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Let phi(t) be the characteristic function, defined as the Fourier transform of the probability density function P(x) using Fourier transform parameters a=b=1, phi(t) = ...

Dirichlet's principle, also known as Thomson's principle, states that there exists a function u that minimizes the functional D[u]=int_Omega|del u|^2dV (called the Dirichlet ...

The essential supremum is the proper generalization to measurable functions of the maximum. The technical difference is that the values of a function on a set of measure zero ...

A continuous statistical distribution which arises in the testing of whether two observed samples have the same variance. Let chi_m^2 and chi_n^2 be independent variates ...

The modular group Gamma is the set of all transformations w of the form w(t)=(at+b)/(ct+d), where a, b, c, and d are integers and ad-bc=1. A Gamma-modular function is then ...

If p_1, ..., p_n are positive numbers which sum to 1 and f is a real continuous function that is convex, then f(sum_(i=1)^np_ix_i)<=sum_(i=1)^np_if(x_i). (1) If f is concave, ...

The German mathematician Kronecker proved that all the Galois extensions of the rationals Q with Abelian Galois groups are subfields of cyclotomic fields Q(mu_n), where mu_n ...

An algorithm for finding roots which retains that prior estimate for which the function value has opposite sign from the function value at the current best estimate of the ...

Let any finite or infinite set of points having no finite limit point be prescribed and associate with each of its points a principal part, i.e., a rational function of the ...

A skewed distribution which is similar to the binomial distribution when p!=q (Abramowitz and Stegun 1972, p. 930). y=k(t+A)^(A^2-1)e^(-At), (1) for t in [0,infty) where A = ...