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Arc length is defined as the length along a curve, s=int_gamma|dl|, (1) where dl is a differential displacement vector along a curve gamma. For example, for a circle of ...

In the field of percolation theory, the term percolation threshold is used to denote the probability which "marks the arrival" (Grimmett 1999) of an infinite connected ...

A factor of a polynomial P(x) of degree n is a polynomial Q(x) of degree less than n which can be multiplied by another polynomial R(x) of degree less than n to yield P(x), ...

Let a particle travel a distance s(t) as a function of time t (here, s can be thought of as the arc length of the curve traced out by the particle). The speed (the scalar ...

A partial differential equation which appears in differential geometry and relativistic field theory. Its name is a wordplay on its similar form to the Klein-Gordon equation. ...

An angle bracket is the combination of a bra and ket (bra+ket = bracket) which represents the inner product of two functions or vectors (or 1-forms), <f|g>=intf(x)g^|(x)dx in ...

A complete metric space is a metric space in which every Cauchy sequence is convergent. Examples include the real numbers with the usual metric, the complex numbers, ...

A standard form of the linear programming problem of maximizing a linear function over a convex polyhedron is to maximize c·x subject to mx<=b and x>=0, where m is a given ...

An extreme point of a subset K of a vector space X is an extreme set S of K which consists of a single point x in K. The collection of all extreme points of K is sometimes ...

The French metro metric is an example for disproving apparently intuitive but false properties of metric spaces. The metric consists of a distance function on the plane such ...