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A Borel set is an element of a Borel sigma-algebra. Roughly speaking, Borel sets are the sets that can be constructed from open or closed sets by repeatedly taking countable ...

Let S be a collection of subsets of a set X, mu:S->[0,infty] a set function, and mu^* the outer measure induced by mu. The measure mu^_ that is the restriction of mu^* to the ...

A sum of the digits in a given transmission modulo some number. The simplest form of checksum is a parity bit appended on to 7-bit numbers (e.g., ASCII characters) such that ...

The American Mathematical Society awards two prizes named in honor of Prof. Frank Nelson Cole, a senior member of the AMS who made a bequest to the society in 1928 upon his ...

Combinatorial matrix theory is a rich branch of mathematics that combines combinatorics, graph theory, and linear algebra. It includes the theory of matrices with prescribed ...

The differential forms on C^n decompose into forms of type (p,q), sometimes called (p,q)-forms. For example, on C, the exterior algebra decomposes into four types: ^ C = ^ ^0 ...

A sophisticated checksum (often abbreviated CRC), which is based on the algebra of polynomials over the integers (mod 2). It is substantially more reliable in detecting ...

A differential k-form omega of degree p in an exterior algebra ^ V is decomposable if there exist p one-forms alpha_i such that omega=alpha_1 ^ ... ^ alpha_p, (1) where alpha ...

An endomorphism is called ergodic if it is true that T^(-1)A=A implies m(A)=0 or 1, where T^(-1)A={x in X:T(x) in A}. Examples of ergodic endomorphisms include the map X->2x ...

The kth exterior power of an element alpha in an exterior algebra LambdaV is given by the wedge product of alpha with itself k times. Note that if alpha has odd degree, then ...