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one can calculate a single point (e.g. the center of an image) using high-precision arithmetic (z), giving a reference orbit, and then compute many points around it in terms of various initial offsets delta plus the above iteration for epsilon, where epsilon-zero is set to 0.
An essential characteristic of the typical set is that, if one draws a large number n of independent random samples from the distribution X, the resulting sequence (x 1, x 2, ..., x n) is very likely to be a member of the typical set, even though the typical set comprises only a small fraction of all the possible sequences.
Note that the values at 0 and 1 are given by the limit := + = (by L'Hôpital's rule); and that "binary" refers to two possible values for the variable, not the units of information. When p = 1 / 2 {\displaystyle p=1/2} , the binary entropy function attains its maximum value, 1 shannon (1 binary unit of information); this is the case of ...
One of the reasons for the importance of the matrix exponential is that it can be used to solve systems of linear ordinary differential equations.The solution of = (), =, where A is a constant matrix and y is a column vector, is given by =.
In addition, if the random variable has a normal distribution, the sample covariance matrix has a Wishart distribution and a slightly differently scaled version of it is the maximum likelihood estimate. Cases involving missing data, heteroscedasticity, or autocorrelated residuals require deeper considerations.
To calculate the pressure drop in a given reactor, the following equation may be deduced: = + | |. This arrangement of the Ergun equation makes clear its close relationship to the simpler Kozeny-Carman equation, which describes laminar flow of fluids across packed beds via the first term on the right hand side.
The probability density, cumulative distribution, and inverse cumulative distribution of any function of one or more independent or correlated normal variables can be computed with the numerical method of ray-tracing [41] (Matlab code). In the following sections we look at some special cases.
It is sufficient to calculate the upper and lower information dimensions when restricting to the exponential subsequence =. d _ ( X ) {\displaystyle {\underline {d}}(X)} and d ¯ ( X ) {\displaystyle {\bar {d}}(X)} are kept unchanged if rounding or ceiling functions are used in quantization.