An important question of ongoing interest for linear time-delay systems is to provide conditions on its parameters guaranteeing exponential stability solutions. Recent works have explored spectral techniques show that, some low-order delay-differential equations retarded type, values maximal multiplicity are dominant, and hence determine the asymptotic behavior system, a property known as multi...

The geometry of the Cayley graphs of monoids defined by regular confluent monadic rewriting systems is studied. Using geometric and combinatorial arguments, these Cayley graphs are proved to be hyperbolic, and the monoids to be word-hyperbolic in the Duncan–Gilman sense. The hyperbolic boundary of the Cayley graph is described in the case of finite confluent monadic rewriting systems.

The direct sum of two term rewriting systems is the union of systems having disjoint sets of function symbols. It is shown that the direct sum of two term rewriting systems is not terminating, even if these systems are both terminating. Keyword: Term rewriting system, termination Introduction A term rewriting system R is a set of rewriting rules M → N , where M and N are terms [1, 3, 5]. The di...

Recently, analytical methods for finding moments of random Vandermonde matrices with entries on the unit circle have been proposed in the literature. Vandermonde matrices play an important role in signal processing and wireless applications, among which the multiple-antenna channel modeling, precoding or sparse sampling theory. Recent investigations allowed to extend the combinatorial approach ...

A scaled version of the lower and the upper triangular factors of the inverse of the Vandermonde matrix is given. Two applications of the q-Pascal matrix resulting from the factorization of the Vandermonde matrix at the q-integer nodes are introduced. c © 2007 Elsevier Ltd. All rights reserved.

In order to evaluate some quantities in Gaussian ensembles, we investigate ”vandermonde ensemble” which represents the distribution of eigenvalues of GUE in the phase space. We derive the integral equation of the level density of vandermonde ensemble and we compute the level density numerically.