Datasets:

OpenCoder-LLM

/

opc-fineweb-math-corpus

like 19

Follow

OpenCoder 74

http://www.dogfartmegapass.com/dogfart-videos/blacksonblondes/claire_robbins/

math

05/13/2014::    ALLIE JAMES INTERRACIAL GANGBANGSee More! 04/22/2014::    PENNY PAX AT INTERRACIAL BLOWBANGSee More! 12/14/2012::    SHEENA SHOW ON A HUGE BLACK CUMGUNSee More! 04/13/2013::    REMY LACROIX INTERRACIAL ANAL SESSIONSee More! 08/16/2013::    VALENTINA NAPPI's INTERRACIAL ANAL DPSee More! 05/12/2014::    BUNNY FREEDOM INTERRACIAL GLORYHOLESee More! Access 22 Exclusive Interracial Porn Sites With One Membership! Claire Robbins Interracial Porn Video Charlie Mac's business venture, a "grow house", isn't living up to his expectations. Charlie is also in debt to a rival grower and his funds aren't there to cover his ass. Charlie- always one to think on his feet- offers up his best bitch, Claire Robbins, in order to settle the debt between himself and Lucas Stone. Charlie wants one last dance with Claire before she goes with Lucas Stone. Claire's slutish ways come out when she sucks on both black pythons in this vile part of town. Charlie and Lucas stab her throat with their big black cocks until her eyes get as watery as the plants in the grow house. Claire's dedication to Charlie, aka "Daddy" is evident when she gets fucked all over by both black entrepreneurs and it's only a matter of time before she gets double stuffed. Claire's ...

s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256586.62/warc/CC-MAIN-20190521222812-20190522004812-00389.warc.gz

CC-MAIN-2019-22

https://vijayakranthinews.com/check-142

math

Trig word problem solver Trig word problem solver can be a useful tool for these scholars. Let's try the best math solver. The Best Trig word problem solver Trig word problem solver is a mathematical instrument that assists to solve math equations. It finds the best set of values for these variables to achieve desired outputs. The sequence solver can solve any system that has multiple equations and one or more unknown inputs. The Solver tab in the Simulink block diagram editor is used to specify what values you want Simulink to find for each input value (e.g., pressure). Once you've specified your solution algorithm, you can run your simulation many times with different combinations of inputs to see how it changes over time. The most important thing about using the sequence solver is that it requires solving for all unknowns at every time step. This means that you will need to make sure all of your inputs are properly defined and that none of them change over time as part of your model's dynamics. This means that when you solve for exponents, you’re essentially solving for one of the factors in the multiplication. The easiest way to do this is to think about each factor as being a multiple of a single base (the number 1). For example, in 4 = 2 × 2, there are two factors: 4 and 2. So, to find out what 4 × 2 is equal to (and therefore which factor you need to solve for), all you need to do is multiply 4 and 2 together. When you multiply two numbers together like this, the product is always equal to the sum of those two numbers multiplied by their product divided by their product. So in this case, since 4 × 2 = 8 and 8 = 4 × 2 less 1 (8 minus 1), 8 must equal 4 x 2 less 1 = 16. Of course, there are exceptions (like when one of the factors ends up being zero or another number) but I think it’s a Unlike with an algebraic equation, you can’t simply substitute one variable for another to solve a system of equations. Instead, you must identify all of the variables in the equation and determine how they affect each other. Once the variables have been identified, their values can be substituted into the original equation to solve for the unknown variable(s). There are several different types of systems of equations that can be solved. Some examples include linear equations (a variable is multiplied by a constant), quadratic equations (a variable is squared), and exponential equations (a variable is raised to a given power). To solve a system of equations, begin by writing down your initial equation and any variables that have been introduced so far in the problem. Now, identify each component of the equation and find the value(s) that satisfies it. If these values are different, then both components must be true; in this case, a solution exists. If no solution exists, then one or more equations must be false, indicating that one or more variables must be incorrect. Once all variables have been checked for validity, substituting known values into your initial By solving math problems, you will build up your mathematical skills. You can also practice by solving math problems for free on websites. Solving math problems is an easy and fun way to practice math. Solving math problems is also good for improving concentration and focus. You can solve math problems with steps by following the steps below: 1) Choose a problem from the list of free math problems 2) Solve the problem by solving the equation 3) Check your answer 4) Repeat Steps 1 through 3 as many times as necessary Great app! Even if it doesn't work on all the math problems it still works on most. And it teaches you how to solve them as a bonus! It also helps me with my math homework. Very good. Useful. But, sometimes solves simple things in a different, kind of robotic way. This is BY FAR the best photo calculator app I have ever used. It may not solve every single math question but when it does solve your questions which is most math questions. The most detailed explanatory with colors to make it easier to see the changes on how to solve your questions. This app has thought me more than my teacher has.

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499710.49/warc/CC-MAIN-20230129080341-20230129110341-00176.warc.gz

CC-MAIN-2023-06

http://www.cellkit.net/index.php?dispatch=products.view&product_id=12924

math

Magnifier Lamp Cellkit A139 Magnifier taking footlights four . Magnifier Lamp Cellkit has the advantage that can zoom up to two to three times magnification , and energy efficient . Another advantage of Magnifier Lamp A139 Cellkit ( CK A139 ) is the Spiral Arm Bend the mast of the Magnifying Glass is flexible so it is easier to use service . Weight 1,140 grams ( 1.14 kg ) .

s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376826856.91/warc/CC-MAIN-20181215131038-20181215153038-00139.warc.gz

CC-MAIN-2018-51

http://thefutureofsearch.com.au/2012/03/new-search-engine-features-wolfram-alpha/

math

Looking for a search engine that delivers results? Tired of search engines that have slow processing speed? It is time for you to experience the power of a new search engine called Wolfram Alpha. Wolfram Alpha is the most powerful search engine that users have experienced in the market place. Unlike conventional search engines, Wolfram Alpha allows an individual to have many optimization abilities that others fail to provide. For instance, Wolfram Alpha allows users to directly input images of all types without the hassle of coding. In addition, users are able to synchronize their data effortlessly as this engine will conduct its own form of analysis. Acting as a facilitator for the user, Wolfram Alpha is also perfect for all types of file uploads. Moreover, this new search engine comes with an extended keyboard, another unique element that Bing and Google do not possess. Users can utilize this special soft keyboard to input symbols and other special characters for their text. Moreover, users can utilize this key board to compute mathematical equations at a professional level. Wolfram Alpha is extremely user-friendly and allows individuals to be dynamic with their computable document format (CDF). CDF interactivity is truly fantastic because it allows users to have full-control of their animations with 3D rotations. The main element that distinguishes Wolfram Alpha from its competitors is the fact that it can allows users to customize at a micro-level. A user can customize graphical and tabular outputs that reflect their style of presentation. Another focal point that allows this search engine to be truly special is due to the fact that it takes extra computation time when needed. This allows it to allocate its resources effectively. An individual is able to have pages bookmarked for quick access along with search history that is saved in a timely manner. With Wolfram Alpha, an individual can freely browse the web in a safe manner without sacrificing security. When it comes to data mining, it is crucial that they have a neat, graphical design. Wolfram Alpha delivers this guarantee with a great design along with no advertisements to slow down the processing speed, the clean and pure look of Wolfram Alpha is bound to impress its users. The possibilities are truly endless with its developer and application tools along with a powerful search engine. Customize and set your own preferences with the all new Wolfram Alpha that is bound to impress you and your organization.

s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368704054863/warc/CC-MAIN-20130516113414-00009-ip-10-60-113-184.ec2.internal.warc.gz

CC-MAIN-2013-20

https://www.physicsforums.com/threads/all-the-stuff-we-do-with-equilibrium-constants.547804/

math

NONE OF IT MAKES ANY SENSE!! For example: If we divide the molar coefficients all by 2, then we raise the original equilibrium constant by the same power (0.5). If we write the reaction in the reverse, then the new equilibrium constant is the multiplicative inverse of the original constant. But the problem with all of this is that, if, suppose I take some fixed amounts of the substances that will eventually form an equilibrium mixture (let's suppose that I take 2 moles of hydrogen gas, 1 mole of nitrogen gas, and 1 mole of ammonia gas; note that all of these numbers are completely random; nitrogen and hydrogen will form ammonia, and ammonia will dissociate into hydrogen and nitrogen) in a closed container. Eventually all the components will even out (equilibrium will be established). And then, suppose, according to the final concentrations in the equilibrium mixture, I calculate the equilibrium constant for the reaction. Now this is where my dilemma begins: how am I to compare my experimental value with other values people have determined? It would be impossible, because, while one person may have determined it with some molar coefficients (1, 3, and 2, suppose), another person may have determined it using doubled molar coefficients (2, 6, and 4). And another person may have determined a value from an equation written in reverse. The thing is, that the gases reacting in the container wouldn't 'know' what chemical equation we are writing out to determine the constant. So how are the such rules justified??

s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247504790.66/warc/CC-MAIN-20190221132217-20190221154217-00416.warc.gz

CC-MAIN-2019-09

http://stackexchange.com/users/510291/david-corwin?tab=accounts

math

I am a graduate student studying mathematics at MIT. I was an undergraduate studying mathematics at Princeton University. Q&A for professional mathematicians Q&A for people studying math at any level and professionals in related fields Q&A for users of TeX, LaTeX, ConTeXt, and related typesetting systems Q&A for active researchers, academics and students of physics

s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860111518.82/warc/CC-MAIN-20160428161511-00114-ip-10-239-7-51.ec2.internal.warc.gz

CC-MAIN-2016-18

http://wirelesspi.com/continuous-time-vs-discrete-time-signals/

math

Classification of continuous-time and discrete-time deals with the type of independent variable. If the signal amplitude is defined for every possible value of time, the signal is called a continuous-time signal. However, if the signal takes values at specific instances of time but not anywhere else, it is called a discrete-time signal. Basically, a discrete-time signal is just a sequence of numbers. Consider a football (soccer) player participating in a 20-match tournament. Suppose that his running speed is recorded at each instant of time in the 90-minute duration of a particular match and plotted against time. The result shown in this Figure is clearly a continuous-time signal. On the other hand, the Figure below shows the number of goals he scored during those 20 matches, which is defined only for each match and not in between. Hence, it is a discrete-time signal. Discrete-time signals usually arise in two ways: - By acquiring values of a continuous-time signal at fixed time instants. This process is called sampling and is discussed in detail later. For example, the actual temperature outside varies continuously throughout the day, but weather stations log the data after specific intervals, say every 30 minutes. - By recording the number of events over finite time periods. For example, number of trees cut every year in a city for housing and development projects. Mathematically, we represent a continuous-time signal as and a discrete-time signal as , where is a real number while is an integer. So a discrete-time signal can be plotted by finding for various values of . Each member of a discrete-time signal is called a sample. Plotting each value of against every is then straightforward as shown below. Another way of representing a discrete-time signal is in the form of a sequence with an underline indicating the time origin (), such as Finally, it is incorrect to assume that a discrete-time signal is zero between two values of . It is simply not defined for non-integer values. In electrical engineering, the time-varying quantity is usually voltage (or sometimes current). Therefore, when we work with a signal, just think of it as a voltage changing over time.

s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891814249.56/warc/CC-MAIN-20180222180516-20180222200516-00298.warc.gz

CC-MAIN-2018-09

http://ovsyankatour.blogspot.com/2009/08/colourless-color.html

math

A thought of the day: how many posts I need to write in order to have more than 1 follower in my blog? A second question of the day: how interesting should my posts be in order to get at least one respond from my reader? I may sound desperate but I'm not really. Ive been just trying to figure out how this Blogger works. How long does it take to become more or less popular on this website? If any of you people have advises for me please feel free to comment :) John Derian Lives in a Sea Captain’s House 21 hours ago

s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267864257.17/warc/CC-MAIN-20180621192119-20180621212119-00092.warc.gz

CC-MAIN-2018-26

https://www.ecuedit.com/touareg-bpe-2-5tdi-edc16u31-question-about-maps-t18218

math

I have Touareg 2.5tdi 2007 BPE. Bosch build EDC16U31 ECU-Nr. Prod. 070906016DE I succesfully disabled EGR system. Find 3 maps 13x16 1C6338, 1C657C, 1C67C0. I filled the maximum value 11000 (MAF 1100mg/str) to all tables and it works normal without any errors. Now I want to increase a power of engine. I find some maps: driver wishes 9 maps 8x16 1C2A64 - 1C3586 Torque limiter (23x4) 1D5F9C 4 SOI maps?? 15x19 1E6BEE 1E6E70 1E70F2 1E7374 They have some negative values. 1EBBF2 N75 13x16 map 1ECCCE 10x16 Boost map 1ECE3A 10x10 Boost limiter 1D7A8C 13x16 Smoke map? 1ECF84 1x1 SVBL ? (value = 2500) and some unrecognized maps: 1D6710 8x8 (fuel temperature and IQ?) 1D8B64 18x16 Torque IQ converter? 3 maps 14x16 1DC4AC - 1DC8AC duration maps? 1E6ADE 10x10 duration? 1ECFB6 10x10 ? 1ED0AE 10x12 ? 1ED1FE 10x10 ? 1ED2F6 10x12 ? 1F2322 8x9 ? I tried to increase values of map 1D7A8C (Smoke map?) up to 10%. After this fuel consumption on idle decreased by 10%. Before 1.1 l/h, after 1.0 l/h. And car went faster, if I feel it right. Please help me reqognize maps. Am I right in smoke map selection? Is it right to increase only smoke map without duration map? I want to improove power on low engine speed. Any help would be appreciated. ECU file in attachment. You do not have permissions to view the files yet. You have to be registered and you have to make at least 3 quality / unique posts.

s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247479159.2/warc/CC-MAIN-20190215204316-20190215230316-00474.warc.gz

CC-MAIN-2019-09

https://dev.wisc-online.com/arcade/games/mathematics2?gameTypes=TICTACTOE_BASEBALL_HAVEUHERD_SNAKE

math

Converting hexadecimal, binary and decimal numbers. Basic Multiplication Tic-Tac-Toe You may need serous Multiplication skills for this game! Solving 1 and 2 Step Equations Intro Solving 1 and 2 step equations Tic Tac Toe: 3rd Grade Math Concepts Review questions for math concepts taught in 3rd grade. An equation of a line and a point is given. Your job is to find a parallel line to the equation that goes through the given point. 3rd Grade Addition, Subtraction, and Place Value Addition, Subtraction, Properties of Addition, Rounding to the tens and hundreds place, and Estimation. MATH: Order a Set of Real Numbers ( TEKS 8.2D) RC1 Readiness Grade: 8 TEK: 8.2D Order a set of real numbers arising from mathematical and real-world contexts. Pythagorean Theorem: Midpoint, Perimeter and Area Unit 5 Lesson 2: We will work on finding the midpoint, the Pythagorean theorem and finding the area and perimeter of triangles and rectangles. Learning about 3-D shapes and their relation to the real world 7th Grade Review: Geometry, Math and Measurement Practice for 7th grade sgo

s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949701.56/warc/CC-MAIN-20230401063607-20230401093607-00798.warc.gz

CC-MAIN-2023-14

https://www.physicsforums.com/threads/analytical-chemistry-introductory.220463/

math

It may seem that I will be taking an analytical chemistry course for my major in Biotechnology, and I have never really taken an analytical chemistry course. I have probably studied the topics in regular chemistry courses but I am unaware as to what exactly this course teaches or the topic(s) it covers. But aside from that I was wondering if you could recommend some books that I could use to get a head start, get some understanding of the topic and practice any forms of problem questions that might appear in the course. I have also heard that such courses are tough, but seeing as I need it I would love to ace it so I really do want to get a head start. Thanks for the help.

s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891814493.90/warc/CC-MAIN-20180223055326-20180223075326-00022.warc.gz

CC-MAIN-2018-09

http://qwessayfplj.locallawyer.us/artificial-neural-networks.html

math

Neural networks is the archival journal of the world's three oldest neural modeling societies: the international neural network society (inns), the. 2 artificial neural networksan artificial neural network , is a biologically inspired computational model formed from hundreds of single units, artificial neurons, connected with coefficients (weights) which constitute the neural structure. In this article, we develop a machine learning technique called deep learning (artificial neural network) by using tensorflow. Computers organized like your brain: that's what artificial neural networks are, and that's why they can solve problems other computers can't. In machine learning and cognitive science, artificial neural networks (anns) are a family of statistical learning models inspired by biological neural networks (the central nervous systems of animals, in particular the brain) and are used to estimate or approximate functions that can depend on a large number of inputs and are generally unknown. Artificial neural networks are computational models which work similar to the functioning of a human nervous system there are several kinds of artificial neural networks these type of networks are implemented based on the mathematical operations and a set of parameters required to determine the . Artificial neural networks (ann) the power of neuron comes from its collective behavior in a network where all neurons are interconnected the network starts evolving : neurons continuously evaluate their output by looking at their inputs, calculating the weighted sum and comparing to a threshold to decide if they should fire. Artificial neural networks are behind a lot of big advances -- a lot of big advances how can one tech . An artificial neural network is an interconnected group of nodes, akin to the vast network of neurons in a brain here, each circular node represents an . Artificial neural networks (ann) are the foundations of artificial intelligence (ai), solving problems that would be nearly impossible by human or statistical standards. Artificial neural networks for beginners carlos gershenson [email protected]ssexacuk 1 introduction the scope of this teaching package is to make a brief induction to artificial neural. Artificial intelligence neural networks - learning artificial intelligence in simple and easy steps using this beginner's tutorial containing basic knowledge of artificial intelligence overview, intelligence, research areas of ai, agents and environments, popular search algorithms, fuzzy logic systems, natural language processing, expert systems, robotics, neural networks, ai issues, ai . Artificial neural network software apply concepts adapted from biological neural networks, artificial intelligence and machine learning and is used to simulate, research, develop artificial neural network neural network simulators are software applications that are used to simulate the behavior of . Today, it's more common to use other models of artificial neurons - in this book, and in much modern work on neural networks, the main neuron model used is one called the sigmoid neuron we'll get to sigmoid neurons shortly. Artificial neural network market expected to reach more than moderate cagr growth forecast period 2018-2023, artificial neural network market categorizes by application type, component and end-user |artificial neural network industry. Neural networks for machine learning from university of toronto learn about artificial neural networks and how they're being used for machine learning, as applied to speech and object recognition, image segmentation, modeling language and human . Applied deep learning - part 1: artificial neural networks overview welcome to the applied deep learning tutorial series we will do a detailed analysis of several deep learning techniques starting with artificial neural networks (ann), in particular feedforward neural networks. Artificial neural networks (or ann) are at the very heart of the ai revolution that is shaping every aspect of society and technology but the anns that we have been able to handle so far are . Neural networks and deep learning currently provide some of the most reliable image recognition, speech recognition, and natural language processing solutions available. Artificial neural networks - application edited by: chi leung patrick hui isbn 978-953-307-188-6, published 2011-04-11. Join barton poulson for an in-depth discussion in this video artificial neural networks, part of data science foundations: fundamentals. Introduction to artificial neural netw orks • what is an artificial neural netw ork the network is provided with a correct answer (output) for every. Deep learning and artificial intelligence are quite buzz words now, aren’t they however, this field is not quite as new as the majority of people thinks we as humans were always interested in the way we think and the structure of our brain. Artificial neural networks (ann) are one of the commonly applied machine learning algorithm this article explains the working behind ann. All artificial neural networks are constructed from this basic building block - the processing element or the artificial neuron it is variety and the fundamental differences in these building blocks which partially cause the implementing of neural networks to be an art. “deep learning,” the machine-learning technique behind the best-performing artificial-intelligence systems of the past decade, is really a revival of the 70-year-old concept of neural networks. Introduction to neural networks, advantages and applications artificial neural network(ann) uses the processing of the brain as a basis to develop algorithms that can be used to model complex patterns and prediction problems. Artificial neural networks (anns) are computational models inspired by the human brain they are comprised of a large number of connected nodes, each of which performs a simple mathematical operation. Neural networks tutorial – a pathway to deep learning march 18, 2017 andy deep learning , neural networks 29 chances are, if you are searching for a tutorial on artificial neural networks (ann) you already have some idea of what they are, and what they are capable of doing. A basic introduction to neural networks what is a neural network the simplest definition of a neural network, more properly referred to as an 'artificial' neural network (ann), is provided by the inventor of one of the first neurocomputers, dr robert hecht-nielsen.

s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039743007.0/warc/CC-MAIN-20181116091028-20181116113028-00279.warc.gz

CC-MAIN-2018-47

https://www.arxiv-vanity.com/papers/hep-th/0310151/

math

Energy of a Regular Black Hole We use Einstein, Landau-Lifshitz, Papapetrou and Weinberg energy-momentum complexes to evaluate energy distribution of a regular black hole. It is shown that for a regular black hole, these energy-momentum complexes give the same energy distribution. This supports Cooperstock hypothesis and also Aguirregabbiria et al. conclusions. Further, we evaluate energy distribution using Mller’s prescription. This does not exactly coincide with ELLPW energy expression but, at large distances, they become same. PACS: 04.20.Dw, 04.30.Bw Key Words: Energy, Regular Black Hole The definition of energy-momentum has always been a focus of many investigations in General Relativity (GR). This, together with conservation laws, has a crucial role in any physical theory. However, there is still no accepted definition of energy-momentum, and generally speaking, of conserved quantities associated with the gravitational field. The main difficulty is with the expression which defines the gravitational field energy part. Einstein used principle of equivalence and conservation laws of energy-momentum to formulate the covariant field equations. He formulated the energy-momentum conservation law in the form where is the stress energy density of matter. He identified as representing the stress energy density of gravitation. He noted that was not a tensor, but concluded that the above equations hold good in all coordinate systems since they were directly obtained from the principle of GR. The choice of a non-tensorial quantity to describe the gravitational field energy immediately attracted some criticism. The problems associated with Einstein’s pseudo-tensor resulted in many alternative definitions of energy, momentum and angular momentum being proposed for a general relativistic system. These include Landau-Lifshitz, Tolman, Papapetrou, Bergmann, Weinberg who had suggested different expressions for the energy-momentum distribution. The main problem with these definitions is that they are coordinate dependent. One can have meaningful results only when calculations are performed in Cartesian coordinates. This restriction of coordinate dependent motivated some other physicists like Mller, Komar and Penrose who constructed coordinate independent definitions of energy-momentum complex. Mller claimed that his expression gives the same values for the total energy and momentum as the Einstein’s energy-momentum complex for a closed system. However, Mller’s energy-momentum complex was subjected to some criticism. Komar’s prescription, though not restricted to the use of Cartesian coordinates, is not applicable to non-static spacetimes. Penrose pointed out that quasi-local masses are conceptually very important. However, different definitions of quasi-local masses do not give agreed results for the Reissner-Nordstrom and Kerr metrics and that the Penrose definition could not succeed to deal with the Kerr. These inadequacies of quasi-local definitions have been discussed in a series of papers. Thus each of these energy-momentum complex has its own drawback. As a result these ideas of the energy-momentum complex were severally criticized. Virbhadra revived the interest in this approach by showing that different energy-momentum complexes can give the same energy-momentum. Since then lot of work on evaluating the energy-momentum distributions of different spacetimes have been carried out by different authors. In a recent paper, Virbhadhra used the energy-momentum complexes of Einstein, Landau-Lifshitz, Papapetrou and Weinberg (ELLPW) to investigate whether or not they can give the same energy distribution for the most general non-static spherically symmetric metric. It was a great surprise that contrary to previous results of many asymptotically flat spacetimes and asymptotically non-flat spacetimes, he found that these definitions disagree. He observed that Einstein’s energy-momentum complex provides a consistent result for the Schwarzschild metric whether one calculates in Kerr-Schild Cartesian coordinates or Schwarzschild Cartesian coordinates. The prescriptions of Landau-Lifshitz, Papapetrou and Weinberg furnish the same result as in the Einstein prescription if the calculations are carried out in Schwarzschild Cartesian coordinates. Thus the prescriptions of Landau-Lifshitz, Papapetrou and Weinberg do not give a consistent result. On the basis of these and some other facts, Virbhadra concluded that the Einstein method seems to be the best among all known (including quasi-local mass definitions) for energy distribution in a spacetime. Recently, Lessner pointed out that the Mller’s energy-momentum prescription is a powerful concept of energy and momentum in GR. It has been shown recently that ELLPW energy-momentum complexes coincide for any Kerr-Schild class metric when one uses Kerr-Schild Cartesian coordinates. In this paper we use ELLPW and Mller energy-momentum complexes to obtain the energy distribution of a regular black hole which is represented by a Bardeen’s model. It is shown that ELLPW energy-momentum complexes give the same and acceptable results for a given space-time. Our results agree with Virbhadra’s conclusion that the Einstein’s energy-momentum complex is still the best tool for obtaining energy distribution in a given spacetime. This also supports Cooperstock’s hypothesis (that energy and momentum in a curved space-time are confined to the the regions of non-vanishing energy-momentum of matter and the non-gravitational field). The paper has been organised as follows. In the next section, we shall describe the regular black holes. In Secs. 3 and 4, we evaluate energy distribution using ELLPW and Mller’s prescriptions respectively. Finally, we shall discuss the results. 2 Regular Black Holes In 1968, Bardeen constructed a well-known model called Bardeen’s model. This model represents a regular black hole obeying the weak energy condition, and it was powerful in shaping the direction of research on the existence or avoidance of singularities. The model uses the Reissner-Nordstrm spacetime as inspiration. The metric expressed in standard spherical coordinates is given by the line element of the form where Bardeen replaced the usual Reissner-Nordstrm function When in Bardeen’s model, there is an event horizon. There are values of such that the region contains trapped surfaces. The spacetime obeys the null convergence, yet it contains no physical singularities. It is to be noticed that if we take charge , the above metric reduces to the Schwarzschild metric. 3 Energy of the Regular Black Hole In this section we shall use ELLPW energy-momentum complexes to evaluate the energy distribution of the regular black hole. To this end, we shall follow the procedure developed by Virbhadra. The basic requirement of the procedure is to bring the metric in the form of Kerr-Schild class and then transform the resulting metric in Kerr-Schild Cartesian coordinates. The metrics of the Kerr-Schild class are written in the following form where is the Minkowski spacetime, is the scalar field and is a null, geodesic and shear free vector field in the Minkowski metric. These can be expressed as where . It is to be noticed that, for the Kerr-Schild class metric, the vector field remains null, geodesic and shear free with the metric . Thus it follows from the above equation that Now we bring the metric given by Eq.(2) in Kerr-Schild class by using the following coordinate transformation which implies that This metric turns out to be static case of the Kerr-Schild class as given by Aguirregabiria et al.. In order to have meaningful results in the prescriptions of ELLPW, it is necessary to transform the metric in Kerr-Schild Cartesian coordinates. Let us now transform the metric in Kerr-Schild Cartesian coordinates by using The corresponding metric in these coordinates will become This is the Kerr-Schild class metric with and . We use the procedure of Aguirregabiria et al. to calculate energy distribution of the regular black hole in the ELLPW prescriptions. It turns out that we get the same energy in these prescriptions which is given as When we replace the value of from Eq.(4), it follows that the energy distribution of the regular black hole is which can be written as follows If we take the charge or at large distances, it reduces to the energy of the Schwarzscild metric given by 4 Energy Distribution in Mller’s Prescription Now we shall use Mller’s energy-momentum complex to evaluate energy of the regular black hole. This is the beauty of Mller’s method that it is independent of coordinates and consequently we can perform computations in spherical polar coordinates. The energy-momentum complex of Mller is given by The energy-momentum complex satisfies the local conservation laws The locally conserved energy-momentum complex contains contributions from the matter, non-gravitational and gravitational fields. and are the energy and momentum (energy current) density components respectively. The energy and momentum components are given as where is the energy and represent the momentum components. Using Gauss’s theorem, the energy expression E can be written as where is the outward unit normal vector over an infintesimal surface element . The only required component of , to evaluate energy of the Bardeen’s model, is given by Substituting this value of in Eq.(19), we have the following energy distribution in Mller’s prescription which can be written as We see that the energy expression for ELLPW and Mller’s prescriptions coincide at large distances. They are exactly the same for the Schwarzschild metric. There are two types of energy-momentum complexes in the literature. The first type depends on the coordinates and the other type is independent of coordinate. However, it has been shown by many authors that the first type give more meaning results. The debate on the localization of energy-momentum is also an interesting and a controversial problem. According to Misner et al, energy can only be localized for spherical systems. However, Cooperstock and Sarracino suggested that if energy can be localized in spherical systems then it can be localized in any spacetimes. The energy-momentum complexes are non-tensorial under general coordinate transformations and hence are restricted to Cartesian coordinates only. In their recent work Virbhadra and his collaborators have shown that different energy-momentum complexes can provide meaningful results. In this paper, we have evaluated energy of the regular black hole using prescriptions of ELLPW. It is worth noting that the energy turns out to be same in the prescriptions of Einstein, Landau-Lifshitz, Papapetrou and Weinberg. It is clear that the definitions of ELPPW support the Cooperstock hypothesis for the regular black hole. We have also calculated this quantity using Mller energy-momentum complex. This is not exactly the same as evaluated by using ELLPW prescriptions. However, it can be seen from Eqs.(14) and (23) that, at large distances, these give the same result and reduces to the energy of Schwarzscild spacetime. We plot the energy distributions of ELLPW () and Mller () in the figures 1 and 2 respectively. I would like to thank Ministry of Science and Technology (MOST), Pakistan for providing postdoctoral fellowship at University of Aberdeen, UK. 1. L.D. Landau and E.M. Lifshitz, The Classical Theory of Fields (Addison-Wesley Press, Reading, MA, 1962)2nd ed. 2. R.C. Tolman, Relativity, Thermodynamics and Cosmology (Oxford Univ. Press, 1934)227. 3. A. Papapetrou, Proc. R. Irish. Acad. A52, 11 (1948). 4. P.G. Bergmann and R. Thompson, Phys. Rev. 89, 400 (1953). 5. S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1972). 6. C. Mller, Ann. Phys. (NY) 4, 347 (1958). 7. C. Mller, Ann. Phys. (NY) 12, 118 (1961). 8. A. Komar, Phys. Rev. 113, 934 (1959). 9. R. Penrose, Proc. Roy. Soc. London A381, 53 (1982). 10. D. Kovacs, Gen. Relatv. and Grav. 17, 927 (1985); J. Novotny, Gen. Relatv. and Grav. 19, 1043 (1987). 11. G. Bergqvist, Class. Quantum Grav. 9, 1753 (1992). 12. D.H. Bernstein and K.P. Tod, Phys. Rev. D49, 2808 (1994). 13. K.S. Virbhadra, Phys. Rev. D60, 104041 (1999). 14. K.S. Virbhadra, Phys. Rev. D41, 1081 (1990); D42, 1066 (1990); D42, 2919 (1990) and references therein. 15. S.S. Xulu, Int. J. Mod. Phys. A15, 2979 (2000); Mod. Phys. Lett. A15, 1511 (2000) and references therein. 16. I.C. Yang and I. Radinschi, Mod. Phys. Lett. A17, 1159 (2002). 17. M. Sharif, Int. J. of Mod. Phys. A17, 1175 (2002). 18. M. Sharif, Int. J. of Mod. Phys. A18, (2003); Erratum A, (2003); gr-qc/0310018. 19. G. Lessner, Gen. Relativ. Grav. 28, 527 (1996). 20. J. Bardeen, Proc. GR5 (Tiflis, USSR, 1968). 21. A. Borde, Phys. Rev. D 50, 3692 (1994); Phys. Rev. D 55, 7615 (1997). 22. C.W. Misner, K.S. Thorne and J.A. Wheeler, Gravitation (W.H. Freeman, New York, 1973)603. 23. F.I. Cooperstock and R.S. Sarracino, J. Phys. A.: Math. Gen. 11, 877 (1978).

s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655878639.9/warc/CC-MAIN-20200702080623-20200702110623-00014.warc.gz

CC-MAIN-2020-29

https://space.stackexchange.com/questions/58834/why-cant-the-falcon-9-first-stage-touch-the-water?noredirect=1

math

SpaceX is spending considerable effort to catch the Falcon 9 first stage onto a giant drone ship. I am aware that salt water ruins almost everything in the long run, but the first stage is a composite material and seems to be painted. If it can survive a 8 km/s reentry, it should be able to survive a little time in the water. Empty of all fuel, the Falcon 9 first stage way just 75,000 pounds. Considering how much surface area it has, it should be able to float. There are carbon fiber (and fiberglass) boats, so why can't the Falcon 9 stages just touch the water (even for brief time)? Modified 1 year, 2 months ago Viewed 100 times $\begingroup$ Some misconceptions in the question that might not be covered by that answer: the Falcon 9 first stage is not composite, it's mostly aluminum. Some of it's painted, some of it's covered with a sort of hydrophobic ceramic felt. And boats aren't dropped vertically into the water and allowed to fall over, and even if more gently capsized or submerged, are likely to require major repair work, and may not be salvageable at all. Even a car that is immersed in saltwater is likely to be considered totaled, and rockets are considerably more complex and less forgiving. $\endgroup$– Christopher James HuffApr 10, 2022 at 21:52 $\begingroup$ @ChristopherJamesHuff more to the point; even if the structural pieces are OK taking a bit of a bath, there's a lot of complex innards which would have to be gutted. As mentioned in the linked question, where the SRB of the shuttle needed a lot of teardown of the internals to re-fly. $\endgroup$– fyrepenguinApr 11, 2022 at 8:28 $\begingroup$ @fyrepenguin that's why I used the example of a capsized or sunken boat. Boats are supposed to be in the water, but only certain parts are supposed to be in extended contact with it. The F9 booster's tanks might float, but the engines and grid fin/stage separation machinery don't have a hull keeping the seawater away. $\endgroup$– Christopher James HuffApr 11, 2022 at 17:54 $\begingroup$ There could also be issues with Very Hot materials coming into contact with relatively Cold seawater. $\endgroup$– FlaStorm32Apr 14, 2022 at 22:28 Add a comment |

s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224657720.82/warc/CC-MAIN-20230610131939-20230610161939-00355.warc.gz

CC-MAIN-2023-23

https://upcommons.upc.edu/browse?authority=630674e0-797d-4b28-aaf2-28cb9cb50511;drac:9465172;gauss:1058882&type=author

math

Rué Perna, Juan José; Serra Albó, Oriol; Vena Cros, Lluís (2017-01-01) Open Access© 2017 Elsevier Ltd. We provide asymptotic counting for the number of subsets of given size which are free of certain configurations in finite groups. Applications include sets without solutions to equations in non-abelian ... Rué Perna, Juan José; Serra Albó, Oriol; Vena Cros, Lluís (2015) Restricted access - publisher's policyWe present a unified framework to asymptotically count the number of sets, with a given cardinality, free of certain configurations. This is done by combining the hypergraph containers methodology joint with arithmetic ... Vena Cros, Lluís (Universitat Politècnica de Catalunya, 2007) Open AccessThe Szemerédi Regularity Lemma (SzRL) was introduced by Endré Szemerédi in his celebrated proof of the density version of Van der Waerden Theorem, namely, that a set of integers with positive density contains arbitrarily ... Vena Cros, Lluís (Universitat Politècnica de Catalunya, 2012-07-02) Open AccessThis thesis presents some contributions in additive combinatorics and arithmetic Ramsey theory. More specifically, it deals with the interaction between combinatorics, number theory and additive combinatorics. This area ...

s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141723602.80/warc/CC-MAIN-20201203062440-20201203092440-00167.warc.gz

CC-MAIN-2020-50

http://www.techadvisor.co.uk/forum/helproom-1/hp-510-volume-control-283719/

math

I know this sounds a bit like a stupid question, but I just recentley accuried an HP 510 notebook and i cant work out how to change the volume apart from the volume icon in the system tray. Looking at the help files, it suggests there is a volume scroll zone which i can not find?!?! Anyone with one of these notebooks, please advise me as to where this volume scroll zone is because i am going out of my mind trying to work it out! Many thanks for your time, This thread is now locked and can not be replied to.

s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128323908.87/warc/CC-MAIN-20170629103036-20170629123036-00090.warc.gz

CC-MAIN-2017-26

https://www.prosebox.net/entry/78895/tomorrow-is-the-big-day/?nav=author

math

We are having our first exam in chemistry tomorrow. I am nervous as hell. I think I am doing very well in this class but at the same time, I know how very wrong I can be. I think I have everything memorized that needs to be memorized but I feel like I'm going to choke when it comes to taking the test. I know I can write the formulas down above all the work... no problem. But to apply those formulas logically to the questions is quite another thing all together. Plus, remembering all the vocabulary... Idk. This test really means a lot to me. I have been trying very hard in this class. I was crying on the second day of class when he said that so much of this class is based on conversions (which require math). I have since memorized as much as possible what the required conversions are. I just think I will prob choke on the test. That would be almost funny if I do choke considering how many people in the class have been coming to me for help. It is also simply amazing to me that my lab partners seem to just stare at me while I do the conversion work in the lab. It's almost like they can't figure this stuff out but they see me doing it 3 steps ahead of them. That actually makes me feel very good. I rely on them pretty heavily to do the actual lab work. I am pretty nervous with that stuff. I haven't really had the confidence to do that. But now that I see them looking to me to do the conversions, I might just build up on that confidence in the actual lab. I have been feeling like the weak link in there but maybe I'm not afterall. Tomorrows test is so important to me. I really want to see how this all plays out. God please help give me the clarity to be able to figure out what is being supplied and what is being asked. Please help give me the memory needed to figure out the conversions and formulas. Please give me the calmness to do it without making a lot of mistakes on stupid things. Please help give me the confidence I need to not panic. Through all of that God, please give me an A on this test.

s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703515235.25/warc/CC-MAIN-20210118185230-20210118215230-00263.warc.gz

CC-MAIN-2021-04

https://scholars.hkbu.edu.hk/en/publications/on-generating-discrete-integrable-systems-via-lie-algebras-and-co

math

In the paper, we introduce the Lie algebras and the commutator equations to rewrite the Tu-d scheme for generating discrete integrable systems regularly. By the approach the various loop algebras of the Lie algebra A1 are defined so that the well-known Toda hierarchy and a novel discrete integrable system are obtained, respectively. A reduction of the later hierarchy is just right the famous Ablowitz-Ladik hierarchy. Finally, via two different enlarging Lie algebras of the Lie algebra A1, we derive two resulting differential-difference integrable couplings of the Toda hierarchy, of course, they are all various discrete expanding integrable models of the Toda hierarchy. When the introduced spectral matrices are higher degrees, the way presented in the paper is more convenient to generate discrete integrable equations than the Tu-d scheme by using the software Maple. Scopus Subject Areas - Physics and Astronomy (miscellaneous) - discrte integrable system - integrable coupling - Lie algebra

s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817729.87/warc/CC-MAIN-20240421071342-20240421101342-00029.warc.gz

CC-MAIN-2024-18

https://www.arxiv-vanity.com/papers/hep-th/0601172/

math

Dilatons in curved backgrounds by the Poisson–Lie transformation Transformations between group coordinates of three–dimensional conformal –models in the flat background and their flat, i.e. Riemannian coordinates enable to find general dilaton fields for three–dimensional flat –models. By the Poisson–Lie transformation we can get dilatons for the dual –models in a curved background. Unfortunately, in some cases the dilatons depend on inadmissible auxiliary variables so the procedure is not universal. The cases where the procedure gives proper and nontrivial dilatons in curved backgrounds are investigated and results given. In the paper we have investigated conformally invariant three–dimensional –models on solvable Lie groups that were Poisson–Lie T–dual or plural to –models in the flat background. Several of them were nontrivial in the sense that they lived in a curved background and had nonvanishing torsion. In some cases we were not able to find the dilaton fields by the plurality procedure given in because necessary conditions for application of Poisson–Lie transformation were not satisfied for the constant dilaton. Recently we have found explicit forms of transformations between the group coordinates of the flat –models and their flat coordinates, i.e. we expressed the Riemannian coordinates of the flat metric in parameters of its solvable isometry subgroups . This enables us to write down the general form of the dilaton field satisfying the vanishing equations for the flat model in terms of the group coordinates and consequently the dilaton fields on the dual or plural nontrivial models. To set our notation let us very briefly review the construction of the Poisson–Lie T–plural –models by means of Drinfel’d doubles (For more detailed description see , , , ). The Lagrangian of dualizable –models can be written in terms of right–invariant fields on a Lie group that is a subgroup of the Drinfel’d double as are components of right–invariant forms (vielbeins) and are local coordinates of . and are submatrices of the adjoint representation of the group on the Lie algebra of the Drinfel’d double 111 t denotes transposition. The fact that for a Drinfel’d double several decompositions of its Lie algebra into Manin triples ) may exist leads to the notion of Poisson–Lie T–plurality . Namely, let be generators of Lie subalgebras of the Manin triple associated with the Lagrangian (1) and are generators of some other Manin triple in the same Drinfel’d double related by the transformation matrix as The transformed model is then given by the Lagrangian of the form (1) but with replaced by and is calculated by (3) from the adjoint representation of the group generated by . Note that for we get the dual model with , corresponding to the interchange so that the duality transformation is a special case of the plurality transformation (5) – (7). 2 Poisson–Lie transformation of dilatons In quantum theory the duality or plurality transformation must be supplemented by a correction that comes from integrating out the fields on the dual group in path integral formulation. In some cases it can be absorbed at the 1-loop level into the transformation of the dilaton field satisfying the so called vanishing equations where the covariant derivatives , Ricci tensor and Gauss curvature are calculated from the metric that is also used for lowering and raising indices, and the torsion is Unfortunately, the right-hand side of the formula (14) may depend on the coordinates of the auxiliary group . That’s why the transformation of the dilaton field cannot be applied in general but only if the following theorem holds The dilaton (14) for the model defined on the group exists if and only if where is extended as a left–invariant vector field on and For applications it is much easier to check a weaker necessary condition. A necessary condition for the existence of the dilaton (14) for the model defined on the group is where is the unit of the Drinfel’d double . For parametrization of in the form where is the submatrix in (5). The condition (18) could not be satisfied for some of the –models with constant dilaton field so that we were not able to find the transformed dilaton that satisfy the vanishing equations. The possibility to find the general dilaton fields for the flat models offers a possibility to overcome this obstacle and obtain more general dilatons in curved backgrounds. 3 Dilatons of –models on solvable three-dimensional groups All models investigated in the following admit nonsymmetric tensor but their torsions vanish so without loss of generality we shall deal with models having . 3.1 General dilatons in flat backgrounds It follows from the construction of classical dualizable models that they are given by decompositions (Manin triples) and matrices . Most of the flat and torsionless models found in can be formulated on the the Drinfel’d doubles with semiabelian decompositions where 1 is the three–dimensional abelian algebra. From the form of the vanishing equations (8–10) it is easy to see that the general form of their dilaton fields is where are coordinates that bring the flat metric to a constant form (see ) and are real constants satisfying By the Poisson–Lie transformation of (19) we can get dilatons for the dual –models but, as mentioned before, only if the necessary conditions are satisfied. Due to (15) and (19) the condition (18) reads Moreover, the matrix vanishes for and the flat coordinates can be chosen to satisfy . The condition (21) then simplifies to 3.2 Dilatons for –models dual to The first –model in the curved background we are going to investigate is given by the metric where and are constants. This metric has nonvanishing Ricci tensor but its Gauss curvature is zero. It belongs to the –model corresponding to the decomposition of the (for notation see ) and . On the other hand, it can be obtained by the Poisson–Lie transformation (6), (7) from the metric where are constants. The latter metric is flat and corresponds to the decomposition of the and . where relations between the constants are In fact, the metric (23) is the most general that can be obtained by the Poisson–Lie transformation from a flat metric corresponding to the decomposition of the . These are the coordinates that bring the flat metric to its constant form . where the coefficients satisfy the equation (20) that in this case reads However, this is not yet the final form of the dilaton field because it is expressed in terms of the coordinates of the –model given by (24) and it must be transformed to the coordinates of the –model given by (23). The transformation formulas between these coordinates follow from two different decompositions of elements of the Drinfel’d double , namely from the relation where are generators corresponding to the decomposition of the Drinfel’d double and are generators of the decomposition . They can be related by (25). Coordinates in terms of are then expressed as We have checked that the vanishing equations for and given by (23) are satisfied. Note that the condition is more strict than the necessary condition (22) that implies only. It means that the necessary condition (16) is not sufficient for the Poisson–Lie transformation of the dilaton. 3.3 Sigma models dual to A bit more complicated –model is given by the metric , where where and are constants. Again, this metric has nonvanishing Ricci tensor and its Gauss curvature is zero. It belongs to the –model corresponding to the decomposition of the and . Besides that it can be obtained by the Poisson–Lie transformation (6), (7) from the metric where are constants. This metric is flat and corresponds to the decomposition of the . where the relations between the constants are where the coefficients satisfy the equation (29). To get the final form of the dilaton field we must transform it to the coordinates . The transformation formulas follow from decompositions of elements of the Drinfel’d double , namely from the relation (30) where are generators corresponding to the decomposition and , related by (5) and (35), correspond to the decomposition . Coordinates in terms of are then expressed as In order that the dilaton does not depend on the coordinate we must set and the general form of the dilaton obtained by the Poisson–Lie transformation for the metric (3.3) is again (32). The vanishing equations are satisfied. Let us mention in the end that there are still other models with curved backgrounds dual to the flat ones, namely those corresponding to the Manin triples of the Drinfel’d doubles DD15 and DD19. Unfortunately, in these cases all coordinates depend on the so that only may be inserted into (14) giving results published in . We have investigated the possibilities to apply the Poisson–Lie transformation to the general solution of the vanishing equations for the flat metric. We have obtained dilaton fields for the metrics (23) and (3.3) having a nontrivial Ricci tensor. They are the most general dilatons that can be obtained by the Poisson–Lie transformation from the general dilatons (28), (37) of the dual flat metrics (24) and (34). An interesting but yet unsolved question is whether the dilaton (32) is the general solution of the vanishing equations for the curved backgrounds (23) and (3.3). This work was supported by the project of the Grant Agency of the Czech Republic No. 202/06/1480 and by the research plan LC527 15397/2005–31 of the Ministry of Education of the Czech Republic. Useful comments of Libor Šnobl are gratefully acknowledged. - L. Hlavatý and L. Šnobl, Poisson–Lie T–plurality of three–dimensional conformally invariant sigma models II : Nondiagonal metrics and dilaton puzzle, J. High En. Phys. 04:10 (2004) 045, [hep-th/0408126]. - R. von Unge, Poisson–Lie T–plurality, J. High En. Phys. 02:07 (2002) 014, [hep-th/00205245]. - L. Hlavatý and M.Turek, Flat coordinates and dilaton fields for three–dimensional conformal sigma models [hep-th/0512082]. - C. Klimčík and P. Ševera, Dual non–Abelian duality and the Drinfeld double, Phys. Lett. B 351 (1995) 455, [hep-th/9502122]. - C. Klimčík, Poisson-Lie T-duality, Nucl. Phys. B (Proc. Suppl.) 46 (1996) 116, [hep-th/9509095]. - L. Šnobl and L. Hlavatý, Classification of 6-dimensional real Drinfel’d doubles, Int.J.Mod.Phys. A17 (2002) 4043 [math.QA/0202210].

s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154302.46/warc/CC-MAIN-20210802012641-20210802042641-00372.warc.gz

CC-MAIN-2021-31

https://questionvoyage.com/how-long-does-it-take-to-travel-200-km

math

Top best answers to the question «How long does it take to travel 200 km» 44 hours to be exact, at the average walking speed of 4.5kph (2.8mph) (as per google maps estimation). In succinct terms, it takes approximately 2 hours to cover 200km by car and almost 2 days to cover 200km by foot. 10 other answers That's easy. 200 km is only 124 miles. Thousands of people of all ages flock to century rides every weekend, and they finish in 6 to 10 hours. I am a 59 year old woman, and I just rode 400K (249 miles) in 23 hours and 43 minutes. SolutionShow Solution. Distance covered by train = 200 km. Speed of train = 60 km h -1. We know speed = `"Distance" / "Time "`. ⇒ 60 = `200/"Time" `. Time = `200/60` = `20/6` `10/3` hours. = 3`1/3` hours = 3 h + `1/3` hours. = 3 h + `1/3` × 60 min. = 3 h + 20 min. Convert: 1km = 1000 m 200000 m * 0.01 s/m = 2000 s or 33 minutes and 20 seconds. Smenevacuundacy and 5 more users found this answer helpful. heart outlined. Example 1: ----- Speed: 50 mile per hour (km/h) Distance: 70 miles Time = Distance / Speed Time = 70 km / (50 km/h) Time = 1.4 h 1 hour = 60 minutes 0.4 h = 0.4 × 60 0.4 h = 24 minutes Time = 1 hour 24 minutes Time = 01:24:00 (HH:MM:SS) Example 2: ----- Speed: 40 kilometer per hour (km/h) Distance: 60 miles Time = Distance / Speed Time = 60 miles / (40 km/h) 1 mile = 1.609344 km Time = 60 × 1.609344 km / (40 km/h) Time = 96.56064 km (40 km/h) Time = 2.414016 h Hours = 2 h 1 hour = 60 ... First, calculate 80 * 4 = 320 km, then convert km to miles by dividing by 1.6093 or by using our km to miles converter to get the answer: 198.84 miles. Duration (Time) formula The time, or more precisely, the duration of the trip, can be calculated knowing the distance and the average speed using the formula: The distance calculator can help you prepare for the road by helping you figure out how far a city is from you. Calculations are made in kilometers and miles and information is available for all countries around the world. Additionally, Distancesto.com provides a way for you to see where you are going, determine the cost of your trip, the time it ... It means that a sound wave in air needs about 2.9 seconds to travel one kilometer, or 4.7 seconds to travel a mile - this data might be useful for storm-hunters to determine the lighting distance. In 2012, Austrian Felix Baumgartner broke the sound barrier (with his body!) during a free-fall from 228 000 feet. He reached the speed of 833.9 mph. With the travel time calculator you can figure out whether it's worth driving to your destination or whether you'll get there on time. Now while driving may often seem like the right choice, certain delays along the way can make your trip take longer. Delays such as stopping for gas, food or sleep can add to the time it takes you to get there. Travelmath provides an online flight time calculator for all types of travel routes. You can enter airports, cities, states, countries, or zip codes to find the flying time between any two points. The database uses the great circle distance and the average airspeed of a commercial airliner to figure out how long a typical flight would take. I've done 160 miles in 12 hours and over 200 miles a few times in 24 hours. Therefore 300 KM is do-able if you've trained enough. I the randonneur world, the time limit for a 300 is 20 hours start to finish (15kph including time off the bike).

s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103645173.39/warc/CC-MAIN-20220629211420-20220630001420-00233.warc.gz

CC-MAIN-2022-27

https://www.assignmentexpert.com/homework-answers/chemistry/inorganic-chemistry/question-83336

math

If Kinetic Energy is directly proportional to mass, than the gas with the larger mass would have the larger kinetic energy, right? But what if the two separate gases are in two non-rigid containers of equal volume (1 Liter), and at the same temperature (25 celsius). The two gases are Carbon monoxide and carbon dioxide. There are 2 atm of carbon monoxide, and 1 atm of carbon dioxide. I used PV=nRT to find the moles of CO and CO2 using these conditions and concluded that there is more of Carbon monoxide than there is Carbon dioxide. Shouldn't this mean that it has more kinetic energy than carbon dioxide? Still, I also know that temperature is indicative of average kinetic energy, and so if they are both the same temperature than they should have the same kinetic energy. So I guess I was confused about which was right.

s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057427.71/warc/CC-MAIN-20210923165408-20210923195408-00442.warc.gz

CC-MAIN-2021-39

https://www.geeksforgeeks.org/sum-of-product-of-all-integers-upto-n-with-their-count-of-divisors/?ref=leftbar-rightbar

math

Given a positive integer N, the task is to find the sum of the product of all the integers in the range [1, N] with their count of divisors. Input: N = 3 Number of positive divisors of 1 is 1( i.e. 1 itself). Therefore, f(1) = 1. Number of positive divisors of 2 is 2( i.e. 1, 2). Therefore, f(2) = 2. Number of positive divisors of 3 is 2( i.e. 1, 3). Therefore, f(3) = 2. So the answer is 1*f(1) + 2*f(2) + 3*f(3) = 1*1 + 2*2 + 3*2 = 11. Input: N = 4 Here f(1) = 1, f(2) = 2, f(3) = 2 and f(4) = 3. So, the answer is 1*1 + 2*2 + 3*2 + 4*3 = 23. Naive Approach: The naive approach is to traverse from 1 to N and find the sum of all the numbers with their count of divisors. Time Complexity: O(N*sqrt(N)) Auxiliary Space: O(1) Efficient Approach: To optimize the above approach, the idea is to consider the total contribution each number makes to the answer. Below are the steps: - For any number X in the range [1, N], X contributes K to the sum for each K from 1 to N such that K is a multiple of X. - Observe that the list of these K is of form i, 2i, 3i, …, Fi where F is the number of multiples of i between 1 and N. - Hence, to find the sum of these numbers generated above is given by i*(1+2+3 + … F) = i*(F*(F+1))/2. Below is the implementation of the above approach: Time Complexity: O(N) Auxiliary Space: O(1) Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready. - Check if count of even divisors of N is equal to count of odd divisors - Check if a number has an odd count of odd divisors and even count of even divisors - Find sum of divisors of all the divisors of a natural number - Find sum of inverse of the divisors when sum of divisors and the number is given - Sum of integers upto N with given unit digit - Sum of integers upto N with given unit digit (Set 2) - Sum of product of all subsets formed by only divisors of N - Sum of product of proper divisors of all Numbers lying in range [L, R] - Count of all values of N in [L, R] such that count of primes upto N is also prime - Count of pairs upto N such whose LCM is not equal to their product for Q queries - Minimise N such that sum of count of all factors upto N is greater than or equal to X - Count number of integers less than or equal to N which has exactly 9 divisors - Count of integers up to N which are non divisors and non coprime with N - Divisors of n-square that are not divisors of n - Maximum possible prime divisors that can exist in numbers having exactly N divisors - Count of divisors of product of an Array in range L to R for Q queries - Count all pairs of divisors of a number N whose sum is coprime with N - Count numbers < = N whose difference with the count of primes upto them is > = K - Maximize count of equal numbers in Array of numbers upto N by replacing pairs with their sum - Sum of GCD of all numbers upto N with N itself If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks. Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400192887.19/warc/CC-MAIN-20200919204805-20200919234805-00222.warc.gz

CC-MAIN-2020-40

https://math.stackexchange.com/questions/3011313/how-many-ways-to-arrange-four-types-of-books-on-the-shelf-so-that-books-of-the-s

math

Janet has $10$ different books that she is going to put on her bookshelf. Of these, $4$ are Book C, $3$ are Book B, $2$ are Book S and $1$ Book P. Janet wants to arrange her books so that all the books dealing with the same subject are together on the shelf. How many different arrangements are possible? My workings are $4! \cdot 3! \cdot 2! \cdot 1!$ but the actual answer has an additional multiplication by $4!$ Why is this so? My guess is because we need the $4$ books to come together, let's say for book C. But isn't that "shown" by the working of $4!$ for Book C and $3!$ for Book B and so on?

s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304261.85/warc/CC-MAIN-20220123111431-20220123141431-00045.warc.gz

CC-MAIN-2022-05

http://mathcentral.uregina.ca/QQ/database/QQ.09.96/doan1.html

math

Date: Tue, 3 Sep 1996 21:01:35 PST Subject: math problemCan you prove that "2n choose n" is not divisible by 3, 5, and 7 for infinitely many n? Erdos, Graham, Rusza and Straus (Math. of Comp., 29(1975),pp 83-92) show that for any two primes p and q there exist infinitely many integers n for which (C(2n,n),pq) = 1. They remark that nothing is known for three primes and, in particular, they ask whether there are infinitely many n for which (C(2n,n),105) = 1 and this is your problem. As far as I know this is still unsettled. I have put a note on the divisibility of 2n choose n by individual primes in the Resource Room. To return to the previous page use your browser's back button.

s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999163.73/warc/CC-MAIN-20190620065141-20190620091141-00328.warc.gz

CC-MAIN-2019-26

https://m.wdfxw.net/doc100614519.htm

math

( ) 1. A. bedroom B. bathroom C. classroom ( ) 2. A. bed B. bag C. red ( ) 3. A. phone B. find C. fridge ( ) 4. A. cute B. cut C. use ( ) 5. A. table B. sofa C. phone 1. 2. 3. 4. 5. ( ) ( ) ( ) ( ) ( ) ( ) 1. There are 6 rooms in the girl’s home. ( ) 2. In the bedroom, the wall is yellow and the floor is white. ( ) 3. A teddy bear is in the living room. ( ) 4. Many books are on the bed. ( ) 5. There is a big table in the kitchen. 1. 2. 3. 4. 5. ( ) 1. table A. 桌子 B. 窗户 C. 椅子 ( ) 2. them A. 他 B. 他的 C. 他(她、它)们 ( ) 3. kitchen A. 书房 B. 卧室 C. 厨房 ( ) 4. find A. 打扫 B. 帮助 C. 找到 ( ) 5. bathroom A. 浴室 B. 客厅 C. 教室 A. desk B. sofa C. bed D. fridge E. crayon 1. watch TV A. 读一本书 2. read a book B. 小憩一下 3. have a nap C. 在电话旁 4. in the study D. 在书房 5. near the phone E. 看电视 ( ) 1. Go to the bathroom. _______. A. Have a nap B. Take a shower C. Have a snack ( ) 2. —Where are my keys? — _______. A. It’s on the table B. They are on the table C. Yes, it is ( ) 3. —Is the girl in the living room? — _______. A. Yes, he is B. No, he isn’t C. Yes, she is ( ) 4. You can have a nap in the _______. A. kitchen B. bedroom C. bathroom ( ) 5. —Are the glasses in the kitchen? — _______. A. Yes, they are B. Yes, it is C. Yes, they aren’t ( ) 1. 当你想知道Amy的爸爸在哪里时，你应该这样问Amy：______ A. Where is your father? B. Is he in the study? C. Where is your mother? ( ) 2. 当你想知道它是不是在桌子上时，你应该问：______ A. Is it on the table? B. Is it in the desk? C. Are they in the desk? ( ) 3. 当别人问你家里那只小猫是否在厨房时，你应该说：______ A. Yes, they are. B. No, she is. C. Yes, it is. ( ) 4. 当你想告诉妈妈钥匙在门上插着时，你应该说：______ A. Look! The key is on the door. B. Look! The key is in the door. C. Look! The key is under the door. ( ) 5. 当你想让别人开门时，你应该说：______ A. No, they aren’t. B. OK! C. Open the door, please! ( ) 1. —Where are the keys? —Look! They are in the door. ( ) 2. My father is in the bedroom. ( ) 3. This is my bedroom. My books are on the bed. ( ) 4. —Is he in the kitchen? —Yes, he is. ( ) 5. Look! The phone is on the desk. ( ) 1. Where are the keys? A. Yes, it is. ( ) 2. Is she in the study? B. Yes, she is. ( ) 3. Are they near the phone? C. She is in the bedroom. ( ) 4. Is it in your hand? D. They’re in the door. ( ) 5. Where is she? E. No, they aren’t. Hello! My name is Alice. This is my new bedroom. Look! There is a blue bed in the room. There are two photos (照片) on the wall. Where is the cat? Oh, it’s under the table. Where are my books? They’re on the table. There is a pen on the book. The table is near the window. There is a chair near the table. ( ) 1. This is Alice’s new bedroom. ( ) 2. There are three photos on the wall. ( ) 3. The cat is on the table. ( ) 4. The books are on the table. ( ) 5. A chair is near the door.

s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296944452.74/warc/CC-MAIN-20230322180852-20230322210852-00745.warc.gz

CC-MAIN-2023-14

https://internetdo.com/bitcoin/bitcoin-and-the-stock-to-flow-model-dont-put-the-cartbefore-the-horse-seeking-alpha.html

math

In the crypto community, an infamous bullish model on Bitcoin has buzzed in recent months, predicting a substantial appreciation in BTC-USD after the forthcoming halving, expected in May this year. This model is referred to as the Stock to Flow (SF or S2F) model, which was initially introduced by Plan B, an anonymous quantitative institutional investor from the Netherlands. The logic behind the model makes sense to us in so far as it treats Bitcoin as a mere commodity (producing no income) and aims at establishing a relationship between the market value of Bitcoin and its scarcity of Bitcoin, proxied by a stock-to flow ratio. Once this relationship is quantified, the price of Bitcoin (BTC-USD) can be inferred. At first glance, this logic seems to work and offers consistent results with other commodities like gold as silver. Source: Plan B The author uses logarithmic values instead of static values to show an actual linear relationship between the two variables. Fitting a model to non-linear data would result in meaningful prediction errors. But contrary to other traditional commodities, the stock-to-flow ratio is predictable because Bitcoin was designed with a fixed supply and predictable inflation schedule. To wit from PlanB: Supply of bitcoin is fixed. New bitcoins are created in every new block. Blocks are created every 10 minutes (on average), when a miner finds the hash that satisfies the PoW required for a valid block. The first transaction in each block, called the coinbase, contains the block reward for the miner that found the block. The block reward consists of the fees that people pay for transactions in that block and the newly created coins (called subsidy). The subsidy started at 50 bitcoins, and is halved every 210,000 blocks (about 4 years). That’s why ‘halvings’ are very important for bitcoins money supply and SF. Halvings also cause the supply growth rate (in bitcoin context usually called ‘monetary inflation’) to be stepped and not smooth. Modeling Bitcoin’s Value with Scarcity, March 2019 Based on PlanB’s model, the near-term outlook for Bitcoin could be extremely exciting considering that the forthcoming halving is scheduled in May 2020: Based on PlanB’s model, the predicted market value of Bitcoin after the May 2020 halving will be $1 trillion, translating into BTC-USD at $55,000, representing a stellar gain from its current price level. Source: PlanB, digitalik In this note, we wish to discuss the veracity of PlanB’s model and propose a more robust statistical approach to tackle the original model’s limitations. Unfortunately, our conclusions invalidate PlanB’s model because we do not find any significant short-term and long-term dynamics of the relationship between the market value of Bitcoin and the stock-to-flow ratio. Therefore, we cannot conclude that a substantial appreciation in BTC-USD will materialize after the May 2020 halving. The model equation, which can be estimated with Ordinary Least Squares (OLS), can be written as follows: Bitcoin=market value of Bitcoin; SF=Stock-to-flow ratio While the assumption of a linear relationship between the independent variable (NYSE:SF) and the dependent variable (Bitcoin) is respected, other assumptions also need to be verified to make sure that the results of the linear regression model are valid and interpretable. To be specific, the Gauss-Markov Theorem states that the OLS estimator gives the best linear unbiased estimator (BLUE) of the regression coefficients as long as: - The OLS residuals have a mean of zero - The OLS residuals are uncorrelated (no autocorrelation) - The OLS residuals have constant variance (homoscedasticity) Let’s check whether these three assumptions are verified by using PlanB’s data. We will use raw data from PlanB’s article, available here. The dataset consists of monthly data of the market value of Bitcoin (Bitcoin) and the stock-to-flow ratio (SF) from December 2009 to February 2019. Here are the key statistics of our dataset: Let’s kick off by double-checking the linear relationship between: There is indeed a clear linear relationship between the two variables. We can proceed. Let’s now fit our linear regression model using OLS. Here is the summary of our results: At first glance, the OLS estimators are statistically significant and the coefficient of determination (R-squared) is very high (94%), suggesting that the model fits very well with the data. R-squared is the % of variance explained by the model. However, we need to be careful and don’t put the cart before the horse. Let’s make sure that our three assumptions about the OLS residuals mentioned above are verified before making any straightforward conclusions. Do the OLS residuals have a mean of zero? We find that the OLS residuals have a mean of -1.63552854942978e-14, confirming that the expectation of our OLS residuals is zero. The first assumption is validated. Do the OLS residuals have constant variance (homoscedasticity)? Let’s plot the OLS residuals to detect potential homoscedasticity, that is, a non-constant variance. The OLS residuals seem to exhibit no clear pattern while the pink line is pretty stable. At first glance, it seems to us that the OLS residuals are homoscedastic. To confirm this, let’s run the Goldfeld-Quandt test, whereby the null hypothesis assumes that the OLS residuals are homoscedastic. Test conclusion: Considering that the p-value is greater than 0.1, we fail to reject the null hypothesis of homoscedasticity, thereby confirming our initial intuition. The second assumption is validated. Do the OLS residuals are uncorrelated (no autocorrelation)? To detect the presence of autocorrelation, we can start by plotting residual autocorrelation. The ACF suggests the presence of autocorrelation. To confirm this, let’s run the Durbin-Watson test, whereby the null hypothesis assumes that errors are uncorrelated. Test conclusion: The Durbin-Watson test confirms the presence of positive autocorrelation in the OLS residuals. Consequently, the assumption of non-serial correlation cannot be verified. We will discuss the implications of it later in the note. Is the model stable? To investigate this, we apply a Recursive Least Square (RLS) filter. Conclusion: The CUSUM statistic moves slightly outside the 10% significance bands, leading us to reject the null hypothesis of the stability of the model at the 10% level. Due to the autocorrelation in the OLS residuals, we cannot make statistically meaningful conclusions. The OLS estimates of the standard errors are likely to be smaller than their true values. As a result, the r-ratios cannot be properly interpretable because they are likely to look more significant than they really are. Because the t-ratios are not interpretable, we cannot know whether the estimators of our linear regression model: are statistically different from zero. The same applies to R-squared. In this regard, the super-high R-squared of 95% in the model above is likely to be misleading. We need to find a way to know whether we are dealing with a spurious regression (showing an apparent strong relationship between unrelated variables) or a genuine relationship. A genuine relationship between two non-stationary variables is possible if we have a stationary equilibrium relationship between these two variables, meaning there exists a linear combination between these two variables that is stationary. In this case, these variables are cointegrated. In our context ln(Bitcoin) and ln((SF)) ar two non-stationary variables integrated of order 1: Test conclusion: In both cases, the null hypothesis of a unit root can be rejected at the 5% level. We say than ln(Bitcoin) and ln((SF)) are cointegrated if there is a linear combination between ln(Bitcoin) and ln((SF)) such as: If these two variables are cointegrated, any deviation from equilibrium will only be temporary, thereby resulting in a genuine relationship. According to Engle and Granger (1987), if a set of variables are cointegrated, then there exists a valid error correction representation of the data. In the section below, we will follow the two-step procedure recommended by Engle and Granger in Co-Integration and Error Correction: Representation, Estimation, and Testing (1987) to develop an error correction model and study the true relationship between the value of Bitcoin and the stock-to-flow ratio. Step 1: Estimate our equilibrium equation and perform a test for cointegration Our long-term equation is written as follows: A test for cointegration consists of testing whether OLS residuals (û) are stationary. To do so, we run an Augmented Dickey-Fuller (ADF) unit root test on the OLS residuals. Here are the results: Test conclusion: The null hypothesis of a unit root can be rejected at the 1% level. Therefore, the OLS residuals do not have a unit root and are stationary. Because the cointegration is verified, we know that our OLS estimators are super-consistent. That said, the serial correlation in the residuals affects their efficiency. Consequently, traditional diagnostic tests need to be overlooked. Step 2: Estimate the Error Correction Model (ECM) Our ECM equation can be written as follows: Because this equation has only I(0) variables, there is no longer autocorrelation in the OLS residuals and as such, traditional diagnostic tests are appropriate. This ECM describes the short-term and long-term dynamics of the relationship between the market value of Bitcoin and the stock-to-flow ratio. The adjustment coefficient, α, which should vary between -1 and 0, measures the speed of the adjustment toward the long-term equilibrium. Should α be positive, the impulse response would be explosive, forcing us to reconsider our model. To determine the lag lengths (p and q) for our ECM, we will run two VAR regressions using each variable as an endogenous variable. We will use Akaike’s Information Criteria (NYSE:AIC) to select the optimal lag length. We initially selected a max lag length of 10. Here are our results: Lag selection: Based on Akaike’s Information Criteria (AIC), we deduce that p = q =2. Let’s now fit our linear regression model using OLS. Here is the summary of our results: Interpretations of our results: As we noted above, traditional diagnostic testing is now appropriate because the model does not suffer from autocorrelation in the OLS residuals. The Durbin-Watson statistic is very close to 2. The OLS estimator on the lagged OLS residuals is statistically significant. α = -0.15. This means that only 15% of the disequilibrium will dissipate in the next period, meaning that adjustment is rather sluggish. The OLS estimators on: - the constant (const) are statistically significant. This means that if the market value of Bitcoin at t-1 changes ceteris paribus by 1% percentage point, the market value of Bitcoin at t changes by 0.25 percentage point. The estimators of the short-run and the long-run elasticities of the market value of Bitcoin with respect to the stock-to-flow ratio are not statistically significant. We, therefore, cannot assert that the market value of Bitcoin is significantly elastic with respect to the stock-to-flow ratio, both in the short and long run. R-squared is decent at 21%, although it has substantially deflated from the R-squared of 95% resulting from PlanB’s model. Stability of the model Let’s finally check the stability of our new model. Again, we apply a Recursive Least Square (RLS) filter. Conclusion: The CUSUM statistic stays within the 10% significance bands, leading us to fail to reject the null hypothesis of the stability of the model (i.e., there is no structural break) at the 10% level. Therefore, it is safe to assert that the new model is stable over time, unlike the original model from PlanB. In our view, PlanB’s infamous model is misleading because the statistical results cannot be properly interpretable. This even prompted Vitalik Buterin, Etherum (ETH) co-founder, to tweet about it, criticizing the approach of being “post-hoc rationalized bullshit”. In our view, PlanB’s model emanates from a good intuition. This is why we have revisited the original model to account for the autocorrelation issue and attempt to investigate both short-term and long-term dynamics of the relationship between the market value of Bitcoin and the stock-to-flow ratio. Unfortunately, our model cannot assert the presence of significant elasticities of the market value of Bitcoin with respect to the stock-to-flow ratio, both in the short and long run. Our conclusions are as follows: - Our new model explains relatively well the market value of Bitcoin, with an R-squared of 21%, though to a much lesser extent than PlanB’s. - Our model cannot confirm the presence of significant short-term and long-term dynamics of the relationship between the market value of Bitcoin and the stock-to-flow ratio, invalidating PlanB’s conclusions. - The adjustment toward the long-term equilibrium is rather sluggish, suggesting that BTC/USD can remain away from its fair-value for a significant amount of time. Did you like this? Click the “Follow” button at the top of the article to receive notifications. Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article. Additional disclosure: Our research has not been prepared in accordance with the legal requirements designed to promote the independence of investment research. Therefore, this material cannot be considered as investment research, a research recommendation, nor a personal recommendation or advice, for regulatory purposes.

s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178359082.48/warc/CC-MAIN-20210227174711-20210227204711-00540.warc.gz

CC-MAIN-2021-10

https://scholarworks.merrimack.edu/mth_facpub/10/

math

Article - Open Access Mathematics Education Student Association A study was conducted at Merrimack College in Massachusetts to compare the grades of students who took the recommended course as determined by their mathematics placement exam score and those who did not follow this recommendation. The goal was to decide whether the mathematics placement exam used at Merrimack College was effective in placing students in the appropriate mathematics class. During five years, first-year students who took a mathematics course in the fall semester were categorized into four groups: those who took the recommended course, those who took an easier course than recommended, those who took a course more difficult than recommended, and those who did not take the placement test. Chi-square tests showed a statistically significant relationship between course grade (getting a C– or higher grade) and placement advice. The results indicate that students who take the recommended course or an easier one do much better than those who take a higher-level course or do not take the placement exam. With achievement in coursework as the measure of success, we concluded that the placement test is an effective tool for making recommendations to students about which courses they should take. (2004). Mathematics Placement Test: Helping Students Succeed. Mathematics Educator, 14(2), 27-33. Available at: https://scholarworks.merrimack.edu/mth_facpub/10

s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221209884.38/warc/CC-MAIN-20180815043905-20180815063905-00640.warc.gz

CC-MAIN-2018-34

https://qyfynitymusaboqe.leslutinsduphoenix.com/hard-math-problems-for-4th-graders-31004pu.html

math

If you are the kind of person who relishes the thought of putting your numerical skills to test, online math solvers can meet that need. Log onto math websites to find really hard math problems which will help you improve your problem solving skills and get ahead in the subject. Also Solutions and explanations are included. The areas, in kilometers squared, of some countries are given below. Answer the following questions: Jim drove miles of a miles journey. How many more miles does he need to drive to finish his journey? The rectangle on the left 15 by 25 and the square on the right have the same perimeter. What is the length of one side of the square? There are boxes of sweets in a store. There are 25 sweets in each box. How many sweets are in the store? There are days in one year, and years in one century. How many days are in one century? Billy read 2 books. He read the first one in one week with 25 pages everyday. He read the second book in 12 days with 23 pages everyday. What is the total number of pages that Billy read? Each van can carry 8 girls only. What is the smallest possible number of vans that are needed to transport all school girls? How much money was left after the shopping? A factory produces toys per week. If the workers at this factory work 4 days a week and if these workers make the same number of toys everyday, how many toys are produced each day? Tom, Julia, Mike and Fran have cards to use in a certain game. They decided to share them equally. How many cards should each one take and how many cards are left? The shaded shape is made of 5 congruent squares. The side of one square is 4 cm. Find the total area of the shaded shape. Sam, Carla and Sarah spent on afternoon collecting sea shells. If we add the number of sea shells collected by Sam and Carla, the total would be · They are ranked by a site called leslutinsduphoenix.com, which asks users progressively harder math and science problems. Dylan Toh, 12, solved this ridiculously hard geometry leslutinsduphoenix.com://leslutinsduphoenix.com · Math Word Problems(Mixed Skills) 2nd through 4th Grades. Mixed Math: C3. This math page contains problems relating to addition, subtraction, and telling time. 2nd through 4th Grades. Mixed Math: C4. To solve these problems, students must use subtraction skills and their knowledge of place leslutinsduphoenix.com://leslutinsduphoenix.com myON reader personalizes reading for students by recommending books based on their interests, reading level, and ratings of books they've read. myON reader tracks book usage and reading growth over time and can project a student’s future reading score based . You think that you are very smart at math? well take this quiz and see for yourself! Math Games and Math Homework. The finding by the National Mathematics Advisory Panel declared math education in the United States “broken” and called on schools to focus on teaching fundamental math skills that provide the underpinning for success in high tech jobs. These 4th grade math word problems and teaching resources will help make your class fun and engaging. Give extra motivation for your 4th graders to answer word problems on subtracting mixed numbers with these coloring worksheets. and they will surely enjoy uncovering the mystery picture after working hard to solve the word problems leslutinsduphoenix.com

s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657139167.74/warc/CC-MAIN-20200712175843-20200712205843-00267.warc.gz

CC-MAIN-2020-29

http://www.croustiglam.com/lib/category/calculus/page/2

math

By Wilbur R. LePage "An first-class textual content; the simplest i've got came upon at the subject." — J. B. Sevart, division of Mechanical Engineering, college of Wichita "An tremendous valuable textbook for either formal sessions and for self-study." — Society for commercial and utilized Mathematics Engineers usually would not have time to take a path in advanced variable idea as undergraduates, but is is among the most vital and worthwhile branches of arithmetic, with many purposes in engineering. this article is designed to therapy that desire via delivering graduate engineering scholars (especially electric engineering) with a direction within the easy concept of complicated variables, which in flip is key to the certainty of remodel conception. Presupposing a very good wisdom of calculus, the booklet offers lucidly and carefully with vital mathematical options, impressive an incredible stability among basically mathematical remedies which are too normal for the engineer, and books of utilized engineering that may fail to emphasize major mathematical ideas. The textual content is split into uncomplicated elements: the 1st half (Chapters 1–7) is dedicated to the speculation of complicated variables and starts with an summary of the constitution of approach research and a proof of uncomplicated mathematical and engineering phrases. bankruptcy 2 treats the basis of the idea of a posh variable, based round the Cauchy-Riemann equations. the following 3 chapters — conformal mapping, advanced integration, and limitless sequence — lead as much as a very very important bankruptcy on multivalued features, explaining the options of balance, department issues, and riemann surfaces. various diagrams illustrate the actual purposes of the mathematical innovations involved. The moment half (Chapters 8–16) covers Fourier and Laplace remodel thought and a few of its purposes in engineering, starting with a bankruptcy on genuine integrals. 3 very important chapters stick to at the Fourier fundamental, the Laplace fundamental (one-sided and two-sided) and convolution integrals. After a bankruptcy on extra houses of the Laplace necessary, the ebook ends with 4 chapters (13–16) at the program of rework conception to the answer of normal linear integrodifferential equations with consistent coefficients, impulse features, periodic features, and the more and more vital Z transform. Dr. LePage's publication is exclusive in its assurance of an surprisingly vast variety of subject matters tough to discover in one quantity, whereas even as stressing primary innovations, cautious realization to info and proper use of terminology. an in depth number of attention-grabbing and useful difficulties follows each one bankruptcy, and a very good bibliography recommends extra interpreting. excellent for domestic learn or because the nucleus of a graduate direction, this helpful, functional, and well known (8 printings in its hardcover version) textual content bargains scholars, engineers, and researchers a cautious, thorough grounding within the math necessary to many components of engineering. "An extraordinary job." — American Mathematical Monthly

s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823705.4/warc/CC-MAIN-20181211215732-20181212001232-00368.warc.gz

CC-MAIN-2018-51

http://apacktobenamedlater.blogspot.com/2010/10/2010-topps-chrome-baseball-hobby.html

math

#31 Carl Crawford #157 Grady Sizemore #144 Alex Rodriguez This is my second A's autograph rookie autograph from Chrome this year. Josh was originally drafted by the Cubs and was traded to the A's as part of the Rich Harden trade in 2008. #191 Josh Donaldson Rookie Autograph

s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296816893.19/warc/CC-MAIN-20240414161724-20240414191724-00044.warc.gz

CC-MAIN-2024-18

https://www.australiabesttutors.com/Recent_Question/19405/Marking-Criteria--You-are-required-to-demonstrate-the

math

Marking Criteria : You are required to demonstrate the following knowledge and skills in • Demonstrate the use of predictive modelling techniques in • Demonstrate the use of computer software to get necessary • Demonstrate the skills of preparation of a managerial report Style & Format : Business Report Detailed Information : Analysts at a company that produces small appliances are looking at sales of 24 food preparation products in a city. They have noticed that sales in this city have not been meeting forecast values for several months and want to look at the problem in more detail. They have collected data on monthly sales ($), advertising expenditure ($), number of competing products available, number of discount opportunities (sales, coupons, etc.) offered during the month, and the warranty period of the item. Data are given in the file TBS910 ASS3 A. 1. Consider the problem that must be solved. What do you think is the dependent variable in this problem? Which are the 2. Formulate the population regression model and comment on the expected signs of independent variables. 3. Use EXCEL to find the multiple regression model you identified 4. Write down the regression equation and interpret the coefficients in the model. How did the actual coefficients agree with your expectation of their effect? 5. Set up the hypotheses and test the significance of the model using 5 percent significance level. 6. What is the value of coefficient of determination of this model and what does it mean? 7. There were four variables in the original analysis, but the company wants to know whether they were all important in the model. Set up the hypotheses to test whether the individual coefficients are different from zero and perform the tests at the 5 percent level of significance. 8. Consider the variables that have coefficients that are zero. Which of these would recommend dropping from the 9. Rerun the analysis, dropping the variable you identified above. How does this change the model as a whole? Does dropping this variable change the contribution of the other variables? If so, how? Would you consider dropping another variable? If so, which one? If you answered yes to above then rerun the analysis dropping that variable. 10. Based on all of your analyses, what model do you think the company should use? Summarise your results in a formal Please make all curve (Its mandatory to draw)

s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358520.50/warc/CC-MAIN-20211128103924-20211128133924-00297.warc.gz

CC-MAIN-2021-49

https://noncommutativeanalysis.wordpress.com/category/politics-in-math/

math

I found an interesting figure in the March 2014 issue of the EMS newsletter, from the article by H. Mihaljevic´ -Brandt and O. Teschke, Journal Profiles and Beyond: What Makes a Mathematics Journal “General”? See the right column on page 56 in this link. (God help me, I have no idea how to embed that figure in the post. Anyway, maybe it is illegal, so I don’t bother learning.) One can see the “subject bias” of Acta, Annals and Inventiones. On the left column, there is a graph showing the percentage of papers devoted to different MSC subjects in what the authors call “generalist” math journals (note carefully that these journals are only a small subclass of all journals, chosen by a method that is loosely described in the article). On the right column there is the interesting figure, showing the subject bias. If I understand correctly, the Y-axis is the MSC number and the X-axis represents the corresponding deviation from the average percentage given in the left figure. So, for example, Operator Theory (MSC 47) is the subject of about 5 percent of the papers in a generalist journal, but in the Annals there is a deviation of minus 4 from the average, so if I understand this figure correctly, that means that about 1 percent of papers in the Annals are classified under MSC 47. Another example: Algebraic Geometry (MSC 14), takes up a significant portion of Inventiones papers, much more than it does in an average “generalist” journal. (I am not making any claims, this could mean a lot of things and it could mean nothing. But it is definitely interesting to note.) Another interesting point is that the authors say that of the above three super-journals, Acta “is closest to the average distribution, though it is sometimes considered as a journal with a focus on analysis”. That’s interesting in several ways.

s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057225.57/warc/CC-MAIN-20210921161350-20210921191350-00194.warc.gz

CC-MAIN-2021-39

https://tigps.in/index.php/question_paper/chemistry_question_4

math

2. KP = KC for a chemical reaction. At equilibrium pressure is increased the equilibrium will be shifted 3. Configurations of Pd – 46 is 4. In a pyro-silicate number of Si–O–Si bond present is 5. Number of LP – BP repulsion is 6. In an LPG cylinder 20 kgs of LPG have been bottled at 27°C under 20 atom pressure. The wall of the cylinder can withstand pressure upto 20 atm. In Kitchen the temperature can raise upto 57°C. Keeping this in view how many kg of LPG should be taken out. 7. CP – CV= R is valid for 8. By solvey process which of the following can be prepared 9. For which of the following elements 1E1 = 737 kj/mol and 1F2 = 1450 kj/mol. 10. 2A(s) + 3B(g) = C(l) + D(g) For the above reactions which of the followings is correct 11. How many degrees of unsaturation are there in 12. In which of the following cases the major product has correctly been shown 13. Which of the following is the structure of messo tartaric acid. 14. Which of the following will not take part in Etard Reactions

s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224644855.6/warc/CC-MAIN-20230529105815-20230529135815-00126.warc.gz

CC-MAIN-2023-23

https://math.iastate.edu/academics/undergraduate/degree-programs/

math

In the 21st century economy, students in mathematics may be studying cryptography and coding theory, cellular automata for modeling in the life sciences, graphs and networks with applications to computing, or the mathematics of finance, to name only a few of the possible applications. In traditional areas such as teaching, there is projected to be a great demand for secondary teachers of Mathematics in the United States over the next decade. Iowa State University offers a variety of undergraduate degrees related to mathematics. Consider the options, and discuss them with your advisor, to find the program of study that is right for you. A summary is offered at the bottom. This is the traditional degree program which offers training suitable for students planning to work in mathematics and computation for industry or government, or to continue their studies in graduate school. Majors normally spend the first two years obtaining a grounding in calculus and differential equations. At the junior and senior levels the department offers more than 25 undergraduate courses, including an introduction to combinatorics, abstract algebra, partial differential equations, complex variables, and mathematics of fractals. In addition, there are other courses at the graduate level which are open to qualified undergraduates. → Learn more This degree option is designed for students who want to major in mathematics with a clear specialization in some area of application. Certain courses in the area of application are counted towards the mathematics major. This also facilitates double majors or major/minor combinations. The major in mathematics + application area is not recommended for students who plan to continue with graduate school in mathematics. It can be very appropriate for students who plan to pursue a graduate degree in the application area. In consultation with a mathematics faculty advisor, the student prepares a program of studies tailor-made to his/her future plans or career needs. A number of programs have already been designed and pre-approved. Deviations from the programs may be proposed, and must be approved by the Mathematics Department Undergraduate Committee. → Learn more This degree will prepare you for teaching mathematics at the middle and high school level. The Mathematics Department and the Curriculum & Instruction Department share responsibility for this program. → Learn more The path to becoming an actuary begins with a college degree, often in mathematics or business, followed by the first actuary exam. The employer will typically pay for on-the-job training and further exams. For more details, see http://www.beanactuary.org/. Math + Actuarial Science is one of the options in the Mathematics + Application Area program of study, where the application electives and further recommended courses have been selected to help you prepare for the actuarial exams. → Learn more Bioinformatics and Computational Biology (BCBio) is an interdisciplinary science at the interface of the biological, informational and computational sciences. The program includes required courses from many different disciplines. Undergraduate study in the BCBio major is jointly administered by the Department of Computer Science, the Department of Genetics, Development, and Cell Biology, and the Department of Mathematics. → Learn more Minor in Mathematics A minor in Mathematics requires the following seven mathematics courses. The six credits of 300 level math classes must be taken at Iowa State University. - Math 165, 166, 265 - Calculus I, II, III - Math 201 - Introduction to Proofs - One of the following: - Math 317 - Theory of Linear Algebra - Math 407 - Applied Linear Algebra - One of the following: - Math 301 - Abstract Algebra I - Math 304 - Combinatorics - Math 314 - Graph Theory - Math 350 - Number Theory - Math 421 - Logic for Mathematics and Computer Science - Math 435 - Geometry I - Math 436 - Geometry II - One of the following: - Math 266 - Elementary Differential Equations - Math 267 - Elementary Differential Equations and Laplace Transforms - Math 331 - Topology - Math 341 - Introduction to the Theory of Probability and Statistics I - Math 365 - Complex Variables with Applications - Math 373 - Introduction to Scientific Computing - Math 414 - Analysis I The programs of study listed above can be grouped into three categories: Light Mathematics Course Load A minor in mathematics requires 7 math courses. Standard Course Load A major in mathematics requires 14 math courses, plus general requirements. A major in mathematics + application area requires between 9 and 11 math courses, plus 3 to 5 courses in the application area, for a total of 14 courses (plus general requirements). Higher Course Load The major in math with secondary teaching certification is essentially a double major. It requires a full math major (with minor variations), plus additional courses in curriculum and instruction. The degree in bioinformatics and computational biology requires more courses than most other majors (26 courses, in several departments, plus general requirements).

s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125948549.21/warc/CC-MAIN-20180426203132-20180426223132-00082.warc.gz

CC-MAIN-2018-17

https://plainmath.net/53576/certain-school-number-student-tickets-sold-home-football-game-modeled

math

a. Write an equation T(p) for the total number of tickets sold for a home football game at this school as a function of the winning percent p. b. What is the domain for the function in part a. in this context? c. Assuming that the football stadium is filled to capacity when the team wins 90% of its home games, what is the capacity of the school's stadium?

s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652663039492.94/warc/CC-MAIN-20220529041832-20220529071832-00243.warc.gz

CC-MAIN-2022-21

https://www.assignmentexpert.com/homework-answers/programming-and-computer-science/cpp/question-38871

math

Answer to Question #38871 in C++ for sara george The input contain an integer N. Print the square of each one of the even valuesfrom two to N, as the given example. 2^2 = 4 4^2 = 16 6^2 = 36 Need a fast expert's response?Submit order and get a quick answer at the best price for any assignment or question with DETAILED EXPLANATIONS!

s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583745010.63/warc/CC-MAIN-20190121005305-20190121031305-00300.warc.gz

CC-MAIN-2019-04

https://perso.lpsm.paris/~coudene/commentIDM.html

math

There are three ingredients in the proofs of the theorems in the article. Neither the L² ergodic theorem, the Banach-alaoglu nor the Banach-Saks results rely on the finiteness of the measure. These are abstract results that hold on any Hilbert space. We also need the density of the Lipschitz square integrable bounded functions in L². This is where the assumption of a countable cover with elements of finite measure is needed. So the result can be used to prove the weak convergence of the sequence f∘Tⁿ in an infinite measure setting. Arguably, the function f is assumed to be square integrable, so this does not really help if one wants to prove ergodicity in an infinite measure setting. See my article entitled "The Hopf argument" for some extension of the results to functions that are not square integrable. Let X be a metric space together with a Borel probability measure μ. Let T a Borel transformation or flow that preserves μ. We denote by E_± the set of all weak accumulation points of the sequence F∘Tᵗ, t → ±∞, for all square integrable F. Then E_+ = E_-. The proof relies on the spectral theorem for unitary operators.

s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710933.89/warc/CC-MAIN-20221203143925-20221203173925-00105.warc.gz

CC-MAIN-2022-49

https://money.stackexchange.com/questions/154267/how-to-calculate-the-apr-on-an-investment

math

APR = I/(PY), where I is the interest, P is the principal, and Y is the number of years. Your interest is $2, and your total principal is 100*$1.50, and the portion of the year is 7/365 (since a week is less than a year, Y is fractional). So you take $2/(100 * $1.50*7/365). We can move the 365 to the top (we're dividing by something divided by 365, which is the same as multiplying by 365), and the dollars cancel out, giving 365*2/(150*7) = 0.69523809523, or 69.52%. If this were to compound over a year, then, using the approximation 7/365 ~= 1/52, we have 52 compoundings of an interest of 2/(100*1.50), so that's (1+0.01333333333)^52-1 = 0.99122851206, or an APY of about 100%. That is, your return corresponds to an APR of 69% compounded weekly, or 100% compounded yearly. If you want to know what APR compounded daily would correspond to this return, the interest rate per day is the total interest rate divided by 365 (because that's how many days are in a year), the multiplication factor is 1 more than that, and it's being applied 7 times, so you have that (1+i/365)^7 = 1.01333333333, so you can take the seventh root of both sides, subtract 1 from both sides, then multiply both sides by 365, which gives 0.6912977881, or 69.13%, which is only slightly lower than the 69.52% from before.

s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679099942.90/warc/CC-MAIN-20231128183116-20231128213116-00740.warc.gz

CC-MAIN-2023-50

https://www.arxiv-vanity.com/papers/nucl-th/9909043/

math

Three-Pion Interferometry of Relativistic Nuclear Collisions Three-pion interferometry is investigated for new information on the space-time structure of the pion source created in ultra-relativistic heavy-ion collisions. The two- and three-pion correlations are numerically computed for incoherent source functions based on the Bjorken hydrodynamical model, over a wide range of the kinematic variables. New information provided by three-pion interferometry, different from that provided by two-pion interferometry, should appear in the phases of the Fourier transform of the source function. Variables are identified that would be sensitive to the phases and suitable for observation. For a positive, chaotic source function, however, a variation of the three-pion phase is found to be difficult to extract from experiments. Effects of asymmetry of the source function are also examined. pacs:PACS number(s): 25.75 Gz Two-pion interferometry has been regarded as an important means of obtaining the space-time structure of dynamics involved in relativistic heavy-ion collisions. Over the years, extensive studies of two-pion interferometry have been carried out theoretically and experimentally to investigate how much information the correlations of two emitted pions can provide. As experiments become refined, measurements of three-pion correlations should become feasible, hopefully providing new information. The first result of such measurements has been recently reported from the CERN NA44 experiment. In the last few years, some theoretical investigations have been made regarding three-pion interferometry[2, 4, 5, 6]. Though the treatments of three-pion interferometry and the issues involved are similar to those regarding two-pion interferometry, three-pion interferometry is technically far more complicated than the two-pion case due to the involvement of an additional momentum and also to new aspects of the particle correlations. Consequently, theoretical work so far has been on limited aspects of the interferometry, focusing on a few kinematic variables, such as the sum of three relative invariant momenta, over small ranges of their values. In the coming years, especially when RHIC becomes in operation, we expect that experiments on three-pion interferometry will become more detailed and will be made over larger ranges of various kinematic variables. We report here an investigation of three-pion interferometry over a wide range of kinematic variables. Our major objective is to clarify how much new information we can extract from three-pion interferometry, regarding the space-time structure of the pion source created in ultra-relativistic heavy-ion collisions. This work is similar to that of Heinz and Zhang in its objective, but it differs in scope. We numerically calculate the two- and three-pion correlations for the same source functions and compare the two types of correlations. The calculations are carried out with various model source functions that are based on the Bjorken hydrodynamical model. Throughout this work, we assume pion emission from the source to be completely chaotic. We also neglect possible final-state interactions (including the Coulomb interactions) between the emitted pions and the source. The new aspect of the correlations that three-pion interferometry can provide is the phase of the source function’s Fourier transform. The information content of the phase differs from that of the magnitude of the Fourier transform. Since two-pion interferometry can provide only the magnitude, we hope that three-pion interferometry can provide new information. To this end, we carefully identify the variables that are sensitive to the phase and suitable for observation. Since the phase is expected to be greatly affected by asymmetry of the source function, we also examine that issue. In Sec. II, we summarize the formulation of both the two- and the three-pion interferometries, mainly to define the correlation functions used. In Sec. III, we describe the various source functions that are used in the calculation, based on the Bjorken hydrodynamical model. The choice of optimal variables in the three-pion correlations is given in Sec. IV, and various numerical results are described in Sec. V. Discussion and conclusions are presented in Sec. VI. The two- and three-particle correlation functions that we discuss are reasonably well-known, but for clarity we sketch the formalism of, in our case, bosons, and we define the correlation functions and various variables that appear in this work. The field operator of emitted bosons, such as pions and kaons, obeys the Klein-Gordon equation, where is the mass of the particle, and the source current. The incoming and outgoing states of are specified in terms of the creation and annihilation operators and for these states. They are related to as where is on-shell and . We define an important quantity in this work, a source function, , in terms of : where denotes the quantum ensemble average over various incoming states. The Fourier transform of is defined as where is the amplitude and the phase. For a real , we have and , and thus . Boson spectra and correlation functions will be expressed in terms of or , and is written in the small-momentum expansion as where , and . Since is written in terms of odd moments of , an asymmetric (about ) source causes a strong, nonlinear dependence of on . In this work, we examine the of simple forms as discussed in Sec. III. The one-particle spectrum is given by Higher-order correlations of are assumed to satisfy Gaussian reduction, such as The two-particle spectrum is then written as where for the pair of the -th and -th momenta, we define their average and relative momenta as respectively. The two-particle correlation function is then expressed as Hereafter, we denote for and for . Equation (11) shows that the two-particle correlation function is independent of . Similarly, the three-particle spectrum and correlation are given by From the preceding discussion of , we have for a real source function. When , Eq. (6) yields is thus expected to vary prominently when the source is asymmetric (in ). Equation (13) shows that the three-particle correlation function depends on , which is absent in the two-particle correlation. The rest of the three-particle correlation is expressed in terms of ’s and can thus be determined from the two-particle correlations. The three-particle correlation is a function of three momenta, , and . For convenience, we introduce the average total momentum, Since ’s satisfy the identity, we have three independent momentum variables, which we will take to be , , and . Among various choices of three variables, another convenient choice is a set of ’s. For completeness, we show the relations between the first set and ’s: Iii Source function We apply the Bjorken hydrodynamical model to describe the evolution of the hot region created in heavy-ion collisions. Based on the Cooper-Frye spectrum, one writes the source function as where , , and denote the coordinate variables defined as , and , respectively; and are the momentum variables defined as and , respectively. Note that we specify the momentum variables for a momentum pair, and , by the subscript , such as , and those for three momenta with no subscript such as . We set the -axis to be the beam direction, and the -axis parallel to , or perpendicular to the beam axis. is a four-velocity of flow, and is in the Bjorken hydrodynamical model. The profile function determines the source shape in the - space. The shape along the transverse direction is taken to be of a Gaussian form. is the freeze-out temperature, and is the measure of freeze-out hypersurface. We assume that freeze-out occurs on the hypersurface where is constant. In this work, we examine the following five forms of the profile function. Simple (box-type) profile: Iv Optimal variables The three-particle correlation function depends on three momenta, which have nine components. As noted in Sec. II, we choose the three momenta to be , , and . In this work, we focus on the dependence of the correlation functions on relative momenta of the emitted bosons by fixing the value of . This leaves the two relative momenta to be the remaining variables. In order to identify new information in the correlation function, we should choose the variables that could provide the most rapid variation of . Figure 1 illustrates the variation of as a function of and with all other components of the relative momenta set to be zero. Here, we use the Heinz profile with the parameters of fm, fm, , and MeV. Figure 1 shows that is unity along the - and -axes and also along the line of , or the -axis (because of Eq. (16)). Figure 1 also shows that varies most prominently along the lines of , , and . Because of symmetry, however, it is sufficient to examine the variation around one of the lines, such as the line of . The reason why the line of provides a prominent variation of is seen as follows. When and , we have where the (weak) dependence on in is not explicitly shown. Setting and , we find where . When and , vanishes at , or , yielding the minimum. It follows then that the optimum choice is . With this constraint, the variables are now reduced to a single relative momentum. The source functions under consideration (as listed in Sec. III) are almost symmetric about the beam and transverse axes, but they can be asymmetric about the time-axis. Which component of should we choose so as to describe most effectively the asymmetric property of the source functions? is an obvious choice, but we find that or is the most convenient variable. From Eq. (10), we have , which gives . Thus as a function of or reflects time-axis asymmetry. Furthermore, for finite , our source functions are not simply a function of without symmetry along the longitudinal direction. Because of this, may be the variable more suitable for identifying the time-axis asymmetry of the source function. In the following, we will examine both and . is parallel to , while is perpendicular to it. Following the practice in the literature on two-pion interferometry, we will also denote and as and , respectively. Note that when the dependence of on or is examined, the other components of are fixed in our calculation. V Numerical results Figures 2, 4, 6, 8, and 10 illustrate the dependence of and on in the Heinz, Simple, Gaussian, Theta, and Exponential profile functions, respectively. Each figure is shown for , and 2. In the figures, we set , 140 MeV, 140 MeV, , and fm for all profile functions, and also fm for the Heinz, Theta, and Exponential profile functions. These parameter values reasonably satisfy the recent CERN-SPS experiment on Pb + Pb at 158 GeV/A. Note that describes the two-particle correlation since is normalized to be unity at , and that is not observed in the experiment. Figures 3, 5, 7, 9, and 11 show and (half of) its coefficient in the three-particle correlation function, , as functions of ( ). Each figure is shown for and 2 and 140 MeV with the parameter values of , , , and as in Figs. 2, 4, 6, 8, and 10. In Figs. 3, 5, 7, 9, and 11, we see that for all profile functions, at , and becomes more prominent as increases. tends to be smaller for the asymmetric profile functions (such as the Simple and Exponential profile functions) than for the symmetric ones, though the difference between them is not substantial. tends to deviate from zero more slowly than the phases of ’s, ’s. For example, we see in Figs. 4 and 5 that when reaches around 150 MeV, we still have . The reason for this is general because is defined as and is constrained by the identity, . In fact, the small-momentum expansion of Eq. (6) applied to yields that the term linear in vanishes, as discussed in Sec. II. Furthermore, when starts to deviate from zero, its coefficient in the three-particle correlation function, , tends to become small. In fact, we see in the figures that gets halved for all profile functions before decreases to 0.9, and even nearly vanishes when decreases further. We expect that in actual experiments it will be difficult to identify with a value much smaller than unity. This is the major finding of this work. We find the same difficulty when we choose as the independent variable. Figure 12 shows and as functions of for the Heinz profile for 140, 200, and 300 MeV, with fm, , , fm, and fm. Figure 13 also shows and as functions of for the three values of with 1.5 and the same values of , , , , and . We see in Fig. 13 that when starts to deviate from unity, its coefficient, , becomes small quite rapidly, as in the previous cases of being the independent variable. Note that decreases more quickly as a function of than of , as seen in Figs. 13 and 3. The quick reduction occurs because of the factor , when the transverse momentum, , is used as the variable. fm is chosen to reproduce experimental results, but we find that even if a much smaller value of is used, becomes quite small when is off unity. The difficulty also remains at different values of . Figures 14 and 15 show , , , and as functions of for (6.5, 0.65), (4,8, 2.8), and (3.2, 3.2) fm, with MeV, MeV, , and . These parameter sets yield the recently measured value of the longitudinal size, 3.5 fm. Figure 15 shows that depends on rather strongly. But the variation of takes place where is small, and will be difficult to observe. Vi Discussions and summary We have investigated the three-particle correlation function for chaotic source, using various profile functions of the source in the Bjorken hydrodynamical model. In all profile functions we have examined, the coefficient of in the three-particle correlation function, , decreases quite rapidly, as decreases from unity. Extraction of is thus difficult when decreases from unity. This result is in agreement with Heinz and Zhang, who previously made a similar investigation for small relative momenta. In order to clarify why is difficult to observe, we first identify the portion of the source function that most strongly influences the phase, . appears in the Fourier transform of as . As noted previously, is an odd function of , and for a real source function. The imaginary part of , , thus represents the behavior of relevant to the present discussion and is an odd function of . The portion of that most strongly affects is thus its odd-function part, , in with and . Consider that and vary over distances of typical scale, and , respectively. Here, and correspond to the spread widths of and the distance to maximum of , respectively, as Fig. 16 illustrates. and also vary over the scales of and , respectively. As increases, increases. The region where is appreciable is . The amplitude becomes small in the region where is larger than . Thus, if , the variation of is not difficult to observe. This is, however, untenable as long as is positive everywhere. Consider in some region: we then have in that region, and furthermore, . The last inequality contradicts the desired inequality. In this discussion, we have assumed the source function, , to be positive everywhere, as done in common practice. How realistic is this assumption? If is a statistical phase-space distribution, should not be negative everywhere. Generally speaking, however, can be locally negative, provided its integrals over or be positive. This property is similar to, for example, that of the Wigner function. Furthermore, that is locally negative suggests that it would be associated with some dynamics involving quantum correlation. This aspect of the interferometry is currently under investigation. Measurement of the three-pion correlations from the CERN NA44 experiment has been recently reported for the total relative momentum of up to about 300 MeV, and the extraction of up to about 60 MeV. This total relative momentum is too small to observe the variation of that is examined in this work. Taken as a constant, is found to be about 0.2 and is much smaller than the value of unity for a chaotic source, as discussed in this work. The reason for the small value is unknown, but it may be because of partial coherence of the source, or even because of a more exotic reason. In summary, we have investigated three-particle interferometry from chaotic sources using the Bjorken hydrodynamical model. The optimal variables are identified suitable for extracting new information through the phase of the source function’s Fourier transform. The three-particle correlations are calculated over a wide range of the kinematic variables. A variation of the three-pion phase is found to be difficult to observe experimentally because its coefficient, as it appears in the three-particle correlation function, becomes small in that region. This is the case if the source function is positive everywhere as conventionally assumed, and suggests the interesting possibility of the source function being locally negative. Acknowledgements.We acknowledge M. C. Chu for his valuable contribution at the initial stage of this work. This research is partially supported by the U.S. National Science Foundation under grants PHY88-17296 and PHY90-13248 at Caltech, and the U.S. Department of Energy under grant DE-FG03-87ER40347 at CSUN. - A. Sakaguchi et al. (NA44 collaboration), Nucl. Phys A638, 103c (1998); J. Schmidt-Sørensen et al. (NA44 collaboration), ibid., 471c (1998); H. Bøggild et al. (NA44 Collaboration), Phys. Lett. B455, 77 (1999). - U. Heinz and Q. H. Zhang, Phys. Rev. C56, 426 (1997). - U. Heinz, Nucl. Phys. A610, 264c (1996). - J. G. Cramer and K. Kadija, Phys. Rev. C53, 908 (1996). - H. Heiselberg and A. P. Vischer, Phys. Rev. C55, 874 (1997). - T. J. Humanic, Phys. Rev. C60, 014901 (1999). - R. Ganz et al. (NA49 collaboration), nucl-ex/9808006. - We follow the conventions of J. D. Bjorken and S. D. Drell, as in their book, Relativistic Fields (McGraw Hill, N. Y., 1964): Four-vectors are denoted in regular letters and three vectors in bold letters, and the square of the four-momentum of a physical particle is the square of its mass. - J. D. Bjorken, Phys. Rev. D17, 140 (1983). - H. Nakamura and R. Seki, Caltech Kellogg preprint (1999).

s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100258.29/warc/CC-MAIN-20231130225634-20231201015634-00718.warc.gz

CC-MAIN-2023-50

https://spainsnews.com/the-mathematical-challenge-that-anyone-understands-but-nobody-has-solved-goldbachs-conjecture/

math

A legendary letter was sealed more than three centuries ago. What was in it was a sort of puzzle, a challenge so simple that any elementary student could understand. However, it is such a complex problem to prove that the greatest minds in history have failed trying. Between the lines of that letter, one said the following: That is the whole problem. The whole numbers are those with which we learned to count: the one, the two, the three ... Without frills. A prime number is all that greater than one and you can only divide it between yourself and the unit without decimals: two, three, five, seven, eleven ... That and adding is the only thing you need to know To understand the problem, there is no more. This is the conjecture that Christian Goldbach proposed to Leonhard Euler in 1742, the unbeatable beast that has defeated every great mind that has dared to face her. However, I am sure that a small part of you has been tempted to test it. So why not try? Let's try the eight. We can do this by adding three and five, so it is fulfilled. And the fourteenth? It would be three plus eleven, and twenty one is two and nineteen. I assure you that you can try with everyone you want, because you will not find a single case in which the conjecture is not fulfilled. And we know this because some machines have tried before you. Computers have checked the first four trillion numbers, a four followed by eighteen zeros. It might seem that this is enough to prove that the conjecture is true, after all, four trillion numbers supporting it are many numbers. However, mathematicians do not get that. You have to be sure that there is not a lost number out there that is not met, because, as huge as it may seem, four trillion are left at nothing compared to the infinite ocean of figures out there. Mathematicians need to be totally and absolutely sure, everything else is pure opinion and only with opinions do not do mathematics. So, there are mostly two ways to be satisfied. The first is the simplest, the one we all try when we are taught the problem: find a counterexample, take the opposite, find a case that is not met so that we can reject the conjecture. That is what we have tried, but as we have seen, it does not seem very fruitful ... although, wait. And the two? It is an integer and even number, but it is not the sum of two cousins because it can only be formed by adding two ones, and the number one is not a cousin. For the 2 Goldbach is not fulfilled! Is it possible that we have resolved Goldbach's conjecture? I'm afraid not, because this apparent lack of confidence is a historical curiosity. In the 18th century, the 1 was still considered a prime number, so Goldbach could express the two as "one plus one" and remain so calm. In fact, excluding one from the list of prime numbers had to update the conjecture. The modern version would be something like this:That every integer even greater than two is the sum of two prime numbers seems to me to be a completely true theorem, but I can't prove it“So let's forget number two and worry about the rest. As we have seen, a counterexample has not yet been found, and although by definition there are still infinite numbers to prove, mathematicians suspect that no matter how much they search they will not find a single case in which Goldbach is not fulfilled. They argue that, as the numbers grow, the ways in which they can express themselves also increase. For example: ten can be done by adding five to itself or three to seven. One hundred, for example, can be constructed in six different ways, and from what we have seen, the number of possible combinations skyrockets as we study larger numbers. In fact, there is a very visual way to see it: Goldbach's comet. It is a graph whose horizontal axis represents the number to study and in the vertical we find how many different forms we can decompose. The key is that the comet does not stop growing and it becomes difficult to think that at some point it will plummet by marking zero on the vertical axis, indicating an even number that cannot be constructed by adding two cousins. However, this is still not enough evidence. It is only a suspicion, but nothing assures us that there is an exception among all the numbers that we cannot check by hand, so we have to change our strategy. Luckily there are other ways to prove a conjecture: finding a general argument applicable to all numbers and showing that, if Goldbach were false, mathematics would have to contradict themselves. Something like looking for a nonsense, showing that we are facing something impossible. A classic example of this strategy is Euclid's theorem, which posed the existence of infinity of prime numbers. His way of demonstrating it was as follows: Let's take a few prime numbers and multiply them together, for example: 2x3x7. The result is never a prime number, because it is divisible among all the previous ones giving, in this case, 42. Now we must add a 1 and bingo! We have already achieved a prime number, 43, because adding 1 stops being divisible among the cousins we have used to build it. However, this is not always the case, for example: 3x5 + 1 gives 16, which is not a cousin. And here is the final trick, because, if the result is not a cousin and at the same time it is not divisible among the cousins we have used to build it, it means that its divisor is a new prime number, in this case the two: 2x2x2x2. Following these steps we can build as many prime numbers as we want, demonstrating that there are infinity of them. This type of reasoning is what mathematicians look for, ways to prove or deny conjectures beyond any doubt avoiding logical inconsistencies. However, these approaches have also failed to resolve Goldbach's conjecture. Nothing has turned out, and although from time to time someone appears saying they have tried it, they are always false alarms that show nothing. However, you may have heard that some years ago a mathematician resolved Goldbach's blissful conjecture, and it is "true," except that it was Goldbach's weak conjecture, something quite different. In 2013 Harald Andrés Helfgott managed to prove Goldbach's weak conjecture, which reads as follows: “Any odd integer greater than 5 can be expressed as the sum of three prime numbers”For example: 15 is the sum of 3, 5 and 7. Helfgott's strategy was somewhat intermediate to the two we have proposed. On the one hand, the computers had already calculated that the weak conjecture was fulfilled for all odd integers between 5 and 8875x10 ^ 30 (representing approximately 9 followed by thirty zeros). On the other hand, some great experts in number theory had shown that, from a sufficiently large number, all of the following had to fulfill the conjecture. The demonstration of the latter is very long for this article, but the important thing is to be clear that this "large enough number" has been reduced with better evidence over the years and that when Helfgot faced the conjecture, he was in 2x10 ^ 1346 (a 2 followed by one thousand three hundred forty-six zeros). That means we already knew that the largest and smallest numbers met the conjecture, but between them there was a huge chasm and their mission was to reduce it. He could have looked for better computing methods so that computers were able to calculate even more numbers by brute force. However, 8875x10 ^ 30 was already something huge (to give you an idea, it is estimated that there are 1x10 ^ 80 protons in the universe) and as much as they improved, the machines could not reach 2x10 ^ 1346. So Helfgot decided to face it in another way and try to reduce that number "large enough" to make it smaller than 8875x10 ^ 30 so that the conjecture was demonstrated for all integers through one or another method. And he succeeded, he managed to lower it to overlap it with computer calculations. Goldbach's weak guess was true. Meanwhile, the strong conjecture remains undefeated and has not advanced much in recent decades. A drought that is largely due to its complexity, but to which many other things may have contributed. Not a few professionals believe that focusing their research on the Goldbach conjecture is almost a condemnation of failure. Many of those who work in it do it timidly, in their free time and without being able to devote the time they deserve. This perception is so popular that it is treated even in one of the most famous mathematical novels: Uncle Petros and the Goldbach conjecture, from Apostolos Doxiadis. At this step the question is obvious: Will Goldbach's conjecture ever be resolved? Will it be true and will be consolidated as a theorem? Or in an unexpected turn of events will it have to be ruled out? It only remains to wait while Goldbach's old statement echoes in our ears, like a siren song that makes anyone who agrees to dance with her run aground against the cliffs. DON'T KEEP IT UP - The conjecture has not yet been proven. It is true that in 2013 Helfgot demonstrated Goldbach's weak conjecture, but when we refer to "Goldbach's conjecture" we are talking about the strong one. - The Fundamental Theorem of Arithmetic implies that 1 cannot be a cousin by saying that: any integer greater than 1 can be written as a single product of prime numbers. If we accept 1 as a cousin there would be infinite ways to break down each number (10 would be 2x5, but also 2x5x1, 2x5x1x1 and so on). There are more reasons, but this is possibly the easiest to understand. - Christian Goldbach, "Letter to Leonhard Euler" (Moscow, June 7, 1742) - Leonard Eugene Dickson “History of the Theory of Numbers, Volume I: Divisibility and Primality” Dover Books on Mathematics (2005) - Harald Andrés Helfgott “Major arcs for Goldbach’s problem” arXiv (2013) - Tomás Oliveira e Silva, Siegfried Herzog & amp; Silvio Pardi, “Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4x10 ^ 18” Mathematics of Computation 83: 2033-2060 (2013)

s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679102697.89/warc/CC-MAIN-20231210221943-20231211011943-00159.warc.gz

CC-MAIN-2023-50

https://www.eauxdubrivadois.fr/library/nonlinear-partial-differential-equations-in-applied-science-seminar-proceedings

math

By H. Fujita,P. D. Lax,G. Strang Read or Download Nonlinear Partial Differential Equations in Applied Science: Seminar Proceedings (North-Holland Mathematics Studies) PDF Best differential equations books Subject matters in Hyperplane preparations, Polytopes and Box-Splines brings jointly many parts of study that concentrate on the right way to compute the variety of fundamental issues in compatible households or variable polytopes. the themes brought extend upon differential and distinction equations, approximation idea, cohomology, and module concept. Distinction algebra grew out of the learn of algebraic distinction equations with coefficients from useful fields. the 1st level of this improvement of the idea is linked to its founder, J. F. Ritt (1893-1951), and R. Cohn, whose ebook distinction Algebra (1965) remained the one basic monograph at the topic for a few years. This ebook includes lecture notes of a chain of classes at the regularity thought of partial differential equations and variational difficulties, held in Pisa and Parma within the years 2009 and 2010. The participants, Nicola Fusco, Tristan Rivière and Reiner Schätzle, offer 3 up-to-date and wide introductions to varied elements of recent Regularity concept referring to: mathematical modelling of skinny movies and comparable loose discontinuity difficulties, research of conformally invariant variational difficulties through conservation legislation, and the research of the Willmore practical. This e-book presents a rigorous yet straightforward advent to the speculation of Markov tactics on a countable country house. it's going to be obtainable to scholars with a high-quality undergraduate historical past in arithmetic, together with scholars from engineering, economics, physics, and biology. issues lined are: Doeblin's idea, basic ergodic homes, and non-stop time methods. - Schaum's Outline of Differential Equations, 4th Edition (Schaum's Outlines) - Linear Partial Differential Equations for Scientists and Engineers - Hermitian Analysis: From Fourier Series to Cauchy-Riemann Geometry (Cornerstones) - Ordinary Differential Equations: Introduction and Qualitative Theory, Third Edition (Chapman & Hall/CRC Pure and Applied Mathematics) - Navier-Stokes-Fourier Equations: A Rational Asymptotic Modelling Point of View Additional resources for Nonlinear Partial Differential Equations in Applied Science: Seminar Proceedings (North-Holland Mathematics Studies) Nonlinear Partial Differential Equations in Applied Science: Seminar Proceedings (North-Holland Mathematics Studies) by H. Fujita,P. D. Lax,G. Strang

s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780054023.35/warc/CC-MAIN-20210917024943-20210917054943-00424.warc.gz

CC-MAIN-2021-39

https://www.jiskha.com/display.cgi?id=1395005653

math

statistic help please posted by shantel . 2. A survey of 259 families was made to determine their vacation habits. The two way table below sorts the families by location and the vacations by the length of the vacation. Rural Suburban Urban Total 1–7 days 80 39 37 156 8ormore days52 32 19 103 Total 132 71 56 259 What is the probability that a randomly selected family was suburban given that they spent 8 or more days on vacation? (1 point) You draw one card from a shuffled standard deck of cards (cards are in four suits —red diamonds, red hearts, black clubs, and black spades— and are numbered 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A). a) What is the probability of drawing a red card? b) What is the probability of drawing a queen? c) What is the probability of drawing a red queen? d) What is the probability of drawing a queen given that you drew a face card (face cards are jacks, queens, and kings)?

s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886104636.62/warc/CC-MAIN-20170818121545-20170818141545-00628.warc.gz

CC-MAIN-2017-34

https://locallivesglobalmatters.org/file-ready/triangles-geometry-study-guide-downloads-book-3

math

Self paced study guide in trigonometry march 31 2011 1 contents trigonometry contents geometry and analytic geometry trigonom etry and exponentials logarithms in addition previous diagnostic 21 right triangles trigonometry if we wish we can of course express the hypotenuse c in terms of a . Geometry study guide lesson 41 classifying triangles identify and classify triangles by angles identify and classify triangles by sides notebook page 20 hw sp wp study guide review and quiz 41 to 43 lesson 42 angles of triangles apply the angle sum theorem. Geometry sol g6 g7 study guide congruent similar triangles page 2 o the endpoints of an altitude are a vertex of a triangle and a point on the vertexs opposite side that makes the altitude and side perpendicular. In triangles notebook page 27 hw sp wp study guide review and quiz 51 to 53 lesson 52 medians and altitudes identify and use medians in triangles identify and use altitudes in triangles notebook page 28 hw sp wp study guide review and quiz 51 to 53 lesson 53 inequalities in one triangle. Two triangles are similar if a 3 angles of one triangle are the same as 3 angles of the other triangle b 3 pairs of corresponding sides are in the same ratio c an angle of 1 triangle is the same as the angle of the other triangle and the sides containing these angles are in the same ratio How it works: 1. Register Trial Account. 2. Download The Books as you like ( Personal use )

s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376829812.88/warc/CC-MAIN-20181218204638-20181218230638-00152.warc.gz

CC-MAIN-2018-51

https://iwritettw.firebaseapp.com/setser46979vis/need-help-solving-a-math-problem-2932.html

math

math problem solving worksheets high school problem solving worksheets for middle school grade common core math skills word problems mathematical pr. GRE Math Problem Solving : Practice tests and explanations 12 free GRE Problem Solving practice tests with explanations. Our tests contain over 100 GRE math questions to help you with your GRE prep. Mind Maps and Math Problem Solving | Prime Number (34K views) Mind Maps and Math Problem Solving - Free download as PDF File (.pdf), Text File (.txt) or read online for free. Basic idea: Use 2 mind maps for problem solving - one problem map for the actual problem, and one tool map with a collection of… In this lesson, you will learn how to solve a probability word problem. Need help with your algebra and geometry? Well... P(event)= Number of favorable outcomes / Total number of outcomes Solving PSLE Math proves a challenge for pupils, but it isn't as difficult as they seem to find it. Many pupils seem to get fed up with trying to learn and Solving the Math Problem - Washburn University Alumni… They all recognize math is a big deal, so this is really a testimony to the entire Washburn community of learning and how we are willing to take big steps forward to help students.” Problem solving - Wikipedia A quick method for solving algebra problems is to re-arrange the equation by placing all x... In Pre-Algebra Pre-Algebra Practice Questions: Cross-Multiply to... They can solve any type of math problem, including the toughest ones, such as simultaneous equations, linear dependence, vectorial spaces, etc. All you need to do is just send us the "help me solve this math problem" message, and we'll make sure that your order is delivered right on time! Highly Qualified Professionals. Cymath | Math Problem Solver with Steps | Math Solving App Solve calculus and algebra problems online with Cymath math problem solver with steps to show your work. Get the Cymath math solving app on your smartphone! Need help solving a math problem for free Jayden Monday the 26th " data-placement="top" data-title="LinkedIn" data-toggle="tooltip" title="LinkedIn"> LinkedIn Google+ perks of being a wallflower essay questions literary analysis essay on fahrenheit 451 product business plan example . Tricky Math Homework: How to Help - understood.org It's common for parents to have trouble helping kids with math homework. Math is a process. It helps to walk through the process with your child. Having examples of a similar math problem can help your child complete tough math homework. Your child needs help with math homework, but you're not ... How You Can Help Children Solve Problems | Scholastic Ask open-ended questions about activities to help children see the problem they are trying to solve in new and different ways. NURTURING PROBLEM SOLVERS Think of yourself as having four roles observer, supporter, facilitator, and model watching, encouraging, interacting as a questioning partner, and sharing with children how you solve problems. SOLVING EQUATIONS - sosmath.com solving equations This sections illustrates the process of solving equations of various forms. It also shows you how to check your answer three different ways: algebraically, graphically, and using the concept of equivalence.The following table is a partial lists of typical equations. I need help solving a math problem in algebra NEED HELP SOLVING THIS MATH PROBLEM.? | Yahoo Answers Please help me understand how to do this problem. I'm completely lost. Thanks! Tim and Andrea Holt want to sell their '95 Chevy pickup and purchase a 2009 Toyota Camry with (14,250 miles on it) that is selling for $18,440. How to Solve a Math Problem Using PEMDAS | Sciencing When solving long strings of arithmetical operations, you have to do the operations in a certain order to get the right answer. PEMDAS is an acronym to help you remember the correct order or operations. It stands for parentheses, exponents, multiplication, division, addition and subtraction.

s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233506669.96/warc/CC-MAIN-20230924223409-20230925013409-00753.warc.gz

CC-MAIN-2023-40

http://www.chegg.com/homework-help/questions-and-answers/problem-2171-three-charges-corners-anisosceles-triangle-500-c-charges-form-adipole-separat-q272117

math

Problem 21.71: Three charges are at the corners of anisosceles triangle. The ±5.00μC charges form adipole are are separated by 3.00 cm. The third charge is-10μC and is 2.00 cm from either ±5.00μCcharge. Find the force that the -10μC charge produces onthe dipole. Which direction is the force on the dipole? b) For an axis perpendicular to the line connecting thedipole at its midpoint, find the torque exerted on thedipole. Which direction is the torque?

s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257826916.34/warc/CC-MAIN-20160723071026-00180-ip-10-185-27-174.ec2.internal.warc.gz

CC-MAIN-2016-30

https://www.slideserve.com/ena/definition

math

Definition:. Preliminary Geometric Design of an Airport in Palestine. Advantages of the airport:. The importance of this research reflects the need for Palestinian airport for: 1) Investment sector. 2) Civilization. 3) Politically advantages 4) Necessity for the PNA. 5) Tourism. 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. Definition: Preliminary Geometric Design of an Airport in Palestine. Advantages of the airport: • The importance of this research reflects the need for Palestinian airport for: • 1) Investment sector. • 2) Civilization. • 3) Politically advantages • 4) Necessity for the PNA. • 5) Tourism Airport site selection • the FAA (Federal Aviation Administration) recommends a minimum site selection analysis that includes the following factors: • Operational capability • Ground access • Development costs • Environmental consequences • Socioeconomic factors • Consistency with area-wide planning site selection according ICAO and FAA codes Al-Buqaiaa site : • The selected site away from any population communities to avoid sound pollution. • The selected site does not affect the population areas growth. • According to the wind rose extracted from the wind movement in the proposed site showed slight wind speed with (N/W) to avoid any cross wind in the runway direction. The selected site discreption: • ± 10m on mean sea level. • Intermediate of the west bank. • Sandy soil. • The weather is moderate and suitable (ambient temp, humidity) . AIRPORT SITE COORDINATION • 1 X:187470 Y:129505 • 2 X:189446 Y:129446 • 3 X:186898 Y:125544 • 4 X:188882 Y:125262 Passengers trends during 20 years of airport operation (Million passengers)/year. Passenger classification / year: • regular daily passengers (Dep/Arr) • High season passengers. • Transit passengers • Omra pilgrims passengers • Haj pilgrims passengers • Christians pilgrims passengers R.W Considerations The following factors should be considered in locating and orienting a runway: • Wind • Airspace availability • Environmental factors (noise, air and water quality) • Obstructions to navigation • visibility • Wildlife hazards Runway Orientation provided Wind rose by ministry of transpiration Runway orientation • The orientation of Runway will be 170o-350o (17-35) Runway. Which is the orientation that satisfies 95% coverage (crosswinds below a critical value) considering yearly wind conditions, with respect to the topography of the airport selected site. Number of Runways • In this project one primary runway has been designed because the following reasons: • 1- Max capacity for one primary runway is 40-50 operation/hour that means; if the average capacity of airplanes for the fleet mix is 125 passenger/operation. Then the hour capacity for the runway is: 45* 125 = 5625 pax/hour As it cleared before the demand for the airport after 20 years will be about 14 million/year, so the peak-hour-flow is: Average monthly passengers =14000000*0.08417 = 1178380 pax Average daily passengers=1178380 * 0.03226 =38014 pax Peak-day-flow=1.26*38014 = 47898 pax Peak-hour-flow= 0.0917* 47898= 4392 Pax/Hour < 5625 pax/hour So one primary runway is sufficient to cover the demand for 20 years coming. • 2- The nature of topography for the selected site VS the provided wind rose general orientation, make a conflicting to construct parallel runway, because of non-satisfaction for FAR requirements. Runway Length Justification • Airplanes today operate in a variety of different environments and available field lengths. However, the suitability of those runway lengths is governed by the existing and forecast fleet mix, critical aircraft operational requirements, and the following variables: • Airport elevation above mean sea level • Mean maximum temperature • Wind velocity • Aircraft operating weights • Takeoff and landing flap settings • Effective runway gradient • Runway surface conditions (dry, wet, contaminated, etc.) • Operational use. • Presence of obstructions within the vicinity of the approach and departure path. • Locally imposed noise abatement restrictions and/or other prohibitions Runway Length Justification • Boeing 747-400 designate as the critical aircraft for determining the primary runway length requirements of this project. • Accordance with FAA guidance, the critical individual aircraft takeoff and landing operating weights for the B747-400, B737-300 and B747-700 were obtained from Boeing’s Airplane Characteristics for Airport Planning manuals associated with these specific aircraft (Table B-2) Takeoff Length Requirements • To accurately determine takeoff length requirements, the takeoff chart for the B747-400 with dry runway, zero wind, and zero effective runway gradient conditions within the airport’s mean daily maximum temperature of the hottest month at the airport was used. Landing Length Requirements • Landing length requirements were determined by obtaining the landing chart for the B747-400 with the highest flap setting (30 degrees), zero wind, and zero effective runway gradients. Runway length design (Sample calculations) • Data: • Airplane Boeing 747-400 Mean daily maximum temperature of hottest month at the airport 34.4 C • Airport elevation 0 (on MSL) • Maximum design landing weight (see table B-2)574,000 pounds (260,362 KG) • Maximum design takeoff weight (see table B-2)875,000 pounds (396,894 KG) • Maximum difference in runway centerline elevations 10 feet Runway length design (Sample calculations) • Proceed horizontally to the length axis to read 3352.8m. Interpolation is allowed for this design parameter for (Takeoff length requirements 100% Useful Load) • – Adjust for non-zero effective runway gradient • 11,000 + (10 x 10) = 11,000+ 100 = 11,100 feet (3383 m) • (5) The takeoff length requirement is 11,100 feet (3383 m) • (6) Step 5 – Adjust for temperature: • Because it its 0 on S.L T1 =59° F • L2= (0.005*(94-59)*11,100) +11,100= 12931.5 feet Takeoff length requirements 100% Useful Load • Where T1 is standard temperature • L2 is adjusted length of Runway • For Takeoff length requirements 95% Useful Load: • – Adjust for temperature: • Because it its 0 on S.L T1 =59° F • L2= (0.005*(94-59)*10,171) +10,171=11951 feet • Adjust for non-zero effective runway gradient=12051 feet OR(3700 m) Takeoff length • Selection of Exit: • As mentioned previously, the critical individual aircraft is B747-400 which has touch-down speed is 141 Knots to 166 Knots. • Assume that the touch-down speed=150 Knots and Dth approximate=1000 ft. and as explained before in the text the suitable exit speed for 30o high speed exit is 60 mil/hr. • So: • Vth=150*1.687=253 ft/s • Ve= 60*1.466=87.98 ft/s • And a=3.3 ft/s2 • Then.. • Dc=(253)^2-(87.96)^2/(2*3.3)= 8526 ft • D=Dth+Dc= 1000+8526=9526 ft (From the edge of the runway). • And equal about 2900m from the beginning of the runway. Selection of Exit: • To be sure that the airport will serve all categories, and in comfortable way, the exit location for category (C) should be determined then. • Category (C) touch-down speed= 121 knots • Assume • Dth=700 ft • Ve= 40 mil/hr for 300 exit flap and.. a=5 ft/sec2 • Vth=121*1.687=204.13 ft/sec • Ve=40*1.466=518.64 ft/sec • And a=5 ft/sec^2 • Dc=(204.13)^2-(58.64)^2/ (2*5)= 3823 ft • Dth=700 ft • D=3823+700=4523 ft which is equal about 1378m from the beginning of the runway. Selection of Exit • Because of the runway is symmetry, the separation between exits will be like shown in figure: Imaginary Surfaces summary • Primary= aligned (longitudinally) with each runwayand extends 200 ft. from each runway end • Approach= longitudinally centered with the run way and extends beyond the primary surface • Horizontal= horizontal plane 150 ft. above the established airport elevation. Constructed by swinging arcs around the end of the primary surface • Conical= 20:1 slope surface extending beyond the horizontal surface • Transitional= constructed to join approach and horizontal or approach and transitional surfaces Imaginary Surfaces summary A = Utility runways B = Runway larger than utility C = Visibility minimums > 3/4 of a mile D = Visibility minimums =< 3/4 of a mile Airport Reference Code • From the manufacturer airplane criteria see appendix A: • The speed Approach is 154 knots. So that the speed is 141 knots or more but less than 166 knots, there for the Aircraft Approach Category is (D). • Wingspan is 213 ft and tail height is 64.3 ft which they are within the flowing limits 171 - <214 and 60 - <66 in order. There for the Airplane Design Group (ADG) is (V) • So that the Airport Reference Code is (D-V) Runway components design • Obstacle Free Zone (OFZ) • Runway Blast Pad • Runway Protection Zone (RPZ): • Runway Safety Area (RSA) • Shoulder • Taxiway Safety Area (TSA) RPZ ARea RPZ Area = 49.978 Acer = 198207 m2 Gradients • Surface gradient standards: Aircraft approach categories C & D: • The longitudinal and transverse gradient standards for runways and stop ways are as follows and as illustrated in following figure • The max longitudinal grade is ± 1.5 %; however, longitudinal grades may not exceed ±0.8% in the first and last quarter of the runway length. It is desirable to keep longitudinal grades to a minimum. • The max allowable grade change is ±1.5%. use longitudinal grade changes only when absolutely necessary. • Vertical curves for longitudinal grade changes are parabolic. The length of the vertical curve is minimum of 1000 ft (300m) for each 1 % change. • The minimum allowable distance between the points of intersection of vertical curves is 1000 ft (300m) multiplied by the sum of the grade changes ( in percent ) associated with the two vertical. Taxiway Dimensional standards • Taxiway and Taxi lane Object Free Area (OFA) • Taxiway Shoulders • Taxiway safety area (TSA) Major Terminal Components • Apron. • Connector. • Main Terminal Building. • Airport Access System. Alternative Terminal Building :Concepts • Simple Terminal Concept. • Linear Concept • Pier Concept. • Satellite Concept. Estimating Number of gates: • To estimate number of gates, a lot of data is needed, for example: • Peak hour passengers • Equivalent airplane factor • Fleet mix not available • Expected destinations at the same time. Peak hour passengers: • Average monthly passengers =3440000*0.08417 = 289545 pax • Average daily passengers=289545 * 0.03226 =9341 pax • Peak-day-flow=1.26*9341 = 11769 pax • Peak-hour-flow= 0.0917* 11769= 1079. Pax That means the capacity of airplane of 1 equivalent factor = about 125-135 pax. • So that number of demand gates =1079/135 = 8 gates • In this project it seen recommended to add 4 gates ,for emergency case • And 4 gates for ceremonial usage. • To be the Total estimated gates are ( 16 )

s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514572484.20/warc/CC-MAIN-20190916035549-20190916061549-00449.warc.gz

CC-MAIN-2019-39

https://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/dp2011-23.html

math

Existence and Uniqueness of a Fixed Point for the Bellman Operator in Deterministic Dynamic Programming We study existence and uniqueness of a fixed point for the Bellman operator in deterministic dynamic programming. We show that removing many of the assumptions of the theorem on the Bellman operator recently shown by Martins-da-Rocha and Vailakis ("Existence and Uniqueness of a Fixed Point for Local Contractions," Econometrica 78, 1127-1141, 2010) does not affect its main conclusions concerning the existence and uniqueness of a fixed point. Under considerably weaker versions of the remaining assumptions, we also show that the value function can be computed by value iteration with an appropriate initial function. Dynamic programming, Bellman operator, value function, fixed point. RIEB, Kobe University Rokkodai-cho, Nada-ku, Kobe

s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233506623.27/warc/CC-MAIN-20230924055210-20230924085210-00246.warc.gz

CC-MAIN-2023-40

https://www.personalitycafe.com/threads/what-would-you-do-with-a-death-note.160559/

math

A Death Note is a notebook that magically kills anyone whose name is written in it, by a heart attack after 40 seconds, if the writer has the face of the victim in mind. Suppose a god of death left a Death Note on the ground, and you happen to find it. Nobody knows about it but you. Would you use it? If so, how? If not, what would you do with it? For this thought experiment, we can ignore all the further complexities of the anime series.

s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710488.2/warc/CC-MAIN-20221128070816-20221128100816-00512.warc.gz

CC-MAIN-2022-49

https://sentencedict.com/ratio.html

math

Synonym: comparison, percentage, proportion. Similar words: operation, migration, separation, AND operation, reparation, immigration, exploration, integration. Meaning: ['reɪʃəʊ /-ʃɪəʊ] n. the relative magnitudes of two quantities (usually expressed as a quotient). Random good picture Not show 1. They have a high ratio of imports to exports. 2. The ratio of men to women was two to one. 3. Longitudinal are easily satisfied, cross ratio is easy to be lost; meet the person is easy to come to a standstill,(Sentencedict.com ) the lost is easy to choose to rise. 4. The adult to child ratio is 1 to 6. 5. The hospital is trying to improve its staff/patient ratio. 6. The ratio of nursing staff to doctors is 2:1. 7. The school has a very high teacher-student ratio. 8. Their sales rose in direct ratio to the amount they spent on advertising. 9. The ratio of men to women at the conference was ten to one/10:1. 10. The ratio of pupils to teachers was 30 to 1. 11. The ratio of applications to available places currently stands at 100:1. 12. Men outnumber women here in the ratio of three to one. 13. We mixed the oil and water in a ratio of one to five. 14. An increasing ratio of mistakes, perhaps induced by tiredness, crept into her game. 15. Compute the ratio of the object's height to its weight. 16. What is the ratio of men to women in the department? 17. Holmes calculated a ratio of approximately 2.4:1. 18. Not the usual patient-to-physician ratio, even hereabouts. 19. This ratio was 0.78 in the high grade group. 20. What is the ratio of dependent to independent clauses? 21. The hydrogen-to-carbon atom ratio is perhaps a better index. 22. Perinatal mortality is measured by the perinatal mortality ratio. 23. Its price-earnings ratio is a hefty 82. 4. 24. Today that ratio as plunged to only 2-1. 25. The bond-dependency ratio peaked this fiscal year, he said. 26. I was over budget for my expense ratio.... 27. It is the inverse of the liquidity ratio. 4. 28. Most firms appear to have a target payout ratio of dividends to long-run reported earnings. 29. Unfortunately, for bankers assessing country risk, this ratio has two major deficiencies. 30. It helped validate that parental leave was for both men and women and helped change the ratio of use. More similar words: operation, migration, separation, AND operation, reparation, immigration, exploration, integration, frustration, corporation, celebration, collaboration, consideration, generation gap, demonstration, concentration, administration, rating, gratify, operating, narrative, cooperative, democratic, concentrating, nation, administrative, location, zonation, donation, formation.

s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224647895.20/warc/CC-MAIN-20230601143134-20230601173134-00385.warc.gz

CC-MAIN-2023-23

http://wwpaperpacg.weareallimmigrants.us/what-are-the-two-dots-over-a-letter-called-in-spanish.html

math

Which languages use single dots over their letters as diacritical dots were used above some letters: how many languages use a u with two dots over it. What's up with the dots in hebrew letters we put a dot, called a dagesh, in middle of these letters to not all siddurim have straight above certain letters. The shortcut for double dots over the letter i is alt + 0207 for an uppercase i and how do you type an i with 2 dots over it on the two dots over a. You can insert an e with two dots over it, which is called diaeresis mark how to make two dots over an e using iphone spanish or german. Lawless spanish weekly newsletter when the letter g precedes a u plus a the two dots over the u are called a dieresis and indicate that two adjacent vowels. The two dots over a vowel is called the umlaut what's the one circle over a which is considered different from the letter it appears over, usually an a or u. We rather casually use umlaut to mean two little dots above a letter, but not all little dots in spanish it indicates that the u everyone should know about. When a mark is placed over a letter it changes what is the mark over the e in cafe called an umlat is the two dots that are often seen above. How to type zoë that's z, o, and e with umlaut or dieresis or two dots two dots mean two syllables select the desired letter. 11 facts yü should know about the umlaut he called it umlaut from um we rather casually use “umlaut” to mean “two little dots above a letter,” but. French accent marks french uses several accent marks to guide pronunciation these are the most commons ones the tréma looks like two dots above a letter. Is a diacritical mark that consists of two dots ( ¨) placed over a letter and spanish make regular a two dots above a letter, called. In spanish, we use umlauts to what does the letter u with 2 dots above mean update cancel answer wiki 1 answer what are the two dots above 'a' in ä called. If you've ever studied german, you've seen an umlaut it's a mark that looks like two dots over a letter, and it signifies a shift in pronunciation. German umlaut - a letter with two dots the two dots above this e is in bulgarian the diacritical mark in the form of 2 dots is often called.

s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221213691.59/warc/CC-MAIN-20180818154147-20180818174147-00326.warc.gz

CC-MAIN-2018-34

https://academicpals.com/mathematics-homework-help/two-trains-leave-a-station-at-the-same-time-traveling-in-opposite-directions-one-travels-20mph-faster-than-the-other-in-4-hours-the-trains-are-900-miles-apart-find-the-speed-of-each-train-let-x/

math

Two trains leave a station at the same time, traveling in opposite directions. One travels 20mph faster than the other. In 4 hours, the trains are 900 miles apart. Find the speed of each train. Let x Two corteges license a place at the similar age, traveling in contradictory directions. One travels 20mph faster than the other. In 4 hours, the corteges are 900 miles aloof. Find the urge of each cortege. Let x enact the urge travelled by cortege A,then the urge for cortege B procure be (x+20) Time=Total Distance/(Total Speed) less age is loving by 4hrs,and the completion urge is similar to sum of urge for cortege A and B and the completion space is 900 miles 900/(x+x+20 )=4 900/(2x+20)=4 cross-multiplying gives 8x+80=900,collecting approve stipulations and solving for x gives 8x=820 x=102.5 Therefore the urge for cortege A is loving by 102.5mph and that of cortege B is 102.5+20=122.5mph Thanks anticipation to product delay you in future

s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141729522.82/warc/CC-MAIN-20201203155433-20201203185433-00270.warc.gz

CC-MAIN-2020-50

https://www.lessonplanet.com/teachers/trigonometric-examples-of-integration-by-substitution

math

Trigonometric Examples of Integration by Substitution In this integration worksheet, students use trigonometric identity and integration by substitution to solve given integrals. This two-page worksheet contains three problems. 3 Views 3 Downloads Solving Integrals Using Substitution The concept of solving integrals by substitution with trigonometric functions is modeled by a video designed for AP Calculus classes. The narrator works an example problem using substitution and shows that careful substitution makes... 3 mins 11th - Higher Ed Math Derivatives of Inverse Trig Functions - Arcsin Put another link in the chain. With the aid of the chain rule, the presentation shows how to take the derivative of an arcsin function with a binomial argument. The 15th video in a 31-part series goes on to work through the... 5 mins 11th - Higher Ed Math Natural Log Function-Integration One of the strongest tools in integration is u-substitution, particularly when working with natural logs. In this step-by-step video presentation, a pleasant-voiced instructor walks through a number of integration problems. She begins... 9 mins 11th - Higher Ed Math CCSS: Adaptable

s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891807825.38/warc/CC-MAIN-20180217204928-20180217224928-00454.warc.gz

CC-MAIN-2018-09

http://forum.xda-developers.com/showthread.php?t=895875

math

Could this be made a sticky.. So far the only codes I have seen are: ##634# - Diagonstic Screen If you go to the CIT test.. about 1/2 way in is a LED test.. the camera LED Comes on and stays on.. if you really need a LED flashlight. ##3282# - T-mobile field test Then you go to settings and you can force 2G or 3G on .. Smart Phones I owned in Chronological order.. HTC Universal (upgraded to WM6) HTC Dash (upgraded to WM6) HTC Dash 3G (My FAVORITE Phone) HTC Tilt2 (AT&T Unlocked on Tmo - speaker went out) HTC HD7 (Phone too big & no keyboard - and too delicate) DELL DVP ( OS 7.8, FW 7720.219 ) Someone tell HTC we want a phone like the DVP, if they make it I will buy. I NEED a Portrait QWERTY WP8 device. That or the 2010 HTC Trophy "protoype" (See Avatar)

s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368696381630/warc/CC-MAIN-20130516092621-00088-ip-10-60-113-184.ec2.internal.warc.gz

CC-MAIN-2013-20

https://en.academic.ru/dic.nsf/enwiki/429269

math

- Time-frequency representation A time-frequency representation (TFR) is a view of a signal (taken to be a function of time) represented over both time and frequency. Time-frequency analysismeans analysis of a TFR. TFRs are often complex-valued fields over time and frequency, where the modulus of the field represents "energy density" (the concentration of the root mean squareover time and frequency) or amplitude, and the argument of the field represents phase. A signal, as a function of time, may be considered as a representation with perfect "time resolution".In contrast, the magnitude of the Fourier transform(FT) of the signal may be considered as a representation with perfect "spectral resolution" but with no time information because the magnitude of the FT conveys frequency content but it fails to convey when, in time, different events occur in the signal. TFRs provide a bridge between these two representations in that they provide "some" temporal information and "some" spectral information simultaneously. Thus, TFRs are useful for the analysis of signals containing multiple time-varying frequencies. Formulation of TFRs One form of TFR can be formulated by the multiplicative comparison of a signal with itself, expanded in different directions about each point in time. Such formulations are known as quadraticTFRs because the representation is quadratic in the signal. This formulation was first described by Eugene Wignerin 1932 in the context of quantum mechanicsand, later, reformulated as a general TFR by Ville in 1948 to form what is now known as the Wigner-Ville distribution. Although quadratic TFRs offer perfect temporal and spectral resolutions simultaneously, the quadratic nature of the transforms creates cross-terms whenever multiple frequencies are superimposed. This was partly addressed by the development of the Choi-Williams distributionin 1989 but most recent applications of TFRs have turned to linear methods. The cross-terms which plague quadratic TFRs may be evaded by comparing the signal with a different function. Such representations are known as linear TFRs because the representation is linear in the signal. The "windowed Fourier transform" (also known as the short-time Fourier transform) localises the signal by modulating it with a window function, before performing the Fourier transform to obtain the frequency content of the signal in the region of the window. Wavelet transforms, in particular the continuous wavelet transform, expand the signal in terms of wavelet functions which are localised in both time and frequency. Thus the wavelet transform of a signal may be represented in terms of both time and frequency. Before 1991, the notions of time, frequency and amplitude used to generate a TFR from a wavelet transform were derived intuitively. In 1991, Nathalie Delpratgave the first quantitative derivation of these relationships, based upon a stationary phase approximation. Continuous wavelet transform * [http://tfd.sourceforge.net/ DiscreteTFDs — software for computing time-frequency distributions] * [http://tftb.nongnu.org/ TFTB — Time-Frequency ToolBox] Wikimedia Foundation. 2010. Look at other dictionaries: Time-frequency analysis — is a body of techniques for characterizing and manipulating signals whose component frequencies vary in time, such as transient signals.Whereas the technique of the Fourier transform can be used to obtain the frequency spectrum of a signal whose… … Wikipedia Bilinear time–frequency distribution — Bilinear time–frequency distributions, or quadratic time–frequency distributions, arise in a sub field field of signal analysis and signal processing called time–frequency signal processing, and, in the statistical analysis of time series data.… … Wikipedia Time series — Time series: random data plus trend, with best fit line and different smoothings In statistics, signal processing, econometrics and mathematical finance, a time series is a sequence of data points, measured typically at successive times spaced at … Wikipedia Frequency domain — In electronics, control systems engineering, and statistics, frequency domain is a term used to describe the domain for analysis of mathematical functions or signals with respect to frequency, rather than time. Speaking non technically, a time … Wikipedia Representation theory of finite groups — In mathematics, representation theory is a technique for analyzing abstract groups in terms of groups of linear transformations. See the article on group representations for an introduction. This article discusses the representation theory of… … Wikipedia Time from NPL — Map showing the location of the Anthorn VLF transmitter within Cumbria … Wikipedia Frequency spectrum — Familiar concepts associated with a frequency are colors, musical notes, radio/TV channels, and even the regular rotation of the earth. A source of light can have many colors mixed together and in different amounts (intensities). A rainbow, or… … Wikipedia Frequency comb — A frequency comb is the graphic representation of the spectrum of a mode locked laser. An octave spanning comb can be used for mapping radio frequencies into the optical frequency range or it can be used to steer a piezoelectric mirror within a… … Wikipedia Time to digital converter — In electronic instrumentation and signal processing, a time to digital converter (abbreviated TDC) is a device for converting a signal of sporadic pulses into a digital representation of their time indices. In other words, a TDC outputs the time… … Wikipedia Time — This article is about the measurement. For the magazine, see Time (magazine). For other uses, see Time (disambiguation). The flow of sand in an hourglass can be used to keep track of elapsed time. It also concretely represents the present as… … Wikipedia

s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107874026.22/warc/CC-MAIN-20201020162922-20201020192922-00056.warc.gz

CC-MAIN-2020-45

http://www.chemicalforums.com/index.php?topic=89014.0

math

Why without having its mass? Most ways of determining MW involve taking a known mass of sample and doing measurements on it. Is it part of a mixture where you don't know the weight fraction of polymer, and can't extract it? The only way I know of to determine MW in that case is GPC with UV or IR detection (provided there are no interferences from other things in the mixture); then you need to calibrate the RT-logM curve using standards of known MW - which aren't always available for your polymer. GPC using viscosity or (I think) light scattering detection can give absolute MWs, but then you need to know the mass of your sample, which must be pure (nothing else to scatter light or contribute to viscosity). The other possibility may be end group analysis, e.g. by NMR, if you have distinct signals for the backbone and the end groups, you can determine Mn from the relative intensity. But that is difficult for high MW polymers because of the low concentration of end groups. I think "the hydroxyl number and the viscosity of the polymer" will only work if you know the sample mass and it's pure.

s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189802.18/warc/CC-MAIN-20170322212949-00160-ip-10-233-31-227.ec2.internal.warc.gz

CC-MAIN-2017-13

https://www.arxiv-vanity.com/papers/nucl-th/9708031/

math

Integrability of the Pairing Hamiltonian Departamento de Física Comisión Nacional de Energía Atómica (CNEA), Ave. del Libertador 8250, 1429 Buenos Aires, Argentina. Centro Brasileiro de Pesquisas Físicas Rua Xavier Sigaud 150, CEP 22290-180, RJ, Rio de Janeiro, Brazil PACS: 21.69n 21.60Jz 74.20Fg 05.45+b 03.65-w 46.90+s Keywords: Pairing Interaction, Integrability, Time dependent Hartree Fock, Constants of the motion, Poincare section. We show that a many-body Hamiltonian that corresponds to a system of fermions interacting through a pairing force is an integrable problem , i.e. it has as many constants of the motion as degrees of freedom. At the classical level this implies that the Time-dependent Hartree-Fock- Bogoliubov dynamics is integrable and at the quantum level that there are conserved operators of two-body character which reduce to the number operators when the pairing strength vanishes. We display these operators explicitly and study in detail the three-level example. Two kinds of simple models are commonly used in nuclear physics for displaying the essential properties of the nuclear interaction, the particle-hole and the particle-particle models. The simplest one, the Lipkin model, consists of two levels of equal degeneracy and fermions interacting through a particle-hole force. It has been extensively used to test various approximation schemes and its classical version, provided by the Time-Dependent Hartree -Fock (TDHF) approach, is integrable. When this model is extended to three or more levels [2, 3, 4] one finds that the TDHF approximation yields a classical problem which is non integrable, displays various degrees of chaotic behavior and has an intricate and interesting phase-space structure . In principle the analogous situation for the particle-particle interaction can be thought to behave in a similar way. A two-level model with a pairing force is integrable [6, 7] and one would expect that the extension to three or more levels would yield non-integrable TDHF-Bogoliubov (TDHFB) dynamics. In this paper we report the fact that this is not so and that the problem of a pairing force acting in a restricted shell model space with single -particle levels turns out to be integrable both classically and quantum mechanically. We display explicitly the constants of the motion involved and we study their properties, their group structure and their classical limits. The outline of the paper is as follows. In Section 2 we review the pairing model, in both its quantum and classical aspects. The classical limit is obtained by a large scale degeneracy argument that leads to the TDHFB equations of motion. Section 3 is devoted to the search for new constants of the motion, i.e. new operators commuting with the Hamiltonian. These constants of the motion, which are not unique, turn out to be non trivial two body operators involving the coupling constant and the single particle energies. A set of commuting operators is thus constructed that renders the problem integrable. In Section 4 we treat the three- level case and show explicitly the consequences of this integrability both at the quantum and classical levels. The last Section is devoted to conclusions and final remarks. 2 The model The pairing force is a very general interacting mechanism that has an ubiquitous role in the quantum many body problem. In electron systems it leads to the superconducting mechanism and in nuclear physics to the collectivity associated to the pairing degree of freedom. In this latter case it provides a simplified description of the short range part of the nuclear interaction . A schematic model that incorporates this basic mechanism can be defined by interacting fermions that can occupy different single-particle shells of degeneracy and single-particle energies . The fermions interact via a monopole pairing force. The Hamiltonian of such a system is The are the usual fermion operators obeying anticommutation relations which create or annihilate a fermion on the i-th shell which has degeneracy . The operators count pairs of particles in each shell by . The operators conform an algebra whose Casimir operator is The full dynamics of the system occurs in the group space of . The classical limit of the model is obtained from the TDHFB approximation when the degeneracy of each level goes to infinity . is the semiclassical parameter analogous to in the usual semiclassical treatments. One way of obtaining this limit is through the time dependent variational principle implemented through coherent states that are constructed from the vacuum (or minimal weight) state , characterized by The coherent state in this representation is The equations of motion obtained through the time-dependent variational principle with this state are equivalent to the TDHFB equations. To obtain them we use the variational principle appropriate for non-normalized states with an action defined as (we set ) A detailed derivation is given in . The variables are not canonical but the transformation yields canonical variables satisfying . The finite range of these variables is a consequence of the Pauli exclusion principle between correlated fermion pairs. In terms of the variational equations become ordinary hamiltonian equations in complex form, where is the classical hamiltonian associated to the problem. In the same way for any quantum operator its classical limit in this representation is, Therefore the operators and have their classical analogues, , which can be written in terms of the variables This last set of operators obey the classical Poisson bracket relations . The classical pairing hamiltonian can then be expressed, in analogy with the quantum one, directly in terms of the generators, Energy conservation is guaranteed by the time-dependent variational principle so that the motion occurs in the -dimensional manifold defined by . There is a further constant of the motion linked to the conservation of the total number of pairs The TDHFB equations are then classical hamiltonian equations in a phase space of variables. The conservation of and implies that the case is classically integrable, a fact that was exploited in to compute energy levels and transition matrix elements semiclassically. 3 Search for additional constants of the motion The proof of the integrability for requires the existence of independent, well defined , global functions (constants of the motion), whose Poisson brackets with each other and with the hamiltonian vanish. Following Hietarinta a quantum mechanical hamiltonian of degrees of freedom is defined to be quantum integrable if there are independent, well defined, global operators (quantum invariants) which commute with each other and with the hamiltonian. Then the energy spectrum of a quantum integrable hamiltonian system is naturally labeled by quantum numbers , which are the eigenvalues of the corresponding quantum invariants. Likewise the stationary states are simultaneous eigenfunctions of the corresponding operators. For the cases and the integrability is trivial. and (or ) provide the commuting operators and and (or ) the corresponding classical conserved quantities. But in the case of no new obvious quantum invariants are present and we could expect the system to be non integrable and therefore display generically regions of chaotic behavior. However we now show how to construct non trivial operators, independent of the hamiltonian and the total number of pairs and commuting with them, which make the problem integrable. For this purpose let us construct the more general two-body operator which is hermitian and conserves the total number of pairs with and , and require it to commute with the hamiltonian The following relations among its coefficients are sufficient for the commutativity but they do not determine completely the coefficients. Thus several solutions can be found, and one should further check that the operator constructed is independent of and . For example if we choose we then would have is the Casimir of the algebra in the ith-level. In this case is not useful because it is not independent of the conserved magnitudes that we already know. However another choice leads to a set of operators In the non interacting limit () these operators become the natural set of commuting operators . A straightforward but tedious calculation shows that for any value of and . On the other hand, it is easy to see that and can be written in terms of the as Therefore we have constructed a set of commuting operators which also commute with the pairing hamiltonian and are number conserving. They extend to the fully interacting case the trivial properties of the number operators of the system. Consideration of these operators then demonstrate the integrability of the quantum problem. The simultaneous eigenvalue equations gives the eigenvalues of the hamiltonian as It should be noticed however that the actual solution is by no means simplified by this knowledge. The operators are two body operators as complicated in principle as the hamiltonian itself and they cannot be used (except by diagonalizing them) to separate the hamiltonian into invariant subspaces. however, as we will see, the simple fact of their existence has very drastic implications on the structure of both eigenvalues and eigenfunctions. In the classical limit the associated operators for the set written in terms of the classical operators are Taking into account (1), (15), (25) and (31) we can see that the classical operators , and have the same structure (in terms of the algebra generators ) as their quantum analogs, except for additive constants. It is then easy to see that Analogously to the quantum case, the mean number of pairs and the energy are The functions are surfaces on the dimensional phase space. The trajectories lie in the intersection of these surfaces, which are dimensional tori labeled by the constants . Chaotic motion therefore cannot occur in this system. 4 Manifestations of integrability in the three-level case In this section we restrict our analysis to the three-level case () and equal degeneracy and show the consequences of the integrable behavior, both in the quantum and in the classical solutions. As in the previous section we will start with the quantum treatment. Although the problem has three degrees of freedom we have already seen that the total number of pairs in the system is a conserved magnitude. We can then use this fact to reduce explicitly the dimensionality to two degrees of freedom and therefore we only need to display another quantum invariant operator to have an integrable quantum problem. We then choose it as which is a linear combination of the operators defined in the previous section, The quantum integrability shows up clearly when we display a grid of the simultaneous eigenvalues of and . This is done in Fig. 1 for the case where the total number of pairs is , which corresponds to a set of levels. We find that the eigenvalues lie on a regular grid that includes all eigenvalues. The fact that this grid is not parallel and equally spaced reflects the fact that and are not action variables that quantize at integer spaced values. Of course a point transformation to a set and exists if and are independent. But we do not construct this variables explicitly. It is clear however that the grid we obtain is a smooth deformation of a regular one. This proves that the two operators ( and ) are independent and that their simultaneous eigenvalues form a set of good quantum numbers. For the classical analysis we introduce the non-interacting action-angle coordinates, where is the mean number of pairs in the level and is now a continuous classical variable. In these variables the classical hamiltonian is, where we have taken as the energy reference. The analysis is best performed by explicit elimination of the conserved quantity . We introduce the canonical transformation, We have scaled the variables so that they are all in the same range and adopted the mid-shell value, i.e. . The problem is reduced to a space of two degrees of freedom whose effective hamiltonian is, In the above coordinates the classical version of is It can be explicitly verified that . We have also tested in the numerical integration of the equations of motion that both and are constants; and use this fact to control the numerical accuracy of the solutions. Integrability is also apparent in Poincaré sections, as Fig. 2 shows. Only separatrices (no chaotic layers) are observed for any value of the coupling constant. The salient feature of this figure is the appearance of forbidden regions, quite a common occurrence in spin systems. Our analysis shows that the simple pairing force is integrable both at the quantum and at the classical levels. The reason why this simple feature has escaped attention can be found in the fact that the pairing force has been used almost exclusively in the context of quantum many-body physics and for energies close to the ground state. Thus there are no significant consequences for ground state or RPA modes, which are in any case integrable. However the structure of the highly excited states and eigenfunctions should show this consequence. For example, the fluctuation properties of the eigenstates will follow a Poisson rather than a GOE statistics , while eigenfuntions will show the traces of conserved quantities and will not be ergodic. There are very few models of interacting particles that are integrable and the fact that this simple model belongs to this class comes as a surprise. We have reported some consequences in the TDHFB dynamics and on the spectrum. Other features should follow naturally, for example the statistics of levels should be very different than the particle-hole case. Also the addition of a small perturbation to this hamiltonian should follow the KAM perturbation scheme and not a fluctuating spectrum characteristic of the perturbation of chaotic systems. From the technical side it is quite useful to have at one’s disposal a model which takes into account important features of the nucleon-nucleon interaction and which remains integrable for arbitrary values of its strength. Thus perturbation expansions can have a steadying point which need not be the non interacting fermion system. We acknowledge stimulating discussions with Prof. O. Bohigas. This work was supported in part by CONICET Pid 3233/92. A.M.F.R. gratefully acknowledges scholarships from Comisión Nacional de Energía Atómica (Argentina) and from CLAF-CNPq (Brasil). - H.J. Lipkin, N. Meshkov and A.J. Glick, Nucl. Phys. 62 (1965) 188,199,211. - R.D. Williams and S.E. Koonin, Nucl.Phys.A391 ,72 (1982) - D.C. Meredith, S.E. Koonin, and M.R. Zirnbauer, Phys. Rev. A37, 3499 (198 8) - P. Lebœuf and M. Saraceno, Phys. Rev. A41, 4614 (1990) - J. Högaasen-Feldman, Nucl. Phys 28 (1961) 258. - M.C. Cambiaggio, G.G. Dussel and M. Saraceno, Nucl. Phys A415 (1984) 70-92. - R. Broglia and B. Sorensen, Nucl. Phys A110 (1968) 241. - A. Bohr and B.R. Mottelson, Nuclear Structure Vol I, (Benjamin New York 1969) - P. Kramer, M. Saraceno , Geometry of the time dependent variational principle in quantum mechanics, Lecture notes in physics, vol 140 (Springer,Berlin 1981). - A. Perelomov, Generalized coherent states and applications (Springer Berlin 1986). - A. K. Kerman and S.E. Koonin, Ann of Phys. 100 (1976) 332. - J. Hietarinta, J. Math Phys 25 (1984) 1833. - N. Srivastava and G. Müller, Z. Phys. B 81 (1990) 137. - O. Bohigas, in Chaos and Quantum Physics, Eds. M.-J. Giannoni, A. Voros and J. Zinn-Justin, (Elsevier Science, New York, 1990). - F. Calogero, J. Math Phys 12 (1971) 419; M.A. Olshanetsky and A.M. Perelomov Phys Rep 94 (1983) 313. - V.I. Arnol’d, Russ. Math. Survey 18 (1963) 9, 85. FIG. 1. Simultaneous eigenvalues of the Hamiltonian () and for and . The variables have been scaled dividing them by . FIG. 2. Poincaré surface of section for the three-level pairing hamiltonian . The mid-shell value has been taken and the section is performed in the case (see text).

s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030336880.89/warc/CC-MAIN-20221001163826-20221001193826-00412.warc.gz

CC-MAIN-2022-40

https://ncatlab.org/nlab/show/p-divisible+group

math

In great generality, for an integer a -divisible group is a codirected diagram of abelian group objects in a category where the abelian-group objects are (equivalently) the kernels of the map given by multiplication with a power of ; these kernels are also called -torsions. In the classically studied case is a prime number, is the category of schemes over a commutative ring (mostly a field with prime characteristic) and the abelian group schemes occurring in the diagram are assumed to be finite. In this case the diagram defining the -divisible group can be described in terms of the growth of the order of the group schemes in the diagram. Note that there is also a notion of divisible group. Some authors refer to (instead of the diagram itself) as the -divisible group. see Lipnowski pg.2, example (b) The eponymous (-divisible groups are sometimes called Barsotti-Tate groups) example is a special case of the previous one - namely the Barsotti-Tate group of an abelian variety. Let be an abelian variety over of dimension , then the multiplication map by has kernel which is a finite group scheme over of order . The natural inclusions satisfy the conditions for the limit denoted to be a -divisible group of height . A theorem of Serre and Tate says that there is an equivalence of categories between divisible, commutative, formal Lie groups over and the category of connected -divisible groups over given by , where . In particular, every connected -divisible group is smooth Given a -divisible group , each individual has a Cartier dual since they are all group schemes. There are also maps that make the composite the multiplication by on . After taking duals, the composite is still the multiplication by map on , so it is easily checked that forms a -divisible group called the Cartier dual. One of the important properties of the Cartier dual is that one can determine the height of a -divisible group (often a hard task when in the abstract) using the information of the dimension of the formal group and its dual. For any -divisible group, , we have the formula that . For the moment see display of a p-divisible group. The dual . For an abelian variety , the dual is where denotes the dual abelian variety. Another proof that has height is to note that and have the same dimension , so using our formula for height we get . The category of étale -divisible groups is equivalent to the category of -adic representations of the fundamental group of the base scheme . Important tools in the study of -divisible groups are Witt rings, Dieudonné modules and more generally Dieudonné theories? assigning to a -divisible group an object of linear algebra such as a display of a p-divisible group. Barsotti, Iacopo (1962), “Analytical methods for abelian varieties in positive characteristic”, Colloq. Théorie des Groupes Algébriques (Bruxelles, 1962), Librairie Universitaire, Louvain, pp. 77–85, MR 0155827 Grothendieck, Alexander (1971), “Groupes de Barsotti-Tate et cristaux”, Actes du Congrès International des Mathématiciens (Nice, 1970), 1, Gauthier-Villars, pp. 431–436, MR 0578496 Messing, William (1972), The crystals associated to Barsotti-Tate groups: with applications to abelian schemes, Lecture Notes in Mathematics, 264, Berlin, New York: Springer-Verlag, doi:10.1007/BFb0058301, MR 0347836 Serre, Jean-Pierre (1995) , “Groupes p-divisibles (d’après J. Tate) web, Exp. 318”, Séminaire Bourbaki, 10, Paris: Société Mathématique de France, pp. 73–86, MR 1610452 Stephen Shatz, Group Schemes, Formal Groups, and -Divisible Groups in the book Arithmetic Geometry Ed. Gary Cornell and Joseph Silverman, 1986 Tate, John T. (1967), “p-divisible groups.” pdf, in Springer, Tonny A., Proc. Conf. Local Fields( Driebergen, 1966), Berlin, New York: Springer-Verlag, MR 0231827 de Jong, A. J. (1998), Barsotti-Tate groups and crystals, “Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998)”, Documenta Mathematica II: 259–265, ISSN 1431-0635, MR 1648076 Dolgachev, I.V. (2001), “P-divisible group” web, in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4 Richard Pink, finite group schemes, 2004-2005, pdf Hoaran Wang, moduli spaces of p-divisible groups and period morphisms, Masters Thesis, 2009, pdf Liang Xiao, notes on -divisible groups, pdf Paul Goerss, p-divisible groups and Lurie’s realization result, 2008, pdf slides Peter Scholze, Moduli of p-divisible groups, arxiv Thomas Zink, a dieudonné theory for p-divisible groups, pdf Thomas Zink, list of publications and preprints, web T. Zink, On the slope filtration, Duke Math. Journal, Vol.109 (2001), No.1, 79-95, pdf T. Zink, Windows for displays of p-divisible groups. in:Moduli of Abelian Varieties, Progress in Mathematics 195, Birkhäuser 2001, pdf

s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501172447.23/warc/CC-MAIN-20170219104612-00170-ip-10-171-10-108.ec2.internal.warc.gz

CC-MAIN-2017-09

http://www.solutioninn.com/a-person-drops-a-stone-from-the-window-of-a

math

Question: A person drops a stone from the window of a A person drops a stone from the window of a building. One second later, she drops another stone. How does the distance between the stones vary with time? Answer to relevant QuestionsHow would free fall on the Moon differ from that on the Earth? A student runs 30 m east, 40 m north, and 50 m west. (a) The magnitude of the student’s net displacement is (1) between 0 and 20 m, (2) between 20 m and 40 m, (3) between 40 m and 60 m. (b) What is his net displacement? The displacement of an object is given as a function of time by x = 3t2 m. What is the magnitude of the average velocity for (a) ∆t = 2.0 s – 0s, and (b) ∆t = 4.0 s – 2.0s? A couple is traveling by car down a straight high-way at 40 km/h. They see an accident in the distance, so the driver applies the brakes, and in 5.0 s the car uniformly slows down to rest. (a) The direction of the ...Figure 2.24 shows a plot of velocity versus time for an object in linear motion. (a) Compute the acceleration for each phase of motion. (b) Describe how the object moves during the last time segment. Post your question

s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886110485.9/warc/CC-MAIN-20170822065702-20170822085702-00270.warc.gz

CC-MAIN-2017-34

http://lydia117.blogspot.com/2013/09/day-4-fractions-subtraction-polygons.html

math

We continued on with Problem 13: Mind Reading An interesting problem that had me clueless for the first 10 minutes! Step 1: Think of 2 digits, make known the 1st digit only. Step 2: Put the 2 digits together, and use that number to minus off the sum of the two digits. (eg: 2 1 - 3 = 18) Have your friend find out: Given the 1st digit only, find out the 2nd digit. That baffled us for a while! Method 1: The 2nd digit can be any digit from 0-9 and the answers will fit into a pattern that will provide the answers for any 1st digits used! 1st digit Final Ans Using this pattern, 2 more methods are found.... Method 2: Take 1st digit and make it a Tens and minus the 1st digit off to get the final answer. Eg: 30 - 3 -27 Method 3: Have any 1st digits x 9 and you get the final answer. Eg: 3 x 9 = 27 Personally, I find Method 3 the best and most straight forward method to do! 1. Learning subtraction 2. Identifying the patterns present 3. Ability to articulate the reasons of the patterns present This is an example of a problem displaying Differentiation. Problem 14: Fractions and Subtraction Using a fairly simple problem, we saw how 2 methods can be used to help children understand ways to calculate the sum 3 1/4 - 1/2 = ? Find Out: How do 3 piggies share 4 pizzas equally?? Method 1: 4 divided by 3 = 3/3 + 1/3 = 1 1/3 Method 2: 4 divided by 3 = 12 thirds = 4/3 = 1 1/3 Problem 16 had us thinking about multiplication. Find Out: How do we get answers for multiple sets of 7 birds? Method 1: By doubling certain sets Eg: 2x7= 14 , so 4x7= 14+ 14 = 28 Method 2: 2 sets of 7 added up together Eg: 2x7= 14 & 3x7= 21, Therefore, 5x7= 14 + 21 = 35 Method 3: Subtract 7 from a larger set of 7 Eg: 10x7= 70 , so 9x7= 70-7 = 63 These provided more efficient ways of using multiplication, addition and subtraction together to arrive at answers at a faster speed! Problem 17 of exploring Polygons made us think deep into the concept as we... Find Out: Forming Possible polygons that has 1 dot left in the center The Geoboard app was a good medium to explore polygons! It was a fruitful time of consolidating our ideas as we found out the smallest to biggest polygons that can be formed! From a few ideas... to a complete set of the best ideas we could come up with! Whether you are a good mathematician or not, Here's a good Quote to advocate Math as A Math Teacher... It's not about the answers, but the Concepts of Math that can enrich our everyday lives!

s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232254882.18/warc/CC-MAIN-20190519121502-20190519143502-00263.warc.gz

CC-MAIN-2019-22

https://nofilmschool.com/boards/questions/blocking-users

math

August 10, 2016 at 11:55AM Is there a way on here to block some users of the forum so you do not see their activity nor they yours? I'm using this website much less now due to aggressive behaviour of some members. I'm all for discussion, but not for aggressive insulting or negative comments. If this isn't a feature would you guys like this as a feature possibly?

s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487582767.0/warc/CC-MAIN-20210612103920-20210612133920-00193.warc.gz

CC-MAIN-2021-25

https://eguruchela.com/physics/learning/Keplers_laws.php

math

Johannes Kepler, working with data painstakingly collected by Tycho Brahe without the aid of a telescope, developed three laws which described the motion of the planets across the sky. . in this law both a radical departure from the astronomical prejudices of the time and profound tools for predicting planetary motion with great accuracy. Kepler, however, was not able to describe in a significant way why the laws worked. Kepler's three laws of planetary motion can be described as follows: The Law of Ellipses: The path of the planets about the sun is elliptical in shape, with the center of the sun being located at one focus. The Law of Equal Areas An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time. The Law of Harmonies The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun.

s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363290.59/warc/CC-MAIN-20211206072825-20211206102825-00422.warc.gz

CC-MAIN-2021-49

https://www.physicsforums.com/threads/factoring-cubic-polynomial-help.431889/

math

1. The problem statement, all variables and given/known data This is probably an easy question, but using the rational zero theorem I have not found any roots for this cubic polynomial. Factor the Following 6x^3-37x^2-8x+12 2. Relevant equations 3. The attempt at a solution I have used all my knowledge of factoring and have yet to factor this expression. I tried many different values a, such that f(a)=0 using remainder theorem, According to Descartes signs there should be one negative root.

s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376830305.92/warc/CC-MAIN-20181219005231-20181219031231-00231.warc.gz

CC-MAIN-2018-51

http://laserclassroom.com/products/measure-wavelength-laser-light/

math

Measure the Wavelength of Light What is the wavelength of a red or green or even violet laser beam? With some simple equipment and a little math, you can figure it out yourself! Grades: 9 to 14 Duration: 1/2 Hour – 1 Hour NGSS Connections PS4.B: Electromagnetic Radiation - Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling in various media. (HS-PS4-1) To set up, you will need a screen or blank wall; a laser source (Laser Pointer or LASER Blox), a meter stick, and a diffraction grating. Set the laser securely on the table. Place the diffraction grating directly in front of the laser aperture. Place the screen 1m from the laser aperture as shown in the photo. In step 2 you will be collecting data using the equation λ = (X) (d)/ L and solving for λ to find the wavelength of the laser you are using. This video is a great summary on how to do this lab. Take Measurements and Record Data Download and fill in the Student Data Sheet in this step. You will need to take measurements and calculate 3 times to find an average. Turn on the laser and observe the diffraction pattern on the screen. You will use the data to calculate λ = (X) (d)/ L and solve for λ to find the wavelength of the laser you are using. Notice that the diffraction grating tells you how many lines (tiny barriers) per mm – you must calculate the slit width: (d) in your equation. L is the distance (in cm) from the diffraction grating (which should be right in front of the laser aperture, very close to the device) to the screen Now look at the diffraction pattern. The CENTRAL dot is 0 (zero) order, the dots immediately to the left and right of the center dot are 1 and -1 order, with 1 to the right and -1 to the left. The next dots out on either side of them are order 2 and -2. X is the distance from the center dot to the first order dot, either + or -. Once you have collected your data, insert your values into the equation λ = (X) (d)/ L and solve for λ to find the wavelength of the laser you are using. You will need to work on converting your units to get the right answer – hint: the wavelength of light is generally stated in nM (nano meters) Note that the SLIT WIDTH must be calculated from the Lines/mm of the Diffraction Grating. Students may need guidance or a review in how to manage the units to come out with the right final answer. The wavelength of light is generally stated in nM (nano meters). Finally, compare your computed average with the stated wavelength on the laser label.

s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891816068.93/warc/CC-MAIN-20180224231522-20180225011522-00754.warc.gz

CC-MAIN-2018-09

https://www.hackmath.net/en/examples/equation?page_num=6

math

Equation - examples - page 6 At 8:40 the ship set sail at 12 km/h. At 19:10 followed by at 29 km/h sail boat. When sail boat catches up the ship? How many minutes will catch up took? - Leg and height Solve right triangle with height v = 9.6 m and shorter cathetus b = 17.3 m. - Number ratio Calculate two positive numbers that its ratio is 6:6 and difference was 0. - I think number I think number.When I add 841 to it and subtract 157, I get a number that is 22 greater than 996. What number I thinking? The football team has 11 players. Their average age is 20 years. During the match due to injury, one player withdraws and the average age of the team is 18. How old was injured player? - Parquet floor Three workers laid parquet floor for 2.9 hour. The first one would do this work alone 9 hours, the second in 7 hours. For how many hours would fulfill this work the third worker, if he worked alone? Seedcake costs 44 cents. How many minimum seedcakes we must buy that we can pay in cash only whole euros? During the spring cleaning ladies going to wash windows. Mother takes wash all the windows 5 hours, the grandmother 3 times longer and Paula wash all windows in 2 hours. How many hours will spend washing the windows this "women's team" if working togethe 104 cow consumes 6968 kg hay per day. How many kg of hay consume one cow in one day? In the city are 3/9 of women married for 3/6 men. What proportion of the townspeople is free (not married)? Express as a decimal number. Equilateral triangle with side 40 cm has the same perimeter as an isosceles triangle with arm of 45 cm. Calculate the base x of an isosceles triangle. We must dilute 16 liters of 8.8% aqueous vinegar to 4.1% one. How much water is necessary to add? If it is true that ? is: From station 130 km away started passenger train and after 2.2 hours after the express train, which travels 37 km an hour more. Express train finish journey 7 minutes early. Calculate the average speed of this two trains. The tank is filled with two pumps in 16 minutes. The first pump is filled in 30 minutes earlier than two one. How many minutes is filled with the first pump? The monthly fee for the phone is 12 USD and for phone unit 0.08 USD. How much family pay phone in the first quarter Q1, if on January 1 had on the counter 97362 units and on April 1 97946 units. Gabo draw n-gon, which angles are consecutive members of an arithmetic sequence. The smallest angle is 70° biggest 170°. How many sides have Gabo's n-gon? - Goat and circles What is the radius of a circle centered on the other circle and the intersection of the two circles is equal to half the area of the first circle? This task is the mathematical expression of the role of agriculture. The farmer has circular land on which g From two different locations distant 232 km started against car and bus. The car started at 5:20 with average speed 64 km/h. Bus started at 7:30 with average speed 80 km/h. When they meet? How many kilometers went the bus? - Unknown x If we add to unknown number 21, then divide by 6 and then subtract 51, we get back an unknown number. What is this unknown number? Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?

s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247489282.7/warc/CC-MAIN-20190219000551-20190219022551-00146.warc.gz

CC-MAIN-2019-09

https://www.geomorphologyjournal.ir/article_102795.html

math

عنوان مقاله [English] Petrological and geological studies are of great importance in natural resources management. The fractal technique is used as an instrument to achieve accurate results in a shorter time. Geological maps are very useful in natural resources management, industry, especially refineries, and mine exploration. Due to the large scale of available geological maps, small scale geological maps should be provided in details. The fractal dimension, as a measure of surface roughness over a variety of scales, can be used to model the dissipation of erosive products due to climatic elements and fluvial transport. Nowadays, by using new fractal technique and terrestrial survey, more accurate results on geological units can be obtained in a shorter time. This research aims to compare the performance of two techniques of quantitative parameters non-dimensionalization in geomorphology such as drainage network density index, and fractal dimension, to separate geological units in the Taft watershed, Yazd province. Materials and Methods Taft watershed, as the study area, located in the Yazd province, that is situated between 53° 43' 38'' to 54° 14' 54'' E. longitude and 31° 33' 22'' to 31° 49' 06'' N. latitude. There is high diversity of geological and lithological units, including gd (Granodiorite), K^(t-1) (Taft lime), and K^S (conglomerate and sandstone) in this watershed. Three geological units selected in the study area. In each geological unit, , 10 plots of 2 km×2 km (samples), and 10 plots of 2 km×2 km (tests) were selected respectively inside and outside of the study area for analysis. To identify and distinguish three studied geological units, drainage network was drawn in each geological units through geological map of the Iranian Geological Survey and satellite images of the Google Earth and field observation. Afterwards, using Fractalyse and ArcGIS softwares, their fractal dimension and density were calculated. Output results of the Fractalyse software is some numbers that one of them indicates the fractal dimension of those lines. Fractal dimension number is between one and two. The area and network length of each plot were calculated by ArcGIS 10.2 software. Then, the drainage network density of each plot was calculated by equation 1. Drainage Network Density= Drainage Network Length (km)/ Plot area (km2) (1) Efficiency of the two dimensionless indices of drainage network density and fractal in separating geological units were compared by two methods: In each geological unit, the calculated numbers of the samples and tests should be averaged individually. Then, equation 2 is used to calculate the validation of each geological units. Validity= sample/test (2) Sample: Average fractal dimension of drain networks for sample plots. Test: The mean fractal dimension of drainage networks for test plots. Sample: Average density of drainage networks for sample plots. Test: The average density of the drainage networks for test plots. B) Comparing the sample and test by using QQ diagram, the line equation, the coefficient of determination and the angel of deviation: In drainage network fractal dimension, QQ diagram is plotted between samples and tests' fractal dimension. Line equation, coefficient of determination and angel of deviation were calculated. Moreover, the QQ graphs were plotted and calculations carried out on the drainage network density. Results and discussion Results of the first comparing method (validation) in both techniques are very good and similar. In second comparing method (i.e. QQ graph, angle of deviation, and coefficient of determination), coefficient of determination in the drainage network density in K^S, gd and K^(t-1)geological units were 0.99, 0.93 and 0.94, respectively, which are more than drainage network fractal dimension. The standard deviation in drainage network fractal dimension in K^S and gd and K^(t-1)geological units are +17.05, - 1.48, and +8.37 respectively, these values in the drainage network density are much lower (i.e. better). The angle of deviation in drainage network density of K^S, gd and K^(t-1) geological units are + 0.21, -2.4, and +0.22, respectively. According to the results, the drainage network density index is better than the drainage network fractal dimension in identifying and separating of the studied geology and lithological units of K^S, gd and K^(t-1) in the region. The results of the accuracy assessment of both techniques are very good and similar to each other. Therefore, in this comparison, both techniques of drainage network density index and drainage network fractal dimension have high efficiency in identifying and separating of the geological studies unit. However, The drainage network density technique is the best technique of quantitative parameters non-dimensionalization in geomorphological studies in identifying and separating of geological units in the Taft watershed, Yazd. Keywords: QQ Diagram, Fractal Technique, Drainage Network Density, Yazd.

s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679101779.95/warc/CC-MAIN-20231210092457-20231210122457-00871.warc.gz

CC-MAIN-2023-50

https://communities.sas.com/t5/Statistical-Procedures/Test-whether-slope-0-with-for-each-class-variable-level-of-class/td-p/897599

math

I am testing the effect of a product applied at four different concentrations (continuous variable), at two sites and six genotypes (class variables). The treatments were blocked at each site. Site*concentration is significant, which is interesting. Two specific follow-up questions are 1. what is the slope for concentration at each site, averaged across genotypes? and 2. are each of those slopes different from zero (i.e., does concentration actually affect the response at both of the sites)? This may not be the most elegant strategy, but I'm able to get the response = slope*concentration + intercept lines for each site by sending the lsmeans through proc reg. However, since the data variability is lost, this does not tell me whether each slope is different from zero. My attempts at proc mixed estimate statements for this test are giving errors; any help would be much appreciated! proc mixed data=data ; class site genotype block; model response = site|genotype|concentration ; random block(site) ; lsmeans site / at concentration = 0 ; lsmeans site / at concentration = 10 ; lsmeans site / at concentration = 20 ; lsmeans site / at concentration = 30 ; ods output lsmeans = lsmeans; proc sort data=lsmeans; by site; proc reg data=lsmeans; model estimate = concentration; Estimate statements for slopes are tricky. It gets even trickier when you have many interactions. Harder still is averaging slopes over one of the model CLASS effects. The best strategies for getting to your end result is to build up your ESTIMATE statements using more simple tests and using the /E option on the ESTIMATE statement to make sure you have coefficients in the correct place. It is scarily easy to write an ESTIMATE statement that is giving you an answer but that is testing the wrong hypothesis! First, try to write ESTIMATE statements for each of the 6 slopes on genotype for the 2 sites. Those ESTIMATE statements will involve the main effect of CONCENTRATION and the interactions of SITE*CONCENTRATION, GENOTYPE*CONCENTRATION, and SITE*GENOTYPE*CONCENTRATION. The coefficients on the ESTIMATE statement will all be 1's here, in the appropriate spots for each of these 4 effects. Again, that /E option will show you if you have your coefficients in the right spot. Then, you can average the coefficients over the genotypes in a site to get your final result. With 6 genotypes, you can either use .1666666 as the coefficients on the G*C and S*G*C interactions, or use 1 and the DIVISOR=6 option on the ESTIMATE statement. The coefficient on C and S*C would be 6 in this case using that DIVISOR= option. If you get a non-estimable result for that ESTIMATE, check the /E option output to make sure you have the coefficients in the right place. Check that output even if you don't get a non-estimable result to make sure you are testing the correct hypothesis. It takes a lot of experience to get estimates like this correct. Working with an experienced statistician is always a good idea when writing post-hoc tests like these. Registration is open! SAS is returning to Vegas for an AI and analytics experience like no other! Whether you're an executive, manager, end user or SAS partner, SAS Innovate is designed for everyone on your team. Register for just $495 by 12/31/2023. If you are interested in speaking, there is still time to submit a session idea. More details are posted on the website.

s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100724.48/warc/CC-MAIN-20231208045320-20231208075320-00117.warc.gz

CC-MAIN-2023-50

https://www.spiedigitallibrary.org/ebooks/TT/Optical-Imaging-in-Projection-Microlithography/Chapter2/Elements-of-Geometrical-Optics/10.1117/3.612961.ch2

math

The wavelengths of concern in photolithography (on the order of 10 -7 m ) are small compared with most physical dimensions. In situations such as transmission through lenses, we can approximate the propagation of light by neglecting the finiteness of its wavelength. In this chapter we derive that in the limit of zero wavelength, Maxwell's equations give rise to optical laws that can be formulated in the language of geometry. Light energy is transported along rays that are orthogonal to geometrical wavefronts. Optical phenomena can be deduced by determining the paths of light rays and their intensities. Online access to SPIE eBooks is limited to subscribing institutions.

s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794867995.55/warc/CC-MAIN-20180527024953-20180527044953-00030.warc.gz

CC-MAIN-2018-22

http://www.mmo-champion.com/threads/1452930-The-point-of-World-of-Warcraft?goto=nextnewest

math

I was doing an MSV LFR today, the part at the beginning with the big dog pull. I used arcane explosion, and got the message on my MSBT - 20 hits, 20 crits. What exactly is the chance of this happening? My crit was around ~20% for simplicity's sake. would it really be (1/5)^20 like I am thinking? What i mean is that there were 20 dogs, and i crit all of them. I got 20 total crits.

s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917123530.18/warc/CC-MAIN-20170423031203-00200-ip-10-145-167-34.ec2.internal.warc.gz

CC-MAIN-2017-17

https://www.ucasprogress.com/course/2307449/a-level-mathematics

math

A level Mathematics at Huddersfield New College A Level Maths builds upon the higher tier algebra topics you have studied at GCSE. You will study topics including: • Coordinate geometry • Sequences and series • Graphs of functions • Exponentials and logarithms • Probability and data This is for you if you enjoy and are successful in algebra. Through studying it, you will learn how to solve increasingly difficult equations, and begin to see how algebra allows us to explain and predict the world around us. You will have enjoyed GCSE topics such as quadratic equations, surds, the Cosine Rule, and want to take these skills further. For example you will: • Build on your GCSE skills with quadratic equations to solve trigonometric equations • Learn how to expand expressions • Discover calculus, which is a set of techniques for finding maximum and minimum values of functions and modelling many really world situations • Learn how to use logarithms to find exact solutions to power equations • Extend your skills in applying maths to solve problems in data handling • Model the motion and interaction of particles using algebraic techniques Grade 7 in GCSE Maths. A Grade 6 in GCSE Maths may be considered if your GCSE average points score is 6.5 or above. General entry criteria will also apply, this is available on our website. A Level Maths is an essential requirement for many degrees. These tend to be STEM subjects (e.g. Engineering, Computer Science, Physics) but also subjects such as Actuarial Sciences, and Economics. There are many other degrees where A Level Maths is often part of the entry criteria, especially at Russell Group universities. As well as the sciences these also include arts and humanities such as Geography, Philosophy and Architecture. Some universities may ask for A Level Maths for entry on to medical related degree programmes such as Medicine, Veterinary Sciences, Optometry and Pharmacy. How to apply You can apply for this course through UCAS Progress. Add this course to your favourites so you can start making an application.

s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039748901.87/warc/CC-MAIN-20181121133036-20181121155036-00247.warc.gz

CC-MAIN-2018-47

https://mikesmathpage.wordpress.com/2015/06/28/happy-tau-day/

math

Since the kids are just back from a week of camping, and consequently a little tired, I thought we’d do a fun Tau day project. Turned out that we got a little sidetracked on a little geometry point. Still a fun project, though, just not what I was expecting. We started with this old Numberphile video about and : After we watched the Numberphile video, we began our conversation about . One point I wanted to focus on for a bit – and I really thought it would be about a 1 minute thing – was Matt Parker’s point that the diameter was easy to measure. The boys didn’t remember this point from the Numberphile video, and talking about how to measure the diameter started us down a long path: We made a circle with our compass off camera to help us explore the question of how to find the diameter. My older son had the interesting idea of drawing a square around the circle. If you could do that, then finding the diameter would be pretty easy. The trouble is – how do you draw that square? At the end of the video, my younger son suggests that we measure the circumference to find the diameter. Now, following the suggestion at the end of the last video, we found some string and tried to measure the circumference. We found the circumference was about 12.5 inches. That measurement led to a long discussion about how to calculate the approximate radius if we knew the length of the circumference. Following the discussion about the circumference, we returned to trying to measure the diameter directly. This measurement problem really gave the boys fits. Part of the confusion, I think, was that they were looking for a way to find the diameter exactly. There are, of course, plenty of ways to do that, but looking for the absolute perfect solution was distracting them from using the ruler to find a close approximation. At the end of this video we stumble on an important idea – the diameter is the longest line segment that you can draw in the circle! The idea at the end of the last video gives as a way to get an approximate measure of a circle’s diameter – we just look for the longest line that we can draw. Both kids had some interesting ideas about how the length of lines would shrink or grow as you moved around the circle. Exploring those ideas allowed us to get better and better approximations for the diameter. Hopefully the shadows don’t obscure the measurements we are making in the video. So, although the project didn’t quite go in the direction that I was expecting, a pretty interesting project. It is nice to see that an offhand comment from a mathematician – in this case that the diameter of a circle is easy to measure – can lead to a fun little project for kids.

s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224657720.82/warc/CC-MAIN-20230610131939-20230610161939-00709.warc.gz

CC-MAIN-2023-23

http://www.numbertheory.org/php/log1.html

math

Calculating the simple continued fraction of logba This performs an algorithm from T.H. Jackson and K.R. Matthews, On Shanks' algorithm for computing the continued fraction of logba, Journal of Integer Sequences 5 (2002) article 02.2.7. We run the algorithm for c = br, r = m,...,n (suggested by Alan Offer). Here a, b, m, n are positive integers satisfying a > b > 1, and 1 ≤ m ≤ n. We find that if we add the restriction Ai,c > c + √c and A'i,c > c + √c, we get better results, though this restriction does not seem to be needed when a = b+1. With c = br, we have found that apart from some initial exceptional values of r, the correct partial quotients will be returned. In fact, if a=b+1, it seems that the correct partial quotients are always returned. This is a BCMath version of the BC program log Last modified 8th may 2018 Return to main page

s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057119.85/warc/CC-MAIN-20210920221430-20210921011430-00562.warc.gz

CC-MAIN-2021-39

https://sports.answers.com/Q/What_Sport_has_the_most_deaths_per_year

math

Mosquitoes. Over 1 000 000 deaths per year. 18 deaths per year. 83 deaths per year im not sure 523 deaths per year on average 5,ooo per year and most of them are car related because their DUI most of them are teens to isn't that sad. =',( 1.78 Deaths Per Second 107 Deaths Per Minute 6,390 Deaths Per Hour 153,000 Deaths Per Day 56.0 Million Deaths per Year 3.9 Deaths Per Life Time (70 Years) Tobacco caused deaths are at 5 million deaths per year worldwide. More than 480,000 of these deaths occur in the United States.

s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104496688.78/warc/CC-MAIN-20220704202455-20220704232455-00408.warc.gz

CC-MAIN-2022-27

https://community.qlik.com/thread/61187

math

This content has been marked as final. Show 2 replies I have written a batch file to copy some files from different folders and place it in a common folder. But only files is copying and other are not copying. Can anyone suggest. copy D:\Publisher\Sleep Aid\DEMON00001_IAI_All_V0.qvw D:\Publisher\DEMON00001\DEMON00001_IAI_All_Sleep_Aid_V0.qvw copy D:\Publisher\GI Insights\DEMON00001_IAI_All_V0.qvw D:\Publisher\DEMON00001\DEMON00001_IAI_All_GI_Insights_V0.qvw copy D:\Publisher\IP Demo Oncology\DEMON00001_Insight_Prescriber_Oncology_All_V0.qvw D:\Publisher\DEMON00001\DEMON00001_Insight_Prescriber_Oncology_All_V0.qvw copy D:\Publisher\Antihistamine\DEMON00001_IAI_All_V0.qvw D:\Publisher\DEMON00001\DEMON00001_IAI_All_Antihistamine_V0.qvw this is the code used

s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221210058.26/warc/CC-MAIN-20180815102653-20180815122653-00170.warc.gz

CC-MAIN-2018-34

http://www.ecuacert.net.ec/pdf/classical-mechanics-point-particles-and-relativity

math

By Walter Greiner The sequence of texts on Classical Theoretical Physics is predicated at the hugely profitable sequence of classes given through Walter Greiner on the Johann Wolfgang Goethe college in Frankfurt am major, Germany. meant for complicated undergraduates and starting graduate scholars, the volumes within the sequence offer not just a whole survey of classical theoretical physics but in addition an important variety of labored examples and difficulties to teach scholars truly how one can observe the summary rules to lifelike difficulties. Read Online or Download Classical Mechanics: Point Particles and Relativity PDF Similar relativity books You by no means knew theoretical physics can be so simple! Why do issues circulation? Why is the growth of the universe accelerating? Is the universe a black gap? This intriguing publication considers many of the inner most and most crucial questions in physics. Enjoy an exhilarating intergalactic journey as Andrew Thomas redefines the strength of gravity and introduces a courageous new view of the universe! "Hidden in simple Sight 2" is an informative theoretical physics e-book that appears at a potential option to the unsolved mysteries at the back of gravity, darkish power, and black holes. i discovered this booklet to be both and in a few respects much more attention-grabbing than his past publication, "Hidden In undeniable Sight". during this rendition, Dr. Thomas seems at quite a few unsolved difficulties in theoretical physics. once more, I'm no longer a professional physicist and can't make any assertions to the validity of the theories offered during this publication yet at least I welcome the author's attractive and available technique that makes such books relaxing for the laypersons to learn. This bold 170-page ebook contains the next 9 chapters: 1. advent, 2. Gravity, three. Cosmology, four. darkish topic and darkish strength, five. Black Holes, 6. The cleaning soap Bubble Universe, 7. Gravity Revisited, eight. find out how to Create your personal Universe, and nine. Conclusion. Even though Einstein is largely credited with abolishing the ether notion, he truly brought a brand new relativistic ether in 1916, constructing the belief in his later works. This e-book relates the tale of Einstein and the rebirth of the ether, demonstrating how Einstein got here to reject the nineteenth century ether. Una moderna presentazione della teoria della Relativit� Ristretta, specificatamente progettata according to i nuovi corsi della Laurea Triennale in Fisica. Un testo essenziale ma autosufficiente, che adotta lo stile e il linguaggio delle lezioni svolte in aula, e che introduce alle trasformazioni di Lorentz, alla formulazione covariante dell'elettromagnetismo e alle basi della cinematica e dinamica relativistiche. - Relativistic effects in heavy-element chemistry and physics - From Eternity to Here: The Quest for the Ultimate Theory of Time - Essential Dynamics and Relativity - Special Relativity: For the Enthusiastic Beginner - Relativity Simply Explained Additional info for Classical Mechanics: Point Particles and Relativity What is the equation of the straight line through A and B? Solution A (b -a ) The straight line AB is parallel to (b − a). Moreover, it passes through point A. Hence, the equation determining any position vector x of a point X on the desired straight line reads a b x = a + t (b − a), B X x x with t being a real number (running parameter −∞ < t < ∞). The point-direction form of a straight If two points A and B are not given but one point A and a vector line. u specifying the orientation of the straight line are given, the equation of the straight line reads x = a + tu . One has |v| = R 2 ω2 + b2 ω2 = ω R 2 + b2 , that is, the magnitude of the velocity is constant. The acceleration is the derivative of the velocity b = −ω2 · (R cos ωt, R sin ωt, 0) = −ω2 r⊥ , where r⊥ = (R cos ωt, R sin ωt, 0) = (r · er )er and er = (cos ωt, sin ωt, 0) is the polar unit vector in the x, y-plane. We thus obtain the same acceleration as for the circular motion. For the magnitude, it holds that |b| = ω2 R. Integration of vectors: The integration rules may be applied also to vectors in the customary way. A strong breeze blows from the west with 120 km/h relative to ground. What are the velocity and direction of flight of the plane, assuming that there is no wind deflection? y w vm vo ϕ West North 45º ey ex x East South The relative directions of wind and airplane velocity. Solution Let |vm | = 930 km/h, the velocity of the plane in the wind, |v0 | = the velocity of the plane without wind, |w| = the wind velocity. 2◦ . 12 COMPONENT REPRESENTATION OF A VECTOR r = xi + yj + zk, |r| = P(x,y,z) or: r = (x, y, z); r= z = x 2+ y 2+ z2 (x , y,z ) y |r| The position vector: A point P in space may be z uniquely fixed by specifying the vector beginning at the origin of the coordinate frame and pointing to the point P as endpoint.

s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583511365.50/warc/CC-MAIN-20181018001031-20181018022531-00315.warc.gz

CC-MAIN-2018-43

https://www.taylorfrancis.com/chapters/mono/10.1201/b10478-9/treatment-comparisons-clinical-trials-ding-geng-din-chen-karl-peace?context=ubx&refId=8ee7167f-c3d6-4121-a0fe-b1e7d8c08adf

math

Although clinical trials are conducted with multiple treatment groups, questions of interest are often expressed as pairwise comparisons among the groups. For example, a clinical trial of two dose (D1 and D2) groups and placebo (P ) may have as its objective the effectiveness of each dose, and whether the doses differ in their effectiveness. That is the objective may be formulated in terms of the three pairwise comparisons: D1 − P , D2 − P , and D2 − D1. Other contrasts among the groups may be of interest; e.g. the average of the doses versus placebo. Of course if a trial consists of only two treatment groups, the objective would be formulated as a single comparison of the two groups. In this chapter, we present statistical methods for comparing treatment groups in clinical trials using the R system. Specifically, we present two data sets from clinical trials in Section 3.1 and in Section 3.2, we introduce the associated Note: to run the R programs in this chapter, the analyst should install the following R packages first: RODBC and bootstrap.

s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882573029.81/warc/CC-MAIN-20220817153027-20220817183027-00520.warc.gz

CC-MAIN-2022-33

http://restlesswanderings.com/nice-pergolas/

math

Is your backyard pergola being used to its fullest advantage? Many people have outdoor structures but most are only being used to have of their capable function. There are many ways to make your outdoor space more functional. Begin by covering your pergola with a rainproof material like plastic or fabric. There are many different types of covers to choose from. Find one that keeps rain out while still allowing the sun's rays to penetrate the area below. This will expand the use of your outdoor space even when the weather is not cooperating. It will also allow you to still grow plants and flowers beneath. Next it is highly recommended that you add some type of floor covering under your structure. There are many types of outdoor flooring alternatives on the market. If you already have an existing concrete base, you can add an outdoor rug or carpet tiles. Either of these are easy to clean and can be changed out if they get worn out. If you can spare the expense, adding stone or ceramic tiles is a more permanent solution. Tiles are also easy to hose off and keep clean. The most important thing to remember about flooring is that it is bound to get dirty because it is going to be exposed to the outdoors so you don't want to purchase an expensive rug or carpet that can easily get ruined with use. #nice pergolas≢Chair ideas#total relais des pergolas nice#total relais des pergolas nice 06200#total relais des pergolas nice sud 06200#tabac les pergolas nice horaires#relais pergolas nice#relais des pergolas nice≢backyard concept#tabac les pergolas nice#les pergolas nice Whats Hot Today

s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247522457.72/warc/CC-MAIN-20190222180107-20190222202107-00198.warc.gz

CC-MAIN-2019-09

https://ipt724.com/qa/what-element-has-3-electrons-in-the-2p-sublevel.html

math

- How many electrons can 3p hold? - How many electrons are in each shell? - What element has most electrons? - What values of L are possible for n 3? - How many 2p electrons are in neon? - Which element has 3 electrons in the n 4 energy level? - How many orbitals are there in n 3? - How many p orbitals are there in n 3? - What is the only metalloid in Period 3? - How many electrons are in a 2p sublevel? - What element has a 4s sublevel with 2 electrons? - Are zn2+ and Ni Isoelectronic? - What is 1s 2s 2p 3s 3p? - Does the 3p sublevel have 3 electrons? - What is the L quantum number? - Which element has the electron configuration of 1s 2 2s 2 2p 6 3s 2 3p 4? - Why is 3d higher energy than 4s? - How many electrons can n 3 hold? - How many p orbitals are there in N 1? - What element has 3 energy levels and 7 valence electrons? - Which atom has three 2p electrons in its ground state? How many electrons can 3p hold? six electronsThe 2p, 3p, 4p, etc., can each hold six electrons because they each have three orbitals, that can hold two electrons each (3*2=6). The 3d, 4d etc., can each hold ten electrons, because they each have five orbitals, and each orbital can hold two electrons (5*2=10). First, we look at the n=1 shell (the first shell).. How many electrons are in each shell? Each shell can contain only a fixed number of electrons: The first shell can hold up to two electrons, the second shell can hold up to eight (2 + 6) electrons, the third shell can hold up to 18 (2 + 6 + 10) and so on. The general formula is that the nth shell can in principle hold up to 2(n2) electrons. What element has most electrons? HydrogenElectronsAtomic NumberElementEnergy Levels or “shells”M1Hydrogen (H)2Helium (He)3Lithium (Li)37 more rows What values of L are possible for n 3? Because n=3, the possible values of l = 0, 1, 2, which indicates the shapes of each subshell. How many 2p electrons are in neon? six electronsNeon is the tenth element with a total of 10 electrons. In writing the electron configuration for neon the first two electrons will go in the 1s orbital. Since 1s can only hold two electrons the next 2 electrons for Ne go in the 2s orbital. The remaining six electrons will go in the 2p orbital. Which element has 3 electrons in the n 4 energy level? Lithium has 3 electrons; 2 of the 3 electrons occupy the s sublevel in principal energy level 1. The 3rd electron must go in the next available sublevel, 2s. How many orbitals are there in n 3? nine orbitalsThere are nine orbitals in the n = 3 shell. There is one orbital in the 3s subshell and three orbitals in the 3p subshell. The n = 3 shell, however, also includes 3d orbitals. The five different orientations of orbitals in the 3d subshell are shown in the figure below. How many p orbitals are there in n 3? Orbitals and Electron Capacity of the First Four Principle Energy LevelsPrinciple energy level (n)Type of sublevelMaximum number of electrons (2n2)2p83s18p7 more rows What is the only metalloid in Period 3? SiliconOne metalloid of period 3 is Silicon. How many electrons are in a 2p sublevel? 6 electronsThere can be two electrons in one orbital maximum. The s sublevel has just one orbital, so can contain 2 electrons max. The p sublevel has 3 orbitals, so can contain 6 electrons max. The d sublevel has 5 orbitals, so can contain 10 electrons max. What element has a 4s sublevel with 2 electrons? calciumEven though the 4s sublevel is filled, the last electron went into that sublevel, making it a member of the s-block. It has 2 valence electrons. The element is calcium, a metal. Are zn2+ and Ni Isoelectronic? So, sure, they’re isoelectronic, but not because of having the same electronic structure; instead, it’s purely due to how many electrons they have, not where they are. … They have the same number of valence electrons, but they aren’t identical compounds. What is 1s 2s 2p 3s 3p? Physicists and chemists use a standard notation to indicate the electron configurations of atoms and molecules. For atoms, the notation consists of a sequence of atomic subshell labels (e.g. for phosphorus the sequence 1s, 2s, 2p, 3s, 3p) with the number of electrons assigned to each subshell placed as a superscript. Does the 3p sublevel have 3 electrons? phosphorus has three electrons in its 3p sub level. neon has its highest energy level completely filled. What is the L quantum number? RulesNameSymbolValue examplesPrincipal quantum numbernn = 1, 2, 3, …Azimuthal quantum number (angular momentum)ℓfor n = 3: ℓ = 0, 1, 2 (s, p, d)Magnetic quantum number (projection of angular momentum)mℓfor ℓ = 2: mℓ = −2, −1, 0, 1, 2Spin quantum numbermsfor an electron s = 12, so ms = −12, +12 Which element has the electron configuration of 1s 2 2s 2 2p 6 3s 2 3p 4? Electron ConfigurationsABSodium1s2 2s2 2p6 3s1Magnesium1s2 2s2 2p6 3s2Aluminum1s2 2s2 2p6 3s2 3p1Sulfur1s2 2s2 2p6 3s2 3p416 more rows Why is 3d higher energy than 4s? We say that the 4s orbitals have a lower energy than the 3d, and so the 4s orbitals are filled first. … The electrons lost first will come from the highest energy level, furthest from the influence of the nucleus. So the 4s orbital must have a higher energy than the 3d orbitals. How many electrons can n 3 hold? Questions and AnswersEnergy Level (Principal Quantum Number)Shell LetterElectron Capacity2L83M184N325O502 more rows How many p orbitals are there in N 1? There are n2 orbitals for each energy level. For n = 1, there is 12 or one orbital. For n = 2, there are 22 or four orbitals. For n = 3 there are nine orbitals, for n = 4 there are 16 orbitals, for n = 5 there are 52 = 25 orbitals, and so on. What element has 3 energy levels and 7 valence electrons? ElementElement NumberNumber of Electrons in each LevelBeryllium42Boron53Carbon64Nitrogen7551 more rows Which atom has three 2p electrons in its ground state? nitrogenSimilarly, for nitrogen in its ground state, Hund’s rule requires that the three 2p electrons singly occupy each of the three 2p orbitals. This is the only way that all three electrons can have the same spin.

s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585380.70/warc/CC-MAIN-20211021005314-20211021035314-00486.warc.gz

CC-MAIN-2021-43

http://www.ask.com/math/quadrangle-parallelogram-27a1231efe985164

math

A trapezoid is a quadrangle that is not a parallelogram. A trapezoid is a quadrangle because it has four sides and four internal angles, but it is not a parallelogram because it only has one pair of parallel sides rather than two. Each of the two parallel sides is called a base of the trapezoid, and each of the two non-parallel sides is referred to as a leg. The perimeter of the trapezoid is determined by adding the lengths of all four sides together. The formula for the area of the trapezoid requires multiplying the height by the sum of both bases and dividing by two.Learn More There are three types of trapezoid. There is the right trapezoid, which has two right angles, isosceles trapezoid, which has two of its non-parallel sides equal in length and the scalene trapezoid, which does not have equal sides or angles.Full Answer > The area of a trapezoid is found by multiplying the average length of the two parallel bases by the height, or 1/2 (b1 + b2) x h. The height is the length of a line connecting one base to the other at a 90-degree angle.Full Answer > The midsegment of a trapezoid is a line that connects to the midpoints of the two non-parallel sides of a trapezoid, according to The Geometry Center at the University of Minnestota. The midsegment of a trapezoid runs parallel with the two other parallel sides.Full Answer > A trapezoid may have right angles, but they are not required. The definition of a trapezoid only specifies that it must be a quadrilateral, or a closed, four-sided shape, and that it must have only one pair of parallel sides.Full Answer >

s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422115857200.13/warc/CC-MAIN-20150124161057-00099-ip-10-180-212-252.ec2.internal.warc.gz

CC-MAIN-2015-06

http://www.expertsmind.com/questions/derivatives-30122975.aspx

math

Customer Service Chat Get quote & make Payment derivatives, Engineering Mathematics At 8am particle A is at point (0,0) and moves horizontally to the right with constant velocity of 60km/hr. At the same time particle B is at the point (0, A+B+C+5) and moves horizontally to the left with a velocity of 30km/hr. what are the rates of change of the distance between the two particles at 8.00am, 9.00am? and in general time t? Posted Date: 11/11/2012 4:54:55 AM | Location : Qatar Ask an Expert derivatives, Assignment Help, Ask Question on derivatives, Get Answer, Expert's Help, derivatives Discussions Write discussion on derivatives Your posts are moderated Write your message here.. Estimate lowest and highest byte memory, What are the lowest and highest a... What are the lowest and highest addresses in a 2 20 byte memory in which a four-byte word is the smallest addressable unit? Dynamics, A stone weighing 50 newton is tied to one end of a cord 0.90 mete... A stone weighing 50 newton is tied to one end of a cord 0.90 meter long. the stone is then whirled in a vertical circle. if the breaking strength of the cord in tension is 60 newto Calculate principal value of the root, Compute the (real and imaginary part... Compute the (real and imaginary parts of the) principal value of the eighth root of (a + ib) to 3 decimal places (accurate to 10 -3 ). Call the real part "m 7 ", and the imagina Chemistry, advantages of langmuir adsorption theory advantages of langmuir adsorption theory Explain how conduction takes place in conductors, With the help of energy b... With the help of energy bands explain how conduction takes place in conductors. On the basis of energy band materials are categorized as conductor is given below: Conducto Six years time, A young couple requires RM30000 for an overseas trip which ... A young couple requires RM30000 for an overseas trip which they want to make in six years time. How much they have to invest now at 18% p.a. compound interest compounded monthly, t Lpp, Use the simplex method to solve the following LP Problem. Max Z = 107... Use the simplex method to solve the following LP Problem. Max Z = 107x1+x2+2x3 Subject to 14x1+x2-6x3+3x4=7 16x1+x2-6x3 3x1-x2-x3 x1,x2,x3,x4 >=0 Draw concentric circles, Draw concentric circles of radii a and b, each cen... Draw concentric circles of radii a and b, each centered at z=id (on the imaginary axis). Suppose φ(x,y) is a harmonic function inside the washer defined by these circles. The circl Some children are afraid of snakes, change each of the following propositio... change each of the following propositions into symbolic form. Dene the universe of discourse and the predicates you use. (i) Some children are afraid of snakes. (ii) All com Accounting Assignment Help Economics Assignment Help Finance Assignment Help Statistics Assignment Help Physics Assignment Help Chemistry Assignment Help Math Assignment Help Biology Assignment Help English Assignment Help Management Assignment Help Engineering Assignment Help Programming Assignment Help Computer Science Assignment Help Why Us ? ~24x7 hrs Support ~Quality of Work ~Time on Delivery ~Privacy of Work Human Resource Management Literature Review Writing Help Follow Us | T & C Copyright by ExpertsMind IT Educational Pvt. Ltd.

s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542414.34/warc/CC-MAIN-20161202170902-00153-ip-10-31-129-80.ec2.internal.warc.gz

CC-MAIN-2016-50

http://mathhelpforum.com/advanced-algebra/198890-set-n-positive-numbers-find-largest-possible-value-n-print.html

math

A set of n positive numbers. Find the largest possible value of n. Sorry I'm new to the forums and I'm not sure if this belongs here but some help on this one would be greatly appreciated. Thanks in advance. The average of some set of n positive numbers is 60. After removing one of the numbers, the average of the remaining numbers is 70. What is the largest possible value of n? Re: A set of n positive numbers. Find the largest possible value of n. Note that I removed x_n you could remove some x_i now substitute in : so n < 7....

s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917121121.5/warc/CC-MAIN-20170423031201-00071-ip-10-145-167-34.ec2.internal.warc.gz

CC-MAIN-2017-17

https://libquotes.com/karl-marx/quote/lbr2a9r

math

Karl Marx Quote Each pursues his private interest and only his private interest; and thereby serves the private interests of all, the general interest, without willing it or knowing it. The real point is not that each individual's pursuit of his private interest promotes the totality of private interests, the general interest. One could just as well deduce from this abstract phrase that each individual reciprocally blocks the assertion of the others' interests, so that, instead of a general affirmation, this war of all against all produces a general negation. Notebook I, The Chapter on Money, p. 76. - Grundrisse (1857/58)

s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882570765.6/warc/CC-MAIN-20220808031623-20220808061623-00553.warc.gz

CC-MAIN-2022-33

http://www.horseforum.com/plus-sized-riders/new-riding-world-confused-breeches-sizes-104083/

math

Hello, I am new to horseback riding. I went to a local store to find the right pants but got confused. My question is lets say a person wears an extra large in bottoms what would be good fitting for these pants. I saw (L) and (R) listed whats the difference? Also what is a 34R would that be like a size number like 11,13 or 14 or something in regular. Please help me out : ) thanks!

s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701155060.45/warc/CC-MAIN-20160205193915-00289-ip-10-236-182-209.ec2.internal.warc.gz

CC-MAIN-2016-07

https://www.docslides.com/briana-ranney/work-supported-in-part-by-us-department

math

Work supported in part by US Department of Energy cont Download Pdf - The PPT/PDF document "Work supported in part by US Department ..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement. Presentation on theme: "Work supported in part by US Department of Energy cont"— Presentation transcript: Page 1 Work supported in part by US Department of Energy contract DE-AC02-76SF00515 Measurement of the Decelerating Wake in a Plasm a Wakefield Accelerator I. Blumenfeld , C.E. Clayton , F.J. Decker , M.J. Hogan , C. Huang , R. Ischebeck , R.H. Iverson , C. Joshi , T. Katsouleas , N. Kirby , W. Lu K.A. Marsh , W.B. Mori , P. Muggli , E. Oz , R.H. Siemann , D.R. Walz and M. Zhou Stanford Linear Accelerator Center, Stanford University, Stanford, California 94305, USA University of California, Los Angeles, California 90095, USA University of Southern California, Los Angeles, California 90089, USA Abstract. Recent experiments at SLAC have shown that high gradient acceleration of electrons is achievable in meter scale plasmas. Results from these experiments show that the wakefield is sen- sitive to parameters in the electron beam which drives it. In the experiment the bunch lengths were varied systematically at constant charge. The effort to extract a measurement of the decelerating wake from the maximum energy loss of the electron beam is discussed. Keywords: PWFA, decelerating wake measurement PACS: 52.40.Mj, 52.70.Nc, 41.75.Lx, 29.20.Ej INTRODUCTION Plasma wakefield accelerators (PWFAs) have shown great potential as a mechanism for acceleration of particles to high energy. Experiments have demonstrated both high gradients and long propagation distances[1, 2]. However, for a future collider design a deeper understanding of the experimental relationship between the wake and the electron beam is necessary. EXPERIMENTAL SETUP In the SLAC experiment E167, a 42 GeV beam with 1 10 10 electrons, 60 and was injected into a confined neutral lithium vapor of density 10 17 per cm with a length of 85cm, full width at half max (FWHM). The en- ergy spectrum of the incoming beam was measured by recording the incoherent x-ray synchrotron radiation emitted by the beam in a soft vertical chicane placed in a region of a high horizontal dispersion. This energy spectrum could then be matched in the 2D tracking code LiTrack to recover the temporal profile of the beam[1, 4]. Bunch lengths were found to be 10 50 . With a transverse spot size of 10 this beam was dense enough to ionize the lithium and drive a non-linear wake[1, 6]. The initial energy spread had a full width of 4%. The measureable effect of the interaction between the beam and the plasma is the large broadening of the energy spectrum as the bunch length and the plasma wavelength SLAC-PUB-13390 September 2008 Presented at the Advanced Accelerator Concepts Workshop 2008, 7/27/2008 to 8/2/2008, Santa Cruz, CA, USA Page 2 Energy 50 100 150 200 250 300 350 20 40 60 80 50 100 150 200 250 300 350 x 10 pixel # counts a) b) Region 1 Region Region 3 Region 4 FIGURE 1. n example of a) and image, and b) derived energy profile, from the energy spectrometer diagnostic. Four distinct regions can be seen. Region 1 contains the accelerated charge, region 2 the beam head which has too low a current to ionize, region 3 the beam core driving the wake, and region 4 the lowest energy charge. Region 4 exhibits a peak followed by a lower energy rolloff. are on the same order, leading to the beam sampling all phases of the wake. The particle energies were measured after exiting the plasma using a magnetic spectrometer and Cerenkov radiation. The electrons were dispersed in energy by a dipole magnet centered 2.18m from the plasma exit with 12 05 kG . The electrons then passed through an air gap where their Cerenkov radiation was imaged at two locations from the magnet center, 0.85m, for low energies, and 1.85m, for high energies. Figure 1 shows an example of the beam as it appears after the energy spectrometer at the first imaging location. The entire beam can be seen on the image with four distinct regions. Region 1, where the accelerated charge sits, and Region 4, where the maximum decelerated charge is, are of most interest. ENERGY MEASUREMENTS Measurement of the accelerating gradient in a PWFA driven by short electron bunches is already well established. The essential problem is identifying the highest energy electrons on the diagnostic images with confidence. There are several strategies, which vary experiment to experiment, for achieving this, from charge contours to two screen methods[2, 7]. The remaining open question, to be addressed here, is how to relate a low energy measurement to the maximum decelerating wake. In the profile shown in Fig. 1 there is a peak in Region 4 where the lowest energy charge sits, followed by a long rolloff of lower energy particles. Understanding this feature will be the key to translating a particle energy measurement into a wake measurement. In reality the raw image is a convolution of various beam attributes, some due to the nature of the incoming beam and others due to effects in the plasma. The three effects Presented at the Advanced Accelerator Concepts Workshop 2008, 7/27/2008 to 8/2/2008, Santa Cruz, CA, USA Page 3 that dominate the interpretation of a low energy measurement are the y-spot size, the peak in the wakefield and radiative losses due to oscillation of beam particles in the plasma. The camera resolution is not large enough to give a contribution. These three effects all contribute to the profile that appears when the image is summed. The strategy for estimating how these affect the measurement will be to reconstruct a theoretical profile, convolving all these effects with some reasonable assumptions, and look at its qualitative and quantitative attributes. The calculated function is d vs. , where N is the number of particles and y is the dispersion direction. This reconstruction will give a guide as to where to choose the low energy point and how to translate it to the wake. Spot Size In the absence of dispersion, the electron beam has a finite spot size at the diagnostic location in the dispersion direction y. This contribution to the measured profile is pot ps (1) where is the beam spot size in y. As the beam is dispersed in y, cannot be directly measured. As an upper limit for this effect, it is reasonable to use the beam spot in x. Since the y-emittance is an order of magnitude smaller, the y-spot is likely smaller. Measured x spot sizes were mm RMS width. Peak in the Wakefield The shape of the wakefield has an effect on the measurement as at the peak deceler- ating field , d 0, where ct is the beam coordinate. In order to quantify this effect the shape of the decelerating field is taken to be a parabola around this point with no variation as the beam propagates, (2) where A defines the sharpness of the field peak. The energy of a beam particle interacting with this field is GL , where is the original energy and L is the interaction length. Using this expression, and inverting from above, it is possible to derive the number of particles per energy slice due to the shape of the wake, L AL 3) where and d is the longitudinal density of the electron beam which is assumed to be constant around the wakefield peak. Then, using the expression for the dispersion 4) Presented at the Advanced Accelerator Concepts Workshop 2008, 7/27/2008 to 8/2/2008, Santa Cruz, CA, USA Page 4 where s the dispersion and is the position of a particle of infinite energy. The contribution to d can be calculated, assuming the energy spread imprinted by the plasma is much larger than the initial spread, yielding akepeak 5) This relationship shows that the energy spectrum peaks around the minimum energy. Radiative Losses Through Propagation in the Plasma The energy radiated off as a particle oscillates in an ion-column is 12 (6) where is the particle energy, s the maximum displacement from the propagation axis as the particle oscillates, is the relativistic factor of the particle, and is the plasma wavenumber, a relationship which has been experimentally verified[9, 10]. This expression is for a single particle and dependent only on the maximum radial displacement from the propagation axis , and not on or independantly. To extend this to a beam distribution the quantity d is needed. Using appropriate transformations of the phase space density for a symmetric beam matched into the ion column and integrating over all angles, (7) Using this, it is now possible to determine the effect of radiative losses on the deceler- ating wake measurement. First, from Eq. 6 an upper limit can be set on the total energy lost to radiation while propagating in the plasma. The relativistic factor of the beam and the plasma density are set as constant. Since the power radiated is proportional to , the actual loss will be less as the particles are also losing energy to the wake as they propagate. The propagation distance is taken to be 90cm as, while the FWHM of the confined plasma was 85cm, deceleration continues past the half density point. This yields the maximum energy lost to radiation, , as 12 (8) In the absence of radiation each longitudinal slice will be at the same energy, as the longitudinal wake has no transverse variation for a symmetric drive beam. Therefore each longitudinal slice has an expression analagous to Eq. 7, which can be used in conjunction with the derivative of Eq. 8 to obtain long long 12 long c kp (9) Presented at the Advanced Accelerator Concepts Workshop 2008, 7/27/2008 to 8/2/2008, Santa Cruz, CA, USA Page 5 0.022 0.024 0.026 0.028 0.03 0.032 0.034 0.036 0.038 0.04 0.2 0.4 0.6 0.8 1.2 dispersion (m) Intensity (arb) 30 GeV maximum decelerating wake Corresponding reconstructed image FIGURE 2. reconstructed profile convolving the dominant effects. The solid red curve shows how a single particle with initial energy of 42 GeV sitting in a 30 GeV decelerating wake would be measured on the diagnostic due to the 2 pixel resolution limit of the optical system. The dotted black curve shows how this maximum decelerating wake actually appears taking into account that it is sampled by a beam with finite transverse and longitudinal size. where long is the number of particles in each longitidinal beam slice. Inverting Eq. 8 yields long long ae (10) where 12 mc kp . This shows that each longitudinal slice develops a tail of lower energy particles as the particles away from the axis of propagation radiate. To calculate the effect on the energy spectrum, the departure from the nominal energy of each longitudinal slice by an off-axis particle, , is taken to be small. Its position can then be calculated through a linearization of the dispersion expression, Eq. 4, 11) where is the position of the measured particle and . Then, utilizing Eq. 10, ad ong ye (12) RESULTS AND CONCLUSIONS The separate contributions of the three dominant effects to a low energy measurement have been calculated. Now these effects must be convolved. Figure 2 shows an example of this convolution, where the maximum decelerating gradient was taken to be 30 GeV/m. The peak of the solid red curve shows how a particle influenced by only this field would appear on the diagnostic, while the dotted black curve shows what actually will be measured. The peak of the dotted black curve is therefore the measurement that should be identified with the wake and corresponds to the peak in Region 4 of Fig. 1. Presented at the Advanced Accelerator Concepts Workshop 2008, 7/27/2008 to 8/2/2008, Santa Cruz, CA, USA Page 6 The peak in the dotted black curve is shifted slightly off that in the solid red curve. This shift can be corrected for by making a series of such reconstructions for all possible maximum decelerating wakes. This allows a one-to-one mapping from the peak in the low energy part of the measured profile to the real decelerating wake. The results of this calculation show that the corrections to the effective gradient, calculated using the plasma length and energy at this peak, are small, on the order of 1-2%. Thus, in order to map the minimum particle energy to the maximum decelerating wake, the location of the peak in the low energy part of the spectrum is the desired measurement. There is a small correction that can be made to account for the shifting of this peak. The particles in the long tail have lower energy due to radiative effects and not the wake by itself, and therefore should be ignored. Using this method, decelerating gradients of 20 35 GeV were measured. These will be combined with accelerating gradient measurements to yield an experimental limit on the transformer ratio. ACKNOWLEDGMENTS This work was supported by US Department of Energy contracts DE-AC02-76SF00515, DE-FG02-93ER40745, DE-FG03-92ER40727, DE-FG52-06NA26195, DE-FC02- 07ER41500, DE-FG02-03ER54721, DE-FG02-92ER40727, and NSF grant NSF-Phy- 0321345. The authors also would like to thank Melissa Berry for her assistance with the energy spectrometer design. REFERENCES 1. M. J. Hogan, et al., Phys. Rev. Let. 95 , 054802 (2005). 2. I. Blumenfeld, et al., Nature 445 , 741–744 (2007). 3. K. Bane, SLAC-PUB-11035, Tech. rep., Stanford Linear Accelerator Center (2005). 4. C. Barnes, Longitudinal Phase Space Measurements and Application to Beam Plasma Physics , Ph.D. thesis, Stanford University, Stanford, CA 94305 (2006), available as SLAC Report 799. 5. I. Blumenfeld, et al., to be submitted (2008). 6. C. L. O’Connell, et al., PRSTAB , 101301 (2006). 7. R. Ischebeck, et al., “Energy Measurement in a Plasma Wakefield Accelerator,” in PAC’07 , 2007, p. 4168. 8. E. Esarey, et al., Phys. Rev. E 65 , 056505 (2002). 9. S. Wang, et al., Phys. Rev. Let. 88 , 135004 (2002). 10. D. Johnson, et al., Phys. Rev. Let. 97 , 175003 (2006). 11. K. A. Marsh, et al., “Beam Matching to a Plasma Wake Field Accelerator using a Ramped Density Profile at the Plasma Boundary,” in PAC’05 , 2005, p. 2702. 12. J. B. Rosenzweig, et al., Phys. Rev. A 44 , 6189 (1991). Presented at the Advanced Accelerator Concepts Workshop 2008, 7/27/2008 to 8/2/2008, Santa Cruz, CA, USA

s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347388012.14/warc/CC-MAIN-20200525063708-20200525093708-00445.warc.gz

CC-MAIN-2020-24

https://kasinorwj.web.app/montrose87143viv/how-to-figure-out-roulette-odds-611.html

math

Roulette Odds Guide 2019 – Understanding Roulette Payouts Calculate Your Odds with These Roulette Charts In roulette, there are calculable odds for any given bet, which depend largely on the variation of the game you choose to play. Calculate the Expected Value in Roulette - ThoughtCo The game of roulette is a good example of the application of expected value. We can analyze what the winnings will be if we continually bet on red. Roulette Payouts and Odds - Online Roulette Odds & Payouts Chart In Combinations roulette the house edge roulette virtually all bets is 5. Essentially, numbers can figure out the edge by dividing the most of zeroes on the wheel by the total number of pockets. Winning is drawn at least for standard roulette games that pay out at odds that would be fair if the wheel only contained the 36 numbers without zeroes. Roulette Payouts - Roulette Payout Charts Explained How Roulette Payouts Give the Casino an Edge. These payouts all have one thing in common—they pay out less than the true odds of hitting a win. That’s why the casino enjoys a house edge of 5.26% on roulette. Your odds of winning are always less than the payout amounts. For example, the odds of winning a straight-up bet are 37 to 1. How to Calculate Roulette Probabilities (Mathematics) Despite all the talk about probabilities and statistics, it seems that few people can actually calculate mathematically the chance of any given roulette outcome. Sometimes they resort to excel or use specialized programs, trying to test millions of spins in order to come up with the right number. Roulette Odds | Probability for Single and Double Zero Games Home > Casino Game Odds > Roulette. Roulette Game Odds. Roulette, like craps, is an independent variable game where luck determines the winners. An air of sophistication graces the table and the possibility of winning up to 35 times your bet creates an enticing lure for many players. How to Calculate Moneyline Odds Payouts - Gambling Sites How to Win at Roulette. Dating back hundreds of years, roulette is one of the oldest gambling games. While the game is based on chance, strict probabilities are at the core of the game's spinning wheel. There are ways of playing the game... In American roulette the house edge on virtually all bets is 5. Essentially, you can figure out the edge by dividing the number of zeroes on the wheel by the total number of pockets. That is true at least for standard roulette strategy that pay out at odds that would be fair if the second only contained the 36 numbers without zeroes. However Roulette Payouts and Odds - Online Roulette Odds & Payouts Chart Roulette Odds - The Probability of Hitting Each Bet & The ... To understand how to play roulette, like all gambling games, you need to know how to play odds. To get the most out of your roulette play it is critical to know how ... How to figure out roulette odds - Online casino roulette ... How to figure out roulette odds - Online casino roulette trick - Restaurants in the sands casino bethlehem Roulette Payouts - Roulette Payout Charts Explained Roulette System: How to Master Chaos – Theory to Beat… So, what bets are less risky and more profitable? To figure it out we have provided a table of the odds of every roulette bet in both the European and American roulette games. When you understand how likely you are to be winning you will see which bets depend on strategies and which on luck only. What Are The Odds? Learn The Odds Of Top Casino Games What Are The Odds? Easily learn the odds of all the major casino games like roulette, blackjack, craps and slots with our expert, free guide. ... and it’s important you figure out how to ... Odds Calculator - Omni Our betting odds calculator takes a step further and calculates the percentage probability of winning and losing. The team would win 5 out of 6 games and lose 1 of them. By converting fraction to percent , we can say that the chances of winning are 5/6 = 83.33% , and of losing 1/6 = 16.67% . Roulette - Wikipedia Calculate the Expected Value in Roulette - ThoughtCo The game of roulette is a good example of the application of expected value. We can analyze what the winnings will be if we continually bet on red. Roulette Payouts and Odds - Online Roulette Odds & Payouts Chart European Roulette Payouts. European roulette wheels don’t have a double zero space so the odds are better for the player. It is the most popular type of roulette played at most of the online casinos, as the house edge and odds of winning make it the best choice for avid players. Roulette Odds and How to Calculate Them - Australian Gambling Gamblers who understand the math behind any casino game they play will make more successful bets and are more likely to have fun on the casino floor. How to Calculate Probabilities at the Roulette Table

s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487623596.16/warc/CC-MAIN-20210616093937-20210616123937-00190.warc.gz

CC-MAIN-2021-25

https://www.geogebra.org/m/ZtsSFbMP

math

- Michal J Wallace Each point (Y) in the spiral is found by taking the right triangle whose sides are the previous point (X), the origin (A), and a new point found by intersecting a unit circle rooted at (X) with the line perpendicular to (AX). Thus the quadrature (length squared) of each successive hypotenuse increases by 1. Since the height of each triangle is 1, the area is equal to half its base, and the area covered by the whole spiral is the sum of the square roots of the natural numbers, divided by two.... until you get to point (S), when the triangles start to overlap. Is there a function that describes the area covered by the entire spiral up to point (X)?

s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233506027.39/warc/CC-MAIN-20230921105806-20230921135806-00719.warc.gz

CC-MAIN-2023-40

https://www.moreland-islington.co.uk/math-10/

math

Length, Mass and Volume In Maths, we have been learning about standard units involving mass, volume and length. We learned how to read a range of scales, we used our rulers to measure different objects in our classroom. We also used measuring cylinders to find the volume of liquids, compared units of measurement. We even added and subtracted mass, capacity and length. converting measurements of length, mass and volume from a smaller unit of measure to a larger unit, and vice versa.

s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662510138.6/warc/CC-MAIN-20220516140911-20220516170911-00451.warc.gz

CC-MAIN-2022-21

https://unexdiaspir.web.app/649.html

math

If dense matrices are to be handled in connection with solving systems of linear algebraic equations by gaussian elimination, then pivoting either partial pivoting or complete pivoting is used in an attempt to preserve the numerical stability of the computational process see golub and van. Gauss elimination method matlab program code with c. C program for gauss elimination method code with c. After outlining the method, we will give some examples. The task below is a case in which partial pivoting is required. Gaussian elimination is usually carried out using matrices. As i have mentioned above, there are several methods to solve a system of equations using matrix analysis. Elimination process begins, compute the factor a 2 1 pivot 3. A symmetric positive definite system should be solved by computing its cholesky factor algorithm 3. Though the method of solution is based on additionelimination, trying to do actual addition tends to get very messy, so there is a systematized method for solving the threeormorevariables systems. For a large system which can be solved by gauss elimination see engineering example 1 on page 62. Hello every body, i am trying to solve an nxn system equations by gaussian elimination method using matlab, for example the system below. The c program for gauss elimination method reduces the system to an upper triangular matrix from which the unknowns are derived by the use of backward substitution method. It is usually understood as a sequence of operations performed on the corresponding matrix of coefficients. Grcar g aussian elimination is universallyknown as the method for solving simultaneous linear equations. Gaussian elimination technique by matlab matlab answers. Now, lets analyze numerically the above program code of gauss elimination in matlab using the same system of linear equations. The entries a ik which are \eliminated and become zero are used to store and save. Origins method illustrated in chapter eight of a chinese text, the nine chapters on the mathematical art,thatwas written roughly two thousand years ago. This method can also be used to find the rank of a matrix, to calculate the determinant of a matrix, and to. How to solve linear systems using gaussian elimination. Gaussian elimination lu factorization qr factorization wz factorization 2 iterative methods generate sequence of approximations that converge in the limit to the solution jacobi iteration gaussseidal iteration sor method successive overrelaxation vasilije perovi. How to use gaussian elimination to solve systems of equations. A system of linear equations and the resulting matrix are shown. And one of these methods is the gaussian elimination method. The goals of gaussian elimination are to make the upperleft corner element a 1, use elementary row operations to get 0s in all positions underneath that first 1, get 1s. The following code performs gauss elimination on a given matrix and reduces it to upper triangular matrix in echelon form. For inputs afterwards, you give the rows of the matrix oneby one. Solving linear equations with gaussian elimination martin thoma. We will never get a wrong solution, such that checking nonsingularity by computing the determinant is not required. Gauss elimination and gauss jordan methods using matlab code. Pdf we present a method by which the breakdown of the interval gaussian elimination caused by division of an interval containing zero can be avoided. The gaussian elimination algorithm, modified to include partial pivoting, is for i 1, 2, n1 % iterate over columns. Lecture 08 system of equations gauss elimination, pivoting. Multiplechoice test gaussian elimination simultaneous linear. Rediscovered in europe by isaac newton england and michel rolle france gauss called the method eliminiationem vulgarem common elimination. It moves down the diagonal of the matrix from one pivot row to the next as the iterations go on. Gaussian elimination with partial pivoting youtube. Each equation becomes a row and each variable becomes a column. Gaussian elimination is the most basic n umerical metho d for solving a dense linear system of equations ax b. In this post i am sharing with you, several versions of codes, which essentially perform gauss elimination on a given matrix and reduce the matrix to the echelon form. So, this method is somewhat superior to the gauss jordan method. The basic idea of gaussian elimination is the factorization of a as the product lu of a lower triangular matrix l with ones on its diagonal and an upper triangular matrix u, the diagonal entries of which are called the pivot elements. Ive found a few sources which are saying different things about what is. Gaussianelimination september 7, 2017 1 gaussian elimination this julia notebook allows us to interactively visualize the process of gaussian elimination. The method of practical choice for the linear system problem ax b is gaussian elimination with partial pivoting section 3. Gaussian elimination with pivoting method file exchange. In this question, we use gaussian elimination to solve a system of linear equations using partial pivoting and backwards substitution. There are man y v ariations on ho w to organize the computations, but tak en as a whole gaussian elimination is probably one of the most widely kno wn n umerical algorithms. Gaussian elimination lecture 10 matrix algebra for. Gaussian elimination is probably the best method for solving systems of equations if you dont have a graphing calculator or computer program to help you. I have some trouble with understanding the difference between partial and complete pivoting in gauss elimination. Recall that the process ofgaussian eliminationinvolves subtracting rows to turn a matrix a into an upper triangular matrix u. Except for certain special cases, gaussian elimination is still \state of the art. An additional column is added for the right hand side. Code without partial pivoting and backsubstitution. Though the method of solution is based on addition elimination, trying to do actual addition tends to get very messy, so there is a systematized method for solving the threeormorevariables systems. Multiplechoice test gaussian elimination simultaneous. Using gaussian elimination with pivoting on the matrix produces which implies that therefore the cubic model is figure 10. Gauss elimination method with partial pivoting the. With the gaussseidel method, we use the new values as soon as they are known. F or decades, scien tists ha v e solv ed problems of ev er. A system of linear equations can be placed into matrix form. Giorgio semenza, in studies in computational mathematics, 2006. First of all, i have to pick up the augmented matrix. The previous example will be redone using matrices. This method is called gaussian elimination with the equations ending up. Gaussian elimination revisited consider solving the linear. I solving a matrix equation,which is the same as expressing a given vector as a linear combination of other given vectors, which is the same as solving a system of. Complete pivoting an overview sciencedirect topics. A diagonal b identity c lower triangular d upper triangular. This implementation isnaivebecause it never reorders the rows. The gaussian elimination algorithm, modified to include partial pivoting, is for i 1, 2, n1. Pdf interval gaussian elimination with pivot tightening. Gaussian elimination september 7, 2017 1 gaussian elimination this julia notebook allows us to interactively visualize the process of gaussian elimination. With the gauss seidel method, we use the new values as soon as they are known. When we use substitution to solve an m n system, we. To avoid this problem, pivoting is performed by selecting. Find gaussian elimination course notes, answered questions, and gaussian elimination tutors 247. Ive found a few sources which are saying different things about what is allowed in each pivoting. This additionally gives us an algorithm for rank and therefore for testing linear dependence. So, we are to solve the following system of linear equation by using gauss elimination row reduction method. Solving simultaneous linear equations using lu decomposition. Comparison of numerical efficiencies of gaussian elimination and gaussjordan elimination methods for the solutions of linear simultaneous equations, department of mathematics m. It is the number by which row j is multiplied before adding it to row i, in order to eliminate the unknown x j from the ith equation. Since we normalize with the pivot element, if it is zero, we have a problem. Eliminate the first term in row 2, then move to the next column and gauss it. It will obviously fail if a zero pivot is encountered. In this section we will reconsider the gaussian elimination approach. Gaussian elimination is summarized by the following three steps. If the optional step argument is supplied, only performs step steps of gaussian elimination. The gaussian elimination algorithm with or without scaled partial pivoting will fail for a singular matrix division by zero. The first step is to write the coefficients of the unknowns in a matrix. To solve such systems, there are direct methods and iterative methods n nnn n. Naive gauss elimination in general, the last equation should reduce to. This function solves a linear system axb using the gaussian elimination method with pivoting. For every new column in a gaussian elimination process, we 1st perform a partial pivot to ensure a nonzero value in the diagonal element before zeroing the values below. Given a matrix a, performs gaussian elimination to convert a into an uppertriangular matrix u. Applications of the gauss seidel method example 3 an application to probability figure 10. Chapter 06 gaussian elimination method introduction to. Introduction to numerical analysis for engineers systems of linear equations mathews cramers rule gaussian elimination 3. Apr 30, 2017 in this question, we use gaussian elimination to solve a system of linear equations using partial pivoting and backwards substitution. Pivoting, partial or complete, can be done in gauss elimination method. If the b matrix is a matrix, the result will be the solve function apply to all dimensions. Can i get the matlab gui implementation of gauss elimination. Apr 19, 2020 as i have mentioned above, there are several methods to solve a system of equations using matrix analysis. The gaussseidel method main idea of gaussseidel with the jacobi method, the values of obtained in the th iteration remain unchanged until the entire th iteration has been calculated. Since here i have four equations with four variables, i will use the gaussian elimination method in 4. Gaussian elimination with partial pivoting applies row switching to normal gaussian. View gaussian elimination research papers on academia. Forward elimination an overview sciencedirect topics. This method reduces the effort in finding the solutions by eliminating the need to explicitly write the variables at each step. Gaussian elimination algorithm no pivoting given the matrix equation ax b where a is an n n matrix, the following pseudocode describes an algorithm that will solve for the vector x assuming that none of the a kk values are zero when used for division. Nonsingularity is implicitly verified by a successful execution of the algorithm. The function accept the a matrix and the b vector or matrix. Course hero has thousands of gaussian elimination study resources to help you. The goals of gaussian elimination are to make the upperleft corner element a 1, use elementary row operations to. Gaussian elimination we list the basic steps of gaussian elimination, a method to solve a system of linear equations. Gaussian elimination, also known as row reduction, is an algorithm in linear algebra for solving a system of linear equations. The reduction of a matrix a to its row echelon form may necessitate row interchanges as the example shows. Uses i finding a basis for the span of given vectors. Motivation partial pivoting scaled partial pivoting gaussian elimination with partial pivoting meeting a small pivot element the last example shows how dif. Applications of the gaussseidel method example 3 an application to probability figure 10. The gauss seidel method main idea of gauss seidel with the jacobi method, the values of obtained in the th iteration remain unchanged until the entire th iteration has been calculated. Gauss elimination and gauss jordan methods using matlab.113 564 878 1412 285 191 1022 613 1152 855 1166 1208 616 1070 1531 403 372 989 456 1428 986 1072 392 793 857 408 1290 207 911 1033 518 715 1106 1259 1525 876 701 636 1463 343 1367 460 1350 542 1096

s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363336.93/warc/CC-MAIN-20211207045002-20211207075002-00014.warc.gz

CC-MAIN-2021-49

http://www.tac.mta.ca/tac/volumes/37/9/37-09abs.html

math

Using full images of accessible functors, we prove some results about combinatorial and accessible model categories. In particular, we give an example of a weak factorization system on a locally presentable category which is not accessible. Keywords: accessible weak factorization system, combinatorial model category, accessible model category 2020 MSC: 18C35, 18N40, 55U35 Theory and Applications of Categories, Vol. 37, 2021, No. 9, pp 266-275. Revised 2021-05-18. Original version at

s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679103464.86/warc/CC-MAIN-20231211013452-20231211043452-00440.warc.gz

CC-MAIN-2023-50

https://www.arxiv-vanity.com/papers/1405.5215/

math

Magnetothermodynamics of BPS baby skyrmions The magnetothermodynamics of skyrmion type matter described by the gauged BPS baby Skyrme model at zero temperature is investigated. We prove that the BPS property of the model is preserved also for boundary conditions corresponding to an asymptotically constant magnetic field. The BPS bound and the corresponding BPS equations saturating the bound are found. Further, we show that one may introduce pressure in the gauged model by a redefinition of the superpotential. Interestingly, this is related to non-extremal type solutions in the so-called fake supersymmetry method. Finally, we compute the equation of state of magnetized BSP baby skyrmions inserted into an external constant magnetic field and under external pressure , i.e., , where is the ”volume” (area) occupied by the skyrmions. We show that the BPS baby skyrmions form a ferromagnetic medium. The Skyrme model skyrme is considered one of the best candidates for an effective model of low energy QCD. Using results from the large expansion, it is known that the proper degrees of freedom in this limit are mesons, while baryons emerge as collective excitations, i.e., solitons called skyrmions, with an identification between baryon number and topological charge. To get phenomenologically precise relations between solitons and baryons (nuclei), one has to perform the standard semiclassical quantization of the spin and isospin degrees of freedom, as well as include the electromagnetic interaction, which obviously contributes to the masses of particles. Fortunately, although the Skyrme model has not yet been derived from the underlying microscopic quantum field theory, its coupling to the electromagnetic field is completely determined by the symmetries and anomalies of QCD wit1 . The resulting gauged Skyrme model is rather difficult to analyse, and the electromagnetic properties of nucleons as well as atomic nuclei, although very important, could not yet be extracted in the full nonlinear Skyrme-Maxwell description. The electric part of the energy of the nuclei is typically approximated by the Coulomb energy Coul , where the back reaction of the Maxwell field on the Skyrme matter field is not taken into account. Let us remark that some first numerical results for the Skyrme model minimally coupled to the electromagnetic field (but without the anomalous or Wess-Zumino-Witten term contribution) have been found in GSk . Further, very recently some knotted soliton solutions have been obtained for the restriction of the minimally gauged Skyrme model i.e., the gauged Faddeev-Skyrme-Niemi model, however within the toroidal ansatz which limits the solutions to the charge sectors shnH . As has been mentioned already, a precise derivation of the Skyrme model (or in fact any effective low energy model) from QCD is one of the most urgent, however still unsolved, tasks in modern theoretical physics. The lack of a systematic derivation means that the precise form of the Skyrme type action is not known. The usual assumption (based on a perturbative approach) restricts the model to three terms: the sigma model part (Dirichlet energy), the Skyrme term (obligatory to avoid the Derrick arguments for the non-existence of static solutions) and a potential (providing a mass for the perturbative pionic excitations). It is, however, one of the main problems of the usual Skyrme model that it leads to unphysical binding energies, which are in strong disagreement with the experimental data. The underlying reason for this is that the usual Skyrme model is not a BPS theory, i.e., the energies of skyrmions are not linearly related to their topological charges. As atomic nuclei seem to be close to BPS objects (the masses are almost linear in the baryon charge with a deviation, at most), the corresponding effective model should be a (near) BPS one. There exist two quite different realizations of this concept. The first proposal is based on the observation that the inclusion of infinitely many vector mesons (Kaluza-Klein modes) can bring the original Skyrme model towards the Yang-Mills action Sut1 , hidden . In the second proposal, the crucial observation is that within all Skyrme type Lagrangians (i.e., with no additional fields) there exists a special one with the BPS property. It has a rather simple form and consists of two mutually balancing terms: a derivative part (the baryon (topological) current squared) and a potential BPS-Sk . Moreover, this model possesses the volume preserving diffeomorphism symmetry, which allows to interpret it as a field theoretical description of the liquid droplet model. In addition, the static energy-momentum tensor of the model is the energy-momentum tensor of a perfect fluid, further strengthening the case for this interpretation. As a consequence, there are infinitely many solitonic solutions saturating a topological bound, which leads to a linear energy - topological charge relation. Therefore, the classical binding energies are zero. Further, finite binding energies have been recently derived by taking into account the semiclassical quantization of the spin-isospin degrees of freedom, the Coulomb interaction as well as the isospin breaking potential. The obtained values are in very good agreement with the nuclear data and the semi-empirical (Weizsäcker) formula, especially for higher nuclei BPS nucl , Marl . This result allows to consider the BPS Skyrme model as a serious candidate for a lowest order approximation of the correct effective model of QCD at low energies, especially for the bulk quantities. In addition to the binding energies, there are many properties of nuclei and nuclear matter which should be understood within the framework of the (near) BPS Skyrme model. It is another advantage of this model that, due to its generalized integrability and BPS nature (solvability), many relevant questions can be answered in an analytical manner. One of the most important ones is related to the thermodynamic and magnetic properties of nuclei and nuclear matter. In particular, an understanding of how BPS skyrmions respond to an external magnetic field and to pressure would provide us with the corresponding equation of state, which is required for the analysis of nuclear matter in various conditions, from heavy nuclei to neutron stars. Unfortunately, even the BPS Skyrme model is quite complicated after the minimal coupling. To overcome the computational difficulties and learn something about the electromagnetic properties of BPS Skyrme type solitons, one can analyze lower-dimensional analogs, as has been done successfully already in many occasions. In fact, there exists a dimensional version of the Skyrme model, usually referred to as the baby Skyrme model, which supports solitonic solutions (baby skyrmions) old -shnir (for the gauged version see GPS , schr1 ). This field theory also possesses its BPS limit, whose Lagrangian consists of the (2+1) dimensional version of the Skyrme term and a potential GP -Sp1 . Moreover, there is again a gauged version of this model, the so-called gauged BPS baby Skyrme model, which has been analyzed recently in the case of an asymptotically vanishing magnetic field BPS-g . It is the aim of the present paper to further investigate baby skyrmions in the gauged BPS baby Skyrme model from the perspective of the equation of state for BPS baby skyrmion matter. In particular, we will focus on the issue of how the energy and volume of the solitons change if they are put in an asymptotically constant magnetic field and exposed to external pressure. The paper is organized as follows. In section II we give a general overview on the gauged BPS Skyrme model. We prove the existence of a topological bound for the regularized energy in the case of a non-vanishing but constant asymptotic magnetic field. The BPS equations saturating the bound are presented. In section III we solve the system for the so-called old baby potential, both numerically and analytically in the weak coupling limit. We find the equation of state and related quantities (magnetic compression, magnetization, susceptibility) and prove a ferromagnetic behavior of the BPS baby skyrmion matter. Then, in section IV we introduce pressure and derive the pressure-modified BPS equations. Section V is devoted to the analysis of the equation of state with nonzero pressure and external magnetic field, again for the old baby potential. In section VI we present a toy model for which the equation of state can be obtained analytically for any value of the electromagnetic coupling constant. Finally, we discuss our results. Ii The BPS baby Skyrme model in a constant magnetic field ii.1 The gauged BPS baby Skyrme model Here we briefly summarize the properties of the BPS Skyrme model coupled minimally with the electromagnetic gauge field. The model is defined by the following Lagrange density BPS-g Without loss of generality we assume that the constant vector and the potential is a function of the third component of the unit vector field . The pertinent field equations are and the inhomogeneous Maxwell equation is The full energy functional is Further, we assume and the standard axially symmetric static ansatz which leads to an identically vanishing electric field and to the magnetic field . Note, that positive (topological charge) corresponds to a negative magnetic field ( is always negative as we will see below), while baby anti-skyrmions (negative ) would lead to a positive magnetic field. Moreover, we are interested in topologically nontrivial matter field (unit vector field) configurations, which requires the appropriate boundary conditions. then provides the topological charge (winding number) of . The field equations can be rewritten as where now and . It is also convenient to introduce the new variable which allows to rewrite the equations as the following system of autonomous second order equations Further, introducing a new target space variable this may be further simplified to where now and . It has been previously found that the model preserves many properties of the original ungauged version GP , restr-bS , Sp1 . First of all, there is a BPS bound which can be saturated by the corresponding BPS configurations. The important assumption in the proof was the boundary condition for the magnetic field that it asymptotically vanishes. Then, the energy is bounded from the below by where the inequality is saturated for the pertinent BPS solutions. Here is the topological charge (winding number) and is the average value of the derivative of the superpotential (see below) over the target space manifold. The resulting BPS baby skyrmions may be of the compacton type with the magnetic field completely confined inside the compact baby skyrmions. Further, the flux is not quantized (except in the large limit). One interesting conjecture, verified in many particular examples, was the absence of gauged BPS baby skyrmions for potentials with more than one vacuum. This strongly differs from the ungauged case where such topological solitons do exist. Secondly, the model is integrable in the sense of generalized integrability gen-int (no conditions for the gauge field) which means that there are infinitely many conservation laws (genuine conservation laws, which are not related to the gauge transformations). Moreover, the static energy functional possesses the area preserving diffeomorphisms as its symmetry group. Therefore, the moduli space of BPS solutions is infinite-dimensional. This also means that our assumed ansatz does not restrict the form of the solutions. One may use the base space area preserving diffeomorphisms to construct solutions with arbitrary (not axially symmetrical) shapes. ii.2 Constant asymptotical magnetic field The problem we want to solve next is how the external constant magnetic field modifies the BPS gauged baby skyrmions originally obtained in BPS-g . Obviously, the field equations remain unchanged but the boundary conditions are different. Now, where the last condition leads to an asymptotically constant magnetic field . Here, can be finite (compactons - for example in the case of the old baby Skyrme potential) or infinite. As the zero boundary conditions played a crucial role for the proof of the existence of the BPS bound, as well as for its saturation by solutions of the BPS equations, it is not obvious whether all these properties survive after the change of the boundary conditions. Here we restrict ourselves to . The corresponding analysis for negative topological charge is straightforward and requires the interchange of to . ii.3 The BPS bound for constant asymptotical magnetic field Here we would like to derive a BPS bound in the case of an asymptotically constant magnetic field. This requires some important improvements in the original derivation. Consider the following non-negative integral where and are (at the moment arbitrary) functions of the field variable . Further, where is a constant equal to the asymptotic value of the magnetic field. Further, the ”superpotential” is a function of the field variable which depends on the potential (see Eq. (II.30)), as we shall see in a moment. The last terms in (II.22) can be written as as the first part vanishes at the compacton boundary where by definition. Then where the superpotential equation relating the potential and the superpotential reads which differs from the expression found in BPS-g for zero asymptotic magnetic field by the term linear in (and in ). By construction, , which leads to . Let us remark that this new superpotential equation can be brought to the form of the original superpotential equation by the following redefinition However, now the boundary conditions for the superpotential are changed. It is convenient to define a regularized energy where we subtract the infinite contribution from the asymptotically constant magnetic field Obviously, the inequality is saturated if which are the BPS equations in the case of a constant asymptotic magnetic field. For the shifted superpotential we get the usual form of the BPS equations It remains to be shown that the solutions of these equations obey the full second order equations of motion, The Maxwell equation follows in the same way as in the case since the derivative of (II.36) does not depend on the value of . Further, from the superpotential equation we get And then we follow the same derivation as in the case. Namely, rewriting the first equation of motion as and using the above formulas we get which is the same as for . The remaining steps: using the covariant derivative definition, use and the definition of , do not depend on . That ends the proof. Finally, let us observe that in the axially symmetric ansatz the BPS equations read or for the shifted superpotential ii.4 The regularized flux Another important quantity is the flux of the magnetic field As the magnetic field extends to infinity the flux will also take an infinite value. However, for compactons, which is the case discussed in the paper, the magnetic field outside the solitons is exactly equal to the external field. Due to that we are rather interested in the value of the flux integrated over the area of the solitons, which is equivalent (up to an additive constant) to the following definition of the regularized flux where the axially symmetric configuration has been assumed. Then, using the definition of the magnetic field and the behavior at the boundary we find It is also possible to prove that this value depends only on the model (coupling constants and the form of the potential) but not on the local behavior of a particular solution. Dividing one BPS equation by the other we find where the constant can be computed from the boundary values of the fields at , Therefore, we get and, specifically at where, by definition, , where the constants depend on the model (potential), It is clear that once or . This behavior is confirmed by numerical results. For the regularized flux we then get where is the ”volume” (area) of the compacton. We use the word ”volume” and the letter to maintain close contact with the standard thermodynamic notation. We already showed that the first part, , may be expressed as a target space integral and, therefore, does not depend on the specific solution . In other words, it is one and the same thermodynamic function for all equilibrium configurations (BPS solutions). In a next step, let us demonstrate that also the ”volume” (and, consequently, the full regularized flux) is a thermodynamic function, i.e., a given function of for all BPS solutions. The BPS equation (II.46) may be re-expressed like where we used (II.58) in the second step. Integrating both sides over their respective ranges leads to and to the regularized flux which, indeed, is a thermodynamic function, as announced. ii.5 The magnetization The thermodynamic magnetization is defined as minus the change of the thermodynamic energy of a sample (in our case, the skyrmion) under a variation of the external magnetic field. Here, the electromagnetic part of the thermodynamic energy must be calculated from the difference of the electromagnetic fields with and without the sample, which precisely corresponds to our definition of the regularized energy, i.e., We use the BPS bound (II.34) for the energy and express the average value of over the target space like where we treated as a function of in the last two terms, which we shall continue to do, i.e., in what follows. The magnetization then is and, obviously, is a thermodynamic function (i.e., the same function of for all equilibrium configurations). In standard thermodynamics there is a simple relation between the magnetization and the difference between full and external magnetic flux in the sample. In our conventions, this relation reads We shall see that this relation continues to hold in our model, although the proof is not trivial and makes use of the BPS nature of the model, specifically of the superpotential equation. Using the variable instead of , the superpotential equation may be re-expressed like To express the first derivative , it is useful to introduce a first order (infinitesimal) shift about a given value , then the magnetization at is and the thermodynamic relation (II.68) becomes The superpotential equation at zeroth order in is and serves to determine for a given , potential and given coupling constants. The first order superpotential equation is (remember that does not depend on ) and serves to determine for a given . Indeed, introducing a new variable the above equation becomes and may be easily solved via the method of the variation of the integration constant, leading to or, in terms of the variable In particular, for we find and was used. From this last result, the thermodynamic relation (II.72) follows immediately. Iii Constant magnetic field and the old baby potential iii.1 Numerical computations The system introduced above significantly simplifies in the case of the old baby Skyrme potential Then the field equations can be integrated to The corresponding energy integral is Effectively, the problem depends on two coupling constants. The dependence on the topological charge can be included into a redefinition of the base space coordinate while a particular value of just fixes the energy scale. So, let us choose and treat and as parameters (now dimensionless) defining different theories. Moreover, the external magnetic field is another free parameter. As in the case we expand the functions at the boundary In the numerical computations we assumed (the results for and are very similar) and then looked for a few different and scanned for a wide range of . Examples of gauged BPS baby skyrmions are plotted in Fig. 1 for different values of the external magnetic field. The electromagnetic coupling constant is . At this point it is useful to remember that the gauged baby BPS skyrmions without external magnetic field have a magnetic field which is everywhere negative (for positive bayon number ) and a negative magnetization proportional to the baryon number BPS-g . In other words, these gauged skyrmions show a ferromagnetic behaviour. For a negative external field we therefore expect that the negative magnetic field will become stronger (i.e., more negative). As the gauge potential for negative magnetic field is restricted to the interval , as follows easily from eq. (II.58), the stronger (more negative) magnetic field is achieved by shrinking the size of the skyrmion. Concretely, for strong negative we approach a singular configuration: the skyrmion profile gets flatter and flatter inside (approximately constant charge density) with a rapid but smooth approach to the vacuum at the boundary whereas has a more and more linear dependence on tending to . In the limit where the size of the compacton goes to 0 as and the solutions approach the step function and a linear function for and , respectively. The approach to the limiting step function solution is faster for higher values of the electromagnetic coupling constant . For high positive values of , the magnetic field changes sign everywhere, and the resulting gauge potential is a simple monotonously increasing function from 0 to . For a positive but sufficiently small , however, the phenomenon of magnetic flux inversion occurs. That is to say, the magnetic field is negative in a ball (because the magnetic field without exterenal field is more negative in the core region), becomes zero at and positive in the shell (because must hold at the compacton boundary). The corresponding gauge potential is, therefore, a decreasing function in the ball close to the center but an increasing function in the shell. Finally, the value of the gauge potential at the compacton boundary determines the total magnetic flux inside the compacton. Specifically, the total magnetic flux inside the compacton may become zero, in constrast to the regularized flux or magnetization, which is always negative for positive baryon number. The baby skyrmion profile is a simple monotously decreasing function for all values of . We show an example of the magnetic flux inversion in Fig. 2. In Fig. 3 and Fig. 4 we show how the compacton size and the compacton energy, respectively, depend on the external magnetic field. iii.2 Non-dynamical constant magnetic field Although the system can be reduced to BPS first order equations it is still too complicated to find analytical solutions. However, one may consider a simplified case where the magnetic field is treated as an external field . That is to say, we do not consider the back reaction of the system on the magnetic field in the vicinity of the BPS baby skyrmion. It has been found, after comparison with the numerical results, that this approximation works quite well and provides an exact description in the small electrodynamical coupling constant limit . iii.2.1 Equation of state and As the magnetic field is only a non-dynamical external field, we may reduce the system to one equation where the magnetic field plays the role of a ”deformed metric” in which baby skyrmions exist. (In fact, curved metrics may arise in some gravitational context grav , which points to another possible application of the BPS skyrmions.) Hence, The resulting equation can be analytically solved for the old baby potential with the boundary conditions where can be finite (compacton) or infinite (usual soliton). However, infinite is excluded by the asymptotic behavior of equation (III.10). Indeed, for large we get that which contradicts the boundary value for at infinity. The final solution is is an equation fixing the size of the compacton. It provides an approximate but exact relation between the two-dimensional ”volume” and the external magnetic field The validity of this approximation is restricted by the following condition which follows from the equation of motion for the magnetic field when the approximated (non-back reaction) solution is inserted. For small magnetic field we may use which agrees with the size of the non-gauged case. For large magnetic field we can use . Thus, i.e., the size of the solution grows linearly with the magnetic field. Next, we consider the energy where . Hence, we find the relation between the total energy and the external magnetic field, however, in an implicit way Equation (III.15) and the last expression are the main results of this section since they provide exact formulas for the and relations in the BPS gauged baby model. iii.2.2 Magnetic compressibility For small magnetic field and the last expression can be computed using the L’Hospital formula In order to find at vanishing we differentiate (III.14) Now, assuming we find that i.e., We plot the numerical results for and for general coupling (i.e., with the backreaction taken into account) in Fig. 5. Then the energy is which agrees with the non-gauged case. On the other hand, for large value of the magnetic field we find that Another consequence of (III.27) is that the magnetic compressibility is finite It is quite interesting that the magnetic compressibility very weakly depends on the electromagnetic coupling constant for a wide range of . In fact, for , see Fig. 6. Hence, the non-backreaction approximation works especially well for the magnetic compressibility. Moreover, we can also obtain the magnetic compressibility for large magnetic field. Now, Hence, asymptotically the magnetic compressibility tends to zero. iii.2.3 Magnetization and ferromagnetic medium Another interesting quantity is the magnetization at vanishing external field, Then,

s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154500.32/warc/CC-MAIN-20210804013942-20210804043942-00111.warc.gz

CC-MAIN-2021-31

http://artofarizona.com/GSFDpaintings.html

math

This Gallery has paintings, photos, prints and colorful notecards. Jewelry     Ceramics & Mirrors Any painting here by Gay Thorson or Judy Thorson VanDerBilt is available as a print or note card, blank inside.   Order individual cards of any painting or photo, or a note card can be made from a photo of any jewelry or ceramic item seen in my other galleries.   Note cards are $1.75 each or purchase 10 cards for $10.   Just call or email me the numbers of the pictures and the quantity you would like.   Order matted prints in 5 x 7 mats (3 x 5 print -$5),   8 x 10 mats (5 x 7 print -$9),   11 x 14 mats (8 x 10 print -$14) or 16 x 20 mats (11 x 15 print -$24).   Quality off-white beveled mats are included FREE with each print. Larger print sizes are available by special order. TOP     CERAMICS     JEWELRY

s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463608642.30/warc/CC-MAIN-20170526051657-20170526071657-00409.warc.gz

CC-MAIN-2017-22

https://studysoup.com/guide/2394659/what-does-scalar-quantity-measure

math

Study Guide Physics 1 - Exam 1 – Feb. 8, 2017 Test will cover Lessons 1-4 + a question from the lab activities: Cars or Freefall and a long answer question from: Freefall and 1D kinematics. 1) S.I. Units and conversions 2.6 Ms = 2.6 X 106 s 12 km = 12000 m 1.7 cm = 0.017 M 3.5 mg = 0.0035 g 0.7 µM = 7.3 X 10 -7 M 55.01 ns = 5.501 X 10-8s 1.06 ps = 1.06 X 10-12 s If you want to learn more check out What are the different oceanic and continental plates? 1 inch = 2.54 cm 1 M = 1 Yard 2 km = 1 Mile 1 thumb width = 2 cm 1 mm = 1 cubic cm 1 mL = 1 cm3 Unit conversion example: Convert 1 m2to cm2 1 m2/1 * (100 cm/1m) * (100 cm/1 m) = 10 000 cm2Don't forget about the age old question of Which type of law involves disputes between private individuals or groups? 2) When solving problems: Diagram with +x or +y direction and origin (or -) List all 6 quantities and the values (unknown and known) Show the physics!! Write down the full equation you intend to use in its original form. Solve the problem and box your final answer. Round answers to 2 decimal places. ∙ The description of motion. ∙ Scalar quantity ∙ Ex: 30 miles ∙ Only a number, with or without units. We also discuss several other topics like Is trade off and opportunity cost the same? ∙ Ex: 30 m/s ∙ Requires magnitude and direction. Average speed = total distance / total time = Distance /change in time Average velocity = total displacement / total time elapsed = r (distance) / change in time We also discuss several other topics like How to get to peace? Displacement = How far is it from its original position. It may have travelled a total of 100 miles, but if it moved 80 miles forward and 20 miles back, the displacement is 60 miles. Average x-component of velocity = change in x / change in t = change in x position / change in time. ∙ Change in time = time final – time initial ∙ Ex: time1 = Distance 1 / Velocity 1 average = mi / (mi/hr) = # hours ∙ Distance / time = miles/hour ∙ Velocity = How fast and in what direction. How far did you get in a given direction and how long did it take you to get there? If you get nowhere and go fast, your x component of velocity is still 0. ∙ Slope of a graph using a given position and time gives velocity. If you want to learn more check out Why is genetic variation in a population necessary for evolution? We also discuss several other topics like What is the concept of yin and yang? ∙ If velocity is 0, the object is not moving. 4) Y = mx+b Slope = rise/run Get your slope from your graph in Excel by using a best fit line on your data and displaying the equation on your chart. Slope remains the same regardless of systematic error. 5) Uncertainty = Error Analysis F. U. (t) = ��(��) The fractional uncertainty of anything is calculated in this manner. The example above is calculating the fractional uncertainty of time. Uncertainty of time divided by time. You must first find your uncertainty in your measurement by deciding what the closest you can read that measurement to, the amount of error in your measurement. When reading a meter stick, that might be 0.2 cm or 0.1 cm. You must calculate your fractional uncertainty for each measurement graphed, seconds and cm for example. Use the biggest uncertainty calculated. Round to 1 significant figure. 6) Know how to calculate Area. ∙ Area = L*W = M2 Area of a rectangle. ∙ �� = ������ Area of a circle 7) Acceleration and 1D Kinematics ∙ Acceleration = the change in velocity over time ∙ Average acceleration = the change in velocity over the change in time ∙ (m/s) / s = m/s2 ∙ X component of acceleration = change in velocity at x point / change in time ∙ Gives the slope Ex: Change in y / change in x ∙ If acceleration is 0, there is no slope. ∙ If the acceleration is going in the same direction as the +x direction, acceleration is positive. ∙ If acceleration is going in the opposite direction of +x or the -x direction, then acceleration is negative. X final = X initial + Velocity initial x * time + ½ acceleration x *time2 ∙ Missing velocity final x X final = X initial + ½ (Velocity initial x + Velocity final x) time ∙ Missing acceleration x Velocity final x = Velocity initial x + acceleration x * time ∙ Missing x final Velocity final x2 = Velocity initial x2 + 2 * acceleration x (x final – x initial) ∙ Missing time If there is only one quantity unknown, choose an equation with that quantity in it and solve using algebra. If there is another quantity missing, choose the equation with that quantity missing and solve for your desired quantity. ∙ Always points at the center of the earth ∙ If the only force acting on an object is gravity, it is in freefall ∙ Acceleration due to gravity = g = 9.8 M/s2 = 32 ft./s2 ∙ Acceleration due to gravity is a magnitude of the vector and is always positive. This is a constant acceleration. ∙ Only direction changes

s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046153791.41/warc/CC-MAIN-20210728185528-20210728215528-00002.warc.gz

CC-MAIN-2021-31

https://guidescroll.com/2013/03/the-hobbit-kom-optimal-tax-guide/

math

The Hobbit: KoM Optimal Tax Guide The Hobbit: KoM Optimal Tax Guide by PeteinSQ This game operates on some very simple maths in terms of population and tax returns. The number of houses you have and their level determines your Population Limit and the Happiness rate equals what percentage of your Population Limit will be filled. For example if your Population Limit was 10,000 and your Happiness rate was 75% you will have a Population of 7,500. So what determines your Happiness rate? It is 100% minus your tax rate, so in the above example the tax rate would have been 25%. The optimum tax rate therefore is 50%. If you had a Population Limit of 10,000 and a tax rate of 50% you would have a Happiness rate of 50%, and a population of 5000 which would generate 2,500 gold in one hour. Whereas if you had a tax rate of 25% you would have a population of 7500 which would only generate 1875 in gold. Once you push the tax rate above 50% the tax take actually starts to fall as your population starts to fall below 50% of your Population Limit. I thinks get a bit more complicated when you’ve got a large army though. Additional Info by Draggin If you set rate to 0, population climbs to 100% of pop. limit. blissfully happy! Upping tax rate to 100% yield equals pop. limit falling to 0 at some rate but not fast. Averages to .5 yield, but then you have to do the reverse, which drops average to the same as the suggested optimal above, .25 for 50% rate. Pop limit = 10,000, rate = 0, yield= 0 Change rate = 100 yield = 10,000 falling to 0, averaging 5,000, I did this to raise gold fast and have little accumulating while away from the game. Less incentive for others to attack me. A few caution. Rate should always be enough to cover Hero salaries, usually 1%. And do not let happiness/population fall below the number of workers you need, (pop – idle)/limit %. Large population increases upkeep cost, which is subtracted from food raised.

s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305317.17/warc/CC-MAIN-20220127223432-20220128013432-00611.warc.gz

CC-MAIN-2022-05

https://houstonarthurbweglein.com/example-439

math

Solve for x solver The solver will provide step-by-step instructions on how to Solve for x solver. So let's get started! Solving for x solver The best way to Solve for x solver is to eliminate as many options as possible. Pythagoras’ theorem states that the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of an adjacent side. The Pythagorean theorem solver can be used to find this value by calculating the length of one leg in terms of the lengths of the other two. The Pythagorean theorem solver can be used to solve simple right triangles with legs and hypotenuse lengths as well as right triangles whose sides are not all equal (other than their length). It can even be used to find values for right triangles whose shape has been distorted, such as when one side has been extended or shortened. The Pythagorean theorem solver can also measure angles from which it can be determined whether or not a given triangle is a right triangle. When inputting values into the Pythagorean theorem solver, it is important to take into account any non-right triangle factors (such as non-integer sides or non-perfect squares) that may affect your results. Values for these factors should be added to your final answer before proceeding. Since it's impossible to solve x by yourself, it's important to work with others to find a solution that works for everyone involved. There are many ways you can go about doing this: You can talk to other people who have had similar experiences so that you can get their perspective. You can also ask them to explain their experience as they see it so that you can understand their point of view. In these cases, you use a graph to show how one variable (e.g. temperature) affects another (e.g. humidity). You can solve graph equations by starting at the origin (0, 0). Graph each variable on the y-axis and see which other variable shows up on the x-axis. For example, if you have temperature in Celsius and humidity in percent, you can solve this by graphing both variables on the x-axis and seeing which variable shows up on the y-axis: C = -5 + 100% => H = 20% + 5°C => H = 20°C/100°C = 5°C => H = 5°C => H = 0.05 If we choose to plot C instead of H, we get C=5+100% => C=-5+200% => C=-125+200% =>C=-25+200% =>=> H=20%. So it’s clear that temperature is controlling humidity in this case While there are several reasons why this could occur, the main culprit is usually inaccurate body weight measurements. While it may be tempting to call this out as a potential error in your paper, remember that this is only one part of a larger investigation. Once you have corrected your data and reanalysed your results, point slope form should not be present. You will be able to find the underlying issue and correct it before publishing your paper. This type of error is hard to detect because it is so small. You can try to make sure that your patients are not underweight or overweight for many reasons: If possible, take an impression of their foot before surgery to get an exact measurement of their leg length. If they are too short, then they will have more difficulty getting into comfortable shoes after surgery. If they are too tall, then they will have more difficulty taking off their shoes when they leave the hospital. The most common way to solve for x in logs is to formulate a log ratio, which means calculating the relative change in both the numerator and the denominator. For example, if your normalized logs show that a particular event occurred 30 times more often than it did last month, you could say that the event occurred 30 times more often this month. The ratio of 30:30 indicates that the event has increased by a factor of three. There are two ways to calculate a log ratio: 1) To first express your data as ratios. For example, if you had shown that an event occurred 30 times more often this month than it did last month, you would express 1:0.7 as a ratio and divide by 0.7 to get 3:1. This is one way of solving for x when you have normalized logs and want to see how much has changed over time. 2) You can also simply calculate the log of the denominator using the equation y = log(y). In other words, if y = log(y), then 1 = log(1) = 0, 2 = log(2) = 1, etc. This is another way of solving for x when you have normalized logs and want to see how much has changed over time. I love the app. It's amazing and being an O levels student, it helps a lot especially when I'm stuck at just silly mistakes but otherwise, I love it. It's a 5/5 experience. Brilliant app. Not sure how I would’ve been able to help my son with his math without it. I LOVE THIS APP! Helps me so much with my Algebra math how. Perfect for people who constantly face problems with understanding the process of solving a particular question. the app goes through the solving steps in an easy-to-understand way. Will always use this!

s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710980.82/warc/CC-MAIN-20221204204504-20221204234504-00592.warc.gz

CC-MAIN-2022-49

http://k12math.com/math-concepts/money

math

Teaching your child about money reinforces the basic number facts of the base 10 number system: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. At first, for younger children, you can count the number of each denomination you have on hand. And, as you move up the currency you can show how each is related to the others. Another important concept to teach here grouping similar coins and bills. One way to reinforce this grouping, is to count more than $2 worth of pennies, nickels and/or dimes. Let your child count until half of the coins have been counted, then distract him/her to read a few pages of his/her favorite book, better if it relates to counting. After that task has been completed, return your child to continue counting the coins. He/she will probably start over, and here is where you step in to show your child how to group the coins in separate piles; doing so makes it easy to return to the task and later to actually find the value of all coins. Notice how I related each denomination to pennies. As your child masters these equivalences he/she will make relationships between the others, like 2 nickels makes a dime. Here we go.... start with a bag of 100 pennies. Use real currency here, you are not doing your child any favors with fake money. Have your child start counting the pennies, as I mentioned earlier. Now interrupt and return. Suggest to you child to place these pennies into separate piles with the same number of pennies in each. 10 is a number familiar to probably every child and is the number to use. Your child already counts 1, 2, 3, ..., 9, 10 and starts over, 11, 12, 13, ..., 19, 20 etc. Interrupt your child again, then return. Point out it is much easier to continue then to start all over again. 10 groups of 10 = 100 = 1 dollar Your child has now separated the pennies into 10 piles of 10. Count these, 10, 20, 30, 40, 50, 60 , 70, 80, 90, 100. Point out if all the pennies are placed in a pile, you wouldn't know there were 100 pennies. We've grouped the pennies into equal piles of 10. Point this out, it is most important. Move the piles next to each other and place a dollar piece next to it (or a dollar bill if you have no dollar piece.) Make the equivalence between the pennies and the dollar. 100 pennies is 1 dollar. As k your child which would be easier to carry around, a bag of 100 pennies or a single dollar coin (or bill). This is still too abstract! What's a penny? What's a dollar? Ok, a "cent" is a "penny." So, in words, if a toy costs 1 dollar and 35 cents, then ask your child how many pennies it would take to buy that toy? Help your child make the connection between the pennies already counted and the price of this toy. Not enough pennies. Now place the dollar piece there and ask your child if there is enough. How many of the pennies would be required with the dollar? How many pennies are left? 10 dimes = 1 dollar Once again, have your child divide the pennies into 10 piles of 10. Ask your child to verify he/she has 100 pennies. Repetition is most important throughout. Now, explain with 10 dimes handy that each dime is the same as each pile of pennies by placing a dime by each pile. Ask your child if the pennies added up to a dollar. Hopefully with the answer yes, then, ask how many dimes add up to a dollar. Help your child arrive to the answer 10. So, help your child make the connection that 10 dimes represents 100 pennies which represents a dollar. Now with the pennies, dimes and dollar, ask your child to pay for the toy mentioned above. Any answer as long as it's correct is fine. For example, use the dollar and 35 pennies. But help your child connect the dimes, the dollar and the pennies to pay for the toy with the dollar, 3 dimes and 5 pennies. 50 cent piece (half dollar) Here we go again, have your child divide the pennies into 10 columns of 10 pennies apiece. Reinforce that 100 pennies in 10 columns of 10 pennies apiece is the same as 1 dollar. Now separate the first 5 columns from the last five columns. Place a 50 cent piece above each group of 5 columns. Explain to your child that each 50 cent piece is 50 pennies. So 2 half dollars is 100 pennies is 1 dollar. Now, ask your child to place the dimes back into the picture, one above each column. then ask, how many dimes are in the half dollar. This time have your child separate the pennies into piles of 5 each. When done, ask how many piles there are. then ask if this makes sense? 10 piles of 10 is 20 piles of 5. this can be hard to grasp, if so, have your child separate into columns of ten, then carefully pull the bottom five pennies from each column a bit below the top five. Now count the groups of 5. Have your child place a nickel by each 5 pennies. And say with your child "5 pennies is a nickel" for each nickel. So 20 nickels represents 100 pennies which is 1 dollar. Recall the half dollar exercise. How many nickels are in the each of the two groups? 10 nickels is a half dollar. Have your child group the pennies in columns of 10 each. Now count the pennies starting from 1 down one column then the next. When your child reaches 25, group those pennies together, then start counting again, 1 to 25. You should have 4 groups of 25 pennies, 2 and 1/2 columns each. Now have your child place a quarter next to each group. So, each quarter is 25 pennies, and 4 quarters are 100 pennies. Now is a good time to have your child relate dimes and nickels to quarters, quarters to half dollars, etc. Ask your child with all of these choices how he/she would pay for that 1 dollar and 35 cent toy. Explore all possibilities. Finally, have your child play play bank teller. Ask your child to convert one denomination to the other. More advance, ask your child to make change for a purchase of some pretend item. Oh, one final note, its fine to tell your child that $1.35 means 1 dollar and 35 cents. That is, the number to the left of the decimal point (dot) is the number of dollars and the number to the right of the dot is the number of pennies. Have fun! And don't try to do this all in one sitting! This takes time!

s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042989018.48/warc/CC-MAIN-20150728002309-00021-ip-10-236-191-2.ec2.internal.warc.gz

CC-MAIN-2015-32

https://www.daviddarling.info/encyclopedia/C/Ceva.html

math

Ceva, Giovanni (1647–1734) Illustrtaion of Ceva's theorem. Giovanni Ceva was a Jesuit-trained Italian mathematician who specialized in geometry. He studied first in Milan and then at the University of Pisa, where eventually he became a professor. In 1686, he was designated as professor of mathematics at the University of Mantua and worked there for the rest of his life. His greatest discovery is the theorem named after him. Ceva's theorem states that three concurrent lines passing through the three vertices of a triangle intersect the sides of the triangles in such a way that the product of three non-adjacent intercepts on the sides is equal to the product of the other three intercepts. Referring to the diagram: AY.BZ.CX = AZ.BX.CY. The term Cevian line was coined by French geometers around the end of the eighteenth century to honor Ceva. It is defined as any line joining a vertex of a triangle to a point on the opposite side. The median, altitude, and angle bisector are all examples of Cevians. The perpendicular bisector, however, in most cases, is not a Cevian because it doesn't usually pass through a vertex.

s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296816879.25/warc/CC-MAIN-20240414095752-20240414125752-00726.warc.gz

CC-MAIN-2024-18

https://www.jiskha.com/display.cgi?id=1332188990

math

posted by running.from.myself . John kept track of all his math and reading test scores throughout the year as shown in the table below. Test 1:90math 80reading Test 2:75math 90reading Test 3:80math 70reading Test 4:90math 75reading Test 5:95math 90reading What is the difference between the median of his math scores and the median score of his reading scores? John made a 100 on his 6th Test in both math and reading. What will the range of his math scores be? What will be the median of his reading scores? 25range 95 median Did the mode of his reading or math scores change after test 6? I don't know this one and I forgot what mode means The subject was suppose to be Math I was helping my brother and I put his name. Sorry 2. Since there are 6 scores, the median of his reading scores is half way between 80 and 90. The mode is the score that is most frequent. For number 2 is it 85? And for the mode question is the answer No? Yes. Both your answers are correct.

s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886133447.78/warc/CC-MAIN-20170824082227-20170824102227-00599.warc.gz

CC-MAIN-2017-34

http://www.amazon.com/Introduction-Topological-Manifolds-Graduate-Mathematics/dp/1441979395

math

- Take an Extra 30% Off Any Book: Use promo code HOLIDAY30 at checkout to get an extra 30% off any book for a limited time. Excludes Kindle eBooks and Audible Audiobooks. Restrictions apply. Learn more. From the reviews of the second edition: “An excellent introduction to both point-set and algebraic topology at the early-graduate level, using manifolds as a primary source of examples and motivation. … The author has … fulfilled his objective of integrating a study of manifolds into an introductory course in general and algebraic topology. This text is well-organized and clearly written, with a good blend of motivational discussion and mathematical rigor. … Any student who has gone through this book should be well-prepared to pursue the study of differential geometry … .” (Mark Hunacek, The Mathematical Association of America, March, 2011) “This book is designed for first year graduate students as an introduction to the topology of manifolds. … The book can be read with advantage by any graduate student with a good undergraduate background, and indeed by many upper class undergraduates. It can be used for self study or as a text book for a fine geometrically flavored introduction to manifolds. One which provides excellent motivation for studying the machinery needed for more advanced work.” (Jonathan Hodgson, Zentralblatt MATH, Vol. 1209, 2011) This book is a clear way to learn manifolds. In my opinion Lee is a great author with a clear knowledge of diferencial geometry. It worth to make this trip.Published on February 8, 2010 by J. Hasbani The only other books I have seen that deserve the title of both a reference and a textbook are by Lang. Read morePublished on June 5, 2008 by Gadjo Dilo I used Lee's 'Introduction to Smooth Manifolds' & 'Introduction to Curvature' for a few months, and I felt like it would be a good idea to complete the collection and acquire some... Read morePublished on April 6, 2008 by Y. Hadad

s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416931009515.14/warc/CC-MAIN-20141125155649-00147-ip-10-235-23-156.ec2.internal.warc.gz

CC-MAIN-2014-49

https://ricthewriter.com/interest-swaps/92959-interest-trades-essay.html

math

International Financial Administration Review on Trades, Solution 1 . The term interest rate exchange A. refers to a " single-currency interest rate swap" shortened to " interest rate swap" M. involves " counterparties" who have make a contractual contract to exchange money flows at periodic intervals C. may be " fixed-for-floating rate" or perhaps " fixed-for-fixed rate" D. All of the above 2 . Suppose the quotation for a five-year swap with semiannual repayments is eight. 50—8. sixty percent. The means: A. The exchange bank will pay semiannual fixed-rate dollar repayments of almost 8. 50 percent against receiving six-month dollar LIBOR. B. The swap traditional bank will receive semiannual fixed-rate dollars payments of 8. sixty percent against paying six-month dollar LIBOR. C. a) and b) D. none of the previously mentioned 3. Company X desires to borrow $10,50, 000, 500 floating to get 5 years; company Sumado a wants to get $10, 000, 000 fixed for 5 years. Their very own external asking for opportunities will be shown listed below: A swap lender proposes this interest simply swap: X will pay the swap bank annual repayments on $12, 000, 1000 with the discount rate of LIBOR - 0. 15%; in exchange the swap financial institution will pay to company Times interest payments on $10, 000, 000 by a fixed rate of 9. 90%. What is the value of this kind of swap to company X? A. Company Back button will lose money on the deal. B. Business X helps you to save 25 basis points per year on $10, 000, 1000 = $25, 000 per year. C. Organization X will simply break even around the deal Deb. Company Times will save your five basis factors per year in $10, 1000, 000 sama dengan $5, 500 per year Firm X can borrow $12, 000, 500 at 10% external for the swap (re-read the question—X needs to raise $10, 500, 000 and prefers to take action at a floating rate). X's all-in-cost will be: 10% + (LIBOR -. 15%) - on the lookout for. 90% sama dengan LIBOR - 0. 05%. This presents a personal savings of your five basis factors over their very own opportunity to get at LIBOR. 4. Company Back button wants to get $10, 000, 000 flying for your five years; business Y would like to borrow $10, 000, 500 fixed pertaining to 5 years. Their external borrowing chances are demonstrated below:...

s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986668569.22/warc/CC-MAIN-20191016113040-20191016140540-00510.warc.gz

CC-MAIN-2019-43

https://topwriteressays.com/the-walk-rite-shoe-company-operates-a-chain-of-shoe-stores-that-sell-10-different-st-4521402/

math

The Walk Rite Shoe Company operates a chain of shoe stores that sell 10 different styles of inexpensive men’s shoes with identical unit costs and selling prices. A unit is defined as a pair of shoes. Each store has a store manager who is paid a fixed salary. Individual salespeople receive a fixed salary and a sales commission. Walk Rite is considering opening another store that is expected to have the revenue and cost relationships shown here: If you want to use Excel to solve this problem, go to the Excel Lab at www.prenhall.com/horngren/ cost12e and download the template for Problem 3-38. Consider each question independently: Required 1. What is the annual breakeven point in (a) units sold and (b) revenues? 2. If 35,000 units are sold, what will be the store’s operating income (loss)? 3. If sales commissions are discontinued and fixed salaries are raised by a total of $81,000, what would be the annual breakeven point in (a) units sold and (b) revenues? 4. Refer to the original data. If, in addition to his fixed salary, the store manager is paid a commission of $0.30 per unit sold, what would be the annual breakeven point in (a) units sold and (b) revenues?

s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358520.50/warc/CC-MAIN-20211128103924-20211128133924-00600.warc.gz

CC-MAIN-2021-49

https://grinebiter.com/Converters/Calc/Deadweight-Long-Tons-to-Kilograms-Converter-and-Formula.html

math

Your can convert any number of deadweight long tons to kilograms by multiplying deadweight long tons by 1016.0469098 to get kilograms. The formula is as follows:| Deadweight Long Tons x 1016.0469098 = Kilograms You do not need to get out your calculator to convert deadweight long tons to kilograms, because we made this easy-to-use Deadweight Long Tons to Kilograms Converter calculator below. Note that the number of kilograms in blue above is rounded to nearest 7 decimals.

s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487586390.4/warc/CC-MAIN-20210612193058-20210612223058-00146.warc.gz

CC-MAIN-2021-25