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In order for a band-limited (i.e., one with a zero power spectrum for frequencies nu>B) baseband (nu>0) signal to be reconstructed fully, it must be sampled at a rate nu>=2B. ...

A pair of dice which have the same odds for throwing every number as a normal pair of 6-sided dice. They are the only such alternate arrangement if face values are required ...

A cubic spline is a spline constructed of piecewise third-order polynomials which pass through a set of m control points. The second derivative of each polynomial is commonly ...

Direct sums are defined for a number of different sorts of mathematical objects, including subspaces, matrices, modules, and groups. The matrix direct sum is defined by ...

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 ...

The Dehn invariant is a constant defined using the angles and edge lengths of a three-dimensional polyhedron. It is significant because it remains constant under polyhedron ...

Let P(x) be defined as the power series whose nth term has a coefficient equal to the nth prime p_n, P(x) = 1+sum_(k=1)^(infty)p_kx^k (1) = 1+2x+3x^2+5x^3+7x^4+11x^5+.... (2) ...

The differential equation obtained by applying the biharmonic operator and setting to zero: del ^4phi=0. (1) In Cartesian coordinates, the biharmonic equation is del ^4phi = ...

A block diagonal matrix, also called a diagonal block matrix, is a square diagonal matrix in which the diagonal elements are square matrices of any size (possibly even 1×1), ...

There are two types of bordism groups: bordism groups, also called cobordism groups or cobordism rings, and there are singular bordism groups. The bordism groups give a ...