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A sufficient condition on the Lindeberg-Feller central limit theorem. Given random variates X_1, X_2, ..., let <X_i>=0, the variance sigma_i^2 of X_i be finite, and variance ...

For the Helmholtz differential equation to be separable in a coordinate system, the scale factors h_i in the Laplacian del ...

The ratio C of the largest to smallest singular value in the singular value decomposition of a matrix. The base-b logarithm of C is an estimate of how many base-b digits are ...

A set of vectors in Euclidean n-space is said to satisfy the Haar condition if every set of n vectors is linearly independent (Cheney 1999). Expressed otherwise, each ...

Partial differential equation boundary conditions which, for an elliptic partial differential equation in a region Omega, specify that the sum of alphau and the normal ...

If {a_j} subset= D(0,1) (with possible repetitions) satisfies sum_(j=1)^infty(1-|a_j|)<=infty, where D(0,1) is the unit open disk, and no a_j=0, then there is a bounded ...

Given a set A, let N(A) be the set of neighbors of A. Then the bipartite graph G with bipartitions X and Y has a perfect matching iff |N(A)|>=|A| for all subsets A of X.

The Lyapunov condition, sometimes known as Lyapunov's central limit theorem, states that if the (2+epsilon)th moment (with epsilon>0) exists for a statistical distribution of ...

For a given positive integer n, does there exist a weighted tree with n graph vertices whose paths have weights 1, 2, ..., (n; 2), where (n; 2) is a binomial coefficient? ...

A theorem which specifies the structure of the generic unitary representation of the Weyl relations and thus establishes the equivalence of Heisenberg's matrix mechanics and ...