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The eigenvalues of a graph are defined as the eigenvalues of its adjacency matrix. The set of eigenvalues of a graph is called a graph spectrum. The largest eigenvalue ...

For any positive integer k, there exists a prime arithmetic progression of length k. The proof is an extension of Szemerédi's theorem.

The harmonic conjugate to a given function u(x,y) is a function v(x,y) such that f(x,y)=u(x,y)+iv(x,y) is complex differentiable (i.e., satisfies the Cauchy-Riemann ...

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 ...

The hemicube, which might also be called the square hemiprism, is a simple solid that serves as an example of one of the two topological classes of convex hexahedron having 7 ...

The Gelfond-Schneider constant is sometimes known as the Hilbert number. Flannery and Flannery (2000, p. 35) define a Hilbert number as a positive integer of the form n=4k+1 ...

Given two modules M and N over a unit ring R, Hom_R(M,N) denotes the set of all module homomorphisms from M to N. It is an R-module with respect to the addition of maps, ...

An abstract algebra concerned with results valid for many different kinds of spaces. Modules are the basic tools used in homological algebra.

A hypergeometric series sum_(k)c_k is a series for which c_0=1 and the ratio of consecutive terms is a rational function of the summation index k, i.e., one for which ...

The invertible matrix theorem is a theorem in linear algebra which gives a series of equivalent conditions for an n×n square matrix A to have an inverse. In particular, A is ...