Search Results for ""

Many authors (e.g., Mendelson 1963; Pervin 1964) use the term arcwise-connected as a synonym for pathwise-connected. Other authors (e.g., Armstrong 1983; Cullen 1968; and ...

An important and fundamental axiom in set theory sometimes called Zermelo's axiom of choice. It was formulated by Zermelo in 1904 and states that, given any set of mutually ...

A band over a fixed topological space X is represented by a cover X= union U_alpha, U_alpha subset= X, and for each alpha, a sheaf of groups K_alpha on U_alpha along with ...

A "beam detector" for a given curve C is defined as a curve (or set of curves) through which every line tangent to or intersecting C passes. The shortest 1-arc beam detector, ...

In discrete percolation theory, bond percolation is a percolation model on a regular point lattice L=L^d in d-dimensional Euclidean space which considers the lattice graph ...

Given a general quadrilateral with sides of lengths a, b, c, and d, the area is given by K = 1/4sqrt(4p^2q^2-(b^2+d^2-a^2-c^2)^2) (1) = (2) (Coolidge 1939; Ivanov 1960; Beyer ...

(1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+alpha^2y=0 (1) for |x|<1. The Chebyshev differential equation has regular singular points at -1, 1, and infty. It can be solved by series ...

The Chu-Vandermonde identity _2F_1(-n,b;c;1)=((c-b)_n)/((c)_n) (1) (for n in Z^+) is a special case of Gauss's hypergeometric theorem _2F_1(a,b;c;1) = ((c-b)_(-a))/((c)_(-a)) ...

A fundamental system of logic based on the concept of a generalized function whose argument is also a function (Schönfinkel 1924). This mathematical discipline was ...

The study of efficient algorithms for solving geometric problems. Examples of problems treated by computational geometry include determination of the convex hull and Voronoi ...