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The m×n rook graph (confusingly called the m×n grid by Brouwer et al. 1989, p. 440) and also sometimes known as a lattice graph (e.g., Brouwer) is the graph Cartesian product ...

A tree is a mathematical structure that can be viewed as either a graph or as a data structure. The two views are equivalent, since a tree data structure contains not only a ...

Two partially ordered sets are said to be isomorphic if their "structures" are entirely analogous. Formally, partially ordered sets P=(X,<=) and Q=(X^',<=^') are isomorphic ...

An ambiguous term which is sometimes used to mean a partially ordered set and sometimes to mean a totally ordered set.

A set R of linear extensions of a partially ordered set P=(X,<=) is a realizer of P (and is said to realize P) provided that for all x,y in X, x<=y iff x is below y in every ...

Let P=(P,<=) be a partially ordered set, and let x,y,z in P. If x<=y<=z, then y is said to be between x and z. If y is between x and z and y not in {x,z}, then y is strictly ...

The quantum electrodynamical law which applies to spin-1/2 particles and is the relativistic generalization of the Schrödinger equation. In 3+1 dimensions (three space ...

Cauchy conditions are initial conditions (time conditions) rather than boundary conditions (space conditions). An initial-value problem is often termed a Cauchy problem. ...

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 ...

As shown by Morse and Feshbach (1953), the Helmholtz differential equation is separable in confocal paraboloidal coordinates.