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The kernel of a module homomorphism f:M-->N is the set of all elements of M which are mapped to zero. It is the kernel of f as a homomorphism of additive groups, and is a ...

There are a number of attractive polyhedron compounds consisting of ten octahedra. These compounds will be implemented in a future version of the Wolfram Language as ...

Let A:D(A)->H and B:D(B)->H be linear operators from domains D(A) and D(B), respectively, into a Hilbert space H. It is said that B extends A if D(A) subset D(B) and if Bv=Av ...

For a parabola oriented vertically and opening upwards, the vertex is the point where the curve reaches a minimum.

An upper semicontinuous function whose restrictions to all complex lines are subharmonic (where defined). These functions were introduced by P. Lelong and Oka in the early ...

Let p be an odd prime, k be an integer such that pk and 1<=k<=2(p+1), and N=2kp+1. Then the following are equivalent 1. N is prime. 2. There exists an a such that ...

A surface constructed by placing a family of figure-eight curves into R^3 such that the first and last curves reduce to points. The surface has parametric equations x(u,v) = ...

A three-dimensional coordinate system in which the axes satisfy the right-hand rule.

In order for a band-limited (i.e., one with a zero power spectrum for frequencies nu>B) baseband (nu>0) signal to be reconstructed fully, it must be sampled at a rate nu>=2B. ...

The Schnirelmann density of a set of nonnegative integers is the greatest lower bound of the fractions A(n)/n where A(n) is the number of terms in the set <=n.