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The Helmholtz differential equation in spherical coordinates is separable. In fact, it is separable under the more general condition that k^2 is of the form ...

A Hermitian form on a vector space V over the complex field C is a function f:V×V->C such that for all u,v,w in V and all a,b in R, 1. f(au+bv,w)=af(u,w)+bf(v,w). 2. ...

A complex line bundle is a vector bundle pi:E->M whose fibers pi^(-1)(m) are a copy of C. pi is a holomorphic line bundle if it is a holomorphic map between complex manifolds ...

A Kähler metric is a Riemannian metric g on a complex manifold which gives M a Kähler structure, i.e., it is a Kähler manifold with a Kähler form. However, the term "Kähler ...

Kontsevich's integral is a far-reaching generalization of the Gauss integral for the linking number, and provides a tool to construct the universal Vassiliev invariant of a ...

In conical coordinates, Laplace's equation can be written ...

A point about which inversion of two circles produced concentric circles. Every pair of distinct circles has two limiting points. The limiting points correspond to the point ...

Consider the local behavior of a map f:R^m->R^n by choosing a point x in R^m and an open neighborhood U subset R^m such that x in U. Now consider the set of all mappings ...

The Minkowski metric, also called the Minkowski tensor or pseudo-Riemannian metric, is a tensor eta_(alphabeta) whose elements are defined by the matrix (eta)_(alphabeta)=[-1 ...

Module multiplicity is a number associated with every nonzero finitely generated graded module M over a graded ring R for which the Hilbert series is defined. If dim(M)=d, ...