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A connection on a vector bundle pi:E->M is a way to "differentiate" bundle sections, in a way that is analogous to the exterior derivative df of a function f. In particular, ...

The Zernike polynomials are a set of orthogonal polynomials that arise in the expansion of a wavefront function for optical systems with circular pupils. The odd and even ...

An algebraic expression in variables {x_1,...,x_n} is an expression constructed with the variables and algebraic numbers using addition, multiplication, and rational powers.

A field K is said to be algebraically closed if every polynomial with coefficients in K has a root in K.

A function f(x) is said to be antiperiodic with antiperiod p if -f(x)=f(x+np) for n=1, 3, .... For example, the sine function sinx is antiperiodic with period pi (as well as ...

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

Three elements x, y and z of a set S are said to be associative under a binary operation * if they satisfy x*(y*z)=(x*y)*z. (1) Real numbers are associative under addition ...

A theorem from information theory that is a simple consequence of the weak law of large numbers. It states that if a set of values X_1, X_2, ..., X_n is drawn independently ...

A method for mapping three-dimensional figures onto the plane.

A man of Seville is shaved by the Barber of Seville iff the man does not shave himself. Does the barber shave himself? This pseudoparadox was proposed by Bertrand Russell.