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https://informationtransfereconomics.blogspot.com/2018/04/what-about-those-markets.html

math

Two of the more hubris-laden forecasts I've made are for the stock and bond markets, specifically the S&P 500 (a dynamic information equilibrium model) and the 10-year Treasury rate (a basic information equilibrium model). The latest gyrations of both are well within the expected model error. Note that the 10 year forecast is the forecast of the green line which represents the trend around which the data fluctuates — by about 1.3 percentage points RMS (this error is shown as a lighter green band) — while the S&P forecast shows the 90% confidence bands for the data. Click to see the full resolution versions. For some additional perspective, here is the longer run for both (click to enlarge):

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https://www.saleh-theory.com/video/electron-tank-a-great-revolution-in-energy-1-kg-of-it-could-support-a-machine-for-years

math

Since the genetrix of photon is the electron and the photons emit from the electrons, in fact, the trajectory of each photon follows the type of motion of the electron. In this article, by using this motion, the motion of the photon was explained and its energy formula was presented. On the other hand, the structure of photons was explained. Universe is expanding at a constant linear velocity and over time the radius of the Universe, simply put, rotational radius, increases. So, in fact, our rotational velocity, which is affected by both the angular velocity parameter and the rotational radius, increases without any force being applied to it. In this paper we have justified the sphericity and the rotation of the Universe by Hubble's law, and we have calculated the real radius of the Universe and its actual rotational velocity by Hubble's law.

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https://www.teacherspayteachers.com/Product/Optimization-Scavenger-Hunt-3183038

math

This set of cards can be used to review the concept of optimizing a function. This would be a great activity for students in Calculus and AP Calculus classes. Each card has a problem written in black and an answer to another problem (in the magnifying glass). By using the 10 cards that have a ♡ at the bottom or you use the 10 cards with a ♧ you will have 10 cards scavenger hunt. If you use the 20 cards with a ♢ you will have a combined scavenger hunt with 20 cards. Suggestions for working with the cards: Post the cards around the classroom (either a set of 10 problems ♡, 10 problems ♧ or 20 problems ♢). The 10 set of ♡ problems focus on optimizing a function that related to a graph of a function and the 10 set of ♧ problems focus on optimizing a function that is related to a real world problem. When you use the 20 ♢ problems you will get both optimization problems. If you are using a 10 card set with a larger class you may want to make more than one copy of each question. Assign different students to start at different numbers. Distribute copies of the recording sheet to each student. Students should record the number of the card they are working on in the small square at the top left of the grid. When the work on the problem is complete, they then go on a scavenger hunt to find the card with their answer in the bottom right corner, in the magnifying glass of a new card. If they can’t find their answer they need to check their work again. When they find their answer on a card, they record that number in the next square and solve the new problem. Students keep working on problem for the allotted time. The goal would be to complete as many questions as they can in the allotted amount of time. Two cards have been designated at Graphing Calculator Problems. With these problems decimal answers with more than 3 decimal places have been rounded to three decimal places. On all other cards the answers be exact answers such as π/2 and not 1.571. Any calculations with numbers will be easy to complete by hand. Awards can be given for the number of problems completed by each student. This activity will get you students out of their seats and moving around the room. A complete set of solutions is provided that the teacher can use with any student who may be having difficulty solving a problem. Another way to use the cards is to pair the students up so two students are working together to solve a scavenger hunt. Comments from buyers: Great range of problems, thank you! Great way to get students to do several optimization problems without realizing it. Thank you! Fun activity. Gets the kids up and engaged. It is not a short activity though. Leave a good 45 minutes for the shortened piece. A full block of 90 minutes for the long piece of the activity.

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https://byjus.com/question-answer/q-consider-the-following-statements-about-drainage-patterns-when-a-river-originates-from-a-hill-2/

math

Q. Consider the following statements about drainage patterns: Which of the above given statements is/are correct? The correct option is B Statement 1 is incorrect: When a river originates from a hill and flows in all directions, the drainage pattern is known as 'radial'. Trellis drainage pattern is when the primary tributaries of river flow parallel to each other and secondary tributaries join them at the right angles. Statement 2 is correct: When the drainage pattern resembles the branches of a tree, it is known as 'dendritic'. Statement 3 is incorrect: When the rivers discharge their waters from all directions in a lake or depression, the drainage pattern is known as 'centripetal'.

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https://repositoriodigital.uct.cl/handle/10925/743

math

Skew-symmetric distributions generated by the distribution function of the normal distribution - In this paper we study a general family of skew-symmetric distributions which are generated by the cumulative distribution of the normal distribution. For some distributions, moments are computed which allows computing asymmetry and kurtosis coefficients. It is shown that the range for asymmetry and kurtosis parameters is wider than for the family of models introduced by Nadarajah and Kotz (2003). For the skew-t-normal model, we discuss approaches for obtaining maximum likelihood estimators and derive the Fisher information matrix, discussing some of its properties and special cases. We report results of an application to a real data set related to nickel concentration in soil samples.

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https://courses.bc.edu/course/MFIN/2250

math

MFIN 2250 Fixed Income Analysis (Fall/Spring: 3 ) This course presents the fundamental theoretical concepts of financial economics. Topics include measuring and managing interest rate risk, the theory of portfolio choice, and introduction to asset such as capital assets pricing models, arbitrage pricing theory, option pricing models and state-preference theory. Instructor(s): The Department Last Updated: 24-Jun-17

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http://www.residentadvisor.net/feed.aspx

math

4 hrs 5 mins ago  /  Max_Cherry DJ Broadcast examines the controversial service, which sells tracks for artists to re-sell as their own. 8 hrs 5 mins ago  /  RA Stefan Kozalla's podcast for FACT is every bit as lush and outlandish as you'd expect. 15 hrs 59 mins ago  /  samlouis The sampler for Trago's upcoming LP on Rush Hour features guest spots from Steffi and San Proper. 20 hrs 4 mins ago  /  808heinz808 The electronic music veteran, who famously every track from his 1999 album , is making much of his recorded output available to indie, non-profit and student filmmakers for free. 1 day ago  /  Bill_Lee Hotflush have released a clip for the duo's banging new single. 1 day 4 hrs ago  /  HerrJordan Kristan Caryl takes a look at the old-school streak running through current dance music on 1 day 8 hrs ago  /  RA The group gets dark on this mix for , stitching together tracks from Markus Suckut and Forward Strategy Group, along with cuts from their recently-released 1 day 12 hrs ago  /  aaroncoultate Electronic Beats speak to the Diagonal Records chief about why he avoids reverb, his musical influences and playing the Hitler-sampling "Warbeat" track at Berghain. 1 day 15 hrs ago  /  p_adkins stars explain why they made the shift to techno in an interview with 1 day 19 hrs ago  /  andrewryce Glaswegian producer Auntie Flo talks to FACT about the complex history and current status of the loaded "world music" term. 1 day 23 hrs ago  /  Birdmanzz The Guardian profiles the highly influential English imprint, currently celebrating 21 years in the business. Viewing 1 - 12 of 7,879 feed items Found a rad video on YouTube, a jaw-dropping new DJ set or an interesting interview on the web? RA members can share URLs with the world in RA's new section The Feed, a wholly contributor-run section of site. The more creative and interesting you make your posts, the more chance they have of getting mod approval and appearing on the front page of RA. You can About the Feed submit posts for The Feed from your . My Feeds page The Feed RSS

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https://www.iop.vast.ac.vn/theor/publication.php?l=0&id=806&lang=en

math

Theoretical and Mathematical Physics 165(2) , 1500–1511 (2010) Symmetry Factors of Feynman Diagrams for Scalar Fields P. V. Dong, L. T. Hue, H. T. Hung, H. N. Long, and N. H. Thao We calculate the symmetry factors of diagrams for real and complex scalar fields in general form using an analysis of the Wick expansion for Green’s functions. We separate two classes of symmetry factors: factors corresponding to connected diagrams and factors corresponding to vacuum diagrams. The symmetry factors of vacuum diagrams play an important role in constructing the effective action and phase transitions in cosmology. In the complex scalar field theory, diagrams with different topologies can contribute the same, and the inverse symmetry factor for the total contribution is therefore the sum of the inverse symmetry factors.

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http://www.advrider.com/forums/showpost.php?p=22180144&postcount=36

math

Thanks...I can't stop thinking about the trip. .up amd downs. I am seriously thinking about doing it again in reverse , being familiar with it may be a little easier. Loved the experience though sent from my Illudium Q-36 explosive space modulator $$$FULL TILT BOOGIE$$$ Pain heals. Chicks dig scars. Glory... lasts forever.

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https://forums.yoyoexpert.com/t/how-do-i-do-these-two-arm-tricks/12197

math

How do I do these two arm tricks? July 12, 2018, 10:57pm How do I do the two around the arm trick at 00:35-00:39? I tried to bend my hand out enough to get the yoyo in there but it doesn’t seem to give enough space for the yoyo. Thanks!

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http://www.buenastareas.com/ensayos/Euclid/1825080.html

math

"Euclid" is the anglicized version of the Greek name(Εὐκλείδης — Eukleídēs) , meaning "Good Glory". Euclid in Raphael's School of AthensBorn fl. 300 BC Residence Alexandria, Egypt Known for Euclidean geometryEuclid's Elements LifeLittle is known about Euclid's life, as there are only a handful of references to him. The date and place of Euclid's birth and the date and circumstances of his death are unknown, and only roughly estimated in proximity to contemporary figures mentioned inreferences. No likeness or description of Euclid's physical appearance made during his lifetime survived antiquity. Therefore, Euclid's depiction in works of art is the product of the artist's imagination. The few historical references to Euclid were written centuries after he lived, by Proclus and Pappus of Alexandria. Proclus introduces Euclid only briefly in his fifth-century Commentary on theElements, as the author of Elements, that he was mentioned by Archimedes, and that when King Ptolemy asked if there was a shorter path to learning geometry than Euclid's Elements, "Euclid replied there is no royal road to geometry." Although the purported citation of Euclid by Archimedes has been judged to be an interpolation by later editors of his works, it is still believed that Euclid wrote hisworks before those of Archimedes. In addition, the "royal road" anecdote is questionable since it is similar to a story told about Menaechmus and Alexander the Great. In the only other key reference to Euclid, Pappus briefly mentioned in the fourth century that Apollonius "spent a very long time with the pupils of Euclid at Alexandria, and it was thus that he acquired such a scientific habit ofthought." It is further believed that Euclid may have studied at Plato's Academy in Athens. ElementsAlthough many of the results in Elements originated with earlier mathematicians, one of Euclid's accomplishments was to present them in a single, logically coherent framework, making it easy to use and easy to reference, including a system of rigorous mathematical proofs that remains the basis ofmathematics 23 centuries later. There is no mention of Euclid in the earliest remaining copies of the Elements, and most of the copies say they are "from the edition of Theon" or the "lectures of Theon", while the text considered to be primary, held by the Vatican, mentions no author. The only reference that historians rely on of Euclid having written the Elements was from Proclus, who briefly inhis Commentary on the Elements ascribes Euclid as its author. Although best-known for its geometric results, the Elements also includes number theory. It considers the connection between perfect numbers and Mersenne primes, the infinitude of prime numbers, Euclid's lemma on factorization (which leads to the fundamental theorem of arithmetic on uniqueness of prime factorizations), and theEuclidean algorithm for finding the greatest common divisor of two numbers. The geometrical system described in the Elements was long known simply as geometry, and was considered to be the only geometry possible. Today, however, that system is often referred to as Euclidean geometry to distinguish it from other so-called non-Euclidean geometries that mathematicians discovered in the 19th century....

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https://melbrownjazzcamp.com/15dnty07/nT1725wD/

math

By h0mT0kt03tY0nK. Kindergarten Worksheets. At Monday, May 11th 2020, 21:54:18 PM. With the dawning of technology, there is no need to hate Math at school or when practicing at home. With a Math software, children starts to develop their confidence and increase their math skills with simple arithmetic calculations. Learners practice performing simple calculations, without the aid of a calculator, as well as to develop recognition and recall of answers to math practice problems at a pace that they can handle with confidence. Other interactive math software programs have a reading and comprehension level that is appropriate for Grades 3 and up and are valuable tools for students in upper elementary and middle school, who are looking to build confidence in performing basic math operations quickly. To practice mathematics, math workbooks are the good source. You learn a concept in a workbook, then in the same booklet there are more problems on the same concept for practice. Another good method to practice mathematical concepts is using math worksheets and you can print math worksheets free of charge from the web. Finally, choice is yours. You can choose the jumping method to reach your math destination or you can use right and proven path to reach your math destination. The right and proven path to math destination has the following steps: Start learning math as soon as you start your kindergarten, Focus in your math classes and listen to your teacher, Ask your teacher lots of question until you are not clear about the concept you are learning. NEVER use "skill and drill" worksheets. These are the worksheets just made up of columns of problems. There are better materials out there, so do not resort to skill and drill. The very worst problem of skill and drill worksheets is the greatly increased chance of a practiced mistake. The same problem will likely appear several times on the same sheet. A wrong answer once means a wrong answer several times; and a practiced mistake takes hundreds of correct repetitions to fix. This danger alone is important enough to never use any worksheet. I am quite serious about how difficult it is to repair a practiced mistake. Learning is hard enough. Re-learning is much more difficult.

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https://www.easynotecards.com/search_all?q=subject%3A%22algebra%22&s=0&img=0&va=1&si=31

math

#1. Linear function - a function in which the graph is a line. #2. parent function - The simplest linear function; f(x) = x #3. Family of graphs - a group of graphs with one or more similar charact... 2474|6 years ago|±0|11 views 4.1 Solving with Graphing #1. Use the graph to find the solution for x2-9=y - x=3 and x=-3 (Hint: Read the boxed information on the bottom of page 324 in your textbook) #2. Use the graph to find the solution for 0.25x3+x2−4.... Joanne_Sullivan_Kiriazes|4 years ago|±0|21 views Basic Properties of Logarithms #1. logb 1=? - 0 #2. logb b=? - 1 #3. logb bx=? - x #4. blogbx = ? - x Joanne_Sullivan_Kiriazes|4 years ago|±0|25 views Academic Vocab-Category #28-33 #1. Graph of an Inequality #2. Linear Equation: Slope-Intercept equation - y = mx + b (slope is m and y-intercept is b) daniel_dickinson|6 years ago|±0|5 views Match the graph to its parent function equation Joe_Minyon_Jr_|6 years ago|±0|14 views Academic Vocab - Relations and Functions (15-20) #1. linear function - Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and on... baileybowdenn|6 years ago|±0|8 views #1. Variance - The mean of the squares of the differences between each element and the man of the data set #2. Standard Deviation - The square root of the mean of the squares of the differences be... ironbat235|6 years ago|±0|9 views What are the transformations made to the basic function? Joanne_Sullivan_Kiriazes|4 years ago|±0|22 views 3.1 Parent Functions #1. x2 =y Quadratic #2. |x|=y Absolute Value #3. y=x3 Cube #4. Square Root #5. y=x Identity #6. y=1/x Reciprocal Joanne_Sullivan_Kiriazes|4 years ago|±0|32 views

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https://quiltedsunshine.blogspot.com/2010/08/stone-soup-project.html

math

Tuesday, August 3, 2010 Stone Soup Quilt Project For our next Humanitarian project, I've come up with the Stone Soup Quilt Project. It's a combination of my Denim Stars, Fun-and-done, and a rag quilt. Here's a Wikipedia link if you don't know the Stone Soup story. http://en.wikipedia.org/wiki/Stone_soup. Basically, a community brings together scraps of food, and makes a really great soup that is shared with the whole community. So, this quilt is done with scraps that have been donated. I give each participant squares of flannel, regular cotton fabrics, and batting squares (all pre-cut into squares). They each take a row or two home to sew. When the rows are complete, we will get together and sew the rows into a quilt. Start with 6" squares of flannel, 4 3/4" squares of regular cotton fabrics, and 4 3/4" squares of thin cotton or cotton/poly batting. Here are some sizes you may want to use: Baby (35" X 45") 7 squares X 9 squares = 63 squares Throw (55" X 70") 11 squares X 14 squares = 154 squares Twin (70" X 85") 14 squares X 17 squares = 238 squares Queen (90" X 105") 18 squares X 21 squares = 378 squares

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https://assistancedogseurope.info/and-relationship/molarity-and-molality-relationship-to-boiling.php

math

How to Calculate Melting & Boiling Points Using Molality | Sciencing As the molality changes, it affects the boiling point and freezing point (also or freezing point of any solution will be using a simple equation. Whenever a non-volatile substance is dissolved in a solvent, the boiling point of the solvent increases. The higher the concentration (molality). Though only one letter different than molarity, molality is a unique unit of concentration. This relationship is based the density of water, which is 1 g/mL. Freezing point depression and boiling point elevation are examples of colligative. When a solution is made of two or more liquids, it is not feasible to identify a solute and solvent. In this situation, liquids are said to be miscible they dissolve in one another or immiscible. Oil and vinegar provide an example of two liquids that are immiscible because they do not dissolve in one another. Concentration - Molarity Quantitatively, concentration is important for determining the relative amount of solute dissolved per unit of solution. There are many units used for measuring the concentration of a solution. Molarity measures the number of moles of solute dissolved per liter of solution. It is important for stoichiometric calculations as it is one of the few units that quantifies moles of solute, and the only unit that does so in terms of the volume of solution. The formula used for calculating molarity is given below. The variable nsolute represents the the number of moles of solute, and Vsolution represents the volume of the solution, in liters or dm3. Problems - Molarity Example 1 - Find the molarity of solution that can be made by dissolving 3. Freezing and Boiling Points There are two important reminders to keep in mind here. The first is that the molarity formula does not gave a variable in which mass can be substituted. The mass of solute must always be converted to moles before using the molarity formula. The second is that the molarity formula requires that the volume is given in liters. Determining Molar Mass For this reason, Example 2 - Determine the mass of potassium bromide needed to make Concentration - Molality Though only one letter different than molarity, molality is a unique unit of concentration. It measures the moles of solute per kilogram of solvent. In an aqueous solution i. One liter mL of water should have a mass of g, which is one kilogram. Therefore, one kilogram of water occupies a volume of one liter. This relationship works for water solutons only! The formula used for calculating the molality of a solution is given below note the molality is represented by the variable b: In this equation nsolute represents the number of moles of solute in the solution. How does molality affect the boiling point? The variable msolvent represents the mass of the solvent, in kilograms. Numerically, for aqueous solutions the molarity and molality are similar, but not identical in value. Electrolytes An electrolyte is a compound that dissociates into ions when dissolved in water. The level of dissociation is important, and serves as the means of further classifying compounds as either strong or weak electrolytes. The boiling point data for some solvents are provided in Table 1. Notice that the change in freezing or boiling temperature depends solely on the nature of the solvent, not on the identity of the solute. One valuable use of these relationships is to determine the molecular mass of various dissolved substances. As an example, perform such a calculation to find the molecular mass of the organic compound santonic acid, which dissolves in benzene or chloroform. A solution of 50 grams of santonic acid in grams of benzene boils at Referring to Table for the boiling point of pure benzene, the boiling point elevation is That concentration is the number of moles per kilogram of benzene, but the solution used only grams of the solvent. The moles of santonic acid is found as follows: You can also find this value by using the freezing point of the solution. In the two previous examples, the sucrose and santonic acid existed in solution as molecules, instead of dissociating to ions. The latter case requires the total molality of all ionic species. Calculate the total ionic molality of a solution of

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https://www.tutorialsmagnet.com/edu/edu-512/fair-coin-experiment/

math

Fair Coin Experiment The following table shows the outcome recorded from flipping a fair coin 40 times |Trial numberstart upoutcomeTotal number of heads% heads1HT002TT003HT004TH1255HH2406TT233.337HH342.868TT337.59HH444.4410TH55011HH654.5512TH758.3313HH861.5414TT857.1415HT853.3316TH956.2517HT952.9418TT95019HH1052.6320TH115521HH1257.1422TH1359.0923HT1356.5224TT1354.1725HH145626TT1453.8527HT1451.8528TH1553.5729HH1655.1730TT1653.3331HH1754.8432TH1856.2533HT1854.5534TT1852.9435HH1954.2936TH2055.5637HH2156.7639TH2256.4139HH2358.9740TT2357.5 A fair coin is an idealized randomizing device with two states, head and tail, which are equally likely to occur. The practical problem of checking whether a coin is fair is considered as easily solved by performing a sufficiently large number of trials, for this case 40 (Papoulis & Pillai, 2002). The mean percentage of heads for each trial in the experiment is 48.34 as shown in the table below. This figure is approximately average. We can therefore say the probability of the coin falling on either side when flipped is almost 50%. Hence, the coin has been experimentally proven to be fair (Papoulis & Pillai, 2002). Below is a graph of percentage of heads against trial number. The graph shows an approximately normal behavior. It’s clear that what is seen in the graph align with what is in the table of experiment outcomes. Coin flipping is a simple and unbiased way of settling a dispute or deciding between two or more arbitrary options (Papoulis & Pillai, 2002). It is widely used in sports to decide arbitrary factors such as which side of the field a team will play from, or which team gets first use of the ball in football matches. Such decisions may tend to favor one side or maybe neutral. Flipping a coin helps make such decision without anyone of the teams complaining since flipping a coin is statistically proven to be fair. Papoulis, A., & Pillai, S. U. (2002). Probability, random variables, and stochastic processes. Tata McGraw-Hill Education. Place an Order

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https://support.gurobi.com/hc/en-us/community/posts/4440107926801-Algorithms-and-solution-methods-to-verify-the-solution-from-gurobi

math

I have the following objective function: where is the only positive decision variable. is a function of . is equivalent to given in the equality constraint below. Other variables are positive constants except a = -4.092*(10^-4), b = -2.167. c = 1.408*(10^-5), d = 6.130. The plot of the objective function is shown below: y is and x is . The objective function value, is z. We are minimizing a concave objective (continuous surface). The constraints are given below: We are minimizing this concave objective so it is a non-convex optimization problem. What are the algorithms used in gurobi that will search for a solution with an objective of this form with sum of exponentials that are functions of a first order term (and with first order term multiplying one exponential term) then all of that multiplying a first order term? Are the solutions optimal or sub-optimal? I want to verify gurobi solution by implementing this algorithm. I have tried 2 pieces of 2nd order polynomials to estimate this surface in Gurobi but even then what algorithms or analytical techniques are used to find the minimum? But what if I want to keep it as accurate as possible by using this exact objective function? What are the analytical techniques then? When I use the exact objective function some solutions take longer to solve than others. Basically, I want to have a algorithm/technique so that I know what is happening when the solution is found. Then I will be able to compare this theoretical solution and Gurobi output. Please also refer me to any papers if possible. Please sign in to leave a comment.

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https://kidmathworld.com/2020/04/07/definitions-and-shapes-day-13-at-home/

math

Learn more about shapes. Count shapes. If you have been reading my posts (thank you!), you probably know I am reluctant to dictate or impose my reasoning. Sometimes though, it is necessary because we need to define things. Supplies: paper, pencil, scissors. Draw shapes on (triangles, squares, rectangles, quadrilaterals). You can cut them out if you want. What to do: 1) Explain to your child that sometimes, we need to explain words or terms so everyone knows what we are talking about. It's called a definition. A good way to introduce the notion is through homonym (words that sound alike), for example, say "flower" and "flour". 2) Invite your child to find other examples. Then ask him/her to explain or define each of the meaning. 3) Then move to math and define - a triangle: A shape with 3 sides. - a quadrilateral: A shape with 4 sides. Depending on the reactions, the definitions might need to be refined: closed shape or straight sides, etc. 4) Explain what a right angle is by showing a lot of examples. And say that "A rectangle is defined to be a shape with 4 right angles". Then ask them to draw different rectangles. Or sort or count how many rectangles there are in the pictures drawn. 5) There are 3 rectangles in the picture below. Can you find them? 6) How many rectangles are there? 7) How many triangles in the picture below? How it went For 1) Bel came up with “fair”. Then Nia wanted to have a turn and said “Megaman” (we have some figurines around) and “fan”. I pounced on “fan” and said it was a good example. Bel came up with “box” and “bound”. Then Nia wanted to participate and said “backpack” as in a bag you put on your back and something you fill with things (?). I wasn’t quite sure. I told that in math, we need definitions too and gave them the one for triangle and quadrilateral. I showed them what a right angle was by pointing at the corner of a sheet of paper and told them that a rectangle was a quadrilateral – what is a quadrilateral again? – with four right angles. When they got the first picture, I asked them how many rectangles they saw. Bel immediately said “3!”, which surprised me. I asked her to show me and she correctly added the large one around everything. Nia said 2. In the next picture, Nia went first and said 5. She would not show me the rectangles. She counted the four small ones and I didn’t understand which one was her fifth one. I asked her to trace around it but she did not do it. I asked her to color them, she colored the four little ones with four different colors. Finally, I asked her how many rectangles were in this picture and she correctly told me there were 5 rectangles and traced them. I think that she sees the little ones and then tries to get the ones around the outer borders. In the case below, she could get the last two ones. Bel figured out that the answer was 9 and was moving on to making her own crazy problems. We both had it wrong at first: I was missing the 1×3 rectangles, and she was missing the 2×2 ones. Then I showed her how to do it systematically: count the - the smaller “1×1” rectangles (6) - the “1×2” which are two squares next to each other (4) - the “2×1” which are two squares stacked on each other (3) - the “1×3” - the “2×2” - the “2×3” We did not get to do the triangle one.

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CC-MAIN-2020-40

https://repository.lboro.ac.uk/articles/The_numerical_solution_of_quadratic_matrix_equations/9374129

math

The numerical solution of quadratic matrix equations 2015-02-06T16:41:14Z (GMT) by Methods for computing an efficient and accurate numerical solution of the real monic unilateral quadratic matrix equation, are few. They are not guaranteed to work on all problems. One of the methods performs a sequence of Newton iterations until convergence occurs whilst another is a matrix analogy of the scalar polynomial algorithm. The former fails from a poor starting point and the latter fails if no dominant solution exists. A recent approach, the Elimination method, is analysed and shown to work on problems for which other methods fail. . The method requires the coefficients of the characteristic polynomial of a matrix to be computed and to this end a comparative numerical analysis of a number of methods for computing the coefficients is performed. A new minimisation approach for solving the quadratic matrix equation is proposed and shown to compare very favourably with existing methods . . A special case of the quadratic matrix equation is the matrix square root problem, where P = o. There have been a number of method proposed for it's solution, the more successful ones being based upon Newton iterations or the Schur factorisation. The Elimination method is used as a basis for generating three methods for solving the matrix square root problem. By means of a numerical analysis and results it is shown that for small order problems the Elimination methods compare favourably with the existing methods. The algebraic Riccati equation of stochastic and optimal control is, where the solution of interest is the symmetric non-negative definite one. The current methods are based on Newton iterations or the determination of the invariant subspace of the associated Hamiltonian matrix. A new method based on a reformulation of Newton's method is presented. The method reduces the work involved at each iteration by introducing a Schur factorisation and a sparse linear system solver. Numerical results suggest that it may compare favourably with well-established methods. Central to the numerical issues are the discussions on conditioning, stability and accuracy. For a method to yield accurate results, the problem must be well-conditioned and the method that solves the problem must be stable-consequently discussions on conditioning and stability feature heavily in this thesis. The units of measure we use to compare the speed of the methods are the operations count and the Central Processor Unit (CPU) time. We show how the CPU time accurately reflects the amount of work done by an algorithm and that the operations counts of the algorithms correspond with the respective CPU times.

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CC-MAIN-2019-35

http://millerreport.blogspot.com/2010_10_12_archive.html

math

I'm sure there will be a slew of miner cartoons in the next few days. My hubby Jack helped with this one. Anybody miss that jerk Sanchez? Not me. Hard hats are really hard to draw, harder than cowboy hats but easier than ball caps. Caves aren't easy either .

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http://slideplayer.com/slide/6815513/

math

2 Parallel LinesParallel lines exist everywhere, if you look for them. Here are some examples of parallel lines. 3 These are lines that never intersect. Parallel LinesThese are lines that never intersect.Intersect means that the lines never touch, they always stay the same distance from each other.For Example:These two pencils are parallel 4 What are not parallel lines? Any lines that intersect are not parallel. 5 Share with your partner Look around the room and see if you can find any parallel lines. What do you see?_____________ has parallel lines.Explain to your partner what a parallel line is and where you can find them.Parallel lines are _______________and you can find them ______________. 6 Pairs of Parallel Lines When we are talking about parallel lines, we are always talking about pairs of parallel lines.What is a “pair”?How many are in a pair?Let’s look at this… 7 What things come in pairs? Things that come in pairs 9 “Pairs”All of these things are pairs, but how many are in the pair?Tell your partner how many socks are in a pair.That’s right, 2!!! 10 Let’s see if you get this… Pairs2 socks = 1 pair of socks 2 shoes = 1 pair of shoes 1 pair of crutches = 2 crutches 1 pair of eyes = 2 eyes 2 hands = 1 pair of handsGood Job!!Let’s see if you get this… 11 Polygons with Parallel Lines Some polygons have parallel lines.Remember, you have to have 2 lines (pair) to make 1 pair of parallel lines.Let’s take a look 12 Parallel lines exist in geometry If you look at polygons you can find parallel lines. Remember that parallel lines never touch. 13 Can you guess which polygon has parallel lines Can you guess which polygon has parallel lines? Talk to your partner and explain which polygon has parallel lines: The polygon on the right/left has parallel lines because ________________. 14 Count the pairs of parallel lines in the polygons 2This shape has _______ pairs of parallel lines.2 pairs1 pair2This shape has _______ pairs of parallel lines.1 pair2 pairs1 pair1This shape has _____ pairs of parallel lines. 15 Find how many pairs of parallel lines are in the polygons. 17 We learned that the prefix quadri means 4, and that a polygon with four sides is called a quadrilateral. Let’s take a look at some different types of quadrilaterals. 18 quadrilaterals How do you know if a polygon is a quadrilateral? If a polygon has 4 sides, it isquadrilateral.The sides and angles arewhat determine the typeof quadrilateral it is.1423 19 square The perfect quadrilateral. What makes a square? A square has 4 equal sides.A square has 4 right angles. 20 rectangle What makes a rectangle? A rectangle has 2 pairs of equal sides.A rectangle has 4 right angles.That means that a square is also a rectangle.Turn to your partner and tell them why a square is a rectangle.A square is a rectangle because ________________. 21 rhombus The rhombus is the cousin of the square. A rhombus has 4 equal sides.But, a rhombus can have any angles.That means that a square is also a rhombus.Turn to your partner andTell them why a square isA rhombus.A square is a rhombus because ________________________. 22 parallelogram The parallelogram is the cousin of the rectangle. A parallelogram has 2 pairs of equal sides.But, a parallelogram can have any angles.Talk to your partner. Do you think that a square or a rectangle is a parallelogram. Why? 23 my turnWhich figure has two pairs of equal sides? A circle B hexagon C rectangle D octagon 24 your turnWhich figure always has 4 equal sides? A circle B hexagon C rectangle D square 25 my turnOne side of a rectangle is 3 ins. long. Another side is 7 ins. long. What are the lengths of the other sides of the rectangle? A They could be any length B 3 ins. and 3ins. C 7 ins. and 7 ins. D 3 ins. and 7 ins.7 in3 in3 in7 in 26 your turnOne side of a square is 5 cms. long. What are the lengths of the other sides of the square? A 5 cms B 10 cms C 15 cms D 20 cms5 cms5 cms5 cms5 cms 27 So what did you learn today? What is a pair?A pair is ________________________.What are parallel lines?Parallel lines are __________________.What is a quadrilateral?A quadrilateral is __________________.What are the 4 different types of quadrilaterals?___________, ___________, __________, and ___________ are different types of quadrilaterals.

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https://www.primidi.com/new_foundations/models_of_nfu

math

Models of NFU There is a fairly simple method for producing models of NFU in bulk. Using well-known techniques of model theory, one can construct a nonstandard model of Zermelo set theory (nothing nearly as strong as full ZFC is needed for the basic technique) on which there is an external automorphism j (not a set of the model) which moves a rank of the cumulative hierarchy of sets. We may suppose without loss of generality that . We talk about the automorphism moving the rank rather than the ordinal because we do not want to assume that every ordinal in the model is the index of a rank. The domain of the model of NFU will be the nonstandard rank . The membership relation of the model of NFU will be We now prove that this actually is a model of NFU. Let be a stratified formula in the language of NFU. Choose an assignment of types to all variables in the formula which witnesses the fact that it is stratified. Choose a natural number N greater than all types assigned to variables by this stratification. Expand the formula into a formula in the language of the nonstandard model of Zermelo set theory with automorphism j using the definition of membership in the model of NFU. Application of any power of j to both sides of an equation or membership statement preserves its truth value because j is an automorphism. Make such an application to each atomic formula in in such a way that each variable x assigned type i occurs with exactly applications of j. This is possible thanks to the form of the atomic membership statements derived from NFU membership statements, and to the formula being stratified. Each quantified sentence can be converted to the form (and similarly for existential quantifiers). Carry out this transformation everywhere and obtain a formula in which j is never applied to a bound variable. Choose any free variable y in assigned type i. Apply uniformly to the entire formula to obtain a formula in which y appears without any application of j. Now exists (because j appears applied only to free variables and constants), belongs to, and contains exactly those y which satisfy the original formula in the model of NFU. has this extension in the model of NFU (the application of j corrects for the different definition of membership in the model of NFU). This establishes that Stratified Comprehension holds in the model of NFU. To see that weak Extensionality holds is straightforward: each nonempty element of inherits a unique extension from the nonstandard model, the empty set inherits its usual extension as well, and all other objects are urelements. The basic idea is that the automorphism j codes the "power set" of our "universe" into its externally isomorphic copy inside our "universe." The remaining objects not coding subsets of the universe are treated as urelements. If is a natural number n, we get a model of NFU which claims that the universe is finite (it is externally infinite, of course). If is infinite and the Choice holds in the nonstandard model of ZFC, we obtain a model of NFU + Infinity + Choice. Read more about this topic: New Foundations Other articles related to "models of nfu, model, nfu": ... The automorphism j of a model of this kind is closely related to certain natural operations in NFU ... For example, if W is a well-ordering in the nonstandard model (we suppose here that we use Kuratowski pairs so that the coding of functions in the two theories will agree to some ... In fact, j is coded by a function in the model of NFU ... Famous quotes containing the words models of and/or models: “The parents who wish to lead a quiet life I would say: Tell your children that they are very naughtymuch naughtier than most children; point to the young people of some acquaintances as models of perfection, and impress your own children with a deep sense of their own inferiority. You carry so many more guns than they do that they cannot fight you. This is called moral influence and it will enable you to bounce them as much as you please.” —Samuel Butler (18351902) “The greatest and truest models for all orators ... is Demosthenes. One who has not studied deeply and constantly all the great speeches of the great Athenian, is not prepared to speak in public. Only as the constant companion of Demosthenes, Burke, Fox, Canning and Webster, can we hope to become orators.” —Woodrow Wilson (18561924)

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http://www.johnagowan.org/gravity30.html

math

(Revised Oct., 2010) John A. Gowan home page (page 1) home page (page 2) Note to Readers Concerning "Entropy": 10) Does matter have an intrinsic spatial motion? The primordial conservation role of gravity is to provide negative energy sufficient to exactly balance the positive energy of the "Creation Event", so the universe can be born from a state of zero net energy as well as zero net charge (the latter due to the equal admixture of matter with antimatter). All subsequent conservation roles of gravity are secondary to and derived from this original creation-role. Following on from its primary role of providing negative energy during the "Big Bang", gravity plays two further major conservation roles in the evolving universe: 1) conserving the spatial entropy drive of light; 2) conserving the non-local distributional symmetry of light. In its entropy conservation role, gravity converts the intrinsic motion of light to the intrinsic motion of time - via the annihilation of space and the extraction of a metrically equivalent temporal residue. In its symmetry conservation role, gravity converts bound to free energy in stars and via Hawking's "quantum radiance" of black holes. These two conservation roles derive from the double gauge role of "velocity c", which regulates both light's intrinsic motion (the entropy drive of free electromagnetic energy), and light's non-local distributional symmetry (vanishing time and distance). Conserving light's non-local energy state via "location" charge, gravity simultaneously conserves light's entropy drive, since time itself is the active principle of "location" charge. Hence gravity's entropy conservation role is by default brought under the mantle of Noether's symmetry conservation theorem, revealing a pathway to the unification of gravitation with the other forces of physics: all charges of matter are symmetry debts of light. IntroductionIn the temporal/historical domain, the graviton plays a role similar to the photon's role in the spatial domain. We might therefore say the graviton is the "photon of time". As the photon is the entropy drive of space, creating, expanding, and cooling the spatial dimensions via its intrinsic motion, so the graviton is the entropy drive of time, creating, expanding, and aging the historical dimension. (added June 2013) Indeed, the graviton is hidden or implicit in the photon as an asymmetric temporal component (necessarily implied by light's "frequency"). This hidden temporal component is revealed in its explicit form when the free energy of the symmetric (non-local) moving photon is converted to the bound energy of asymmetric (local) immobile mass/matter. The intrinsic (pos-entropic) motion of light is thus instantly converted into the intrinsic (neg-entropic) motion of time, establishing and entraining matter's self-feeding and self-perpetuating gravitational field - which creates (reveals) time via the annihilation of (metrically equivalent) space. The non-local symmetric photon is converted to the local asymmetric graviton, whose intrinsic, negentropic, one-way, spatially contractile motion into the historic domain identifies the spatio-temporal location of the asymmetric (because undistributed) concentration of immobile mass-energy (matter). The 4th dimension of time is necessary to exactly specify the 3-D location of matter within a constantly expanding spatial domain. Time is therefore the active element of matter's gravitational symmetry debt or "location" charge. Bound energy's (matter's) gravitational symmetry debt of "location" arises whenever light's non-local, symmetrically distributed energy (moving freely with intrinsic motion "c") is converted into local concentrations of immobile mass-matter. (See: "The Conversion of Space to Time".) Both space and history are entropy domains which function to guarantee (via their "infinite" velocity or their one-way character) the conservation of energy within their respective domains: space for free electromagnetic energy (light), history for bound electromagnetic energy (matter). As matter is an alternative form of light, so time is an alternative entropy drive of light - creating history as an alternative form of space. Charge is an alternative form of symmetry; gravity is an alternative form of inertia. The negative energy and entropy of gravity are necessary to balance the positive energy and entropy of light, allowing the Universe to be born from zero net energy and zero net charge (when we include the primordial/original antimatter). (See: "Spatial vs Temporal Entropy".) The gravitational metric is the temporal metric of matter, directed oppositely to the spatial metric of light, contractile and inwardly directed rather than expansive and outwardly directed in its spatial expression (but expansive in its historical expression). The historical/temporal dimension is at right angles to all three spatial dimensions simultaneously. Time is one-way due to the linkage between causality and energy conservation. A gravitational field is the spatial consequence of the intrinsic motion of time. We live in a universe composed of both free and bound forms of electromagnetic energy (light and matter), space and time (their respective conservation/entropic domains), and a combined spatio-temporal metric gauged by the universal electromagnetic constant "c" and the universal gravitational constant "G". The gravitational metric modifies the spatial metric by the creation of time from space - annihilating space and replacing it with a metrically equivalent temporal residue. The temporal/gravitational component of the combined metric becomes increasingly dominant as matter concentrations grow increasingly greater and denser. Ultimately, the gravitational/temporal metric of matter completely displaces the spatial metric of light at the "event horizon " of a black hole. At the "event horizon", space vanishes and time "stands still" - one second of time becoming of infinite duration where g = c. This ultimate, local, temporal/gravitational metric of matter is in contradistinction to a pure, non-local, spatial/electromagnetic metric of light - in which space stands still and time vanishes. Gravity is united with the other forces through Noether's Theorem of symmetry conservation - all four forces are caused by charges which arise as symmetry debts of light - when freely moving, non-local forms of electromagnetic energy are converted to bound, immobile, local forms of electromagnetic energy. See: "A Rationale for Gravity"; and "Symmetry Principles of the Unified Field Theory". The gravitational symmetry debt is repaid via the conversion of bound to free energy (mass to light) in various gravitationally driven astrophysical processes, such as stars, supernovas, quasars, etc. The final and total gravitational conversion of mass to light is accomplished via Hawking's "quantum radiance" of black holes, completely fulfilling the symmetry conservation mandate of Noether's Theorem, and completely repaying the symmetry debt of gravity's "location" charge. (See: "Noether's Theorem and Einstein's Interval".) 1) Gravity plays a double conservation role in nature, conserving: A) the spatial entropy drive of free electromagnetic energy, converting light's intrinsic motion to the historical entropy drive of bound electromagnetic energy - time's intrinsic motion. This gravity accomplishes by the annihilation of space, which reveals a temporal residue, the metric equivalent of the collapsed space. Because entropy is an embedded corollary of energy conservation, this is gravity's major energy conservation role, seen from elementary particles to galaxies and cosmological spacetime. B) the non-local distributional symmetry of light's energy - as required by "Noether's Theorem". This gravity accomplishes by the conversion of bound electromagnetic energy (mass) to free electromagnetic energy (light), in stars, supernovas, quasars, etc., and ultimately and completely, by Hawking's "quantum radiance" of black holes. The two conservation roles of gravity are a consequence of the double regulating role of "velocity c", the electromagnetic constant, which gauges both the entropy drive of free energy (light's intrinsic motion), and the "non-local" distributional symmetry of light's energy. The "intrinsic" (entropic) motion of light creates, expands, and cools the spatial cosmos; "velocity c" also vanishes the time dimension and a single spatial dimension (in the direction of propagation): clocks stop and meter sticks shrink to nothing at the speed of light (metric and distributional symmetry function). Light therefore acquires an "infinite" velocity in its own reference frame, having forever to go nowhere. Light is a 2-dimensional transverse wave whose intrinsic (entropic) motion "sweeps out" a third spatial dimension. When gravity conserves either gauge function of "velocity" c (in accordance with Noether's Theorem and the requirements of energy and/or symmetry conservation), it conserves the other by default. Space is the conservation domain of free electromagnetic energy, created by light's own embedded entropy drive (intrinsic motion). 2) Like the other four forces of physics, gravity is the consequence of a charge which arises as a symmetry debt of light. "Noether's Theorem" requires that the symmetry of light, no less than the energy of light, be conserved. The charges of matter are the symmetry debts of light. Identifying the (broken) symmetries of light from which the charges and their associated forces arise provides a simple conceptual basis for a Unified Field Theory: all forces trace back to a common origin as symmetry debts of light - just as all matter finds the origin of its energy in light. Matter is an asymmetric, bound form of light whose symmetries are conserved as charge and spin, whose energy is conserved as mass and momentum, and whose entropy drive or intrinsic motion is conserved as time/gravity. All matter's inherent charges and forces work spontaneously and incessantly to return matter to its primordial symmetric form - as our Sun bears daily witness. In the case of gravity, the charge (carried by all forms of bound energy in amount Gm) is the "location" charge, whose active principle is time. "Location" charge identifies the 4-dimensional spacetime location of immobile, undistributed bound energy, which as we have seen above, breaks the non-local distributional symmetry of light's free energy as gauged by "velocity c" (because mass has no intrinsic spatial motion), and results in the eventual return of bound to free energy, as we should expect (in stars, for example). (See: "The Double Conservation Role of Gravity".) 3) Gravity is the spatial consequence of the intrinsic motion of time. Time is the active principle of the gravitational "location" charge. Time has "intrinsic" (entropic) motion which causes the expansion and aging of history, the temporal analog of space. The dimensions of space and history are conservation domains created by the entropic drives of light and matter, the "intrinsic" motions of free and bound electromagnetic energy. Gravity connects and conjoins these two entropic conservation domains, actually converting either into the other, creating the compound conservation domain of spacetime, wherein both free and bound forms of electromagnetic energy can find their conservation needs satisfied. The flight of time into history drags space along behind it, causing the symmetric collapse of space, which we perceive as a gravitational field. The collapse of space, in turn, liberates a metrically equivalent temporal residue, which continues the self-feeding entropic cycle. (See: "The Conversion of Space to Time".) 4) Gravity pays the entropy-interest on the symmetry debt of matter by creating the time dimension for bound energy, through which charge conservation can have an extended significance - as a means whereby a symmetry debt can be contracted and held as a "promissory note" (a "conserved charge"), which may be redeemed at some future time, as guaranteed by the invariant principle of charge conservation (and the existence of a temporal or historical dimension as created by gravity). Our material universe functions in an historical or "karmic" (causal) mode through charge conservation in which symmetry debts, held as temporal charges, allow matter to "buy now and pay later": gravity pays the entropy-"interest" through the creation of time. Gravity funds the expansion of the historical cosmos by subtracting energy from the expansion of the spatial cosmos - via the direct conversion of space to time. As matter's symmetry debt is paid off (by the conversion of bound to free energy in stars, for example), the cosmic gravitational field is reduced and the suppressed expansion of the spatial universe begins to relax, resulting in the recently perceived "acceleration" of the cosmic expansion. (See: "Dark Energy: Does Light Produce a Gravitational Field?".) Symmetric massless light is "non-local", atemporal, and acausal, with intrinsic (entropic) spatial motion "c", and produces no gravitational field. Asymmetric massive matter is local, temporal, and causal with intrinsic (entropic) historical motion "T", and produces a gravitational field (the source of matter's time dimension). 5) The conversion of space to time is accomplished by the gravitational annihilation of space, which reveals a hidden, latent, or implicit component of time, the metric equivalent of the annihilated space. Einstein has taught us that space is not "just" space but spacetime: destroy space and you have a metrically equivalent temporal component remaining. This temporal component is in fact the hidden entropic principle that also causes the spatial expansion of the cosmos (the "Hubble expansion" of cosmology). Freed of its spatial envelope, in which it was implicit (as "frequency"), time becomes explicit and creates, expands, and ages history by its own "naked" intrinsic and entropic motion. 6) The entropic expansive motion of space and history is necessary for reasons of energy, symmetry, and causality conservation. The dimensions of spacetime are conservation domains created by entropy which must have intrinsic (entropic) drives of light, time, and gravity in order to conserve energy, symmetry and causality via the "infinite" and/or one-way velocity of light, time, and gravitation. Gravity is the force which converts either entropy drive into the other. These reversible and interconvertible entropy drives actually oppose each other in practice. In the Sun for example, they create a dynamic balance of opposing expansive radiative (spatial) vs contractile gravitational (temporal) forces. Similarly, they cause a cosmic-scale battle between the entropic forces of light and cosmological spatial expansion, vs the gravitational entropic forces of matter, historical expansion, and consequent cosmological spatial contraction. (See: "Entropy, Gravity, and Thermodynamics".) 7) The incredible weakness of gravity has been a perennial puzzle. However, from the viewpoint of gravity as a conservation force that converts the spatial entropy drive of free energy (light's intrinsic motion) to the historical entropy drive of bound energy (time's intrinsic motion), we can finally begin to see a plausible explanation for gravity's weakness. The first thing to note is that the weakness of gravity means that (in the context of the theory espoused here) on a per given mass basis, gravity needs to annihilate only a small amount of space to extract a sufficient amount of time to serve as the entropy drive for matter. Matter doesn't seem to require much time to energize its historical entropy drive (either that, or the extracted spatial entropy drive of light is enormously more potent than the historical entropy drive of time it replaces). Why should this be? Thinking along these lines, a rather obvious explanation comes readily to mind: massive objects such as ourselves (which are the only energy forms or states which require a historical causal dimension and its associated temporal entropy drive) are only tangentially connected to their historical entropy/conservation domain. We live only in the "now", not in the historical and causal past. Contrast this with the energy state of free energy or light, which is coextensive with its entropy domain (space). (Due to its effectively "infinite" velocity, light, in its own reference frame, is everywhere simultaneously within its spatial conservation domain.) The "now" is a tangent point on the surface of historical spacetime. P. A. M. Dirac pointed out that the ratio between the strength of gravity and the strength of the electromagnetic force was very similar to the ratio between the size of an electron and the size of the Cosmos - which quantitatively is essentially the same comparison that I am making between the tangential "now" and "bulk" historic spacetime. Our conclusion is that gravity produces only enough temporal entropy to service matter's point-like connection to its historical entropy domain. (See: "Proton Decay and the 'Heat Death' of the Cosmos".) 8) Black Holes are the most extreme expression of gravitational force - the "limiting case" - and they have much to teach us. A black hole is a region of spacetime in which the gravitational field is so powerful that its local field strength "g" is equal to the velocity of light "c". Consequently, no light can escape from a black hole - or at least not much. Stephen Hawking has calculated that a quantum mechanical effect due to the extreme shear forces at or near the "event horizon" or "surface" of a black hole actually converts the gravitational energy of the hole into a form of radiation which will eventually, over immense stretches of time, cause the total conversion of the mass or bound energy of the black hole into radiation, completely fulfilling Noether's Theorem with respect to the gravitationally held entropy and symmetry debt. Jacob Bekenstein and Stephen Hawking have also produced a theorem which relates the surface area of the event horizon of a black hole to its entropy. In the theory advanced here (see the "Tetrahedron Model"), this surface of the black hole must be a time surface, and so the entropy in question must be temporal (historical) entropy. The logic is that once the limiting case of increasing field strength is reached (g = c), the only way to accommodate the temporal entropy requirements of any further mass inputs to the hole is to increase the effective surface area through which space can be sucked in and converted to time, so the Bekenstein-Hawking theorem makes perfect sense with regard to the notion that gravity converts space to time - just as Hawking radiation is a sensible resolution to the question of the final and complete payment of the gravitational symmetry debt. (See: Scientific American August 2003, page 58) According to Einstein, in a gravitational field, meter sticks shrink and clocks run slow, and at the black hole's event horizon meter sticks shrink to nothing and clocks stop. The local gravitational metric as gauged by "g", which is superimposed upon the global electromagnetic metric as gauged by "c", completely overwhelms the latter. A gravitational metric of time and matter replaces the electromagnetic metric of space and light. Just as gravity overwhelms and replaces the atomic and nuclear binding forces in the white dwarf and the neutron star, so in the black hole gravity also overwhelms and replaces the regulatory function of the electromagnetic spacetime metric. Time stands still at the event horizon because it is being replaced as fast as it moves away into history; meter sticks vanish because space is completely replaced by time. The event horizon represents the end point of temporal entropy, the triumph of time and gravity over space and light, and yet Hawking radiation tells us that this triumph of darkness and matter is incomplete, ephemeral, and cannot last. We should have known, even without Hawking's brilliant deduction: Noether's Theorem requires the conservation of symmetry, and the all-way spatial entropy drive of light's intrinsic motion has more symmetry than the one-way historical entropy drive of time's intrinsic motion. At a black hole's event horizon, gravity and temporal entropy return immobile matter to an intrinsic spatial motion equal to velocity c - revealing their hidden agenda of symmetry conservation, which is nevertheless fulfilled only through Hawking's "quantum radiance". While outside the black hole, symmetry conservation is proceeding via Hawking radiation, it is likely that inside the black hole symmetry conservation is proceeding via proton decay. The extreme gravitational pressures at the central singularity squeeze the quarks of baryons back to their primordial leptonic configuration (the "leptoquark"), vanishing the color charge in the limit of "asymptotic freedom", and proton decay proceeds via the weak force "X" IVB with the emission of a leptoquark neutrino. (See: "The Origin of Matter and Information".) The inside of a black hole is therefore full of nothing but light, solving the problem of the infinite compression of matter at the central singularity. A black hole is apparently a gravitationally bound state of light, somewhat similar to a gigantic baryon, the next stage of simplification beyond the neutron star, which is essentially a gigantic gravitationally bound atomic nucleus. At the "event horizon" of a black hole, both clocks and light come to a halt, as the electromagnetic metric is completely replaced by the gravitational metric. Within the event horizon, all former functions of the electromagnetic metric are either defunct or performed by the gravitational metric, including those of the the binding forces between particles. Also absent are the primordial entropy drives of space and history, the intrinsic motions of light and time. Hence the black hole is just that physical environment in which entropy, in its usual electromagnetic expressions, does not exist, and hence no change is possible as we ordinarily experience it. But gravitation is also a form of (negative) entropy, and indeed we find, just at the boundary between the electromagnetic and gravitational domains, entropy operating to convert the mass of the black hole entirely to light - via the mechanism of "Hawking radiation". This is the ultimate expression of Noether's symmetry conservation theorem, the complete gravitational conversion of bound to free energy, definitively revealing the final conservation rationale for gravitation, and by extension, for time as well.9) Finally, although I have no talent in mathematics (as my family is fond of reminding me), I have nevertheless attempted to formulate a "concept equation" representing the gravitational conversion of space to time. Obviously I accept Einstein's gravitational field equations as essentially correct (without the "cosmological constant"), except for the caveat expressed in: "Dark Energy: Does Light Produce a Gravitational Field?". In my "concept equation" (S) represents the spatial volume annihilated or collapsed by gravity "-Gm" in order to produce the historical entropy drive (T) or time dimension of matter for any given mass "m". -Gm(S) = (T)m -Gm(S) - (T)m = 0 It is to be understood that the temporal component is the metric equivalent of the annihilated space (as gauged by the electromagnetic constant "c"), and is "hidden" in ordinary space as "spacetime", elucidated by Einstein. Since every massive elementary particle, atom, or other form of bound energy produces its own gravitational field: -Gm(S), every mass produces its own time dimension (T)m, as gauged by the universal gravitational constant "G". The gravitational constant is negative because it requires energy to annihilate space and to convert a symmetric spatial entropy drive (the intrinsic motion of light) to an asymmetric historical entropy drive (the intrinsic motion of time). Furthermore, it is this same temporal component (at work in the electromagnetic wave through "frequency") that is also ultimately responsible for the spatial entropy drive of light's intrinsic motion. The symmetric, spatial component of light's entropy drive ("wavelength") must "flee" the embedded asymmetric temporal component ("frequency") to maintain light's non-local symmetric energy state and suppress the asymmetric time dimension, which, like the proverbial "bur under the saddle", is an intrinsic feature of light's own nature - the embedded entropy corollary of energy. Energy plus symmetry conservation, spurred by the implicit presence of time, is the cause of light's intrinsic motion. Implicit in "frequency", time is the universal entropy element embedded in every form of energy: frequency multiplied by wavelength = c; E = hv; hv = mcc. Time is the entropic motivator of cosmic expansion, whether implicit in the intrinsic motion of light and the expansion of space, or explicit in the intrinsic motion of gravity and the expansion of history. (See: "A Description of Gravitation".) 10) The gravitational field of bound energy gives the impression that matter actually does have an intrinsic spatial motion. However, due to the perfectly symmetric character of matter's gravitational field (caused by the equivalent coupling of time to all 3 spatial dimensions, conserving both inertial symmetry and energy), matter has no "net" intrinsic spatial motion via its own gravity. Rather, the intrinsic (entropic) motion of matter's time dimension collapses space and provides bound energy with true intrinsic (and one-way) motion in the historical domain, at right angles to all three spatial dimensions. The one-way character of time and gravity are thus linked, and both are due to the causal nature of matter and matter's historical domain of "karmic" or causal information. A gravitational field is the spatial consequence of time's intrinsic motion. 11) The conservation role of gravity addresses the four conservation parameters of the "Tetrahedron Model": entropy (converting light's intrinsic motion to time's intrinsic motion), symmetry (the conversion of bound to free energy), causality (the creation of time and historic spacetime, and including "Lorentz Invariance"), and finally energy itself (providing negative energy to balance matter's positive energy). All these roles are intimately connected and related to the regulatory or "gauge" functions of "velocity c". Negative gravitational energy is provided by an imploding rather than exploding spatial metric, which in turn is caused by the intrinsic motion of time, matter's entropy drive (time and gravity induce each other endlessly). Time provides matter's causal linkage and creates matter's historic conservation domain of information, while simultaneously providing matter with a "location" charge representing light's non-local distributional symmetry debt. "Location" charge (whose active principle is time) identifies the 4-dimensional location of immobile, undistributed mass-energy, and eventually converts matter back to its original and symmetric form, light (in stars, black holes, and other astrophysical/gravitational processes). The active "push" or "drive" of this chain of conservation effects is provided by entropy - the implicit or explicit presence of time causing the expansion of space or history. 12) Entropy allows the transformation of free energy to "work"; symmetry conservation allows the conversion of free energy to information (charge); energy conservation allows the conversion of free energy to bound energy (mass); gravity allows the conversion of light's entropy drive to matter's entropy drive (time). Add in the asymmetric action of the weak force to break the primordial symmetry of light and its particle-antiparticle pairs, and you have the makings of a Universe such as our own, composed of free and bound forms of electromagnetic energy and their compound metric conservation domain, historic spacetime. home page (page 1) home page (page 2)

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http://fa-elsesser.weebly.com/math.html

math

Math: November 13, 2017 Upcoming Assessments: Home Practice: Monday November 13th Mid Chapter Check 1. xtra math Tuesday November 14th Fraction FSQ 2. iready 45 minutes per week Thursday November 15 Fraction Vocab Quiz 3. math vocab flash cards due 11/14 Friday November 16th Fraction USA Mad Minutes Monday, Wednesday, and Friday What We Are Learning: Standards: MAF.3.NF.1.1 Questions: How can you represent and model fractions greater than 1? How can you relate fractions to whole numbers? How can you divide models to make equal shares? How can we solve problems involving fractions? Lines of Inquiry: Represent a fraction greater than 1. Relate fractions to whole numbers. Divide models to make equal shares. Solve problems involving fractions.

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CC-MAIN-2017-47

https://www.brightstorm.com/tag/length-distance/page/1

math

How to define arc length and how it is different from arc measure; how to calculate the length of an arc. How to derive the equation for the distance between two points using the Pythagorean Theorem. How to derive the distance formula for polar coordinates. How to find the speed of transit when the time of two different legs is known. How to define the components and length of a position vector in three dimensions. How to determine the triangle side inequalities. How to derive the equation for a circle using the distance formula. How to use the distance formula to derive the equation for a circle. How to find the shortest distance between a point and a line. How to derive the formula for the midpoint of a segment in three dimensions. How to define a chord; how to describe the effect of a perpendicular bisector of a chord and the distance from the center of the circle. An explanation of displacement. How to understand and find the length of waves. The RFLP method of DNA Fingerprinting.

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https://www.jiskha.com/display.cgi?id=1358356954

math

posted by rezny . two forces 20N each are inclined at 100 degree to each other.find the single force that will; replace the given force system balance the given force system α =(360⁰ - 2•100⁰)/2=80⁰ F1 is directed along the positive X-axis ,and F2 is 100⁰ measured from the positive X- axis with the counter-clockwise, F is 230⁰measured from the positive X- axis with the counter-clockwise

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CC-MAIN-2017-34

https://library.keldysh.ru/preprint.asp?lg=e&id=2019-86

math

About approximation of stream sizes on spatial grids of irregular structure Spatial approximations of derivatives for the construction of flux quantities in the finite volume method are presented. Formulas for finite volumes with faces representing triangles, quadrangles, as well as five- and hexagons are given. Approximations are constructed for use in open-source platform OpenFOAM. finite volume method, unstructured grids, spatial approximations, open program complex OpenFOAM Publication language:russian, pages:22 Mathematical modelling in actual problems of science and technics

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CC-MAIN-2023-40

https://feelbooks.in/product/a-first-course-in-probability-and-statistics/

math

A First Course In Probability And Statistics 122 in stock |Author||B L S Prakasa Rao| |Edition||World Scientific Low Price Edition (WSLPE)| Explanation of the basic concepts and methods of statistics requires a reasonably good mathematical background, at least at a first-year-level knowledge of calculus. Most of the statistical software explain how to conduct data analysis, but do not explain when to apply and when not to apply it. Keeping this in view, we try to explain the basic concepts of probability and statistics for students with an understanding of a first course in calculus at the undergraduate level. Designed as a textbook for undergraduate and first-year graduate students in statistics, bio-statistics, social sciences and business administration programs as well as undergraduates in engineering sciences and computer science programs, it provides a clear exposition of the theory of probability along with applications in statistics. The book contains a large number of solved examples and chapter-end exercises designed to reinforce the probability theory and emphasize statistical applications.

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CC-MAIN-2023-40

http://tileforlessnw.com/library/an-introduction-to-mathematical-reasoning-numbers-sets-and-functions

math

By Peter J. Eccles Read or Download An Introduction to Mathematical Reasoning: Numbers, Sets and Functions PDF Best number theory books Algebraic numbers can approximate and classify any genuine quantity. the following, the writer gathers jointly effects approximately such approximations and classifications. Written for a large viewers, the booklet is obtainable and self-contained, with entire and certain proofs. ranging from persevered fractions and Khintchine's theorem, Bugeaud introduces numerous thoughts, starting from specific buildings to metric quantity idea, together with the speculation of Hausdorff size. This e-book introduces the idea of modular varieties, from which all rational elliptic curves come up, with an eye fixed towards the Modularity Theorem. dialogue covers elliptic curves as advanced tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner thought; Hecke eigenforms and their mathematics homes; the Jacobians of modular curves and the Abelian forms linked to Hecke eigenforms. When you consider that its e-book, C. F. Gauss's Disquisitiones Arithmeticae (1801) has received a virtually legendary popularity, status as an amazing of exposition in notation, difficulties and strategies; as a version of business enterprise and thought development; and as a resource of mathematical notion. Eighteen authors - mathematicians, historians, philosophers - have collaborated during this quantity to evaluate the impression of the Disquisitiones, within the centuries in view that its e-book. Combining 3 books right into a unmarried quantity, this article contains Multicolor difficulties, facing a number of of the classical map-coloring difficulties; difficulties within the concept of Numbers, an effortless advent to algebraic quantity conception; and Random Walks, addressing uncomplicated difficulties in chance concept. Additional info for An Introduction to Mathematical Reasoning: Numbers, Sets and Functions An Introduction to Mathematical Reasoning: Numbers, Sets and Functions by Peter J. Eccles

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CC-MAIN-2019-18

https://www.lessonplanet.com/teachers/dizzy-heights

math

Fifth graders explore ways to measure the height of an inaccessible object. They measure lengths using a tape measure or ruler. Students measure angles using a protractor and estimate heights. 5th Math 3 Views 2 Downloads Practice: Measuring Angles and Using a Protractor and More! Four fabulous worksheets are included in this resource, all having to do with the measurement of angles. On the first, anglers will use a protractor to determine the degrees of 10 different angles. An arc is drawn on each. On the second,... 4th - 6th Math CCSS: Adaptable Comparing Volumes of Cereal Boxes Explore the deceptive world of food packaging with this fun math activity. Using prior knowledge about measuring the volume of three-dimensional figures, young mathematicians determine the difference between the volume of cereal boxes... 4th - 7th Math CCSS: Adaptable Area and Perimeter of Regular and Irregular Polygons Extend young mathematicians' understanding of area with a geometry lesson on trapezoids. Building on their prior knowledge of rectangles and triangles, students learn how to calculate the area of trapezoids and other irregular... 3rd - 6th Math CCSS: Adaptable

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CC-MAIN-2016-44

http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA296703

math

Accession Number : ADA296703 Title : A Combined Stochastic and Deterministic Approach for Classification Using Generalized Mixture Densities. Descriptive Note : Professional paper, Corporate Author : NAVAL COMMAND CONTROL AND OCEAN SURVEILLANCE CENTER RDT AND E DIV SAN DIEGO CA Personal Author(s) : Waagen, D. E. ; McDonnell, J. R. PDF Url : ADA296703 Report Date : JUN 1995 Pagination or Media Count : 20 Abstract : This work investigates a combined stochastic and deterministic optimization approach for multivariate mixture density estimation. Mixture probability density models are selected and optimized by combining the optimization characteristics of a multiagent stochastic optimization algorithm based on evolutionary programming and the expectation-maximization algorithm. Unlike the traditional finite mixture model, generally composed of a sum of normal component densities, the generalized mixture model is composed of shape-adaptive components. Rissanen's minimum description length criterion provides the selection mechanism for evaluating mixture model fitness. The classification problem is approached by optimizing a mixture density estimate for each class. A comparison of each class's posterior probability (Bayes rule) provides the classification decision procedure. A classification problem is posed, and the classification performance of the derived generalized mixture models is compared with the performance of mixture models generated using normally distributed components. While both approaches produced excellent classification results, the generalized mixture approach produced more parsimonious density models from the training data. (KAR) P. 1 Descriptors : *STOCHASTIC PROCESSES, *MULTIVARIATE ANALYSIS, *CLASSIFICATION, MATHEMATICAL MODELS, OPTIMIZATION, DECISION MAKING, COMPUTER PROGRAMMING, PROBABILITY, PROBABILITY DENSITY FUNCTIONS, MIXTURES, MATHEMATICAL PROGRAMMING, ESTIMATES, NONPARAMETRIC STATISTICS, LENGTH, EVOLUTION(GENERAL), SELECTION, NORMAL DISTRIBUTION. Subject Categories : Statistics and Probability Distribution Statement : APPROVED FOR PUBLIC RELEASE

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CC-MAIN-2018-09

http://cosmoquest.org/forum/showthread.php?42533-Speculations-on-the-speeds-of-gravity-and-light&p=760135

math

When it comes to the speed of gravity, it appears we are in a quandary. Relativity says that nothing can travel faster than the speed of light. But if this is the case, orbits would decay very rapidly. They could never be as stable as they are observed to be.This is because if it takes time for the information that a body has moved to reach another through gravitation, a body will not be pulled to where the other is now (in its current position), but to where it was when the gravitational waves started out. According to Newtonian gravity, the transmission is instantaneous. According to relativity, it appears to depend upon the situation, which is iffy at best. It says that gravitational waves travel at the speed of light, but that the effects of gravity are felt instantaneously. In other words, the warping of space-time moves with the body at all times, as if it were physically adhered to it. But then, how is the information transferred through such a permanent fixture to another when the body is in motion? And if this is the case, what is the meaning of gravitational waves (implying change of state through transmission)? This is the "scissors paradox". I have determined (although some might disagree) that this is very similar to the effect that promoted relativity to begin with. That is, the Michelson-Morley experiment. In this, a light beam which was split, directed at perpendicular directions to each other, one in the direction of the motion of the Earth (through the ether) and the other perpendicular to this, and then realigned should have produced interference with each other which could be measured. However, no such interference could be found, just as no aberration is found with gravity. The underlying concepts are virtually the same. Special relativity does very well when explaining the absence of interference in terms of time dilation and the contraction of distances in the line of motion, and has even resulted in the famous E=mc2. But when it comes to the aberration of gravity, it is a different matter. The time dilation necessary in order to explain it is on the order of billions of times greater, and vise versa for the distance contraction, so this is out of the question. And a non-Euclidean geometry would only serve to make matters worse, as a curved path only increases the time necessary for the interaction. As far as the Michelson-Morley experiment is concerned, however, I believe I have found a flaw in the experiment. I have recreated it geometrically on paper and found that in any frame of reference other than at rest, it is in fact impossible to exactly realign the beams. That is to say, the two beams, once split, cannot be redirected by the mirrors so that they meet at the same point at final reflection and then travel in the same direction. The angles will instead diverge. The best we can do is to adjust the mirrors slightly so that the beams travel in the same final direction, but they won't meet at the same point at final reflection, and will travel parallel to each other as separate beams with a distance between them that increases with increased speed for Earth through the ether. We cannot even be sure that the angle of incidence equals the angle of reflection for all frames of reference. What we need, then, is a way to measure the discrepencies of light for motion through the ether without the use of mirrors, the splitting of beams, or a measure of interference. How would we do that, you ask? Simple. No matter what the frame of refence, the Earth must travel with at least 1/10000 of the speed of light at some point in its orbit because of its revolutions around the sun. Let's consider this to be its velocity through the ether at the moment. If we were to direct a light beam down a ten meter long pole, that is directed perpendicularly to the motion through the ether, then according to the original expectations of the Michelson-Morley experiment and classical physics, the light would fall back away from the line of motion as it travels this distance since the Earth is moving forward during this time. When the pole is directed opposite this, the light will fall back the other way. The distance between these two points for this velocity as seen on a screen at the end of the pole will be 1/5 cm. Of course, we would not originally know the velocity and direction of the Earth through the ether, but directing the pole at all possible angles will create a filled in circle on the screen at the end of the pole if all of the points are marked. The ratio of the radius of the circle to the length of the pole will equal the ratio of the velocity of the Earth through the ether to the speed of light. If the pole is then turned to where the light is pointed to the center of the circle and the light moves in the same direction as the pole when the pole is then turned away from the center, then the pole will be pointing in the direction of the Earth's direction of travel. This experiment is so simple that it has probably already been tried (as at least 99% of what I propose seems to have already been thought of, but at least that shows I'm on the right track), but I have never heard of anything other than the Michelson-Morley experiment. With relativity being as successful as it seems to be, and with the aberration of gravity necessarily cancelling itself out, this probably will too (but it would still be an advantage to know for sure). But if it didn't, well, that would just be a whole different bag of tomatoes, wouldn't it? If it cancels itself out, then we must consider how gravity would do the same thing (time dilation and contraction aren't enough with gravity). If it doesn't, then we must show how the distance between two parallel beams of light cancel the interference that would otherwise be observed if they were aligned, and then somehow apply that to gravity.

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CC-MAIN-2013-48

https://www.mycoursehelp.com/QA/Refer-to-the-table-aboveIn-a-simple-econ/183090/1

math

Home / Questions / U.S. Cloth 300 Machine 100 India Cloth 300 0 Machi Refer to the table above,In a simple ec... Refer to the table above,In a simple economy with two countries, the U.S. and India. Consider two products, cloth and machines . Show all the math work a.) Draw the PPC for both Countries b.) What should each country specialize in? c.) Exchange rates are: 4 cloth for one machine, 0.25 machine for one cloth? d.) Draw the trading possibilities line for both countries. e.) Currently U.S. is producing 150 cloth and 50 machines. India is producing 100 cloth and 40 machines, what are the gains from specialization? Jul 01 2021 View more View Less Using the Ratio Test In Exercises 17-38, use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the con...Jul 28 2021 What will be the monthly payment if you borrow with a $100,000 15-year mortgage at an interest rate of 1% per month? How much of the first payment is interest? How much i...Jul 11 2021 Why did the court conclude that this case should be submitted to a jury? Explain.Jul 30 2021 What is the difference between express and implied contracts?Aug 18 2021 Estimating r For each of the following, estimate the value of the linear correlation coefficient r for the given paired data obtained from 50 randomly selected adultsThei...May 18 2021 How to compute the sum of three vectors?Jun 13 2021 Presented below is the production data for the first six months of the year showing the mixed costs incurred by Euclid Company. Month ...Jun 10 2021 Refer to the data and information in Problem 5-3B. Required Prepare and complete the entire 10-column work sheet for FAB Products Company. Follow the structure of Exhib...May 22 2020 What mass of sodium acetate, NaCH3CO2, must be added to 1.00 L of 0.10M acetic acid to give a solution with a pH of 4.50?Jun 28 2021 What is the expected ground-state electron configuration for the element with one unpaired 5p electron that forms a covalent compound with fluorine?Jun 28 2021

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CC-MAIN-2023-23

https://paulorenato.com/index.php/book-reviews/122-journey-through-genius-the-great-theorems-of-mathematics

math

Author: William Dunham When it comes to the history of mathematics, there is perhaps no more gifted author than William Dunham. Besides performing the role of a knowledgeable guide through the history of math, the author rewards us with a very engaging and entertaining writing style. His passion for the subject is obvious, and so is his admiration for the people and histories he presents in these pages. This book is very well organized. It starts with Greek mathematics, a time where most proofs were done in geometric rather than algebraic notation. After an impressive presentation of the work of the likes of Euclid and Archimedes, William Dunham brings us to the Renaissance period and the fascinating works of Bernoulli, Newton, Euler and others. I really appreciated how, besides presenting each theorem in itself, the author added an "Epilogue" section for each chapter explaining what other developments derived from this theorem in later years. The book ends with the more abstract, but nonetheless fascinating work of Georg Cantor with his Set Theory. This book is a must read for anyone who appreciates the beauty in Mathematics. Highly recommended.

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CC-MAIN-2023-50

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&arnumber=1054853&sortType%3Dasc_p_Sequence%26filter%3DAND(p_IS_Number%3A22664)

math

Skip to Main Content Let be a sequence of independent identically distributed observations with a common mean . Assume that with probability 1. We show that for each there exists an integer , a finite-valued statistic and a real-valued function defined on such that ) ; ii) . Thus we have a recursive-like estimate of , for which the data are summarized for each by one of states and which converges to within of with probability 1. The constraint on memory here is time varying as contrasted to the time-invariant constraint that would have for all .

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CC-MAIN-2016-30

http://quant.stackexchange.com/questions/tagged/auction?sort=active&pageSize=15

math

Quantitative Finance Meta to customize your list. more stack exchange communities Start here for a quick overview of the site Detailed answers to any questions you might have Discuss the workings and policies of this site tag has no wiki summary. Art market specificities I am looking for some reference on the art market in light of quantitative finance. I am interested in some things: The market in general, how is it compared to financial market ? What about common ... Aug 24 at 23:40 newest auction questions feed Hot Network Questions In Pacific Rim, why didn't they just build the Jaegers twice as big as the Kaiju to crush them easily? A query that lists all mapped users for a given login Help with mathematical side of programming? Is there a 'local undo' extension for Emacs? How to quit without saving using just the keyboard? Beginner number guessing game in Java How to report vulnerabilities without being regarded as a hacker? ASCII's 95 Characters...95 Movie Quotes Do all planets in Stargate series have exactly the same atmospheric pressure? How can I bring back `nil`? Take photo using webcam Are there periodic functions without a smallest period? Hide ouput of bash while running automated script. How long would it take for a new intelligent species to evolve if humans disappeared? If the product of two continuous functions is zero, must one of the functions be zero? Why does the arrow notation of categorical limit go from right to left? Is there still a reason to choose a 10,000 RPM hard drive over an SSD? What is the purpose of a PCB with no copper tracks, but only unconnected copper rings? What's a less obscure word for "sinecure"? What is the difference in meaning between "A majority of" and "The majority of"? I was caught cheating on an exam, how can I minimize the damage? How to increase the value of a number to the next multiple of 10, 100, 1000, 10,000 and so on How to do simple calculation in latex tables more hot questions Life / Arts Culture / Recreation TeX - LaTeX Unix & Linux Ask Different (Apple) Geographic Information Systems Science Fiction & Fantasy Seasoned Advice (cooking) Personal Finance & Money English Language & Usage Mi Yodeya (Judaism) Cross Validated (stats) Theoretical Computer Science Meta Stack Exchange Stack Overflow Careers site design / logo © 2014 stack exchange inc; user contributions licensed under cc by-sa 3.0

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CC-MAIN-2014-42

http://physics.stackexchange.com/questions/tagged/string-field-theory+string-theory

math

String theory was originally formulated from a perturbative description (using quantum mechanics (QM) and replacing points by strings and evaluating path integral). Still, although QM has an upgrade ... Hi Guys generally when you evaluate the 3 open string tachyon tree level amplitude in CFT, you do a conformal transformation mapping the worldsheet to the upper half of the complex plane and the ... This is a follow-up to an intriguing question last year about tension in string theory. What are the strings in string theory composed of? I am serious. Strings made of matter are complex objects ... In string theory, we are told strings can split and merge if the string coupling is nonzero, even while the worldsheet action remains Nambu-Goto or Polyakov plus a topological term. However, a ... Analogous to the background independent open string field theory by Witten. If there isn't, what are the main stumbling blocks preventing its construction? By locality I mean something like the Atiyah-Segal axioms for Riemannian cobordisms (see e.g. http://ncatlab.org/nlab/show/FQFT). I.e. to any (spacelike) hypersurface in the target we associate a ... String field theory (in which string theory undergoes "second quantization") seems to reside in the backwaters of discussions of string theory. What does second quantization mean in the context of a ...

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CC-MAIN-2014-41

http://calendariu.com/b/blank-coordinate-grids-printable.html

math

Grid game kids - learn grids & coordinates, Grid game for kids. learn about grids and coordinates with this interactive grid game for kids. your goal is to pass your driving test by moving the car with the red. Printable graph paper! - mathbits, Title: microsoft word - 10x10.doc author: donna roberts mathbits.com created date: 9/27/2007 3:47:23 pm. Free online graph paper / grid paper pdfs - incompetech, Free online graph paper / grid paper pdfs. downloadable and very printable, i find these pdfs extremely useful.. Coordinate plane grid - math salamanders, Here printable coordinate plane grid collection sheets. grids sizes, choice 1,2 4 quadrants.. http://www.math-salamanders.com/coordinate-plane-grid.html Free printable charts, grids graph paper pdfs, 4 15x15 dotted coordinate grids numbers; 9 10x10 dotted coordinate grids numbers; 9 10x10 coordinate grids; note printables .. https://www.thoughtco.com/charts-grids-and-graphs-ready-to-print-2312658 Printable graph paper - math bits, Graph paper - forms high school math.. http://mathbits.com/MathBits/StudentResources/GraphPaper/GraphPaper.htm

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CC-MAIN-2017-22

https://eng.kakprosto.ru/how-92645-how-to-calculate-oxidation-number

math

You will need - - the periodic system of chemical elements (Mendeleev's table). Remember one General rule: the oxidation number of any element in a simple substance is equal to zero (examples of elements: Na, Mg, Al, i.e. substances composed of atoms of one element). To determine the degree of oxidation of the complex substances in the beginning just write it down without losing the indexes, digits, standing at the bottom right next to the element symbol. An example would be sulfuric acid — H2SO4. Next, open the table of D. I. Mendeleev find the oxidation state of the leftmost element in the substance — hydrogen in the case of this example. Under the current rules, its oxidation number will always be positive, and it is written with the sign "+", as it occupies the leftmost position in the record formula of a substance. To determine the numeric value of the degree of oxidation, note the location of the item relative to groups. Hydrogen is in the first group, therefore, its degree of oxidation +1, but since sulfuric acid two hydrogen atoms (this shows us the index), then write the symbol +2. Then determine the oxidation state of the rightmost element in the recording — oxygen in this case. His conditional charge (or oxidation state) is always negative, as it occupies the right position in the recording substance. This rule holds true in all cases. The numerical value of the right element is the subtraction from the number of his group of 8. In this case, the oxidation state of oxygen is -2 (6-8=-2), given the index is -8. To find the conditional charge of the atom of a third element, use the rule — sum of oxidation States of all elements must equal zero. Then, the conditional charge of the oxygen atom in a substance is equal to +6: (+2)+(+6)+(-8)=0. After this, write +6 over the symbol for sulfur.

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CC-MAIN-2022-49

https://venuscozy.com/how-many-years-are-in-a-day-on-venus

math

How many years are in a day on venus? - Top best answers to the question «How many years are in a day on venus» - FAQ. Those who are looking for an answer to the question «How many years are in a day on venus?» often ask the following questions - Your answer - 20 Related questions Top best answers to the question «How many years are in a day on venus» A day on Venus lasts 243 Earth days. A year on Venus lasts 225 Earth days. Those who are looking for an answer to the question «How many years are in a day on venus?» often ask the following questions: 📢 Venus how many years on venus? - Transits of Venus are among the rarest of predictable astronomical phenomena. They occur in a pattern that generally repeats every 243 years, with pairs of transits eight years apart separated by long gaps of 121.5 years and 105.5 years. - How many years old is venus williams? - Seven venus days equal how many earth years? - Seven venus days equals how many earth years? 📢 How many years away is venus? Venus has not been closer to Earth than 24.5 million miles (39.5 m km) since 1623. After the year 5683, Venus won't come within 24.8 million miles (40 m km) of Earth for more than 60,000 years. - How many earth years is one year in venus? - How many games have venus williams won over the years? - How many venus years is equal to one earth year? 📢 How many years is 1 venus day? 243A day on Venus lasts 243 Earth days. A year on Venus lasts 225 Earth days. - How many venus years is equivalent to an earth year? - How many years on earth is 1 year on venus? - How many earth years does it take to get to venus? We've handpicked 20 related questions for you, similar to «How many years are in a day on venus?» so you can surely find the answer! How many earth years does it take to travel to venus? Typical Hohmann transfer trajectories from Earth to Venus take about 3.5 months. How many light years does it take to reach venus earth? Venus is another planet in our solar system. Venus at its closest is about 2 light-minutes from Earth, and when it is on the opposite side of the Sun, is about 14 light-minutes away. For space probes launched from Earth to Venus using our existing rockets, it takes about 15 months to reach Venus. How many earth years does it take venus to orbit the sun? It takes 225 Earth days, or about 71/2 months, for Venus to orbit the sun. How many earth years for one orbit of venus around the sun? Venus orbits the sun ever 224.7 Earth days, so 1 Venus year is equal to 0.6152 Earth years. How many light years does it take to reach venus from earth? At its closest, Venus is 23.7 million miles away and at its farthest, it is 162 million miles away. It would take between 2 and 15 light minutes to reach Venus form Earth. How many years does it take the earth to revolve around venus? The Earth does not revolve around Venus. Both the Earth and Venus revolve around the Sun. The Earth takes about 365.25 days to do so, and Venus takes about 224.7 days to do so. How many light years does it take to get from earth to venus? Depending on the orbits of Venus and the Earth around the Sun, the distances between Venus and Earth vary. It as been as close as 38.2 million km, but average distance of 41 million km. 41 million km is approximately 0.000004333703419500923 Light Years How many light years does it take to get to venus from earth? Earth is at 499. The distance of Venus from Earth varies from 4.4 E-06 light years (ly), at conjunction, and 2.7 E-05 ly, at opposition.. How many years does venus take to complete an orbit around the sun? How many light years does it take to reach venus from earth not in light minutes i need light years please? You are confused. "Light-year" is a measurement of DISTANCE, the distance that light travels in one year; it is not a time period. Venus is, depending on where Venus and Earth are in our respective orbits, between 2 and 14 light-minutes away; light would take somewhere between 2 and 14 minutes to span the distance. You can convert easily minutes into years; there are 60 minutes in an hour, 24 hours in a day, and 365.26 days in a year. If you visited venus for a year how many earth years would it be? a little less htan 1 What years did satellite and robot explored venus? venus has no sattelite Does venus take 1.9 years to orbit the sun? Like every other planet in the solar system, Venus travels around the Sun in an ellipse—an offset oval. The completion of one such orbit constitutes a year. Venus moves around the Sun at more than 78,000 miles per hour and completes one year in about 225 earth days, or about 7.5 months. How did venus support life billions of years ago? - Creating the different simulations involved adapting a 3D general-circulation model, which accounted for atmospheric compositions as they were 4.2 billion years ago and 715 million years ago, and as they are today. The model also accounts for the gradual increase in solar radiation, as the sun gets warmer over the course of its lifetime. Is the planet venus habitable billions of years ago? - (Image credit: NASA) The hellish planet Venus may have had a perfectly habitable environment for 2 to 3 billion years after the planet formed, suggesting life would have had ample time to emerge there, according to a new study. In 1978, NASA's Pioneer Venus spacecraft found evidence that the planet may have once had shallow oceans on its surface. What is the orbital period on venus for years? Venus' orbital period is 0.616 Earth years. How far away is venus from earth in light years? Venus is much less than a light-year away. Venus varies in its distance from Earth between about 26 million and 160 million miles, as they orbit the sun separately. This works out to a range of 0.000004 to 0.000027 light years. Within the solar system it would be better to measure distances in light minutes than light years. How far away is venus from the sun light years? Not light years, 107 milllion km. How long is a year on venus in earth years? 224.7 earth days, or about 0.62 Earth years because venus is closer to the sun and that means it takes less time to go around it. Is it true that venus' days are longer than its years? Yes and no. Venus rotates very slowly and in a "retrograde" direction. The effect is to make the "solar day" on Venus much shorter than the "sidereal day" (the rotation period). The orbital period for Venus (its "year") is about 225 Earth days. The sidereal day is about 243 Earth days. The solar day is about 117 Earth days. That's why the answer is "yes and no". It depends upon which "day "you mean.

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CC-MAIN-2021-43

http://www.problemsphysics.com/practice_tests/waves.html

math

Sat Physics subject questions on waves and their properties, with detailed solutions, similar to the questions in the SAT test are presented. Answers at the bottom of the page and detailed solutions Hows as well it take a wave of frequency 0.2 Hz and wavelength 2 m to travel along a rope of length 4 m? A) 2 s B) 8 s C) 0.8 s D) 0.4 s E) 10 s What is the frequency of a pendulum that swings at the rate of 45 cycles per minute. A) 0.75 Hz B) 1.3 Hz C) 45 Hz D) 2700 Hz E) 60 Hz What is the wavelength of a wave of velocity 10 m/s and frequency 200 Hz? A) 2000 m B) 20 cm C) 0.05 m D) 0.05 cm E) 5 mm A standing wave is produced along a string of 100 cm whose ends are fixed. What is the wavelength of the wave if there are 3 nodes between the fixed ends of the string? A) 300 cm B) 40 cm C) 20 cm D) 50 cm E) 33.3 cm A train arriving at a station, at 40 km/hr, whistles at a frequency of 600 Hz. What frequency will you hear if you were at that station?(speed of sound in air is 340 m/s) A) 537 Hz B) 680 Hz C) 600 Hz D) 720 Hz E) 340 Hz The frequencies of the sound of an ambulance sirene are f1 while the ambulance is approaching a fixed point and f2 while it is moving away from the same point. If Vs is the speed of sound in air, which of the formulas below may be used to find the speed of the ambulance Va? A) Va = Vs ( f1 / (f1 + f2) ) B) Va = Vs (f1 + f2) / (f1 - f2) C) Va = Vs (f1 + f2) / (f1 + f2) D) Va = Vs (f1 - f2) / (f1 + f2) E) Va = Vs (f1/(f1 - f2)) A string of length L is stretched out with a tension T. What happens to the velocity of the wave travelling down the string if the tension is quadrupled? A) The velocity is multiplied by 2 B) The velocity is multiplied by 1 / 2 C) The velocity is multiplied by 4 D) The velocity is multiplied by 1 / 4 E) The velocity does not change Which of the following statements is NOT correct? A) Sound travelling through air is an example of a longitudinal wave. B) Water waves may be considered as longitudinal and transverse waves C) In a longitudinal wave, particles move in a direction parallel to the motion of the wave D) In a transverse wave, particles move in a direction perpendicular to the motion of the wave E) Electromagnetic waves cannot propagate in vacuum(empty space) If the square of the period of a simple pendulum is plotted against its length, the graph obtained is A) a horizontal line B) a vertical line C) a parabola D) a line through the origin with positive slope E) a line through the origin with negative slope A string of length 3 m vibrates as the third harmonic with 60 complete vibrations in 10 seconds. Find the speed of of this wave. A) 1 / 6 m/s B) 12 m/s C) 6 m / s D) 18 m / s E) 4 m / s Answers to the Above questions

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CC-MAIN-2023-50

http://dz.kidzarella.com/read/math-triumphs-foundations-for-geometry

math

By McGraw-Hill Education Math Triumphs is a radical intervention source for college kids who're or extra years under grade point. The sequence accompanies Glencoe Algebra 1, Geometry, and Algebra 2 and gives step by step intervention, vocabulary help, and data-driven choice making to aid scholars achieve highschool arithmetic. Read or Download Math Triumphs--Foundations for Geometry PDF Best geometry books Illuminating, commonly praised e-book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries. "This publication might be in each library, and each professional in classical functionality conception may be conversant in this fabric. the writer has played a unique provider by way of making this fabric so very easily available in one ebook. Geometric tomography bargains with the retrieval of knowledge a few geometric item from facts bearing on its projections (shadows) on planes or cross-sections by means of planes. it's a geometric relative of automatic tomography, which reconstructs a picture from X-rays of a human sufferer. the topic overlaps with convex geometry and employs many instruments from that zone, together with a few formulation from crucial geometry. Differential geometry arguably bargains the smoothest transition from the traditional collage arithmetic series of the 1st 4 semesters in calculus, linear algebra, and differential equations to the better degrees of abstraction and facts encountered on the higher department via arithmetic majors. this day it truly is attainable to explain differential geometry as "the learn of buildings at the tangent space," and this article develops this standpoint. - Galois Representations in Arithmetic Algebraic Geometry - Geometry from Euclid to Knots - Positivity in Algebraic Geometry (Draft for Parts 1 and 2) - Convex Bodies: The Brunn-Minkowski Theory Extra resources for Math Triumphs--Foundations for Geometry 8 Barb is paid $15 an hour up to 40 hours a week. If Barb works more than 40 hours, she is paid $22 an hour for each hour over 40. Barb worked 46 hours this week. How much did Barb earn? Number of hours that Barb worked over 40 hours: 46 - 40 = 6 ( · 15) + ( · 6) = + = Check off each step. Understand: I underlined key words. Plan: To solve the problem, I will . Solve: The answer is . Check: I checked my answer by . GO ON Lesson 1-5 Order of Operations 27 Skills, Concepts, and Problem Solving Evaluate each expression. 36 = or = 30 is closer to and . 36 - = . 4. Because 30 is closer to , √30 is between 5 and 6, but closer to . Guided Practice Circle the word that classifies each number. 125 2 Can it be written as a ratio? Can it be written as a ratio? rational 3 irrational _4 Can it be written as a ratio? rational rational 4 9 irrational √50 irrational √81 Can it be written as a ratio? rational irrational GO ON Lesson 2-1 Rational and Irrational Numbers 39 Step by Step Practice 5 Estimate the value of √95 . Escalante’s grades are distributed in his social studies classes. Write the percent of students earning A’s and B’s as a decimal. 7% 36% Vocabulary Check Write the vocabulary word that completes each sentence. 34 A(n) is a comparison of two numbers by division. 35 A(n) is a ratio that compares a number to 100. 36 52 Write a percent and a decimal that show the same amount. 5%. Chapter 2 Real Numbers 15% 12% 30% A' s B' s C's D's F's Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

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CC-MAIN-2019-30

http://mathhelpforum.com/algebra/199734-factor-radicals.html

math

ans = Its wrong I tried a4-1+7a2+16 Follow Math Help Forum on Facebook and Google+ Originally Posted by zbest1966 (a2+1)2-7(a2+1)+10 There are no radicals here. Did you make a mistake when typing the problem? Anyway, this is a quadratic in form. Let . Then . Now factor that trinomial on the right, and then substitute for to get everything back in terms of . a^4 + 1-7a^2-7+10 Originally Posted by zbest1966 a^4 + 1-7a^2-7+10 Im stuck Did you not read what I wrote? We have a quadratic in . You don't need to multiply everything out. And if you were to multiply everything out, you're doing it wrong: . I've shown you how to reduce the problem to factoring . Can you factor this trinomial? View Tag Cloud

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CC-MAIN-2017-13

http://maths2017shs.blogspot.com/2017/03/making-all-combinations-to-10.html

math

Tuesday, 14 March 2017 Making all the combinations to 10 Here we have are answering our problem: " If we have 10 felts. Some are red and some are blue. How many different combinations could we have?" Together we found different combinations and then created a model of our thinking using the red and blue multilink cubes. - Emily and Liam said the multi-link pattern looked like stairs - Can you see this? This activity helps us see what numbers make 10, this is very useful for lots of mathematics questions. We are practicing this a lot!

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CC-MAIN-2019-04

https://www.varsitytutors.com/lawrence-in-physics-tutoring

math

Recent Tutoring Session Reviews "In this tutoring session, we focused on circuits, as led by a problem set. We covered and worked with the concepts of resistors in series and parallel, Kirchhoff loop/junction rules, circuits of resistors, and capacitors." "The student and I began to cover trigonometry, in preparation for her algebra 2/ trig class next school year. We reviewed the special right triangles, 30-60-90, 45-45-90, the six trigonometric ratios, inverse trigonometric functions, the complement of angles, converting from degrees to radians and vice versa, coterminal angles, reference angles, and the unit circle." "The student and I continued a more challenging problem we had left off with on Saturday, and he seemed to understand the concept better than at the first attempt. He had trouble with keeping his units right sometimes, so we discussed strategies to avoid these mistakes. As he works more problems, I can see he is gaining more confidence and understanding of how to apply the kinematic equations for certain situations, such as when time isn't given in a problem. I sent him the collection of problems we discussed so far to help him work through them again in his free time, to help his understanding further, and also work on his pacing for an exam situation. Next session, he will have had class, so we can discuss new material or possibly review some exams or quizzes to make sure he isn't missing anything." "The student and I continued working on logic gates. Last time he didn't finish making his own circuit. Today, he was very successful and made his own custom circuit. We started talking about boolean algebra. This topic is pretty difficult because it is a form of math that he has never seen before. We will test it out next lesson to see how far we can get." "The student and I covered basic mechanics: 1 and 2D motion, vector addition, acceleration, velocity, and displacement." "The student and I covered capacitors, resistors, and circuits, including all of the applicable rules and concepts. She most struggled with relating the algebraic manipulations to the simplification and analysis of circuits, but she was willing to ask the right questions and challenge herself. I explained that the best way to understand circuits is to think of the laws as just logical implications rather than arbitrary rules. I left her with a few practice circuits to work through, and she told me she did well on the last quiz that was on circuits."

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CC-MAIN-2017-09

https://nrich.maths.org/public/leg.php?code=-99&cl=3&cldcmpid=535

math

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning. Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information. Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear. The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it? Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them? Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw? You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest? The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails. Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem? Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card? A Sudoku with a twist. Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring? Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential. A Sudoku with a twist. Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers? Find out about Magic Squares in this article written for students. Why are they magic?! Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku. This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set. Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring? In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9. A pair of Sudoku puzzles that together lead to a complete solution. Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas. Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number? You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance? A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article. The challenge is to find the values of the variables if you are to solve this Sudoku. An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length? Solve the equations to identify the clue numbers in this Sudoku problem. There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules? Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way? Different combinations of the weights available allow you to make different totals. Which totals can you make? Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line. Given the products of adjacent cells, can you complete this Sudoku? There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper. This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid. The clues for this Sudoku are the product of the numbers in adjacent squares. Two sudokus in one. Challenge yourself to make the necessary connections. A Sudoku with clues as ratios. A Sudoku that uses transformations as supporting clues. My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be? This Sudoku combines all four arithmetic operations. If you are given the mean, median and mode of five positive whole numbers, can you find the numbers? The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . . Four small numbers give the clue to the contents of the four surrounding cells. This sudoku requires you to have "double vision" - two Sudoku's for the price of one A Sudoku with clues as ratios. A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both? This Sudoku, based on differences. Using the one clue number can you find the solution? 60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra? Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

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CC-MAIN-2018-13

http://biblioteca.ssc.unict.it/cgi-bin/koha/opac-ISBDdetail.pl?biblionumber=2756

math

Crux Mathematicorum : with Mathematical Mayhem / Canadian Mathematical Society ; V. Linek, chief-redactor. - Ottawa : Canadian Mathematical Society/Société mathématique du Canada - v. : ill. ; 26 cm. Crux Mathematicorum is an internationally respected source of unique and challenging mathematical problems published by the CMS. Designed primarily for the secondary and undergraduate levels, and also containing some pre-secondary material, it has been referred to as "the best problem solving journal in the world". All the problems and solutions are fully peer-reviewed for clarity, completeness and rigour by academic and professional mathematicians. Crux includes an "Olympiad Corner" which is particularly helpful for students preparing for math competitions. Prefactory text in English and French. Mathematics,--Periodicals. Mathematics,--Problems and exercises.

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CC-MAIN-2021-17

http://www.chegg.com/homework-help/questions-and-answers/let-s-set-bit-strings-1-bits-let-t-set-bit-strings-begin-end-1-provide-recursive-definitio-q3204284

math

500 pts endedThis question is closed. No points were awarded. Image text transcribed for accessibility:Let S be the set of bit strings that have no 1 bits. Let T be the set of bit strings that begin and end with a 1. Provide a recursive definition of S. Remember the empty string.

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CC-MAIN-2014-15

https://www.hackmath.net/en/math-problem/21813

math

The diameter of a circle is 4 feet. What is the circle's circumference? We will be pleased if You send us any improvements to this math problem. Thank you! Thank you for submitting an example text correction or rephasing. We will review the example in a short time and work on the publish it. You need to know the following knowledge to solve this word math problem: We encourage you to watch this tutorial video on this math problem: video1 Related math problems and questions: - Circle simple Circumference of a circle is 6.28. What is the area of the circle? - Square and circle Into square is inscribed circle with diameter 10 cm.What is difference between circumference square and circle? - Circle - simple The circumference of a circle is 198 mm. How long in mm is its diameter? The diameter of a circular plot is 14 dm. Find the circumference and area. How big is an area of a circle if its circumference is 80.6 cm? - Central angle What is the length of the arc of a circle with a diameter of 46 cm, which belongs to a central angle of 30°? - Diameter to area Find the area of a circle whose diameter is 26cm. The front wheel of velocipede from the year 1880 had a diameter 1.8 m. Suppose the front wheel turned again one, then the rear wheel 6 times. What was the diameter of the rear wheel? - Perimeter of square The square has a circumference 17cm. What is its area? - The perimeter The triangle has one side 5 cm long and the another 11 cm long. What can be the smallest and what is the largest perimeter? Rectangular floor of living room has a length 5.4 meters and a circumference 17.2 meters. What is its width? - Circle - easy 2 The circle has a radius 6 cm. Calculate: - Rectangle 39 Find the perimeter and area of the rectangular with vertices (-1, 4), (0,4), (0, -1), and (-4, 4) Martin is making a model of a Native American canoe. He has 5 1/2 feet of wood. He uses 2 3/4 feet for the hull and 1 1/4 feet for a paddle. How much wood does he have left? Martin has feet of wood left. - Radius of the circle Calculate the radius of the circle whose length is 107 cm larger than its diameter How long track travel the second hand of a clock in 46 hours, which is 4 cm long. - The central The central angle of a sector is 30° and the radius is 15 m. Determine its perimeter.

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CC-MAIN-2021-17

https://finnolux.com/enzyme-lab-report-5/

math

It is hypothesized that a greater concentration of product is achieved through an increased substrate concentration. P-international (p-an) is produced from An-Benzene-ODL-Argentine p-international hydrochloride (PAPA) with the aid of the enzyme trying. Analyzing the initial reaction rates that were calculated from p-an concentration in different test tubes which contained varying concentrations of PAPA the relative contribution of substrate availability on initial reaction rate was accessed. Initial reaction rates significantly increased at higher initial concentrations of PAPA. However, at a PAPA concentration above 0. Mm, there was no significant increase in initial reaction rate. This suggests that a higher initial reaction rate achieved at a raised initial PAPA concentration from lower levels was due to increases in reactions that formed p-international. The effects from elevating initial PAPA concentration to 0. Mm and above proved insignificant, which may indicate enzyme saturation. Luminescence Jenny Shin; Ivan Richard Low Introduction This study investigates the effect of substrate concentration on the initial rate of reaction when its concentration is much greater than the enzyme concentration. It is hypothesized that the initial rate of a chemical reaction increases as the substrate concentration becomes more abundant. A possible explanation to this phenomenon could be due to the increased probability of collisions occurring between substrate molecules and its associated enzyme, therefore increasing the number of substrate molecules involved with enzyme activity (Moses and Schultz 2008). Whereas, a low concentration of substrate will reduce enzyme activity as less number of substrate molecules are available to bind to the active site of enzymes (Moses and Schultz 2008). Therefore, it is proposed that an increase in substrate concentration will increase initial reaction ate through greater enzymatic activity. Materials and Methods The reaction from An-Benzene-ODL-Argentine p-international hydrochloride (PAPA) to p-international (p-an) accelerated by the enzyme trying is utilized as a model to test our hypothesis. Five test tubes were prepared with differing PAPA concentrations and constant trying concentrations, temperature and PH. Trying concentration in the test tubes was much lower than the PAPA concentration. Initial reaction rate was measured by the amount of p-an produced every thirty seconds for the first five minutes of the reaction. All solutions used in this study have been prepared and brought to room temperature before the beginning of every laboratory session. Trying was obtained from bovine pancreas and all chemicals used were brought in from Sigma, a pharmaceutical company. Quantitative analysis of transmittance to obtain optical density and p-an concentration was collected from a spectrophotometer. A calibration curve was produced from five calibration tubes for each spectrophotometer used to generate the calibration slope, the k value. A system composed of reference trying concentrations and varying PAPA concentrations as applied to access the relative contribution of substrate availability on initial reaction rate. The k value was utilized to convert optical density (obtained from transmittance), into p-an concentration. Data Analysis The concentration of p-international was determined by the negative log of (transmittance/ 1 00) divided by the k value. To calculate the initial reaction rates for each trial, the difference between p-an concentration at 2 minutes and p-an concentration at 30 seconds was divided by the time difference (1. 5 min). Although 10-12 data sets were collected, only 9 data sets were chosen at random or data analysis. One of the data sets was incomplete due to missing data collection for 0. Mm of PAPA solution so the average initial rate for 0. Mm PAPA was calculated with only 8 trials. Furthermore, another data set was revised by applying a new formula to replace an erroneous calculation for all p-an concentrations. The average of the initial reaction rates for each of the five different initial PAPA concentrations were calculated from the sum of the initial reaction rates from 9 separate trials (and an exception of 8 trials using 0. Mm PAPA) divided by the number of trials. A significance level of 0. 5 was used to calculate confidence intervals of the average initial reaction rates to create error bars. All statistical functions above were performed through excel. Data analysis determined if range included by confidence interval (i. E. Mean – CLC value through mean + CLC value) does not overlap, so we can be 95% confident that the difference between the rate the formation of p-international is due to differing substrate concentrations rather than random chance or sampling error; we can therefore accept our null hypothesis and consider the difference statistically significant. If range included by confidence interval does overlap, we can be 95% confident that the rate the formation of p-international is due to sampling error and/or random chance and is not statistically significant. Results Data analysis in Figure 1 indicates a steady trend of increased rate of p- international formation with an increasing amount of PAPA concentration over duration of 1. 5 minutes. To illustrate this inclination, the initial reaction rate rose significantly from 0. 003В±0. Mm/min in a test tube containing 0. Mm PAPA to 0. 006В±0. Mm/min in a test tube containing 0. Mm PAPA. Moreover, the initial rate of formation of p-an in the 0. Mm PAPA tubes are significantly lower than in any other tubes. In the 0. Mm PAPA tube, the initial reaction rate is significantly lower than in the 0. Mm, 0. Mm and 0. Mm PAPA tubes. For example, the initial reaction rate of 0. Mm PAPA is 0. 006В±0. Mommy/min as compared to a much higher rate at 0. 0110В±0. Mommy/min for. Mm PAPA. However, as PAPA concentration increases to 0. Mm, the initial reaction rate in tubes containing 0. Mm, 0. Mm and 0. Mm PAPA are not significantly different from each other. At 0. Mm PAPA, the initial reaction rate is 0. 001В±0. Mommy/ min which is identical to the initial reaction rate of 0. Mm. Discussion Through the investigation on the effects of substrate concentration on initial reaction rate, we hypothesized that the initial rate of a chemical reaction increases as the substrate concentration increases. If my hypothesis is correct, then through the protocol using trying, the test tube containing the highest PAPA concentration will have the highest reaction rate and the test tube intonating the lowest PAPA concentration will have the lowest reaction rate. Through data analysis, we observed a significant increase in the rate of formation of p-an with a greater amount of PAPA concentration when comparing the initial reaction rates between the tubes with 0. Mm, 0. Mm and 0. Mm PAPA solution as there is no overlap in confidence intervals between the three means (Figure 1). However, the confidence intervals of the average initial reaction rate of 0. Mm, 0. Mm and 0. Mm PAPA do overlap and therefore are not significantly different from each other (Figure 1). For example, this is displayed with a mean initial rate of p-an formation as 0. 009В±0. Mommy/min for 0. Mm that overlaps the confidence interval of the initial rate of reaction of 0. Mm which is 0. 0110В±0. Mommy/min (Figure 1). The null hypothesis is supported by significant increases in initial reaction rates with an increase of substrate concentration at lower concentrations. Although, in this experimental design, any concentration above 0. Mm PAPA began to plateau in initial reaction rates, causing an overlap in confidence intervals which showed insignificance in the proposed trend (Figure 1). A plausible explanation to the results of this study is that a higher substrate concentration increases the frequency of collisions between substrate and the active site of enzymes, which in turn increases the probability of substrate binding to an enzyme (Moses and Schultz 2008). The enzyme-substrate complex that results upon binding activates enzymatic activity in accelerating the conversion of reactants to products (Moses and Schultz 2008). Although trying concentration was set constant at 5. EYE-mm, which was much lower than initial PAPA concentration for all five test tubes, the readily available PAPA molecules were not sufficient to convert all available enzymes to the enzyme-substrate complex (Moses and Schultz 2008). In Figure 1, the initial rate plateau starting at 0. Mm PAPA may be justified by trying saturation (Moses and Schultz 2008). Therefore, all the trying present were in the midst of a reaction cycle with another PAPA molecule, so free floating PAPA encountering trying were unable to bind to the active site (Moses and Schultz 2008). When this occurs, the initial reaction rate is unable to increase, as the maximal rate is reached (Moses and Schultz 2008). If this experiment continued using a higher concentration of PAPA with an unchanging concentration of trying, the initial rate of formation of p-an will not be significantly different from 0. Mm PAPA due to the saturation of all trying molecules. Trying has a limited number of active sites and a characteristic number of catalytic cycles per unit time, restricting the initial reaction rate to further increase (Moses and Schultz 2008). Conclusion It has been demonstrated that an increase in substrate concentration increases the initial rate of a chemical reaction by utilizing the model reaction of the abstract An-Benzene-ODL-Argentine p-international hydrochloride converted to the product p-international by the enzyme trying. The results from this study support our null hypothesis, but only limited to lower substrate concentrations. At higher substrate concentrations, initial reaction rates cease to increase which indicates a maximum initial reaction rate. Further studies can be conducted to gain a better understanding in the plateau observed with higher substrate concentrations. Literature Cited Moses, C. D. And Schultz, P. M. (2008). Principles of Animal Physiology 2nd Edition. San Francisco. Pearson Education Inc.

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https://schoolofschool.com/educational-podcast-series/episode-103-functions-number-and-verbal-problems-seeing-the-maths-in-things/

math

Custard powder, Swan formations, and more. In this episode, Andy, Robin and Adam are joined by the amazing Tim Oates to discuss seeing the maths in things. Do we teach the everyday maths around us enough in schools? What topic is always presented in a confusing way to children? Plus, Tim talks on the importance of rich questions that push towards helping the understanding of mathematical structures. The school of school podcast is presented by: Subscribe to get the latest The School of School podcasts delivered to your inbox. Hi, I'm Andy Psarianos. Hi, I'm Robin Potter. Hi, I'm Adam Gifford. This is the School of School podcast. Welcome to The School of School podcast. Are you a maths teacher looking for CPD to strengthen your skills? Maths — No Problem! has a variety of courses to suit your needs from textbook implementation to the essentials of teaching maths mastery. Visit mathsnoproblem.com today to learn more. Welcome back everyone to another episode of The School of School podcast. We've got Tim Oates with us. Very exciting. So Tim, do you want to tell us a little bit about yourself? Thanks Andy, and thanks so much for the invitation to talk today. So yeah, I'm Tim Oates. I'm group director of assessment, research, and development at Cambridge University Press & Assessment. We're a big non-teaching department of Cambridge University. I run a research group of around about 40 people. And, we work in over 140 countries around the world providing assessment services, learning services, and we look at educational reform as well. I particularly enjoy looking at different education systems, have done that for years. Really thinking deeply about how different systems perform and drawing insights from those differences to improve education around the world. Tim, we're here with Adam and Robin here today, and we're going to talk about functions, number and verbal problems, Seeing the Maths in Things. Okay, what does that mean and what is this all about? Yeah. I mean, it's quite a careful title because people don't necessarily see the maths in things. The world is full of sense perceptions, isn't it? Colour, and shape, and movement, well, where's the maths in that? It's pretty bewildering. Maths is fascinating because it's a deeper structure. It's a structure within and beneath the surface of things. It exists in terms of relationships. Of course, we can find fascinating geometric patterns in the eyes of flies. But when we look at things like the ocean, where's the pattern in the turbulence? Where's the pattern in that? Where are the mathematical relationships between the things that we see around us? Gases, solids? I mean, it's amazing that we have developed this language which apprehends laws, deep structures in things, that's been a remarkable human attainment. You're not born with an understanding of the kind of mathematics which we now use to understand the world deeply. You have to acquire it. You have to work at it. Some of the things we know. We can look at two oranges and know they're two oranges. Other things, the issue of say, for example, parabola and the relationship between velocity and distance in an object affected by gravity, that takes a long time to get hold of, and we have to teach that. Quadratics, not obvious, you have to learn it. But once you understand it, you can see that it applies to the real world. It helps you solve real things. I mean, we're all in awe, I'm in awe all the time. And when you start thinking that way, when you start thinking of the world in a mathematical sense, you very quickly recognise, well, I mean, it's almost a philosophy of mathematics is what we're discussing here because we don't even really know. I don't think we really understand, is mathematics a language that we wrote, that we invented? Or, is it something we observed? Is it just the nature of things and we're just recording it? I don't know that we even really have an answer for that. When I was young, I read a couple of things which really opened my eyes. So, one of them was, I just became interested in watching migrating swans. Why do they fly in a V? Why do Canada geese fly the way they do? Well, why do they do it? Turns out it's maths. The formation that they fly in, if they make a navigation error, it minimises that error and makes it easier for them to get back onto course. I mean, of course, we sorted out how they navigate. It's complicated, but the maths that they've adopted helps. Likewise, pigeons eating in fields - why do they cluster the way they do? And there's a mathematical reason for that. It's really, really efficient in terms of clearing the grain and the seeds in the field. That's when you begin to know that there are mathematical principles underneath the surface appearance of things, things that are remarkably persistent. That's right. And in that, even things that are really difficult to understand, and Marcus du Sautoy from Cambridge speaks a lot about this actually. The fact that that pie keeps showing up in all these places where there's no obvious circle and somewhere in there lurking as a circle, but we don't really know where it is. But it keeps popping up and especially in statistics and probability and like you say, "why do bees make their honeycombs in hexagons?" I mean, what a curious question, right? Well it turns out that's the most efficient tessellation you can do. So uses the least amount of wax. Now that's a fascinating thing. So there's maths everywhere you look in nature, in the universe in general. Do you think we teach enough of that in schools? Yeah, no, that's interesting. That's an interesting question. "Do we teach enough of that?" We could have application and the wonders of the outside world, is it kind of a thing that we go to every so often to try to keep kids interested? But you can do it more often, Tim, because I've had both my kids over the years say to me, "I don't understand. I'm never going to need this again." And usually they're talking about maths. "I'm never going to use this again. Why do I need to learn this?" So maybe if we did present it more often, as in it's in everything, there's maths everywhere, maybe they could get more excited about it. I don't know. Yeah, I mean I think what we need to do is to do what Japanese teachers do brilliantly, which is that they move between these things and the abstract representations and the language of mathematics continuously, not "okay, for the last few weeks we've been doing this, and by the way, there's this amazing thing that you can observe in the outside world" and presenting it just as a stimulus and sort of unrelated to the maths, no, no, no. What you have to do is to move between these things and the abstract representation of mathematics continually, because then it encourages seeing the deep structure in the world and the meaningfulness and the power of mathematics. There was a great incident that happened outside the gates of a school in Kent where somebody had been teaching a particular programme called Cognitive Acceleration in Science Education. And it was in science, it helped kids to really accelerate their understanding of mathematics. And as Phillip Aiden was leaving the school, a child came up to him and said, "I want to talk about case. So Phillip said,"Oh, okay". And the child said, "I hate case, I hate it". And Phillip said, "Well what's the problem?" And so the child said, "It makes me think about science all the time." And when Phillip began to talk to this kid, he realised that "boy, it was really working". This kid was beginning to really think "okay" about, he kind of proceeded with his intrusive thoughts but what we know from the research is if you encourage a child, if a child begins to think about something outside contact time, their attainment in the subject really begins to accelerate. And that's what I mean by this issue of functions, number and verbal problems, Seeing the Maths in Things. It has not just to be an exciting lesson, it has to shift the way you think, it has to shift the way you see the world. In Singapore, they actually state that, I can't remember exact the exact wording in the national curriculum, but the purpose for teaching mathematics is to improve someone's intellectual competence. So for them, I mean they go as far as stating that "we don't actually teach, obviously we want them to know all the things that we're teaching them, but the ultimate goal is for them to be able to make better logical decisions in their lives." And as a contributor, so let's say for us, we publish textbooks, how does that apply? How do we get that into the real world? Well, I can think of an example. Imagine that what we're teaching is ratio and proportion and we could just create some convoluted, very mechanical question around ratio and proportion and present it to them that way. But why not take the opportunity to, let's say, use a recipe for example, to teach ratio and proportion because now all of a sudden you can go so much deeper into the understanding of how the world works. Because you can ask them a very simple question which will get their mind spinning in a, not everyone, some of them will just ignore the question because maybe they're not quite ready for it, but others will start pondering on things. So a recent example that I can think of is of a word problem was, it was a pizza dough recipe. And it was like, "okay, here's a recipe," something like, here's a recipe for making four circular, nine inch pizza doughs, right? Pizza bases. Now you want to make three. Now all the measures are given in different, so some are given in mass, some are given in volume, so you've got to do the calculation, even though they're in different, but some of them are given in time. So the amount of time that the dough needs to rise. So do you also need to perform that calculation for that? If it's just mechanical, you're just going to do the same process for all the numbers, regardless of what the measures are, but it doesn't apply to all the measures. The rising time is the same because you've now separated them into three pieces instead of four pieces and you're going to put them on counter to rise, but the rising time stays the same. Why doesn't the rising time change and things like that, understanding these structures of mathematics and how the universe actually works. Those are great opportunities. Now if you ask that as a test question, a lot of people say that's a really unfair test question. I disagree. I think that's a great assessment question, but I don't know, what do you think of that? Oh, I think rich questions which actually push understanding as well as illustrating, being a good carrier of the concept, illustrating the concept and encouraging that iteration between the abstract expression of mathematics and the mathematical structure inherent in the real situation are just great and it's well worth undertaking research on, "which are really good questions and which are good problems". We looked at that in respect of science. Robin Miller has looked at that in terms of science. And what he's found is that there are some questions which are very revealing of structure and are worthwhile using year after year after year and being incorporated alongside other questions which elaborate the idea and having a battery of examples and questions, which then, you're not just relying on one context to encourage kids to understand the deeper structure. You can vary it and that helps with the understanding of all of the children in the group. Fractions is a case in point. Again, very good studies of how Japanese teachers use real examples, different vessels full of liquid, boxes with sand and so on to present the abstract expression of the relationships in fractions through practical real world examples which really embed the understanding, and build up the understanding. I love things that can become elaborated. So an example is, well you have, there's a well, it is this kind of depth, you know, you give all the information. This is the speed, this is the rate at which something will fall. Now the question becomes quite important. "How do you know when it will hit the bottom?" So of course what the students do is they just look at it, they calculate the distance, they look at the distance, they look at the rate, the acceleration, and they say, "look, well it hits the bottom then." And then you say, but that's not the question. The question is "how do you know when it hits the bottom?" Because you only know it hits the bottom and when you hear it, so you then got the speed of sound to take into the equation. Oh, now it's a really interesting question. So absolutely, Andy. I mean the point is it is not arbitrary how you choose these things. You choose them carefully. You choose them carefully because they are an excellent vehicle for carrying knowledge of the mathematical structure. They're not so opaque that you can't understand the deep mathematical structure, that wouldn't work. They have to be highly illustrative of the deeper mathematical structure, and they have to be age appropriate. But you can actually push kids understanding far more than people realise. I did this in respect and I'm afraid again, it's a science example. This is the one that immediately comes to mind. I did this in the respect of oxidation. So there were kids who were being shown that things can explode if they're a fine powder. It's very exciting for primary school kids. You can blow the lid off a tin. He had a big kids explosion. Yeah. "Wow. how's that possible? cause it's a powder, so how's that possible? It's just custard powder." And indeed the demonstration was done and there was a bit of discussion and then I talked to the kids. As you say Robin, they were excited by it, but they hadn't, the questioning hadn't revealed what was actually happening, which was combustion. And for combustion there has to be a fuel, there has to be heat, there has to be oxygen. You know, you can immediately start to ask some questions which build up complex understandings of the process of oxidation. "Why doesn't just a pile of custard powder combust as opposed to when it's finally distributed in the air?" Because you've got the same, you've got the fuel and you've got the heat, but there isn't enough oxygen available to it until you distribute it. Now what I've found is that if you push the questions with very young children, they can develop very complex ideas. But you have to know what question it is, which practical example you're going to use, a real world example. And it has to relentlessly, I mean a bit relentlessly drive towards the mathematical structure. And I think the question, the kind of question that you've just talked about, the kind of example, you could easily get sort of distracted, couldn't you, by just surface features of the issue of pizza dough. You have to make sure it constantly drives at the underlying mathematical structure. You highlighted here was the verbal problems. What role do verbal problems play in seeing the maths in things? Because I think a lot of people think mathematics, when I say a lot of people, I'm not talking about educators, I think mostly educators understand, but when you talk to parents or people who have not come through any kind of formal training on how to teach or why you teach or anything like that, they would think of mathematics as, call it "sums", which I know is not the right word, but that's what they think. Why are verbal problems important? Yeah, I mean verbal problems are important because they present the complexity of the context in which we find the mathematical structures. Most obvious example of a parents would be family debt, for example. That presents as a very complex problem to families and often families make poor decisions about incurring debt. And we've had big shocks recently about, in terms of what's been happening in the global economy, which has had impacts on interest rates which have retaken families by surprise. Well maths is at the heart of that, issues of growth in the economy, wage, wage-price relationships. It's only when we think about these more complex settings that adults experience that I think we can really hook onto is a discourse whereby they can understand the importance of mathematical education in schools. But it's seeing the maths in things and knowing that if you approach certain things using mathematical techniques and mathematical understanding, you can take actions which are good for you, good for society, and good for the economy. That's where I would immediately start bridging between the immediate experience of parents and the realities of what their children need to learn at a pretty early age. I think it strikes me too that something that is schools, it's really important that we foster that attitude because I think there is still an attitude that mathematics is just, or at least it's not responding to the world mathematically, it's just about finding correct answers in some people's view, like parents or possibly people outside of school. And it strikes me that the importance of what's being taught about here, there's such rich conversation to be had in terms of responding mathematically to the world and the creativity and the art, the artistic nature of it, and that it's a language in itself. And I think that for me, what comes across loud and clear is the importance that the subject itself, we need to make sure that it's seen in that way too to everyone. Yeah, I think that's absolutely right. And let's just look at a very simple thing, a seemingly simple thing. I think Andy, in the past, you and I have talked about the teaching of negative numbers and the fact that an awful lot of materials and textbooks teach negative numbers through the temperature scale. That is not negative numbers and it gives rise to a misconception amongst children. The late Richard Dunn said that "You need to teach negative numbers not as the movement, that way and that way, that way is positive, that way is negative with zero being the line in the middle, you need to teach it as the absence of something." Now, just going back to family finances, we talk about a hole of debt, don't we? A big hole of debt opening up. Well, that's exactly how Richard Dunn would teach negative numbers. He would say "Imagine a house in which in the front you've got a pile, a pile which is one, a pile which is twice as big, which is two a pile, which is three times as big of earth, which is three. Well, in the back you've got a hole, which is one, a hole twice as big, which is two and a hole three times as big, which is three." Now, that's an appropriate way to teach or give bridge between a mathematical problem, a real world instance rather and a mathematical problem and the concept. And it's conceptually correct. Minus one is the absence of something. It's not just to the left of something. And don't get me started on the number line, but you're absolutely right. I mean I think that it's understanding that numbers have different types of representations and that just, there's this idea of cardinal numbers, there's this idea of nominal numbers, there's this idea of other manifestations through measurement and ordinal numbers and all these kinds of things. And sometimes we just take the easy way out and we just think what's the easiest real world type example I can come up with a negative number, let me use that. But not really challenging "what is the concept that I'm trying to teach here?" That's why it's dangerous to let teachers write all their own content. I m.ean this is not me taking a stab at teachers, but people who make it their life's business to do this sort of thing, spend an awful lot of time thinking and researching and looking at the impact of doing it one way versus another. It takes a lot of time and it takes a lot of expertise and you can't leave some of those things to chance because you can get misconceptions in really early on that are hard to unpick later on if you do it wrong. That's why this topic is so important, Andy. I couldn't summarise the way in which we should approach this better than you have just done. It is very easy to choose a concept which is of immediate appeal, but can actually give rise to a misconception in the child's mind or in a group of children's mind. We know from Singapore maths, we know from the instances of verbal problems contexts in the textbooks that there is very thorough selection of particular instances to encourage application and to reveal the mathematical structure, and careful variation in those against a particular concept. It is something that has to be done systematically and in the light of good evidence. And a lot of the evidence is from good practise. And it's from good practise, but it's also from looking at what the long-term effect is of doing something and saying, "okay, well we did it this way, what happened, how do you judge whether or not your year three lesson is effective?" Maybe it's by what happens when those children go into key stage three? I had a great example of this. I was talking with some teachers where we were doing some international comparisons and it was some Japanese teachers and some Chinese teachers, and one particular question came up, which was "there is a pile of sand, where do you have to cut it to get one third of the pile of sand?" And I said, "The way that's expressed is very interesting and very challenging." And I asked the teacher and I said, "well, when did you first use that as an example?" He said, "No, well I've always used it. We've been using it for 500 years. It goes back to the first mathematical textbooks in China. Why wouldn't you use it?" You see, this is very different from the kind of approach that we teach, which is, "Oh, you've got to be innovative, you've always got to use new stuff, don't use the same stuff over and over." It's a completely different approach. Why do you use it? Cause it works because it's been carefully chosen. Cause it reveals a mathematical structure. Because you can elaborate it to make it more complicated if the kids have already grasped it. You can ask the additional question, "ok that's when it hit the ground, at the bottom of the well but how do you know that it actually, how can you actually know that it hit the bottom" and then incorporate the speed of sound into it? You can elaborate these things. That's right. And otherwise you end up with answers like "how many children travelled in that car? It'd be three and one third children". No, there's no such thing as a third of a child, but that's what happens. And I'm sure people who write exam papers find those types of answers all the time because it's an example of a well-structured question. You can't put a third of a child in a car, so that's not the answer. So "how many children actually went in a car? Was it four or three?" Yeah. I came across this teacher who was using a particular set of examples in a primary school in terms of mathematics and science, and she said, "Oh, these are so boring I've used these for years and I think I'm going to use something different." And I said, "Well, why do you want to use something different? Do they work?" she said, "Oh yeah, they work brilliantly". "So just carry on using them. The only person who's bored is you, just don't let your boredom show." That's right. That's fair. Carry on. They're brilliant questions. I'm still working on the one third of a child in the car. That's very disturbing. But I think what we just described is something about pedagogy. It's something about how you create your own materials as a teacher. It's how you judge between materials. It's what people who produce materials should be concerned with. And we see this in the best and highest quality textbooks from Hong Kong, from Shanghai, from Singapore. Tim, one final question before we let you go. It seems to me, I might be wrong. It seems to me that there's a large, if you look at the mathematics journey that we push most people down, there's a more of an emphasis on calculus versus statistics and probability. Do you think we should have more statistics and probability in mathematics? If you look at where the world is going in the future, I think the push towards calculus has always been an engineering view of the world, but is there an argument for putting more statistics and probability back into mathematics? That's a very general question, I know, but I'd just be interested in knowing what you think. Oh, you might think it's a general question but there's quite a specific thing going on in England about this. Okay. I'm going to reveal quite something that may sound quite traditional, but we introduced different roots in our advanced level qualifications. In other words, 16 to 18 prior to university, roundabout the 1970s, we began to introduce a statistics route and before it, there'd been a strong mechanics route. Boy, you should have seen the kids migrate to statistics. Actually, that created quite a problem in our system. If you set them up in opposition, one with another, then you can get ready migration. I don't think it's about setting them up in opposition. I think you can have a kind of different flavour, but if you completely remove mechanics from 16 to 18, and you introduce it as well, you can do statistics or mechanics, then I think actually you've got a problem. If you look at say, the German system, then you can major a bit more in statistics, but hell, you can't escape the mechanics. Likewise, if you are really committed to mechanics, you still need to do some statistics. I think that's about the right sort of balance. I do like an upper advanced system where people can follow their preferences and their aspirations. I think that's a time in education when we can begin to really follow people's aspirations and preferences because that means they're enjoying themselves and they really probably learn more. That's a good thing for them. But I think it sounds terrible. I think it's a question of balance. We don't want one to the exclusion of the other. Tim, always a pleasure speaking with you. Thank you so much for joining us today. Well, thank you very much, Andy. It's been a real pleasure today. Thank you very much. Thank you. Joining us on the School of School podcast.

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https://www.jove.com/science-education/12719/gyroscope-precession

math

11.14: Gyroscope: Precession Precession can be demonstrated effectively through a spinning top. If a spinning top is placed on a flat surface near the surface of the Earth at a vertical angle and is not spinning, it will fall over due to the force of gravity producing a torque acting on its center of mass. However, if the top is spinning on its axis, it precesses about the vertical direction, rather than topple over due to this torque. Precessional motion is a combination of a steady circular motion of the axis and the spin motion of the top about the axis. The torque produced due to the spinning top is perpendicular to the angular momentum; thus, the direction of the torque changes, but its magnitude does not. The top precesses around a vertical axis since the torque is always horizontal and perpendicular to the angular momentum. If the top is not spinning, it acquires angular momentum in the direction of the torque, and it rotates around a horizontal axis, falling over just as expected. The concept of precession can be seen in bicycles; it is easy for a bicycle to tip over when stationary. However, when riding the bicycle at a good pace, tipping the bike over involves changing the angular momentum vector of the spinning wheels. Another way that we can demonstrate this is if we put a spinning disk in a box, such as a DVD player. Though it is easy to translate the box in a given direction, it is difficult to rotate it about an axis perpendicular to the axis of the spinning disk. This is because the torque being applied to the box is causing the angular momentum vector of the spinning disk to precess. The precession angular velocity adds a small component to the angular momentum along the z-axis, seen in the form of a swaying motion as the gyroscope precesses, referred to as nutation. The Earth acts like a gigantic gyroscope; its angular momentum is along its axis and currently points towards Polaris, the North Star. However, the Earth is slowly precessing (once in about 26,000 years) due to the torque of the Sun and the Moon acting on its nonspherical shape. This text is adapted from Openstax, University Physics Volume 1, Section 11.4: Precession of a Gyroscope.

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http://fordhamitac.org/category/home-improvement/page/2/

math

Category: home improvement common core math practices posters common core standards best standards of mathematical practice images on common core standards for mathematical. solving compound inequalities worksheet inequalities equations worksheet how to solve compound inequalities math linear inequalities and compound inequalities solving compound. maths problem solving heuristics. math city calculus chapter 1 integrals. educational math games for 2nd grade fourth grade holiday activities new math games second fun summer worksheets. number bonds to 10 kite number bonds to worksheet. fractions decimals and percents worksheet math worksheets fractions decimals percents worksheet fraction and percentages converting to with answers. 2 digit by one digit multiplication two digit multiplication worksheets printable double free pin medium two digit multiplication. probability spinners chapter probability. meaningful math geometry answers the five platonic are the only geometric solids whose faces are composed of regular.

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http://ggessayopbd.taxiservicecharleston.us/microeconomic-terms-and-graph.html

math

You know the saying “a picture is worth a thousand words” the same applies to graphs: they're a very effective means of conveying information visually—without a thousand words in addition to being a “picture,” a graph is also a math-based model math is one way of working with (or manipulating) economic models. Ap microeconomics: exam study guide circular flow diagram: this is so crucial to understand for both micro and macro in other words, one monopolistic provider can meet market demand at a lower atc than if multiple firms were to split the market among themselves study the graph below and understand how the. The following is an adapted excerpt from my book microeconomics made simple: basic microeconomic principles explained in 100 pages or less “consumer surplus” refers to the value that we can use a chart of supply and demand to show consumer surplus in a market example: the following chart. In this scenario, more corn will be demanded even if the price remains the same, meaning that the curve itself shifts to the right (d2) in the graph below in other words, demand will increase other factors can shift the demand curve as well, such as a change in consumers' preferences if cultural shifts cause the market to. Consumer surplus is a term used to describe the difference between the price of a good and how much the consumer is willing to pay demand curves are graphed with the same axis as supply curves in order to allow the two curves to be combined into a single graph: the y-axis (vertical line) of the graph is price and the. Video created by university of california, irvine for the course the power of microeconomics: economic principles in the real world 2000+ courses from schools like stanford and yale - no application required build career skills in data. The core ideas in microeconomics supply, demand and equilibrium. Reffonomics videos microeconomics terms in 3 minutes or less afc, avc, and atc showing fc, vc, and tc long-run average total cost fc, vc, and tc graph, part ii production costs: utility maximization afc, avc, and atc graph perfect competition graph, part iii perfectly competitive characteristics part i. Principles of microeconomics, v 10 by libby understand how graphs show the relationship between two or more variables and explain how a graph elucidates the nature of the relationship define the the key to understanding graphs is knowing the rules that apply to their construction and interpretation this section. Even if a graph is not required, it may be to your advantage to draw one anyway a correct graph can indicate that you understand what is happening even if you use the wrong economic terminology on the other hand, graphs are not magical tools that ensure high scores they are useful in making arguments, but they don't. A summary of seven important details that cut across ap microeconomics graphs enabling students to easily grasp micro econ graphs and important exam tips. B the graphical analysis that will be used in the class will rely upon the cartesian coordinate system this system is shown in the graph below there exist two variables, x and y, which may both take either positive or negative values any specific pairs of values for x and y can be represented on the graph by a single point. Please read/background info i this resource is not meant to teach you economics rather it is meant to serve as a concise guide for you to review economic knowledge you have already learned (translation: you still need to pay attention in class) ii very few parts of this study guide are bolded so pay special attention to. Learning to think like an economist can be a daunting task for beginners introductory economics courses often begin with a jargon-loaded discussion of opportunity costs and marginal benefits versus marginal costs—in other words, what is the benefit of continuing to read the rest of this post, and what else. Key terms economics resource maintenance production distribution consumption positive questions normative questions intermediate goal final goal wealth in the graph shown above, at point b, society is producing the maximum possible microeconomics is the study of national and international economic trends 12. Reading: creating and interpreting graphs it's important to know the terminology of graphs in order to understand and manipulate them let's begin with a visual representation of the terms (shown in figure 1), and then we can discuss each one in greater detail a standard graph with an x- and y-axis there is a positive. Graphs and microeconomics you will see a remarkable number axes - in economics, a graph is not complete without a label on each of its axes telling you what it measures production possibility is just about the hardest bit of algebra we will encounter all term, and it is not really very hard suppose the supply curve is. The term game here implies the study of any strategic interaction between people applications include a wide array of economic phenomena and approaches, such as auctions, bargaining, mergers & acquisitions pricing, fair division, duopolies, oligopolies, social network formation, agent-based computational economics,. Take a look at this graph to help you understand the when and where shutdown point while we're on the topic, what is the supply curve for each firm looking at the graph you'll note the mc curve the supply curve for each firm is simply its marginal cost (mc) curve above the minimum point on the average variable cost. Microeconomics examines smaller units of the overall economy it is different than macroeconomics, which focuses primarily on the effects of interest rates, employment, output and exchange rates on governments and economies as a whole both microeconomics and macroeconomics examine the effects of actions in terms. Microeconomics macroeconomics deals with aggregate economic quantities, such as national output and national income macroeconomics has its roots in it is the inverse of that coefficient solution to 4: in the demand function, change the value of i to 3,000 from 2,300 and collect constant terms: q p p eb d eb eb =. 2 draw the diagram (0 words) the diagram (and it's titles, etc) do not count in your word count you need to diagram the problem explained in the article and also diagram your solution sometimes both the problem and the solution can be shown on one diagram sometimes not of course don't include a diagram (or any. The normal way of expressing a relative price is in terms of a “basket” of demanded of that good demand is illustrated by the demand curve and the demand schedule the term quantity demanded refers to a point on a demand curve—the quantity we graph the demand schedule as a demand curve with the quantity. 21 the cicular-flow-diagram 22 the production possibilities frontier 23 microeconomics and macroeconomics 24 positive versus normative analysis 25 graphs of a single variable 26 graphs of two economists use the term marginal chanes to describe small incremental adjustments to an exiting plan of action.

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CC-MAIN-2018-43

http://www.ai.rug.nl/~lambert/projects/miami/taxonomy/node164.html

math

In this category, the entry of mathematical formulas or musical scores is considered. In both these types of graphical behavior there is an aspect of symbolical and structural information. This means that apart from a symbol identity like ``Greek alpha'', its geometrical relation to the other graphical objects plays an essential role. Interestingly, the entering of formulas is sometimes used as an example of the ease of Direct Manipulation. It has become clear however, that the correct entry of formulas with the pen is a tedious process, if rules for graphical style are not applied within the interface algorithm. As a worst case example, the user must enter four similar formulas with a tantalizing accurate positioning of subscripts and superscripts etc. four times, with the risk of very annoying spacing differences between these formulas. A combination of rule-based approaches, as in LaTeX, and the actual use of interactive pen input is the best solution to this problem. Finally, both in the automatic recognition of mathematical formulas and musical scores, context information is needed and is in practice actually used to solve shape classification ambiguities.

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CC-MAIN-2018-30

https://findanyanswer.com/what-is-half-of-34-in-fraction

math

What is half of 3/4 in fraction? Besides, what's half of 3/4 in cups? If you want to add half of 3/4 cup sugar (3/8 cup) to a recipe, you can use a few different ways to measure this amount. Measure half of 3/4 cup sugar by using a tablespoon. The number of tablespoons that adds up to 3/4 cup is 12, so divide 12 in half and add 6 tablespoons of sugar to your recipe for half of 3/4 cup. Secondly, what is 0.375 as a fraction? Move the decimal point of the denominator to the right by the same number of places that the decimal point of the numerator moves which is 3. and hence 1 in denominator become 1000. The fraction would be 3751000. Therefore, 0.375 in fraction is 38. Also asked, what is half of 3/4 on a tape measure? As an example, the image below shows a length that goes from the inch mark to an unlabeled marking. We know it's more than 3/4 of an inch and less than one full inch. The marking is half way between 3/4 (6/8) and 7/8. Therefore, the marking is half of 1/8, or 1/16. What's half of 3 and 3/4 cup? - Quora. 3 and 3/4 = 15/4 computed by taking the whole integer 3 in the 3 3/4 and multiplying it by the denominator of the fraction (4) and adding the numerator (3) . This will yield 3 times 4 PLUS 3 = 15.

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https://www.lddgo.net/en/base/class?classID=7

math

Factorial Calculator Online The online factorial calculator supports factorial calculation of positive integers of any size. Factorial calculation results can be downloaded locally. Fibonacci Sequence Calculator Online The online Fibonacci sequence calculator supports the calculation of Fibonacci sequence with super large values, and the calculation results can be downloaded locally. Prime Factor Decomposition Online The online free decomposition prime factor tool supports the decomposition of prime factors of large numbers, and gives the prime factor decomposition formula. Fraction Calculator Online The online fraction calculator supports the addition, subtraction, multiplication and division of fractions. Fraction to decimal, decimal to fraction calculation. Support fraction reduction calculation.

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https://en.m.wikibooks.org/wiki/Linear_Algebra_over_a_Ring/Modules_and_linear_functions

math

Let be a ring. A left -module is an abelian group together with a function , denoted by juxtaposition, that satisfies the following axioms for all and : Let , be left modules over a ring . A function is called homogenous if and only if for all and the identity Let , be left modules over a ring . A function is called linear if and only if it is both homogenous and a morphism of abelian groups from to . Theorem (first isomorphism theorem): Let and be left modules over a ring . Let be linear. Then

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https://www.mendeley.com/papers/dynamical-model-solving-degenerate-quadratic-minimax-problems-constraints/

math

This paper presents a new neural network model for solving degenerate quadratic minimax (DQM) problems. On the basis of the saddle point theorem, optimization theory, convex analysis theory, Lyapunov stability theory and LaSalle invariance principle, the equilibrium point of the proposed network is proved to be equivalent to the optimal solution of the DQM problems. It is also shown that the proposed network model is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the original problem. Several illustrative examples are provided to show the feasibility and the efficiency of the proposed method in this paper. © 2011 Elsevier B.V. All rights reserved. Nazemi, A. R. (2011). A dynamical model for solving degenerate quadratic minimax problems with constraints. Journal of Computational and Applied Mathematics, 236(6), 1282–1295. https://doi.org/10.1016/j.cam.2011.08.012

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CC-MAIN-2018-47

https://www.physicsforums.com/threads/magnetic-field-strength.403909/

math

A current I flows to the right on the x-axis from the origin to x = infinity. What's the magnitude of the magnetic field at (x,y) = (0,L)? B = u sub 0 time I/(2 pi R) The Attempt at a Solution We use above equation since we have an extremely long wire. I would think I should just replace the R for the L as the given point value of y. However, this is an old exam question and the professor's solution states that B ' = 1/2 B and therefore the answer is: u sub 0 times I / (4pi L) Could someone please explain why the statement of B' = 1/2 B makes sense. If I know that then of course the answer in the exam key would make perfect sense! Thanks for your time and effort, Frostking

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https://insights.ovid.com/general-relativity-gravitation/gerg/2003/35/060/complete-classification-curvature-collineations/6/00009364

math

|| Checking for direct PDF access through Ovid Curvature collineations are symmetry directions for the Riemann tensor, as isometries are for the metric tensor and Ricci collineations are for the Ricci tensor. Complete listings of many metrics possessing some minimal symmetry have been given for a number of symmetry groups for the latter two symmetries. It is shown that a claimed complete listing of cylindrically symmetric static metrics by their curvature collineations [1&] was actually incomplete and is completed here. It turns out that in this complete list, unlike the previous claim, there are curvature collineations that are distinct from the set of isometries and of Ricci collineations. The physical interpretation of some of the metrics obtained is given.

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CC-MAIN-2020-24

http://www.docstoc.com/docs/82823862/D2C9197ECDDC4956993C158E2C984FEE

math

• There are 6 basic types of simple machines. Simple machines are the most basic tools used to decrease force while increasing distance. They are: – The Lever – The Pulley – The Inclined Plane – The Wedge – The Screw – The Wheel and Axle • Levers are simple machines that involve a rigid arm and a fulcrum. The fulcrum is the point about which a lever pivots. “Give me a place to stand and a lever long enough, and I will move the world.” Class 1: Input (effort) is on opposite side of fulcrum from Class 2: Effort (input) is farther from fulcrum than load Class 3: Effort (input) is closer to fulcrum than load (output). This lever is does not have much mechanical advantage. • Pulleys are devices that change the direction of tension in a rope or wire. allow you to over a greater • Inclined planes are useful because they require less force to ascend. What sorts of situations might you expect to see • What is the mechanical advantage to the inclined plane shown below? • Wedges are essentially • An axe blade is a great example of a wedge. • A screw is a central axle with a helical • Rotary force is • Some car jacks work on the principle of a • A wheel is a circular device which rotates around a central pivot called an axle. • When you turn a steering wheel, you exert relatively little force, but large amounts of force are felt closer to the axle. Why do you think truckers have such big • Mechanical energy is generally classified in two – Kinetic energy – energy associated with movement. Examples: running, car moving, a ball thrown with a – Potential energy – energy associated with temporary storage of mechanical. That is, it has the “potential” to be converted to kinetic. Examples: a rubber band wants to move when stretched; a ball wants to fall off a tall building b/c it possesses gravitational potential energy. • To measure energy, the SI unit we use is the Joule. This is the equivalent energy needed to exert a force of 1 N over a distance of 1 m. • Other units of energy include the kWhr, eV, Calorie, BTU, and even the erg. • Energy is NOT to be confused with Power! Power is the dissipation of energy over time. Without a time description, one cannot have • Objects that have mass and move at a non-zero speed have kinetic energy. The amount of this energy is supplied by a simple equation: • 1.) If you have an object with a mass of 3kg that moves at a constant speed of 5 m/s, what is the kinetic energy associated with this movement? • 2.) If you triple an object’s speed, what happens to its kinetic energy? • When you have a mass at any height above the Earth’s surface, what happens to the mass when it is released? Why? • We like to describe the energy that is available to masses by putting them at given heights above Earth’s surface by gravitational potential energy. • For example, when an object falls from a building, it begins with a height (and gravitational potential energy). As it falls, that potential energy is directly converted to kinetic. At the bottom of the fall, the object now has zero gravitational potential, because it has all converted to kinetic, and there is no more height to supply additional potential. • We have a simple equation for gravitational potential energy near Earth’s surface: This equation is only valid for situations in which objects are close to Earth’s surface. This is b/c when we move away from Earth, the gravitational force decreases exponentially. • We can actually prove this equation based on our knowledge of work: Say you pull an object from the reference level shown such that the object moves at a constant speed (equilibrium). The amount of work performed by our pull force is: W F d mg h mgh • 1.) A diver jumps off a 10-m platform. Assuming the diver “weighs” 52 kg, what is his or her potential energy on the platform? • 2.) What is his or her potential energy when he or she reaches a height of 7 m? • 3.) 5m? • 4.) The water? • Anytime there is frictionless “freefall” occuring, potential is converted directly into kinetic. There is no energy lost: the first law of thermodynamics. One cannot create or • That is, the sum of kinetic and potential must always add to a constant, mechanical energy

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CC-MAIN-2014-41

https://madeforflight.com/personalized-flight-lesson-packages/

math

# Personalized Flight Lesson Packages Flying has always been a fascinating dream for many of us. The thrill and freedom of soaring above the clouds, feeling the wind rushing through our hair and the picturesque views from the top are some of the reasons that make it an unforgettable experience. However, often the first step of achieving this dream seems intimidating, especially in terms of safety and cost. But, with personalized flight lesson packages, you can start fulfilling your dream of becoming a pilot with ease and at an affordable cost. ## What are personalized flight lesson packages? Personalized flight lesson packages are tailored to meet the specific needs of individuals who want to learn how to fly. These packages are designed to provide a comprehensive training program for aspiring pilots, starting from the basics to advanced techniques. These packages include various components, such as ground school instruction, flight simulator training, and actual flight time. ## Benefits of personalized flight lesson packages ### Tailored to your needs Personalized flight lesson packages are customized to meet the individual needs of the student. This means that the training is tailored to your learning style, skill level, and schedule. Purchasing a personalized flight lesson package is more cost-effective than buying individual lessons. These packages are designed to provide a comprehensive training program at a reduced cost, allowing students to save money in the long run. ### Accelerated learning Personalized flight lesson packages are designed to help students learn faster and more efficiently. By providing a structured training program, students can progress quickly through the learning process and achieve their goals in a shorter time frame. ### Experienced instructors Personalized flight lesson packages are taught by experienced flight instructors. These instructors are certified by the Federal Aviation Administration (FAA) and have extensive experience in both flight instruction and piloting. They provide students with the knowledge and skills necessary to become a safe and confident pilot. ## Components of personalized flight lesson packages Personalized flight lesson packages typically include three components: ### Ground school instruction Ground school instruction is the first component of a personalized flight lesson package. It covers the theoretical knowledge required for flying, such as aerodynamics, weather patterns, air traffic control procedures, and navigation. This component is crucial to understanding the fundamentals of flight and preparing for the FAA written exam. ### Flight simulator training Flight simulator training is the second component of a personalized flight lesson package. It provides students with a simulated flight experience, allowing them to practice various scenarios, such as takeoffs, landings, and emergency procedures. This component is essential for developing practical skills and gaining confidence in the cockpit. ### Actual flight time Actual flight time is the third component of a personalized flight lesson package. It is the most exciting part of the training, as it involves flying an actual aircraft with a certified flight instructor. During this component, students learn how to apply the theoretical knowledge and practical skills they have acquired in the previous two components. Personalized flight lesson packages provide aspiring pilots with a structured and comprehensive training program, tailored to their individual needs. These packages are cost-effective, efficient, and taught by experienced instructors. They offer a unique opportunity to turn your dream of flying into a reality. So, if you are ready to take the next step towards becoming a pilot, consider investing in a personalized flight lesson package today.

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CC-MAIN-2023-40

https://outschool.com/classes/pre-algebra-and-algebra-i-tutoring-uHtxZuhZ

math

learner per class How does a "One-Time" class work? Meets once at a scheduled time Live video chat, recorded and monitored for safety and quality Great for exploring new interests and different styles of teachers How Outschool Works 🔥 This class is in high demand! 1 of 4 classes have sold out. 🔥 This class is in high demand! 1 of 4 classes have sold out.There are no open spots for this class, but you can request another time or scroll down to find more classes like this. How the class will work: Students will send (upload) questions at least 24 hours before the start of class. (This will make the class more productive) I will answer the questions and or exercises alternating between students in order to give everyone and equal amount of time. The chat will be in private mode, so that students can feel free to ask questions and post answers. (This is great for students that might get anxious in group settings) Naturally, if there is a common topic the... NOTE: This is course specific (algebra 1). The following are topics that can be covered. Combining like terms, using the distributive property. Graphing ordered pairs and naming graphs. Relations, mapping and definition of function. Introduction to slope. Positive,negative,no slope,zero slope. Graphing basic inequalities . Determining slope from a graph. Graphing using the slope - Y intercept method. Graphing using the X- intercept , Y intercept method. Slope from an equation. Converting standard form to slope- Y intercept method. (Writing equations given information) Writing equations in point slope form, when given two points. Writing equations in slope - Y intercept method. Graphing systems of equations. Graphing systems of inequalities. (Solving systems of equations algebraically) Introduction to the substitution method. Substitution method with additional manipulation. (Solving systems of equations algebraically) Introduction to the elimination method. The elimination method with additional manipulation. It does not matter if you are home-schooled or go to regular school. Before enrolling in this class please note the following requirements: NOTE: 1) Student should have ready exercises with which assistance is required. 2) In order for the class to be productive upload exercises 24 hrs before the start of class. How the class will work. I will show the studenthow to do an exercise on the white board. The student will be provided an opportunity to ask questions on topic areas where they are struggling. I will show examples and repeat with more exercises and will explain as many times as needed until the student are ready to do the exercises by themselves. Once started, I will check their answers for accuracy and follow up with any necessary explanations. I encourage all participants to try as many exercises as possible. I follow up the class with an upload of additional (optional) exercises along with the solutions. The student provides a note book and pencil. 50 minutes per week in class, and an estimated 0 - 1 hours per week outside of class. Math Specialists LLC 🇺🇸Lives in the United States 817 total reviews 817 completed classes Hello parents: I teach Arithmetic, Pre-Algebra , Algebra I, Algebra II, College Algebra ,Geometry, Analytic Trigonometry , Trigonometry,Pre-Calculus, Business Calculus, Calculus and High School and College Statistics. I have a Bachelors of...

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CC-MAIN-2023-06

https://ems.press/journals/zaa/articles/10821

math

A parametric class of series generated by integration of complete elliptic integrals is valuated in closed form. Alternative proofs to results of Ramanujan and others are given. Also, a particular case of the Saalschützian hypergeometric series is derived. Cite this article V.S. Adamchik, A Certain Series Associated with Catalan’s Constant. Z. Anal. Anwend. 21 (2002), no. 3, pp. 817–826DOI 10.4171/ZAA/1110

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CC-MAIN-2023-50

http://www.chegg.com/homework-help/questions-and-answers/position-mass-m-moving-attached-spring-constant-k-friction-medium-mechanical-vibration-cau-q1043392

math

The position of a mass(m), is moving attached to a spring with constant(k) in a friction-less medium. The mechanical vibration is caused by a periodic external force of frequency(w) and a)When would resonance occur? Describe the property of the position function with resonance as time changes. b) Show that the postition of the mass at any time (t) is given by: ((2F0)/m(w0^2 - w^2))sin((w0 - w)t/2)sin((w0 + w)t/2)

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CC-MAIN-2013-20

https://itecnotes.com/electrical/electronic-ohms-law-of-a-circuit-which-has-both-a-voltage-source-and-current-source/

math

The voltage source has a specific voltage through it regardless of the circuit's current and its resistance while the current source has a specific current through it regardless of the voltage through it and its resistance. My question is: When there's a circuit which has both a voltage source and a current source with a load, a resistor R for example. How can people apply Ohm's law on it. The sum of both voltage and current must be reserved. For example, the circuit has a current source and a voltage source connected in a series with a single resistor which - The voltage source supply 10V - The current source supply 3A - The resistance of the resistor is 4 ohm. How can Ohm's law be applied in this case. If we take 10V then the current will be 2.5A which is lack of 0.5 A to make the sum of current equal 3 as the current source supply while if we take the current through it is 3 A then the voltage through it wil be 12 V that over the one which voltage source can supply. I have seen many circuit which have both of these source without knowing how to apply Ohm's law on it.

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CC-MAIN-2022-49

http://www.mamzelle-deybow.com/xml/free-online-book-fb2-pdf-i-smooth-analysis-183214.html

math

The edition introduces a new class of invariant derivativesand shows their relationships with other derivatives, such as the Sobolev generalized derivative and the generalized derivative of the distribution theory. This is a new direction in mathematics. Read alsoRed Mesa Navajo Police Special Investigator Ella Clah is on the run. Justine, Ella's cousin and fellow officer, disappeared after the two women argued publicly over Justine's new boyfriend. Human bones are discovered at the spot where the younger woman had told her family she and Ella were to meet late one night. Suddenly Ella Clah, cop, is Ella Clah,… i-Smooth analysis is the branch of functional analysis that considers the theory and applications of the invariant derivatives of functions and functionals. The important direction of i-smooth analysis is the investigation of the relation of invariant derivatives with the Sobolev generalized derivative and the generalized derivative of distribution theory. Until now, i-smooth analysis has been developed mainly to apply to the theory of functional differential equations, and the goal of this book is to present i-smooth analysis as a branch of functional analysis.The notion of the invariant derivative (i-derivative) of nonlinear functionals has been introduced in mathematics, and this in turn developed the corresponding i-smooth calculus of functionals and showed that for linear continuous functionals the invariant derivative coincides with the generalized derivative of the distribution theory.This book intends to introduce this theory to the general mathematics, engineering, and physicist communities.

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CC-MAIN-2016-44

https://community.smartsheet.com/discussion/21226/how-to-use-formulas-to-change-the-value-of-symbols-and-check-boxes

math

How to use Formulas to change the value of Symbols and Check Boxes? I'm kinda new to this. I'm a little familiar with how formulas worked in Microsoft Excel, but not a pro in the slightest. I only know basic stuff. How do you use a formula to change the value of symbols and check boxes and drop down menus? Also, I've been having trouble pulling the data from dates. I always get the #UNPARSEABLE error. Here is my formula: = IF(MONTH([Column2]1) = 3, "X',"XX") What's wrong with my syntax? Help Article Resources Check out the Formula Handbook template!

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CC-MAIN-2023-50

https://m.scirp.org/papers/69675

math

Received 31 May 2016; accepted 8 August 2016; published 11 August 2016 The Burgers equation was first presented by Bateman and treated later by J. M. Burgers (1895-1981) then it is widely named as Burgers’ equation . Burgers’ equation is nonlinear partial differential equation of second order which is used in various fields of physical phenomena such as boundary layer behaviour, shock weave formation, turbulence, the weather problem, mass transport, traffic flow and acoustic transmission . In addition, the two dimentional Burgers’ equations have played an important role in many physical applications such as investigating the shallow water waves and modeling of gas dynamics . In order to a great applications for burgers’ equations many researchers have been interested in solving it by various techniques. Analytic solution of one dimensional Burgers’ equation are get by many standard methods such as Backland transformation method, differential transformation method and tanh-coth method , while an analytical solution of two dimensional Burgers’ equations was first presented by Fletcher using the Hopf-Cole transfor- mation . The finite difference, finite element, spectral methods, Adomian decomposition method, the varia- tional iteration method, homotopy perturbation method HPM and Eulerian-Lagrangian method gave an nu- merical solution of Burgers’ equations - . Recently, the OHAM was proposed by Marinca and Herisaun - . OHAM is independent of the existence of a embedding parameter in the problem then overcome the limitations of perturbation technique. However, OHAM is the most generalized form of HPM as it uses a general auxiliary function H(p). This method has been studied by a number of researchers for solving linear and nonlinear partial differential equations - . In - proved OHAM is more efficient to solve Burgers’ equations. In 2006, a new method by Daftardar-Gejji and Jafari for solving nonlinear functional appeared . Convergence of it has been proved in . This method is named later as Daftardar-Jafari method DJM in . J. Ali et al. used DJM in the OHAM for solving non-linear differential equations and they named this method as OHAM with DJ polynomials OHAM-DJ . In 2016, OHAM-DJ has been used to solve linear and nonlinear Klein-Gordon equations . The motive of this paper is to show the efficiency of OHAM-DJ for solving the system of Burger’s equations. We consider the system of Burger’s equations as the following : with the initial conditions: and the boundary conditions: where and is its boundary, and are the velocity components to be determined, and are known functions and R is the Reynolds number. This paper is organized into three sections. In Section 2 methodology of OHAM-DJ is presented. In Section 3 application of this method is solved and absolute error of approximate solutions of proposed method is com- pared with exact solutions. In all cases the proposed method yields better results. 2. Methodology of OHAM-DJ Consider (1.1) and let where are boundary operators. According to the basic idea of OHAM , we can construct the optimal homotopy: where is an embedding parameter while and is initial approximation of Equation (1.1) which satisfies the boundary condition, and are nonzero auxiliary functions for, and. Clearly, When and, it holds that, and, respectively. Therefore, as p change from 0 to 1, the solution and varies from to and to respectively, where the initial approximations and are obtained from (2.3) and (2.4). Now, choosing The auxiliary functions and as the form where, are constants to be determined later. Assume that the solutions of (1.1) has the form: The nonlinear terms are decomposed as where are (DJ) polynomials, . For simplicity these polynomials are expressed as: Substiting, (2.5),(2.6), (2.7) and (2.9) into (2.3), and comparing the coefficients of like powers of p, we get The convergence of (2.6) depend upon the auxiliary constants and, which known convergence control parameters or optimal convergence control parameters , if it is convergent at we have Substituting (2.11) into (1.1) we get the residuals and, these parameters can be optimal identified by various methods . Optimization method is one of theses methods to find out the optimal convergence control parameters by means of the minimum of the squared residuals. 3. Numerical Examples In this section, two numerical examples are used to prove the efficiency and the accuracy of the method which we proposed for the system of Burgers’ equations. 3.1. Example 1 Consider the system of two dimensional of Burgers’ equations with the initial conditions as following with the initial conditions: The exact solutions are Accordance to the methodology of OHAM-DJ, Their solutions are By substituting (3.6) into (3.1) we get the residuals and using the optimization method we have computed that and. Finally, putting the values of and into (3.6), to get the approximate solutions (Tables 1-3, Figure 1 and Figure 2). Figure 1. Approximation solutions by OHAM-DJ of example 1, t = 0.01,. Figure 2. Exact solutions of example 1, t = 0.01,. Table 1. Comparison of OHAM-DJ solutions with exact solutions at mesh point x = 2, y = 1 (example 1). 3.2. Example 2 We consider the following two-dimensional Burgers’ equations On square domain, with the initial condition: for which the exact solution is. Where the and in (1.1) are symmetry in this example, and the initial condition are symmetry also. Table 2. Comparison of OHAM-DJ solutions with exact solutions at mesh point x = 1, y = 2 (example 1). Table 3. Comparison of OHAM-DJ solutions with exact solutions at mesh point x = 1.5, y = 2 (example 1). Their solutions are Substituting (3.11) into (3.7) we get the residuals and using the optimization method we have computed that. Finally, putting the values of into (3.11) to get the approximate solutions (Table 4 and Table 5, Figure 3 and Figure 4). In this work, the OHAM-DJ is applied to obtain numerical solutions of the system of Burgers’ equations. The method is efficient and easy to implement where the first or second order solutions rapidly converges to the exact solutions. Furthermore, OHAM-DJ does not need any discretization in time or in space. Thus the solutions of system of Burgers’ equations are not influenced by computer round off errors. The method can be easily Table 4. Comparison of OHAM-DJ solutions with exact solutions at mesh point x = 1, y = 1, (example 2). Table 5. Comparison of OHAM-DJ solutions with exact solutions at mesh point x = 1, y = 1.5, (example 2). Figure 3. Approximation solutions by OHAM-DJ of example 2, t = 0.01,. Figure 4. Exact solutions of example 2, t = 0.01,. extended to other nonlinear equations. Nutshell, OHAM-DJ is a better numerical method for solving nonlinear equations. This paper was funded by King Abdulaziz City for Science and Technology (KACST) in Saudi Arabia. The authors therefore, thank them for their full collaboration. Srivastava, V.K., Ashutosh and Tamsir, M. (2013) Generating Exact Solution of Three Dimensional Coupled Unsteady Nonlinear Generalized Viscous Burgers’ Equations. International Journal of Mathematical Sciences, 5, 1-13. Fletcher, C.A. (1983) Generating Exact Solutions of the Two-Dimensional Burgers’ Equations. International Journal for Numerical Methods in Fluids, 3, 213-216. Fletcher, C.A.J. (1983) A Comparison of Finite Element and Finite Difference Solutions of the One- and Two-Dimensional Burgers’ Equations. Journal of Computational Physics, 51, 159-188. Kutluay, S., Bahadir, A.R. and Ozdes, A. (1999) Numerical Solution of One-Dimensional Burgers Equation: Explicit and Exact-Explicit Finite Difference Methods. Journal of Computational and Applied Mathematics, 103, 251-261. M.A. Abdou and A.A. Soliman. Variational iteration method for solving burger's and coupled burger's equations. Journal of Computational and Applied Mathematics, 181(2):245-251, 2005. Desai, K.R. and Pradhan, V.H. (2012) Solution of Burger’s Equation and Coupled Burger’s Equations by Homotopy Perturbation Method. International Journal of Engineering Research and Applications (IJERA), 2, 2033-2040. Young, D.L., Fan, C.M., Hu, S.P. and Atluri, S.N. (2008) The Eulerian-Lagrangian Method of Fundamental Solutions for Two-Dimensional Unsteady Burgers’ Equations. Engineering Analysis with Boundary Elements, 32, 395-412. Marinca, V. and Herisanu, N. (2015) The Optimal Homotopy Asymptotic Method: Engineering Applications. Springer International Publishing, Gewerbestrasse. Marinca, V., Herisanu, N., Bota, C. and Marinca, B. (2009) An Optimal Homotopy Asymptotic Method Applied to the Steady Flow of a Fourth-Grade Fluid Past a Porous Plate. Applied Mathematics Letters, 22, 245-251. Marinca, V. and Herisanu, N. (2008) Application of Optimal Homotopy Asymptotic Method for Solving Nonlinear Equations Arising in Heat Transfer. International Communications in Heat and Mass Transfer, 35, 710-715. Gupta, A.K. and Ray, S.S. (2014) Comparison between Homotopy Perturbation Method and Optimal Homotopy Asymptotic Method for the Soliton Solutions of Boussinesq-Burger Equations. Computers & Fluids, 103, 34-41. Ullah, H., Nawaz, R., Islam, S., Idrees, M. and Fiza, M. (2015) The Optimal Homotopy Asymptotic Method with Application to Modified Kawahara Equation. Journal of the Association of Arab Universities for Basic and Applied Sciences, 18, 82-88. Iqbal, S., Idrees, M., Siddiqui, A.M. and Ansari, A.R. (2010) Some Solutions of the Linear and Nonlinear Klein-Gordon Equations Using the Optimal Homotopy Asymptotic Method. Applied Mathematics and Computation, 216, 2898-2909. Nawaz, R., Ullah, H., Islam, S. and Idrees, M. (2013) Application of Optimal Homotopy Asymptotic Method to Burger Equations. Journal of Applied Mathematics, 2013, Article ID: 387478. Daftardar-Gejji, V. and Jafari, H. (2006) An Iterative Method for Solving Nonlinear Functional Equations. Journal of Mathematical Analysis and Applications, 316, 753-763. Bhalekar, S. and Daftardar-Gejji, V. (2011) Convergence of the New Iterative Method. International Journal of Differential Equations, 2011, Article ID: 989065. Ali, J., Shah, S., Islam, S. and Khan, H. (2013) Application of Optimal Homotopy Asymtotic Method with Daftardar-Jaffari Polynomials to Non-Linear Differential Equations. World Applied Sciences Journal, 28, 1456-1462. Shah, Z., Nawaz, R., Shah, S., Shah, S.I.A. and Shah, M. (2016) Use of the Daftardar-Jafari Poly-Nomials in Optimal Homotopy Asymptotic Method for the Solution of Linear and Nonlinear Klein-Gordon Equations. Journal of Applied Environmental and Biological Sciences, 6, 71-81. Yu, X., Zhao, G. and Zhang, R. (2011) The New Numerical Method for Solving the System of Two-Dimensional Burgers’ Equations. Computers & Mathematics with Applications, 62, 3279-3291.

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http://dtcourseworkizdp.locksmith-everett.us/shortest-mathematics-dissertation.html

math

A doctor of philosophy the most common procedure is a short-term supervising postgraduate and undergraduate research for doctoral theses and dissertations. Shortest math dissertation, apr 15, 2014 i have sent a very secret list of the 12 most inutile phd phrases (plural of rapport) in history. I tried - and couldn't find any of lesser length funny, all the short ones i found were math-related i thought i had a record (3 pages) from princeton - but it turned out to be a senior. Recent ma grads (arizona teacher initiative) can math performance benefit from short focused thesis title: make mathematics easier for left-handed. Title: nashpdf created date: 12/11/2001 4:05:15 pm. Dissertations 2018 2017 theodore hui saúl blanco rodríguez shortest path poset of bruhat intervals and the department of mathematics 310 malott hall. Short phd thesis physics short phd thesis physics help german homework shortest phd thesis in physics math homework answers ohio university plargiarism masters thesislatex thesis template. Mathematics dissertations as of 2014 countable short recursively saturated models of arithmetic, erez shochat dissertations from 2005 pdf. Mixed zeta functions pieter mostert a dissertation in mathematics chapter 5 is very short. Earlier this week i read through my phd dissertation my research was in an area of pure mathematics called functional analysis which, in short, meant it was self-motivated and void of. How to write a dissertation or the discussions in a dissertation must satisfy the most stringent rules of logic applied to mathematics and science a short. Master thesis in mathematics / applied mathematics master thesis in mathematics / applied mathematics 2 short note on interest rate swaps and swaptions 4. Mathematics students and the effect of the chosen assessment method in foundation as measured with short-answer this dissertation follows the style of. Having problems with writing mathematics papers seeking some professional help with your math this means that even if you place an order for a dissertation. Department of mathematics abstract april 2003 shortest path problems arise in a variety of applications ranging this thesis addresses the problem of nding. Essayoneday provides students with professionally written essays, research papers, term papers, reviews, theses, dissertations and more. I have compiled a very solid list of the 12 most famous phd theses (plural of thesis) the hardest problems in mathematics 12 most famous phd theses in history. The best part about writing a dissertation is finding clever ways to economics, mathematics, and biostatistics had the lowest median page. Thesis format guide the natural sciences, mathematics short references to items in the list appear in parentheses in the text itself. Youngest phd and shortest thesis of india' and `shortest phd thesis' in the limca book of records i'm good in mathematics and have a sharp memory. Created date: 4/5/2011 3:15:50 pm. Database of free mathematics essays - we have thousands of free essays across a wide range of subject areas sample mathematics essays. Using excel solver in optimization problems mathematics and computer science department at least 50% of the money goes to short term issues. Harvard mathematics department harvard department of mathematics phd dissertations archival listing short time behavior of logarithmic derivatives of the heat. Mathematics msc dissertations the department of mathematics and statistics was host until 2014 to the msc course in iain davison - scale analysis of short term. Master thesis company sweden shortest phd thesis how to write the perfect college essay writing a cv for an academic position. Length of the average dissertation may 8 mathematics, and biostatistics tarski, would not give him his phd he thought the thesis was too short. Thesis title by a u thor abstract of thesis submitted in partial ful llment of the requirements for the degree of sample mathematics and text a short line above.

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https://mathstats.uncg.edu/undergraduate/placement/which-gmt-course-should-i-take/

math

Which Math or Stats Course Should I Take ? The Department of Mathematics and Statistics offers several courses (STA 108, MAT 112, MAT 118, MAT 120, MAT 190, MAT 196, MAT 253) that satisfy the Mathematics (GMT or quantitative reasoning) requirement of the General Education Program. This document and conversations with your advisor will help you decide which one(s) to take. STA 108 Elementary Introduction to Probability and Statistics helps you understand you understand what is going on in today’s data-driven world around you. STA 108 will expose the students to the basic statistical rudiments necessary to be an informed member of society. STA 108 is a course that teaches how to collect, organize, analyze, and make sense out of collected data. Take STA 108 if: - You want to learn how to read numbers/data correctly, make predictions, and draw your own conclusions from it. - You want to learn how the result of a survey, poll, or study makes or doesn’t make methodological sense. - You want to learn how the mean (or average) is not the most trusted measure that we should use in our daily lives. All students planning to take Elementary Statistics should take the Statistics Readiness and Diagnostic Test to determine which path into Statistics is right for them. (Ancient and) Contemporary Topics in Mathematics MAT 112 Contemporary Topics in Mathematics covers basic mathematics starting with discoveries by ancient greeks to present day applications of their ideas. God made the integers, all else is the work of humans, Leopold Kronecker, 1886 Following Kronecker’s premise, we assume knowledge of the integers along with the operations addition (plus), subtraction (minus), and multiplication (times). We give examples of the work of humans that is called mathematics that is build on the integers and present practical applications of this work. The material covered includes applications of mathematics that are relevant for the digital age and to other liberal arts disciplines. The course culminates with the topic of public key cryptography. The presentation is rigorous but basic enough for its intended audience to follow. Take MAT 112 if: - You are looking for a course that only requires minimal prior knowledge, that is, addition, subtraction, and multiplication of integers. - You are not comfortable with algebra. - You want to see several ‘unexpected’ applications of mathematics and learn a little about several deep areas of mathematics. - You want to understand what your computer does, when it establishes a secure connection to webpage. - You want to see that public key cryptography is not magic. To get a better idea of what this course is about check out the interactive MAT 112 notes. Mathematics with Business Applications MAT 118 Algebra with Business Applications is an introductory survey of algebra with emphasis on techniques and applications related to business. It also serves as a one-semester preparation for MAT 120 Calculus with Business Applications. It is not intended for students that plan to take MAT 196 Calculus A. Take MAT 118 if: - You want to learn real-world applications of algebra to various subjects that you might use in your personal life or job. - You are thinking of becoming a business major: MAT 118 is a prerequisite to MAT 120 Business Calculus which is a requirement of most degrees in the business school. MAT 118 teaches you the algebra techniques you need to master in order to succeed in MAT 120 In MAT 118 Students will complete projects in case studies to apply these techniques to real-world situations. Students will formulate decisions based on quantitative arguments and communicate these decisions in laymen terms. MAT 120 Calculus with Business Applications provides students an opportunity to appreciate certain concepts in fundamental mathematics, especially functions, limits, derivatives, and applications of the derivative with emphasis on applications in business and social sciences. MAT 120 is a terminal course and not adequate preparation for MAT 296 Calculus B. Take MAT 120 if: - Your program requires you to take MAT 120 Calculus with Business Applications. - You liked algebra and are interested in a brief overview of differential calculus. - You want to learn how math can be useful for business & economics majors. All students who need to take MAT 120 with sufficient background should take the MAT 120 Placement Test to see whether you need to take MAT 118 before MAT 120 or can directly enroll in MAT 120. MAT 196 Calculus A, MAT 296 Calculus B and MAT 396 Calculus C are the main courses of our calculus sequence. The course MAT 190 Precalculus gets you ready for MAT 196 and there is also a support course MAT 181 Foundations of Calculus which can be taken concurrently with MAT 196. Take Calculus if: - Your program requires you to take Calculus. - You will need Calculus for graduate or professional school. - You want to strengthen your degree with a Mathematics or Statistics Minor. - You like mathematics. All students planning to take Calculus should take the Calculus Readiness and Diagnostic Test to determine which path into Calculus is right for them.

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CC-MAIN-2024-18

https://irinsubria.uninsubria.it/handle/11383/4707

math

The spectral and Jordan structures of the web hyperlink matrix G(c) = cG + (1 − c)evT have been analyzed when G is the basic (stochastic) Google matrix, c is a real parameter such that 0 < c < 1, v is a nonnegative probability vector, and e is the all-ones vector. Typical studies have relied heavily on special properties of nonnegative, positive, and stochastic matrices. There is a unique nonnegative vector y(c) such that y(c)TG(c) = y(c)T and y(c)T e = 1. This PageRank vector y(c) can be computed effectively by the power method. We consider a square complex matrix A and nonzero complex vectors x and v such that Ax = λx and v ∗ x = 1. We use standard matrix analytic tools to determine the eigenvalues, the Jordan blocks, and a distinguished left λ-eigenvector of A(c) = cA + (1 − c)λxv ∗ as a function of a complex variable c. If λ is a semisimple eigenvalue of A, there is a uniquely determined projection P such that limc→1 y(c) = Pv for every v such that v ∗ x = 1; this limit may fail to exist for some v if λ is not semisimple. As a special case of our results, we obtain a complex analog of PageRank for the web hyperlink matrix G(c) with a complex parameter c. We study regularity, limits, expansions, and conditioning of y(c), and we propose a complex extrapolation algorithm that may provide an efficient way to compute PageRank. |Data di pubblicazione:||2006| |Titolo:||A general setting for the parametric google matrix| |Digital Object Identifier (DOI):||10.1080/15427951.2006.10129131| |Codice identificativo Scopus:||2-s2.0-77955279653| |Appare nelle tipologie:||Articolo su Rivista|

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CC-MAIN-2019-09

https://thecorporategiveaways.com/journal/radial-wave-equation-for-hydrogen-atom-8ba591

math

But then, that’s the key to calculus: recognizing that 99.999999 effectively approaches 100. In this case, n = 1 and l = 0. Completing the CAPTCHA proves you are a human and gives you temporary access to the web property. The proton has one indivisible positive charge while the electron has one indivisible negative charge. Note that the creators of this cartoon didn’t have the wherewithall to make a ‘right’ atom, giving the nucleus four plus charges and the shell three minus… this would be a positively charged ion of Beryllium. The process of normalization is just to make certain that the value ‘under the curve’ contained by the square of the wave function, counted up across all of space in the integral, is 1. I then divide out the exponential so that I don’t have it cluttering things up. The hydrogen atom problem is a classic problem mainly because it’s one of the last exactly solvable quantum mechanics problems you ever encounter. If the savvy reader so desires, the prescriptions given here can generate any hydrogenic wave function you like… just refer back to my Ylm post where I talk some about the spherical harmonics, or by referring directly to the Ylm tables in wikipedia, which is a good, complete online source of them anyway. Hydrogen atom is simplest atomic system where Schrödinger equation can be solved analytically and compared to experimental measurements. The divergence operation uses Green’s formulas to say that a volume integral of divergence relates to a surface integral of flux wrapping across the surface of that same volume… and then you simply chase the constants. For the power series to be a solution to the given differential equation, each coefficient is related to the one previous by a consistent expression. With the new version of U, the differential equation rearranges to give a refined set of differentials. That’s part of why solving the radial equation is challenging. The modification I made allows me to write U as a portion that’s an unknown function of radius and a second portion that fits as a negative exponent. Why not, I figured; the radial solution is actually a bit more mind boggling to me than the angular parts because it requires some substitutions that are not very intuitive. Operationally, this is just another choice for spherically symmetric potential (i.e. Change ), You are commenting using your Google account. The Bohr radius ao is a relic of the old Bohr atom model that I started off talking about and it’s used as the scale length for the modern version of the atom. A small exercise I sometimes put myself through is defining the structure of del. The simplest case to consider is the hydrogen atom, with one positively charged proton in the nucleus and just one negatively charged electron orbiting around the nucleus. The value produced by divergence is a scalar quantity with no direction which could be said to reflect the ‘poofiness’ of a vector field at any given point in the space where you’re working. Here are the first few generalized Laguerre polynomials: Steven Holzner is an award-winning author of technical and science books (like Physics For Dummies and Differential Equations For Dummies). Hard to sweat the small stuff. The ‘8’ wedged in here is crazily counter intuitive at this point, but makes the quantization work in the method I’ve chosen! If you were to consider an infinitesimal volume of these perpendicular dimensions, at this locally cartesian point, it would be a volume that ‘approaches’ cubic. It’s basically just saying “What if my solution is some polynomial expression Ar^2 -Br +C,” where I can include as many ‘r’s as I want. Coulomb). The recurrence relation also gives a second very important outcome: The energy quantum number must be bigger than the angular momentum quantum number. Some of the higher energy, larger angular momentum hydrogenic wave functions start looking somewhat crazy and more beautiful, but I really just had it in mind to show the math which produces them. Calculate the Wave Function of a Hydrogen Atom Using the…, Find the Eigenfunctions of Lz in Spherical Coordinates, Find the Eigenvalues of the Raising and Lowering Angular Momentum…, How Spin Operators Resemble Angular Momentum Operators, If your quantum physics instructor asks you to find the wave function of a hydrogen atom, you can start with the radial Schrödinger equation, Rnl(r), which tells you that. In between the Sakurai problems, I decided to tackle a small problem I set for myself. ‘Quantized’ is a word invoked to mean ‘discrete quantities’ and comes back to that pesky little feature Deepak Chopra always ignores: the first thing we ever knew about quantum mechanics was Planck’s constant –and freaking hell is Planck’s constant small! The Laplace operator combines gradient with divergence as literally the divergence of a gradient, denoted as ‘double del,’ the upside-down triangle squared. Calculate the Wave Function of a Hydrogen Atom Using the Schrödinger Equation. Further, the electrons are not stacked into a decent representation for the actual structure: cyclic orbitals would be P-orbitals or above, where Beryllium has only S-orbitals for its ground state, which possess either no orbital angular momentum, or angular momentum without any defined direction. Click hereto get an answer to your question ️ The radial wave equation for hydrogen atom is Ψ = 116√(pi) (1a0)^3/2 [ ( x - 1 ) ( x^2 - 8x + 12 ) ] e^-x/2 where, x = 2r/a0 ; a0 = radius of first Bohr orbit.The minimum and maximum position of radial nodes from nucleus are: Also, in that last line, there’s an “= R” which fell off the side of the picture –I assure you it’s there, it just didn’t get photographed. I then perform the typical Quantum Mechanics trick of making it a probability distribution by normalizing it. The Hydrogen Atom Lecture 24 Physics 342 Quantum Mechanics I Monday, March 29th, 2010 We now begin our discussion of the Hydrogen atom. All that I do to find the divergence differential expression is to take the full integral and remove the infinite sum so that I’m basically doing algebra on the infinitesmal pieces, then literally divide across by the volume element and cancel the appropriate differentials. A general form for the radial wave equations appears at the lower right, fabricated from the back-substitutions. is a generalized Laguerre polynomial. You have to solve this by separation of variables. Further, you may not realize it yet, but something rather amazing happened with that number Q. Divergence creates a scalar from a vector which represents the intensity of ‘divergence’ at some point in a smooth function defined across all of space. The first image, where the box size was a little small, was perhaps the most striking of what I’ve seen thus far…, I knew basically that I was going to find a donut, but it’s oddly beautiful seen with the outsides peeled off. Since I was just sitting on all the necessary mathematical structures for hydrogen wave function 21-1 (no work needed, it was all in my notebook already), I simply plugged it into mathematica to see what the density plot would produce. This little bit of math is defining the geometry of the coordinate variables in spherical polar coordinates. I keep finding interesting structures here. I spent some significant effort thinking about this point as I worked the radial problem this time; for whatever reason, it has always been hazy in my head which powers of the sum are allowed and how the energy and angular momentum quantum numbers constrained them. Radius would be some complicated combination of x, y and z. So then, this framework allows you to define the calculus occurring in spherical polar space. A scalar function defines the topography of the hill… it says simply that at some pair of coordinates in a plane, the geography has an altitude. Here is how you construct a specific hydrogen atom orbital from all the gobbledigook written above. After all those turns and twists, this is a solution to the radial differential equation, but not in closed form. It isn’t exactly crippling to the field because the solutions to all the other atoms are basically variations of the hydrogen atom and all, with some adjustment, have hydrogenic geometry or are superpositions of hydrogen-like functions that are only modified to the extent necessary to make the energy levels match. There are three possible area integrals because the normal vector is in three possible directions, one each for Rho, Theta and Phi. After the hydrogen atom, the water gets deeper and the field starts to focus on tools that give insight without actually giving exact answers. Psi basically just becomes R. The first thing to do is take out the units. 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s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703527850.55/warc/CC-MAIN-20210121194330-20210121224330-00512.warc.gz

CC-MAIN-2021-04

https://nl.mathworks.com/matlabcentral/answers/276246-sundials-solver-in-matlab-simulink

math

Support for Sundials is limited in SimBiology. There is no hint that this will be more broadly available anytime soon. Hint and tips: - Use the Simscape modeling language to define DAE's of problems in a way that MATLAB/Simulink can better understand and reformulate the DAE for solving. For instance, SimMechanics is optimized to deal with Index 3 DAE's that arise in rigid motion of multiple bodies moving together. There is no need to algebraically remove the constraints. - If you must work in Simulink, then add states with known dynamics in places that have the algebraic states. For instance, replace an algebraic state with a first order transfer function with 10-1000 times faster dynamics than the rest of the model. This adds stiffness to the ODE system but the DAE already added stiffness in the first place. Choosing the dynamics so they are just faster than the rest of the system will allow the model to run reasonably while minimizing solver performance penalties because of added stiffness.

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CC-MAIN-2021-04

https://math.answers.com/Q/What_is_your_score_if_you_miss_5_questions_on_a_35_question_test

math

Assuming the questions are all weighted the same, you can miss 5 and score 90%. If you miss 6 questions you will get an 85% on a 40 question test. To calculate various test score questions, simply divide the number of correct answers by the number of total questions. For example, on your particular question, if you divide 34 (the number of correct answers) by 40 (the total number of test questions), the answer is .85, or 85%. In order to score 70 or below on a 50-question test, you must answer at least 15 of them wrong. Your score is 73.33% You can miss 10% of questions, or 12 questions If the TABE test has 90 questions, how many I can miss to pass the test? The answer to how many questions you can miss (assuming each question is worth 1 mark) is given below: ((100-90)/100) * 125 = 12.5 questions. You must round this down unless you can be awarded half marks. Assuming no half marks are awarded you can miss up to 12 questions on a 125 question test and score 90% or more. You must get 19 questions right on a 25 question test to earn a score of 75% To get a 50% on the test, you need at least (50/100) * 35 = 17.5 questions correct. If half credit is not possible, you need to get at least 18 questions correct to get a score of at least 50%. A score of 17 will be just shy of 50%. In order to score 95% or better, you must answer at least 76 questions correctly. We're hoping it's not a math test. If you miss five questions out of 30, your score is a 83.33% To get exactly 90% you need to miss 5.6 questions. The answer will depend on the total score for the test and whether or not all the questions are score the same. 25 - 8 = 17 Providing each of the questions carry the same mark. If you miss 28 questions out of 70, your score would be 60% 24 of them. To score 65% you would need to answer 32.5 questions correctly. As you can't answer half a question correctly, you will need to answer 33 correctly resulting in a mark of 66%. Thus you can miss 17. To get at least 90% on a 50 question test, you can miss no more than 5 questions. In order to score 80% on a test with 30 questions, you must give 6 wrong answers. You can do it! Assuming thatall questions carry the same score,there no penalties for unanswered questions, andall the ones that you do answer are correct,you can miss two.

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CC-MAIN-2021-43

https://byjus.com/ncert-exemplar-class-8-science-chapter-11-force-and-pressure/

math

NCERT Exemplar Solutions Class 8 Science Chapter 11 – Free PDF Download The NCERT Exemplar for Class 8 Science Chapter 11 Force and Pressure explains the topics mentioned in CBSE Class 8 Chapter 11. By studying this Exemplar thoroughly, students are able to strengthen their exam preparation. This will help them determine their strengths and weaknesses. NCERT Exemplar Problems provided here are not meant to provide you only with a question bank for examinations, but are primarily meant to enhance your learning process. Practising Exemplar will help you solve different kinds of questions and numericals, which are important from the examination point of view. Force and Pressure is one of the most important chapters of CBSE Class 8 Science. In this chapter, students will learn about the basic concepts of force and pressure. To understand the concepts of force and pressure and to score good marks in the exam, students must understand the basics of the chapter and solve the important questions. To help students, we have provided the NCERT Exemplar for Class 8 Science Chapter 11 Force and Pressure. Download the PDF of the NCERT Exemplar Class 8 Science Solutions for Chapter 11 – Force and Pressure Access Answers to the NCERT Exemplar Class 8 Science Chapter 11 – Force and Pressure Multiple Choice Questions 1. In Fig 11.1, two boys A and B are shown applying force on a block. If the block moves towards the right, which one of the following statements is correct? (a) The magnitude of force applied by A is greater than that of B. (b) The magnitude of force applied by A is smaller than that of B. (c) The net force on the block is towards A. (d) The magnitude of force applied by A is equal to that of B. Answer is (a) Magnitude of force applied by A is greater than that of B. The magnitude of force applied by A is bigger than that of B as a result of the block moves towards right i.e. towards B. 2. In the circuit shown in Fig.11.2, when the circuit is completed, the hammer strikes the gong. Which of the following force is responsible for the movement of the hammer? (a) gravitational force alone (b) electrostatic force alone (c) magnetic force alone (d) frictional force alone Answer is (c) magnetic force alone As electric current flows through the coil it behaves like an electromagnet which creates magnetic force. Hence the answer is magnetic force alone. 3. During dry weather, while combing hair, sometimes we experience hair flying apart. The force responsible for this is (a) force of gravity. (b) electrostatic force. (c) the force of friction. (d) magnetic force. The answer is (b) electrostatic force. On combing the hair, comb and hair get oppositely charged due to electrostatic force. 4. Fig.11.3 shows a container filled with water. Which of the following statements is correct about the pressure of water? (a) The pressure at A > Pressure at B > Pressure at C. (b) The pressure at A = Pressure at B = Pressure at C. (c) The pressure at A < Pressure at B > Pressure at C. (d) The pressure at A < Pressure at B. The answer is (d) Pressure at A < Pressure at B Increase in water leads to an increase in depth. 5. Two objects repel each other. This repulsion could be due to (a) frictional force only (b) electrostatic force only (c) magnetic force only (d) either a magnetic or an electrostatic force The answer is (d) either a magnetic or an electrostatic force Explanation: when two objects are experiencing repulsive force because there may be an electrostatic force or a magnetic force. 6. Which one of the following forces is a contact force? (a) force of gravity (b) force of friction (c) magnetic force (d) electrostatic force The answer is (b) force of friction Force of attraction acts only when the bodies are in contact. 7. A water tank has four taps fixed at points A, B, C, D as shown in Fig. 11.4. The water will flow out at the same pressure from taps at (a) B and C (b) A and B (c) C and D (d) A and C Answer is (a) B and C B and C are at the same level, hence pressure will be the same at B and C. 8. A brick is kept in three different ways on a table as shown in Fig. 11.5. The pressure exerted by the brick on the table will be (a) maximum in position A-C (b) maximum in position B (c) maximum in position (d) equal in all cases. Answer is (a) maximum in position A-C Since the area of contact is minimum pressure will be maximum in A. Very Short Answer Questions 9. A ball of dough is rolled into a flat chapatti. Name the force exerted to change the shape of the dough. 10. Where do we apply a force while walking? While walking we apply force on the ground. 11. A girl is pushing a box towards the east direction. In which direction should her friend push the box so that it moves faster in the same direction? Towards the east. 12., In the circuit shown in Fig.11.6, when the key is closed, the compass needle placed in the matchbox deflects. Name the force which causes this deflection. Answer is Magnetic force. 13. During dry weather, clothes made of synthetic fibre often stick to the skin. Which type of force is responsible for this phenomenon? Answer is Electrostatic force 14. While sieving grains, small pieces fall down. Which force pulls them down? Force of gravity. 15. Does the force of gravity act on dust particles? Yes, the force of gravity act on dust particles. 16. A gas-filled balloon moves up. Is the upward force acting on it larger or smaller than the force of gravity? The upward force is larger than the force of gravity. 17. Does the force of gravitation exist between two astronauts in space? Yes, the force of gravitation exists between two astronauts in space. Short Answer Questions 18. A chapati maker is a machine which converts balls of dough into chapati. What effect of force comes into play in this process? Force works on the dough to convert it to chapati. 19. Fig.11.7 shows a man with a parachute. Name the force which is responsible for his downward motion. Will he come down with the same speed without the parachute? Force of gravity is responsible for his downward motion. If he comes down without parachute his speed will be higher. 20. Two persons are applying forces on two opposite sides of a moving cart. The cart still moves with the same speed in the same direction. What do you infer about the magnitudes and direction of the forces applied? Force applied is of equal magnitude in the opposite direction hence the cart moves with the same speed in the same direction. 21. Two thermocol balls held close to each other move away from each other. When they are released, name the force which might be responsible for this phenomenon. Explain. Two Thermocol balls held close to each other move away from each other, which is because of electrostatic force. The balls having similar charges move away due to repulsion between similar charges. 22. Fruits detached from a tree fall down due to force of gravity. We know that a force arises due to the interaction between two objects. Name the objects interacting in this case. Earth and fruits. 23. A man is pushing a cart down a slope. Suddenly the cart starts moving faster and he wants to slow it down. What should he do? He should apply a force to pull the cart up the slope. 24. Fig. 11.8 shows a car sticking to an electromagnet. Name the forces acting on the car? Which one of them is larger? Magnetic force (in the upward direction) force of gravity or the weight of the car (downward) act on car. Magnetic force is larger than the force of gravity. Long Answer Questions 25. An archer shoots an arrow in the air horizontally. However, after moving some distance, the arrow falls to the ground. Name the initial force that sets the arrow in motion. Explain why the arrow ultimately falls down. Archer puts muscular force to stretch the string. This will change the shape of the arrow. When the string is released arrow regains its original position which gives it the initial force to set the motion. Because of gravitational from it comes down towards after some time. 26. It is difficult to cut cloth using a pair of scissors with blunt blades. Explain. The blunt blade has a larger area than shard edged blades. Because of this, blunt blade produces a low pressure which makes it difficult to cut the cloth. Whereas in sharp blade surface area is much is very less which increase the pressure produced. This makes the cutting of cloth easier with sharp blades. 27. Two rods of the same weight and equal length have different thickness. They are held vertically on the surface of sand as shown in Fig.11.9. Which one of them will sink move? Why? In Rod B area of contact is smaller. Hence the weight of the rod (Force) produces more pressure. In Case of the rod, the same force produces less pressure. 28. Two women are of the same weight. One wears sandals with pointed heels while the other wears sandals with flat soles. Which one would feel more comfortable while walking on a sandy beach? Give reasons for your answer. Women’s height are same and they apply the same weight when they walk. But women wearing sandal with a flat heel will be more comfortable while walking on a sandy beach. This is because flat soles have larger area compared to the sandals with pointed heels. Also, the pressure exerted by the pointed heels will be more compared to that with sandals having flat soles. This pressure will make the sandals with pointed soled sink in the sand which will make difficult to walk on sand. 29. It is much easier to burst an inflated balloon with a needle than by a finger. Explain. The pressure exerted on an inflated balloon by the needle will be more as it has a smaller area of contact compared to the finger. This larger pressure pierces the surface of the balloon easily which will make the balloon burst. 30. Observe the vessels A, B, C and D shown in Fig.11.10 carefully. The volume of water taken in each vessel is as shown. Arrange them in the order of decreasing pressure at the base of each vessel. Explain. B, D, A, C. Because the pressure of a liquid column depends upon the height of the liquid column and not on volume of the liquid. Sub-topics of the CBSE syllabus Class 8 Science Chapter 11 Force and Pressure - Force – A Push or Pull - Forces Are Due to an Interaction - Exploring Forces - A Force Can Change the State of Motion - Force Can Change the Shape of an Object - Contact Forces - Non-contact Forces - Pressure Exerted by Liquids and Gases - Atmospheric Pressure BYJU’S presents outstanding NCERT Solutions, study materials, sample papers, previous years’ question papers and video and animation lessons for a thorough understanding and to memorise topics for a longer period. To get access to all study materials we provide, log on to BYJU’S website or download BYJU’S – The Learning App. |NCERT Solutions for Class 8 Science Chapter 11| |CBSE Notes for Class 8 Science Chapter 11| Frequently Asked Questions on NCERT Exemplar Solutions for Class 8 Science Chapter 11 What are the topics covered under Chapter 11 of NCERT Exemplar Solutions for Class 8 Science? 1. Force – A Push or Pull 2. Forces Are Due to an Interaction 3. Exploring Forces 4. A Force Can Change the State of Motion 5. Force Can Change the Shape of an Object 6. Contact Forces 7. Non-contact Forces 9. Pressure Exerted by Liquids and Gases 10. Atmospheric Pressure What are non-contact forces in Chapter 11 of NCERT Exemplar Solutions for Class 8 Science? Can students rely on NCERT Exemplar Solutions for Class 8 Science Chapter 11 from BYJU’S? |NCERT Exemplar Class 8 Science Chapter 12 Friction| |NCERT Exemplar Class 8 Science Chapter 13 Sound| |NCERT Exemplar Class 8 Science Chapter 14 Chemicals Effects of Electric Current| |NCERT Exemplar Class 8 Science Chapter 15 Some Natural Phenomena|

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CC-MAIN-2023-40

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&arnumber=1094385&sortType%3Dasc_p_Sequence%26filter%3DAND(p_IS_Number%3A23911)

math

Skip to Main Content The class of switching networks, composed of stages of identical square switches arranged symmetrically around a center stage (Benes' networks), is considered. The synthesis problem of selecting from this class a rearrangeable network with the minimum number of crosspoints is solved. Benes' approach, (using relation of covering), is taken into consideration. The new structures of the networks are in some cases different than those already known. Modifications of Benes' theorems result in lowering the number of stages of a switching network with the minimum number of crosspoints. This lowering can bear some practical significance, which could simplify the control devices. A model comparison is given of the known and new results.

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CC-MAIN-2016-30

https://plainmath.net/31174/following-generalized-determine-convergence-particular-applications

math

Maurice and Lester are twins who have just graduated from college. They have both been offered jobs where their take-home pay would be $2500 per month. Their parents have given Maurice and Lester two options for a graduation gift. Option 1: If they choose to pursue a graduate degree, their parents will give each of them a gift of $35,000. However, they must pay for their tuition and living expenses out of the gift. Option 2: If they choose to go directly into the workforce, their parents will give each of them a gift of $5000. Maurice decides to go to graduate school for 2 years. He locks in a tuition rate by paying $11,500 for the 2 years in advance, and he figures that his monthly expenses will be $1000. Lester decides to go straight into the workforce. Lester finds that after paying his rent, utilities, and other living expenses, he will be able to save $200 per month. Their parents deposit the appropriate amount of money in a money market account for each twin. The money market accounts are currently paying a nominal interest rate of 3 percent, compounded monthly. Lester works during the time that Maurice attends graduate school. Each month, Lester saves $200 and deposits this amount into the $5000 money market account that his parents set up for him when he graduated. If Lester's initial balance is u0=5000,un is the current month's balance, and un−1 is last month's balance, write an expression for un in terms of un−1.

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CC-MAIN-2022-21

http://www.sufog.com/index.php?sb=d&s=mathematics&n=Mathematics&u=Circle

math

|Page 1 of 7,085,507 Results| TAMU Math Circle | The Official TAMU Math Circle Website TAMU Math Circle | The Official TAMU Math Circle Website TAMU Math Circle The Official TAMU Math Circle Website Menu Skip to content Home About Contact Google Group Orga-nizers Meetings Next Meetings Past Meetings Registration Manual Videos ... more pages Berkeley Math Circle Berkeley Math Circle Home Purpose Program BMC Calendar BMC Apply for BMC BMC Ele-mentary Monthly Contest People Sponsors FAQ Parents Evaluation Circle Archives Books Links News Contact BAMO Info Awards Gallery Speakers BAMO Archives Donate to ... more pages Free PowerPoint Presentations about Circles for Kids & Teachers ... ... Areas of Circles Finding the Areas of Circles Fundamentals of Geometric Shapes Circles Circle Terminology Circle Vocabulary Circle Theorems Equations of Circles Tangents of a Circle What Is a Circle? See Also: Geometry , Shapes , Perimeter ... more pages UCSB Math Circle UCSB Math Circle UCSB Math Circle University of California, Santa Barbara Menu Home Schedule Problems of the week People Registration Donations FAQ Links Contact UCSB Math ... more pages Stanford Math Circle Stanford Math Circle Stanford Math Circle Stanford Math Circle SMC Home Current Schedule SMC Elementary Apply to the Math Circle Programs Frequently Asked Questions Directions Who We Are SMC Archives Links The Stanford Math Circle is jointly ... more pages Michigan Math Circle Michigan Math Circle Home Schedule Register Directions FAQ Sponsors Links About UM Math The Michigan Math Circle welcomes high school and middle school students to the Mi-chigan Ann Arbor campus on Thursday evenings from 6:30 to 8 for ... more pages Interactive Mathematics - Learn math while you play with it! ... some of the story behind this interesting map... more » Reuleaux triangles Reuleaux tri-angles have a property similar to circles - they have constant diameter when rotated... more » Popular classics Ten Ways to Survive the Math Blues How ... more pages National Association of Math Circles | National Association of Math ... ... Circle Community Resources AMS/ MAA Math Circle Library Circle in a Box Math Circle Videos (Youtube Channel) Math Circle Activities and Lesson Plans List of Math Circle Pro-blems Math Circle Problems as Problem Sets Math Circle Partnership ... more pages ... chord: a line segment within a circle that touches 2 points on the circle. circumference: the distance around the circle. diameter: the longest distance from one end of a circle to the other. origin: the center of the circle pi ( ): A ... more pages ... we could be right on the circle. Example: "A" is outside the circle, "B" is inside the ci-rcle and "C" is on the circle. Activity: Approximate Value For Pi Pi Plane Unit Circle Circle Sector and Segment Plane Geometry Geometry Index ... more pages

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CC-MAIN-2020-29

http://www.chegg.com/homework-help/questions-and-answers/given-a-distribution-3000-numbers-that-are-assumed-to-be-normally-distributed-with-and-120-q3406662

math

Given a distribution 3,000 numbers that are assumed to be normally distributed with and ? = 120 and ? = 25 a. Use the central limit theorem to describe the sampling distribution of the mean for the samples of size 144 (including the mean and standard error for the sampling distribution). b. Use the sampling distribution of the mean for a sample of size 144. Based on the properties of the normal distribution, determine the following probabilities: i. Probability of selecting a random sample with the mean larger than 121.4. ii. Probability of selecting a random sample with the mean smaller than 118.2. Present your calculation procedures for the calculation problems.

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CC-MAIN-2013-20

https://www.jiskha.com/display.cgi?id=1275622925

math

chemistry(check my steps) posted by eng . The electrochemical cell described by the cell notation has a standard cell potential of -0.35 V. Calculate the Wmax (kJ) the cell has done if 1893.5 g of MnO42-(aq) (Molar Mass - 118.94 g/mol) forms. Round your answer to 3 significant figures. Pt(s) | Hg22+(aq), Hg2+(aq)||MnO4-(aq), MnO42-(aq) | Pt(s) since there are 2 transferred eletrons chemistry(check my steps) - Other than omitting a negative sign on the -nEF I don't see anything wrong but you haven't answered the question.

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CC-MAIN-2018-05

http://www.hotukdeals.com/deals/hetty-het-200a-or-henry-hvr-200-22-545299

math

A good deal and at the lowest price listed on hotukdeals for this Hetty model - HVR 200-22. Priced at £84.99 and use attached 15% voucher to bring the price down to £72.24. Reserve and Collect price only. Edit: Thanks to Poodyboy who found that Henry is also available instore at the same price, but not listed on the Homebase Website at £84.99. # 1200 watts. # Hose length 2.4m. # 9 litre dust bag. 4 bags included 1 x 4 Hepa flow bags. # Variable power control - hi/low. # Commercial grade filter system. # Washable filter. # Includes accessories 2.4 meter hose floor nozzle, extension tubes, crevice tool, dusting brush, upholstery brush. # Stainless steel extension tubes. # Adjustable floor head for carpet and hard floor cleaning. # 10m power cord. Weight 6.9kg. # Manufacturer's 2 year guarantee.

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CC-MAIN-2017-26

http://www.swtor.com/community/showpost.php?p=7301917&postcount=141

math

OP needs to learn how basic probability works. 2/10 chance =/= guaranteed 2 successes in 10 trials. That is all. While there are people in this thread that have basic confusions on the subject of probability, the OP (Darth_Sweets) is certainly not one of them. He used a type of statistical analysis called a confidence interval, and performed sophisticated math analyzing his raw data. The only disagreement I had with his analysis was the sample size, not his methods or understanding of probability. Either you didn't actually read the OP, or you didn't understand what he was saying.

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CC-MAIN-2016-50

https://www.hometheaterforum.com/community/threads/aspect-ratio-and-stanley-kubrick.64138/

math

A coworker just told me he accidently got the wrong full metal jacket. This is full frame. I told him Kubrick had everything on video in full frame. I then went to various sites to prove this to him. When we hit imdb I became confused... It seems Kubrick shot most of his stuff (aside from sparticus) at 1.37:1. Here's my question.... two parts. 1.37:1 sure is close to 1.33:1 and it would seem that full frame is the "correct" choice. What was done for things like Full Metal Jacket Laser Disc which was 1.85:1? Was it cropped?

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CC-MAIN-2019-04

https://www.physicsforums.com/threads/photon-polarization-question.280735/

math

1. The problem statement, all variables and given/known data Hi, I have a question regarding a set of equations in Feynmann volume 3. On chapter 11, page 11, Feynmann discusses the right-hand and left-hand circulation for the polarization of the photon. He states: "In the classical theory, right-hand circular polarization has equal components in x and y which are 90 out of phase. In the quantum theory, a right-hand circularly polarized (RHC) photon has equal amplitudes to be polarized |x> or |y>, and the amplitudes are 90 out of phase. Calling a RHC photon a state |R> and a LHC photon a state |L>, we can write: 2. Relevant equations |R> = (|x> + i|y>) / sqrt(2) |L> = -(|x> - i|y>) / sqrt(2)." 3. The attempt at a solution This is more of a question, but isn't it true that for RHC the x-component is 90 ahead rather than behind? Thus, shouldn't we place the i (which is a 90 phase factor) in front of the |x> instead of the |y>? Same question goes for the LHC equation, but with phases reversed. Thanks.

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CC-MAIN-2018-39

https://fatcat.wiki/release/uyfhnbohk5aszdkqkuoaapk6gi

math

The fermion masses in the standard model are introduced as arbitrary parameters and there is no understanding of their origin. In this letter it is suggested that small non zero neutrino masses may be a reflection of broken stochastic supersymmetry that guarantees the equivalence of Parisi Wu stochastic quantization scheme to standard quantum field theory. Archived Files and Locations |application/pdf 92.4 kB ||

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CC-MAIN-2021-49

https://www.slideserve.com/jariah/secants-and-tangents-section-10-4

math

Secants and Tangents Section 10.4. By: Matt Lewis. Secants and Tangents. -Objectives Identify secant and tangent lines and segments. Distinguish between two types of tangent circles. Recognize common internal and common external tangents . Definitions. Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. By: Matt Lewis - - - - - - - - - - - - - - - - - - Sample Problem #1 Step 1 - Constructing radius PB at the point of tangency as shown. Since lengths of all the radii of a circle are equal, PB = 8. Step 2 - Since the tangent and the radius at the point of tangency are always perpendicular, ΔABP is a right angled triangle. Step 3 - Using the Pythagorean theorem, Step 4 - Substituting for AP, AB and BP, Step 5 - Since the negative value of the square root will yield a negative value for x, taking the positive square root of both sides, x = 9. Given: AC is Tangent to circle P Calculate the value of X. Sample Problem #2 OA is AP and OB PB. AOBP is a quadrilateral. 90 + 90 + 140 + X = 360 X = 40 PA and PB are Tangents to Circle O. a, b, and c. JK is tangent to circles Q & P. Given: Two tangent circles, is a common external tangent, is the common internal tangent. Prove: D is the midpt. of BC. OS = 20 PS = 12 What is QS? 2. BC is a common 3. DA is a common 4. Any two tangents drawn to a circle from the same point are . 4. DB DA 5. DC DA 5. Same as 4. 6. DB DC 7. If a point divides a line into two seg., then it is the midpt. 7. D is the midpt. of Rhoad, Richard. Geometry for Enjoyment and Challenge. Boston: McDougal Littell, 1991. Wolf, Ira. Barron’s SAT Subject Test- Math Level I. Barron Publishing, 2008. 27 May 2008. Practice Problems Geometry. http://www.hotmath.com, 27 May 2008.

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https://qualitygradeprofessors.com/quantitative-analysis/

math

Please use the fileand complete the following: a. Please use the descriptive statistics tool to analyze with appropriate measures of central tendency and dispersion the fields “sales” and “profit” and “profit margin”. b. Please calculate out the following percentiles for the field “sales”: 10th, 25th, 50th, 75th, and 90th percentile. c. Please use the Pivot Table tool to analyze “sales” by region. The analysis should include the number of sales by each region (count), the total amount of sales (sum) by each region, the average sales amount by each region, and the standard deviation of sales by each region. Make sure to attach the excel document showing work, and all answers

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https://electronics.stackexchange.com/questions/166532/control-leds-with-pwm-and-transistors

math

Your problem is pretty straightforward. Your current limiting resistor is much too large. If your LEDs are in fact allowing as much current as you assert, the voltage across the resistor will be .08 x 30, or 2.4 volts. This leaves (at most) 0.9 volts across the LEDs, and that is not enough to allow them to produce much light at all. You should resize your resistor, taking into account the forward voltage (Vf) of the LEDs, to allow maximum current with transistor fully on, and a transistor voltage drop of about 0.1 to 0.2 volts. Either that, or increase your source voltage. Once you do that, you're still likely to have problems. With 5 LEDs in parallel, whichever one has the smallest Vf will hog current and glow more brightly than the others. In the worst case, this will cause it to get hotter, its Vf will drop, and it will hog even more current and get even brighter. At this worst-case limit, it will draw nearly 5 times as much current as you expect. If this level is too high, the LED may fail open, leaving the process to repeat in turn with the other 4, then the other 3, etc. Finally, you need to examine the data sheet for your transistor and determine its current gain. This is the hfe which Ignacio referred to his comment. To make life more difficult, gain changes with current level, as you will see if you pay attention to the data sheet. But let's say that the gain is 100, which is a decent starting point for modern NPN signal transistors running at less than 100 mA. Keep in mind that, due to your large limit resistor, the current will never approach the 80 mA you think it will. Let's say 10 mA, just as a start. Then any base current above (10 mA / 100) will make no difference to the LED current, since the transistor is pulling as much current as it can, and the current is limited by the resistor and the LEDs. 10 mA/100 is 0.1 mA, or 3% of your nominal drive, and is entirely consistent with what you see. In order to check this, fire up your circuit and connect the collector of your transistor to ground. Now measure the voltage across the 30 ohm resistor, and divide by 30, to give your total, maximum current. Divide this by 10 or so to get the base current you need. To understand why you divide by 10 rather than 100, start learning about transistor saturation.

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http://mathhelpforum.com/trigonometry/98680-angular-intersection-i-think-trig-used-but-im-well-confused-pls-pls-pls-help.html

math

Intersection.... how would u do this? the following clock wise angles were observed: at A from B to P the angle is 64d 42m 42s at B from A to P the angle is 296d 15m 31s the co-ordinates of A are 500E 500N the co-ordinates of B are 703.501E 240.809N Find the co-ordinates of P I have added two points: C is due north of point P & C is due west of point A D is due east of A Points D, A, & C all have north coordinate of 500.000 The difference of the Northing coordinates from A to B: ( 240.809N - 500.000N ) = -259.191 The difference of the Easting coordinates from A to B: ( 703.501E - 500.000E ) = +203.501 The distance AB can be computed: At this moment you should calculate the angle DAB since it will be needed later: [NOTE: We know that DAB is a negative angle, but that attribute will be ignored] Angle CAP = 180d - ( 51d 51m 47s ) - ( 64d 42m 42s) = 63d 25m 31s <- NEED THIS! Angle APC = 90d - ( 63d 25m 31s ) = 26d 34m 29s <-- do not need this but there it is. You are given the interior angle BAP = 64d 42m 42s The interior angle at B is 360d - (296d 15m 31s) = 63d 44m 29m The third angle at P is: 180deg minus angles A & B 180d - (64d 42m 42s) - (63d 44m 29m) = 51d 32m 49s Using the Rule of Sines (or The Law of Sines, or Sine Law) which leads to We do not require the distance BP. The northing coordinates of P: North coord of A MINUS distance AP x sin(angle CAP) The easting coordinates of P: East coords of A MINUS distance AP x cos(angle CAP) Run this and determine the values. I will do the math parts later as a check. From the image it is clear that Point P is SOUTH & WEST of Point A. If you do not have the visual aid, it is imperative to be cognizant of the signs of the computed values.

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https://mathshistory.st-andrews.ac.uk/Biographies/Wu/

math

BiographySijue Wu's school and undergraduate education were in China. She studied at Beijing University, being awarded her first degree in 1983 and a Master's Degree in 1986. Even before the award of the Master's Degree, she had a paper published, namely Hilbert transforms for convex curves in Rn. She then went to the United States to undertake research. Her doctoral studies were undertaken at Yale University with Ronald Raphael Coifman as her thesis advisor. She submitted her thesis, Nonlinear Singular Integrals and Analytic Dependence, in 1990 and was awarded a Ph.D. She begins her introduction to her thesis as follows:- This thesis is composed of three interrelated parts: w-Calderón-Zygmund operators, a wavelet characterization for weighted Hardy spaces, and the analytic dependence of minimal surfaces on their boundaries.After the award of her doctorate, Wu was appointed as Courant Instructor at the Courant Institute, New York University. She was a member at the Institute for Advanced Study at Princeton in the autumn of 1992 and was then she was appointed Assistant Professor at Northwestern University, holding this position for four years until 1996. Her publications during this period included: A wavelet characterization for weighted Hardy spaces (1992); (with Italo Vecchi) On L1 -vorticity for 2-D incompressible flow (1993); Analytic dependence of Riemann mappings for bounded domains and minimal surfaces (1993) and w-Calderón-Zygmund operators (1995). After spending the year 1996-97 as a member of the Institute for Advanced Study at Princeton, she was appointed as Assistant Professor at the University of Iowa. In 1997 she published the important paper Well-posedness in Sobolev spaces of the full water wave problem in 2-D. Shu Ming Sun begins a very informative review as follows:- Everyone is familiar with the motion of water waves in everyday experience, and there has been an extremely rich variety of phenomena observed in the motion of such waves. However, the full equations governing the motion of the waves are notoriously difficult to work with because of the free boundary and the inherent nonlinearity, which are non-standard and non-local. Although many approximate treatments, such as linear theory and shallow-water theory as well as numerical computations, have been used to explain many important phenomena, it is certainly of importance to study the solutions of the equations which include the effects neglected by approximate models. The well-posedness of the fully nonlinear problem is one of the main mathematical problems in fluid dynamics. Here, the motion of two-dimensional irrotational, incompressible, inviscid water waves under the influence of gravity is considered.Promoted to Associate Professor at Iowa in 1998, Wu was appointed as an Associate Professor at the University of Maryland, College Park, in 1998. The university announced her appointment as follows:- Sijue Wu comes to us from the University of Iowa. Her research interests centre on harmonic analysis and partial differential equations, in particular nonlinear equations from fluid mechanics. Her recent work concerns the full nonlinear water wave problem and the motion of general two-fluid flows.At the 107th Annual Meeting of the American Mathematical Society in January 2001 in New Orleans, Wu was awarded the 2001 Satter Prize. The citation reads :- The Ruth Lyttle Satter Prize in Mathematics is awarded to Sijue Wu for her work on a long-standing problem in the water wave equation, in particular for the results in her papers (1) "Well-posedness in Sovolev spaces of the full water wave problem in 2-D" (1997); and (2) "Well-posedness in Sobolev spaces of the full water wave problem in 3-D" (1999). By applying tools from harmonic analysis (singular integrals and Clifford algebra), she proves that the Taylor sign condition always holds and that there exists a unique solution to the water wave equations for a finite time interval when the initial wave profile is a Jordan surface.Of the paper (2) Emmanuel Grenier writes:- In this very important paper the author investigates the motion of the interface of a 3D inviscid, incompressible, irrotational water wave, with an air region above a water region and surface tension zero.In her response Wu thanked her teachers, friends, and colleagues, making special mention of her thesis advisor Ronald Coifman for the constant support he had given her and Lihe Wang for his friendship and his help. Also in 2001 Wu received a Silver Morningside Medal at the International Congress of Chinese Mathematicians held in Taiwan in December:- ... for her establishment of local well-posedness of the water wave problems in a Sobolev class in arbitrary space dimensions.In August 2002 Wu was an invited speaker at the International Congress of Mathematicians held in Beijing where she delivered the lecture Recent progress in mathematical analysis of vortex sheets. She gave the following summary of her lecture:- We consider the motion of the interface separating two domains of the same fluid that move with different velocities along the tangential direction of the interface. We assume that the fluids occupying the two domains are of constant densities that are equal, are inviscid, incompressible and irrotational, and that the surface tension is zero. We discuss results on the existence and uniqueness of solutions for given data, the regularity of solutions, singularity formation and the nature of the solutions after the singularity formation time.Wu was awarded a Radcliffe Institute Advanced Study Fellowship for the academic year 2002-2003. Her project Mathematical Analysis of Vortex Dynamics was described in an announcement of the award :- Recently, Wu's research has focused on nonlinear equations from fluid dynamics. Using harmonic analysis technique, she has established the local well-posedness of the full two- and three-dimensional waterwave problem. This settled a longstanding problem. As a Radcliffe fellow, Wu will continue her study of vortex sheet dynamics, a phenomenon that arises from the mixing of fluids, such as occurs during aircraft takeoffs. A vortex sheet is the interface separating two domains of the same fluid across which the tangential component of the velocity field is discontinuous. Achieving a better understanding of the motion of a vortex sheet requires proper mathematical modelling; Wu's long-term goal is to establish a successful model. She will also work on the boundary layer problem, another problem arising from fluid dynamics.One outcome of this project, and of an NFS grant she was awarded for 2004-2009, was the paper Mathematical analysis of vortex sheets (2006). Helena Nussenzveig Lopes begins a review of this paper by explaining what vortex sheets are:- Vortex sheets are an idealized model of flows undergoing intense shear. In planar flows they are mathematically described as curves along which the velocity is tangentially discontinuous. Vortex sheets arise in a wide range of physical problems, and hence it is of fundamental importance to understand their evolution. The Birkhoff-Rott equations provide a mathematical description of the evolution of a vortex sheet. However, they have been shown to be ill-posed in several function spaces. It is a longstanding open problem to determine a function space in which these equations are well-posed, or, alternatively, to describe the evolution past singularity formation; this is the problem addressed in the present paper.Wu was named Robert W and Lynne H Browne Professor of Mathematics at the University of Michigan and delivered her inaugural lecture Mathematical Analysis of Water Waves on 29 October 2008. The Browne Professorship recognizes the Wu's outstanding contributions to science and teaching. Finally, let us mention her recent important paper Almost global wellposedness of the 2-D full water wave problem (2009). - 2001 Satter Prize, Notices Amer. Math. Soc. 48 (4) (2001), 411-412. - 2002-2003 Radcliffe Institute Fellows, Sijue Wu, Mathematics, Mathematical Analysis of Vortex Dynamics. http://www.radcliffe.edu/fellowships/fellows_2003swu.aspx Additional Resources (show) Other websites about Sijue Wu: Honours awarded to Sijue Wu Written by J J O'Connor and E F Robertson Last Update February 2010 Last Update February 2010

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https://math.biu.ac.il/node/1557

math

Free profinite subgroups and Galois representations Mark Shusterman (Tel Aviv University) 06/05/2015 - 12:15 - 11:15 Third floor seminar room The talk is going to be about the work carried out as part of my MSc thesis. Motivated by recent arithmetic results, we will consider new and improved results on the freeness of subgroups of free profinite groups: 1.The Intermediate Subgroup Theorem - A subgroup (of infinite index) in a nonabelian finitely generated free profinite group, is contained in a free profinite group of infinite rank. 2. The Verbal Subgroup Theorem - A subgroup containing the normal closure of a (finite) word in the elements of a basis for a free profinite group, is free profinite. These results shed light on several theorems in Field Arithmetic and may be combined with the twisted wreath product approach of Haran, an observation on the action of compact groups, and a rank counting argument to prove a generalization of a result of Bary-Soroker, Fehm, and Wiese on the profinite freeness of subgroups arising from Galois representations. תאריך עדכון אחרון : 26/04/2015

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https://alternativeeconomics.co/blogline/85493-richard-feynman-om-mathematics

math

Lars Jörgen Pålsson Syll is a Swedish economist who is a Professor of Social Studies and Associate professor of Economic History at Malmö University College. Nobel prize winner Richard Feynman on the use of mathematics: “Mathematicians, or people who have very mathematical minds, are often led astray when “studying” economics because they lose sight of the economics. They say: ‘Look, these equations … are all there is to economics; it is admitted by the economists that there is nothing which is not contained in the equations. The equations are complicated, but after all they are only mathematical equations and if I understand them mathematically inside out, I will understand the economics inside out.’ Only it doesn’t work that way. Mathematicians who study economics with that point of view — and there have been many of them — usually make little contribution to economics and, in fact, little to mathematics. They fail because the actual economic situations in the real world are so complicated that it is necessary to have a much broader understanding of the equations.“ I have replaced the word “physics” (and similar) by the word “economics” (and similar) in this quote from Page 2-1 in: R. Feynman, R. Leighton and M. Sands, The Feynman Lectures on Physics, Volume II, Addison-Wesley Publishing, Reading, 1964,

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https://www.finesoftware.de/hilfe/geo5/pl/prostokatny-przekroj-zelbetowy-obciazony-momentem-zginajacym-normalna-sila-sciskajaca-i-sila-tnaca-m-n-v-07/

math

Verification of Rectangular RC Cross-Section The cross-section is rectangular, unilaterally reinforced and loaded by the bending moment and normal compression force. The program verifies a reinforced concrete section using the method of limit deformation (Art. 8.1). The maximum allowable strain of concrete in compression is 0.003. Compression reinforcement is not taken into account. The computed degree of reinforcement is checked using the following expressions: Interaction diagram N-M Usage ratio of concrete cross-section subject to the combination of bending moment and normal force is determined as |0L| / |0R|. Where L is load and R is strength with prescribed excentricity. Bending without normal force The cross-section is rectangular, reinforced on one side and loaded by the bending moment M. The permissible moment for a given area of reinforcements As reads: for L class reinforcement (Art. 2.2.2): for N class reinforcement: The program further checks whether the neutral axis parameter ku is less than the limit value (Art 8.1.5) : First, the program computes the ultimate shear strength of concrete Vuc (Art. 184.108.40.206). where (Art. 220.127.116.11, Art. 18.104.22.168): If the ultimate shear strength of concrete is exceeded, the ultimate shear strength Vu,max is checked (Art. 22.214.171.124). Next, the necessary reinforcement area is given by (Art. 126.96.36.199):

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https://community.nxp.com/thread/359295

math

I have a question about i.MX6 PMIC_ON_REQ. Please see Table 100 in IMX6DQCEC Rev.3. I understand PMIC_ON_REQ is default "High" logic after supply VDD_SNVS_IN since the value of out of reset condition is "Open Drain with PU (100k)", right? Next, please see Table 60-3 in IMX6DQRM Rev.2. If the above my understanding is correct, i.MX6DQ cannot behave as "ON, first time" in this table, can it? Would you give me your comment whether my understanding is wrong or the "ON, first time" is unfeasible?

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https://branemrys.blogspot.com/2005/09/on-flaw-with-island-objection.html

math

There's an interesting discussion at FQI about Gaunilo's objection to Anselm's ontological argument. I think the objection is usually overrated. One reason (of several) is that it equivocates. Anselm's argument uses the following description: (A) that than which no greater can be thought It argues from this to the existence of (A). Gaunilo's objection attempts to build a parallel description that allows one to reduce to absurdity: (B) that island than which no greater can be thought But (B) is ambiguous. It can mean either: (C) that island than which no greater island can be thought And if we look at what people say about the objection, they almost always seem to take it in this sense. But (C) is not parallel to (A). The true parallel is: (D) that island than which nothing greater can be thought This is obviously problematic in a way that (A) is not, namely, that we can easily think of a being greater than any island. More can be said about this matter, but I only have this terminal for a few more minutes. I'll say more about other issues that come up with the Island Objection when I'm at a campus computer.

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https://onestopgate.com/gate-syllabus/instrumentation-engineering.asp

math

GATE Syllabus for Instrumentation Engineering - IN Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors. Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series. Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green's theorems. Differential equations: First order equation (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy's and Euler's equations, Initial and boundary value problems, Partial Differential Equations and variable separable method. Complex variables: Analytic functions, Cauchy's integral theorem and integral formula, Taylor's and Laurent' series, Residue theorem, solution integrals. Probability and Statistics: Sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Discrete and continuous distributions, Poisson, Normal and Binomial distribution, Correlation and regression analysis. Numerical Methods: Solutions of non-linear algebraic equations, single and multi-step methods for differential equations. Transform Theory: Fourier transform, Laplace transform, Z-transform. Basics of Circuits and Measurement Systems: Kirchoff's laws, mesh and nodal Analysis. Circuit theorems. One-port and two-port Network Functions. Static and dynamic characteristics of Measurement Systems. Error and uncertainty analysis. Statistical analysis of data and curve fitting. Transducers, Mechanical Measurement and Industrial Instrumentation: Resistive, Capacitive, Inductive and piezoelectric transducers and their signal conditioning. Measurement of displacement, velocity and acceleration (translational and rotational), force, torque, vibration and shock. Measurement of pressure, flow, temperature and liquid level. Measurement of pH, conductivity, viscosity and humidity. Analog Electronics: Characteristics of diode, BJT, JFET and MOSFET. Diode circuits. Transistors at low and high frequencies, Amplifiers, single and multi-stage. Feedback amplifiers. Operational amplifiers, characteristics and circuit configurations. Instrumentation amplifier. Precision rectifier. V-to-I and I-to-V converter. Op-Amp based active filters. Oscillators and signal generators. Digital Electronics: Combinational logic circuits, minimization of Boolean functions. IC families, TTL, MOS and CMOS. Arithmetic circuits. Comparators, Schmitt trigger, timers and mono-stable multi-vibrator. Sequential circuits, flip-flops, counters, shift registers. Multiplexer, S/H circuit. Analog-to-Digital and Digital-to-Analog converters. Basics of number system. Microprocessor applications, memory and input-output interfacing. Microcontrollers. Signals, Systems and Communications: Periodic and aperiodic signals. Impulse response, transfer function and frequency response of first- and second order systems. Convolution, correlation and characteristics of linear time invariant systems. Discrete time system, impulse and frequency response. Pulse transfer function. IIR and FIR filters. Amplitude and frequency modulation and demodulation. Sampling theorem, pulse code modulation. Frequency and time division multiplexing. Amplitude shift keying, frequency shift keying and pulse shift keying for digital modulation. Electrical and Electronic Measurements: Bridges and potentiometers, measurement of R,L and C. Measurements of voltage, current, power, power factor and energy. A.C & D.C current probes. Extension of instrument ranges. Q-meter and waveform analyzer. Digital voltmeter and multi-meter. Time, phase and frequency measurements. Cathode ray oscilloscope. Serial and parallel communication. Shielding and grounding. Control Systems and Process Control: Feedback principles. Signal flow graphs. Transient Response, steady-state-errors. Routh and Nyquist criteria. Bode plot, root loci. Time delay systems. Phase and gain margin. State space representation of systems. Mechanical, hydraulic and pneumatic system components. Synchro pair, servo and step motors. On-off, cascade, P, P-I, P-I-D, feed forward and derivative controller, Fuzzy controllers. Analytical, Optical and Biomedical Instrumentation: Mass spectrometry. UV, visible and IR spectrometry. X-ray and nuclear radiation measurements. Optical sources and detectors, LED, laser, Photo-diode, photo-resistor and their characteristics. Interferometers, applications in metrology. Basics of fiber optics. Biomedical instruments, EEG, ECG and EMG. Clinical measurements. Ultrasonic transducers and Ultrasonography. Principles of Computer Assisted Tomography.

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https://www.arxiv-vanity.com/papers/hep-ph/9603404/

math

Virtual corrections to the inclusive decay 111Work supported in part by Schweizerischer Nationalfonds and the Department of Energy, contract DE-AC03-76SF00515 Stanford Linear Accelerator Center Stanford University, Stanford, California 94309, USA Tobias Hurth 222 address after March 1996: ITP, SUNY at Stony Brook, Stony Brook NY 11794-3840, USA and Daniel Wyler Institute for Theoretical Physics, University of Zürich Winterthurerstr. 190, CH-8057 Zürich, Switzerland We present in detail the calculation of the virtual corrections to the matrix element for . Besides the one-loop virtual corrections of the electromagnetic and color dipole operators and , we include the important two-loop contribution of the four-Fermi operator . By applying the Mellin-Barnes representation to certain internal propagators, the result of the two-loop diagrams is obtained analytically as an expansion in . These results are then combined with existing Bremsstrahlung corrections in order to obtain the inclusive rate for . The new contributions drastically reduce the large renormalization scale dependence of the leading logarithmic result. Thus a very precise Standard Model prediction for this inclusive process will become possible once also the corrections to the Wilson coefficients are available. Submitted to Physical Review D In the Standard model (SM), flavor-changing neutral currents only arise at the one-loop level. This is why the corresponding rare B meson decays are particularly sensitive to “new physics”. However, even within the Standard model framework, one can use them to constrain the Cabibbo-Kobayashi-Maskawa matrix elements which involve the top-quark. For both these reasons, precise experimental and theoretical work on these decays is required. In 1993, was the first rare B decay mode measured by the CLEO collaboration . Recently, also the first measurement of the inclusive photon energy spectrum and the branching ratio in the decay was reported . In contrast to the exclusive channels, the inclusive mode allows a less model-dependent comparison with theory, because no specific bound state model is needed for the final state. This opens the road to a rigorous comparison with theory. The data agrees with the SM-based theoretical computations presented in [3, 4, 5], given that there are large uncertainties in both the experimental and the theoretical results. In particular, the measured branching ratio overlaps with the SM-based estimates in [3, 4] and in [6, 7]. In view of the expected increase in the experimental precision, the calculations must be refined correspondingly in order to allow quantitative statements about new physics or standard model parameters. So far, only the leading logarithmic corrections have been worked out systematically. In this paper we evaluate an important class of next order corrections, which we will describe in detail below 333Some of the diagrams were calculated by Soares . We start within the usual framework of an effective theory with five quarks, obtained by integrating out the heavier degrees of freedom which in the standard model are the top quark and the -boson. The effective Hamiltonian includes a complete set of dimension-6 operators relevant for the process (and ) with being the Fermi coupling constant and being the Wilson coefficients evaluated at the scale , and with being the CKM matrix elements. The operators are as follows: In the dipole type operators and , and ( and ) denote the electromagnetic (strong) coupling constant and field strength tensor, respectively. and stand for the left and right-handed projection operators. It should be stressed in this context that the explicit mass factors in and are the running quark masses. QCD corrections to the decay rate for bring in large logarithms of the form , where or and (with ). One can systematically resum these large terms by renormalization group techniques. Usually, one matches the full standard model theory with the effective theory at the scale . At this scale, the large logarithms generated by matrix elements in the effective theory are the same ones as in the full theory. Consequently, the Wilson coefficients only contain small QCD corrections. Using the renormalization group equation, the Wilson coefficients are then calculated at the scale , the relevant scale for a meson decay. At this scale the large logarithms are contained in the Wilson coefficients while the matrix elements of the operators are free of them. As noted, so far the decay rate for has been systematically calculated only to leading logarithmic accuracy i.e., . To this precision it is consistent to perform the ’matching’ of the effective and full theory without taking into account QCD-corrections and to calculate the anomalous dimension matrix to order . The corresponding leading logarithmic Wilson coefficients are given explicitly in [6, 12]. Their numerical values in the naive dimensional scheme (NDR) are listed in table 1 for different values of the renormalization scale . The leading logarithmic contribution to the decay matrix element is then obtained by calculating the tree-level matrix element of the operator and the one-loop matrix elements of the four-Fermi operators (). In the NDR scheme the latter can be absorbed into a redefinition of 444For the analogous transition, the effects of the four-Fermi operators can be absorbed by the shift . In the ‘t Hooft-Veltman scheme (HV) , the contribution of the four-Fermi operators vanishes. The Wilson coefficients and in the HV scheme are identical to and in the NDR scheme. Consequently, the complete leading logarithmic result for the decay amplitude is indeed scheme independent. Since the first order calculations have large scale uncertainties, it is important to take into account the next-to-leading order corrections. They are most prominent in the photon energy spectrum. While it is a -function (which is smeared out by the Fermi motion of the -quark inside the meson) in the leading order, Bremsstrahlung corrections, i.e. the process , broaden the shape of the spectrum substantially. Therefore, these important corrections have been taken into account for the contributions of the operators and some time ago and recently also of the full operator basis [4, 14, 15]. As expected, the contributions of and are by far the most important ones, especially in the experimentally accessible part of the spectrum. Also those (next-to-leading) corrections, which are necessary to cancel the infrared (and collinear) singularities of the Bremsstrahlung diagrams were included. These are the virtual gluon corrections to the contribution of the operator for and the virtual photon corrections to for . A complete next-to-leading calculation implies two classes of improvements: First, the Wilson coefficients to next-leading order at the scale are required. To this end the matching with the full theory (at ) must be done at the level and the renormalization group equation has to be solved using the anomalous dimension matrix calculated up to order . Second, the virtual corrections for the matrix element (at scale ) must be evaluated and combined with the Bremsstrahlung corrections. The higher order matching has been calculated in ref. and work on the Wilson coefficients is in progress. In this paper we will evaluate all the virtual correction beyond those evaluated already in connection with the Bremsstrahlung process. We expect them to reduce substantially the strong scale dependence of the leading order calculation. Among the four-Fermi operators only contributes sizeably and we calculate only its virtual corrections to the matrix element for . The matrix element vanishes because of color, and the penguin induced four-Fermi operators can be neglected 555 This omission will be a source of a slight scheme and scale dependence of the next-to-leading order result. because their Wilson coefficients 666It is consistent to calculate the corrections using the leading logarithmic Wilson coefficients. are much smaller than , as illustrated in table 1. However, we do take into account the virtual corrections to associated with the magnetic operators (which has already been calculated in the literature) and (which is new). Since the corrections to and are one-loop diagrams, they are relatively easy to work out. In contrast, the corrections to , involve two-loop diagrams, since this operator itself only contributes at the one-loop level. Since the virtual and Bremsstrahlung corrections to the matrix elements are only one (well-defined) part of the whole next-to-leading program, we expect that this contribution alone will depend on the renormalization scheme used. Even within the modified minimal subtraction scheme used here, we expect that two different “prescriptions” how to treat , will lead to different answers. Since previous calculations of the Bremsstrahlung diagrams have been done in the NDR scheme and also the leading logarithmic Wilson coefficients are available in this scheme, we also use it here. For future checks, however, we also consider in Appendix A the corresponding calculation in the HV scheme. The remainder of this paper is organized as follows. In section 2 we give the two-loop corrections for based on the operator together with the counterterm contributions. In section 3 the virtual corrections for based on are reviewed including some of the Bremsstrahlung corrections. Then, in section 4 we calculate the one-loop corrections to associated with . Section 5 contains the results for the branching ratio for and especially the drastic reduction of the renormalization scale dependence due to the new contributions. Appendix A contains the result of the two-loop calculation in the HV scheme and, finally, to make the paper self-contained, we include in Appendix B the Bremsstrahlung corrections to the operators , and . 2 Virtual corrections to in the NDR scheme In this section we present the calculation of the matrix element of the operator for up to order in the NDR scheme. The one-loop matrix element vanishes and we must consider several two-loop contributions. Since they involve ultraviolet singularities also counterterm contributions are needed. These are easy to obtain, because the operator renormalization constants are known with enough accuracy from the order anomalous dimension matrix . Explicitly, we need the contributions of the operators to the matrix element for , where denote the order contribution of the operator renormalization constants. In the NDR scheme, the non-vanishing counterterms come from the one-loop matrix element of and as well as from the tree level matrix element of the operator . We also note that there are no contributions to from counterterms proportional to evanescent operators multiplying the Wilson coefficient . 2.1 Regularized two-loop contribution of The dimensionally regularized matrix element of the operator for can be divided into 4 classes of non-vanishing two-loop diagrams, as shown in Figs. 1–4. The sum of the diagrams in each class (=figure) is gauge invariant. The contributions to the matrix element of the individual classes 1–4 are denoted by and , where e.g. is The main steps of the calculation are the following: We first calculate the Fermion loops in the individual diagrams, i.e., the ’building blocks’ shown in Fig. 5 and in Fig. 6, combining together the two diagrams in Fig. 6. As usual, we work in dimensions; the results are presented as integrals over Feynman parameters after integrating over the (shifted) loop-momentum. Then we insert these building blocks into the full two-loop diagrams. Using the Feynman parametrization again, we calculate the integral over the second loop-momentum. As the remaining Feynman parameter integrals contain rather complicated denominators, we do not evaluate them directly. At this level we also do not expand in the regulator . The heart of our procedure which will be explained more explicitly below, is to represent these denominators as complex Mellin-Barnes integrals . After inserting this representation and interchanging the order of integration, the Feynman parameter integrals are reduced to well-known Euler Beta-functions. Finally, the residue theorem allows to write the result of the remaining complex integal as the sum over the residues taken at the pole positions of certain Beta- and Gamma-functions; this naturally leads to an expansion in the ratio , which numerically is about . We express the diagram in Fig. 5 (denoted by ) in a way convenient for inserting into the two-loop diagrams. As we will use subtraction later on, we introduce the renormalization scale in the form , where is the Euler constant. Then, corresponds to subtracting the poles in . In the NDR scheme, is given by 777The fermion/gluon and the fermion/photon couplings are defined according to the covariant derivative where is the four-momentum of the (off-shell) gluon, is the mass of the charm quark propagating in the loop and the term is the ”-prescription”. The free index will be contracted with the gluon propagator when inserting the building block into the two-loop diagrams in Figs. 1 and 2. Note that is gauge invariant in the sense that . where is the four-momentum of the photon. The index in eq. (2.4) is understood to be contracted with the polarization vector of the photon, while the index is contracted with the gluon propagator in the two-loop diagrams in Figs. 3 and 4. The matrix in eq. (2.4) is defined as In a four-dimensional context these quantities can be reduced to expressions involving the Levi-Cività tensor, i.e., (in the Bjorken-Drell convention). The dimensionally regularized expressions for the read where and are given by The range of integration in is restricted to the simplex , i.e., and . Due to Ward identities, not all the are independent. The identities given in ref. in the context of the full theory simplify in our case as follows: They allow to express and in terms of the other which have a more compact form. These relations read Of course, eq. (2.1) can be checked explicitly for all values of , using partial integration and certain symmetry properties of the integrand. We are now ready to evaluate the two-loop diagrams. As both and are transverse with respect to the gluon, the gauge of the gluon propagator is irrelevant. Also, due to the absence of extra singularities in the limit of vanishing strange quark mass, we set from the very beginning (the question of charm quark mass “singularities” will be discussed later). As an example, we present the calculation of the two-loop diagram in Fig. 1c in some detail. Using in eq. (2.3), the matrix element reads In eq. (2.13), and are the Dirac spinors for the and the quarks, respectively, and . In the next step, the four propagator factors in the denominator are Feynman parametrized as where , , and . Then the integral over the loop momentum is performed. Making use of the function in eq. (2.14), the integral over is easy. The remaining variables , and are transformed into new variables , and , all of them varying in the interval [0,1]. The substitution reads Taking into account the corresponding jacobian and omitting the primes() of the integration variables this leads to where , and are matrices in Dirac space depending on the Feynman parameters , , , in a polynomial way. is given by In what follows, the ultraviolet regulator remains a fixed, small positive number. where and denotes the integration path which is parallel to the imaginary axis (in the complex -plane) hitting the real axis somewhere between and . In this formula, the ”momentum squared” is understood to have a small positive imaginary part. In ref. [19, 21] exact solutions to Feynman integrals containing massive propagators are obtained by representing their denominators according to the formula (2.18) with subsequent calculation of the corresponding massless integrals. In our approach, we use formula (2.18) in order to simplify the remaining Feynman parameter integrals in eq. (2.16). We represent the factors and in eq. (2.16) as Mellin-Barnes integrals using the identifications By interchanging the order of integration, we first carry out the integrals over the Feynman parameters for any given fixed value of on the integration path . These integrals are basically the same as for the massless case (in eqs. (2.16) and (2.17)) up to a factor (in the integrand) of Note that the polynomials , and have such a form that the Feynman parameter integrals exist in the limit . If the integration path is chosen close enough to the imaginary axis, the factor in eq. (2.20) does not change the convergence properties of the integrals, i.e., the Feynman parameter integrals exist for all values of lying on . It is easy to see that the only integrals involved are of the type For the integration we use the residue theorem after closing the integration path in the right -halfplane. One has to show that the integral over the half-circle vanishes if its radius goes to . As we explicitly checked, this is indeed the case for , which is certainly satisfied in our application. The poles which lie inside the integration contour are located at The other two-loop diagrams are evaluated similarly. The non-trivial Feynman integrals can always be reduced to those given in eq. (2.21) after some suitable substitutions. The only change is that there are poles in addition to those given in eq. (2.1) in those diagrams where the gluon hits the -quark line; they are located at The sum over the residues naturally leads to an expansion in through the factor in eq. (2.20). This expansion, however, is not a Taylor series because it also involves logarithms of , which are generated by the expansion in . A generic diagram which we denote by has then the form where the coefficients and are independent of . The power in eq. (2.24) is in general a natural multiple of and is a natural number including 0. In the explicit calculation, the lowest turns out to be . This implies the important fact that the limit exists; thus, there cannot be large logarithms (from a small up-quark mass) in these diagrams. From the structure of the poles one can see that the power of the logarithm is bounded by independent of the value of . To illustrate this, take as an example. There are 3 poles located near n=100, viz., at , respectively (see eq. (2.1)). Taking the residue at one of them, yields a term proportional to coming from the remaining two poles. In addition there can be an explicit term from the integration of the two loop momenta. Therefore the most singular term can be . Multiplying this with in eq. (2.20) leads to where can be 4 at most. We have retained all terms up to . Comparing the numerical result with the one obtained by truncating at leads to a difference of about only. We have made further checks of our procedure. For example we have calculated diagram 1b directly. Expanding the result, we reproduce the expressions obtained by applying the Mellin-Barnes integral at the Feynman parameter level as described above. A similar exercise for the imaginary part of diagram 1c shows that the exact and the expanded result (up to terms) in these examples agree at the level. In addition, we checked that the imaginary part of the sum of all diagrams coincides numerically with the results of Soares [23, 8] (note, however that in the physical region only the diagrams in Fig. 1 and Fig. 3 contribute to the imaginary part). In ref. , Soares applied dispersion techniques to calculate the real part. However, using the imaginary part in the physical region, only the real part of the diagrams in Fig. 1 and Fig. 3 is obtained. We have checked that our numbers for these two sets of diagrams indeed coincide with the results of Soares. However, the contribution of the diagrams in Fig. 2 and Fig. 4 is missing in because the additional unphysical cuts were not taken into account. We also note that a separate consideration of the subtraction terms would be required to obtain the correct dependence. We mention that the Dirac algebra has been done with the algebraic program REDUCE 888Some checks have been done with TRACER . The Feynman parameter integrals and the determination of the residues have been done with the symbolic program MAPLE . We now give the results for the diagrams shown in Figs. 1 to 4. As mentioned already, the individual diagrams in each figure are not gauge invariant but only their sum. Note, that the leading ultraviolet singularity in the individual two-loop diagrams is in general of order . In the gauge invariant sums the cancel and we are left with -poles only. The results read (using and ): In these expressions, the symbol denotes the Riemann Zeta function, with ; and are the charge factors for up- and down-type quarks, respectively. The matrix element is the tree level matrix element of the operator ; its explicit form is In formula (2.29) should be identified with the running mass in principle (see eq. (1)). However, as the corrections to are explicitly proportional to , can be identified with the pole mass as well (apart from corrections which we systematically neglect). The operators mix under renormalization and thus the counterterm contributions must be taken into account. As we are interested in this section in contributions to which are proportional to , we have to include, in addition to the two-loop matrix elements of , also the one-loop matrix elements of the four Fermi operators () and the tree level contribution of the magnetic operator . In the NDR scheme the only non-vanishing contributions to come from . (For the contribution comes from the diagram in which the internal -quark emits the photon). The operator renormalization constants are listed in the literature in the context of the leading order anomalous dimension matrix. The entries needed in our calculation are we find the following contributions to the matrix elements We note that there is no one-loop contribution to the matrix element for from the counterterm proportional to , where the evanescent operator (see e.g. the last ref. in ) reads 2.3 Renormalized contribution proportional to Of course, the ultraviolet singularities cancel in . Inserting , and , we get the main result of this paper, which in the NDR scheme reads: Here, and denote the real and the imaginary part of , respectively. The quantity is defined as and . In Fig. 7 we show the real and the imaginary part of . For the imaginary part must vanish exactly; indeed we see from Fig. 7 that the imaginary part based on the expansion retaining terms up to indeed vanishes at to high accuracy. 3 corrections to The virtual corrections associated with the operator as shown in Fig. 8b (together with the selfenergy diagrams and the counterterms) have been taken into account in the work of Ali and Greub, see e.g. [3, 4, 14], where was retained. Since we neglect in this work, we are interested only in the limit . Because of the mass singularities in the virtual corrections (which will be cancelled when also taking into account Bremsstrahlung corrections), we only keep as a regulator. Including the lowest order contribution, the result then becomes (using ) in the NDR scheme Note, that eq. (3.1) contains all the counterterm contributions. The -poles in this equation are therefore of infrared origin as indicated by the notation. The last term in the curly bracket in eq. (3.2) represents a dependence of ultraviolet origin. The additional dependence, which is generated when expanding in is cancelled at the level of the decay width together with the -poles when adding the Bremsstrahlung correction due to the square of the diagrams associated with the operator . As all intermediate formulae are given in the literature, we only give the final result for the corrections (virtual+Bremsstrahlung) to the decay width. Denoting this contribution by we get in the limit where the lowest order contribution reads

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Schroeck, Chapter 5: Capital Structure in Banks Study Notes contain 13 pages covering the following learning objectives: * Evaluate a bank’s economic capital relative to its level of credit risk * Identify and describe important factors used to calculate economic capital for credit risk: probability of default, exposure, and loss rate. * Define and calculate expected loss (EL). * Define and calculate unexpected loss (UL). * Estimate the variance of default probability assuming a binomial distribution. * Calculate UL for a portfolio and the risk contribution of each asset. * Describe how economic capital is derived. * Explain how the credit loss distribution is modeled. * Describe challenges to quantifying credit risk. After reviewing the notes you will be able to apply what you learned with practice questions and answers. No Sample AvailableShop Courses

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