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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 ...

There are at least two theorems known as Weierstrass's theorem. The first states that the only hypercomplex number systems with commutative multiplication and addition are ...

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 ...

A helix, sometimes also called a coil, is a curve for which the tangent makes a constant angle with a fixed line. The shortest path between two points on a cylinder (one not ...

To predict the result of a measurement requires (1) a model of the system under investigation, and (2) a physical theory linking the parameters of the model to the parameters ...