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A connected graph G is distance-regular if for any vertices x and y of G and any integers i,j=0, 1, ...d (where d is the graph diameter), the number of vertices at distance i ...

The correlation coefficient, sometimes also called the cross-correlation coefficient, Pearson correlation coefficient (PCC), Pearson's r, the Perason product-moment ...

There are essentially three types of Fisher-Tippett extreme value distributions. The most common is the type I distribution, which are sometimes referred to as Gumbel types ...

The volumes of any n n-dimensional solids can always be simultaneously bisected by a (n-1)-dimensional hyperplane. Proving the theorem for n=2 (where it is known as the ...

The standard deviation sigma of a probability distribution is defined as the square root of the variance sigma^2, sigma = sqrt(<x^2>-<x>^2) (1) = sqrt(mu_2^'-mu^2), (2) where ...

A square matrix U is a unitary matrix if U^(H)=U^(-1), (1) where U^(H) denotes the conjugate transpose and U^(-1) is the matrix inverse. For example, A=[2^(-1/2) 2^(-1/2) 0; ...

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 ...

There are a number of attractive polyhedron compounds consisting of five cubes. The first of these (left figures) consists of the arrangement of five cubes in the polyhedron ...

Two graphs which contain the same number of graph vertices connected in the same way are said to be isomorphic. Formally, two graphs G and H with graph vertices ...

The symmetric group S_n of degree n is the group of all permutations on n symbols. S_n is therefore a permutation group of order n! and contains as subgroups every group of ...