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A knot K embedded in R^3=C_z×R_t, where the three-dimensional space R^3 is represented as a direct product of a complex line C with coordinate z and a real line R with ...

The transformation T(x) = frac(1/x) (1) = 1/x-|_1/x_|, (2) where frac(x) is the fractional part of x and |_x_| is the floor function, that takes a continued fraction ...

A function A such that B=del xA. The most common use of a vector potential is the representation of a magnetic field. If a vector field has zero divergence, it may be ...

If f is a schlicht function and D(z_0,r) is the open disk of radius r centered at z_0, then f(D(0,1)) superset= D(0,1/4), where superset= denotes a (not necessarily proper) ...

A generalized hypergeometric function _pF_q[alpha_1,alpha_2,...,alpha_p; beta_1,beta_2,...,beta_q;z] is said to be well-poised if p=q+1 and ...

The nesting of two or more functions to form a single new function is known as composition. The composition of two functions f and g is denoted f degreesg, where f is a ...

Analytic continuation gives an equivalence relation between function elements, and the equivalence classes induced by this relation are called global analytic functions.

A graph or directed graph together with a function which assigns a positive real number to each edge (Harary 1994, p. 52).

The number of different triangles which have integer side lengths and perimeter n is T(n) = P(n,3)-sum_(1<=j<=|_n/2_|)P(j,2) (1) = [(n^2)/(12)]-|_n/4_||_(n+2)/4_| (2) = ...

A set function mu possesses countable additivity if, given any countable disjoint collection of sets {E_k}_(k=1)^n on which mu is defined, mu( union ...