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The polyhedron compound of the truncated icosahedron and its dual, the pentakis dodecahedron. The compound can be constructed from a truncated icosahedron of unit edge length ...

The space |K| which is the subset of R^n that is the union of the simplices in a simplicial complex K. The term polytope is sometimes used as a synonym for underlying space ...

A quantity which takes on the value zero is said to vanish identically, or sometimes simply to vanish. The term "vanish identically" is preferred when emphasis is needed that ...

A quantity which takes on the value zero is said to vanish. For example, the function f(z)=z^2 vanishes at the point z=0. For emphasis, the term "vanish identically" is ...

The probability law on the space of continuous functions g with g(0)=0, induced by the Wiener process.

The zero product property asserts that, for elements a and b, ab=0=>a=0 or b=0. This property is especially relevant when considering algebraic structures because, e.g., ...

A Cartan matrix is a square integer matrix who elements (A_(ij)) satisfy the following conditions. 1. A_(ij) is an integer, one of {-3,-2,-1,0,2}. 2. A_(ii)=2 the diagonal ...

Adding a damping force proportional to x^. to the equation of simple harmonic motion, the first derivative of x with respect to time, the equation of motion for damped simple ...

Given a first-order ordinary differential equation (dy)/(dx)=F(x,y), (1) if F(x,y) can be expressed using separation of variables as F(x,y)=X(x)Y(y), (2) then the equation ...

In one dimension, the Gaussian function is the probability density function of the normal distribution, f(x)=1/(sigmasqrt(2pi))e^(-(x-mu)^2/(2sigma^2)), (1) sometimes also ...