Let X,, X,,. be a sequence of regular graphs with degree ~a2 such that n(X,)cc and ck(X,)/n(X,)-0 as i -cc for each ka3, where n(X,) is the order of Xi, and ck( X,) is the number of k-cycles in Xi. We determine the limiting probability density f(x) for the eigenvalues of X, as i-cc. It turns out that i o/4(“-1)-x” f(x)= 2n(u”_x’) for IrlG2JFi, IO otherwise It is further shown that f(x) is the e...

Although optimal staff scheduling often requires elaborate computational methods, those cases which are not highly constrained can be efficiently solved using simpler approaches. This paper describes how a simple procedure, combining random and greedy strategies with heuristics, has been successfully applied in a Spanish hospital to assign guard shifts to the physicians in a department. In this...

we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...

In a regular distribution family, Cramér-Rao inequality holds, and the maximum likelihood estimator (MLE) converges to a normal distribution whose variance is the inverse of the Fisher information because the Fisher information converges and is well-defined in this family. However, in a non-regular location shift family which is generated by a distribution of R whose support is not R (e.g., a W...

The pegging algorithm is a method of generating large random regular graphs beginning with small ones. The ǫ-mixing time of the distribution of short cycle counts of these random regular graphs is the time at which the distribution reaches and maintains total variation distance at most ǫ from its limiting distribution. We show that this ǫ-mixing time is not o(ǫ−1). This demonstrates that the up...

This paper proves a conjecture of Fomin and Shapiro that their combinatorial model for any Bruhat interval for any finite Weyl group is a regular CW complex which is homeomorphic to a ball. The model consists of a stratified space which may be regarded as the link of an open cell in a larger closed cell, all within the totally nonnegative part of the unipotent radical of an algebraic group. A k...