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If X is any compact space, let A be a subalgebra of the algebra C(X) over the reals R with binary operations + and ×. Then, if A contains the constant functions and separates ...

Let U subset= C be an open set and f a real-valued continuous function on U. Suppose that for each closed disk D^_(P,r) subset= U and every real-valued harmonic function h ...

Universality is the property of being able to perform different tasks with the same underlying construction just by being programmed in a different way. Universal systems are ...

The vertex set of a graph is simply a set of all vertices of the graph. The cardinality of the vertex set for a given graph g is known as the vertex count of g. The vertex ...

There are (at least) two mathematical objects known as Weierstrass forms. The first is a general form into which an elliptic curve over any field K can be transformed, given ...

A figure used in many Asian cultures to symbolize the unity of the two "opposite" female and male elements, the "yin" and "yang." The solid and hollow parts composing the ...

Differential Equations

The constants C_n defined by C_n=[int_0^infty|d/(dt)((sint)/t)^n|dt]-1. (1) These constants can also be written as the sums C_n=2sum_(k=1)^infty(1+x_k^2)^(-n/2), (2) and ...

An invariant of an elliptic curve given in the form y^2=x^3+ax+b which is closely related to the elliptic discriminant and defined by j(E)=(2^83^3a^3)/(4a^3+27b^2). The ...

First published in Riemann's groundbreaking 1859 paper (Riemann 1859), the Riemann hypothesis is a deep mathematical conjecture which states that the nontrivial Riemann zeta ...