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Let the n×n matrix A satisfy the conditions of the Perron-Frobenius theorem and the n×n matrix C=c_(ij) satisfy |c_(ij)|<=a_(ij) for i,j=1, 2, ..., n. Then any eigenvalue ...

An algorithm that can be used to factor a polynomial f over the integers. The algorithm proceeds by first factoring f modulo a suitable prime p via Berlekamp's method and ...

If F(x) is a probability distribution with zero mean and rho=int_(-infty)^infty|x|^3dF(x)<infty, (1) where the above integral is a stieltjes integral, then for all x and n, ...

Let A denote an R-algebra, so that A is a vector space over R and A×A->A (1) (x,y)|->x·y. (2) Now define Z={x in A:x·y=0 for some y in A!=0}, (3) where 0 in Z. An Associative ...

In geometry, the term "enlargement" is a synonym for expansion. In nonstandard analysis, let X be a set of urelements, and let V(X) be the superstructure with individuals in ...

First-passage percolation is a time-dependent generalization of discrete Bernoulli percolation in which each graph edge e of Z^d is assigned a nonnegative random variable ...

There are no fewer than two closely related but somewhat different notions of gerbe in mathematics. For a fixed topological space X, a gerbe on X can refer to a stack of ...

The polynomials G_n(x;a,b) given by the associated Sheffer sequence with f(t)=e^(at)(e^(bt)-1), (1) where b!=0. The inverse function (and therefore generating function) ...

A nonassociative algebra obeyed by objects such as the Lie bracket and Poisson bracket. Elements f, g, and h of a Lie algebra satisfy [f,f]=0 (1) [f+g,h]=[f,h]+[g,h], (2) and ...

A tree having four branches at each node. Quadtrees are used in the construction of some multidimensional databases (e.g., cartography, computer graphics, and image ...