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The number of elements in a group G, denoted |G|. If the order of a group is a finite number, the group is said to be a finite group. The order of an element g of a finite ...

A formal logic developed by Alonzo Church and Stephen Kleene to address the computable number problem. In the lambda calculus, lambda is defined as the abstraction operator. ...

Let G=(V,E) be a (not necessarily simple) undirected edge-weighted graph with nonnegative weights. A cut C of G is any nontrivial subset of V, and the weight of the cut is ...

Isolated resonances in a dynamical system can cause considerable distortion of preserved tori in their neighborhood, but they do not introduce any chaos into a system. ...

The maximal number of regions into which space can be divided by n planes is f(n)=1/6(n^3+5n+6) (Yaglom and Yaglom 1987, pp. 102-106). For n=1, 2, ..., these give the values ...

Let h:{0,1}^(l(n))×{0,1}^n->{0,1}^(m(n)) be efficiently computable by an algorithm (solving a P-problem). For fixed y in {0,1}^(l(n)), view h(x,y) as a function h_y(x) of x ...

The Frobenius number is the largest value b for which the Frobenius equation a_1x_1+a_2x_2+...+a_nx_n=b, (1) has no solution, where the a_i are positive integers, b is an ...

n weighings are sufficient to find a bad coin among (3^n-1)/2 coins (Steinhaus 1999, p. 61). vos Savant (1993) gives an algorithm for finding a bad ball among 12 balls in ...

The lines connecting the vertices and corresponding circle-circle intersections in Malfatti's problem coincide in a point X_(179) called the first Ajima-Malfatti point ...

A circle packing is an arrangement of circles inside a given boundary such that no two overlap and some (or all) of them are mutually tangent. The generalization to spheres ...