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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 ...

The equation of motion for a membrane shaped as a right isosceles triangle of length c on a side and with the sides oriented along the positive x and y axes is given by where ...

There are at least two theorems known as Weierstrass's theorem. The first states that the only hypercomplex number systems with commutative multiplication and addition are ...