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A partial differential diffusion equation of the form (partialU)/(partialt)=kappadel ^2U. (1) Physically, the equation commonly arises in situations where kappa is the ...

In two-dimensional Cartesian coordinates, attempt separation of variables by writing F(x,y)=X(x)Y(y), (1) then the Helmholtz differential equation becomes ...

On the surface of a sphere, attempt separation of variables in spherical coordinates by writing F(theta,phi)=Theta(theta)Phi(phi), (1) then the Helmholtz differential ...

Consider a first-order logic formula Phi in Skolemized form forall x_1... forall x_nS. Then the Herbrand universe H of S is defined by the following rules. 1. All constants ...

There are two important theorems known as Herbrand's theorem. The first arises in ring theory. Let an ideal class be in A if it contains an ideal whose lth power is ...

A Hermitian inner product on a complex vector space V is a complex-valued bilinear form on V which is antilinear in the second slot, and is positive definite. That is, it ...

A Hermitian metric on a complex vector bundle assigns a Hermitian inner product to every fiber bundle. The basic example is the trivial bundle pi:U×C^k->U, where U is an open ...

The term "higher dimensional group theory" was introduced by Brown (1982), and refers to a method for obtaining new homotopical information by generalizing to higher ...

The Hilbert transform (and its inverse) are the integral transform g(y) = H[f(x)]=1/piPVint_(-infty)^infty(f(x)dx)/(x-y) (1) f(x) = ...

Let G be a k-regular graph with girth 5 and graph diameter 2. (Such a graph is a Moore graph). Then, k=2, 3, 7, or 57. A proof of this theorem is difficult (Hoffman and ...