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A function has compact support if it is zero outside of a compact set. Alternatively, one can say that a function has compact support if its support is a compact set. For ...

Functions which can be expressed in terms of Legendre functions of the first and second kinds. See Abramowitz and Stegun (1972, p. 337). P_(-1/2+ip)(costheta) = (1) = ...

The mathematical study of how to manipulate the parameters affecting the behavior of a system to produce the desired or optimal outcome.

Attractive compounds can be constructed from the cube 3-compounds and their octahedron 3-compound duals. One is illustrated above. This compound will be implemented in a ...

The double bar symbol | is used to denote certain kinds of norms in mathematics (e.g., ||x|| or ||x||_2). It is also used to denote parallel lines, as in A∥B, and in an older ...

A group action phi:G×X->X is called faithful if there are no group elements g (except the identity element) such that gx=x for all x in X. Equivalently, the map phi induces ...

A group acts freely if there are no group fixed points. A point which is fixed by every group element would not be free to move.

The abscissas of the N-point Gaussian quadrature formula are precisely the roots of the orthogonal polynomial for the same interval and weighting function.

If A is a unital Banach algebra where every nonzero element is invertible, then A is the algebra of complex numbers.

Let S be a set of n+1 symbols, then a Howell design H(s,2n) on symbol set S is an s×s array H such that 1. Every cell of H is either empty or contains an unordered pair of ...