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Let V be a vector space over a field K, and let A be a nonempty set. Now define addition p+a in A for any vector a in V and element p in A subject to the conditions: 1. ...

A quasigroup with an identity element e such that xe=x and ex=x for any x in the quasigroup. All groups are loops. In general, loops are considered to have very little in the ...

The mathematical study of how given quantities can be approximated by other (usually simpler) ones under appropriate conditions. Approximation theory also studies the size ...

Let phi:M->M be a C^1 diffeomorphism on a compact Riemannian manifold M. Then phi satisfies Axiom A if the nonwandering set Omega(phi) of phi is hyperbolic and the periodic ...

Use the definition of the q-series (a;q)_n=product_(j=0)^(n-1)(1-aq^j) (1) and define [N; M]=((q^(N-M+1);q)_M)/((q;q)_m). (2) Then P. Borwein has conjectured that (1) the ...

The Brent-Salamin formula, also called the Gauss-Salamin formula or Salamin formula, is a formula that uses the arithmetic-geometric mean to compute pi. It has quadratic ...

Due to nonlinearities in weather processes, a butterfly flapping its wings in Tahiti can, in theory, produce a tornado in Kansas. This strong dependence of outcomes on very ...

A function H that maps an arbitrary length message M to a fixed length message digest MD is a collision-free hash function if 1. It is a one-way hash function. 2. It is hard ...

A set of orthogonal functions {phi_n(x)} is termed complete in the closed interval x in [a,b] if, for every piecewise continuous function f(x) in the interval, the minimum ...

A computation is an operation that begins with some initial conditions and gives an output which follows from a definite set of rules. The most common example are ...