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A popular acronym for "principal ideal domain." In engineering circles, the acronym PID refers to the "proportional-integral-derivative method" algorithm for controlling ...

Given a sequence {a_k}_(k=1)^n, a partial sum of the first N terms is given by S_N=sum_(k=1)^Na_k.

A perfect cubic polynomial can be factored into a linear and a quadratic term, x^3+y^3 = (x+y)(x^2-xy+y^2) (1) x^3-y^3 = (x-y)(x^2+xy+y^2). (2)

A perfect field is a field F such that every algebraic extension is separable. Any field in field characteristic zero, such as the rationals or the p-adics, or any finite ...

An adjoint curve which bears a special relation to the base curve.

Let V be a variety, and write G(V) for the set of divisors, G_l(V) for the set of divisors linearly equivalent to 0, and G_a(V) for the group of divisors algebraically equal ...

The class m, curve order n, number of ordinary double points delta, number of cusps kappa, number of inflection points (inflection points) iota, number of bitangents tau, and ...

The Poincaré group is another name for the inhomogeneous Lorentz group (Weinberg 1972, p. 28) and corresponds to the group of inhomogeneous Lorentz transformations, also ...

Let {y^k} be a set of orthonormal vectors with k=1, 2, ..., K, such that the inner product (y^k,y^k)=1. Then set x=sum_(k=1)^Ku_ky^k (1) so that for any square matrix A for ...

A divergenceless field can be partitioned into a toroidal and a poloidal part. This separation is important in geo- and heliophysics, and in particular in dynamo theory and ...