Search Results for ""

Let G(V,E) be a graph with graph vertices V and graph edges E on n graph vertices without a (k+1)-clique. Then t(n,k)<=((k-1)n^2)/(2k), where t(n,k) is the edge count. (Note ...

The Wiener sausage of radius a>0 is the random process defined by W^a(t)= union _(0<=s<=t)B_a(beta(s)) where here, beta(t) is the standard Brownian motion in R^d for t>=0 and ...

The Carlson elliptic integrals, also known as the Carlson symmetric forms, are a standard set of canonical elliptic integrals which provide a convenient alternative to ...

The matrix decomposition of a square matrix A into so-called eigenvalues and eigenvectors is an extremely important one. This decomposition generally goes under the name ...

Let lambda be (possibly complex) eigenvalues of a set of random n×n real matrices with entries independent and taken from a standard normal distribution. Then as n->infty, ...

The term "parameter" is used in a number of ways in mathematics. In general, mathematical functions may have a number of arguments. Arguments that are typically varied when ...

Stanley's theorem states that the total number of 1s that occur among all unordered partitions of a positive integer is equal to the sum of the numbers of distinct members of ...

Two non-coincident plane angles alpha and beta in angle standard position are said to be coterminal if the terminal side of alpha is identically the same as the terminal side ...

In continuum percolation theory, the so-called germ-grain model is an obvious generalization of both the Boolean and Boolean-Poisson models which is driven by an arbitrary ...

An invertible knot is a knot that can be deformed via an ambient isotopy into itself but with the orientation reversed. A knot that is not invertible is said to be ...