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A variable x is memoryless with respect to t if, for all s with t!=0, P(x>s+t|x>t)=P(x>s). (1) Equivalently, (P(x>s+t,x>t))/(P(x>t)) = P(x>s) (2) P(x>s+t) = P(x>s)P(x>t). (3) ...

Module multiplicity is a number associated with every nonzero finitely generated graded module M over a graded ring R for which the Hilbert series is defined. If dim(M)=d, ...

Let A={a_1,a_2,...} be a free Abelian semigroup, where a_1 is the identity element, and let mu(n) be the Möbius function. Define mu(a_n) on the elements of the semigroup ...

A monoid is a set that is closed under an associative binary operation and has an identity element I in S such that for all a in S, Ia=aI=a. Note that unlike a group, its ...

Given an m×n matrix B, the Moore-Penrose generalized matrix inverse is a unique n×m matrix pseudoinverse B^+. This matrix was independently defined by Moore in 1920 and ...

There are two functions commonly denoted mu, each of which is defined in terms of integrals. Another unrelated mathematical function represented using the Greek letter mu is ...

Let A be a non-unital C^*-algebra. There is a unique (up to isomorphism) unital C^*-algebra which contains A as an essential ideal and is maximal in the sense that any other ...

The Nechushtan graph, illustrated above, is a 10-vertex 5-chromatic graph that is unit-distance in 3 dimensions. It was used by Nechushtan (2002) in the construction of of a ...

Newton's method, also called the Newton-Raphson method, is a root-finding algorithm that uses the first few terms of the Taylor series of a function f(x) in the vicinity of a ...

A nilpotent Lie group is a Lie group G which is connected and whose Lie algebra is a nilpotent Lie algebra g. That is, its Lie algebra lower central series ...