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The four-dimensional version of the gradient, encountered frequently in general relativity and special relativity, is del _mu=[1/cpartial/(partialt); partial/(partialx); ...

The set of points of X fixed by a group action are called the group's set of fixed points, defined by {x:gx=x for all g in G}. In some cases, there may not be a group action, ...

There are at least three definitions of "groupoid" currently in use. The first type of groupoid is an algebraic structure on a set with a binary operator. The only ...

The Helmholtz differential equation is not separable in bispherical coordinates.

An absolutely continuous measure on partialD whose density has the form exp(x+y^_), where x and y are real-valued functions in L^infty, ||y||_infty<pi/2, exp is the ...

Let A be a C^*-algebra. A C^*-subalgebra (that is a closed *-subalgebra) B of A is called hereditary if bab^' in B for all b,b^' in B and a in A, or equivalently if for a in ...

The Hilbert-Schmidt norm of a matrix A is a matrix norm defined by ||A||_(HS)=sqrt(sum_(i,j)a_(ij)^2).

In a chain complex of modules ...->C_(i+1)->^(d_(i+1))C_i->^(d_i)C_(i-1)->..., the module B_i of i-boundaries is the image of d_(i+1). It is a submodule of C_i and is ...

The identity element I (also denoted E, e, or 1) of a group or related mathematical structure S is the unique element such that Ia=aI=a for every element a in S. The symbol ...

Let A be a unital C^*-algebra, then an element u in A is called an isometry if u^*u=1.