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The system size expansion, also known as van Kampen's expansion or the Ω-expansion, is a technique pioneered by Nico van Kampen [1] used in the analysis of stochastic processes. Specifically, it allows one to find an approximation to the solution of a master equation with nonlinear transition rates.
The primary difference between a computer algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The precise uses and capabilities of these systems differ greatly from one system to another, yet their purpose remains the same: manipulation of symbolic equations.
A log–log plot of y = x (blue), y = x 2 (green), and y = x 3 (red). Note the logarithmic scale markings on each of the axes, and that the log x and log y axes (where the logarithms are 0) are where x and y themselves are 1. Comparison of linear, concave, and convex functions when plotted using a linear scale (left) or a log scale (right).
The math template formats mathematical formulas generated using HTML or wiki markup. (It does not accept the AMS-LaTeX markup that <math> does.) The template uses the texhtml class by default for inline text style formulas, which aims to match the size of the serif font with the surrounding sans-serif font (see below).
The identities of logarithms can be used to approximate large numbers. Note that log b (a) + log b (c) = log b (ac), where a, b, and c are arbitrary constants. Suppose that one wants to approximate the 44th Mersenne prime, 2 32,582,657 −1. To get the base-10 logarithm, we would multiply 32,582,657 by log 10 (2), getting 9,808,357.09543 ...
Engineering Equation Solver (EES) is a commercial software package used for solution of systems of simultaneous non-linear equations.It provides many useful specialized functions and equations for the solution of thermodynamics and heat transfer problems, making it a useful and widely used program for mechanical engineers working in these fields.
A logarithmic chart allows only positive values to be plotted. A square root scale chart cannot show negative values. x: the x-values as a comma-separated list, for dates and time see remark in xType and yType; y or y1, y2, …: the y-values for one or several data series, respectively. For pie charts y2 denotes the radius of the corresponding ...
A Poisson compounded with Log(p)-distributed random variables has a negative binomial distribution. In other words, if N is a random variable with a Poisson distribution , and X i , i = 1, 2, 3, ... is an infinite sequence of independent identically distributed random variables each having a Log( p ) distribution, then