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The series h_q(-r)=sum_(n=1)^infty1/(q^n+r) (1) for q an integer other than 0 and +/-1. h_q and the related series Ln_q(-r+1)=sum_(n=1)^infty((-1)^n)/(q^n+r), (2) which is a ...

Let a random n×n (0,1)-matrix have entries which are 1 (with probability p) or 0 (with probability q=1-p). An s-cluster is an isolated group of s adjacent (i.e., horizontally ...

The partial differential equation u_t=(1+ia)u_(xx)+(1+ic)u-(1+id)|u|^2u.

When a measure lambda is absolutely continuous with respect to a positive measure mu, then it can be written as lambda(E)=int_Efdmu. By analogy with the first fundamental ...

A real matrix is a matrix whose elements consist entirely of real numbers. The set of m×n real matrices is sometimes denoted R^(m×n) (Zwillinger 1995, p. 116).

A vector whose elements are real numbers.

Calculating the 13th root of a large number (that is a perfect 13th power) is a famous mental calculation challenge. However, because of difficulties in standardizing the ...

An abstract group is a group characterized only by its abstract properties and not by the particular representations chosen for elements. For example, there are two distinct ...

A function representable as a generalized Fourier series. Let R be a metric space with metric rho(x,y). Following Bohr (1947), a continuous function x(t) for (-infty<t<infty) ...

A 1-variable unoriented knot polynomial Q(x). It satisfies Q_(unknot)=1 (1) and the skein relationship Q_(L_+)+Q_(L_-)=x(Q_(L_0)+Q_(L_infty)). (2) It also satisfies ...