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Let B, A, and e be square matrices with e small, and define B=A(I+e), (1) where I is the identity matrix. Then the inverse of B is approximately B^(-1)=(I-e)A^(-1). (2) This ...

The dimension d of any irreducible representation of a group G must be a divisor of the index of each maximal normal Abelian subgroup of G. Note that while Itô's theorem was ...

The partial differential equation u_t=u_(xxxxx)+5/2u_(xxx)u+(25)/4u_(xx)u_x+5/4u^2u_x.

The length is the longest dimension of an object.

Polynomials s_k(x) which form the Sheffer sequence for f(t)=-(2t)/(1-t^2) (1) and have exponential generating function ...

A multiple root is a root with multiplicity n>=2, also called a multiple point or repeated root. For example, in the equation (x-1)^2=0, 1 is multiple (double) root. If a ...

A permutation cycle is a subset of a permutation whose elements trade places with one another. Permutations cycles are called "orbits" by Comtet (1974, p. 256). For example, ...

A relation is any subset of a Cartesian product. For instance, a subset of A×B, called a "binary relation from A to B," is a collection of ordered pairs (a,b) with first ...

A regular graph that is edge-transitive but not vertex-transitive is called a semisymmetric graph (Marušič and Potočnik 2001). In contrast, any graph that is both ...

Let n be an elliptic pseudoprime associated with (E,P), and let n+1=2^sk with k odd and s>=0. Then n is a strong elliptic pseudoprime when either kP=0 (mod n) or 2^rkP=0 (mod ...