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Define the "information function" to be I=-sum_(i=1)^NP_i(epsilon)ln[P_i(epsilon)], (1) where P_i(epsilon) is the natural measure, or probability that element i is populated, ...

A method which can be used to solve the initial value problem for certain classes of nonlinear partial differential equations. The method reduces the initial value problem to ...

An iterated map is a map that is applied repeatedly to an object. The Wolfram Language function NestList[f, expr, n] gives a list of the results of iterating the function f n ...

Since each triplet of Yff circles are congruent and pass through a single point, they obey Johnson's theorem. As a result, in each case, there is a fourth circle congruent to ...

Johnson's theorem states that if three equal circles mutually intersect one another in a single point, then the circle passing through their other three pairwise points of ...

A Kähler metric is a Riemannian metric g on a complex manifold which gives M a Kähler structure, i.e., it is a Kähler manifold with a Kähler form. However, the term "Kähler ...

The Lebesgue integral is defined in terms of upper and lower bounds using the Lebesgue measure of a set. It uses a Lebesgue sum S_n=sum_(i)eta_imu(E_i) where eta_i is the ...

The function defined by chi_nu(z)=sum_(k=0)^infty(z^(2k+1))/((2k+1)^nu). (1) It is related to the polylogarithm by chi_nu(z) = 1/2[Li_nu(z)-Li_nu(-z)] (2) = ...

There are several conflicting meanings associated with the notation lgx. In German and Russian literature, the notation lgx is used to mean the common logarithm log_(10)x. ...

Consider a collection of diagonal matrices H_1,...,H_k, which span a subspace h. Then the ith eigenvalue, i.e., the ith entry along the diagonal, is a linear functional on h, ...