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A nonzero and noninvertible element a of a ring R which generates a prime ideal. It can also be characterized by the condition that whenever a divides a product in R, a ...

Let (X,A,mu) and (Y,B,nu) be measure spaces, let R be the collection of all measurable rectangles contained in X×Y, and let lambda be the premeasure defined on R by ...

Quantization is a nonlinear process which generates additional frequency components (Thompson et al. 1986). This means that the signal is no longer band-limited, so the ...

A groupoid S such that for all a,b in S, there exist unique x,y in S such that ax = b (1) ya = b. (2) No other restrictions are applied; thus a quasigroup need not have an ...

If A is a class of recursively enumerable sets, then the set of Gödel numbers of functions whose domains belong to A is called its index set. If the index set of A is a ...

A ring homomorphism is a map f:R->S between two rings such that 1. Addition is preserved:f(r_1+r_2)=f(r_1)+f(r_2), 2. The zero element is mapped to zero: f(0_R)=0_S, and 3. ...

The special orthogonal group SO_n(q) is the subgroup of the elements of general orthogonal group GO_n(q) with determinant 1. SO_3 (often written SO(3)) is the rotation group ...

Given a complex measure mu, there exists a positive measure denoted |mu| which measures the total variation of mu, also sometimes called simply "total variation." In ...

A total order (or "totally ordered set," or "linearly ordered set") is a set plus a relation on the set (called a total order) that satisfies the conditions for a partial ...

The vertex set of a graph is simply a set of all vertices of the graph. The cardinality of the vertex set for a given graph g is known as the vertex count of g. The vertex ...