Search Results for ""

A New Kind of Science is a seminal work on simple programs by Stephen Wolfram. In 1980, Wolfram's studies found unexpected behavior in a collection of simple computer ...

Determination of whether predicate P(x_1,...,x_n) is true or false for any given values of x_1, ..., x_n is called its decision problem. The decision problem for predicate ...

The symbol tau (the lower case Greek letter tau) has many common uses in mathematics, as summarized in the following table. 1. tau(n) is an alternate notation for the divisor ...

The condition for isoenergetic nondegeneracy for a Hamiltonian H=H_0(I)+epsilonH_1(I,theta) is |(partial^2H_0)/(partialI_ipartialI_j) (partialH_0)/(partialI_i); ...

An extremely powerful theorem in physics which states that each symmetry of a system leads to a physically conserved quantity. Symmetry under translation corresponds to ...

The mean square deviation of the best local fit straight line to a staircase cumulative spectral density over a normalized energy scale.

A map u:M->N, between two compact Riemannian manifolds, is a harmonic map if it is a critical point for the energy functional int_M|du|^2dmu_M. The norm of the differential ...

The Hénon-Heiles equation is a nonlinear nonintegrable Hamiltonian system with x^.. = -(partialV)/(partialx) (1) y^.. = -(partialV)/(partialy), (2) where the potential energy ...

The thin plate spline is the two-dimensional analog of the cubic spline in one dimension. It is the fundamental solution to the biharmonic equation, and has the form ...

One of the Zermelo-Fraenkel axioms, also known as the axiom of regularity (Rubin 1967, Suppes 1972). In the formal language of set theory, it states that x!=emptyset=> exists ...