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One of the numbers 1, 2, 3, ... (OEIS A000027), also called the counting numbers or natural numbers. 0 is sometimes included in the list of "whole" numbers (Bourbaki 1968, ...

A statistical distribution published by William Gosset in 1908. His employer, Guinness Breweries, required him to publish under a pseudonym, so he chose "Student." Given N ...

Ball point picking is the selection of points randomly placed inside a ball. n random points can be picked in a unit ball in the Wolfram Language using the function ...

There are a number of attractive polyhedron compounds involving four cubes, several of which are illustrated above. The first (left figures), also known as Bakos' compound, ...

Let a distribution to be approximated be the distribution F_n of standardized sums Y_n=(sum_(i=1)^(n)(X_i-X^_))/(sqrt(sum_(i=1)^(n)sigma_X^2)). (1) In the Charlier series, ...

The generalized Gell-Mann matrices are the n^2-1 matrices generating the Lie algebra associated to the special unitary group SU(n), n>=2. As their name suggests, these ...

If J is a simple closed curve in R^2, then the Jordan curve theorem, also called the Jordan-Brouwer theorem (Spanier 1966) states that R^2-J has two components (an "inside" ...

Intuitively, a d-dimensional discrete percolation model is said to be long-range if direct flow is possible between pairs of graph vertices or graph edges which are "very ...

A 2-dimensional discrete percolation model is said to be mixed if both graph vertices and graph edges may be "blocked" from allowing fluid flow (i.e., closed in the sense of ...

A projection matrix P is an n×n square matrix that gives a vector space projection from R^n to a subspace W. The columns of P are the projections of the standard basis ...