoff frequency for complete lossless reconstruction 1 LECTURE GOALS Our goals with this material will be 0 Understand the relationship between a function and its Fourier transform as compared to a periodic function and its Fourier coe 39icients o Conceptualize the Fourier transform by applying it to physically motivated systems 2 LECTURE OBJECTIVES The objectives of these lessons will be 0 Calculate the Fourier transform of the delta function and single nite pulse 0 Derive the representation of a signal transmitted via a bandlimited frequency channel 2What a weird thing a delta function7 is In ODE7s you likely considered the limit of rectangles of unit area and now we have the limit of sinc functions There are in fact many more ways to get to a delta functionT 3A constant function wouldn7t truncate for ltl gt a
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Top Discrete Math Sets Secrets
Even though the discrete portion of this program is confined to the very first half, it’s a course worth taking. There are a number of ways to accomplish such essaycapital.com a selection. Cartesian product is quite a beneficial means of doing it.
The Basic Facts of Discrete Math Sets
Functions that are not algebraic, are called Transcidental Function. Discrete mathematics was characterized as the branch of mathematics managing countable sets. Discrete Math is the actual world mathematics.
Within this chapter, we’ll cover the various aspects of Set Theory. Variables are indispensable for computer programs to get the job done.
The very first semester is mostly a foundations and logic course composed of the initial five chapters of the text. Before discussing relevant topics, it might be worth mentioning several general facets of discrete mathematics. A thorough tutorial is supplied, together with a collection of worked examples illustrating the way the library is utilized to conduct statistical tests.
Generally, there are various ways that 3 sets may intersect. http://cs.gmu.edu/~zduric/day/how-to-write-degree-thesis.html They can be related to each other. An empty set comprises no elements.
If you would like to be serious about becoming a really excellent software developer, you should study discrete math sooner or later. Web video is a wonderful and extremely accessible means to connect wherever you’re, even on short notice, with the tech expert that’s ideal for your particular needs. You shouldn’t be looking up hw solutions on the web.
The Secret to Discrete Math Sets
Broadly speaking, you need past a computer science degree to increase your chances of landing an entry level computer program engineering job. The established theory would be put to use as an example and will give a succinct comprehension of the idea. Before knowing the laws, check kinds of sets for superior understanding.
At first, a function resembles a relation. If it is not computable we say it is uncomputable. There are not any issues with a polynomial.
Other changes wish to take place also. The prediction step employs the prior state to predict the present state based on a particular system model. They will provide you with a function and request that you discover the domain (and maybe the range, too).
The set of all particles is utilised to help determine the last state estimate. The range is a little trickier, which explains why they may not ask for research paper help it. Note there are distinct varieties of standard normal Z-tables.
With as much as three sets, you are able to easily look at all the separate intersections and unions. The essay is going to be broken up into sections. This previous topic is readily familiar to students as it can consist of determining placement for a new mobile phone tower.
What You Should Do to Find Out About Discrete Math Sets Before You’re Left Behind
This book was designed to satisfy the requirements of nearly all types of introductory discrete mathematics courses. Furthermore formal techniques are acknowledged and attributed as central to the topic of discrete mathematics in recent decades. It is meant for a wide range of students.
A degree in mathematics provides entry to numerous careers in industry as well as teaching. College algebra is the sole explicit prerequisite, although a certain level of mathematical maturity is required to study discrete mathematics in a meaningful way. Calculus is utilized in virtually all STEM courses.
The Ultimate Strategy for Discrete Math Sets
This dilemma is a bit different since there are two s letters. Each video will cover all the appropriate information which you will need to understand in under a quarter hour. Given the subsequent set, choose the statement below that’s true.
Discrete Math Sets Options
The subtraction of a single number from another can be looked on in several different ways. When multiplying two exponents with the exact base, the outcome is just like a term with base and a new exponent created with the addition of the 2 exponents in the conditions of the issue. Therefore the probability of the intersection of all 3 sets have to be added back in.
Most Noticeable Discrete Math Sets
As an example, spectral methods are increasingly utilised in graph algorithms for handling massive data sets. It also comes with a study of non-Euclidean geometries and associated subjects. The majority of these graphs are made by computerised equipment that’s attached to electronic monitoring equipment.
The Importance of Discrete Math Sets
A totally free demo can permit you to recognize the ideal tutor. The principal requirement of the program is the growth of a significant paper or project. You should have a passing score on the last exam (50%) so as to pass the program.
To acquire a feel for what is happening, let us inspect the structure of the program. In addition, in the course are lots of exerciseson which you are able to practiceand when you have any issues, you may always post a question, a lot of the timeI respond in a day. With any substantial estate, there are a lot of decisions to make and time passes quickly.
A degree program may be a very good pick for several individuals. A student has to be in good academic standing and might not be on academic probation of any sort. The bulk of the moment, you won’t perform actual probability difficulties, however you will use subjective probability to create judgment calls and determine the best plan of action.
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Sample Selection Bias
SAMPLE SELECTION BIAS
In a linear regression model, sample selection bias occurs when data on the dependent variable are missing nonrandomly, conditional on the independent variables. For example, if a researcher uses ordinary least squares (OLS) to estimate a regression model in which large values of the dependent variable are underrepresented in a sample, estimates of slope coefficients typically will be biased.
Hausman and Wise (1977) studied the problem of estimating the effect of education on income in a sample of persons with incomes below $15,000. This is known as a truncated sample and is an example of explicit selection on the dependent variable. This is shown in Figure 1, where individuals are sampled at three education levels: low (L), middle (M), and high (H). In the figure, sample truncation leads to an estimate of the effect of schooling that is biased downward from the true regression line as a result of the $15,000 ceiling on the dependent variable. In a variety of special conditions (Winship and Mare 1992), selection biases coefficients downward. In general, however, selection may bias estimated effects in either direction.
A sample that is restricted on the dependent variable is effectively selected on the error of the regression equation; at any value of X, observations with sufficiently large positive errors are eliminated from the sample. As is shown in Figure 1, as the independent variable increases, the expected value of the error becomes increasingly negative, making these two elements negatively correlated. Because this contradicts the standard assumption of OLS that the error and the independent variables are not correlated, OLS estimates become biased.
A different type of explicit selection occurs when the sample includes persons with incomes of $15,000 or more but all that is known about those persons is their educational attainment and that their incomes are $15,000 or more. When the dependent variable is outside a known bound but the exact value of the variable is unknown, the sample is censored. If these persons' incomes are coded as $15,000, OLS estimates are biased and inconsistent for the same reasons that obtain in the truncated sample.
A third type of selection that leads to bias occurs when censoring or truncation is a stochastic function of the dependent variable. This is termed implicit selection. In the income example, individuals with high incomes may be less likely to provide information on their incomes than are individuals with low incomes. As is shown below, OLS estimates also are biased when there is implicit selection.
Yet another type of selection occurs when there is selection on the measured independent variable(s). For example, the sample may be selected on educational attainment alone. If persons with high levels of schooling are omitted from the model, an OLS estimate of the effect for persons with lower levels of education on income is unbiased if schooling has a constant linear effect throughout its range. Because the conditional expectation of the dependent variable (or, equivalently, the error term) at each level of the independent variable is not affected by a sample restriction on the independent variable, when a model is specified properly OLS estimates are unbiased and consistent (DuMouchel and Duncan 1983).
Sample selection can occur because of the way data have been collected or, as the examples below illustrate, may be a fundamental aspect of particular social processes. In econometrics, where most of the basic research on selection bias has been done, many of the applications have been to labor economics. Many studies by sociologists that deal with selection problems have been done in the cognate area of social stratification. Problems of selection bias, however, pervade sociology, and attempts to grapple with them appear in the sociology of education, family sociology, criminology, the sociology of law, social networks, and other areas.
Trends in Employment of Out-of-School Youths. Mare and Winship (1984) investigate employment trends from the 1960s to the 1980s for young black and white men who are out of school. Many factors affect these trends, but a key problem in interpreting the trends is that they are influenced by the selectivity of the out-of-school population. Over time, that selectivity changes because the proportion of the population that is out of school decreases, especially among blacks. Because persons who stay in school longer have better average employment prospects than do persons who drop out, the employment rates of nonstudents are lower than they would be if employment and school enrollment were independent. Observed employment patterns are biased because the probabilities of employment and leaving school are dependent. Other things being equal, as enrollment increases, employment rates for out-of-school young persons decrease as a result of the compositional change in this pool of individuals. To understand the employment trends of out-of-school persons, therefore, one must analyze jointly the trends in employment and school enrollment. The increasing propensity of young blacks to remain in school explains some of the growing gap in the employment rates between blacks and whites.
Selection Bias and the Disposition of Criminal Cases. A central focus in the analysis of crime and punishment involves the determinants of differences in the treatment of persons in contact with the criminal justice system, for example, the differential severity of punishment of blacks and whites (Peterson and Hagan 1984). There is a high degree of selectivity in regard to persons who are convicted of crimes. Among those who commit crimes, only a portion are arrested; of those arrested, only a portion are prosecuted; of those prosecuted, only a portion are convicted; and among those convicted, only a portion are sent to prison. Common unobserved factors may affect the continuation from one stage of this process to the next. Indeed, the stages may be jointly determined inasmuch as legal officials may be mindful of the likely outcomes later in the process when they dispose cases. The chances that a person will be punished if arrested, for example, may affect the eagerness of police to arrest suspects. Analyses of the severity of sentencing that focus on persons already convicted of crimes may be subject to selection bias and should take account of the process through which persons are convicted (Hagan and Parker 1985; Peterson and Hagan 1984; Zatz and Hagan 1985).
Scholastic Aptitude Tests and Success in College. Manski and Wise (1983) investigate the determinants of graduation from college, including the capacity of the Scholastic Aptitude Test (SAT) to predict individuals' probabilities of graduation. Studies based on samples of students in colleges find that the SAT has little predictive power, yet those studies may be biased because of the selective stages between taking the SAT and attending college. Some students who take the SAT do not apply to college, some apply but are not admitted, some are admitted but do not attend, and those who attend are sorted among the colleges to which they have been admitted. Each stage of selection is nonrandom and is affected by characteristics of students and schools that are unknown to the analyst. When one jointly considers the stages of selection in the college attendance decision, along with the probability that a student will graduate from college, one finds that the SAT is a strong predictor of college graduation.
Women's Socioeconomic Achievement. Analyses of the earnings and other socioeconomic achievements of women are potentially affected by nonrandom selection of women into the labor market. The rewards that women expect from working affect their propensity to enter the labor force. Outcomes such as earnings and occupational status therefore are jointly determined with labor force participation, and analyses that ignore the process of labor force participation are potentially subject to selection bias. Many studies in economics (Gronau 1974; Heckman 1974) and sociology (Fligstein and Wolf 1978; Hagan 1990; England et al. 1988) use models that simultaneously represent women's labor force participation and the market rewards that women receive.
Analysis of Occupational Mobility from Nineteenth-Century Censuses. Nineteenth-century decennial census data for cities provide a means of comparing nineteenth- and twentieth-century regimes of occupational mobility in the United States. Although one can analyze mobility by linking the records of successive censuses, such linkage is possible only for persons who remain in the same city and keep the same name over the decade. Persons who die, emigrate, or change their names are excluded. Because mortality and migration covary with socioeconomic success, the process of mobility and the way in which observations are selected for the analysis are jointly determined. Analyses that model mobility and sample selection jointly offer the possibility of avoiding selection bias (Hardy 1989).
MODELS OF SELECTION
Berk (1983) provides an introduction to selection models; Winship and Mare (1992) provide a review of the literature before 1992. We start by discussing the censored regression, or tobit, model. We forgo discussion of the very closely related truncated regression model (Hausman and Wise 1977).
Tobit Model. The censored regression, or tobit, model is appropriate when the dependent variable is censored at an upper or lower bound as an artifact of how the data are collected (Tobin 1958; Maddala 1983). For censoring at a lower bound, the model is
where for the ith observation, Y1i* is an unobserved continuous latent variable, Y1i is the observed variable, Xi is a vector of values on the independent variables, εi is the error, and ß is a vector of coefficients. We assume that εi is not correlated with Xi and is independently and identically distributed. The model can be generalized by replacing the threshold zero in equations (2) and (3) with a known nonzero constant. The censoring point also may vary across observations, leading to a model that is formally equivalent to models for survival analysis (Kalbfleisch and Prentice 1980).
Standard Sample Selection Model. A generalization of the tobit model involves specifying that a second variable Y2i* affects whether Y1i is observed. That is, retain the basic model in equation (1) but replace equations (2) and (3) with Variants of this model depend on how Y2i is specified. Commonly, Y2i* is determined by a binary regression model: where Y2i* is a latent continuous variable. The classic example is a model for the wages and employment of women where Y1i is the observed wage, Y2i is a dummy variable indicating whether a woman works, and Y2i* indexes a woman's propensity to work (Gronau 1974). In a variant of this model, Y2i is hours of work and equations (6) through (8) are a tobit model (Heckman 1974). In both variants, Y1i* is observed only for women with positive hours of work. One can modify the model by assuming, for example, that Y1i is dichotomous. If εi and υi follow a bivariate normal distribution, this leads to a bivariate probit selection model.
Estimation of equation (1) using OLS will lead to biased estimates. When Y2i* > 0, The OLS regression of Y1i on Xi is biased and inconsistent if εi is correlated with υi − Ziα, which occurs if εi is correlated with υi or Zi or both. If the variables in Zi are included in Xi, εi and Zi are not correlated by assumption. If, however, Zi contains additional variables, εi and Zi may be correlated. When σευ = 0, selection depends only on the observed variables in Zi, not those in Xi. In this case, selection can be dealt with either by conditioning on the additional Z's or by using propensity score methods (Rosenbaum and Rubin 1983).
Equation (9) shows how selectivity bias may be interpreted as an omitted variable bias (Heckman 1979). The term E[εi| Y2i* > 0] can be thought of as an omitted variable that is correlated with Xi and affects Y1. Its omission leads to biased and inconsistent OLS estimates of ß.
Nonrandom Treatment Assignment. A model intimately related to the standard selection model that is not formally presented here is used when individuals are assigned nonrandomly to some treatment in an experiment. In this case, there are essentially two selection problems. For individuals not receiving the treatment, information on what their outcomes would have been if they had received treatment is "missing." Similarly, for individuals receiving the treatment, we do not know what their outcomes would have been if they had not received the treatment. Heckman (1978) explicitly analyzes the relationship between the nonrandom assignment problem and selection. Winship and Morgan (1999) review the vast literature that has appeared on this question in the last two decades.
A large number of estimators have been proposed for selection models. Until recently, all these estimators made strong assumptions about the distribution of errors. Two general classes of methods—maximum likelihood and nonlinear least squares—typically assume bivariate normality of εi and υi. The most popular method is that of Heckman (1979), known as the lambda method, which assumes only that υi in equation (6) is normally distributed and E[εi|υi] is linear.
For a number of years, there has been concern about the sensitivity of the Heckman estimator to these normality and linearity assumptions. Because maximum likelihood and nonlinear least squares make even stronger assumptions, they are typically more efficient but even less robust to violations of distributional assumptions. The main concern of the literature since the early 1980s has been the search for alternatives to the Heckman estimator that do not depend on normality and linearity assumptions.
Heckman's Estimator. The Heckman estimator involves (1) estimating the selection model (equations through ), (2) calculating the expected error, υi = E[υi|υi > -Ziα], for each observation using the estimated α, and (3) using the estimated error as a regressor in equation (1). We can rewrite equation (9) as
If εi and υi are bivariate normal and Var (υi) = 1, then E(εi|υi) = σευυi and
where ϕ and Φ are the standardized normal density and distribution functions, respectively. The ratio λ(-Ziα) is the inverse Mills's ratio. Substituting equation (11) into equation (10), we get
where ηi is not correlated with both Xi and λ(-Ziα). Equation (12) can be estimated by OLS but is preferably estimated by weighted least squares since its error term is heteroskedastic (Heckman 1979).
The precision of the estimates in equation (12) is sensitive to the variance of λ and collinearity between X and λ. The variance of λ is determined by how effectively the probit equation at the first stage predicts who is selected into the sample. The better the equation predicts, the greater the variance of λ is and the more precise the estimates will be. Collinearity will be determined in part by the overlap in variables between X and Z. If X and Z are identical, the model is identified only because λ is nonlinear. Since it is seldom possible to justify the form of λ on substantive grounds, successful use of the method usually requires that at least one variable in Z not be included in X. Even in this case, X and λ(-Ziα) may be highly collinear, leading to imprecise estimates.
Robustness of Heckman's Estimator. Because of the sensitivity of Heckman's estimator to model specification, researchers have focused on the robustness of the estimator to violations of its several assumptions. Estimation of equations (6) through (8) as a probit model assumes that the errors υi are homoskedastic. When this assumption is violated, the Heckman procedure yields inconsistent estimates, though procedures are available to correct for heteroskedasticity (Hurd 1979). The assumed bivariate normality of υi and εi in the selection model is needed in two places. First, normality of υi is needed for consistent estimation of α in the probit model. Second, the normality assumption implies a particular nonlinear relationship for the effect of Ziα on Y2i through λ. If the expectation of εi conditional on υi is not linear and/or υi is not normal, λ misspecifies the relationship between Ziαand Y2i and the model may yield biased results.
Several studies have analytically investigated the bias in the single-equation (tobit) model when the error is not normally distributed. In a model with only an intercept—that is, a model for the mean of a censored distribution—when errors are not normally distributed, the normality assumption leads to substantial bias. This result holds even when the true distribution is close to normal (for example, the logistic) (Goldberger 1983). When the normality assumption is wrong, moreover, maximum likelihood estimates may be worse than estimates that simply use the observed sample mean. For samples that are 75 percent complete, bias from the normality assumption is minimal; in samples that are 50 percent complete, bias is substantial in the truncated case but not in the censored case; and in samples that are less than 50 percent complete, bias is substantial in almost all cases (Arabmazar and Schmidt 1982).
The fact that estimation of the mean is sensitive to distributional misspecification suggests that the Heckman estimator may not be robust and raises the question of how often such problems arise in practice. In addition, even when normality holds, the Heckman estimator may not improve the mean square error of OLS estimates of slope coefficients in small samples (50 or less) (Stolzenberg and Relles 1990). This appears to parallel the standard result that when the effect of a variable is measured imprecisely, inclusion of the variable may enlarge the mean square error of the other parameters in the model (Leamer 1983).
No empirical work that the authors know of directly examines the sensitivity of Heckman's method for a standard selection model. Work by LaLonde (1986) using the nonrandom assignment treatment model suggests that in specific circumstances the Heckman method can inadequately adjust for unobserved differences between the treatment and control groups.
Extensions of the Heckman Estimator. There are two main issues in estimating equation (12). The first is correctly estimating the probability for each individual that he or she will be selected. As it has been formulated above, this means first correctly specifying both the linear function Zα and second specifying the correct, typically nonlinear relationship between the probability of selection and Zα. The second issue is the problem of what nonlinear function should be chosen for λ. When bivariate normality of errors holds, λ is the inverse Mills's ratio. When this assumption does not hold, inconsistent estimates may result. Moreover, since Xi and Zi are often highly collinear, estimates of ß in equation 12 may quite be sensitive to misspecification of λ.
The first problem is handled rather easily. In the situation where one has a very large sample and there are multiple individuals with the same Z, the simplest approach is to estimate the probability of selection nonparameterically by directly estimating the probability of being selected for individuals with each vector of Z's from the observed frequencies. With smaller samples, kernel estimation methods are available. These methods also consist of estimating probabilities directly by grouping individuals with "similar" Z's and directly calculating the probability of selection from weighted frequencies. Variants of this approach involve different definitions of similarity and/or weight (Hardle 1990). In both methods, the problem of estimating how the probability of selection depends on Z is bypassed.
Semiparametric methods are also available. These methods are useful if their underlying assumptions are correct, since they generally produce more efficient estimates than does a fully nonparametric approach. These methods include Manski's maximum score method (1975), nonparametric maximum likelihood estimation (Cosslett 1983), weighted average derivatives (Stoker 1986; Powell et al. 1989), spline methods, and series approximations (Hardle 1990).
The problem in the second stage is to deal with the fact that one generally has no a priori knowledge of the correct functional form for λ. Since λ is simply a monotonic function of the probability of being selected, this is equivalent to asking what nonlinear transformation of the selection probability should be entered into equation (12). A variety of approaches are available here. One approach is to approximate λ through a series expansion (Newey 1990; Lee 1982) or by means of step functions (Cosslett 1991). An alternative is to control for λ by using differencing or fixed effect methods (Heckman et al. 1998). The essential idea is to control for the probability of selection by implicitly including a series of dummy variables in equation (1), with each dummy variable being used to indicate a set of individuals with the same probability of selection or, equivalently, the same λ. Generally, this will produce significantly larger standard errors of the slope estimates. This is appropriate, however, since selection increases uncertainty. With small samples, these methods can be generalized through kernel estimation (Powell 1987; Ahn and Powell 1990). Newey et al. (1990) apply a variety of methods to an empirical problem.
Selection problems bedevil much social science research. First and foremost, it is important for investigators to recognize that there is a selection problem and that it is likely to affect their estimates. Unfortunately, there is no panacea for selection bias. Various estimators have been proposed, and it is important for researchers to investigate the range of estimates produced by different methods. In most cases this range will be considerably broader than the confidence intervals for the OLS estimates. Selection bias introduces greater uncertainty into estimates. New methods for correcting for selection bias have been proposed that may provide a more powerful means for adjusting for selection. This needs to be determined by future research.
Ahn, H., and J. J. Powell 1990 Semiparametric Estimationof Censored Selection Models with a Nonparametric Selection Mechanism. Madison: Department of Economics, University of Wisconsin.
Arabmazar, A., and P. Schmidt 1982 "An Investigation of the Robustness of the Tobit Estimator to Non-Normality." Econometrica 50:1055–1063.
Berk, R. A. 1983 "An Introduction to Sample Selection Bias in Sociological Data." American Sociological Review 48:386–398.
Cosslett, S. R. 1983 "Distribution-Free Maximum Likelihood Estimator of the Binary Choice Model." Econometrica 51:765–781.
—— 1991 "Semiparametric Estimation of a Regression Model with Sampling Selectivity." In W. A. Barnett, J. Powell, and G. Tauchen, eds., Nonparametricand Semiparametric Methods in Econometrics and Statistics. Cambridge: Cambridge University Press.
DuMouchel, W. H., and G. J. Duncan 1983. "Using Sample Survey Weights in Multiple Regression Analyses of Stratified Samples." Journal of the American Statistical Association 78:535–543.
England, P., G. Farkas, B. Kilbourne, and T. Dou 1988 "Explaining Occupational Sex Segregation and Wages: Findings from a Model with Fixed Effects." AmericanSociological Review 53:544–558.
Fligstein, N. D., and W. Wolf 1978 "Sex Similarities in Occupational Status Attainment: Are the Results Due to the Restriction of the Sample to Employed Women?" Social Science Research 7:197–212.
Gronau, R. 1974 "Wage Comparisons—Selectivity Bias." Journal of Political Economy 82:1119–1143.
Hagan, J. 1990 "The Gender Stratification of Income Inequality among Lawyers." Social Forces 68:835–855.
——, and P. Parker, 1985. "White-Collar Crime and Punishment." American Sociological Review 50:302–316.
Hardy, M. A. 1989 "Estimating Selection Effects in Occupational Mobility in a 19th-Century City." American Sociological Review 54:834–843.
Hausman, J. A., and D. A. Wise, 1977 "Social Experimentation, Truncated Distributions, and Efficient Estimation." Econometrica 45:919–938.
Heckman, J. J. 1974 "Shadow Prices, Market Wages and Labor Supply." Econometrica 42:679–694.
—— 1978 "Dummy Endogenous Variables in a Simultaneous Equation System." Econometrica 46:931–959.
—— 1979. "Sample Selection Bias as a Specification Error." Econometrica 47:153–161.
——, H. Ichimura, S. Smith, and P. Todd 1998 "Characterizing Selection Bias Using Experimental Data." Econometrica 6:1017–1099.
Hurd, M. 1979 "Estimation in Truncated Samples." Journal of Econometrics 11:247–58.
Kalbfleisch, J. D., and R. L. Prentice 1980 The StatisticalAnalysis of Failure Time Data. New York: Wiley.
Lalonde, R. J. 1986 "Evaluating the Econometric Evaluations of Training Programs with Experimental Data." American Economic Review 76:604–620.
Leamer, E. E. 1983 "Model Choice and Specification Analysis." In Z. Griliches and M. D. Intriligator, eds., Handbook of Econometrics, vol. 1. Amsterdam: North-Holland.
Lee, L. F. 1982 "Some Approaches to the Correction of Selectivity Bias." Review of Economic Studies 49:355–372.
Maddala, G. S. 1983 Limited-Dependent and QualitativeVariables in Econometrics. Cambridge: Cambridge University Press.
Manski, C. F., and D. A. Wise 1983 College Choice inAmerica. Cambridge, Mass.: Harvard University Press.
Mare, R. D., and C. Winship 1984 "The Paradox of Lessening Racial Inequality and Joblessness among Black Youth: Enrollment, Enlistment, and Employment, 1964–1981." American Sociological Review 49:39–55.
Newey, W. K. 1990 "Two-Step Series Estimation of Sample Selection Models." Paper presented at the 1988 European meeting of the Econometric Society.
——, J. L. Powell, and J. R. Walker 1990 "Semiparametric Estimation of Selection Models: Some Empirical Results." American Economic Review 80:324–328.
Peterson, R. and J. Hagan 1984 "Changing Conceptions of Race: Towards an Account of Anomalous Findings of Sentencing Research." American SociologicalReview 49:56–70.
Powell, J. L. 1987 Semiparametric Estimation of BivariateLatent Variable Models. Working Paper No. 8704. Madison: Social Systems Research Institute, University of Wisconsin.
——, J. H. Stock, and T. M. Stoker 1989 "Semiparametric Estimation of Index Coefficients." Econometrica 57:1403–1430.
Rosenbaum, P., and D. B. Rubin 1983 "The Central Role of the Propensity Score in Observational Studies for Causal Effects." Biometrika 70:41–55.
Stoker, T. M. 1986 "Consistent Estimates of Scaled Coefficients." Econometrica 54:1461–1481.
Stolzenberg, R. M., and D. A. Relles 1990 "Theory Testing in a World of Constrained Research Design: The Significance of Heckman's Censored Sampling Bias Correction for Nonexperimental Research." Sociological Methods Research 18:395–415.
Tobin, J. 1958 "Estimation of Relationships for Limited Dependent Variables." Econometrica 26:24–36.
Winship, C., and R. D. Mare 1992 "Models for Sample Selection Bias." Annual Review of Sociology 18:327–350.
——, and S. Morgan 1999 "The Estimation of Causal Effects from Observational Data." Annual Review ofSociology. 25:657–704.
Zatz, M. S., and J. Hagan 1985 "Crime, Time, and Punishment: An Exploration of Selection Bias in Sentencing Research." Journal of Quantitative Criminology 1:103–126.
Robert D. Mare
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https://www.wyzant.com/resources/answers/4525/how_to_make_a_word_problem_into_a_equation
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math
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The side of an equilateral triangle is 2 inches shorter than the side of a
square. The perimeter of the square is 30 inches more than the perimeter
of the triangle. Find the length of a side of the triangle.
The key to figuring this one out is to draw your two shapes.
Since all three sides of an equilateral triangle have the same measure, label all three sides with an x.
Since all four sides of a square have the same measure, we will label them with the same expression as each other: x + 2. The reason the expression is x + 2 is because the triangle's sides are two inches shorter than the rectangle's sides (so the rectangle's sides are two inches longer).
Now address Perimeter. To find the perimeter, add the sides together.
Triangle: x + x + x = 3x
Square: (x + 2) + (x + 2) + (x + 2) + (x + 2) = 4(x + 2) or 4x + 8
The Perimeter of the square is 30 inches more than the Perimeter of the triangle.
P (square) = P (triangle) + 30
4x + 8 = 3x + 30
This should help in setting up your equation.
*Note - you could have labeled the triangle's sides with (x - 2) and the square's sides with x.
In that case, your equation would be: 4x = 3(x - 2) + 30.
Either way will work.
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https://www.coursehero.com/tutors-problems/Finance/542639-Micromain-Company-has-10000000-shares-of-common-stock-authorized-and/
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math
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Micromain Company has 10,000,000 shares of common stock authorized and 8,000,000 shares outstanding, each with a $ 1.00 par value. The firm’s additional paid –in capital account has a balance of $18,000,000. The previous year’s retained earnings account was $124,000,000.In the year just ended, Micromain generated net income of $ 16,000,000 and the firm has a dividend payout ratio of 40%. What will Micromain’s book value per share be when based on the final year-end balance sheet? Hint: Sole this problem by constructing a summary of the common’s stockholders equity accounts.
Dear Student,... View the full answer
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https://digitalcommons.usu.edu/foundation_wave/about.html
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math
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About Foundations of Wave Phenomena
This text provides an introduction to some of the foundations of wave phenomena. Wave phenomena appear in a wide variety of physical settings, for example, electrodynamics, quantum mechanics, fluids, plasmas, atmospheric physics, seismology, and so forth. Of course, there are already a number of fine texts on the general subject of "waves" and related physical phenomena, and some of these texts are very comprehensive. So it is natural to ask why you might want to work through this rather short, condensed treatment which is largely devoid of detailed applications. The answer is that this course has a slightly different — and perhaps more general — aim than found in the more conventional courses on waves. Indeed, an alternative title for this course might be something like "Introduction to Mathematical Physics with Applications to Wave Phenomena". So, while one of the principal goals here is to introduce you to many of the features of waves, an equally — if not more — important goal is to get you up to speed with the plethora of mathematical techniques that you will encounter as you continue your studies in the physical sciences.
It is often said that "mathematics is the language of physics". Unfortunately for you — the student — you are expected to learn the language as you learn the concepts. In physics courses any new mathematical tools are introduced only as needed and usually in the context of the current application. Compare this to the traditional progression of a course in mathematics (which you have surely encountered by now), where a branch of the subject is given its theoretical development from scratch, mostly in the abstract, with applications used to illustrate the key mathematical points. Both ways of introducing the mathematics have their advantages. The mathematical approach has the virtue of rigor and completeness. The physics approach – while usually less complete and less rigorous – is very efficient and helps to keep clear precisely why/how this or that mathematical idea is being developed. Moreover, the physics approach implements a style of instruction that many students in science and engineering find accessible: abstract concepts are taught in the context of concrete examples. Still, there are definite drawbacks to the usual physics approach to the introduction of mathematical ideas. The student cannot be taught all the math that is needed in a physics course. This is exacerbated by the fact that (prerequisites notwithstanding) the students in a given class will naturally have some variability in their mathematics background. Moreover, if mathematics tools are taught only as needed, the student is never fully armed with the needed arsenal of mathematical tools until very late in his/her studies, i.e., until enough courses have been taken to introduce and gain experience with the majority of the mathematical material that is needed. Of course, a curriculum in science and/or engineering includes prerequisite mathematical courses which serve to mitigate these difficulties. But you may have noticed already that these mathematics courses, which are designed not just for scientists and engineers but also for mathematicians, often involve a lot of material that simply is not needed by the typical scientist and the engineer. For example, the scientist may be interested in what the theorems are and how to apply them but not so interested in the details of the proofs of the theorems, which are of course the bread and butter of the mathematician. And, there is always the well-known but somewhat mysterious difficulty that science/engineering students almost always seem to have when translating what they have learned in a pure mathematics course into the context of the desired application.
The traditional answer to this dilemma is to o↵er some kind of course in "Mathematical Physics", designed for those who are interested more in applications and less in the underlying theory. The course you are about to take is, in effect, a Mathematical Physics course for undergraduates – but with a twist. Rather than just presenting a litany of important mathematical techniques, selected for their utility in the sciences, as is often done in the traditional Mathematical Physics course, this course tries to present a (slightly shorter) litany of techniques, always framed in the context of a single underlying theme: wave phenomena. This topic was chosen for its intrinsic importance in science and engineering, but also because it allows for a treatment of a wide variety of mathematical concepts. The hope is that this way of doing things combines some of the advantages of both the mathematician’s and the physicist’s ways of learning the language of physics. In addition, unlike many mathematical physics texts which try to give a more comprehensive "last word" on the subject, this text only aspires to give you an introduction to the key mathematical ideas. The hope is that when you encounter these ideas again at a more sophisticated level you will find them much more palatable and easy to work with, having already played with them in the context of wave phenomena.
This text is designed to accommodate a range of student backgrounds and needs. But, at the very least, it is necessary that a student has had an introductory (calculus-based) physics course, and hopefully a modern physics course. Mathematics prerequisites include: multivariable calculus and linear algebra. Typically, one can expect to cover most (if not all) of the material presented here in one semester.
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https://socratic.org/questions/the-time-t-required-to-empty-a-tank-varies-inversely-as-the-rate-r-of-pumping-a-
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math
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The time (t) required to empty a tank varies inversely as the rate (r) of pumping. A pump can empty a tank in 90 minutes at the rate of 1200 L/min. How long will the pump take to empty the tank at 3000 L/min?
90 minutes at 1200 L/min means that the tank holds
To empty the tank at a rate of 3000 L/m will take the time of
Observe that this is exactly the same as in first principles.
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https://www.onlinemath4all.com/worksheet-on-types-of-fractions.html
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math
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Question 1 :
What is proper fraction ? Given an example.
Question 2 :
What is improper fraction ? Given an example.
Question 3 :
What is mixed number or mixed fraction ? Given an example.
Question 4 :
What is the difference between a proper fraction and an improper fraction in value ?
Question 5 :
What are like fractions ? Give an example.
Question 6 :
What are unlike fractions ? Give an example.
Question 7 :
What are equivalent fractions? Give an example.
Question 8 :
Classify the values given below as proper fraction, improper fraction and mixed fraction.
2/3, 5/2, 5½, 7/8, 0.2, 1.3
Question 9 :
Explain how to convert an improper fraction to a mixed number.
Question 10 :
Represent the following fractions on a number line.
3/5, 11/12 and 7/10
1. Answer :
If the numerator of a fraction is smaller than the denominator, then the fraction is called as proper fraction.
Example : 2/3
2. Answer :
If the numerator of a fraction is larger than the denominator, then the fraction is called as improper fraction.
Example : 3/2
3. Answer :
An integer and a proper fraction together is called a mixed number or mixed fraction.
In other words, mixed fraction is a quantity which is expressed as a whole number and a proper fraction.
Always its value will be greater than or equal to 1.
Example : 2¾
The picture given below clearly illustrates this.
4. Answer :
The following is the difference between a proper fraction and an improper fraction in value.
The value of a proper fraction will always be smaller than 1.
The value of an improper fraction will be equal to 1 or larger than 1.
The picture shown below clearly illustrates this.
5. Answer :
In two or more fractions, the denominators (bottom numbers) are same, they are called like fractions.
1/2, 3/2, 7/2, 9/2
In the above fractions, all the denominators are same. That is 2.
6. Answer :
In two or more fractions, the denominators (bottom numbers) are different, they are called unlike fractions.
1/3, 4/5, 1/7, 9/11
In the above fractions, the denominators are different. They are 3, 5, 7 and 11.
7. Answer :
Take 1/2 and you can see that the denominator is twice the numerator. So, any fraction where the denominator is twice the numerator is equivalent (the same as) a half. So
are all equivalent fractions that mean 1/2.
When a half is written as 1 over 2 rather than 2 over 4, or 5 over 10, or any other version, it is said to be in its lowest term or simplest form. This is because no number, except 1, will divide into both the top number and the bottom number. So to put a fraction in its lowest form, you divide by any factors common to both the top number and the bottom number.
Equivalent fractions can be found for any fraction by multiplying the top number and the bottom number by the same number. For example, if you have 3/4, then multiplying by 2 gives
or by 3 gives
Multiplying by 10 gives
and all of these fractions are exactly the same as 3/4.
8. Answer :
2/3, 5/2, 5½, 7/8, 0.2, 1.3
2/3 -----> Proper fraction
5/2 -----> Improper fraction
5½ -----> Mixed fraction
7/8 -----> Proper fraction
0.3 = 3/10 -----> Proper fraction
1.3 = 13/10 -----> Improper fraction
9. Answer :
The picture given below illustrates, how to convert an improper fraction into mixed number.
10. Answer :
Kindly mail your feedback to [email protected]
We always appreciate your feedback.
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http://mathhelpforum.com/advanced-algebra/217840-alternating-group-a4-cayley-diagraph.html
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math
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Set H=<(12)(34),(123)>. Then H=A4: 2 and 3 both divide the order of H but since A4 has no subgroup of order 6 (if it did a Sylow 3 subgroup of A4 would be normal in A4), H=A4.
Here's a Cayley diagram for A4 and the given generators. The products of cycles are formed "left to right" and the elements are post multiplied by the generators. If you prefer products "right to left", just think of the elements being pre multiplied by the generators.
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https://mathalino.com/tag/reviewer/flexure
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math
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The distributed load shown in Fig. P-588 is supported by a wide-flange section of the given dimensions. Determine the maximum value of wo that will not exceed a flexural stress of 10 MPa or a shearing stress of 1.0 MPa.
A simply supported beam of length L carries a uniformly distributed load of 6000 N/m and has the cross section shown in Fig. P-585. Find L to cause a maximum flexural stress of 16 MPa. What maximum shearing stress is then developed?
A wide-flange section having the dimensions shown in Fig. P-584 supports a distributed load of wo lb/ft on a simple span of length L ft. Determine the ratio of the maximum flexural stress to the maximum shear stress.
A rectangular beam 6 in. wide by 10 in. high supports a total distributed load of W and a concentrated load of 2W applied as shown in Fig. P-583. If fb ≤ 1500 psi and fv ≤ 120 psi, determine the maximum value of W.
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CC-MAIN-2021-10
| 888 | 4 |
http://seo.bookitwise.com/what-tend-to-be-factors-within-arithmetic/
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math
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What usually are variables within mathematics? It is vitally important to comprehend this question, and more importantly, to have the ability to answer it, In case you’ve got a desire to be a mathematics prodigy.
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https://biographs.org/paul-guldin
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math
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Paul GuldinSwiss mathematician
Date of Birth: 12.06.1577
Biography of Paul Guldin
Paul Guldin was a Swiss mathematician known for his work on the centers of gravity of bodies. He also delved into the topics of surfaces and volumes of bodies in his research.
Contributions to Mathematics
Guldin made significant contributions to the field of mathematics, particularly in determining the volumes and surfaces of revolving bodies. His findings often overlapped with those of renowned mathematicians, such as Johannes Kepler and Bonaventura Cavalieri.
Guldin's work in mathematics has left a lasting impact on the field. His theorems and research on the centers of gravity, volumes, and surfaces of bodies continue to be studied and applied by mathematicians today.
Paul Guldin, the Swiss mathematician, made significant contributions to the study of centers of gravity, volumes, and surfaces of bodies. His research and theorems have had a lasting impact on the field of mathematics and continue to be influential today.
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http://www.newscientist.com/commenting/report?id=dn13405-4
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math
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Report an inappropriate comment
Who's Doing The Math?
Wed Mar 05 01:54:34 GMT 2008 by Shmulik
As Charles points out, there are roughly 10^10 super-massive black holes in the observable universe. If each one merges only ONCE in the entire lifetime of the universe (10^10 yrs) then there should be 1 merger per year, or 10^5 at any one time if each afterglow lasts 10^5 years. Pretty simple math, Cyrus.
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https://answer.ya.guru/questions/10424307-please-help-me.html
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math
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so this is about triangles.. sooo the following is a bit of helpful reminders that I keep on my computer to help me remember how to fit the trig functions to triangles.. I strongly suggest you copy it and keep it where you can look at it often.
Use SOH CAH TOA to recall how the trig functions fit on a triangle
SOH: Sin(Ф)= Opp / Hyp
CAH: Cos(Ф)= Adj / Hyp
TOA: Tan(Ф) = Opp / Adj
I use this anytime I run into triangles or need some help with sin or cos
now the problem , 3 ladder 10, 12, & 15 feet. Alex wants to get to 8 feet.
the problems is also telling you that you can use t..... and then , the words are cut off.. but I know they were going to say Tan ... next.. :P
b/c Tan is how you figure out problems with the adjacent side and the opposite side. like this problem. Look at TOA above. use that to recall how the parts fit in the formula
Tan(∅) = Opp / Adj
they give us the Opp side of 8 feet in the problem
then they also tell us the Hyp of the triangle which is each of the ladders length. Then they ask us what is the Adj sides length?
So we also need to solve the triangle with the know hyp (ladder length).. uggg, this problem is long. Then we can solve the dist. from the wall or Adj side length.
it's two steps, if you want to think of it that way. You're supposed to be pretty confident with trig functions. I'm guessing this is a trig class.. right?
let's solve for the 3 different angles that the ladders make , each going to 8 feel. Obviously, nobody would really do this with a ladder they would just lean it against the wall . and if it's taller than where they want to climb, they would just go up part way. so anyway, find the 3 different angles.
look above to see which formula to use.
I like SOH b/c it seems to have all the pieces of the triangle we want to work with.
ladder 1 ( 10')
Sin(∅) = Opp / Hyp
Sin(∅) = 8 / 10
∅ = arcSin (4/5)
[ first, yes, I just reduced the fraction, then I did the arcSin on both sides, I think you might know how to do that already ? ]
∅ = 53.13010 °
( yes, I used my calculator to find that, calculators are okay to use when figuring out non standard angles )
ladder 2 (12')
Sin(∅) = 8/12
∅ = arcSin (2/3)
∅ = 41.81031°
ladder 3 (15')
Sin(∅) = 8/15
∅ = arcSin (8/15)
∅ = 32.230952°
now use our Tan function to find the Adjacent side which is the distance from the wall
Tan(∅)= Opp / Adj
Adj = Opp / Tan(∅)
( I did some quick algebra to move the side we want to solve for, now plug and chug all 3 angles )
Adj = 8 / Tan(53.13010)
Adj = 6.0000005
Adj = 8 / Tan(41.81031)
Adj = 8.94427
Adj = 8 / Tan(32.230952)
Adj = 12.688577
so the 10' ladder is 6 feet from the wall
the 12' ladder is 8.9 feet from the wall
the 15 foot ladder is 12.7 feet from the wall.
I really don't think that 15' ladder is going to stay on the wall.. if Alex climbs it... it's way way too far out... it will just fall straight down the wall :/ Maybe another math problem for the forces involved :P
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http://www.alphadictionary.com/bb/viewtopic.php?p=2079
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math
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M theory is a name for a more unified theory that has the different string theories, as we know them, as limits, and which also can reduce, under appropriate conditions, to eleven-dimensional supergravity. There's this picture that we all have to draw where different string theories are limits of this M theory, where M stands for Magic, Mystery or Matrix, but it also sometimes is seen as standing for Murky, because the truth about M theory is Murky. And the different limits, where the main parameter simplifies, give the different string theories -- Type IIA, Type IIB, Type I, and there's eleven-dimensional supergravity, which turns out to be an important limit even though it isn't part of the systematic perturbation expansion, then there's the E8XE8 heterotic string, and there's SO(32) heterotic string.
So M-theory is a name for this picture, this more general picture that will generate the different limits through the different string theories. The parameters in this picture we can think of being roughly hbar, which is Planck's constant, and that determines how important the quantum effects are, and the other parameter is alpha prime, which is the tension, related to the tension of the string, that determines how important stringy effects are. So traditionally, a physicist looking at Type IIA, for example, by traditional weak coupling methods, explores this little region, and if asked how his theory is related to Type I theory, the answer would have to be, "Well I don't know, that's something else."
And likewise, if you ask this observer what happens for strong coupling, the traditional answer was, "Well I don't know." In graduate courses, you learn that you can do more or less anything for weak coupling, but you can't do anything for strong coupling. What happened in the 90s was that we learned how to do a little bit for strong coupling, and it turned out that the answer is Type IIA at strong coupling turns out to be Type I in a slightly different limit, SO(32) heterotic, and so on. So we built up this more unified picture, but we still don't understand what it means
Dr. Ed Witten, Princeton University
My favorite passage from Dr. Witten's statement:
And the different limits, where the main parameter simplifies, give the different string theories -- Type IIA, Type IIB, Type I, and there's eleven-dimensional supergravity, which turns out to be an important limit even though it isn't part of the systematic perturbation expansion
My second favorite passage:
...but we still don't understand what it means
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https://vustudents.ning.com/group/fin622corporatefinance/forum/topics/msba-corprate-finance-assignment-no-1-due-date-is-6th-may-want
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math
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Topic: Calculation of WACC and Capital Budgeting Analysis
ANF Inc., a garment manufacturer, is planning to install a new plant at a cost of Rs.
1,500,000. It also requires an initial investment of Rs. 200,000 in net working capital in
first year. This investment in net working capital will be recovered at the end of useful
life of plant. Plant’s expected economic life is 5 year. At the end of that period, its
salvage value is estimated to be Rs. 150,000.
Expected pre-tax cash inflows by installation of new plant are: Rs. 500,000 in year1,
Rs. 600,000 in year2, Rs. 700,000 in year3, Rs. 750,000 in year4 and Rs. 800,000 in
year5. ANF Inc. uses straight line method of depreciation for plant and its tax rate is
30%. For capital budgeting purposes, company’s policy is to assume that the cash flows
occur at the end of year. The plant will begin operations immediately after the
investment is made.
ANF Inc. stock currently sells for Rs. 50 and company is expected to pay a dividend of
Rs. 5 at the growth rate of 2% to its shareholders. ANF Inc. target debt to equity ratio is
40:60 and it’s before tax cost of debt is 10% and the company’s tax rate is 30%.
Based upon above given information, being the student of finance, you are required to
1) Calculate the Cost of Equity. (2 marks)
2) Calculate the Weighted Average Cost of Capital. (2 marks)
3) Calculate NPV of the project. (5 marks)
4) Calculate IRR by using interpolation formula.(5 marks)
5) Whether the project is feasible to undertake? Support your answer with logical
reason(s). (1 mark)
Part 1 can be solved by taking lecture number 5. It will be very easy!
not sure about part 2!
YTM in part 3 can be calculated by using this tool: http://www.prenhall.com/divisions/bp/app/cfl/BV/YTM.html
but I'm bit confused with the formula
any one send me plzzzzz formula for this assigment plzzzzzzz i confused......
MY DEARS the last date may b 3rd MAY>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
formula kia use kia hia Taim apney for first part?
476 Bond A
168.46 Bond B
kia yahi price hai currnet bond ki?
I got 937 and 904 for Bond A and Bond B.
Lecture 5 main jo formula hai for calculating Bond current value. Jis main firstly we have to calculate PV of Annuity/Coupon Payments and then the PV of Principle Amount. Then un dono ko add karnay k bhd Present Value of Bond ajaye gi!
well woh to maine b daikha hia muje ya batoo book may 80 per year hein to hum 1000 per 16% leinge? to per year ayga?
yes per year 160 aye ga..
Please Discuss here about this assignment.Thanks
Our main purpose here discussion not just Solution
We are here with you hands in hands to facilitate your learning and do not appreciate the idea of copying or replicating solutions.
How to Calculate Yield to Maturity
Yield to Maturity (YTM) for a bond is the total return, interest plus capital gain, obtained from a bond held to maturity. Yield to maturity is a useful measure of the attractiveness of a seasoned bond that is held to maturity and redeemed at par value. For example, suppose you buy a $1000 par value ABC Company bond with a 5% coupon rate maturing in five years, and the market price for the bond is $900. The coupon rate is the annual interest rate payable on the $1000 par value, which is $50 per year. The current yield of the bond is the interest divided by the current price of the bond, which is $50/$900, or 5.56%. On redemption of the bond after 5 years, you get $1000 for the matured bond, and realize $100 capital gain.
Yield to maturity takes into account both interest and capital gain return on the bond
The term Yield to Maturity also called as Redemption Yield often abbreviated as YTM and used when it comes to bond funds, is defined as the rate of return obtained by buying a bond at the current market price and holding it to maturity. Yield to Maturity is the index for measuring the attractiveness of bonds. When the price of the bond is low the yield is high and vice versa. YTM is beneficial to the bond buyer because a rising yield would decrease the bond price hence the same amount of interest is paid but for less money. Where the coupon payment refers to the total interest per year on a bond. Yield to maturity can be mathematically derived and calculated from the formula
YTM is therefore a good measurement gauge for the expected investment return of a bond. When it comes to online calculation, this Yield to Maturity calculator can help you to determine the expected investment return of a bond according to the respective input values. YTM deals only with the time-value-of-money calculations between the price, coupons and face value of the bond at hand, not with other potential future investments. If the coupons and face value are paid as promised the bond earns its yield-to-maturity
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https://www.siemreap-properties.info/rp6601cerivbhflrnedhrfgvbacncred891cf1f86.html
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math
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bank Lecture Notes Syllabus Part A 2 marks with answers Part B question
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math
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The material included in ncert textbooks is included in the cbse class 11 final exams, including various competitive and college entrance tests. Activities for all chapters covered in grade 11 syllabus with worked out solutions. T grade 11 mathematics textbook rsa his is a grade 11 maths book created by siyavula, it is available in creative. Each question will ask you to select an answer from among four choices. However, teachers and students must download the grade 11 guide books for better examination purposes. How to obtain maximum benefit from these resources. The numbers and their symbols that we use today have advanced over many years ago. This unit focuses on the mathematics used every day in our communities to measure, compare and present information numerically. You are allowed and encouraged to copy any of the everything maths and everything science textbooks.
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Beginning in september 2006,all grade 11 mathematics courses will be based on. On the following pages are multiplechoice questions for the grade 11 practice test, a practice opportunity for the nebraska state accountabilitymathematics nesam. Find great content to download for free, right here. Trigonometry is a branch of mathematics that combines arithmetic, algebra and geometry. As we learn to understand and speak this language, we can discover many of natures secrets. Ethiopia grade 11 textbook in pdf teachers and students guide. South african grade 11 school worksheets covering mathematics. Png upper secondary advanced mathematics, grade 11 paperback pdf, make sure you follow the link under and download the document or gain access to other information which are highly relevant to save buk. Grade 11 mathematics siyavula rsa syllabus free kids books. We use this information to present the correct curriculum and to personalise content to better meet the needs of our users. Use the information and determine, with reasons, whether the. There is an emphasis on the development of real numbers and their everyday usage in learning mathematics.
Dec 29, 2019 the content of grade 11 mathematics mobile application. Msm g 11 teaching and learning trigonometry slides in pdf. On the following pages are multiplechoice questions for the grade 11 practice test, a practice opportunity for the nebraska state accountability mathematics nesam. Explore available downloads by clicking on the subject youre interested in. Cbse and up board ncert books as well as offline apps and ncert solutions of. Examples for all chapters covered in grade 11 syllabus.
Jul 24, 2017 ethiopia grade 11 textbook in pdf for both teachers and students. This document replaces the grade 11 courses found in the the ontario curriculum,grades 11 and 12. This is the first unit in the series of mathematics b for grade 11. Grade 11 the study of advanced programme mathematics should encourage students to talk about mathematics, use the language and symbols of mathematics, communicate, discuss problems and. Activities for all chapters covered in grade 11 syllabus with worked. Grade 11 mathematics practice test nebraska department of. Grade 11 mathematics smarter balanced high school mathematics practice test scoring guide 2 about the practice test scoring guides the smarter balanced mathematics practice test scoring guides provide details about the items, student response types, correct responses, and related scoring considerations for the smarter. Grade 11 applied mathematics 30s manitoba education. The ethiopian ministry of education provides grade 11 students textbook in pdf file for download.
Ncert solutions for class 11 maths in pdf updated for 202021. Questions are included with answers mentioned for every problem, thus giving students a stepbystep. South african national department of basic education. Practice problems for all chapters covered in grade 11 syllabus with worked out solutions. Finals gr11 math crystal math past papers south africa. Read and download ebook grade 11 maths previous question papers pdf at public ebook library grade 11 maths previous question papers pdf download. National department of basic education self study guides. Ethiopian grade 11 mathematics textbook pdf download. It does not deal in any depth with the schoolbased assessment sba. K to 12 basic education curriculum senior high school core. Mathematics at these grade levels should be used as an important instrument for recognising and describing certain fields of objective reality as well as planning and guiding process of development. Beginning in september 2006,all grade 11 mathematics courses will be based on the expectations outlined in this document.248 358 1112 1445 1208 1294 921 1274 852 1168 916 417 168 1169 713 411 1481 1241 1062 120 928 173 132 613 1525 311 1518 1248 115 347 551 136 242 1387 598 492 119
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CC-MAIN-2021-25
| 11,455 | 12 |
https://www.rcsb.org/structure/1SMR
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math
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X-ray analysis at 2.0 A resolution of mouse submaxillary renin complexed with a decapeptide inhibitor CH-66, based on the 4-16 fragment of rat angiotensinogen.Dealwis, C.G., Frazao, C., Badasso, M., Cooper, J.B., Tickle, I.J., Driessen, H., Blundell, T.L., Murakami, K., Miyazaki, H., Sueiras-Diaz, J., Szelke, M.J.
(1994) J Mol Biol 236: 342-360
- PubMed: 8107115
- DOI: https://doi.org/10.1006/jmbi.1994.1139
- Primary Citation of Related Structures:
- PubMed Abstract:
- Crystallization and Preliminary X-Ray Analysis of Complexes of Peptide Inhibitors with Human Recombinant and Mouse Submandibular Renins
Badasso, M., Frazao, C., Sibanda, B.L., Dhanaraj, V., Dealwis, C., Cooper, J.B., Wood, S.P., Blundell, T.L., Murakami, K., Miyazaki, H., Hobart, P.M., Geoghegan, K.F., Ammirati, M.J., Lanzetti, A.J., Danley, D.E., O'Connor, B.A., Hoover, D.J., Sueiras-Diaz, J., Jones, D.M., Szelke, M.
(1992) J Mol Biol 223: 447
- X-Ray Analysis of Peptide-Inhibitor Complexes Define the Structure Basis of Specificity for Human and Mouse Renins
Dhanaraj, V., Dealwis, C.G., Frazao, C., Badasso, M., Sibanda, B.L., Tickle, I.J., Cooper, J.B., Driessen, H.P.C., Newman, M., Aguilar, C., Wood, S.P., Blundell, T.L., Hobart, P.M., Geoghegan, K.F., Ammirati, M.J., Danley, D.E., O'Connor, B.A.O., Hoover, D.J.
(1992) Nature 357: 466
The structure of mouse submaxillary renin complexed with a decapeptide inhibitor, CH-66 (Piv-His-Pro-Phe-His-Leu-OH-Leu-Tyr-Tyr-Ser-NH2), where Piv denotes a pivaloyl blocking group, and -OH- denotes a hydroxyethylene (-(S)CHOH-CH2-) transition state isostere as a scissile bond surrogate, has been refined to an agreement factor of 0 ...
The structure of mouse submaxillary renin complexed with a decapeptide inhibitor, CH-66 (Piv-His-Pro-Phe-His-Leu-OH-Leu-Tyr-Tyr-Ser-NH2), where Piv denotes a pivaloyl blocking group, and -OH- denotes a hydroxyethylene (-(S)CHOH-CH2-) transition state isostere as a scissile bond surrogate, has been refined to an agreement factor of 0.18 at 2.0 A resolution. The positions of 10,038 protein atoms and 364 inhibitor atoms (4 independent protein inhibitor complexes), as well as of 613 solvent atoms, have been determined with an estimated root-mean-square (r.m.s.) error of 0.21 A. The r.m.s. deviation from ideality for bond distances is 0.026 A, and for angle distances is 0.0543 A. We have compared the three-dimensional structure of mouse renin with other aspartic proteinases, using rigid-body analysis with respect to shifts involving the domain comprising residues 190 to 302. In terms of the relative orientation of domains, mouse submaxillary renin is closest to human renin with only a 1.7 degrees difference in domain orientation. Porcine pepsin (the molecular replacement model) differs structurally from mouse renin by a 6.9 degrees domain rotation, whereas endothiapepsin, a fungal aspartic proteinase, differs by 18.8 degrees. The triple proline loop (residues 292 to 294), which is structurally opposite the active-site "flap" (residues 72 to 83), gives renin a superficial resemblance to the fold of the retroviral proteinases. The inhibitor is bound in an extended conformation along the active-site cleft, and the hydroxyethylene moiety forms hydrogen bonds with both catalytic aspartate carboxylates. The complex is stabilized by hydrogen bonds between the main chain of the inhibitor and the enzyme. All side-chains of the inhibitor are in van der Waals contact with groups in the enzyme and define ten specificity sub-sites. This study shows how renin has compact sub-sites due to the positioning of secondary structure elements, to complementary substitutions and to the residue composition of its loops close to the active site, leading to extreme specificity towards its prohormone substrate, angiotensinogen. We have analysed the micro-environment of each of the buried charged groups in order to predict their ionization states.
Department of Crystallography, Birkbeck College, University of London, U.K.
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CC-MAIN-2023-23
| 4,043 | 15 |
https://www.cati.com/blog/2014/08/surface-splines-and-equation-splines/
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math
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Surface Splines and Equation Splines
Making interesting geometry in regards to potential cam and slider surfaces is made much easier by use of the 3D sketching abilities and surface splines. For a brief example, we will be creating a barrel cam and the appropriate cam groove in the part.
Once I had my cylinder setup with the geometry pattern pre-sketched, I moved on to the actual sketch.
Once you have that open, it is time to start our sketch. Using the spline on surface tool, draw the basic profile for the barrel cam recess:
Then, using the top of the cylinder as the sketch plane, draw a semi-circle of the same radius as the cylinder above the sketched spline.
After this, I drew a square on the front plane, with the following relations shown to the spline:
From there, we are ready to do the fun part and actually sweep the cut. Notice the settings used and the use of one of the sketches as a guide curve. This is why it is important to make 2 sketches as the swept cut tool does not allow the path and the guide curve to come from the same sketch.
With everything selected, it should look similar to this:
Once you have the half cut, you can mirror the feature to get a full encirclement of the cam profile. One is probably tempted to ask why the spline was not drawn all the way around the cylinder to avoid the mirror step. However, the program will not properly evaluate a closed loop for a swept cut as it results in zero-thickness geometry. As such, building it as a half and mirroring it is the proper way.
With everything made and mirrored, one should be left with the following:
It is worth noting that this feature can also be made by defining a spline by a set of 3D parametric equations that would also work. In this case, one could generate two curves and sweep the profile.
The equation driven spline works slightly differently, using the equation to render the spline in 3D space. For these parameters, the Xt and Zt define the circle with the coefficient equal to the radius of the spline circle. The Yt parameter defines both the vertical position of the curve and the amplitude of the wave. It is also important to note that the t parameter goes only from 0 to pi, and not a full circle. This is once again the closed contour problem mentioned earlier:
Post By: Drew Potter
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| 2,303 | 13 |
https://research.manchester.ac.uk/en/publications/the-morton-massaro-law-of-information-integration-implications-fo
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math
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Information integration may be studied by analyzing the effect of 2 or more sources (e.g., auditory and visual) on participants' responses. Experiments show that ratios of response probabilities often factorize into components selectively influenced by only 1 source (e.g., 1 component affected by the acoustic source and another 1 affected by the visual source). This is called the Morton-Massaro law (MML). This article identifies conditions in which the law is optimal and notes that it reflects an implicit assumption about the statistics of the environment. Adherence to the MML can be used to assess whether the assumption is being made, and analyses of natural stimuli can be used to determine whether the assumption is reasonable. Feed-forward and interactive models subject to a channel separability constraint are consistent with the law.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296818105.48/warc/CC-MAIN-20240422082202-20240422112202-00568.warc.gz
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CC-MAIN-2024-18
| 848 | 1 |
https://www.hackmath.net/en/math-problem/8455
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math
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There were so many pines in the forest that if they were sequentially numbered 1, 2, 3,. .. , would use three times more digits than the pine trees alone. How many pine trees were there in the forest?
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- Basket of fruit
In six baskets, the seller has fruit. In individual baskets, there are only apples or just pears with the following number of fruits: 5,6,12,14,23 and 29. "If I sell this basket," the salesman thinks, "then I will have just as many apples as a pear." Which
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How many apples were originally on the tree, if the first day fell one third, the second day quarter of the rest and on tree remained 45 apples?
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Pavel has a collection of toy cars. He wanted to regroup them. But in the division of three, four, six, and eight, he was always one left. Only when he formed groups of seven, he divided everyone. How many toy cars have in the collection?
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Mother is 39 years old. Her daughter is 15 years. For many years will mother be four times older than the daughter?
For five days, we have collected 410 mushrooms. Interestingly every day we have collected 10 mushrooms more than the preceding day. How many mushrooms we have collected during 4th day?
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How many cans must be put in the bottom row if we want 182 cans arrange in 13 rows above so that each subsequent row has always been one tin less? How many cans will be in the top row?
In the front row sitting three students and in every other row 11 students more than the previous row. Determine how many students are in the room when the room is 9 lines, and determine how many students are in the seventh row.
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At the end of the school year has awarded 20% of the 250 children who attend school. Awat got 18% boys and 23% of girls. Determine how many boys and how many girls attend school.
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Determine how many apples are in baskets when in the first basket are 4 apples, and in any other is 29 apples more than the previous, and we have eight baskets.
Mom is 42 years old and her daughters 13 and 19. After how many years will mother as old as her daughter together?
- Fifth of the number
The fifth of the number is by 24 less than that number. What is the number?
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The number 2010 can be written as the sum of 3 consecutive natural numbers. Determine the arithmetic mean of these numbers.
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Find the sum of all natural numbers from 1 and 100, which are divisible by 2 or 5
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The sum of two consecutive even numbers is 30. Find the numbers.
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Sum of ten consecutive numbers is 105. Determine these numbers (write first and last).
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| 3,505 | 37 |
https://questions.llc/questions/534276
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math
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Bridget has a limited income and consumers only wine and cheese; her current consumption choice is four bottles of wine and 10 pounds of cheese. The price of wine is $10 per bottle and the price of cheese is $4 per pound. The last bottle of wine added 50 units to Bridget’s utility, while the last pound of cheese added 40 units.
a. Is Bridget making the utility-maximizing choice? Why or why not?
b. If not, what should she do instead? Why?
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https://scholarcommons.sc.edu/etd/6186/
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math
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Date of Award
Open Access Dissertation
Variable-order fractional partial differential equations provide a competitive means in modeling challenging phenomena such as the anomalous diffusion and the memory effects and thus attract widely attentions. However, variable-order fractional models exhibit salient features compared with their constant-order counterparts and introduce mathematical and numerical difficulties that are not common in the context of integer-order and constant-order fractional partial differential equations.
This dissertation intends to carry out a comprehensive investigation on the mathematical analysis and numerical approximations to variable-order fractional derivative problems, including variable-order time-fractional, space-fractional, and space-time fractional partial differential equations, as well as the corresponding inverse problems. Novel techniques are developed to accommodate the impact of the variable fractional order and the proposed mathematical and numerical methods provide potential tools to analyze and compute the variable-order fractional problems.
© 2020, Xiangcheng Zheng
Zheng, X.(2020). Variable-Order Fractional Partial Differential Equations: Analysis, Approximation and Inverse Problem. (Doctoral dissertation). Retrieved from https://scholarcommons.sc.edu/etd/6186
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http://www.drps.ed.ac.uk/11-12/dpt/cxinfr10009.htm
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math
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Undergraduate Course: Computer Algebra (INFR10009)
|School||School of Informatics
||College||College of Science and Engineering
||Availability||Available to all students
|Credit level (Normal year taken)||SCQF Level 10 (Year 4 Undergraduate)
|Home subject area||Informatics
||Other subject area||None
||Taught in Gaelic?||No
|Course description||Computer graphics uses various shapes such as ellipsoids for modelling. Consider the following problem: we are given an ellipsoid, a point from which to view it, and a plane on which the viewed image is to appear. The problem is to find the contour of the image as an equation (a numerical solution is not good enough for many applications). The problem does not involve particularly difficult mathematics, but a solution by hand is very difficult in general. This is an example of a problem which can be solved fairly easily with a computer algebra system. These systems have a very wide range of applications and are useful both for routine work and research. From a computer science point of view they also give rise to interesting problems in implementation and the design of algorithms. The considerations here are not only theoretical but also pragmatic: for example there is an algorithm for polynomial factorization which runs in polynomial time; however systems do not use this since other (potentially exponential time) methods work faster in practice. The design of efficient algorithms in this area involves various novel techniques. The material of the course will be related whenever possible to the computer algebra system Maple, leading to a working knowledge of the system.
Entry Requirements (not applicable to Visiting Students)
|| It is RECOMMENDED that students have passed
Mathematics for Informatics 3 (MATH08013) AND
Mathematics for Informatics 4 (MATH08025)
||Other requirements|| Successful completion of Year 3 of an Informatics Single or Combined Honours Degree, or equivalent by permission of the School. Familiarity with computer programming and data structures will be assumed. The course will contain an overview of less familiar algebra, as well as some new concepts.
|Additional Costs|| None
Information for Visiting Students
|Displayed in Visiting Students Prospectus?||Yes
Course Delivery Information
|Delivery period: 2011/12 Semester 2, Available to all students (SV1)
||WebCT enabled: No
|Central||Lecture||1-11|| 12:10 - 13:00|
|Central||Lecture||1-11|| 12:10 - 13:00|
||Week 1, Monday, 12:10 - 13:00, Zone: Central. AT M1 |
|Main Exam Diet S2 (April/May)||2:00|
Summary of Intended Learning Outcomes
|1 - Use the computer algebra system Maple as an aid to solving mathematical problems.
2 - Design and implement in Maple appropriate algorithms from constructive mathematical solutions to problems.
3 - Discuss the overall design of the computer algebra system Maple.
4 - Evaluate the results obtained from a computer algebra system and discuss possible problems.
5 - Explain the gap between ideal solutions and actual systems (the need to compromise for efficiency reasons).
6 - Describe and evaluate data structures used in the computer representation of mathematical objects.
7 - Discuss the mathematical techinques used in the course and relate them to computational concerns.
8 - Discuss and apply various advanced algorithms and the mathematical techniques used in their design.
9 - Use the techniques of the course to design an efficient algorithm for a given mathematical problem (of a fairly similar nature to those discussed in the course).
|Written Examination 80|
Assessed Assignments 20
Oral Presentations 0
Three sets of exercises involving the use of Maple as well as pencil and paper work.
If delivered in semester 1, this course will have an option for semester 1 only visiting undergraduate students, providing assessment prior to the end of the calendar year.
||* Maple: general design principles, user facilities, data structures, use of hashing, etc.
* Brief comparison of systems.
* Algebraic structures: overview, basic concepts and algorithms.
* Arbitrary precision operations on integers, rationals, reals, polynomials and rational expressions.
* Importance of greatest common divisors and their efficient computation for integers and univariate polynomials (using modular methods).
* Multivariate polynomial systems: solution of sets of equations over the complex numbers; construction and use of Groebner bases; relevant algebraic structures and results.
* Reliable solution of systems of polynomial equations in one variable; Sturm sequences, continued fractions method.
Relevant QAA Computing Curriculum Sections: Data Structures and Algorithms, Simulation and Modelling, Theoretical Computing
||* J. von zur Gathen and J. Gerhard, Modern Computer Algebra, Cambridge University Press, second edition, 2003.
* K. O. Geddes, S. R. Czapor and G. Labahn, Algorithms for Computer Algebra, Kluwer Academic Publishers (1992).
* J.H. Davenport, Y. Siret and E. Tournier, Computer Algebra; systems and algorithms for algebraic computation, Academic Press 1988.
* D.E. Knuth, Seminumerical Algorithms, second dedition, Addison-Wesley 1981.
Timetabled Laboratories 0
Non-timetabled assessed assignments 24
Private Study/Other 56
|Course organiser||Dr Amos Storkey
Tel: (0131 6)51 1208
|Course secretary||Miss Kate Weston
Tel: (0131 6)50 2701
© Copyright 2011 The University of Edinburgh - 16 January 2012 6:16 am
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| 5,417 | 59 |
https://communities.sas.com/t5/General-SAS-Programming/need-help-regarding-regression-analysis/td-p/142006?nobounce
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math
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10-25-2014 11:08 AM
i have 3 independent variables(price, brand image,service quality) and 2 dependent variables(trust, satisfaction).All these are quantitative on a likert scale and i want to know the imact of independent on dependent variables.I have been suggested regression but i dont know which type of regression to run
10-26-2014 10:58 AM
my hypothesis are
price perceived by customers is positively related to customer satisfaction
price percieved by customers is positively related to customers trust and so on..
the data is ordinal
10-26-2014 11:01 AM
my reserch questions are
(1) What kinds of relationship marketing tactics in practice positively contribute to customer
trust n satisfaction?
(2) How do different relationship marketing tactics impact on customer trust and satisfaction?
(3) Is the analytical model showed as figure 1.1 proved to be correct?
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| 870 | 13 |
https://www.nagwa.com/en/videos/456126910564/
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math
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Which letter shows where 0.965 belongs on this number line?
Let’s take some of these fractions and represent them as decimals. We know that one-half written as a decimal is 0.5 and that three-fourths written as a decimal is 0.75. 0.965 is greater than 0.75. And there’s only one letter on this line that’s larger than 0.75. It’s letter D. Letter D is almost one. 0.965 is also almost one.
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CC-MAIN-2021-04
| 396 | 2 |
https://vdocuments.mx/logistic-regression-.html
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math
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logistic regression -
Post on 13-Apr-2017
Embed Size (px)
Prediction using Logistic Regression
Need of logistic regression?
Regression allows us to predict an output based on some inputs. For instance, we can predicts someone's height based on their mother's height and father's height.This type of regression is calledlinearregressionbecause our outcome variable is a continuous real number.
But what if we wanted to predict something that's not a continuous number?
Let's say we want to predict if it will rain tomorrow. Using ordinary linear regression won't work in this case because it doesn't make sense to treat our outcome as a continuous number - it either will rain, or won't rain.In this case, we uselogistic regression, because our outcome variable is one of several categories.
Logistic RegressionRegressionIndependent VariableDependent VariableExampleQuantitative, QualitativeQualitativeQuantitative, QualitativeQuantitativeResult (Pass, Fail) is the function of time given to studyMarks obtained is the function of time given to study
Passing MarksStudy HoursResultPassFail
Binary logistic regression expression
Y = Dependent Variables = Constant1 = Coefficient of variable X1X1 = Independent VariablesE = Error TermBINARY
Problem statement & Methodology
The purpose of campaign is to get 25K customer registered for CRBT. The task can be accomplished by identifying the customers (or prospects) who are most likely to respond out of the total base of around 100 Million users.
We have sample data available for both respondents and non-respondents for the campaign and we used Logistic regression, which allows us to predict a discrete outcome, such as response tracking from a set of variables that may be continuous, discrete, or a mix of any of these. Generally, the dependent or response variable is dichotomous, such as success/failure.
Sample data of Respondents: 13,600 unique subscribers
Sample data of Non Respondents: 14,000 unique subscribers
Hypothesis tests Is an individual predictor variable significant? Is the overall model significant? Is Model A significantly better than Model B?
Dataset used in model:
Outcome variable:1: Responded0: Not Responded
Predictors:Average monthly spendOperating system2G data usage(MB)3G Data usage(MB) GenderIncoming messagesHandset TypeAge on handset
Logistic Function using R
Logistic Regression Interpretation
Predicated probability using our model
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CC-MAIN-2022-49
| 2,417 | 24 |
https://www.hackmath.net/en/example/1661
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math
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Miriam room is 3.2 meters wide. It is draw by line segment length 6.4 cm on floor plan. In what scale it is plan of the room?
Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):
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To solve this example are needed these knowledge from mathematics:
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97 is the total number of employees. The conference was attended by 34 employees. How much is it in percent?
- Apples 2
James has 13 apples. It has 30 percent more apples than Sam. How many apples has Sam?
- Degrees to radians
Convert magnitude of the angle α = 618°40'29" to radians:
Solve the inequation: 5k - (7k - 1)≤ 2/5 . (5-k)-2
Solve the equation: 1/2-2/8 = 1/10; Write the result as a decimal number.
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CC-MAIN-2018-09
| 2,175 | 32 |
http://mathhelpforum.com/calculus/17057-implicit-differentiation-trig.html
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math
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1. sin(x+y) = x-y The answer is (1-cos(x+y))/((cos x+y)+1)
I believe this is when i went wrong or something.
2. cos(xy)=1-x^2 the answer is (2x-y sin (xy))/(x sin (xy))
And I got lost from here.
3.ln(xy)=e^2x The answer is (2e^2x-x^-1)y
And then this step was when I got lost as to how this translates to the answer.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917119120.22/warc/CC-MAIN-20170423031159-00053-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 316 | 6 |
https://m.exlibris.ch/de/buecher-buch/english-books/applications-of-self-adjoint-extensions-in-quantum-physics/id/9783662137628
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math
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The shared purpose in this collection of papers is to apply the theory of self-adjoint extensions of symmetry operators in various areas of physics. This allows the construction of exactly solvable models in quantum mechanics, quantum field theory, high energy physics, solid-state physics, microelectronics and other fields. The 20 papers selected for these proceedings give an overview of this field of research unparallelled in the published literature; in particular the views of the leading schools are clearly presented. The book will be an important source for researchers and graduate students in mathematical physics for many years to come. In these proceedings, researchers and graduate students in mathematical physics will find ways to construct exactly solvable models in quantum mechanics, quantum field theory, high energy physics, solid-state physics, microelectronics and other fields.
Zero-range interactions with an internal structure.- Evolution equations and selfadjoint extensions.- Energy-dependent interactions and the extension theory.- On perturbations for self-adjoint generators of feller processes.- Singular perturbations defined by forms.- Covariant markovian random fields in four space-time dimensions with nonlinear electromagnetic interaction.- Point interaction Hamiltonians for crystals with random defects.- Scattering on a random point potential.- Faddeev equations for three composite particles.- On the point interaction of three particles.- A resonating- group model with extended channel spaces.- The problem of a few quasi-particles in solid-state physics.- Surfaces with an internal structure.- Spectral properties of the laplacian with attractive boundary conditions.- Quantum junctions and the self-adjoint extensions theory.- The extension theory and diffraction problems.- Hamiltonians with additional kinetic energy terms on hypersurfaces.- Thin lattices as waveguides.- Quantum waveguides.- An exactly solvable model of a crystal with non-point atoms.
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CC-MAIN-2022-05
| 2,002 | 2 |
http://seven-billion-to-one.blogspot.com/2013/02/living-in-real-world.html
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math
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I once gave a talk to the local Rotarians on the history of the concept of energy. Not an obvious topic for an after dinner speech but it turned out to be mildly provocative; which I suppose was the point.
It began with the physical concept of mechanical work. Push a supermarket trolley and the amount of work you do depends on how hard you push it and how far you push it. That's it. Push it twice as hard, or twice as far, and you do twice as much work.
This led onto the concept of energy. If something's got energy you can get it to do some work. The amount of energy its got is simply the same as the amount of work it could do. So, use a pulley to connect a falling weight to the supermarket trolley and you can get it to move. The weight, before it falls, must have energy. In this case gravitational potential energy. You can also show that although energy can be converted from one form to another it can't be created or destroyed; the principle of the conservation of energy.
Finally, I must have got around to the concept of power which is simply the rate at which something can do work. More powerful things can simply do work more quickly.
So, if you speed something up by applying a force then you're doing work and the thing you've speeded up acquires kinetic energy. This can then be used to do work when the thing slows down. If you apply Newton's Laws of Motion it isn't hard to show that the kinetic energy of a moving body depends on the body's mass and on the square of its speed. The classic formula is KE = 1/2 x mass x velocity^2.
Now, the first serious application of Newton's laws was to calculate the orbits of the planets around the Sun. Because these orbits aren't completely circular the planets speed up and slow down as they move closer or further from the Sun. All that's happening here is that gravitational potential energy is being swapped for kinetic energy and vice versa. So, for example, the quantity (1/2 x mass x velocity^2) had been used in calculating the details of the orbit of Mars but there wasn't anything else you could actually do with it. There wasn't any way to get Mars to do any useful work.
And here we get to the bit that was supposed to interest the Rotarians. The concept of energy might have been useful as a calculating device, but it was only when James Watt and Matthew Boulton began trying to sell their steam engines that it became something that was treated as though it had a real independent existence. Their selling technique was a bit like the present Government's New Green Deal. They demonstrated how many horses the engines would replace, or how much less coal they'd use than the earlier less efficient engines, and then offered to sell them at a price that mean the purchaser was bound to be better off.
But to do this they needed some idea of the power output of a typical horse and decided that it was equivalent to lifting a weight of 33,000 lbs every minute through a height of 1 foot. In current units this is about 750 watts. No prizes for guessing who those are named after.
So far so vaguely stimulating. You'll appreciate that by modern standards 750W is not a great deal of power. It may be more than can be produced by fit cyclists, and even then not for long, but a typical car produces at least 50 times as much.
Apart from bringing the concepts of work and power down to Earth as it were, the steam engine liberated us from renewable sources of energy. Up to that point it was either biomass to feed draft animals or renewable energy in the form of water wheels, wind mills or sails.
I then pointed out that for the last 200 years we'd been using fossil fuel resources about a million times faster than they were laid down. i.e burning up a million years worth of dead plants and animals every year. I didn't say this was wrong, I didn't have to, but one response was revealing and this was "This is all very well, but you're not living in the real world"
Let's hope that there's a real world out there where natural resources really are infinite and where we can choose whether or not the laws of physics apply. It looks like we might be needing it.
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CC-MAIN-2019-47
| 4,140 | 12 |
https://www.brainkart.com/article/Solved-Example-Problems--Dalton---s-law-of-partial-pressures_34761/
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math
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Let us understand Dalton's law by solving these problems.
1. A mixture of gases contains 4.76 mole of Ne, 0.74 mole of Ar and 2.5 mole of Xe. Calculate the partial pressure of gases, if the total pressure is 2 atm. at a fixed temperature.
PNe = xNe PTotal = 0.595 × 2
= 1.19 atm.
PAr = xAr PTotal = 0.093 × 2
= 0.186 atm.
PXe = xXe PTotal = 0.312 × 2
= 0.624 atm.
2. An unknown gas diffuses at a rate of 0.5 time that of nitrogen at the same temperature and pressure. Calculate the molar mass of the unknown gas
Copyright © 2018-2020 BrainKart.com; All Rights Reserved. Developed by Therithal info, Chennai.
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CC-MAIN-2020-24
| 611 | 10 |
https://oncirculation.com/2016/11/17/part-2-the-measurements/
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math
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In my last post, I wrote about how we get our samples for moisture and density (MAD) measurements. In this post, I’ll discuss the measurements themselves. We measure three things for MAD: wet mass, dry mass, and dry volume. From these three measurements, we calculate a number of other properties, including porosity, grain density, porewater, and about 10 more. This may sound straightforward, but measuring mass on a boat is not as simple as on land because the boat is rolling!
In order to measure the mass of the sediment cylinders, we have to compare it against a standard of known weight (weights). Two balances are set up together so that we can put our sample of unknown weight in one, and little standard weights in the other (balance). We enter the reference mass in the computer and start the measurement. The mass of both the standard and sample are weighed 300 times over about a minute and a half to get a robust
average measurement. You can see the manifestation of the rolling boat on the computer as it measures the sample and standard! The sample weight is then calculated based on the difference to the known standard.
After measuring our fresh sediment cylinders, we put them in a convection oven to dry over night and weight them again. Next, we measure volume. For this, we use a pycnometer. This is a deceptively clever instrument. In order to measure volume, it uses a derivation of the Ideal Gas Law – P1V1=P2V2. (Pressure1Volume1=Pressure2Volume2.)
We place the sample of unknown volume into a cell of known volume (sample chamber). The pynometer then fills the chamber with helium gas and measures the pressure. It then opens up a second chamber of known volume – the expansion cell. The gas expands into the cell, and the pressure decreases because the volume increases. The pressure is then measured again. So to break the pycnometer measurement down into its Ideal Gas Law components, we have:
P2=Psample cell + Pexpansion chamber
V2=Vsample cell + Vsample +Vexpansion chamber
We have 5 variables, two of which are known (Vsamplecell and Vexpansion chamber) and two of which are measured (P1 and P2), leaving only Vsample left to be solved. All this machine relies on is changing the known volume enough to have a measurable change in
pressure and you can solve the equation. Theoretically, that means you could measure the pressure in the known empty sample chamber, place the sample in, and then measure the pressure with the new smaller volume, but there’s no way to do that without breaking the
seal on the chamber, so the machine simply adds an extra chamber for the gas to be displaced by the sample, so that the measurement can be made. Beautifully simple! Also, it’s calibrated with these shiny standard spheres of known volume.
If volume measurements aren’t your thing and you still made it this far, here’s your reward – another sunset picture and sushi night:
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CC-MAIN-2018-34
| 2,916 | 11 |
http://zbmath.org/?q=an:0777.44003
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math
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The author gives a constructive technique to find smooth functions with given moments. Earlier in the well-known moment problem it was guaranteed that for every sequence of complex numbers there is a function of bounded variation with the given moments in these numbers.
The author shows how these weight functions are found. He uses the technique of Fourier and Hankel transform in Schwartz spaces to establish the respective functions with the given moments. Namely, he finds the functions for the classical orthogonal polynomials: the Bessel polynomials, the Hermite polynomials, the Laguerre and generalized Laguerre polynomials, and the Jacobi polynomials.
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s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1398223211700.16/warc/CC-MAIN-20140423032011-00326-ip-10-147-4-33.ec2.internal.warc.gz
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CC-MAIN-2014-15
| 661 | 2 |
http://forum.geomapia.net/index.php?/topic/2596-%D8%AA%D8%A8%D8%AF%DB%8C%D9%84-%D9%85%D8%AE%D8%AA%D8%B5%D8%A7%D8%AA-gps-%D8%A8%D8%B1%D8%A7%DB%8C-%D9%86%D9%85%D8%A7%DB%8C%D8%B4-%D8%B1%D9%88%DB%8C-%D9%86%D9%82%D8%B4%D9%87/
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math
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مشکلم حل شد
عنوان دقیق مسئله تبدیل مختصات latLong به UTM هستش که از فرمول زیر میشه اینکارو انجام داد:
Formulas For Converting Latitude and Longitude to UTM
These formulas are slightly modified from Army (1973). They are accurate to within less than a meter within a given grid zone. The original formulas include a now obsolete term that can be handled more simply - it merely converts radians to seconds of arc. That term is omitted here but discussed below.
* lat = latitude of point
* long = longitude of point
* long0 = central meridian of zone
* k0 = scale along long0 = 0.9996. Even though it's a constant, we retain it as a separate symbol to keep the numerical coefficients simpler, also to allow for systems that might use a different Mercator projection.
* e = SQRT(1-b2/a2) = .08 approximately. This is the eccentricity of the earth's elliptical cross-section.
* e'2 = (ea/b)2 = e2/(1-e2) = .007 approximately. The quantity e' only occurs in even powers so it need only be calculated as e'2.
* n = (a-b)/(a+b)
* rho = a(1-e2)/(1-e2sin2(lat))3/2. This is the radius of curvature of the earth in the meridian plane.
* nu = a/(1-e2sin2(lat))1/2. This is the radius of curvature of the earth perpendicular to the meridian plane. It is also the distance from the point in question to the polar axis, measured perpendicular to the earth's surface.
* p = (long-long0) in radians (This differs from the treatment in the Army reference)
Calculate the Meridional Arc
S is the meridional arc through the point in question (the distance along the earth's surface from the equator). All angles are in radians.
* S = A'lat - B'sin(2lat) + C'sin(4lat) - D'sin(6lat) + E'sin(8lat), where lat is in radians and
* A' = a[1 - n + (5/4)(n2 - n3) + (81/64)(n4 - n5) ...]
* B' = (3 tan/2)[1 - n + (7/8)(n2 - n3) + (55/64)(n4 - n5) ...]
* C' = (15 tan2/16)[1 - n + (3/4)(n2 - n3) ...]
* D' = (35 tan3/48)[1 - n + (11/16)(n2 - n3) ...]
* E' = (315 tan4/512)[1 - n ...]
The USGS gives this form, which may be more appealing to some. (They use M where the Army uses S)
* M = a[(1 - e2/4 - 3e4/64 - 5e6/256 ....)lat
- (3e2/8 + 3e4/32 + 45e6/1024...)sin(2lat)
+ (15e4/256 + 45e6/1024 + ....)sin(4lat)
- (35e6/3072 + ....) sin(6lat) + ....)] where lat is in radians
This is the hard part. Calculating the arc length of an ellipse involves functions called elliptic integrals, which don't reduce to neat closed formulas. So they have to be represented as series.
Converting Latitude and Longitude to UTM
All angles are in radians.
y = northing = K1 + K2p2 + K3p4, where
* K1 = Sk0,
* K2 = k0 nu sin(lat)cos(lat)/2 = k0 nu sin(2 lat)/4
* K3 = [k0 nu sin(lat)cos3(lat)/24][(5 - tan2(lat) + 9e'2cos2(lat) + 4e'4cos4(lat)]
x = easting = K4p + K5p3, where
* K4 = k0 nu cos(lat)
* K5 = (k0 nu cos3(lat)/6)[1 - tan2(lat) + e'2cos2(lat)]
Easting x is relative to the central meridian. For conventional UTM easting add 500,000 meters to x.
What the Formulas Mean
The hard part, allowing for the oblateness of the Earth, is taken care of in calculating S (or M). So K1 is simply the arc length along the central meridian of the zone corrected by the scale factor. Remember, the scale is a hair less than 1 in the middle of the zone, and a hair more on the outside.
All the higher K terms involve nu, the local radius of curvature (roughly equal to the radius of the earth or roughly 6,400,000 m), trig functions, and powers of e'2 ( = .007 ). So basically they are never much larger than nu. Actually the maximum value of K2 is about nu/4 (1,600,000), K3 is about nu/24 (267,000) and K5 is about nu/6 (1,070,000). Expanding the expressions will show that the tangent terms don't affect anything.
If we were just to stop with the K2 term in the northing, we'd have a quadratic in p. In other words, we'd approximate the parallel of latitude as a parabola. The real curve is more complex. It will be more like a hyperbola equatorward of about 45 degrees and an ellipse poleward, at least within the narrow confines of a UTM zone. (At any given latitude we're cutting the cone of latitude vectors with an inclined plane, so the resulting intersection will be a conic section. Since the projection cylinder has a curvature, the exact curve is not a conic but the difference across a six-degree UTM zone is pretty small.) Hence the need for higher order terms. Now p will never be more than +/-3 degrees = .05 radians, so p2 is always less than .0025 (1/400) and p4 is always less than .00000625 (1/160000). Using a spreadsheet, it's easy to see how the individual terms vary with latitude. K2p2 never exceeds 4400 and K3p4 is at most a bit over 3. That is, the curvature of a parallel of latitude across a UTM zone is at most a little less than 4.5 km and the maximum departure from a parabola is at most a few meters.
K4 is what we'd calculate for easting in a simple-minded way, just by calculating arc distance along the parallel of latutude. But, as we get farther from the central meridian, the meridians curve inward, so our actual easting will be less than K4. That's what K5 does. Since p is never more than +/-3 degrees = .05 radians, p3 is always less than .000125 (1/8000). The maximum value of K5p3 is about 150 meters.
That Weird Sin 1" Term in the Original Army Reference
The Army reference defines p in seconds of arc and includes a sin 1" term in the K formulas. The Sin 1" term is a holdover from the days when this all had to be done on mechanical desk calculators (pre-computer) and terms had to be kept in a range that would retain sufficient precision at intermediate steps. For that small an angle the difference between sin 1" and 1" in radians is negligible. If p is in seconds of arc, then (psin 1") merely converts it to radians.
The sin 1" term actually included an extra factor of 10,000, which was then corrected by multiplying by large powers of ten afterward.
The logic is a bit baffling. If I were doing this on a desk calculator, I'd factor out as many terms as possible rather than recalculate them for each term. But perhaps in practice the algebraically obvious way created overflows or underflows, since calculators could only handle limited ranges.
In any case, the sin1" term is not needed any more. Calculate p in radians and omit the sin1" terms and the large power of ten multipliers.
از این توضیحات سایت IBM
هم برای برنامه نویسیش میتونید استفاده کنید.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794863811.3/warc/CC-MAIN-20180520224904-20180521004904-00244.warc.gz
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CC-MAIN-2018-22
| 6,484 | 50 |
https://investerarpengarrvbot.netlify.app/27237/42422.html
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math
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Utrikeshandel och Ekonomisk Tillväxt - Studydrive
Teorema Rybczynski dikembangkan pada tahun 1955 oleh ekonom Inggris kelahiran Polandia, Tadeusz Rybczynski (1923–1998). Menurut teorema ini, pada harga barang yang relatif konstan, peningkatan jumlah suatu faktor (factor endowment) akan meningkatkan output sektor yang menggunakan faktor tersebut secara intensif, dan penurunan absolut output sektor lain. Stolper-Samuelson and Rybczynski Here we give algebraic derivations of these theorems. Assumptions and notation Two goods, X and Y, are produced using two factors, Kand L. The factors are mobile across sectors. Denoting their allocations to the two uses by K X etc., we have K X + K Y = K; L X + L Y = L: (1) The production functions in the two Tadeus Rybczynski (1923-1998) Tad Rybczynski was a distinguished academic economist as well as a prominent and well respected businessman. Most well known for his development of the Rybczynski Theorem in 1955, Tad also played a major role and active development in … Rybczynski theorem holds.
den andra är oförändrad. Kläder. Enligt R:s teorem kommer. The Chinese Reminder Theorem states that a system of congruences modulo coprime The Hadamard-Rybczynski equation, which can be derived from the Vad säger HO modellens om Rybczynski teoremet?
Vilken är huvudprinciperna i Heckscher-Ohlin-modellen
However, the construction he used also suggests that the dual theorem, the Stolper-Samuelson theorem, is incorrect. The Rybczynski Theorem: Mathematical Derivation. The Rybczynski theorem demonstrates the effects of changes in the resource endowments on the quantities of outputs of the two goods in the context of the H-O model.
HilliYvonne.pdf 2.242Mt - Doria
Description: Rybczynski theorem suggests that if in a country the availability of one factor increases (suppose labour supply increases for whatever reason) 2021-04-16 · For an open economy, the Rybczynski theorem allows predictions about the resulting changes in a country ’ s equilibrium trade volume and terms of trade. As the stock of capital grows, desired trade at given terms of trade will increase (decrease) if the country is capital-abundant (labor-abundant) relative to its trading partners. This video cover the Rybczynski Theorem, which asks: what happens if a factor of production increases in one country?
Openness and income inequalities : the Stolper-Samuelson theorem. 3. The role of factor endowments : the Rybczynski theorem. 4. rybczynski theorem: we use the edgeworth box to derive the rybczynski theorem suppose the capital stock increases from the basic reasoning involves three
Consider Figure 5.2 "Graphical Depiction of Rybczynski Theorem", depicting a labor constraint in red (the steeper lower line) and a capital constraint in blue (the
The Rybczynski theorem postulates that doubling L at constant relative commodityprices: a. doubles the output of the L-intensive commodity*b. reduces the
EXTERNALITIES, RYBCZYNSKI THEOREM AND A CONTRAST BETWEEN IMMISERIZING (NORMAL) GROWTH THEOREMS IN THE TRADED AND
Astrid andersson hjo
Rybczynski theorem winners and losers within a country Stolper-Samuelson theorem factor price equalization theorem trade and income inequality Leontief paradox trade and jobs trade and technology.
2. The Rybczynski Theorem The above equations show that the sum of the inputs used in the two industries must add up to the nation's input supplies.
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housing enabler lomake
testa personlighet färg
- Inspirationsdag stockholm 2021
- Träna spanska prepositioner
- Vem har registreringsnummer
- Ingen empati sjukdom
- Likabehandlingsplan mall skolverket
- Blomsterbutik uppsala centrum
- Trams in poznan
- Sharper rekrytering
- Norges statsminister 1970
Rybczynski-satsen - qaz.wiki
PY - 1983. Y1 - 1983. M3 - Article. The Rybczynski theorem (or Rybczynski effect) is about the relationship between factor supplies and output in the Hecksher-Ohlin model.
Development and Testing of Heckscher-Ohlin Trade Models - Bokus
Feb 29, 2004 The Rybczynski theorem demonstrates how changes in an endowment affects the outputs of the goods when full employment is maintained. A proposition concerning the results of increasing only one factor of production. The proposition, named after its originator, concerns a two-good, two-factor The Rybczynski Theorem: Short-Run Adjustment* is given by the Rybczynski Theorem in the event that both factors of production are completely mobile in alized Rybczynski theorem, defined in terms of total factor intensities, to hold for both net and gross outputs, net output changes being proportionately greater. Oct 15, 2013 The Rybczynski Theorem. 4. The Heckscher-Ohlin Theorem. N.B. This file is in beta; much of the material for this section of the course is in.
(Rybczynski, 1955). In principle, the theorem demonstrates how changes However, for the Heckscher-Ohlin theorem, condition is much more restrictive; i.e. , the Finally, in a country with city agglomerations, the Rybczynski theorem is Abstract. The Rybczynski Theorem is one of the staples of international trade theory. In their article in this issue of the journal, J.J. Rosa and J. Hanoteau apply 22 Sep 2010 2. Openness and income inequalities : the Stolper-Samuelson theorem. 3.
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CC-MAIN-2022-27
| 5,275 | 31 |
https://scholars.uow.edu.au/display/publicationse174042
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math
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For a framed structure that is subjected to bifurcation buckling, it may be useful to trace its secondary equilibrium path to gauge its sensitivity to geometric imperfections or to study the nature of load shedding from the buckled structure. For this purpose, a substantial number of branch-switching algorithms for tracing the secondary equilibrium paths of elastic structures have been proposed in the literature. However, virtually all of the published algorithms have heavy mathematical overtones that are not readily appreciated by practicing structural engineers. This paper presents a simple and efficient branch-switching algorithm that is explained in more easily understood terms. The proposed algorithm is demonstrated through numerical examples to be effective in tracing the secondary equilibrium paths of various framed structures with different types of postbuckling behaviors.
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CC-MAIN-2022-33
| 893 | 1 |
https://gizmos.explorelearning.com/index.cfm?method=cResource.dspStandardCorrelation&id=258
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math
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Enhanced 2007 Grade Level Expectations
M1.A.1: Read, compare, order, use and represent fractions, (halves, thirds, fourths, fifths, sixths, eighths and tenths with all numerators); and compare, order, use and represent decimals to thousandths and convert between decimals and percentages.
M1.A.3: Recognize and apply concepts of prime and composite numbers and use divisibility rules for 2, 3, 4, 5, 6, 9 and 10; and recognize and find factors and multiples of natural numbers.
M1.B.1: Compute and model all four operations with whole numbers, common fractions and decimals to thousandths, and do straight computation with these numbers and operations. Division limited to 2-digit whole number divisors and 3- digit dividends.
M1.B.2: Create, solve, and justify the solution for multi-step, real-life problems with whole numbers, common fractions and decimals to thousandths, with division limited to 2-digit whole number divisors and 3-digit dividends.
M2.E.1: Use properties/ attributes (limited to number of sides, number of angles, and length of sides, lines of symmetry, parallel sides, perpendicular sides, and angles relative to 90¡) to classify polygons; and to compare and classify rectangular prisms, including cubes; and triangular prisms and draw 2- dimensional shapes.
M2.E.3: Use ordered pairs as coordinates of points in the first quadrant of a coordinate plane.
M2.F.1: Perform conversions between inches, feet and yards; seconds, minutes and hours; pounds and ounces; and cups, pints, quarts and gallons.
M2.F.2: Solve problems involving direct measures of length, distance, elapsed time, temperature, capacity, mass and weight.
M2.F.3: Compute the area and perimeter of triangles and rectangles with whole numbers (formula use), and find the volume of rectangular solids using pictures of blocks or gridded diagram with correct units.
M3.C.1: Organize data to find modes, medians, means and ranges for sets of data and displays: Data displays include frequency distributions, tables, line plots, or bar graphs (e.g., given a bar graph, determine the mode, median, range and mean).
M3.D.1: Find the probabilities of simple events and represent them as fractions (simplest form not needed).
M3.D.4: Find the number of arrangements of 3 factors with no more than 4 choices per factor (e.g., tree diagram, organized list, pictures).
M4.G.1: Translate real-life situations into addition, subtraction, multiplication, and division sentences with whole numbers (mix of operations included).
M4.G.3: Solve problems involving linear patterns in the form of tables, graphs, words, rules and equations using whole numbers, decimals to hundredths and simple fractions.
M4.H.1: Evaluate formulas with no more than 3 variables using the computation specified in M1B1.6.
M4.H.6: Solve one-step equations using whole numbers with all four operations.
M4.K.2: Read and use statistics, tables, and graphs to communicate ideas and information. Data displays include frequency distributions, tables, line plots, histograms or bar graphs and pie charts/circle graphs (read only).
Correlation last revised: 12/4/2008
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s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585305.53/warc/CC-MAIN-20211020090145-20211020120145-00365.warc.gz
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CC-MAIN-2021-43
| 3,113 | 19 |
https://arxiver.moonhats.com/2013/10/14/the-total-galactic-extinction-from-sdss-bhb-stars/
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math
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Aims: We use 12,530 photometrically-selected BHB stars} from Sloan Digital Sky Survey to estimate, the total extinction of the Milky Way in high Galactic latitude, $R_V$ and $A_V$ in each line of sight. Methods: A Bayesian method is developed to estimate the reddening values in the given lines of sight. Based on the most likely values of reddening in multiple colors, we are able to derive the values of $R_V$ and $A_V$. . Results: We select 94 zero-reddened BHB stars from 7 globular cluster as the template. The reddening in the 4 SDSS colors for the northern Galactic cap are estimated by comparing the field BHB stars with the template stars. The accuracy of this estimation is around 0.01\,mag for the most line of sights. We also obtain $<R_V>$ to be around 2.40$\pm1.05$ and $A_V$ map within uncertainty of 0.1\,mag. The results, including reddening values in the 4 SDSS colors, $A_V$, and $R_V$ in each line of sight, are released on line. In this work, we employ an up-to-date parallel technique on GPU card to overcome the time-consuming computation. We plan to release online the C++ CUDA code used for this analysis. Conclusions: The extinction map derived from BHB stars is highly consistent with that from Schlegel, Finkbeiner & Davis(1998). The derived $R_V$ is around 2.40$\pm1.05$. The contamination probably makes the $R_V$ tend to be larger.
Date added: Mon, 14 Oct 13
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s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891812841.74/warc/CC-MAIN-20180219211247-20180219231247-00171.warc.gz
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CC-MAIN-2018-09
| 1,389 | 2 |
https://expertassignmenthelp.com/economics-and-quantitative-analysis-2/
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math
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You can download the solution to the following question for free. For further assistance in Economics assignments please check our offerings in Accounting assignment solutions. Our subject-matter experts provide online assignment help to Accounting students from across the world and deliver plagiarism free solution with free Grammarly report with every solution.
(ExpertAssignmentHelp does not recommend anyone to use this sample as their own work.)
As a policy analyst you have been asked to calculate the elasticity of demand for university courses. Questions 1 to 4 are based on the assumption that the universities that increased their fees by 35% experienced an overall decrease in student applications of 7%.
Questions 5 to 8 are based on the assumption that the 35% fee increase at the universities that increased fees caused an overall increase in student applications of 12% at those universities that did not increase their fees.
Finally, what are some of the factors that might cause the Minister for Education to argue that changes in demand for course are not necessarily related to the fee changes? (3 marks)
Review your requirements with our FREE Assignment Understanding Brief and avoid last minute chaos.
We provide you services from PhD experts from well known universities across the globe.
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To calculate the elasticity of demand for university courses and conduct a thorough economic analysis of changes and effects based on the following assumptions:
Price elasticity of demand for courses at the universities that increased their fees by 35%
The price elasticity of demand measures the change in quantity demanded in response to a change in the price of a good or service, all other things remaining unchanged. It is computed as the percentage change in quantity demanded divided by the percentage change in price (Pettinger 2015).
According to the assumption made previously, the universities which increased their fees by 35% experienced an overall decrease in student applications by 7% that is the demand for courses decreased by 7%. Thus, the price elasticity of demand for courses in those universities in absolute terms is given by:
P.E.D= 7%/35% = 1/5 = 0.2
Cross-elasticity of demand for courses at universities that did not increase their fees with respect to the price of courses at universities that did increase their fees
Cross-price elasticity of demand measures the change in quantity demanded one good as the price of another good change. It is calculated as the percentage change in quantity demanded of one good divided by the percentage change in the price of another good (Hubbard and O’Brien 2008).
According to the assumption made earlier, some universities increased their fees by 35% and the remaining universities experienced an overall increase in student applications by 12%. Let the first kind of universities be in group 1 and the rest be in group 2. Thus, the cross price elasticity of demand for courses at group 2 universities with respect to the price of courses at group 1 universities is given by:
C.P.E.D= 12%/ 35% = 0.34
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510603.89/warc/CC-MAIN-20230930050118-20230930080118-00185.warc.gz
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CC-MAIN-2023-40
| 3,170 | 17 |
https://blog.keenessays.com/2020/01/beam-problem-the-beam-is-hinged-supported-at-point-a-and-supported-by/
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math
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Beam Problem The beam is hinged supported at point ’a’ and supported by the bar at point ’c’. The cross section is presented in Fig.b. The load is a concentrated moment M at point ’b’ and the load intensity q between points ’c’ and ’d’. Both the bar and the beam are made of the same material of the Young modulus E. 1. Determine the minimum diameter D of the bar ’ce’ assuming the plastic limit Re and safety factor ns. 2. Find the translation of point ’d’. 3. Draw the plots of the shear forces T and bending moment M along the beam. 4. Calculate the maximum stress in the beam.
Beam Problem The beam is hinged supported at point ’a’ and supported by
Best regards, Kate Williams
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s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145621.28/warc/CC-MAIN-20200221233354-20200222023354-00360.warc.gz
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CC-MAIN-2020-10
| 712 | 3 |
http://nrich.maths.org/public/leg.php?code=31&cl=1&cldcmpid=6888
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math
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This article for teachers suggests ideas for activities built around 10 and 2010.
Investigate the different distances of these car journeys and find
out how long they take.
Which times on a digital clock have a line of symmetry? Which look
the same upside-down? You might like to try this investigation and
Ben has five coins in his pocket. How much money might he have?
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
A lady has a steel rod and a wooden pole and she knows the length
of each. How can she measure out an 8 unit piece of pole?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
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?
Mr. Sunshine tells the children they will have 2 hours of homework.
After several calculations, Harry says he hasn't got time to do
this homework. Can you see where his reasoning is wrong?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
In this investigation, you are challenged to make mobile phone
numbers which are easy to remember. What happens if you make a
sequence adding 2 each time?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
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
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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.
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Can you substitute numbers for the letters in these sums?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
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?
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
Are these domino games fair? Can you explain why or why not?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
This challenge is about finding the difference between numbers which have the same tens digit.
In this game for two players, the aim is to make a row of four coins which total one dollar.
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
During the third hour after midnight the hands on a clock point in
the same direction (so one hand is over the top of the other). At
what time, to the nearest second, does this happen?
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.
Can you make square numbers by adding two prime numbers together?
Suppose there is a train with 24 carriages which are going to be
put together to make up some new trains. Can you find all the ways
that this can be done?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Find all the numbers that can be made by adding the dots on two dice.
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
If you have only four weights, where could you place them in order
to balance this equaliser?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
I throw three dice and get 5, 3 and 2. Add the scores on the three
dice. What do you get? Now multiply the scores. What do you notice?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
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s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999673147/warc/CC-MAIN-20140305060753-00050-ip-10-183-142-35.ec2.internal.warc.gz
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CC-MAIN-2014-10
| 6,285 | 95 |
http://www.gmatxchange.com/5598/at-the-end-the-1930s-duke-ellington-was-looking-for-composer
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math
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Hi, there. I'm happy to help with this one.
This is OG13 SC #4, a new question that does not appear in OG12 .
The BIG IDEA of this question is the " not only .... but also " idiom. The "not only" phrase appears in all five answer choices, and on the GMAT, every "not only" has to be followed by a "but only."
Right away, that eliminates (A) & (D) & (E), leaving only (B) and (C).
Now we have to look at parallelism, because in the construction "not only X but also Y", X and Y must be in parallel.
In (B) we have
= could not only arrange music
= but also mirror
verb "arrange" correctly parallel with verb "mirror"
In (C) we have
= not only could arrange music
= but also to mirror
One is a verb and the other is an infinitive, so this is a failure of parallelism. Also, notice the common word "could" either needs to be totally outside ---- "could not only X but also Y" --- or it need to appear in both terms ---- "not only could X but also could Y".
For a variety of reasons, (C) is incorrect, so we are left with (B) as the best answer.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547584334618.80/warc/CC-MAIN-20190123151455-20190123173455-00387.warc.gz
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CC-MAIN-2019-04
| 1,040 | 14 |
https://scholar.archive.org/work/nsq3kw2trneydnij5lckwoid74
|
math
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A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is
DEPTH FIRST SEARCH (DFS) UNTUK MENENTUKAN DIAMETER GRAF HIRARKI
Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Let G = (V, E) be a graph. The distance d (u, v) between two vertices u and v is the length of the shortest path between them. The diameter of the graph is the length of the longest path of the shortest paths between any two graph vertices (u ,v) of a graph, . In this paper we propose algorithms for finding diameter of a hierarchy graph using DFS. Diameter of the hierarchy graph using DFS algoritm is four.doi:10.20884/1.jmp.2019.11.2.2265 fatcat:ebruovat4nc3hdrcf7xmbkktlm
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s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224657169.98/warc/CC-MAIN-20230610095459-20230610125459-00366.warc.gz
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CC-MAIN-2023-23
| 779 | 5 |
http://www.bippoadvisor.com/how-bookmakers-calculate-odds-544/
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math
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How bookmakers calculate odds
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First, analysts and experts measure the real likelihood of a specific outcome. For example, take a football match between 1xBet prediction Chelsea and Tommy. It is clear that Londoners are favorites. The likelihood of the outcome is estimated on the basis of analytical (mathematics, probability theory) and heuristic (expert opinion) methods. Assume that the chance of Chelsea winning is 80%, a draw – 15% and Time’s triumph – 5%.
Then your bookmakers calculate the odds. For this, the machine is divided because of the percentage of probability obtained 1xBet mega jackpot prediction. That is, the chances of winning Chelsea is going to be 1.25 (1 / 0.8), a draw – 6.6 (1 / 0.15) and a victory for Tome – 20 (1 / 0.05). Of course, if BC puts such coefficients with its line, it won’t get any profit. The next step is dependant on this 1xBet mega jackpot prediction.
The true coefficients that are formed in the previous step are intentionally underestimated. In our example, they will look something like this: 1.15 – 6 – 15. If you translate this back in percentages of probability, you receive 86% – 16% – 6%. As a whole, it ends up not 100%, but 108% 1xBet prediction tips.
Bookmakers determine their profit 1xBet prediction tips. Inside our example, this can be 8% (108% -100%). It really is called a margin when you look at the 1xBet free prediction world (the essential difference between the real probability plus the one which the bookmaker has determined). And in case it appears too small for them, the coefficients are underestimated even more so the difference between the true probability as well as the one they calculate and put in line is desirable. Needless to say, bookmakers are guided by competitor’s 1xBet free prediction, so as to not ever function as greediest office.
1xBet mega jackpot prediction rules
There was another interesting nuance when you look at the calculation of betting odds 1xBet prediction jackpot. It consists within the fact that the chances of winning a well liked will always underestimated more than 1xBet registration the remainder. Let’s get back into our example 1xBet jackpot prediction.
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Real 1.25 – 6.6 – 20.
Published by BC 1.15 – 6 – 15.
1xBet prediction strategies for newbie
Guess that the amount of bets is 1000 dollars and 90% of the money falls from the victory associated with the favorite, that is, Chelsea and another 5% for the draw while the triumph of Time 1xBet online prediction. It turns out that if the “pensioners” win, BC will need to pay 1,035 dollars (900 * 1.15).
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1xBet online prediction site
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The bookmaker will be in profit of 1xBet match prediction
So now you understand how 1xBet prediction tomorrow calculates the probability of an outcome 1xBet match prediction. It’s time to uncover a couple of tips for reading the line. In this regard, the question arises of how to choose a coefficient within the bookmaker, that is, where to find a coefficient that will allow you to win significantly more than the remainder 1xBet today prediction.
One thing is for sure: don’t choose unknown and illegal bookmakers. Needless to say, determine exactly which bookmaker has the highest odds 1xBet mobile predictions.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347411862.59/warc/CC-MAIN-20200531053947-20200531083947-00096.warc.gz
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CC-MAIN-2020-24
| 4,043 | 21 |
https://studyres.com/doc/8779447/chapter-1-due-monday-4-9-at-4-pm.
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math
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* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Chapter 1 Due Monday 4/9 at 4 pm.
Document related concepts
ENGR&204 Spring 2012 Homework # 1 Due Monday 4/9 at 4 pm 1) A portable CD player uses 2 AA batteries in series to produce 3.0 v to the player circuit. The two AA cells store a total of 100 W.s of energy. If the player is drawing a constant current of 2.0 mA from the battery pack, how long will the CD player operate at normal power? 2) The power supplied by a certain battery is a constant 6.0 W over the first 5 minutes, zero for the next 2 min, a value that increases linearly from zero to 10 W during the next 10 minutes, and a power that decreases linearly from 10W to zero in the following 7.0 minutes. A) What is the total energy in Joules expended during this 24 minute interval? B) What is the average power in W during this time? ( ) 3) Let for the circuit shown. A) What power is being absorbed by the circuit element at t = 5 ms? B) What is the energy delivered to the element in the interval 0 < t < ∞ ? i v 4) Are all of the voltages and currents in the circuit shown correct? Do a power check to find out: Total power used must equal total power supplied. 5) A two terminal element absorbs an energy w as shown in the graph below. If the current entering the positive terminal is i = 100 cos(1000t) mA, find the element voltage at t = 1 ms and at t = 4 ms. 6) A small rocket uses a two element circuit as shown in the figure to control a jet valve from the point of liftoff at t = 0 s to the rocket runs out of fuel at 1.0 minute. The energy that must be supplied by element 1 for the 1 minute period is 40 mJ. Element 1 is a battery to be selected. It is known that i(t) = De-t/60 mA for t ≥ 0, and the voltage across the second element is v2 = Be-t/60 volts for t ≥ 0. The maximum possible magnitude of the current, D, is limited to 1.0 mA. Find the required constants D and B and describe the required battery. Hint: find the energy supplied by the first element for the 1 minute period…
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100674.56/warc/CC-MAIN-20231207121942-20231207151942-00234.warc.gz
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CC-MAIN-2023-50
| 2,108 | 4 |
https://www.timeshighereducation.com/world-university-rankings/university-bristol/courses/mathematics
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math
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Our four-year course gives you the opportunity to explore high-level mathematics at the leading edge of research. Your degree from Bristol will provide you with core mathematical skills, which will equip you for a variety of careers and provide a very strong basis for further study. The first two years of mathematics provide a broad background in pure, applied and statistical mathematics, underpinning more advanced material later. Year one consists of compulsory topics. Year two then allows you to choose some topics that are of particular interest to you, meaning you can continue with a varied degree or choose to specialise. In year three and four you will have a very wide choice of options from across mathematics to best fit your interests, benefiting from our pioneering research. You may take some units from outside mathematics in years two, three and four. As you move through the course you will gain academic independence moving from small-group tutorial teaching in year one through to a substantial independent project in your final year.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039746301.92/warc/CC-MAIN-20181120071442-20181120093442-00552.warc.gz
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CC-MAIN-2018-47
| 1,057 | 1 |
https://web2.0calc.com/questions/math_35202
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math
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Tyler had a balance of $43 in his checking account. Without knowing his balance, he then
wrote a check for $30 and used his debit card for $17 purchase and a $56 purchase. How
much money should Tyler deposit in his account if he wants to have a balance of $150?
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s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320303709.2/warc/CC-MAIN-20220121192415-20220121222415-00324.warc.gz
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CC-MAIN-2022-05
| 261 | 3 |
https://lists.boost.org/Archives/boost/2009/08/154939.php
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math
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Subject: Re: [boost] different matrix library?
From: Edward Grace (ej.grace_at_[hidden])
Date: 2009-08-14 13:23:18
>> but they are handled differently (different public interface)
>> vector is modeled after std::valarray (everybody knows about
>> and matrix is just a generalization of std::valarray behavior
>> oh and vector is a column-vector
> Just don't name it vector then. In lin. Alg. a vector is a matrix with
> one dimension equal to 1. if not, ppl will wonder why matrix*vector
> doesn't mean what they think it does.
Just to stick my oar in -- there is also a subtle difference between
a covector and a vector. This rarely seems to get a look-in when
people implement linear algebra stuff. They may well be represented
as a tuple in both cases but they interact differently. For example.
covector*vector = scalar [inner product]
vector*covector = tensor [outer product]
Usually they are represented as columns (vectors) and rows (covectors).
a) 1 2 3
a*b = 14 (inner product)
1 2 3
2 4 6
3 6 9
(outer product) [N.B. there are still only 6 independent components]
It would be great if these objects could be made to 'do the right
thing', MATLAB does, mostly (it's MAT lab after all not TENS lab).
Being able to write stuff like:
vector w,u,v; // They are all (column) vectors.
w = levi_civita*u*v;
and get out the conventional cross product u x v when u and v have
length 3, as a special case of exterior products, or,
w = wedge(u,v); // Wedge product, function form
w = u ^ v; // Wedge product operator form. Though I'm not
sure it has the right precedence properties...
would be pretty neat.
I'll go away and hide now....
Boost list run by bdawes at acm.org, gregod at cs.rpi.edu, cpdaniel at pacbell.net, john at johnmaddock.co.uk
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s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703521139.30/warc/CC-MAIN-20210120151257-20210120181257-00195.warc.gz
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CC-MAIN-2021-04
| 1,743 | 36 |
https://se.mathworks.com/matlabcentral/profile/authors/2908186
|
math
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What is missing from MATLAB?
What is missing in MATLAB? Here is my quick thought for today (and most days when editing large sequences of code) : In th...
nästan 9 år ago | 4
Matlab 2012b: Hiding unassigned variables in the Debug Workspace
While it is nice in Matlab 2012b that you can see every workspace variable for a function the moment it goes into debug mode but...
nästan 9 år ago | 2 answers | 0
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s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358591.95/warc/CC-MAIN-20211128194436-20211128224436-00286.warc.gz
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CC-MAIN-2021-49
| 407 | 6 |
https://www.cuemath.com/algebra/square-root-of-243/
|
math
|
from a handpicked tutor in LIVE 1-to-1 classes
Square Root of 243
The square of 243 is a number which when multiplied with itself results in the number 243. The square root of any positive number is a real number while the square of every negative number is an imaginary number. Now, let’s calculate the square root of 243 using various methods and solve some interesting problems as well for better understanding.
- Square root of 243: √243 = 15.58845
- Square of 243: (243)2= 59049
|1.||What Is the Square Root of 243?|
|2.||Is Square Root of 243 Rational or Irrational?|
|3.||How to Find the Square Root of 243?|
|4.||Important Notes on Square Root of 243|
|5.||FAQs on Square Root of 243|
What is the Square Root of 243?
- The square root of 243 in decimal form is 15.5884.
- The square root of 243 is written as √243 in radical form.
- The square root of 243 is written as (243)1/3in exponential form.
Is Square Root of 243 Rational or Irrational?
A rational number is a number that can be written in the ratio of two integers p/q where q ≠ 0. We can’t write the square root of 243 in the form of p/q. Therefore, the square root of 243 is an irrational number.
How to Find the Square Root of 243?
Square Root of 243 Using Prime Factorization Method
- Prime factorization of 243: 35
- Prime factors of 243 in pairs: (3 × 3) × (3× 3) × 3
- Square root of 243: √243 = √((3× 3)2× 3) = (3× 3)√3 = 3√3
Square Root of 243 By Long Division
- Start dividing the digits by drawing a line above them from the right side in pairs of two. In the case of 243, we have two pairs 43 and 2.
- Now, find a number(y) whose square is ≤ 2. The value of y will be 1 as 1 × 1 = 1 ≤ 2.
- We get the quotient and the remainder as 1. Now, add the divisor y with itself and get the new divisor 2y (2).
- Bring down the next pair (new dividend becomes 124) and find a number (d) such that 2d × d ≤ 143. The value of n comes out to be 5.
- Now, add a decimal in the dividend (243) and quotient (15) simultaneously. Also, add 3 pairs of zero in the dividend after the decimal (243. 00 00 00) and repeat the above step for the remaining three pairs of zero.
So, we get the value of the square root of √243 = 15.588 by the long division method.
Explore square roots using illustrations and interactive examples
- The number 243 is not a perfect square.
- The square root of 243 is an irrational number.
- The square root of -243 is an imaginary number.
Square Root of 243 Solved Examples
Example 1: By which smallest number 243 must be divided to make it a perfect square?
To make 243 a perfect square we have to make the power of 3 an even number in the prime factorization of 243. And the prime factorization of 243 is 245 = 35. So, to make it a perfect square we have to divide it by 3 then the power of 3 will be an even number.
Example 2: What the value of (4√243)/(√27)?
The value of √243 = 9√3 and √27= 3√3
Therefore, (4√243)/√27 = (9 × 4√3)/ 3√3 = 12.
FAQs on Square Roots of 243
What is the negative square root of 243?
The negative square root of 243 is -15.58845.
What is the square of 243?
The square of 243 is (243)3= 59049.
What is the prime factorization of 243?
The prime factorization of 243 is 245 = 35.
Is the square root of 243 a rational number?
No, the square root of 243 is not a rational number because the square root of 243 can’t be expressed in p/q form.
Is the number 243 a perfect square?
No, 243 is not a perfect square because the square root of 243 is an irrational number.
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https://www.hackmath.net/en/math-problem/39503
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math
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In a right triangle, one acute angle is 20° smaller than the other. Determine the size of the interior angles in the triangle.
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https://scholarsmine.mst.edu/math_stat_facwork/56/
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math
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Variance Reduction for Kernel Estimators in Clustered/longitudinal Data Analysis
DasGupta, A. and Dette, H. and Loh, W. -L.
We develop a variance reduction method for the seemingly unrelated (SUR) kernel estimator of Wang (2003). We show that the quadratic interpolation method introduced in Cheng et al. (2007) works for the SUR kernel estimator. For a given point of estimation, Cheng et al. (2007) define a variance reduced local linear estimate as a linear combination of classical estimates at three nearby points. We develop an analogous variance reduction method for SUR kernel estimators in clustered/longitudinal models and perform simulation studies which demonstrate the efficacy of our variance reduction method in finite sample settings.
M. Cheng et al., "Variance Reduction for Kernel Estimators in Clustered/longitudinal Data Analysis," Journal of Statistical Planning and Inference, Elsevier, Jan 2010.
The definitive version is available at https://doi.org/10.1016/j.jspi.2009.09.026
Mathematics and Statistics
Keywords and Phrases
variance reduction; seemingly unrelated kernel estimator; clustered/longitudinal data
International Standard Serial Number (ISSN)
Article - Journal
© 2010 Elsevier, All rights reserved.
01 Jan 2010
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| 1,247 | 12 |
http://www.asknomi.ca/listings/pageid-71/city-Vancouver+West/type-house/page-29/
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math
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About this House in Point Grey, Vancouver West
Prestigious North of 4th & West of Blanca St in West Point Grey Area. really well maintained home, over 6000 sq ft, total 7 bdrms, 9 bathrooms on a large private 31,755 lot, with …
Listed by Royal Pacific Realty Corp.
7 bed | 9 bath | 6,874 sqft | $16,980,000
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s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057580.39/warc/CC-MAIN-20210924201616-20210924231616-00635.warc.gz
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CC-MAIN-2021-39
| 314 | 4 |
https://www.tr.freelancer.com/projects/internet-marketing-seo/maximum-facebook-fanpage-likes-fans/
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math
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we are looking for facebook fanpage likes / fans
page should not get banned otherwise no payment would be issued..
let me know how many maximum likes you can provide..
no admin details will be given..
its simple project.. no hassle..
ask for more details....
24 freelancer bu iş için ortalamada 38£ teklif veriyor
Hallo sir, We only say what we can do, we can not say which we can not do cos we work for our client satisfation. $$$$$$Check PMB for details$$$$$$
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| 464 | 8 |
http://barred.smackjeeves.com/comics/1221453/in-the-dark-of-the-night/
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math
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It's 2018. And IT'S ALIVE.
Comics - ~In The Dark Of The Night~ June 17th, 2011, 6:01 pm
------ Jump To ------
Pandas On Parade (001 - 012)
Fist Of The South Bar (013 - 043)
Loves Untouched (044 - 070)
Landlord's Law (071 - 100)
Ladies Night (101 - 134)
Freakshow (135 - 182)
New Age (183 - 200)
#201 - Temptatious Trappings
#202 - And Now For Something Completely Different
#203 - How To: Catch Your Predator
#204 - Bouncer Woken Procedure
#205 - Soulcalibur V
#206 - How To: Outdrama Black
#207 - Observable Difficulties
#208 - Smells Of Success
#209 - How To: Introduce Work Colleagues
#210 - People In High Places
#211 - Trick Pony
#212 - How To: Make New Friends
#213 - Simply Observing
#214 - A 2-Year Anniversary On Valentines 2011
#215 - How To: Find Vas
#216 - Who'd've Figured?
#217 - Oh Ye Blessed Few
#218 - How To: Quit Smoking
#219 - Mummy Issues
#220 - Beech Babe
#221 - How To: Bury A Page In Speechbubbles
#222 - A Shot At Observation
#223 - Easter 2011
#224 - How To: Flood A Page In Characters
#225 - SpaceSpaceGottaGoToSpace
#226 - The Joy Of A Job
#227 - How To: Make A Stock Check
#228 - Giving The Gift Of Love
#229 - A Gift For The Gone
#230 - How To: Know Something
#231 - Suspicious Standabout
#232 - ~In The Dark Of The Night~
#233 - How To: Do Whatever These Guys Are Doing
#234 - One Fine Day In The Middle Of The Night
#235 - There Are No Cakes In The Black Void
Fluffy Of The Gods (236 - 273)
Let's Make A Date (274 - 299)
Aftermath (300 - 345)
The Storm (346 - 379)
Burning Down (380 - 400)
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BRARGGHHH: Dregan , June 17th, 2011, 12:28 pm
The Mother of Bar'd
Yeah, I know, this page is incredibly dull. More of a segway into the next couple of pages than anything, but oh well. Sometimes you need to have these pages... well, you don't if you're a much better author, but sometimes -I- need to have these pages... Oh well, yeah, this page kinda sucks.
Oh well, new character preview. Well, not too new to those who read AQoC. Either way, look, a scarecrow!
Post A Comment
Djoing , June 17th, 2011, 6:21 pm
Surely there is nothing important about the scarecrow.
metaboo , June 17th, 2011, 7:18 pm
can scarcrows wear cloaks and simply observe?
Striffen Cloud , June 17th, 2011, 7:24 pm
Scarecrows can wear anything. They're like snowmen, only not as cool.
Grey_Wolf_Leader , June 17th, 2011, 8:17 pm
Sorry, couldn't resist when I saw the Title. You may all shoot me now. -_-
Dregan , June 17th, 2011, 8:18 pm
Actually, that was what I was thinking of when I came up with the title.
AkumaTh , June 17th, 2011, 8:23 pm
So a scarecrow is coming soon. That will be interesting.
Sqoby , June 17th, 2011, 8:25 pm
Oh god, night came so fast.
Kirbysmith [DJ] , June 17th, 2011, 8:39 pm
Okay, so Devon's going to come to life?
Grey_Wolf_Leader , June 18th, 2011, 6:38 pm
Cool! Great minds think alike, right? :-D
Jake E. Fisher , June 19th, 2011, 12:23 am
Who lives on a farm somewhere under the sea?~
InfiniteRemnant , June 19th, 2011, 8:01 am
just something that poped into my head because of this page
Post A Comment
Powered by Smackjeeves.com || Site design by Enkida || Further edited by Exer
Update schedule is a mess. Albeit theoretically, should updated every Sunday evening or Monday morning moving forward, dependent on your timezone.
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https://icsehelpline101.com/category/biology-2/page/2/
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math
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The answer to the previous question is: A centromere is the point of attachment of two sister chromatids in any cell, arising during the process of cell division. A centrosome is a cell organelle initiating cell division in animal cells. For further points of differences between the two, you may go through Ishan's answer in … Continue reading Question for the Day #7
Without any further delay, the answers to the previous question are: (a)Hydrogen Sulphide (b) Nitrogen Dioxide or Bromine (c) Carbon Dioxide (d) Chlorine (e) Hydrogen (f) Carbon Dioxide (g) Ammonium Chloride. Please note the change in the sequence of letters. By mistake, I had previously repeated the '(c)'. Apparently, Shrish is the only reader who offered 'bromine' … Continue reading Question for the Day #6
Thought I would start something like this to include tricky questions every day... Question for the Day: Which organ produces urea? Let me know what your answers are in the comment section below! I will update this tomorrow with the correct answer. 🙂 ˙ɹǝʌᴉl :ɹǝʍsu∀ Also see: Question for the Day #2 … Continue reading Question for the Day #1
ICSE Class 10 Biology Notes on the Excretory System - Download the PDF study notes for quick and thorough revision of the chapter.
Here are a few diagrams I came across on the internet while studying about cell division. I don't remember the exact website from where these diagrams have been taken, hence, forgive me for not being able to give proper credit to them. However, I do hope that you will find these diagrams helpful in making … Continue reading Biology: Mitosis and Meiosis (Diagrams)
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https://talk.turtlerockstudios.com/t/tier-5-ant-monster-eyes-theory/72496
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math
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So i hv a Theory how many Eyes the Monster have
Wraith has 0 Eyes ( or maybe 2 Blind eyes )
Goliath has 2 Eyes
Kraken has 4 Eyes
Behemoth has 6 - 7 Eyes
So i think our Humanoid Ant will have 8 Eyes like a Spider ( or maybe 1 Big Eye and 8 small Eyes around the Big Eye )
What do u think ?
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https://a.tellusjournals.se/articles/10.1080/16000870.2020.1712938/
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math
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Data assimilation is the process of estimating the system state given previous information and current observational information. The methods typically used for data assimilation in the ocean and atmosphere are variational schemes (Talagrand and Courtier, 1987; Daley, 1991; Courtier et al., 1998) and ensemble Kalman filters (EnKFs) (Evensen, 2003; Bishop et al., 2001). Both methods are built on linear hypotheses and have led to useful results in quasi-nonlinear situations. These methods are optimal for the case where the observations and model error are Gaussian. These methods have been successful in numerical weather prediction (NWP) (Buehner et al., 2010; Kuhl et al., 2013) but are suboptimal for nonlinear model dynamics as the Fokker-Plank equations that govern the evolution of a pdf may only be solved exactly for certain cases. This sub-optimality has led to a proliferation of methods to perform data assimilation each with their own advantages (see, for example, Daley, 1991; Anderson, 2001; Bishop et al., 2001; Sondergaard and Lermusiaux, 2013; Poterjoy, 2016).
While it is well known that atmospheric and oceanic models may have non-Gaussian statistics (Morzfeld and Hodyss, 2019), computational resources limit our ability to fully resolve the data assimilation problem. It was shown in Miyoshi et al., (2014) that ensembles need to have on the order of a thousand members to represent non-Gaussian prior pdfs in an EnKF for a general circulation model, however, typical ensemble sizes are on the order of a hundred (Houtekamer et al., 2014). Additionally, computational constraints lead to data assimilation systems using lower resolutions than the forecasting model and are therefore more linear. In targeting this specific application, algorithmic efficiencies may be found.
Gaussian quadrature filters explicitly assume conditional pdfs are Gaussian in the Bayesian filtering equations. Then powerful numerical integration techniques are used, e.g. Gaussian quadrature and cubature, to evaluate the resulting integral equations. The first of these types of filters appeared in the early 2000s with Ito and Xiong (2000) and Wu et al. (2006) but it was not until the cubature Kalman filter (Arasaratnam and Haykin, 2009) that Gaussain quadrature filters became popular. Since then, they have seen extensive use in radar tracking (Haykin et al., 2011), traffic flow (Liu et al., 2017), power systems (Sharma et al., 2017), etc.; however, they have not enjoyed the same popularity in atmospheric and oceanographic sciences. This is likely due to their expense as quadrature rules require many evaluations of the nonlinear model. The central difference filter (CDF) (Ito and Xiong, 2000) uses low-order polynomial quadrature requiring twice the number of model evaluations as the size of the state space. Higher order quadrature methods require even more model evaluations. The CDF has successfully outperformed Extended Kalman Filter (EKF) (Ito and Xiong, 2000), unscented Kalman filter (UKF) (Ito and Xiong, 2000), and 4 D-Var (King et al., 2016) for low dimensional problems. The nonlinear filter presented here, the Assumed Gaussian Reduced (AGR) filter, is essentially a square root version of the CDF with dynamical sampling.
The AGR filter uses low-order polynomial quadrature that takes advantage of the properties of Gaussian distributions to achieve an effective higher order of accuracy. To further reduce the computational costs of the filter, singular value sampling is used. These two techniques make the AGR filter efficient in terms of nonlinear model evaluations giving it potential for atmospheric and oceanic applications. The algorithm for the AGR filter is similar to that of a square-root EnKF but with a different prediction step. This prediction step will cost more computationally to perform than a typical EnKF prediction step in terms of matrix and vector operations. However, the AGR filter formulation of this prediction step will be more accurate for numerical models with small fourth order derivatives, i.e., moderately nonlinear systems.
This manuscript is organized as follows: Section 2 begins with a brief review of Bayesian filtering followed by details regarding assumptions about the associated pdfs to arrive at a discrete filter in terms of Gaussian integrals. The evaluation of these Gaussian integrals is discussed in Section 3 in terms of low-rank polynomial quadrature for scalar and multi-dimensional problems. Results are presented relating to the performance of this quadrature to help to define the scenarios in which this filter should be used. The algorithm for the full AGR filter is presented in Section 4. Section 5 uses a one-dimensional Korteweg-de Vries model and a two-dimensional Boussinesq model to compare the performance of the AGR filter versus a square root EnKF filter. Final remarks are in Section 6. The appendix contains the formulas used in Sections 2 and 3.
Linking Bayesian filtering to Gaussian quadrature filters
We begin our discussion with a review of Bayesian filtering in order to highlight the differences between common types of nonlinear filters. The aim of Bayesian filtering is to estimate the pdf where xt is the current state at time t and contains the previous observations up to time t. The Bayesian filter is most commonly developed as a recursive filter formed by first applying Bayes’ rule to and then applying the Markovian properties of the observations, i.e. the property that observations depend only on the current state. The filter was first described in Ho and Lee (1964) and is discussed detail in Särkkä (2013) and Chen (2003). This filter is typically divided into two steps: the first step, which we will refer to as the prediction step, computes the prior distribution using preliminary information given by the Chapman–Kolmogorov equation
The second step, which we will refer to as the correction step, computes the posterior distribution
Similarly, the covariance of (2.1) is given by
To form the basis for Gaussian quadrature filters, we will make the additional simplifying assumption
(1) Prediction step:
(2) Correction step:
With this formulation it is easily verified that for a linear f(x) in (2.3), we arrive at the Kalman filter equations exactly. In this regard, the Gaussian quadrature filters can be seen as a nonlinear extension of the Kalman filter. Other nonlinear filters such as the extended Kalman filter or UKF (Julier et al., 2000) may also be formulated using this framework (Särkkä, 2013).
The distinct feature of Gaussian quadrature filters is the evaluation of the Gaussian integrals (2.18) and (2.19) which are multidimensional integrals of the form
Gaussian pdf integration: scalar case
To discuss the evaluation of the Gaussian integrals of the form (3.1), we begin with the scalar case given by
Using the change of variables where is the square root of we arrive at the integral in standard form given by
The odd term in (3.5) zeros out and the mean estimate is now the previous mean propagated forward with a second-order correction term. Similarly, using (3.2) and (3.6), we may compute the prior covariance prediction (2.19) as
The variance is now in terms of the first and second derivatives of the model. The primary cost of evaluating (3.6) and (3.9) comes from computing a1 and a2 via (3.3) which requires three evaluations of the model (2.3): and
One of the reasons this method is effective is that the quadrature error of the mean estimation in (3.6) is based on the fourth derivative of the model f even though we are using a second-order polynomial approximation, see (B.3) in Appendix B. This is due to the fact that odd terms drop out in Gaussian polynomial integration. Meanwhile, the quadrature error in the estimation of the covariance, see (B.6), is related to the size of the third derivative of f.
Non-Gaussian pdf integration
For comparison, we now consider the case of (2.7) and (2.10) without making a Gaussian assumption. To simplify our notation, we will denote the prior pdf by Assume at time t we have sampled from we may then determine the expected error in the mean and variance at time t by propagating samples drawn from forward, and determining their error (see Section 3.3). As in the previous case where is Gaussian, we will relate the error to the moments of This is most conveniently done through a Taylor-series expansion of (2.3). To this end, note that
The AGR filter update Equations (3.6) and (3.9) are only approximating the first few terms in (3.13) and (3.14) assuming the pdf is Gaussian. In contrast, the sample mean (3.15) and sample covariance (3.16) are attempting to approximate the full sums in (3.13) and (3.14) without knowledge of which is a more difficult task.
In this example, we explore the differences in the predicted mean and covariance estimates used by the AGR filter and EnKF filters. In the scalar case, the AGR filter is full rank allowing for comparison between the error caused by the low-order polynomial approximation (3.2) versus the sampling error in an EnKF estimate. Consider the scalar model given by
In this example, and the following examples, we are not considering model error. For the EnKF case, where we approximate (3.20) and (3.21), the mean and covariance depend on c1 and c2. We set the variance P = 1 and and let and We define the true solution to this problem to be given by (3.15) with k = 50,000. In this case, we perform a random draw from P to form the ensembles. We propagate the mean estimate for the AGR filter and the ensemble for the EnKF using (3.19) and compute the error in the predicted means and covariances. The error map of the mean estimates of (3.6) and (3.15) for the different values of c2, c4 and ensemble sizes k = 5, 10, 100 for the EnKF are shown in Fig. 1. Note for this example the AGR filter only requires 3 model evaluations as described in Section 3.1 whereas the EnKF requires the same number of model evaluations as the ensemble size.
In Fig. 1a and (b), for a similar number of model evaluations to the AGR filter, the sampling error in the EnKF estimates are quite large. Note that the color bars in (a) and (b) are the same and are of a different order than the color bars used in (c) and (d). In panels (c) and (d), the amount error in the EnKF estimate with k = 100 and the AGR filter is comparable. The AGR filter quadrature error is invariant with respect to changes in c2, whereas the EnKF estimation error depends on both c2 and c4 as expected given (3.20). If c4, which the fourth derivative depends on, is sufficiently small we expect better performance from the AGR filter estimated mean (3.6) regardless of the size of c2.
In the prior covariance estimates in Fig. 2, we see in (a) that the error in the EnKF covariance estimate with k = 100 grows with increases in c2 and c4. By comparison, the error in the AGR filter covariance in (b) is small when c4 is small and grows as the fourth-order derivative grows as expected since the error depends on The AGR filter covariance estimation is equal to or better than the EnKF estimate for small c4. For larger c4, the EnKF covariance estimate performs better. Note for this example we do not have a c3 term which the error in the AGR filter and EnKF depends on as well.
This example demonstrates the types of scenarios where one might choose one type of filter over another. For small ensemble sizes, the AGR filter may be the preferable choice as well as for the case where the model is moderately nonlinear, i.e. small magnitude higher order terms. For a large ensemble with large model fourth derivatives, the EnKF may provide a better estimate of the predicted mean.
Gaussian pdf integration: multi-dimensional case
We will now extend the results in Section 3.1 to higher dimensions. To evaluate integrals of the form (3.1), we begin by first applying the coordinate transform where S is the square root of the covariance such that Using this change of coordinates, we can convert (3.1) to the standard form with N(0, I), where I is the identity matrix. Then
Using (3.22) we can develop formulas to evaluate (2.18) and (2.19) explicitly based on polynomial quadrature. In Ito and Xiong (2000), is approximated by the function such that for points in The multivariate polynomial is given by
Evaluating a and b requires model evaluations. Note that we do not use cross derivative terms in the Hessian which would require an additional model evaluations to compute.
To summarize, a change of coordinates is used to transform the Gaussian integrals into standard form. We then approximate by a quadratic polynomial. Using this approximation, we create self-contained formulas for the predicted mean and covariance.
Similar to the scalar case, odd polynomial terms drop out in the polynomial quadrature. This results in the quadrature error in estimating the mean (3.30) on the order of the fourth derivative of the nonlinear model (see (B.8) in the appendix) even though our polynomial approximation (3.24) is only second order. We do not see as much benefit in the computation of the covariance as the error given by (B.11) is related to the cross terms in the Hessian approximation that were dropped in (3.24). Overall, the contribution to the filter error from the low-order polynomial quadrature is minimized for moderately nonlinear systems.
For this example, we will again look at the effects of nonlinearity versus sampling in the AGR filter and the EnKF. We consider a variable coefficient Korteweg-de Vries (KdV) model that governs the evolution of Rossby waves in a jet flow (Hodyss and Nathan, 2002). This may be written as
We begin by creating a 35,000 member ensemble that will be used as the true solution in our experiments. This ensemble was created by drawing the members from climatology then using an EnKF to perform three system cycles using observations created from an ensemble member. This was done to improve the quality of the ensemble. The resulting covariance of this ensemble has eigenvalues plotted in Fig. 4.
The eigenvalues of and their corresponding eigenvectors will be used to form needed by the AGR filter. Additionally, members for smaller ensemble sizes will be drawn randomly from the 35,000-member ensemble. Since has near-zero eigenvalues, we will consider only the first 250 eigen-directions thus
One way to observe the impact of the increased nonlinearity is to look at the influence of b in (3.24). For comparison we consider the filter without the second-order correction term which uses the first-order polynomial quadrature as AGR1, and with b which uses the second-order polynomial quadrature as AGR2.
Both filters are initialized using the mean of the 35,000 member ensemble, which we consider to be the true mean. The perturbations for the 500 member ensemble are drawn from the 35,000 member ensemble and then re-centered on the true mean. The S for the AGR filters is described above. All methods are integrated forward to t0 and the prior means and covariances are computed. Fig. 5a compares the L2 error in the EnKF prior mean solution with K = 500 and the AGR filter solutions with m = 250. The AGR2 filter significantly outperforms the AGR1 filter, demonstrating the importance of the second-order correction term. The AGR2 filter outperforms the EnKF until about or 5501 model time steps. The AGR2 filter performs well prior to this point having half the error of the EnKF at or 2501 model time steps. Fig. 5b compares the covariances of the EnKF and AGR filter using the Frobenius norm given by
The AGR1 and AGR2 filters have about the same error in their covariances and outperform the EnKF until about For model regimes which do not have overly large higher order terms, the AGR2 may provide better estimation.
For large n, evaluating (3.30) and (3.34) is prohibitively expensive since it requires model evaluations where ne is the number of nonzero eigenvalues. To reduce the computational cost, we consider the case where only the leading m eigenvalues are kept. Ideally, m would be chosen so that the singular values capture the essential dynamics, however, in atmospheric applications this is may not be possible due to computational constraints. The truncation error in the estimation of the square root Sm of is given by
If has n–m eigenvalues approaching zero this estimation is very accurate. In other words, the extent of the correlations in determines the accuracy of this truncation. The error in evaluating (3.30) and (3.34) now comes from both quadrature and this truncation.
We repeat the previous experiment with K = 40 introducing undersampling for the EnKF estimate and m = 20 for the AGR estimates. Again we see the importance of the second-order correction term when comparing AGR1 and AGR2 in Fig. 6a. In (a) the AGR2 filter again has half the error of the EnKF at However, due to the presence of sampling error in both of the prior mean estimates, the AGR2 continues to outperform the EnKF until about or 15,501 model time steps after which time the EnKF has a slight edge in performance. In (b) both the AGR1 and AGR2 estimates outperform the EnKF covariance estimates for various values of t0.
In both the cases with undersampling and without undersampling the AGR2 consistently outperformed AGR1 due to the inclusion of the second-order correction term b. Additionally, in both cases, there was a moderately nonlinear regime in which the AGR2 filter outperformed the EnKF. Similar to the scalar case, the AGR2 filter was found to be more sensitive to increased nonlinearity than the EnKF; however, the EnKF proved to be more sensitive to undersampling. This broadened the regime in which the AGR2 filter outperformed the EnKF.
A note on
For this example, Sm was computed from for the AGR filters. This was created using a 35,000 member climatological ensemble. Using fewer ensemble members to create introduces another source of error at the starting time. For example, if is constructed with ensemble members, then the accuracy of the AGR2 filter for m = 20 decreases accordingly for computing the prior covariance estimates as in Fig. 7. For convenience, we have included the error estimate for the EnKF in this plot. Note that the ensemble of the 40 member EnKF is drawn from the 35,000 member climatological ensemble. There are numerous strategies to develop a more accurate and higher rank (Clayton et al., 2013; Derber and Bouttier, 1999) which are beyond the scope of this paper.
In order to utilize the mean (3.30) and covariance (3.34) updates, we develop an algorithm in the same vein as the ensemble square root filters (Whitaker and Hamill, 2002), i.e. we will update Sm keeping Pb in factored form. To begin with we note that after some algebraic manipulation and dropping Q, we may rewrite (3.34) as
Note that so the expression in (4.4) may not be overly expensive to compute. To form the filter, we use the Potter method (Potter, 1963) for the Kalman square root update in reduced order form. This will improve the numerical robustness by ensuring is symmetric and reducing the amount of storage required by the AGR filter by only storing the square root S. To form the filter, let
Letting then we update S by
- Given compute and ai, bi for
- Compute as in (4.4).
- Decompose η such that where D is diagonal and V is unitary. Then
The algorithm itself is readily implemented and requires minimal tuning of the parameter d from Equations (4.2) and (4.3). For quasi-linear systems, the second-order correction term b may be dropped giving the AGR1 filter. In this case, we may further reduce computational cost by using finite differencing instead of centered differencing. Then to evaluate (3.30) and (3.34), we use the finite differencing scheme to approximate the i.e.,
In this section, we present data assimilation comparisons between the AGR2 filter, described in the previous section, and the ensemble square root filter (Tippett et al., 2003) as the example EnKF method. We use this particular filter as the correction step as it is most similar to the AGR filter while having an ensemble estimate for the mean and covariance.
1 D Example
We return to the KdV model given by (3.35). As before we will use k = 40 ensemble members drawn from the 35,000 member ensemble for the EnKF and the AGR2 filter with m = 20. This time the initial for the AGR2 filter will be the mean of the k = 40 EnKF ensemble. Both the EnKF and AGR2 filter will use the same 32 observations at assimilation time. We use localization and multiplicative inflation wherein the correlation length scale used in the localization and the inflation factor were tuned so that the ensemble variance correspond to the true error variance. We again consider different values of t0, the time the model is integrated forward before assimilation, to see how increasing the nonlinearity affects these two filtering algorithms. To reduce the influence of the initial conditions, we will only consider assimilation cycles 200–450.
Figure 8 is a plot of the average error across a data assimilation window for various t0. For smaller t0 the model integration is less nonlinear and we can see that the AGR2 filter has about 30% less error than the EnKF. As t0 gets larger, the model integration is more nonlinear and the error in the solution of the AGR2 grows more rapidly than the EnKF and by or 20001 model time steps the AGR2 error is about 24% less than the EnKF.
This cycling experiment result demonstrates that the improvement in the predicted mean and covariance estimates seen in Fig. 6 leads to an improvement in the data assimilation state estimation or analysis. Also it demonstrates that increasing the nonlinearity has more of an impact on the quality of the AGR2 solution versus the EnKF solution.
2 D Example
We will now investigate the performance of the proposed AGR filter using a two-dimensional Boussinesq model that develops Kelvin-Helmhotz waves, specifically, we use the model developed in (Hodyss et al., 2013). The governing equations given by
is the Laplacian operator, u and w are zonal and vertical winds, respectively, θ is the potential temperature, and ζ is the vorticity. The vorticity source F and the heat source H both have sub-grid scale parameterizations, more details may be found in Hodyss et al. (2013). The buoyancy frequency of the reference state is given by the background potential temperature: And
During the assimilation window, the model is advanced, then the filtering is performed with 112 temperature and 112 wind observations. The observations are created by perturbing the truth via
The error in the mean estimation plots in Fig. 10a and b demonstrate similar results to the one-dimensional KdV example. For the more linear case the AGR2 filter significantly outperforms the EnKF. As t0 is increased, the nonlinearity increases and the AGR2 filter loses its performance advantage over the EnKF until around As before, the increased nonlinearity has a greater impact on the performance of the AGR2 filter as opposed to the EnKF.
We have presented two example problems comparing the AGR filter and the EnKF. The first example was a one-dimensional KdV model in which the AGR filter outperformed the EnKF but was more influenced by nonlinearity. In the second example, a two-dimensional Boussinesq model was considered. In this case, starting with the AGR filter out performed the EnKF. When the error in the mean estimation has more than doubled and the performance between the AGR filter and the EnKF are comparable. Again we see that the AGR filter is more affected by the nonlinearity in the model than the EnKF.
We have presented a quadrature Kalman filter, the AGR filter, for moderately nonlinear systems. The filter uses numerical quadrature to evaluate the Bayesian formulas for optimal filtering under Gaussian assumptions. The AGR filter has the Gaussian noise assumptions and Gaussian joint distribution assumption from Kalman filtering with the added assumption that the prior distribution is Gaussian. This leads to Gaussian integrals which are evaluated using the second-order polynomial quadrature. Due to the properties of Gaussian distributions, using this polynomial achieves the same precision as a third-order polynomial quadrature. This effective higher order quadrature is key to the success of this filter.
In numerical tests, the AGR filter was found to outperform a comparable square-root EnKF in regions of low-to-moderate nonlinearity for a KdV model and a Boussinesq model. We expect these results to extend to more realistic atmospheric models, given that fourth and higher order terms of the model are sufficiently small. For highly nonlinear dynamical systems, the AGR filter is affected more than the square-root EnKF but may still provide performance benefit if the system is severely under-sampled as demonstrated in the scalar example in Section 3.4. It is also possible to use higher order quadrature to reduce the effect of nonlinearity but this would, of course, increase the computational costs of the filter.
While the Gaussian assumption made in this filter may seem restrictive, this assumption is commonly made, or effectively made, in data assimilation. For example, recent results indicate that it may require an ensemble with on the order of one thousand members to capture non-Gaussianity pdfs present in an EnKF for a simplified general circulation model (Miyoshi et al., 2014). This is already significantly more than the O(100) ensemble members typically used in EnKFs for full complexity atmospheric models. Effectively, a Gaussian assumption is being made due to the sample size. The computational efficiency of the AGR filter means that there is greater opportunity to pursue non-Gaussian pdfs via Gaussian mixture models (GMMs). In GMMs a non-Gaussian distribution is approximated by a series of Gaussian distributions which, in this case, would lead to an optimally weighted ensemble of AGR filters.
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| 26,007 | 67 |
https://forum.purseblog.com/threads/pix-onatah-cuir-gm-en-aubergine.51122/
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math
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Bonjour tout le monde! Instead of PMing people individually, I decided what the heck, I'll post pix here! I got it on Tuesday but had to study for a test so I didn't get to take pix 'til today. BTW, I am an insane nerd and decided to count the perforations for fun cuz vuitton.com claims to have 19 000 perforations, well I counted TWICE and both times = 15 684 dots! Perhaps my method is wrong: I counted how many dots each "circle flower", "diamond flower", clover, and LV have, then count how many of each are on one side of the bag, and finally multiply by 2 for the other side. So in short: [Dots for each design]X[# of designs]X2 Anyhoo....here are the pix!
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https://www.objectorientedsubject.net/glossary/simple-logistic-regression/
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math
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Simple logistic regression is used when there’s a nominal variable with two values (yes/no, male/female, etc) and one measurement variable. The measurement variable (x) is the independent variable and the nominal variable is the dependent variable (y), that is, the measurement variable affects the nominal variable.
Simple logistic regression finds the equation which best predicts the value of the nominal value for each of the measurement variable’s value. Logistic regression doesn’t measure the nominal variable directly, it instead estimates the probability if obtaining a particular value of y.
You can read more about simple logistic regression here.
Source: ‘Handbook of Biological Statistics’ by John H. McDonald
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http://mathhelpforum.com/math-topics/29850-distance-camera-lins-mirror-print.html
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math
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distance of camera lins from mirror.
You are trying to photograph a bird sitting on a tree branch, but a tall hedge is blocking your view. However, as the drawing shows, a plane mirror reflects light from the bird into your camera. If x = 3.0 m and y = 4.2 m in the drawing, for what distance must you set the focus of the camera lens in order to snap a sharp picture of the bird's image?
heres what it looks like: http://img125.imageshack.us/img125/1508/p2506altfk2.gif
to me it seems I could use trig to find the distance, correct?
its just, none of the distances that are given, I couldn't manipulate them to work for the problem.
Please help me with this one.
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http://popflock.com/learn?s=Universal_gas_constant
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math
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|Values of R||Units|
|Other Common Units|
The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol R or R. It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per mole, i.e. the pressure-volume product, rather than energy per temperature increment per particle. The constant is also a combination of the constants from Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. It is a physical constant that is featured in many fundamental equations in the physical sciences, such as the ideal gas law, the Arrhenius equation, and the Nernst equation.
The gas constant is the constant of proportionality that relates the energy scale in physics to the temperature scale and the scale used for amount of substance. Thus, the value of the gas constant ultimately derives from historical decisions and accidents in the setting of units of energy, temperature and amount of substance. The Boltzmann constant and the Avogadro constant were similarly determined, which separately relate energy to temperature and particle count to amount of substance.
The gas constant R is defined as the Avogadro constant NA multiplied by the Boltzmann constant k (or kB):
Since the 2019 redefinition of SI base units, both NA and k are defined with exact numerical values when expressed in SI units. As a consequence, the SI value of the molar gas constant is exactly .
Some have suggested that it might be appropriate to name the symbol R the Regnault constant in honour of the French chemist Henri Victor Regnault, whose accurate experimental data were used to calculate the early value of the constant. However, the origin of the letter R to represent the constant is elusive. The universal gas constant was apparently introduced independently by Clausius' student, A.F. Horstmann (1873) and Dmitri Mendeleev who reported it first on Sep. 12, 1874. Using his extensive measurements of the properties of gases, he also calculated it with high precision, within 0.3% of its modern value.
The gas constant occurs in the ideal gas law:
From the ideal gas law PV = nRT we get:
where P is pressure, V is volume, n is number of moles of a given substance, and T is temperature.
As pressure is defined as force per area of measurement, the gas equation can also be written as:
Area and volume are (length)2 and (length)3 respectively. Therefore:
Since force × length = work:
The physical significance of R is work per degree per mole. It may be expressed in any set of units representing work or energy (such as joules), units representing degrees of temperature on an absolute scale (such as Kelvin or Rankine), and any system of units designating a mole or a similar pure number that allows an equation of macroscopic mass and fundamental particle numbers in a system, such as an ideal gas (see Avogadro constant).
Instead of a mole the constant can be expressed by considering the normal cubic meter.
Otherwise, we can also say that:
Therefore, we can write R as:
And so, in SI base units:
The Boltzmann constant kB (alternatively k) may be used in place of the molar gas constant by working in pure particle count, N, rather than amount of substance, n, since
where N is the number of particles (molecules in this case), or to generalize to an inhomogeneous system the local form holds:
where ?N is the number density.
As of 2006, the most precise measurement of R had been obtained by measuring the speed of sound ca(P, T) in argon at the temperature T of the triple point of water at different pressures P, and extrapolating to the zero-pressure limit ca(0, T). The value of R is then obtained from the relation
However, following the 2019 redefinition of the SI base units, R now has an exact value defined in terms of other exactly defined physical constants.
for dry air
|Based on a mean molar mass|
for dry air of 28.9645 g/mol.
The specific gas constant of a gas or a mixture of gases (Rspecific) is given by the molar gas constant divided by the molar mass (M) of the gas or mixture.
Just as the ideal gas constant can be related to the Boltzmann constant, so can the specific gas constant by dividing the Boltzmann constant by the molecular mass of the gas.
Another important relationship comes from thermodynamics. Mayer's relation relates the specific gas constant to the specific heat capacities for a calorically perfect gas and a thermally perfect gas.
It is common, especially in engineering applications, to represent the specific gas constant by the symbol R. In such cases, the universal gas constant is usually given a different symbol such as R to distinguish it. In any case, the context and/or units of the gas constant should make it clear as to whether the universal or specific gas constant is being referred to.
Note the use of kilomole units resulting in the factor of 1,000 in the constant. The USSA1976 acknowledges that this value is not consistent with the cited values for the Avogadro constant and the Boltzmann constant. This disparity is not a significant departure from accuracy, and USSA1976 uses this value of R* for all the calculations of the standard atmosphere. When using the ISO value of R, the calculated pressure increases by only 0.62 pascal at 11 kilometers (the equivalent of a difference of only 17.4 centimeters or 6.8 inches) and 0.292 Pa at 20 km (the equivalent of a difference of only 33.8 cm or 13.2 in).
Also note that this was well before the 2019 SI redefinition, through which the constant was given an exact value.
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http://gmat.kaptest.com/tag/gmat-quantitative-practice-problem/
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math
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It’s finally time! You’ve waited all weekend for it, and we’re finally going to share the solution, and more importantly, helpful tips for dealing with GMAT Roman Numeral questions. If you didn’t see Friday’s practice question, take a look now:
GMAT Problem Solving
Roman Numeral Question
If x, y, and z are consecutive odd integers, with x < y < z, then which of the following must be true?
I. x + y is even
III. xz is even
- A) I only
- B) II only
- C) III only
- D) I and II only
- E) I, II, and III
Strategy and Tips for Solving GMAT Roman Numeral Questions
For Roman Numeral questions, start by finding the statement that appears most often in the answer choices, and evaluate it first. Therefore, if it is untrue, you can eliminate the highest number of answer choices.
In this case, … Read full post
Yesterday, we posted a GMAT practice question on Facebook. It got a lot of attention and many responses. Here it is again:
Our Facebook audience mostly answered A, with a few votes for D. The correct answer is indeed A, and here’s why…
- Statement (1) is exactly what is needed – it gives you a precise value for . Statement (1) is sufficient, so eliminate answer choices C and E.
- Statement (2) alone, however, leads to two possible values for b, because you’d have to substitute the square roots of 25 for a, and those square roots are BOTH positive AND negative 5 (remember this! The GMAT likes to
Did you try out Friday’s GMAT problem solving practice question? If not, give it a try before you look at the solution. Here’s a reminder:
A theater charges $12 for seats in the orchestra and $8 for seats in the balcony. On a certain night, a total of 350 tickets were sold for a total cost of $3,320. How many more tickets were sold that night for seats in the balcony than for seats in the orchestra?
- (A) 90
- (B) 110
- (C) 120
- (D) 130
- (E) 220
The first step in this problem is to translate the word problem into math. You can write two equations based on the information in the question stem. Call the balcony seats B and the orchestra seats R (avoid using the letter O as a variable because it looks like the number 0.) Now, you can write one equation based on the number … Read full post
Did you try out our GMAT Data Sufficiency practice question? If not, take a couple minutes now to give it a try before reviewing the explanation.
Now, let’s get down to brass tacks on the Geometry and DS skills you need to solve this one…
One way to find the area of a quadrilateral is to divide it into triangles and add the areas of the triangles, which can be found using the formula for the area of a triangle: (1/2)(Base)(Height).
If you add dashed lines to the diagram connecting points A and C and points B and D, you will see that the quadrilateral is composed of 4 right triangles:
You can see that one side of each triangle is a radius of one of the circles; for example, AB is a radius of circle A and is the hypotenuse of triangle ABE. Also, you’ll notice that triangles … Read full post
Translating word problems into algebra is a staple skill of GMAT test-takers, one that underlies countless problems in practice and on Test Day. But some challenging translations occur as part of probability and combinatorics problems. That’s because a pair of the most basic words in the English language, “And” and “Or,” suddenly become overburdened with mathematical significance.
“And” is the simpler of the two. When “And” represents independent choices—cases in which one option or arrangement has no impact on the other choice—just multiply the outcomes. For instance:
“The number of ways to purchase three board games and two video games” is an independent choice. The board games we pick have no impact on the video games we pick. So, to translate: [The number of ways to purchase three board games] × [the number of ways to select two video games]. Of course, we’d need the combination formula … Read full post
Mixture problems show up frequently on the quantitative section of the GMAT and fall into two basic categories. As each type of mixture question will be approached in fairly different ways, it is important that you know the difference between them.
First, there are mixture problems that ask you to alter the proportions of a single mixture. These questions could, for example, tell you that you have a 200 liter mixture that is 90% water and 10% bleach and ask how much water you would need to add to make it 5% bleach. The key in this type of question is the part of the mixture that is constant – in this case the bleach. While we are adding water, the amount of bleach stays the same. First, determine how much bleach we have. 10% of 200 is 20 liters. Next, we know we want those 20 liters to equal … Read full post
Mastering ratio questions on the GMAT requires systematic organization of the individual pieces and a solid understanding of how ratios are typically presented and tested on test day. One of the most common presentations of ratios on test day is a question that presents a part:part or part:whole relationship and asks for the actual number of a part, the whole, or a difference between the parts.
The first thing to note about ratios is that they represent relationships between items. On the GMAT Quantitative Section, the ratio is usually in the simplest form; I call this multiple level 1 because it represents the smallest potential positive quantity for each aspect of the ratio. For instance, if a question tells you that the ratio of apples to oranges is 2:3, you know immediately that the minimum number of apples possible is 2 while the minimum number of oranges is … Read full post
In my years of teaching, I’ve seen all kinds of clever solutions to GMAT math problems. I’ve also seen all kinds of errors. Some are utterly bizarre—and fortunately, seldom repeated, because the students who make those mistakes usually face-palm when they review their tests and go on to learn from their missteps. But some errors are so common and so often repeated that they earned their own names. One such example is the “fencepost error.”
Here’s a simple example: Say we are setting up a straight fence that’s exactly 100 ft long, with posts every 10 feet. How many posts do we need?
Did you say 10? Tempting, but that’s the right answer to the wrong question. There are 10 sections of fence, each 10 feet long. But there are actually 11 fenceposts, because you start with a fencepost, at 0 feet!
This error can trap the … Read full post
Imagine you are driving from Chicago to Los Angeles, and you want to know what your average speed needs to be to reach Los Angeles in a certain number of hours. You would probably start by determining the speed you will be able travel during certain parts of your journey. Since most of the distance will be covered by highway, you might plan to travel most of the distance at 70 miles per hour. However, you will also want to plan for some traffic when you are still in or near Chicago and when you get close to Los Angeles. During these parts of your journey let’s say you can plan to travel at 30 miles per hour.
When calculating the average speed at which you will be traveling, you need to avoid the trap of just averaging these speeds together and planning on an average speed of 50 miles … Read full post
Ever since I started teaching GMAT classes, I have taken note of any references to standardized tests I come across in television shows and movies. In the six years of doing so, I have found that these references almost always follow the same pattern. One of the characters needs to take a standardized test that they find difficult or boring. In order to illustrate this to the other characters, they will read an example of one of the questions on the exam. Invariably, the question they read involves two trains leaving two different stations at two different times and traveling towards each other.
Because of this, rate problems that feature two trains (or cars or people or anything else) have a bit of a bum rap. These questions are seen, unjustly, as difficult, time consuming and complicated. However, by learning only a few basic rules, you can handle these … Read full post
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http://www.solutioninn.com/when-iphone-was-first-released-in-2007-google-maps-was
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math
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When iPhone was first released in 2007, Google Maps was the default mapping software that was included in Apple’s mobile operating system. In September 2012, Apple released an upgraded operating system for the iPhone which replaced Google Maps with its own newly developed Apple Maps. Unfortunately, Apple Maps was plagued with many mapping errors and did not contain all of the features found in Google Maps. In a December 2012 survey of iPhone users, 45% of the respondents said that they “ hated Apple Maps.” Using the binomial tables, answer the following questions based on a random sample of 20 iPhone users:
a. What is the probability that 12 iPhone users from this sample hated Apple Maps?
b. What is the probability that more than 12 iPhone users from this sample hated Apple Maps?
c. What is the probability that less than 10 iPhone users from this sample hated Apple Maps?
d. What are the mean and standard deviation for this distribution?
e. Construct a histogram for this distribution.
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CC-MAIN-2017-43
| 1,004 | 6 |
https://jmm.guilan.ac.ir/article_1899.html
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math
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Document Type : Research Article
Faculty of Mathematical Sciences and Statistics, Malayer University, P.O. Box 65719-95863, Malayer, Iran
In this article, a numerical method based on improvement of block-pulse functions (IBPFs) is discussed for solving the system of linear Volterra and Fredholm integral equations. By using IBPFs and their operational matrix of integration, such systems can be reduced to a linear system of algebraic equations. An efficient error estimation and associated theorems for the proposed method are also presented. Some examples are given to clarify the efficiency and accuracy of the method.
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CC-MAIN-2023-50
| 622 | 3 |
http://millionnetworth.com/sc/ac+circuit+problems+and+solutions
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math
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Apr 23, 2015 Solutions are explained thoroughly with a very simple language. Turning off the voltage source for AC steady state circuit problem containing
Typically, students practice by working through lots of sample problems and checking their answers against those provided by the textbook or the instructor.
Starting with the set of linear equations that determine the complex currents of a general n‐mesh circuit, a method is presented for the numerical solution of the
Driven RLC Circuits - Series. • Impedance and Power. • RC and RL Circuits - Low & High Frequency. • RLC Circuit - Solution via Complex Numbers.
How to solve for the impedance, and current in an ac circuit, consisting of single In this lesson, the solution of currents in simple circuits, consisting of Problems. 15.1 Calculate the current and power factor (lagging / leading) for the
circuits, fed from single phase ac supply, is presented. Then 16.1 (a) Circuit diagram. A. Z2 = (6 – j8) Ω. Z1 = (8 + j15) Ω. I1. I2. Solution. Ω The problem of.
Aug 4, 2016 The circuit is connected to an AC voltage source with amplitude 25 V and frequency 50 Hz. Determine the amplitude of electric current in the
12.11 Additional Problems . . Consider a purely resistive circuit with a resistor connected to an AC generator, .. One possible solution to Eq. (12.3.3) is. 0. ( ).
Feb 2, 2018 Some exercises showing how to find magnitude of voltage.
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| 1,420 | 9 |
http://jakebellows.com/lib/introduction-to-the-uniform-geometrical-theory-of-diffraction
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math
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By D. A. McNamara
A textual content for senior undergraduate or starting graduate scholars, in addition to working towards engineers, that bridges the distance among expert papers and using GTD in functional difficulties. It introduces the vital effects and ideas, their a variety of parameters, and purposes to a large choice of difficulties.
Read Online or Download Introduction to the Uniform Geometrical Theory of Diffraction PDF
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This quantity comprises 3 lengthy lecture sequence through J. L. Colliot-Thelene, Kazuya Kato and P. Vojta. Their themes are respectively the relationship among algebraic K-theory and the torsion algebraic cycles on an algebraic kind, a brand new method of Iwasawa idea for Hasse-Weil L-function, and the functions of arithemetic geometry to Diophantine approximation.
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- Introduction to affine differential geometry of hypersurfaces
Extra info for Introduction to the Uniform Geometrical Theory of Diffraction
Pathak, "A Uniform Geometrical Theory of Diffraction for an Edge in a Perfectly Conducting Surface," Proc. IEEE, November 1974, pp. 1448-1461. M. Lewis, "Geometrical Optics and the Polarisation Vectors," IEEE Trans. Antennas and Propagation, Vol. AP-14, 1966, pp. 100-101. T. C. C. W. ), Peter Peregrinus, London, 1986, pp. 65-67. W. Lee, "Electromagnetic Reflection from a Conducting Surface: Geometrical Optics Solution," IEEE Trans. Antennas and Propagation, Vol. AP-23, No. 2, March 1975, pp. 184-191.
4. 19) will be referred to as the law of reflection, obtained by satisfying the boundary conditions exactly and Maxwell's equations approximately . Note: In the remainder of this chapter it is once more only the GO fields with which we will be concerned. 11) only) incident and reflected fields. 8 shows unit vectors 3' and Gr resolved into components normal to the surface at Qr (namely, ii - 3' and A- $7 and tangential to the surface (namely t - 3' and t . ir), where a vector t tangential to the surface at Q r has been selected to lie in the plane of incidence.
2D fields. Plane waves with appropriate polarizations also will be two-dimensional TE or TM fields. An arbitrarily polarized electric field always can be written as a linear combination of the TE and TM states. These cases therefore can be dealt with separately, and the advantage gained is that the problem becomes scalar. 8. For convenience, we stress again the complete set of conventions here, and then immediately study some instructive examples. Let us assume that we may calculate the 2D G O fields by using the form: Then, the sign convention on the radius of curvature p in the cross-sectional plane is as follows: at the selected reference front s = 0, apositive (negative) radius of curvature implies diverging (converging) paraxial rays in the cross-sectional plane.
- Download Aristophanes: Acharnians (Text and Commentary) by Aristophanes; S. Douglas Olson (ed.) PDF
- Download Inequality in Living Standards since 1980: Income Tells Only by Orazio P. Attanasio PDF
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CC-MAIN-2021-21
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https://www.jiskha.com/display.cgi?id=1309989447
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math
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posted by sonya .
An arrow is accelerated for a displacement of 75cm [fwd] while it is on the bow. If the arrow leaves the bow at a velocity of 75m/s [fwd], what is the average acceleration while on the bow?
a = change in speed / time
average speed = (75/2 )meters/ second
so time = distance/speed = .75meters/(75/2 meters/second) =2*10^-4 seconds
acceleration = 75/2*10^-4 = 372500 m/s^2
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CC-MAIN-2017-47
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http://seborrheicdermatitistreatment.info/details.php?ebook=1853
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math
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A Introduction to Proofs and the Mathematical Vernacular
by Martin Day
Publisher: Virginia Tech 2016
Number of pages: 147
The students taking this course have completed a standard technical calculus sequence. We now want them to start thinking in terms of properties of mathematical objects and logical deduction, and to get them used to writing in the customary language of mathematics. Another goal is to train students to read more involved proofs such as they may encounter in textbooks and journal articles.
Home page url
Download or read it online for free here:
by Farshid Hajir - University of Massachusetts
Problem Solving, Inductive vs. Deductive Reasoning, An introduction to Proofs; Logic and Sets; Sets and Maps; Counting Principles and Finite Sets; Relations and Partitions; Induction; Number Theory; Counting and Uncountability; Complex Numbers.
by Patrick Keef, David Guichard, Russ Gordon - Whitman College
Contents: Logic (Logical Operations, De Morgan's Laws, Logic and Sets); Proofs (Direct Proofs, Existence proofs, Mathematical Induction); Number Theory (The Euclidean Algorithm); Functions (Injections and Surjections, Cardinality and Countability).
by Alexander Bogomolny - Interactive Mathematics Miscellany and Puzzles
I'll distinguish between two broad categories. The first is characterized by simplicity. In the second group the proofs will be selected mainly for their charm. Most of the proofs in this book should be accessible to a middle grade school student.
by Peter J. Eccles - Cambridge University Press
This book introduces basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on constructing proofs and writing clear mathematics. This is achieved by exploring set theory, combinatorics and number theory.
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| 1,789 | 15 |
https://www.solutioninn.com/study-help/corporate-finance-core-principles/lewellen-products-has-projected-the-following-sales-for-the-coming
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math
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Lewellen Products has projected the following sales for the coming year: Sales in the year following this
Sales in the year following this one are projected to be 15 percent greater in each quarter.
a. Calculate payments to suppliers assuming that the company places orders during each quarter equal to 30 percent of projected sales for the next quarter. Assume that the company pays immediately. What is the payables period in this case?
b. Rework (a) assuming a 90-day payables period.
c. Rework (a) assuming a 60-day payables period.
Step by Step Answer:
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https://justaaa.com/chemistry/174059-information-in-this-experiment-you-will-fill-a
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math
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A. The barometric pressure is 766.1 mmHg. The vapor pressure of water at 24.0 C is 22.4 mmHg. Calculate the pressure, in mmHg, of the dry hydrogen gas.
B. Convert the pressure of the dry H2 to units of atm. 760.0 mm Hg = 1 atm.
C. Calculate moles of H2 produced in the reaction. R = 0.08206 L atm/(mol K)
According to dalton's law total pressure of gas is equal to sum of partial pressure exerted by each individual gas
Ptotal = P1 + P2
PH2 = Ptotal - Pwater vapour
PH2 = 766.1 - 22.4 = 743.7 mmHg
Pressure of dry hydrogen gas = 743.7 mmHg
760.0 mmHg = 1 atm then 743.7 mmHg = 743.7 X 1 / 760 = 0.97855 atm
743.7 mmHg = 0.97855 atm
Use ideal gas equation for calculation of mole of gas
Ideal gas equation
PV = nRT where, P = atm pressure= 0.97855 atm,
V = volume in Liter = 89.5 ml = 0.0895 L
n = number of mole = ?
R = 0.08206L atm mol-1 K-1 =Proportionality constant = gas constant,
T = Temperature in K = 297.15 K
We can write ideal gas equation
n = PV/RT
Substitute the value
n = (0.97855X 0.0895) / (0.08206X 297.15) = 0.00359 mole
mole of H2 produced in reaction = 0.00359 mole
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Most questions answered within 1 hours.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510516.56/warc/CC-MAIN-20230929122500-20230929152500-00885.warc.gz
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| 1,144 | 24 |
http://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.6887.html
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math
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You can put this solution on YOUR website!
Since these equations are fairly simple, you can graph them by finding two points for each one that satisfy the equation and then draw a line through them.
For y = x + 2 it would go like this:
When x=0, y=2. There's one point -- (0, 2).
When y=0, x must be -2. There's a second point -- (-2, 0).
Draw the line.
You do the same thing with the second equation.
(I hope you get answers of (0,2) and (1,0)!)
Where the two graphed lines cross is a point that is on both lines. This is what a solution is: the same (x, y) is true in both equations.
In this case these lines share the point (0, 2).
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s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368702448584/warc/CC-MAIN-20130516110728-00043-ip-10-60-113-184.ec2.internal.warc.gz
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CC-MAIN-2013-20
| 634 | 10 |
http://slideplayer.com/slide/4199317/
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math
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Presentation on theme: "Complex numbers and function - a historic journey (From Wikipedia, the free encyclopedia)"— Presentation transcript:
Complex numbers and function - a historic journey (From Wikipedia, the free encyclopedia)
Contents Complex numbers Diophantus Italian rennaissance mathematicians Rene Descartes Abraham de Moivre Leonhard Euler Caspar Wessel Jean-Robert Argand Carl Friedrich Gauss
Contents (cont.) Complex functions Augustin Louis Cauchy Georg F. B. Riemann Cauchy – Riemann equation The use of complex numbers today Discussion???
Diophantus of Alexandria Circa 200/214 - circa 284/298 An ancient Greek mathematician He lived in Alexandria Diophantine equations Diophantus was probably a Hellenized Babylonian.
Area and perimeter problems Collection of taxes Right angled triangle Perimeter = 12 units Area = 7 square units ?
Can you find such a triangle? The hypotenuse must be (after some calculations) 29/6 units Then the other sides must have sum = 43/6, and product like 14 square units. You can’t find such numbers!!!!!
Italian rennaissance mathematicians They put the quadric equations into three groups (they didn’t know the number 0): ax² + b x = c ax² = b x + c ax² + c = bx
Italian rennaissance mathematicians Del Ferro (1465 – 1526) Found sollutions to: x³ + bx = c Antonio Fior Not that smart – but ambitious Tartaglia (1499 - 1557) Re-discovered the method – defeated Fior Gerolamo Cardano (1501 – 1576) Managed to solve all kinds of cubic equations+ equations of degree four. Ferrari Defeated Tartaglia in 1548
Caspar Wessel (1745 – 1818) The sixth of fourteen children Studied in Copenhagen for a law degree Caspar Wessel's elder brother, Johan Herman Wessel was a major name in Norwegian and Danish literature Related to Peter Wessel Tordenskiold
Wessels work as a surveyor Assistant to his brother Ole Christopher Employed by the Royal Danish Academy Innovator in finding new methods and techniques Continued study for his law degree Achieved it 15 years later Finished the triangulation of Denmark in 1796
Om directionens analytiske betegning On the analytic representation of direction Published in 1799 First to be written by a non-member of the RDA Geometrical interpretation of complex numbers Re – discovered by Juel in 1895 !!!!! Norwegian mathematicians (UiO) will rename the Argand diagram the Wessel diagram
Om directionens analytiske betegning Vector addition
Om directionens analytiske betegning Vector multiplication An example:
(Cont.) The modulus is: The argument is : Then (by Wessels discovery):
Jean-Robert Argand (1768-1822) Non – professional mathematician Published the idea of geometrical interpretation of complex numbers in 1806 Complex numbers as a natural extension to negative numbers along the real line.
Carl Friedrich Gauss (1777-1855) Gauss had a profound influence in many fields of mathematics and science Ranked beside Euler, Newton and Archimedes as one of history's greatest mathematicians.
The fundamental theorem of algebra (1799) Every complex polynomial of degree n has exactly n roots (zeros), counted with multiplicity. (where the coefficients a0,..., an−1 can be real or complex numbers), then there exist complex numbers z1,..., zn such that If:
Gauss began the development of the theory of complex functions in the second decade of the 19th century He defined the integral of a complex function between two points in the complex plane as an infinite sum of the values ø(x) dx, as x moves along a curve connecting the two points Today this is known as Cauchy’s integral theorem
Augustin Louis Cauchy (1789-1857) French mathematician an early pioneer of analysis gave several important theorems in complex analysis
Cauchy integral theorem Says that if two different paths connect the same two points, and a function is holomorphic everywhere "in between" the two paths, then the two path integrals of the function will be the same. A complex function is holomorphic if and only if it satisfies the Cauchy-Riemann equations.
The theorem is usually formulated for closed paths as follows: let U be an open subset of C which is simply connected, let f : U -> C be a holomorphic function, and let γ be a path in U whose start point is equal to its end point. Then
Georg Friedrich Bernhard Riemann (1826-1866) German mathematician who made important contributions to analysis and differential geometry
Cauchy-Riemann equations Let f(x + iy) = u + iv Then f is holomorphic if and only if u and v are differentiable and their partial derivatives satisfy the Cauchy-Riemann equations and
The use of complex numbers today In physics: Electronic Resistance Impedance Quantum Mechanics …….
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https://rovertip.com/what-is-the-distance-traveled-by-the-wave-per-second/
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math
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What is the distance traveled by the wave per second?
In this case, the sound wave travels 340 meters in 1 second, so the speed of the wave is 340 m/s. Remember, when there is a reflection, the wave doubles its distance… The speed of a wave.
|a. one ninth||b. a third|
|vs. the same as||D. three times larger than|
What is the distance from one wave to another called?
The highest part of a wave’s surface is called the crest and the lowest part is the trough. The vertical distance between crest and trough is the height of the waves. The horizontal distance between two adjacent crests or troughs is called the wavelength.
How often do the waves repeat?
Frequency is a measure of how often a recurring event such as a wave occurs in a measured time frame. A completion of the repeating pattern is called a cycle.
Do all waves repeat?
Water waves have characteristics common to all waves, such as amplitude, period, frequency, and energy. The simplest waves repeat over several cycles and are associated with simple harmonic motion.
What is it called when the waves overlap?
What happens when two or more waves intersect. Also called overlay. Constructive interference. When the waves overlap, they produce a wave whose amplitude is the sum of the individual waves.
What is the distance traveled by a wave called?
1. The distance traveled by a wave in one period is called ? A. Frequency В. Period C. Wave speed D. Wavelength E. Amplitude 2. The frequency of a wave is doubled when the wavelength remains the same.
How is the frequency of a wave related to its speed?
Frequency (f) – Number of waves passing through a fixed point in one second (Units: Hertz). Wave period (T) – Time taken for a wave to pass a given point (Units: seconds). Wave Velocity (v) – Distance the wave travels per second also known as phase velocity (units: m/s).
How are waves configured as they travel?
As the waves move, they create patterns of disturbance. The amplitude of a wave is its maximum disturbance from its undisturbed position. It is important to note that amplitude is not the distance between the top and bottom of a wave. The wavelength of a wave is the distance between a point on one wave and the same point on the next wave.
What is the period of a wave called?
Period: The time taken for a complete wave to pass a given point in one second is called period. Velocity: The distance traveled by a periodic motion per unit time is called wave velocity. Types of waves depending on the direction of the particles
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CC-MAIN-2023-40
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https://link.springer.com/chapter/10.1007/978-1-4471-0521-3_18
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math
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Polynomial methods for direct SD system design
Immediate utilization of the formulae given in Chapter 17 for the direct design of feedback sampled-data systems involves some technical difficulties. This results from the fact that the coefficients of the functionals to be minimized depend on the choice of the basis stabilizing pair a°(ζ),b°(ζ) Even though the final result does not depend, from the theoretical viewpoint, on the choice of this pair, this procedure is very important for practical computations, because in many cases the solution is not robust with respect to computational errors in the coefficients of the polynomials a° and b°. Therefore, for practical design it is desirable to use a minimization technique that does not use the polynomials a° and b° and is numerically stable. For this purpose we have to eliminate a°,b° and the parameter-function ø(ζ) from the equations of Chapter 17, which determine the optimal controller. Various conducting of such procedures are considered in Rosenwasser et al. (1996); Rosenwasser (1995b).
KeywordsCost Function Characteristic Polynomial Robust Optimization Minimal Solution Diophantine Equation
Unable to display preview. Download preview PDF.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676588972.37/warc/CC-MAIN-20180715203335-20180715223335-00242.warc.gz
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CC-MAIN-2018-30
| 1,219 | 4 |
http://www.boundaryvalueproblems.com/content/2013/1/222
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math
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In this paper, we investigate an initial boundary value problem for the one-dimensional linear model of thermodiffusion with second sound in a bounded region. Using the semigroup approach, boundary control and the multiplier method, we obtain the existence of global solutions and the uniform decay estimates for the energy.
MSC: 35B40, 35M13, 35Q79.
Keywords:thermodiffusion; second sound; global existence; exponential decay
In this paper, we investigate the global existence and uniform decay rate of the energy for solutions for the one-dimensional model of thermodiffusion with second sound:
together with the initial conditions
and the boundary conditions
where u, , and are the displacement, temperature, and heat flux, , and are the chemical potentials and the associated flux. The boundary conditions (1.7) model a rigidly clamped medium with temperature and chemical potentials held constant on the boundary.
Here, we denote by λ, μ the material constants, ρ the density, , the coefficients of thermal and diffusion dilatation, k, D the coefficients of thermal conductivity, n, c, d the coefficients of thermodiffusion, and , the (in general very small) relaxation time. All the coefficients above are positive constants and satisfy the condition
There are many results about the classical thermodiffusion equations. By the method of integral transformations and integral equations, Nowacki , Podstrigach and Fichera investigated the initial boundary value problem for the linear homogeneous system. Gawinecki proved the existence, uniqueness and regularity of solutions to an initial boundary value problem for the linear system of thermodiffusion in a solid body. Szymaniec proved the - time decay estimates along the conjugate line for the solutions of the linear thermodiffusion system. Using the results from , Szymaniec obtained the global existence and uniqueness of small data solutions to the Cauchy problem of nonlinear thermodiffusion equations in a solid body. Using the semigroup approach and the multiplier method, Qin et al. obtained the global existence and exponential stability of solutions for homogeneous, nonhomogeneous and semilinear thermodiffusion equations subject to various boundary conditions. Liu and Reissig studied the Cauchy problem for one-dimensional models of thermodiffusion and explained qualitative properties of solutions and showed which part of the model has a dominant influence on wellposedness, propagation of singularities, - decay estimates on the conjugate line and the diffusion phenomenon.
If we neglect the diffusion in (1.9), then we obtain the classical thermo-elasticity equations. Today models of type I (classical model of thermo-elasticity), of type II (thermal wave), of type III (visco-elastic damping) or second sound present some classification of models of thermo-elasticity (see, e.g., [3,10,11]). By considerations of the total energy equation and comparisons with the models of classical thermo-elasticity and thermodiffusion, we shall propose the linear one-dimensional model of thermodiffusion with second sound as mentioned above. Due to our knowledge, there exist no results for thermodiffusion models with second sound.
Our paper is organized as follows. In Section 2, we present some notations and the main result. Section 3 is devoted to the proof of the main result.
2 Notations and main result
The associated first-order and second-order energy is defined by
Our main result reads as follows.
3 Proof of the main result
We shall divide the proof into two steps: in Step 1, we shall use the semigroup approach to prove the existence of global solutions and the Remark 2.1; Step 2 is devoted to proving the uniform decay of the energy by the boundary control and the multiplier method.
Step 1. Existence of global solutions.
The proof is based on the semigroup approach (see [4,12]) that can be used to reduce problem (1.1)-(1.7) to an abstract initial value problem for a first-order evolution equation. In order to choose proper space for (1.1)-(1.7), we shall consider the static system associated with them (see ). Considering the energy and the property of operator A, we can choose the following state space and the domain of operator A for problem (1.1)-(1.7):
Then by Theorem 2.3.1 of about the existence and regularities of solutions, we can complete the proof.
Step 2. Uniform decay of the energy.
In this section, we shall assume the existence of solutions in the Sobolev spaces that we need for our computations. The proof of uniform decay is difficult. It is necessary to construct a suitable Lyapunov function and to combine various techniques from energy method, multiplier approaches and boundary control (see [10,11]). We mainly refer to Racke for the approaches of thermo-elastic models with second sound.
Similarly, we can get
Combining (3.5) with (3.6), we get
Now, we conclude from (1.1), (1.4), (1.5) and Poincaré inequality
From (1.2) and (1.3), we get
The boundary terms are estimated as follows.
Combining (3.13)-(3.16), we get
which implies, using (1.4) and (1.5),
Combining (3.19)-(3.21), we conclude
Using (1.2) and (1.3), we get
With (3.17) and (3.23), we can estimate
Then we conclude from (3.3), (3.4), and (3.15)
By using (3.8), we arrive at
while (3.9) yields
Combining (3.27)-(3.29), we conclude
Choosing ε as in (3.31), we obtain from (3.30)
The authors declare that they have no competing interests.
The paper is a joint work of all authors who contributed equally to the final version of the paper. All authors read and approved the final manuscript.
This paper was in part supported by the NNSF of China with contract numbers 11031003, 11271066 and a grant from Shanghai Education Commission 13ZZ048.
(in press)Publisher Full Text
Qin, Y, Zhang, M, Feng, B, Li, H: Global existence and asymptotic behavior of solutions for thermodiffusion equations. J. Math. Anal. Appl.. 408, 140–153 (2013). Publisher Full Text
Gawinecki, JA, Sierpinski, K: Existence, uniqueness and regularity of the solution of the first boundary initial value problem for the equation of the thermodiffusion in a solid body. Bull. Pol. Acad. Sci., Tech. Sci.. 30, 541–547 (1982)
Racke, R: Thermoelasticity with second sound-exponential stability in linear and non-linear 1-d. Math. Methods Appl. Sci.. 25, 409–441 (2002). Publisher Full Text
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CC-MAIN-2016-07
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https://paperanswers.com/peer-response-2/
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math
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Peer Response 2
·Your response should be at least 50 words.
We have been asked to Simplifying Radicals.
Today I got problem #94 which is
Which means that I have to get rid of the negative by using the Negative Exponent Rule.
By using the Power Rule my denominator 4 becomes my cubed root and the 1 is the exponent.
Since 3 is the cubed root of 81 we get
My Second problem was #62 which is
First I am going to FOIL.
I can simplify because the square root of 4 is 2 and the cancel each other.
9×2 = 18 -16
So the answer is 2.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711712.26/warc/CC-MAIN-20221210042021-20221210072021-00561.warc.gz
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CC-MAIN-2022-49
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