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A hexahedral graph is a polyhedral graph on six vertices. There are seven distinct hexahedral graphs (illustrated above) which, through duality, correspond to seven convex ...

If and only if (i.e., necessary and sufficient). The terms "just if" or "exactly when" are sometimes used instead. A iff B is written symbolically as A<->B, A<=>B, A<->B, or ...

Denoted zn(u,k) or Z(u). Z(phi|m)=E(phi|m)-(E(m)F(phi|m))/(K(m)), where phi is the Jacobi amplitude, m is the parameter, and F(phi|m) and K(m) are elliptic integrals of the ...

Long division is an algorithm for dividing two numbers, obtaining the quotient one digit at a time. The example above shows how the division of 123456/17 is performed to ...

A polyhedral graph on five nodes. There are two topologically distinct pentahedral graphs which, through duality, correspond to the skeletons of the square pyramid (left ...

In statistics, sampling is the selection and implementation of statistical observations in order to estimate properties of an underlying population. Sampling is a vital part ...

A square matrix with nonzero elements only on the diagonal and slots horizontally or vertically adjacent the diagonal (i.e., along the subdiagonal and superdiagonal), [a_(11) ...

Let J be a finite group and the image R(J) be a representation which is a homomorphism of J into a permutation group S(X), where S(X) is the group of all permutations of a ...

The elliptic modulus k is a quantity used in elliptic integrals and elliptic functions defined to be k=sqrt(m), where m is the parameter. An elliptic integral is written ...

Roughly speaking, isospectral manifolds are drums that sound the same, i.e., have the same eigenfrequency spectrum. Two drums with differing area, perimeter, or genus can ...