Search Results for ""

Quicksort is the fastest known comparison-based sorting algorithm (on average, and for a large number of elements), requiring O(nlgn) steps. Quicksort is a recursive ...

A sequence produced by the instructions "reverse, add to the original, then sort the digits." For example, after 668, the next iteration is given by 668+866=1534, so the next ...

By analogy with the sinc function, define the tanc function by tanc(z)={(tanz)/z for z!=0; 1 for z=0. (1) Since tanz/z is not a cardinal function, the "analogy" with the sinc ...

A set of positive integers is called weakly triple-free if, for any integer x, the set {x,2x,3x} !subset= S. For example, all subsets of {1,2,3,4,5} are weakly triple-free ...

One form of van der Waerden's theorem states that for all positive integers k and r, there exists a constant n(r,k) such that if n_0>=n(r,k) and {1,2,...,n_0} subset C_1 ...

A two-dimensional binary (k=2) totalistic cellular automaton with a von Neumann neighborhood of range r=1. It has a birth rule that at least 2 of its 4 neighbors are alive, ...

Gauge theory studies principal bundle connections, called gauge fields, on a principal bundle. These connections correspond to fields, in physics, such as an electromagnetic ...

A branch of mathematics that is a sort of generalization of calculus. Calculus of variations seeks to find the path, curve, surface, etc., for which a given function has a ...

Every semisimple Lie algebra g is classified by its Dynkin diagram. A Dynkin diagram is a graph with a few different kinds of possible edges. The connected components of the ...

The inverse cosine is the multivalued function cos^(-1)z (Zwillinger 1995, p. 465), also denoted arccosz (Abramowitz and Stegun 1972, p. 79; Harris and Stocker 1998, p. 307; ...