let $d$ be a digraph with skew-adjacency matrix $s(d)$. then the skew energyof $d$ is defined to be the sum of the norms of all eigenvalues of $s(d)$. denote by$mathcal{o}_n$ the class of digraphs on order $n$ with no even cycles, and by$mathcal{o}_{n,m}$ the class of digraphs in $mathcal{o}_n$ with $m$ arcs.in this paper, we first give the minimal skew energy digraphs in$mathcal{o}_n$ and $mat...

let g = (v, e) be a simple graph. hosoya polynomial of g isd(u,v)h(g, x) = {u,v}v(g)x , where, d(u ,v) denotes the distance between vertices uand v. as is the case with other graph polynomials, such as chromatic, independence anddomination polynomial, it is natural to study the roots of hosoya polynomial of a graph. inthis paper we study the roots of hosoya polynomials of some specific graphs.

The inversion of combinatorial sums is a fundamental problem in algebraic combinatorics. Some combinatorial sums, such as a n = P k d n;k b k , can not be inverted in terms of the orthogonality relation because the innnite, lower triangular array P = fd n;k g's diagonal elements are equal to zero (except d 0;0). Despite this, we can nd a left-inverse P such that P P = I and therefore are able t...

Let M be a finite monoid. In this paper we describe how the Cartan invariant matrix of the monoid algebra of M over a field K of characteristic zero can be expressed using characters and some simple combinatorial statistic. In particular, it can be computed efficiently from the composition factors of the left and right class modules of M . When M is aperiodic, this approach works in any charact...

Sunto: Questo articolo considera una successione di equazioni diieren-ziali a derivate parziali non lineari in forma di divergenza del tipo ?div (Q " G(x; N " ru)) = f " ; in un dominio limitato dello spazio n-dimensionale; Q " = Q " (x) e N " = N " (x) sono matrici con coeecenti limitati, N " e' invertibile e la sua matrice inversa R " ha anche coeecenti limitati. La non linearita' e' dovuta a...

In this note, we consider the non-negative least square method with a random matrix. This problem has connections with the probability that the origin is not in the convex hull of many random points. As related problems, suitable estimates are obtained as well on the probability that a small ball does not hit the convex hull. Abstract Dans cette Note nous appliquons la méthode des moindres carr...

We consider the implicit time integration of the compressible Navier-Stokes equations. Each implicit step involves the solution of a costly non linear system. In this paper, we deene a preconditioner to solve each linear system more cheaply within the framework of matrix-free algorithm. The main idea is to reuse the Krylov subspace across the time steps. We demonstrate some properties of the pr...

In a spiked population model, the population covariance matrix has all its eigenvalues equal to units except for a few fixed eigenvalues (spikes). This model is proposed by Johnstone to cope with empirical findings on various data sets. The question is to quantify the effect of the perturbation caused by the spike eigenvalues. A recent work by Baik and Silverstein establishes the almost sure li...

Let Γ\X be a Q-rank one locally symmetric space. We describe the frequencies of oscillation of scattering matrices on Γ\X in the energy variable in terms of sojourn times of scattering geodesics. Scattering geodesics are the geodesics which move to infinity in both directions and are distance minimizing near both infinities. The sojourn time of a scattering geodesic is the time it spends in a f...