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A horizontal line placed above multiple quantities to indicate that they form a unit. It is most commonly used to denote 1. A radical (sqrt(12345)), 2. Repeating decimals ...

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 ...

The two-dimensional map x_(n+1) = [x_n+nu(1+muy_n)+epsilonnumucos(2pix_n)] (mod 1) (1) y_(n+1) = e^(-Gamma)[y_n+epsiloncos(2pix_n)], (2) where mu=(1-e^(-Gamma))/Gamma (3) ...

A complete graph is a graph in which each pair of graph vertices is connected by an edge. The complete graph with n graph vertices is denoted K_n and has (n; 2)=n(n-1)/2 (the ...

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 ...