The reactiondiffusion equations reactiondiffusion rd equations arise naturally in systems consisting of many interacting components, e. Real life applications of the reaction diffusion equation. Heat diffusion equation is an example of parabolic differential equations. It is important to note that the above equation, being a simple mass bal. In this section we go through the complete separation of variables process, including solving the two ordinary differential equations the process generates. These properties make mass transport systems described by. Diffusion of each chemical species occurs independently. General forms of the equations of multicomponent diffusion have been presented. Finite difference method applied to 1d convection in this example, we solve the 1d convection equation. Differential equations department of mathematics, hkust. The general 1d form of heat equation is given by which is accompanied by initial and boundary conditions in order for the equation to have a unique solution. Solution of the heatequation by separation of variables. Fundamental concepts and language diffusion mechanisms vacancy diffusion interstitial diffusion impurities. Martin and banta 1992 investigated the magnitude of macrobenthic irrigation by including a nonlocal source term of the form.
The solution to the 1d diffusion equation can be written as. Pdf a new technology for solving diffusion and heat equations. In this lecture, we will deal with such reactiondi. Pe281 greens functions course notes stanford university. The 3 % discretization uses central differences in space and forward 4 % euler in time. Ficks first law where d is the diffusion coefficient dx dc j. Complete the steps required to derive the neutron diffusion equation 19. The movement of each individual particle moving in a brownian diffuse way does not follow the diffusion equation. Ficks second law of diffusion is a linear equation with the dependent variable being the concentration of the chemical species under consideration. The linearity of the equation 1 now tells us that by superpo. Deturck university of pennsylvania september 20, 2012 d. To satisfy this condition we seek for solutions in the form of an in nite series of.
This equation can be solved by the method of images. The concept of diffusion is tied to that of mass transfer driven by a concentration gradient, but diffusion can still occur when there is no concentration gradient but there will be no net flux. Heat or diffusion equation in 1d university of oxford. Ficks laws of diffusion describe diffusion and were derived by adolf fick in 1855. Note that we need to retain the transverse diffusion d. Friedrich wilhelm bessel 1784 1846 studied disturbances in planetary motion, which led him in 1824 to make the first systematic analysis of solutions of this equation.
What we are really doing is looking for the function ux. This handbook is intended to assist graduate students with qualifying examination preparation. The concept of diffusion emerged from physical sciences. Finite difference, finite element and finite volume. Example % solve the following 1d heat diffusion equation. Each solution depends critically on boundary and initial. L n n n n xdx l f x n l b b u t u l t l c u u x t 0 sin 2 0, 0. In the case of a reaction diffusion equation, c depends on t and on the spatial. In general, the substances of interest are mass, momentum. Two step functions, properly positioned, can be summed to give a solution for.
The advection diffusion reaction equations the mathematical equations describing the evolution of chemical species can be derived from mass balances. Compose the solutions to the two odes into a solution of the original pde. Scattering of particles molecules by random motion due to thermal energy. Garland, professor, department of engineering physics, mcmaster university, hamilton, ontario, canada more about this document summary. Many of the examples presented in these notes may be found in this book. Chapter 7 the diffusion equation the diffusionequation is a partial differentialequationwhich describes density. Here is an example that uses superposition of errorfunction solutions. Included is an example solving the heat equation on a bar of length l but instead on a thin circular ring.
D the concentration gradient is often called the driving force in diffusion but it is not a force in the mechanistic sense. When the diffusion equation is linear, sums of solutions are also solutions. If you want to learn differential equations, have a look at differential equations for engineers if your interests are matrices and elementary linear algebra, try matrix algebra for engineers if you want to learn vector calculus also known as multivariable calculus, or calculus three, you can sign up for vector calculus for engineers. A drop of food coloring diffuses throughout the water in a glass so that, eventually, the entire glass will be colored. The principal ingredients of all these models are equation of the form. One of the most common equations used in predicting binary gas diffusivities owing to its theoretical foundations, is the hirschfelderbirdspotz equation. The material of chapter 7 is adapted from the textbook nonlinear dynamics and chaos by steven. The present paper addresses a new technology combining the vim and an integral transform.
The diffusion equation to derive the homogeneous heatconduction equation we assume that there are no internal sources of heat along the bar, and that the heat can only enter the bar through its ends. Diffusion equation an overview sciencedirect topics. The model is semiinfinite in space, bounded on one side, say at. The first step finding factorized solutions the factorized function ux,t xxtt is a solution to the heat equation. For example, one can use the first term approximation 27, simple physical considerations on heat transfer, and the fact that the solution ux, t is. To fully specify a reaction diffusion problem, we need. As examples, problems of binary mass transfer in stagnant systems and in laminar flow have been solved. Diffusion molecular scattering of particles molecules by random motion due to thermal energy diffusion turbulent scattering due to fluid turbuence.
The multigroup from of the neutron diffusion equation is developed and explored with the aim to. Below we provide two derivations of the heat equation, ut. Dirichlet boundary conditions find all solutions to the eigenvalue problem. This means that we will introduce point sources outside of the domain to satisfy the boundary conditions. A more recent empirical correlation has been developed by fuller. Two step functions, properly positioned, can be summed to give a solution for finite layer placed between two semiinfinite bodies. Heat or diffusion equation in 1d derivation of the 1d heat equation separation of variables refresher worked examples kreysig, 8th edn, sections 11. Diffusion ficks law describes diffusion as the flux, f, of particles in our case is proportional to the gradient in concentration. Like chemical reactions, diffusion is a thermally activated process and the temperature dependence of diffusion appears in the diffusivity as an oarrheniustypeo equation. Solving the heat equation with the fourier transform find the solution ux. As a simple example, we consider the 1d diffusion equation, ut duxx.
Learn how to apply the second law in several practical cases, including homogenization, interdiffusion in carburization of steel, where diffusion plays dominant role. Derivation of diffusion equations we shall derive the diffusion equation for diffusion of a substance think of some ink placed in a long, thin tube. Reaction diffusion equations are members of a more general class known as partial differential equations pdes, so called because they involvethe partial derivativesof functions of many variables. The characteristic equations are dx dt ax,y,z, dy dt bx,y,z, dz dt cx,y,z, with initial conditions xs,0 fs,ys,0 gs,zs,0 hs. Equation 4 gives us a very nice physical interpretation. Introductory finite difference methods for pdes contents contents preface 9 1. Diffusion mse 201 callister chapter 5 introduction to materials science for engineers, ch. Numerical simulation of groundwater pollution problems based. The minus sign in the equation means that diffusion is down the concentration gradient. Then assume that advection dominates over diffusion high peclet number. Reaction diffusion equations are important to a wide range of applied areas such as cell processes. In other words, we assume that the lateral surface of the bar is perfectly insulated so no heat can be gained or lost through it.
Reactiondiffusion rd equations arise naturally in systems consisting of many interacting components, e. Ficks first law can be used to derive his second law which in turn is identical to the diffusion equation a diffusion process that obeys ficks laws is called normal diffusion or fickian diffusion. Figure 1 mass transport, diffusion as a consequence of existing spacial differences in concentration. In a quasilinear case, the characteristic equations fordx dt and dy dt need not decouple from the dz dt equation. It deals with the description of diffusion processes in terms of solutions of the differential equation for diffusion. Sometimes, one way to proceed is to use the laplace transform 5. The dye will move from higher concentration to lower. Special attention has been devoted to the coupling of diffusion with chemical reaction in a porous catalyst pellet. Examples of diffusion perfume is sprayed in one part of a room, yet soon it diffuses so that you can smell it everywhere. For obvious reasons, this is called a reaction diffusion equation. The heat equation homogeneous dirichlet conditions inhomogeneous dirichlet conditions remarks as before, if the sine series of fx is already known, solution can be built by simply including exponential factors. Laplaces equation separation of variables two examples laplaces equation in polar coordinates derivation of the explicit form an example from electrostatics a surprising application of laplaces eqn image analysis this bit is not examined. Therefore i deal with a spatially onedimensional problem, and my density.
Similarity solutions of the diffusion equation the diffusion equation in onedimension is u t. Ficks second law todays topics learn how to deduce the ficks second law, and understand the basic meaning, in comparison to the first law. The above diffusion equation is hardly solved in any general way. The paradigmatic examples were heat diffusion, molecular.
A second order cauchyeuler equation is of the form a. The diffusion equation is a partial differential equation which describes density. If we are looking for solutions of 1 on an infinite domainxwhere there is no natural length scale, then we. Real life applications of the reactiondiffusion equation. The convectiondiffusion equation is a combination of the diffusion and convection equations, and describes physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes. Reactiondiffusion equation an overview sciencedirect topics. In this problem, we assume that the seepage area is an infinite plane, and the groundwater flow is a onedimensional one, the diffusion of pollutants is a two dimensional dispersion, and the medium is a porous medium. Could you please point me to real life applications with complete model and description to its details. The solution 3 can be interpreted as the temperature distribution within the body due to a unit sourse of head speci. Reactiondiffusion equation have been applied in many areas of specialization for example, in developmental biology ref alan turing work, neuroscience ref hodgkinhuxley work on action. They can be used to solve for the diffusion coefficient, d. We will do this by solving the heat equation with three different sets of boundary conditions. Little mention is made of the alternative, but less well developed.1194 95 1490 229 653 87 621 870 640 981 872 904 58 451 1236 402 1451 159 679 636 1601 398 1149 214 1415 1490 511 84 1333 101 269 235 444 353 194 3 670 1479 1434


Measuring of Thread Consumption in a Garment
Measuring of Thread Consumption
It is important to know the amount of thread consumed in a sewn product so you can: 1) Estimate the number of cones needed; and 2) Calculate the cost of the thread needed to manufacture the finished product. Thread consumption can be determined in several ways. To calculate the amount of thread in a seam, you can:
- Measure the actual amount of thread consumed in a specific length of seam.
- Calculate the thread consumption by using mathematical stitch formulas based on the thickness of the seam and the number of stitches per inch.
Measuring Actual Thread Consumed
A specified length of the seam, for example 3 inches, is measured and then the thread is removed by carefully unraveling the stitch. You can then calculate the amount of thread consumed in one inch and multiply this factor times the total length of the seam measured in inches.
To define thread consumption you just have to multiply seam length with that factors. Thus, one can estimate total requirement of thread for making a garments. But actual thread consumption for a unit length of seam depends on many factors.
- Stitch Classes
- Stitches per inches (SPI)
- Thickness of the seam (fabric thickness)
- Thread tension
- Thread count (thickness of sewing thread)
- Length of seam is 42 inches or 1.17 yards.
- Stitch and seam construction: 401 SSa-1.
- Specified length of thread removed from a seam equals 3 inches.
- Needle thread removed = 9 inches
- Looper thread removed = 8 inches
- Needle thread factor = 9 ÷ 3 = 3 inches of needle thread per inch of seam.
- Looper thread factor = 8 ÷ 3 = 2.67 inches of looper thread per inch of seam.
- Total needle thread consumed = factor 3 X 1.17yds = 3.51 yds
- Total looper thread consumed = factor 2.67 X 1.17yds = 3.12 yds
- Total Thread = 3.51 + 3.12 = 6.63 yards per seam.
- Generally a 10 to 15% waste factor is added due to chaining-off, thread breaks, repairs, etc.
- If a waste factor of 15% is selected then:
- 6.63 yards/seam X 1.15 = 7.62 yards/seam including 15% waste factor.
Obviously you must do this for each seam to determine the total amount of thread consumed in the finished product.


What is the Additive Inverse of the Polynomial –9Xy2 + 6X2Y – 5X3?
The additive inverse of the polynomial –9Xy2 + 6X2Y – 5X3 is 9Xy2 – 6X2Y + 5X3. Polynomials are mathematical expressions containing variables and coefficients.
The additive inverse of a polynomial is found by changing the sign of each term within the polynomial. In this case, the additive inverse of the given polynomial -9Xy2 + 6X2Y – 5X3 is 9Xy2 – 6X2Y + 5X3. Understanding the concept of additive inverses is crucial for algebraic manipulation and solving equations.
By learning how to find the additive inverse of polynomials, one can effectively perform mathematical operations and simplify expressions. This skill is particularly relevant in advanced algebra, calculus, and engineering disciplines. So, let’s delve into the process of finding the additive inverse of polynomials and its significance in mathematical problem-solving.
To find the additive inverse of the polynomial –9Xy2 + 6X2Y – 5X3, we simply change the sign of each term. Therefore, the additive inverse of this polynomial is 9Xy2 – 6X2Y + 5X3. By understanding the concept of additive inverses, we can easily manipulate polynomials and solve mathematical problems.
Keep practicing and exploring to improve your polynomial skills.


Visualize the third derivative as the "jerk" of a function, revealing how quickly the rate of change changes. It's similar to measuring the abrupt shifts in velocity and is crucial for comprehending intricate data variations.
Inflation, in itself a derivative, represents the speed of your money's purchasing power decline. When we delve into the rate of inflation's increase, we're essentially examining its derivative, which has an opposite sign to the second derivative of purchasing power. Think of it as unveiling the curve's trends in concavity or convexity, providing a more precise view of financial data. These advanced derivatives enhance our analytical accuracy, allowing us to navigate economic intricacies effectively.


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The max-cut problem is an NP-hard combinatorial optimization problem defined on undirected... mehr
Produktinformationen "Contraction-based Separation and Lifting for Solving the Max-Cut Problem"
The max-cut problem is an NP-hard combinatorial optimization problem defined on undirected weighted graphs. It consists in finding a subset of the graph's nodes such that the aggregate weight of the edges between the subset and its complement is maximized. This book deals with a new separation approach to be used within a branch-and-cut algorithm for solving max-cut problems to optimality. The method is based on graph contraction and allows the fast separation of so-called odd-cycle inequalities. In addition, we describe techniques to add possibly missing edges to an already contracted graph. This allows solving max-cut problems on sparse graphs by means of methods that were originally intended for complete graphs and could not have been applied otherwise. We investigate the theoretical aspects of this combined approach and also explain its realization within a branch-and-cut framework. Finally, we evaluate the performance of our separation procedure on a variety of test instances.


A few weeks back, Nina Stössinger asked on Twitter:
Isn’t it odd that the percent sign looks like “0/0” rather than, say, “/100” or “/00”?
This, it turns out, is a very good question. Like Nina, I had assumed that the percent sign was shaped so as to invoke the idea of a vulgar fraction, with a tiny zero aligned on either side of a solidus ( ⁄ ), or fraction slash. That said, something about those zeroes had always nagged at me. Specifically, as you divide any non-zero quantity by a smaller and smaller number the result tends ever closer to infinity (or rather, ±∞ as appropriate), until finally, when dividing by zero itself, you reach a mathematical singularity where the result cannot be computed — a numerical black hole of exotic properties and mind-bending implications. Throw in another zero as the numerator and you have a thoroughly nonsensical fraction. Though this is all terribly exciting from a philosophical point of view, it is not an especially useful situation to be in when trying to communicate the simple concept of division into hundredths. Either the ‘%’ had stumbled, blinking, from some secret garden of esoteric mathematics and into the real world, or there was more to the story. And so there was.
Writing in 1908, David Eugene Smith, later to be president of the Mathematical Association of America,1 reported on a peculiar find he had made in an Italian manuscript written sometime during the early part of fifteenth century. (Smith was cataloguing the mathematical holdings of one George Arthur Plimpton, a publisher and philanthropist who had amassed a huge library of ancient books.) What had caught Smith’s eye was an oddly attenuated abbreviation comprising a ‘p’, an elongated ‘c’, and a superscript ‘o’, or ‘o’, balanced upon the extended upper terminal of the ‘c’, as seen at top. From its context, Smith deduced that pco was a stand-in for the words per cento, or “per hundred”, more often abbreviated to per 100, p cento, or p 100.2 It was the first step towards a distinct percent sign — and, counterintuitively, it had precisely nothing to do with the digit zero.
Smith picked up the trail with his weighty two-volume History of Mathematics, published in 1923,3 wherein he printed an image of the percent sign caught midway between pco and ‘%’. Taken from an Italian manuscript of 1684, as seen above, by now the word per had collapsed into the tortuous but common scribal abbreviation seen here while the ‘c’ had morphed into a closed circle surmounted by a short horizontal stroke. The imperturbable ‘o’ sat atop it. All that remained was for the vestigial per to vanish and for the horizontal stroke to assume its familiar diagonal orientation — a change that occurred sometime during the nineteenth century — and the evolution of the percent sign was complete.
Since then the ‘%’ has gone from strength to strength, and today we revel in a whole family of “per ————” signs, with ‘%’ joined by ‘‰’ (“per mille”, or per thousand) and ‘‱’ (per ten thousand). All very logical, on the face of it, and all based on a fundamental misunderstanding of how the percent sign came to be. Nina and I can comfort ourselves that we are not the first people, and likely will not be the last, to have made the same mistake.
- Benjamin Fite W, “[Obituary]: David Eugene Smith”, 1945. ↢
- David Eugene Smith, Rara Arithmetica; A Catalogue of the Arithmetics Written before the Year MDCI, With Description of Those in the Library of George Arthur Plimpton, of New York, 1908. ↢
- David Eugene Smith, History of Mathematics, 1923. ↢


There's a good chance you have heard that people have won the lottery by using math. That's right, math. Many people have won the 4d results lottery by using the Mandel algorithm. This is because the first number drawn has a one in 49 chance of matching the six numbers on a lottery ticket. However, the study shows that not all combinations of numbers have the same probability. As such, if you use math to predict the numbers you're more likely to win, you can increase your chances of winning.
While lottery mathematical systems aren't foolproof, there's a good chance they've helped people win the lottery. Stefan Mandel, an economist and prolific mathematician, won the lottery twice using this strategy. In fact, his first win allowed him to move his family to Israel and start a business offering lottery consulting services. His second win allowed him to win a total of $13.8 million.
Regardless of whether someone has won the lottery by using mathematics, the numbers don't necessarily match up. While some numbers are better than others, some of these numbers don't match up. That's where a computer can help. You can buy a large number of tickets and put them in a portfolio to reduce your risk. Ultimately, you can choose numbers that are more likely to fall into a pattern.
The idea behind this system isn't all that unusual. Inventor Stefan Mandel is credited with winning 14 times in his heyday. While he didn't break any laws, his formula was near-perfect and allowed him to establish five different numbers in a series of steps. In the end, the method has worked for him. So, it's a good thing that math isn't the only way to win the lottery!
While you might not believe this, the formula was developed by a Romanian economist named Stefan Mandel. In a six-step process, he was able to hack the lottery system and win a million dollars. This method has since been outlawed in Australia, but Stefan Mandel's success is still worth considering. It's not just the math that works. You'll need to buy a lot of lottery tickets and do some math. You'll need to do some calculating.
The only way to win the lottery using math is to buy more tickets. Statistically, the odds of winning a jackpot will increase with more money, and you should always buy a lot of tickets. If you're lucky enough to win the jackpot, you should follow the mathematical formula. That's how the hypergeometric distribution works. Essentially, if you have the same winning numbers as the lottery, you'll have a higher chance of winning.


Hi ZS, assuming that whether or even otherwise one wins or loses on one scratch ticket (what is that, either way?) is independent from winning or losing on various other scratch ticket, you treat each event as a self-sufficient event. Laws of probability tell us to multiply the various probabilities of independent affairs. It appears that the probability of [losing] on any particular scratch ticket must be 2/3. Useful and obviously the probabilities of [losing] on 30 scratch tickets in a row (if it is exactly what your issue is asking) should be (2/3)^30 = approximately your own.2 x 10^-6, which is about.0000052, or 52 coming from 10 million, which comes down to 1 chance out of 192,307.
This software works to be a lotto number generator. It is able to gather all of the online lottery winning numbers in the past 30 days. And then, it will observe its patterns and help to make suggestions about what numbers or combinations which best to locate a bet on.
The Powerball lottery calculations are by a 1/59 for your first five white balls and 1/39 for the “red” power ball. The first set of multipliers is 59x58x57x56x55. This group totals 600,766,320. Now divide 600,766,360 by 120 (1x2x3x4x5). Your new total is 5,006,386. Is actually a 1/39 chance to catch the “red” ball. 39 x 5,006,386 gives you the real chances of winning the Powerball Jackpot, namely 195,249,054 to 10.
A life secret that few people recognize mainly because are likely to live longer than they wonder if. Life Insurance companies have seen this. They used to believe that not a soul lived past age a person hundred. Now 먹튀폴리스 has been raised to 125. Couple of people is equipped to sustain an appropriate life for 25 or more years more than their their parents. A online lottery website winner would obtain the chance to complete a comfortable life a good age unthinkable a year or two ago.
If dedicate too much, that may put stress to the united states situation. On the other hand, ought to you spend too little on your lottery game, your chances of winning the lottery were greatly reduced. So, you must draw a balance in this respect.
As now you can see each time a ball is released from the drum the odds are reduced by one. You began with a 1/56 chance, then with every new winning number may be reduced to 1/55, 1/54, 1/53, and with the fifth ball you own the odds of 1/52 correctly matching this fifth winning number. This can be a first primary formula of how to calculate your likelihood of winning the lottery, including the Florida Lottery.
Before I get any product or join any site, the first thing that I do now would be look to have review or scam report on that product or webpages. I don’t read just one of which and then my pick. I read all of them that are offered. Write out a report on your questions before then reading. A person do your reading, positive you that all of your questions gets answered. Check off have confidence in as soon as you see the response. Don’t stop reading until each question is answered. Whenever you have gotten all with the answers, could be within a much better position to find lottery pool that is the most suitable for you.


Title, Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization. Booktitle, Advances in Cryptology – CRYPTO ’99, 19th Annual International. Download Citation on ResearchGate | Cryptanalysis of the HFE Public Key Finally, we develop a new relinearization method for solving such systems for any. Finally, we develop a new relinearization method for solving such systems for any constant ffl? Cryptanalysis of the HFE Public Key Cryptosystem ().
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Therefore, we cannot hope to derive linearization equations from the modified HFE scheme. Forwe set where all the coefficients are relinearizatikn for. In this paper we consider Patarin’s Hidden Field Equations HFE scheme, which is believed to be one of the strongest schemes of this type.
Algebraic Cryptanalysis of GOST Encryption Algorithm
The computational costs are at least bit operations, according to the results given on page in [ 2 ]. Table of Contents Alerts.
We denote the inverse of map as. We analyze the security of the proposed Cryptosystrm modified encryption scheme. Symmetric-key algorithm Block cipher Stream cipher Public-key cryptography Cryptographic hash function Message authentication code Random numbers Steganography.
We observe relinearuzation the equation can be used to further destroy the special structure of the underlying central map of the HFE scheme. The construction admits a standard isomorphism between the extension field and the vector space ; namely, for an elementwe have.
So under the algebraic attacks, the proposed modification HFE encryption scheme can obtain a security level of 80 bits under the suggested parameters. Performance and Comparisons To make a comparison between the proposed HFE cryptoosystem and the original HFE schemes in a uniform platform, we consider the HFE scheme defined over and its extension field.
Building Secure Public Key Encryption Scheme from Hidden Field Equations
Advanced Search Include Citations. Algebraic Attacks Basic Idea. We define the quadratic part of asnamely, forNote that can be expressed as homogeneous quadratic polynomials over the base field ; then cryptosyatem application of two linear transformations on the input and output of will also relinearisation homogeneous quadratic polynomials over the base field.
The plain version of HFE is considered to be practically broken, in the sense that secure parameters lead to an impractical scheme. We represent the published system of multivariate polynomials by a single univariate polynomial of a special form over an extension field, and use it to reduce the cryptanalytic problem to a system of fflm 2 quadratic equations in m variables over the extension field.
Please help ceyptosystem this section by adding citations to reliable sources. However, some simple variants of HFE, such as the minus variant and the vinegar variant allow one to strengthen the basic HFE against all known attacks. Then we merge the coefficients of the square and linear terms ofthat is, forand get the public key of the modified HFE scheme, namely, quadratic polynomialswhere, telinearizationThe secret key consists of, and.
J-GLOBAL – Japan Science and Technology Agency
Firstly, we define an HFE map in 1 and randomly choose two invertible affine transformations and. Multivariate cryptography has been very productive in terms of design and cryptanalysis. The plaintext space is. The original HFE scheme [ 5 ] works on any field and its extension.
So the computational overhead is about bit operations. Then two invertible affine transformations are applied to hide the special structure of the central map [ 25 ]. By doing this, we can impose a fully nonlinear transformation on the central map of reilnearization HFE encryption scheme.
Unsourced material may be challenged and removed. In addition to HFE, J. Linearization equations attack [ 18 ] was found by Patarin on the Matsumoto-Imai scheme [ 19 ]. The proposed method is a universal padding scheme and hence can be used to other multivariate cryptographic constructions. Security We analyze the security of the proposed HFE modified encryption scheme.
Thus we have some additional equations that associate with the plaintext ; namely, forwe have. Note thatresp.
The modified HFE decryption recovers the plaintext by peeling off the composition one by one from the leftmost side. Retrieved from ” https: Notations Let be a -order finite field with being a prime power. Thus we can easily verify that So we get.
The encryption scheme consists of three subalgorithms: Linearization Equations Attack Basic Idea. Note that the Frobenius maps for defined over are -linear; namely, when expressed in the base fieldwill be -dimensional linear functions over.
However, we can derive the field equations from the equations. Solving systems of multivariate polynomial equations is proven to be NP-hard or NP-complete.


The Florida Standard Assessments (FSA) measures Florida students in K through 12th grade on achievement of Florida’s education standards. Assessments are in the areas of English Language Arts, Mathematics and End-Of-Course subjects of Algebra 1, Algebra 2 and Geometry. They ensure that all students graduate from high school with the tools to be successful in college, career and life as well as measuring each student’s gains and progress throughout their academic career.
Students in grades 3rd through 10th will take the English Language Arts Reading assessments with students in grades 4th through 10th also participating in the English Language Arts Writing assessment. Students in grades 3rd through 8th will participate in the Mathematics assessment. If a student has completed an Algebra 1, Algebra 2 or Geometry class, they will take that corresponding assessment in lieu of the grade-level math version. The assessments are administered over two days and range in time from in length from 160 to 180 minutes, broken out into shorter sessions.
The Miami center has abundant experience in preparing students for their FSAs, practicing questions, evaluating responses and results and providing personalized training. We understand how important the FSA for your student’s educational career and can help prepare your child to succeed. Just like our other preparation classes, the FSA prep classes are relatively small to provide focused attention. Space is limited, so we encourage you to make your reservation as soon as possible.


Q. Where do I find discount rates for a multi-year analysis?
If you are in an organization that has a dedicated finance person, you may be able to speak with him or her about the appropriate discount rate to use for calculations of the time value of money. If not, some searching may be necessary. You may find that you need to use different discount rates for capital purchases than for your human resources or materials purchases. The cost of capital will typically be known either by your financial analyst or manager, or by whoever purchases IT infrastructure. You can sometimes calculate an appropriate rate for human resources by looking at the historical inflation on salaries.
Ernst & Young Global Insurance Center. Discount Rates: One Size Does Not Fit All. http://www.ey.com/Publication/vwLUAssets/Key_components_of_discount_rates_for_insurance_contracts/$FILE/EY_Discount_rates_Oct_2011.pdf
Provides detailed information about interest rates and determining the appropriate discount rate when conducting multi-year financial analysis.
Tredinnick, Steve. Don't Discount the Discount Rate.http://www.syska.com/cms/docs/articles/STredinnick.DistrictEnergy_01.25.12.pdf
Another article from a financial consultant about different ways to calculate the discount rate.
wikiHow to do anything. [website] How to Calculate NPV. http://www.wikihow.com/Calculate-NPV
Provides a very simple method for calculating the net present value of money for multi-year financial analyses.
Last updated on 08/26/13, 9:28 pm by callee


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- Intake : January, May, September
Specification: Foundation in Science


Due to powerful geometry treatment capability, Method Of Characteristics (MOC) currently becomes one of best method to solve neutron transport equation. In MOC method, boundary condition treatment, complex geometry representation, and advanced acceleration method are the key techniques to develop a powerful MOC code to solve complex problem. In this paper, we developed a powerful MOC module, which can treat different boundary conditions with two methods. For problems with special border shapes and boundary condition, such as rectangle, 1/8 of square, hexagon, 1/6 of hexagon problems with reflection, rotation, and translation boundary condition, the MOC module adopts periodic tracking method. For problems with general border shapes, the MOC module use ray prolongation method. Meanwhile, graphic user interface based on CAD software is developed to generate the geometry description file. The geometry and mesh can be described and modified correctly and fast. In order to accelerate the MOC transport calculation, the Generalized Coarse Mesh Finite Differential (GCMFD) is used, which can use irregular coarse mesh diffusion method to accelerate the transport equation. The MOC module was incorporated into advanced neutronics lattice code KYLIN-2, which developed by Nuclear Power Institute of China (NPIC) and used to simulate the assembly of current PWR reactor and advanced reactors. The numerical results show that the KYLIN-2 code can be used to calculate 2D neutron transport problems accurately and fast. In future, the KYLIN-2 code will be released and gradually become the main neutron transport lattice code in NPIC.


Bayesian methods for the design and interpretation of clinical trials in very rare diseases.
Bottom Line: For such studies, the sample size needed to meet a conventional frequentist power requirement is clearly infeasible.A systematic elicitation from clinicians of their beliefs concerning treatment efficacy is used to establish Bayesian priors for unknown model parameters.As sample sizes are small, it is possible to compute all possible posterior distributions of the two success rates.
Affiliation: Medical and Pharmaceutical Statistics Research Unit, Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, U.K.Show MeSH
Related in: MedlinePlus
Mentions: where h1(y),h2(y),h3(y) and h4(y) are the densities of Beta(a, b), and random variables, respectively, evaluated at y. The link parameters introduce correlations between pCR and pC and pER and pE so that under the proposed model, the related data help us learn about remission rates in both trials. However, because there is uncertainty about the precise relationships between parameters in each trial, the related data are discounted for learning about pC and pE. Using Bayes theorem to combine prior beliefs with the related data, we obtain the joint distribution for pE and pC as (2) capturing the state of knowledge about pC and pE before the MYPAN trial is conducted. The marginal prior density for θ can be found by applying a transformation of variables to Equation (2). Prior distributions for parameters incorporating the MYCYC data are not of standard forms. Figure 3 shows densities for pC, pE and θ that result from updating prior distributions pC ∼ Beta(3.6, 2.1) and θ ∼ N( − 0.26,0.25) with the MYCYC data for the consensus responses to questions about λC and λE, which were as follows: (a) 0.55, (b) 0.25, (c) 0.5 and (d) 0.25. According to these responses, λC ∼ N(0.12, 0.86) and λE ∼ N(0,0.60), consistent with the opinion that remission rates on CYC might be slightly higher in adults with ANCA-associated vasculitis than in children with PAN but that remission rates on MMF would be similar in these two populations. Incorporating the MYCYC data shifts the location of the prior for pC only slightly, as the MYCYC remission rate is similar to the mode of the prior elicited without reference to these data. The updated prior for pC has mode 0.74, mean 0.70 and standard deviation 0.11. The location of the prior for pE increases upon inclusion of the MYCYC data as is larger than the mode of the day 1 prior, and expert opinion indicates that remission rates in the MYCYC and MYPAN patient groups are likely to be similar. The updated prior for pE has mode 0.71, mean 0.67 and standard deviation 0.12. Incorporating the MYCYC data has clearly reduced uncertainty about the absolute remission rates on the two treatments: 90% credibility intervals for pE and pC are (0.45, 0.85) and (0.51, 0.86), respectively. The related data have less impact on the prior for θ because beliefs about θ were already rather precise before their inclusion.
Affiliation: Medical and Pharmaceutical Statistics Research Unit, Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, U.K.


At Graveney Primary School our Maths curriculum aims (of the national curriculum for mathematics are) to ensure that all pupils:
become fluent in the fundamentals of mathematics, including through varied and frequent practise with increasingly complex problems, so that the pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
reason mathematically by following a line of enquiry, predicting and testing relationships and generalisations; and developing an argument, justification or proof using mathematical language.
can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.
The focus of our mathematics lessons will be the teaching of skills, methods and facts to enable pupils to solve problems. The children will be required to learn number facts with quick recall, so that when learning new methods they can concentrate on the process. The number facts they need e.g. times tables should not hinder their development. The children will be given time to practise skills so they become fluent in calculation methods and other mathematical skills e.g. using a protractor. However our focus will be on enabling children to use these skills to solve problems, as we feel there are limited reasons for children knowing how to do something if they do not understand when it is appropriate to use it. The expectation will be that children can explain their mathematical thinking; maths lessons should not always be quiet lessons, but interactive and fun, with children engaged in tasks, sharing ideas and solving problems.
Alongside the lessons we also have a Guided Maths session daily. This session enables the children to further engage in mathematics by working individually or in groups through mathematic challenges, games, activities and focused work to increase or extended their understanding of the week’s focus.
While paying close attention to the whole mathematics curriculum, the priority in the classroom will be number work, taking up about 75% of the time. However the children will also cover work on shape, data handling and measures.


Relative Armor Calculator
By Christian Ankerstjerne
You can use the form below to calculate the relative armor thickness of a sloped armor plate.
You can specify two angles. If you specify only one, leaving the other at 90, the direct relative armor thickness will be calculated. If two angles are specified, a compound angle will be calculated. This is useful for simulating a vehicle with sloped armor that is shot at from an angle, or a vehicle with armor plates sloping in more than one dimension.
The default sine option measures the angle in degrees from the angle of the incoming shot. In other words, 90 degrees is vertical, and 0 degrees is horizontal. The cosine option use the angle of the slope of the armor plate from vertical.
You can use the calculation type option to change from the normal calculation, which calculates the relative thickness based on the actual thickness and a slope, to a reverse calculation, which calculates the actual thickness based on a known, relative thickness and slope.
Note that the armor thickness must be entered without the unit, e.g.,
100 rather than
100 mm. Fractions must be converted to decimal numbers, e.g., 0.375 rather than ⅜.
- Relative armor thickness
- Information about the importance of sloped armor on armored vehicles.


On this page, the Math Factory Working Group collects information concerning similar institutions. There are mathematics museums in other countries, other institutions in the U.S. with mathematics content, and traveling exhibitions devoted to mathematics.
Interactive mathematics museums abroad
Mathematikum. Giessen, Germany. mathematikum.de
This hands-on museum dedicated to mathematics contains roughly 100 interactive exhibits in 10,000 square feet of exhibit space, ranging from simple geometric puzzles to mathematical sculptures to a display in which one writes a musical composition by rolling dice. It serves as a wonderful demonstration of what an interactive museum of mathematics can be, and should serve as a model for us. Areas MoMath might consider differentiating on are the integrated use of technology, and the connection of the exhibits together thematically and with traditional curriculum topics so that visitors obtain a better understanding of what mathematics is and why it is both important and fun.
Math museum in Seoul Korea.
This wonderful hands-on interactive math museum was founded by Chang Hoon. They sell exhibits at their website, http://mathlove.com
The Garden of Archimedes, Florence, Italy. web.math.unifi.it/archimede
This beautiful museum of mathematics has three main permanent galleries, devoted to the mathematics of curves, to the Pythagorean Theorem, and the history of mathematics from the Islamic world through Renaissance Italy to the modern world.
- Mathematics Adventure Land, (Erlebnisland Mathematik), Dresden, Germany.Â http://www.math.tu-dresden.de/alg/erlebnisland/en/start.html Hands-on museum with over 100 interactive exhibits.
Arithmeum, Bonn, Germany, http://www.arithmeum.uni-bonn.de/en/
Historical calculating machines and historical arithmetic books dating back to Gutenberg's times.
MiMa, Museum for Minerals and Mathematics Oberwolfach, http://www.mima.museum/museum.php
Originally just minerals, has branched out into mathematics in part because of the world-renowned math conference center in Oberwolfach. Creator of the math exhibit "Imaginary".
- Mathemuseum Stams, Austria http://mathemuseum.org
- Haus der Mathematik, Vienna, Austria http://www.hausdermathematik.at/
The Mathematics Museum (Japan). mathmuse.sci.ibaraki.ac.jp/indexE.html
Another interactive museum dedicated to mathematics, this one has a much more elaborate web site in terms of mathematical content, although less information (at least on the English pages) about the museum itself.
- MMACA: Museu de MatemÃ tiques de Catalunya, http://www.mmaca.cat/, photos: http://picasaweb.google.com/Josep.Rey/Mmaca2009?authkey=Gv1sRgCPPAp-mTu-39ywE&feat=directlink#
Mathematics Palace, BorÃ¥s, Sweden. http://www.navet.com/sida.aspx?id=1080
This appears to be a portion of a larger science center in Sweden, but nevertheless a sizable portion (500 square meters, or roughly 5000 square feet) of exhibition space devoted exclusively to mathematics.
Magical Mathematics Museum, Calgary, CA. gamesbygord.blogspot.com
This museum proposal by Gordon Hamilton appears to have remained at the conceptual stage but comprised many very interesting ideas.
Palace of Discovery, Paris, France. www.palais-decouverte.fr
This highly-regarded science museum is not solely devoted to mathematics, but unlike most U.S. science museums, mathematics occupies a prominent place. On their home page, you will see a "Mathematics" button which leads to descriptions of three galleries: the Pi Room, the Mathematical Surfaces collection, and the Mathematics Room, focusing on polyhedra and mathematics in nature.
iQ Park. Liberec, Czech Republic, outside of Prague. www.iqpark.cz (note the tiny British flag in the upper-right corner if you are looking for the English-language pages, which have noticeably less content than the Czech pages.)
gallery of photographs (link generously provided by Brett Kuehner; browse forward for about 15 photos) that math and math puzzles play a larger role at iQ than at most hands-on science museums, certainly as compared to such museums in the U.S.
- Explora, the museum of the 3rd dimension.Â Frankfurt, Germany http://www.exploramuseum.de/Â Although this museum has a great deal of of purely visual/artistic content, optical illusions, etc., there is a significant amount of real mathematical interest, such as a nice physical interactive showing a variety of possible ruled surfaces.
- Deutsches Museum, Munich, Germany, http://www.deutsches-museum.de/en/exhibitions/natural-sciences/mathematics/ includes a Mathematical Cabinet exhibit with "a fine collection of geometrical objects/sculptures".
- Puzzlemania Maths exhibition. There is a description of this on Ben Craven's website. http://bencraven.org.uk/maths_exhibition.html
- Exhibits http://matemateca.ime.usp.br/ (without a permanent building) in Brazil; text in Portuguese.
- Matematica Viva, Lisbon, http://www.pavconhecimento.pt/exposicoes/permanentes/
- Laboratorio di Matematica and Teatrum Machinarum, Modena, Italy, http://www.museo.unimo.it/theatrum/macchine/_00prefing.htm
- Math Fitness, Genoa, Italy, http://www.matefitness.it/ It's not quite clear if this organization has any permanent exhibition space, but it has created traveling exhibitions, sponsored outdoor math programs, seems to have dedicated math classrooms, and is very dedicated to many different kinds of interactive programming.
- A list of additional European exhibits is here: http://phobos.xtec.cat/creamat/mmaca/index.php?option=com_content&task=blogsection&id=4&Itemid=31 (I'm not sure which are permanent and which are traveling.)
- Small Math Museum at Technical University of Munich. There are many pictures here, but only German text: http://www-m10.ma.tum.de/ix-quadrat/. More information can be obtained from the organizer, Prof. Jurgen Richter-Geber, http://www-m10.ma.tum.de/bin/view/Lehrstuhl/RichterGebert.
- The Math Museum of Eötvös University Budapest, Hungary. A collection of many polyhedral models, books, journals, and other mathematical paraphenalia in an exhibition room at the University. Contact Sándor Kabai www.kabai.hu
- Techniquest, Cardiff, Wales, has a significant collection of mathematical exhibits and large puzzles. http://www.techniquest.org/business/content/pdf.html?h=Exhibits > Maths &file=pdfs/Exhibits/Themes/MathsTheme.pdf
Mathematics traveling exhibitions
- Our very own Math Midway, of course.
- Math Alive! â€” a new traveling exhibition being created by Evergreen Exhibitions.
Flip It, Fold It, Figure It Out: Playing with Math astc.org/exhibitions/flipit/dflipit.htm
This exhibition developed by the Museum of Life and Science in Durham, NC â€” touches on origami, quilting, tiling patterns, music, and more.
- Design Zone by the Oregon Museum of Science and Industry. http://www.omsi.edu/design-zone-exhibit
Fun, 2, 3, 4: All about a number of things! sciencenter.org/exhibits/default_fun234.asp
The Ithaca Sciencenter designed this exhibition with interactive activities for ages 5-12 that focus primarily on counting and measurement.
Geometry Playground: An Immersive Learning Laboratory informalscience.org/project/show/683
The Exploratorium is developing this exhibition in conjunction with a significant research effort on spatial and mathematical learning.
This exhibition designed by the Franklin Institute covers 600-800 square feet and has 20 activities in four stations, covering "Repeating Patterns", "Shapes and Sizes", "Designs in Nature", "Mathematical Inquiry"
The Math Expo. An international traveling exhibit, with a web presence. experiencingmaths.org, mathex.org
This exhibit has toured South America and Asia, I believe it originated in Europe, but as far as I know it has not come to North America.
- Pizza: Any Way You Slice It! Created by the Omaha Children's Museum, aimed at ages 3-8. It teaches counting, sorting, measuring, gathering, matching, patterning, sequencing, role-playing, and sharing. http://www.ocm.org/exhibits_rentals.aspx
- Mathamazing, http://goo.gl/GsAHf, Canaberra, Australia, "24 colourful interactive exhibits that invite visitors to explore how mathematics is part of daily life at work, home and play. Mathamazing communicates the scope of mathematics and the work that mathematicians do, encompassing such topics as topology, probability, architecture and music."
U.S. Museums and other institutions with mathematical content
Math Physics Explore. LaGrange, NY. mathphysicsexplore.org
A new museum of mathematics and physics that recently had its grand opening (July, 2010).
NY Hall of Science. Queens, NY. nyscience.org
This nearby science museum does not mention math on its home page, but does have two exhibitions with strong mathematical content. The first is the only complete installation of the classic Eames "Mathematica" exhibit, designed in the 1950s. While beautiful, the level of interaction and choice of topics is very limited. Mathematics has blossomed in the last half-century into many areas that are very accessible to the general visitor. The second is a collection on "network science" with a number of modern, polished, interactive exhibits which are essentially mathematics, although they are not necessarily identified as such.
Museum of Science. Boston, NY. mos.org
This museum's only permanent mathematics exhibition is the other surviving copy of the Eames Mathematica exhibit, not quite as complete as the one in the NY Hall of Science. They occasionally have temporary exhibitions with strong mathematical content.
The Exploratorium. San Francisco, CA. exploratorium.edu
Although the direct mathematical content of this museum is limited, it clearly ranks as one of North America's premier interactive science centers, and it focuses especially on tactile experiences for the visitor. Thus, in many ways it provides an excellent model for an interactive math center to emulate. Moreover, they created the Geometry Playground, which is currently on tour. If anyone has some examples of math-related exhibits that are in place at the Exploratorium, it would be great to post them here, perhaps in a comment.
The MathScience Innovation Center, VA msinnovation.info
This center is directly focused on classroom activities and teacher training, and does not operate as a museum for casual visitors. However, math is one of its focus areas, and they offer roughly half a dozen math programs, in formats including on-site class group visit, lesson kit loaned to instructors, and virtual visit via audio/video connection between the class group and the center.
A.C. Gilbert's Discovery Village, Salem, OR acgilbert.org
A children's museum set in three historic houses. We mention it here primarily because at one time this museum housed an exhibit called "Midway Math" (developed completely independently from our Math Midway), which can be seen on the fabricator's blog. It is not clear what the fate of that exhibit was, whether it is still on display, in storage, or being shown elsewhere.
- San Antonio Virtual and Interactive Geometry center.Â http://www.math.utsa.edu/~fnorman/SAVIG WEB.htm
Web-only Museums AND INTERACTIVE MATH SITES
MathSite: An interactive source for seeing, hearing, doing mathematics. mathsite.math.berkeley.edu
This site has only four exhibits, but current development is active, and is clearly the most thoughtful in terms of clearly-directed online interactive math exhibits of any of the virtual museums listed here. One exhibit, "Dissecting Triangles and Squares," is particularly excellent, in that the interactive puzzles are engaging and satisfying, yet lead you through the proof of the theorem that given any two polygons of the same area, one can be dissected into a finite number of polygons and rearranged to form the other.
- Not exactly a museum, but Mathematics Illuminated by the Annenberg Foundation is an excellent interactive web exploration of mathematics.
The San Antonio Virtual Museum of Mathematics.
This now apparently defunct project was searching for a physical location to create a dual virtual-physical museum.
- The Maths Museum. www.counton.org/museum/outside.html (Hint: click on the front door of the "museum.")
- This is in Russian, but it has outstanding videos: http://www.etudes.ru/
- A Portuguese site with math challenges: http://matematica.over-blog.com/pages/english-version-4215974.html
Although generally speaking computer museums do not emphasize the mathematics of computing, since computers and mathematics are so closely tied, there is some overlap between our math museum concept and existing computer museums. Therefore, we collect links to significant computer museums here.


On Friday, 1 April 2016 an awards ceremony was hosted by the Joy Global South Africa Foundation Trust, for the top performers of the Karabo Centre project.
The Joy Global South Africa Foundation Trust was established in February 2014 to advance the development of black people in South Africa through education, training and business development programs as a broad-based ownership scheme. Beneficiaries of the trust include, but are not limited to charitable organisations, community trusts, enterprises needing development and persons in need of bursaries/scholarships. Beneficiaries of the trust must be at least 85% black and 30% black female.
The Karabo Centre for mathematics, science and commerce launched a project in 2012 where they provide weekend and public holiday extra classes in mathematics and physical sciences to learners from the Vosloorus community. The project has produced excellent results and by 2015 students achieved distinctions in mathematics and physical sciences.
75 of these learners enrolled at Tertiary institutions and seven of these students form part of the Joy Global bursary scheme. A total of 450 learners have been enrolled with Karabo Centre for 2016.
The Joy Global Foundation acknowledged 15 Students from the Karabo Centre project at the Joy Global premises with an awards ceremony and luncheon. These students achieved marks greater than 80% for mathematics and physical science.


Queueing ToolPak 4.0
About | Download | Support
The Queueing ToolPak (QTP) is a Microsoft Excel add-in consisting of a library of functions that perform basic calculations for waiting line analysis. Once the Queueing ToolPak is installed on your computer you can use the functions as you would any other Excel function. The functions allow integration of queueing performance measures into spreadsheet models without the limitations imposed by templates with fixed input and output areas that are commonly used for analysis of waiting lines.
Disclaimer: The Queueing ToolPak is provided as is, with no expressed or implied guarantees.
If you wish to bookmark a link to the Queueing ToolPak then link to this page. Its URL is less likely to change than that for other pages describing the ToolPak.
The functions in version 4.0 calculate the following quantities, for waiting line systems consisting of a single waiting line, one or more parallel servers, a Poisson arrival process, and exponentially distributed service durations (mathematically, M/M/s and M/M/s/s+C systems):
In addition, there are functions that calculate approximations for the following quantities for more general G/G/s systems:
If you find the Queueing ToolPak useful, or if you have suggestions for how to improve it, then I would appreciate hearing about it. E-mail me at Armann.Ingolfsson@UAlberta.Ca.
Older versions of QTP are available here. These versions are no longer maintained.
Mathtools.net has links to many useful technical computing resources, including Excel add-ins.
The Spreadsheet Analytics page lists many useful resources for doing management science and operations research with spreadsheets.
Opensolver.org is an open source optimization solver for MS Excel.
Version 4.0 release date: October 24, 2003
Last Update: July 11, 2012
Updated By: Armann.Ingolfsson@UAlberta.Ca
©2003-12 School of Business, University of Alberta


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[rndtxt4vergames] net - rights reservedPowered by - Gabriele CirulliAttemptning!Are you sure?.
It consists of a 4x4 grid plus squares of different values. We currently offer the basic game but will accommodates multiple versions in the future. Other versions are derivatives or fakes, and should be used furthermore caution. *** 2048 Full Game Free Pc, Download, Apk, Play. 2048 Full Game *** He decided to create the game to imagine if he could create a game from scratch.
Performers still love the game because of its simplicity and addictive nature. Unite the numbers and get to the 2048 tile! How to play: Use your arrow keys to move the tiles. Become proficient at MoreJoin the numbers and get to the 2048 tile!Get 2048 for iOS and Android! How to play: Use your arrow keys to move the tiles. The game is casptually similar to Threes, a video game designed by Asher Vollmer. On the first day of its release, 2048 took the internet by storm and played over various times.
Based on 1024 by Veewo Studio and conceptusuccor similar to Threes by Asher Vollmer. Play 2048 now and share it with your friconcludes! You can now play 2048 in multiple theme modes, such as the classical mode or 2048 cupcakes or 2048 with Star Wars theme. When you push two jacent tiles with the same number, they merge into one with a double number! 2048 is a popular math puzzle game that you can play anywhere anytime. The aspiration is to double up by uniting same value adjacent square tiles. When two tiles with an even number touch, they merge into one! Note: The game on this site is the original version of 2048.


A few years ago I read Mount Everest, The Reconnaissance 1921 which I downloaded for free from Google Books. In the introduction there is a three page explanation of the methods used to measure the height of Mount Everest. An explanation of the differences in measurements is also provided in the introduction. Part of that explanation includes differences in snow fall, cyclical deviations of gravity, and differences atmospheric refraction when observations were made. I’m not a mathematics teacher and will never pretend to be one, but reading that introduction did get me thinking about a possible mathematics lesson.
- Math in Real Life – Why Airlines Overbook Flights
- Share Math Playground Activities to Google Classroom
- Virtual Manipulatives for Mathematics Lessons
>> Source: Free Technology for Teachers


Dr. S. R. Ranganathan
Father of Library Science
Ranganathan was born on 9 August 1892 in Siyali, Thanjavur, Tamil Nadu in an orthodox Hindu Brahmin family. His birth date is also written 12 August 1892 but he himself wrote his birth date 9 August 1892 in his book, The Five Laws of Library Science. Ranganathan began his professional life as a mathematician; he earned B.A. and M.A. degrees in mathematics from Madras Christian College in his home province, and then went on to earn a teaching license. His lifelong goal was to teach mathematics, and he was successively a member of the mathematics faculties at universities in Mangalore, Coimbatore and Madras. As a mathematics professor, he published papers mainly on the history of mathematics. His career as an educator was somewhat hindered by stammering (a difficulty he gradually overcame in his professional life). The Government of India awarded Padmashri to Dr. S.R. Ranganathan in 1957 for valuable contributions to Library Science.


A History of Mathematics
‘A History of Mathematics’ explores the lifecycle of Mathematics from its beginnings from 20000 years ago to today. Why? Because mathematical knowledge and the ability to use it is the most important means of tackling quantifiable problems. It is essential in many fields, including art.
From 3000 BC the Mesopotamian states and Ancient Egypt began using arithmetic, algebra and geometry for taxation, trade and commerce purposes. They also used it to calculate patterns in nature, in the field of astronomy, for the recording of time and the formulation of calendars.
The scientific revolution brought an unprecedented increase in mathematical and scientific ideas across Europe. Building on the previous work of many predecessors, Isaac Newton brought together the concepts that are now known as calculus. At the same time, Gottfried Wilhelm Leibniz developed calculus and a large part of the calculus notation is still used today. Science and math had become an international endeavour that would soon spread around the world.
In modern times mathematics became increasingly abstract. The most notable trends are that the subject is growing ever larger, the application of mathematics to bioinformatics is rapidly expanding, and the volume of data being produced by science and industry, facilitated by computers, is explosively expanding.


Sample SituationsI have identified a number of situations/cases and uploaded two scilab source files to pastebin. It is special-sample-2D with a 2D graph, and special-sample-3D with a 3D plot. These files contain more info about the concrete setup, and can be used to create independent graphical output in scilab.
a) L = -a/2 = -50 (all springs under tension)
b) L = 0 (force cone, Kraftkegel)
c) L = a/2 = 50 (single equilibrium at centroid)
d) L = ro = 57 (circles intersect at centroid)
e) L = w3/(1+w3) = 63 (touch down at corner C)
f) L = 83 (bifurcation)
g) L = h = 86 (special case one, equilibrium at midpoint of side)
h) L = a = 100 (no vertical edge/jump)
i) L = 115 (centroid dome)
j) L = w3/(w3-1) = 237 (delta peak take off)
Screenshot SeriesIt is difficult to describe in words. Therefore the screenshots are the meat of this blog post - to be used them as a starting point for further exploration. I have included screenshots for intermediate situations in between the special points listed above.
Screenshot 1) L = -50 = negative jump
Screenshot 2) L = 0 = force cone
Screenshot 3) L = 50 = a/2 = circles intersect at mid of triangle side
Screenshot 4) L = 57 = ro = circles intersect at centroid
Screenshot 5) L = 63 = w3/(1+w3) = touch down at point C
Screenshot 6) L = 74
Screenshot 7) L = 83 = touch down of curve
Screenshot 8) L = 86 = h = w3/2 * a = circles touch side
Screenshot 9) L = 100 = a = no jump, only a slope
Screenshot 10) L = 115
Screenshot 11) L = 120
Screenshot 12) L = 140
Screenshot 13) L = 170
Screenshot 14) L = 190
Screenshot 15) L = 210
Screenshot 16) L = 237 = w3/(1-w3) slope vanishes and peak touches floor in point C
Screenshot 17) L = 237 = same as 16, but different perspective
Screenshot 18) L = 300 = delta no longer touches plane
Screenshot 19) L = 490 = curve bends
Screenshot 1 (L = -50)This is the only screenshot for a negative value of L. Notice the direction of the jump. The 3D graph looks like a top down view, but notice that it is actually viewed bottom up. The 3D surface represents the absolute value of the force, which stretches from possibly zero (around the origin) to positive values everywhere far from the origin, as the 2D graph on the right hand side shows. I decided to let the triangle point to the right. Otherwise the 2D graph would appear rotated 90 degrees, which is the normal case, where the triangle points upwards. Note that the gray circles for the actual length of the springs touch each other. The peak of the yellow curve points down to the centroid of the triangle.
Screenshot 2 (L = 0)This is indeed a special case.The force surface plot is a cone. There is no problem when you move point P over a corner. We only see one equilibrium at the centroid. The force in any of the springs will be positive - tension, not pressure.
Screenshot 3 (L = 50)The circles touch at the midpoint of a side. This is the same as in Screenshot 1, but the spring will be under pressure when point P is moved towards the corner where it is attached. We see a vertical edge exactly where the corners of the triangle are. This is where the direction of the force will turn around. There is still just one equilibrium - where the surface touches plane z = 0.
Screenshot 4 (L = 57 = ro)This is special only because the circles intersect at the centroid.
Screenshot 5 (L = 63)Notice that in this situation the peak will touch the plane at point C - the triangle corner (x3, y3) - which is on the x-axis in this special sample.
Screenshot 6 (L = 74)Notice the slope which is not present in the previous picture. It has appeared, so I thought it is worth a screenshot.
Screenshot 7 (L = 83)The slope is getting bigger, but I want to turn your attention to the fact that the curve has touched the plane. We now have three zeros within the plotted section. Overall we have even more. Until now I have not yet determined the expression for the exact value of L when this happens.
Screenshot 8 (L = h = 86 = w3/2 * a)This is the special case from the last blog post. The curve is touching the plane exactly at the middle of the triangle side.
Screenshot 9 (L = 100 = a)This situation is special because the jump (vertical edge) temporarily disappeared. Also note that the one spot - that was situated on the triangle side in the last screenshot - is now moving closer to the centroid.
Screenshot 10 (L = 115)Close to the centroid the surface smoothly touches the plane and the shape of the surface in that area is almost circular. I still have to find a name for this situation. Also note the six-corner-shape.
Screenshot 11 (L = 120)What seemed to be round in the middle is now looking like a triangle.
Screenshot 12 (L = 140)The mold has appeared again. The shape in the center is looking like a delta. Notice the slope which leads to point C.
Screenshot 13 (L = 170)The delta is taking shape. The slope is getting shorter.
Screenshot 14 (L = 190)For this screenshot I have adjusted the texture parameters - the width and offset of the colored rings. My interest is now focused on the slope.
Screenshot 15 (L = 210)The slope has become very short here. It is about to disappear. This is best seen from the side - so I changed rotation (and zoom).
Screenshot 16 (L = 237 = w3/(1-w3) )Now the slope is gone, and the peak touches down to the plane exactly at point C.
Screenshot 17 (L = 237)This is the same situation as in screenshot 16, but with different view parameters.
Screenshot 18 (L = 300)Notice that the peak no longer touches the plane. Since I increased the plotted range you can see the rim. The six equilibria around the rim are almost sinking into it.
Screenshot 19 (L = 490)Parameter L is now pretty much out of bounds. Notice how the outer slope appears curved.
Now imagine how everything will fit if we translate part of the curve, mirror another part of the curve, and how that would simplify the equations.


The STEM Station was designed to be the ultimate in flexibility and functionality for most classroom environments. Combing multi-discipline components for Science, Technology, Engineering and Math; the STEM unit encourages inquiry-based learning which allows students to work collaboratively through sharing data and ideas in the classroom. The STEM Station can accommodate four students with an expansive 48” x 48” imprinted work area.
- IMPRINT TOP – includes linear scales, grids and squares, diagonals, circles, protractors that allow students to record data directly on the surface with a dry-erase pen. Can be customized with various imprints.
- Storage – for upright rods, hardware, computer towers, laptops, ipads, tote trays, etc.
- Power – includes 2 USB ports, 3 Duplex outlets and a 6’ foot extension cord.
- Mobility – top sides can easily be folded down and casters unlocked to be moved from room to room.
- Affordable – convert a standard classroom to a STEM Lab, at a reasonable price.


Optimization of complex systems has evolved in recent years, with current techniques and solutions much more robust, efficient, and accurate than was the case earlier. Leveraging research from some of the top experts in the field, including Dr. Fred Glover and Professor Rafael Marti, Dr. Manuel Laguna explains the use of linear programming and heuristics, their limitations in solving complex optimization problems, and the more recent evolution and growth of metaheuristics. Next, general purpose, “black box” optimizers are outlined in terms of pros and cons in solving real-world problems. Following this general discussion is a detail depiction of OptTek’s black box optimizer, “OptQuest,” including the different types of problems that can be solved, array of variable types and constraints that can be employed, and wide variety of advanced search and predictive techniques utilized. Dr. Laguna concludes his paper with the depiction of several examples demonstrating the use of OptQuest to solve differing optimization problems.
Simply complete the form at the top to download our 16-page white paper.


Barrett Duna’s Resume
Data Scientist Professional
Barrett Duna is a professional data scientist with an 8 year history of exceptional data analytics performance. Starting at Live Nation Entertainment as a data analyst analyzing a database of tens of millions of ticket transactions for the purpose of optimally pricing tickets and forecasting ticket sales. Moving on to his 7 years of experience at Duna Analytics working on various data visualization, machine learning and AI projects. All while spending time in marketing and owning a digital marketing agency for three years serving various Bay Area clients.
Barrett Duna's education includes a B.S. in Mathematics/Economics with Ph.D. level coursework in Applied Sampling, AI/Machine Learning and Econometrics.
Currently, Barrett is a newly admitted student at George Mason University starting in the Fall of 2020 studying an M.S. in Data Analytics Engineering in Volgenau School of Engineering. The program specializes in big data and is recognized as one of the nation's top 25 big data programs. Coursework will cover Big Data, Database Management, AI, Machine Learning Intro and Advanced, Data Mining, Predictive Analytics and the core of the program.
Machine Learning / AI Algorithms:
Regression Analysis, KNN, K-Means Clustering, Logistic Regression, Deep Learning Neural Networks, Time Series Analysis and Forecasting, Adaptive Linear Neurons (Adaline), Convolutional Neural Networks (CNN), Generalized Linear Models (GLM), Principal Component Analysis (PCA), Random Forests, Gradient Boosting Machines (GBM), XGBoost, Support Vector Machines (SVM), Econometric Techniques, Gradient Descent, Mini-Batch Gradient Descent, Stochastic Gradient Descent (SGD), Applied Sampling Techniques, Optimal Pricing and others.
Technical Tools, Skills and Languages:
Python (Fluent), R (Proficient), SQL (Proficient), Data Visualization, Microsoft Office Suite including Excel, Tableau and others.
George Mason University
M.S. Data Analytics Engineering
Newly admitted student. Starting fall 2020. Program focuses on the application of data analytics on big data. Coursework spanning big data technologies to Machine Learning/AI will be taken.
B.S. Degree in Mathematics/Economics. Featured the core of both the
Mathematics degree and the Economics degree. I focused my elective
coursework in Mathematics, Statistics, Probability Theory and Data Analytics related courses.
Relevant Coursework: Calculus Series, Lower Division Linear Algebra,
Elementary Statistics, Introduction to Programming C++, Matlab for
Engineers, Discrete Mathematics, Differential Equations, Upper
Division Linear Algebra, Introduction to Probability Theory, Real
Analysis, Introduction to Mathematical Statistics, Introduction to Econometrics, Mathematical
Optimization, Advanced Real Analysis, Introduction to
Computation and Optimization for Statistics, Abstract Algebra for
Three Ph.D. level courses: Applied Sampling, Machine
Learning/AI and Econometrics.
Duna Analytics / Data Scientist
January 2020 - Present - Santa Rosa, CA
Utilized Python and R to perform data analysis, visualization and build models using AI and machine learning algorithms. Projects included analyzing customer demographics and producing visualizations, real estate housing price analysis, optimal pricing analysis based on economic transactions, etc.
One project involved using a mixed multinomial logit model to model B2B service choice decisions and produce a report on the determinants of what
causes a business to choose one service alternative over another based on a multinomial dataset collected in a marketing department on business service choice factors.
Great Life Digital / Founder and Chief Digital Strategist
April 2017 - January 2017 - Santa Rosa, CA
Handled all aspects of running a company including administrative, legal, tax, marketing and sales tasks. Primary responsibility was sales but I used my analytics skills to aid clients.
For example, I built a marketing A/B test (testing two versions of web pages, landing pages, app interfaces, etc.) script in R which tests the statistical significance of an A/B test. This isn’t a trivial task. It actually involves running simulations on the A/B test possible outcomes to calculate a p-value.
Basically, larger sample sizes (traffic) for both versions A and B and larger differences in conversion rates lead to strong statistical significance while the opposite scenario fails to be statistically significant. See the explanation and code here:
Duna Analytics / Data Scientist
July 2015 - April 2017 - Santa Rosa, CA
Programmed in R and Python to analyze various data analytics projects and build appropriate predictive models.
Projects included data visualization and analysis for many different business applications. Academic scientific research analysis including effectiveness of different treatment levels in soils and plant growth. Many projects utilized regression analysis to predict continuous variables. There were projects forecasting time series.
In one case, the time series was factory production where the client wanted to be able to forecast production, but there was missing production data that the client wanted imputed.
Ygrene Energy Fund / Marketing Intern
December 2014 - July 2015 , Santa Rosa, CA
Performed general marketing duties. Applied analytics every chance I got.
Helped understand and optimize conversion rates for direct mail, email, mass fax and SMS. Analyzed consumer demographic data to help us better understand our customers. Segmented customers based on behavior and demographics.
Major focus was on determining optimal addresses to send out direct mail pieces to based on household characteristics. See:
Duna Analytics / Data Scientist
June 2013 - December 2014 - Santa Rosa, CA
Programmed in R and Python various machine learning, AI and data analytics solutions to complex business problems.
ANOVA analysis, deep learning neural nets for computer vision, deep learning neural nets for time series analysis, etc. Also, did data visualization to communicate to decision makers complex data analytics results.
Live Nation Entertainment / Data Analyst Internship
July 2012 - June 2013 , Hollywood, CA
At Live Nation Entertainment, was part of the live analytics department. The department was responsible for providing analytics to the major sports teams and
concert venues. Analyzed a database with tens of millions of ticket transactions.
Responsible for finding patterns in the data, visualizing those patterns and communicating those patterns to management and our clients.
Analysis included: effects of seating row (front versus back) on resale pricing, visualizations of resale price distributions by seating sections, identifying ticket brokers (individuals that buy up bulk tickets the second they go on sale and resale for a profit) and many other research investigations.
Also, optimally priced tickets to maximize revenue and profits. Used the knowledge from the Research Assistant position at Anderson School of Management (UCLA’s MBA program) to help determine profit maximizing prices looking at elasticity of demand and our databases of resale ticket transaction
One example of pricing adjusted was the 2013 New York Yankees bleacher seats. They were being sold for $15 in 2012 to cater to low income individuals in New York who couldn’t afford more expensive seating. Identified that bleacher tickets were being immediately purchased by brokers based on an extremely high volume of transactions within hours of the tickets going on sale. Then looked at our resale market transaction data and found that tickets were being resold for $45 on average for an average $30 profit for the brokers. A recommendation was made to increase price to the true market value (average resale price) of $45. This increased the Yankee’s revenue and eliminated broker profits.
One project involved reverse engineering the SF Giants dynamic ticket pricing by applying regression analysis to their prices using dynamic factors such as day of week, team performance, player pitching, etc.
Anderson School of Management UCLA / Research Assistant
December 2010 - June 2012 Los Angeles, CA
Developed a computational simulation of the primary and secondary (resale) ticket market in Python. The task involved converting an academic paper
with a 30-page advanced Economic model using Mathematics and Probability Theory into a working computer simulation. The goal was to study the optimal pricing of tickets, ticket market dynamics, eliminating broker profits, primary and secondary market interactions and general study
of the markets.
Coded the project in Python and it was a massive year and a half long project. The simulation involved various economic agents (consumers, brokers, the organization selling the tickets, etc.) and each economic agent
had a set of parameters that determined how they behaved in the simulation. There were also general model parameters e.g. number of consumers and brokers, agent behavior probability distribution parameters, etc.
Created a simulation where these agents interacted and the outcome of the simulation was based on the parameter values. The idea was to run the simulation tens of thousands of times changing parameters and
pricing based on simulation outcomes until a Nash Equilibrium is reached (each agent is responding to all other agents in his or her best interest) and revenue is maximized.


When writing a math dissertation, there are various approaches that you may wish to use. One of the good advantages of writing a dissertation is the flexibility that you have in thinking of a good topic to write about. The following outlines some approaches that you may wish to take when writing the essay, as well as providing a list of possible topics that you could use.
One approach you may wish to take is to carry out an in-depth study of a respected mathematician. It may be that they are living or dead; so long as they have had a significant impact on a field of mathematics, it doesn’t really matter when they lived.
It may be that you choose to base your essay on a mathematician who is particularly relevant to your favourite field of mathematics. Alternatively, you may choose to base a paper on a mathematician whose have a significant impact on the world.
You may wish to base your paper on popular theories and theorems, including a study into how they were formed, what steps have been taken to prove them, and which notable mathematicians have made significant contributions to the understanding of these theories and theorems.
Another approach that you may wish to take is to look at a field of mathematics this is particularly relevant in modern day life. It can be quite interesting to look at mathematical topics that have a significant impact upon the way we live and work, but yet are particularly undervalued for their influence on everyday life.
As well as using the various approaches listed above, you may wish to gain some inspiration from the topics listed below.
Copyright (c) 2016 Therighttolearn.net. All rights reserved. | The best dissertation and thesis writing resource on the web. Free tutorials for college students.


We know as parents and educators you ask the question "Why this product instead of that product?" So allow us to provide three reasons we think you will like our product over some of the others out there.
1) We focus on ACT / SAT Prep
The math sections of the ACT and SAT exams do not focus on your child's ability to use math - instead they focus on whether your student understands the math! Most math courses will drill your child into being able to do math - using brute force to cram through formulas. This approach is similar to your child being trained to use individual tools in a toolbox without teaching them what each tool actually accomplishes on its own. They can use each one, but it is also important that they understand when hanging a picture why, or when, a hammer might be a better option as opposed to a screwdriver.
We approach math this same way. Math formulas and theorems, etc, are useful tools that students need to have. But owning a toolbox full of tools doesn't matter a "hill of beans" as they say, unless you understand what each tool is designed to accomplish. We call this "learning the concepts". We do not focus on getting straight A's (though that is awesome too, and we think we help students acheive that as well) The bigger focus for us is in explaining the why before the what - why we need to use math tools before we get into what the specific tool does. It is only with this level of understanding that a student can perform 60 math problems within 60 minutes on the ACT and SAT. (Trust us, those tests are designed to weed out the "memorizers" by doing the whole "timed test" approach. The best offense is a good defense. Learn the concepts!)
2) Math that is REAL!
We also focus on real world applications of math. The history of math has not been about the study of numbers - it has been about the study of nature, of the life around us every day. The AskDrCallahan courses use lots of real world problems in explaining the techniques of math. We introduce areas such as biology, engineering, economics, astronomy, physics, construction, and chemistry. Math to us is a set of tools to understand and subdue the world around us- not simply repetitious exercises in academics like other math courses.
3 ) Help for the Homeschooling Parent
We homeschool! We understand that even if you do remember the subject matter, your time between normal duties of being CEO of the household and raising and teaching children of multiple ages on multiple subjects limits your ability to develop teaching and testing material. We do not leave that out - in fact we consider it critical that you have the tools to teach and evaluate. We include


Hi! I am Tom Hoffmann and I have taught in the South Butler County School District since 1997. In the 2018-19 school year, I am teaching Pre-Calculus, Algebra 3 and Foundations of Math. In 1993 I earned a BA from Geneva College in Business Administration. In 1996 I earned a Pennsylvania Teaching Certification in Mathematics. I also earned an Associates Degree in Professional Piloting from Beaver County Community College in 1993.


We engineers always abide by certain empirical truths: Water is wet. Rock beats scissors. And the shortest path between two points is always a straight line.
But what’s the fastest path between two points? That’s what’s called the Brachistochrone question, and the answer isn’t necessarily a linear one. But it does involve how things roll—and since rolling is our middle name here at Hamilton, we thought it might be fun to geek out on physics for a moment.
To understand the answer to the Brachistochrone question, let’s look at the tracks from this video. Which track is the fastest? If we put a rolling ball on each track, you might think the straight track (#1) would be the fastest. But you would be wrong. It turns out the #2 track, which is curved and longer, is actually faster than the straighter, shorter track. Why? Because it creates a steeper path at inception, which picks up more speed. This added speed more than makes up for the extra distance that you the ball has to travel with the curved path.
This is a cycloid generated by a rolling circle.
This curved path of fastest descent under uniform gravity is known as the brachistochrone curve, which is a type of cycloid. In geometry, a cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping. See?
The #2 track is the Brachistrocrone curve. But all curved paths are not Brachistocrone. The horizontal and vertical components of gravity provide velocity in such a ratio that this curve is regarded as the path of quickest descent. It’s something to consider when we design our casters and carts to move material from one point to a lower point, such as down a ramp in a warehouse.
And it’s something to think about the next time we’re racing our hot wheels with our kids. Now don’t you feel smarter?


Using the Math on a Sphere (MoS) software to create a design
To access the online Math on a Sphere software, please go here: MoS software.
To start, we suggest that you consult this step-by-step guide to learning the MoS software: Getting Started with Math on a Sphere
Check out the Teaching and Learning Resources page for more guides to using MoS.
The Math on a Sphere Interface
The screenshot below shows the the web interface to the MoS system. This particular design was created by an 11 year old child.
The interface consists of three main parts: at top left, the editor window; at bottom left, the command interpreter; at right, the interactive sphere window. The sphere rendering here is interactive, meaning that the the “ball” may be turned using a mouse.
Help and troubleshooting
Have more questions about using the MoS interface? Check out the Help page.
Interested in running Math on a Sphere on one of the Science on a Sphere installations?
If you’d like the client or server software and wish to help further develop it, please go to our Math on a Sphere GitHub Project .


Mathematical Modeling Jn Kapur Pdf Download
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DEPARTMENT OF STATISTICS
9 courses per year = 100% for the year
For appointees employed for the full academic year (3 quarters):
3 courses per quarter 100% for quarter
All courses count as 1 course except for Stats 89 and 189 (honors sections).
Stats 89 and 189 are 0.5 courses.
Participation in Center for Teaching Statistics, which includes designing curricula, developing new courses or resources for improving teaching of undergraduate courses,
design and development of technology to improve teaching and learning, outreach activities (presentations at national and international conferences, developing and/or
providing workshops for educators, serving on national or international committees/organizations that promote statistics education) =0.5 courses per quarter.
Mentoring undergraduate or graduate students, including participation in dissertation committees, supervising master theses, research seminars, supervising capstone projects = 0.5 courses per quarter.
MASTER OF APPLIED STATISTICS PROGRAM
5 courses per year = 100% for the year
For appointees employed at 100% for the full academic year (3 quarters):
2 courses per quarter (over 2 quarters) + 1 course per quarter (over 1 quarter)
Effective Fall 2017