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An orientation on an n-dimensional manifold is given by a nowhere vanishing differential n-form. Alternatively, it is an bundle orientation for the tangent bundle. If an ...

Mann's theorem is a theorem widely circulated as the "alpha-beta conjecture" that was subsequently proven by Mann (1942). It states that if A and B are sets of integers each ...

A map is a way of associating unique objects to every element in a given set. So a map f:A|->B from A to B is a function f such that for every a in A, there is a unique ...

A point x^* which is mapped to itself under a map G, so that x^*=G(x^*). Such points are sometimes also called invariant points or fixed elements (Woods 1961). Stable fixed ...

A general formula giving the number of distinct ways of folding an m×n rectangular map is not known. A distinct folding is defined as a permutation of N=m×n numbered cells ...

Consider the local behavior of a map f:R^m->R^n by choosing a point x in R^m and an open neighborhood U subset R^m such that x in U. Now consider the set of all mappings ...

A method for computing the prime counting function. Define the function T_k(x,a)=(-1)^(beta_0+beta_1+...+beta_(a-1))|_x/(p_1^(beta_0)p_2^(beta_1)...p_a^(beta_(a-1)))_|, (1) ...

The game of nim appearing in Alain Resnais' film Last Year at Marienbad (L'année dernière à Marienbad, 1961). In Marienbad, two players alternately draw counters from one of ...

Formulas obtained from differentiating Newton's forward difference formula, where R_n^'=h^nf^((n+1))(xi)d/(dp)(p; n+1)+h^(n+1)(p; n+1)d/(dx)f^((n+1))(xi), (n; k) is a ...

Markov's theorem states that equivalent braids expressing the same link are mutually related by successive applications of two types of Markov moves. Markov's theorem is ...