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Let J be a finite group and the image R(J) be a representation which is a homomorphism of J into a permutation group S(X), where S(X) is the group of all permutations of a ...

A p-variate multivariate normal distribution (also called a multinormal distribution) is a generalization of the bivariate normal distribution. The p-multivariate ...

The term "quotient" is most commonly used to refer to the ratio q=r/s of two quantities r and s, where s!=0. Less commonly, the term quotient is also used to mean the integer ...

Ai(z) and Ai^'(z) have zeros on the negative real axis only. Bi(z) and Bi^'(z) have zeros on the negative real axis and in the sector pi/3<|argz|<pi/2. The nth (real) roots ...

Let N samples be taken from a population with central moments mu_n. The sample variance m_2 is then given by m_2=1/Nsum_(i=1)^N(x_i-m)^2, (1) where m=x^_ is the sample mean. ...

Let a random n×n (0,1)-matrix have entries which are 1 (with probability p) or 0 (with probability q=1-p). An s-cluster is an isolated group of s adjacent (i.e., horizontally ...

A complete k-partite graph is a k-partite graph (i.e., a set of graph vertices decomposed into k disjoint sets such that no two graph vertices within the same set are ...

Given a function f(x_1,...,x_n) defined on a domain U, the graph of f is defined as the set of points (which often form a curve or surface) showing the values taken by f over ...

In a plane, consider a sum of N two-dimensional vectors with random orientations. Use phasor notation, and let the phase of each vector be random. Assume N unit steps are ...

Ball tetrahedron picking is the selection of quadruples of points (corresponding to vertices of a general tetrahedron) randomly placed inside a ball. n random tetrahedra can ...