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A random permutation is a permutation containing a fixed number n of a random selection from a given set of elements. There are two main algorithms for constructing random ...

On July 10, 2003, Eric Weisstein computed the numbers of n×n (0,1)-matrices all of whose eigenvalues are real and positive, obtaining counts for n=1, 2, ... of 1, 3, 25, 543, ...

The Banach-Saks theorem is a result in functional analysis which proves the existence of a "nicely-convergent" subsequence for any sequence {f_n}={f_n}_(n in Z^*) of ...

A complete metric space is a metric space in which every Cauchy sequence is convergent. Examples include the real numbers with the usual metric, the complex numbers, ...

A functional is a real-valued function on a vector space V, usually of functions. For example, the energy functional on the unit disk D assigns a number to any differentiable ...

A set of real numbers x_1, ..., x_n is said to possess an integer relation if there exist integers a_i such that a_1x_1+a_2x_2+...+a_nx_n=0, with not all a_i=0. For ...

Let f_1(x), ..., f_n(x) be real integrable functions over the closed interval [a,b], then the determinant of their integrals satisfies

Cauchy's functional equation is the equation f(x+y)=f(x)+f(y). It was proved by Cauchy in 1821 that the only continuous solutions of this functional equation from R into R ...

In the most commonly used convention (e.g., Apostol 1967, pp. 202-204), the first fundamental theorem of calculus, also termed "the fundamental theorem, part I" (e.g., Sisson ...

The topology on the Cartesian product X×Y of two topological spaces whose open sets are the unions of subsets A×B, where A and B are open subsets of X and Y, respectively. ...