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The Jacobi theta functions are the elliptic analogs of the exponential function, and may be used to express the Jacobi elliptic functions. The theta functions are ...

An ambient isotopy from an embedding of a manifold M in N to another is a homotopy of self diffeomorphisms (or isomorphisms, or piecewise-linear transformations, etc.) of N, ...

Let phi:M->M be a C^1 diffeomorphism on a compact Riemannian manifold M. Then phi satisfies Axiom A if the nonwandering set Omega(phi) of phi is hyperbolic and the periodic ...

A quartic surface which can be constructed as follows. Given a circle C and plane E perpendicular to the plane of C, move a second circle K of the same radius as C through ...

A Brocard line is a line from any of the vertices A_i of a triangle DeltaA_1A_2A_3 to the first Omega or second Omega^' Brocard point. Let the angle at a vertex A_i also be ...

Given a set S with a subset E, the complement (denoted E^' or E^_) of E with respect to S is defined as E^'={F:F in S,F not in E}. (1) Using set difference notation, the ...

A number of attractive 6-compounds of the regular dodecahedron can be constructed. The first (left figures) can be obtained by combining six dodecahedra, each rotated by 1/10 ...

Let X(x)=X(x_1,x_2,...,x_n) be a random vector in R^n and let f_X(x) be a probability distribution on X with continuous first and second order partial derivatives. The Fisher ...

For any nonzero lambda in C, either 1. The equation Tv-lambdav=0 has a nonzero solution v, or 2. The equation Tv-lambdav=f has a unique solution v for any function f. In the ...

The eigenvalues of a graph are defined as the eigenvalues of its adjacency matrix. The set of eigenvalues of a graph is called a graph spectrum. The largest eigenvalue ...