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A Numerical Study of One-Dimensional Hyperbolic Telegraph
A Numerical Study of One-Dimensional Hyperbolic Telegraph

... encounter these equations in the study of pulsate blood flow in arteries and in one- dimensional random motion of bugs along a hedge [33]. Also the propagation of acoustic waves in Darcy-type porous media [35], and parallel flows of viscous Maxwell fluids [1] are just some of the phenomena governed ...
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... Introduce the concept of slack variables. To illustrate, use the first functional constraint, x1 ≤ 4, in the Wyndor Glass Co. problem as an example. x1 ≤ 4 is equivalent to x1 + x2=4 where x2 ≥ 0. The variable x2 is called a slack variable. (3) Some functional constraints with a greater-than-or-equa ...
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Blue Border - Courant Institute of Mathematical Sciences

... Have (u,v) where u=rA and v=+z(q/2) Compute ( - v) If - v is closer to 0 than to q/2, then decrypt to 0 If - v is closer to q/2 than to 0, then decrypt to 1 - v = rAs – r(As+e) -z(q/2) = - z(q/2) if all coefficients of e are < sqrt(q), || < m*sqrt(q) So if q >> ...
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Solving Linear Equations - A Mathematical Mischief Tutorial

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... avoid the step of reducing it to an ODE system? Obviously sometimes the answer is “yes” (or we wouldn’t be discussing it here!) For this example it works fine after we handle a minor difficulty. However, there are networks (and other systems) that can’t be solved with such a simple approach. Looking ...
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Inverse problem

An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in computer tomography, source reconstructing in acoustics, or calculating the density of the Earth from measurements of its gravity field.It is called an inverse problem because it starts with the results and then calculates the causes. This is the inverse of a forward problem, which starts with the causes and then calculates the results.Inverse problems are some of the most important mathematical problems in science and mathematics because they tell us about parameters that we cannot directly observe. They have wide application in optics, radar, acoustics, communication theory, signal processing, medical imaging, computer vision, geophysics, oceanography, astronomy, remote sensing, natural language processing, machine learning, nondestructive testing, and many other fields.
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