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Replacing the logistic equation (dx)/(dt)=rx(1-x) (1) with the quadratic recurrence equation x_(n+1)=rx_n(1-x_n), (2) where r (sometimes also denoted mu) is a positive ...

Connecting the centers of touching spheres in a three-dimensional Apollonian gasket by edges given a graph known as the Apollonian network. This process is illustrated above ...

Assume that n numbered pancakes are stacked, and that a spatula can be used to reverse the order of the top k pancakes for 2<=k<=n. Then the pancake sorting problem asks how ...

Marsaglia (1972) has given a simple method for selecting points with a uniform distribution on the surface of a 4-sphere. This is accomplished by picking two pairs of points ...

For a single variate X having a distribution P(x) with known population mean mu, the population variance var(X), commonly also written sigma^2, is defined as ...

Discrepancy is a measure of the deviation of a point set from a uniform distribution. In general, the computation of the discrepancy of a point set is computationally ...

Integrals over the unit square arising in geometric probability are int_0^1int_0^1sqrt(x^2+y^2)dxdy=1/3[sqrt(2)+sinh^(-1)(1)] int_0^1int_0^1sqrt((x-1/2)^2+(y-1/2)^2)dxdy ...

Probability and Statistics

A Poisson process is a process satisfying the following properties: 1. The numbers of changes in nonoverlapping intervals are independent for all intervals. 2. The ...

The tilde is the mark "~" placed on top of a symbol to indicate some special property. x^~ is voiced "x-tilde." The tilde symbol is commonly used to denote an operator. In ...