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Let H_n denote the nth hexagonal number and S_m the mth square number, then a number which is both hexagonal and square satisfies the equation H_n=S_m, or n(2n-1)=m^2. (1) ...

Given a finitely generated Z-graded module M over a graded ring R (finitely generated over R_0, which is an Artinian local ring), define the Hilbert function of M as the map ...

The branch of mathematics dealing with the efficient and accurate storage, transmission, and representation of information.

Admitting an inverse. An object that is invertible is referred to as an invertible element in a monoid or a unit ring, or to a map, which admits an inverse map iff it is ...

An illusion named after the psychologist Joseph Jastrow. In the above figure, the left edges of the laminas A and B are colinear, creating an illusion of different size. ...

The operator tpartial/partialr that can be used to derive multivariate formulas for moments and cumulants from corresponding univariate formulas. For example, to derive the ...

Leakage, more explicitly called spectral leakage, is a smearing of power across a frequency spectrum that occurs when the signal being measured is not periodic in the sample ...

The Lommel polynomials R_(m,nu)(z) arise from the equation J_(m+nu)(z)=J_nu(z)R_(m,nu)(z)-J_(nu-1)(z)R_(m-1,nu+1)(z), (1) where J_nu(z) is a Bessel function of the first kind ...

If p>1, then Minkowski's integral inequality states that Similarly, if p>1 and a_k, b_k>0, then Minkowski's sum inequality states that [sum_(k=1)^n|a_k+b_k|^p]^(1/p) ...

A set in which no element divides the sum of any nonempty subset of the other elements. For example, {2,3,5} is dividing, since 2|(3+5) (and 5|(2+3)), but {4,6,7} is ...