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A measure lambda is absolutely continuous with respect to another measure mu if lambda(E)=0 for every set with mu(E)=0. This makes sense as long as mu is a positive measure, ...

A golden rhombohedron is a trigonal trapezohedron (and therefore rhombohedron with congruent rhombic faces) whose faces consist of six equal golden rhombi. There are two ...

Given a triangle DeltaABC, construct the contact triangle DeltaT_AT_BT_C. Now extend lines parallel to the sides of the contact triangle from the Gergonne point. These ...

Let k be a field of finite characteristic p. Then a polynomial P(x) in k[x] is said to be additive iff P(a)+P(b)=P(a+b) for {a,b,a+b} subset k. For example, P(x)=x^2+x+4 is ...

Algorithmic graph theory is the study of graph traversal and generation and the complexity of these operations. Topics in algorithmic graph theory include Eulerian and ...

Let M^n be a compact n-dimensional oriented Riemannian manifold without boundary, let O be a group representation of pi_1(M) by orthogonal matrices, and let E(O) be the ...

An antisymmetric matrix, also known as a skew-symmetric or antimetric matrix, is a square matrix that satisfies the identity A=-A^(T) (1) where A^(T) is the matrix transpose. ...

An antisymmetric (also called alternating) tensor is a tensor which changes sign when two indices are switched. For example, a tensor A^(x_1,...,x_n) such that ...

Consider the circle map. If K is nonzero, then the motion is periodic in some finite region surrounding each rational Omega. This execution of periodic motion in response to ...

The associated Legendre differential equation is a generalization of the Legendre differential equation given by d/(dx)[(1-x^2)(dy)/(dx)]+[l(l+1)-(m^2)/(1-x^2)]y=0, (1) which ...