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The crystallographic point groups are the point groups in which translational periodicity is required (the so-called crystallography restriction). There are 32 such groups, ...

The edge chromatic number, sometimes also called the chromatic index, of a graph G is fewest number of colors necessary to color each edge of G such that no two edges ...

The Euler formula, sometimes also called the Euler identity (e.g., Trott 2004, p. 174), states e^(ix)=cosx+isinx, (1) where i is the imaginary unit. Note that Euler's ...

Let X be a set of urelements, and let V(^*X) be an enlargement of the superstructure V(X). Let A in V(X) be a finitary algebra with finitely many fundamental operations. Then ...

The Floyd-Warshall algorithm, also variously known as Floyd's algorithm, the Roy-Floyd algorithm, the Roy-Warshall algorithm, or the WFI algorithm, is an algorithm for ...

Let there be m doctors and n<=m patients, and let all mn possible combinations of examinations of patients by doctors take place. Then what is the minimum number of surgical ...

Given a square n×n nonsingular integer matrix A, there exists an n×n unimodular matrix U and an n×n matrix H (known as the Hermite normal form of A) such that AU=H. ...

One of the numbers ..., -2, -1, 0, 1, 2, .... The set of integers forms a ring that is denoted Z. A given integer n may be negative (n in Z^-), nonnegative (n in Z^*), zero ...

An algebra <L; ^ , v > is called a lattice if L is a nonempty set, ^ and v are binary operations on L, both ^ and v are idempotent, commutative, and associative, and they ...

A Lie group is a smooth manifold obeying the group properties and that satisfies the additional condition that the group operations are differentiable. This definition is ...