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The set of elements belonging to one but not both of two given sets. It is therefore the union of the complement of A with respect to B and B with respect to A, and ...

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) where x·y is vector multiplication which is assumed to be bilinear. Now define ...

In category theory, a tensor category (C, tensor ,I,a,r,l) consists of a category C, an object I of C, a functor tensor :C×C->C, and a natural isomorphism a = a_(UVW):(U ...

Tomography is the study of the reconstruction of two- and three-dimensional objects from one-dimensional slices. The Radon transform is an important tool in tomography. ...

Suppose that A and B are two algebras and M is a unital A-B-bimodule. Then [A M; 0 B]={[a m; 0 b]:a in A,m in M,b in B} with the usual 2×2 matrix-like addition and ...

A triply periodic function is a function having three distinct periods. Jacobi (1835) proved that a single-valued univariate function cannot have more than two distinct ...

The union of two sets A and B is the set obtained by combining the members of each. This is written A union B, and is pronounced "A union B" or "A cup B." The union of sets ...

A unique factorization domain, called UFD for short, is any integral domain in which every nonzero noninvertible element has a unique factorization, i.e., an essentially ...

A unit ring is a ring with a multiplicative identity. It is therefore sometimes also known as a "ring with identity." It is given by a set together with two binary operators ...

Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. This partitions graphs into ...