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Alpha is the name for the first letter in the Greek alphabet: alpha. In finance, alpha is a financial measure giving the difference between a fund's actual return and its ...

When the Gaussian curvature K is everywhere negative, a surface is called anticlastic and is saddle-shaped. A surface on which K is everywhere positive is called synclastic. ...

For positive numbers a and b with a!=b, (a+b)/2>(b-a)/(lnb-lna)>sqrt(ab).

Let p be an odd prime, a be a positive number such that pa (i.e., p does not divide a), and let x be one of the numbers 1, 2, 3, ..., p-1. Then there is a unique x^', called ...

Let the characteristic polynomial of an n×n complex matrix A be written in the form P(lambda) = |lambdaI-A| (1) = ...

The bend of a circle C mutually tangent to three other circles is defined as the signed curvature of C. If the contacts are all external, the signs of the bends of all four ...

An experiment in which s trials are made of an event, with probability p of success in any given trial.

If a function phi:(0,infty)->(0,infty) satisfies 1. ln[phi(x)] is convex, 2. phi(x+1)=xphi(x) for all x>0, and 3. phi(1)=1, then phi(x) is the gamma function Gamma(x). ...

A sequence {nu_i} of nondecreasing positive integers is complete iff 1. nu_1=1. 2. For all k=2, 3, ..., s_(k-1)=nu_1+nu_2+...+nu_(k-1)>=nu_k-1. A corollary states that a ...

A bilinear functional phi on a normed space E is called coercive (or sometimes elliptic) if there exists a positive constant K such that phi(x,x)>=K||x||^2 for all x in E.