In this paper, we establish some Bernstein type inequalities for the complex polynomial. Our results constitute generalizations and refinements of some well-known polynomial inequalities.

-Internal friction associated with the volume change during melting was studied in an aluminum-16wt% indium alloy. This alloy was processed to obtain microstructures consisting of nominally pure indium inclusions embedded in an aluminum matrix. Two sharp internal friction peaks were observed near the indium melting temperature of 156°C and both were associated with the formation and growth of l...

ABSTRACT. Suppose G is a graph, A(G) its adjacency matrix and f(G, x)=x^n+a_(n-1)x^(n-1)+... is the characteristic polynomial of G. The matching polynomial of G is defined as M(G, x) = x^n-m(G,1)x^(n-2) + ... where m(G,k) is the number of k-matchings in G. In this paper, we determine the relationship between 2k-th coefficient of characteristic polynomial, a_(2k), and k-th coefficient of matchin...

‎    The Narumi-Katayama index is the first topological index defined by the product of some graph theoretical quantities. Let G be a simple graph. Narumi-Katayama index of G is defined as the product of the degrees of the vertices of G. In this paper, we define the Narumi-Katayama polynomial of G. Next, we investigate some properties of this polynomial for graphs and then, we obtain ...

Let G = (V, E) be a simple graph. Hosoya polynomial of G is d(u,v) H(G, x) = {u,v}V(G)x , where, d(u ,v) denotes the distance between vertices u and v. As is the case with other graph polynomials, such as chromatic, independence and domination polynomial, it is natural to study the roots of Hosoya polynomial of a graph. In this paper we study the roots of Hosoya polynomials of some specific g...

Résumé—Ce papier a pour but de donner une vue générale des différents résultats récemment obtenus sur la stabilisation interne des systèmes linéaires de dimension infinie. On s’attachera à faire ressortir les principales idées plus que la technique utilisée. En particulier, nous donnerons des conditions nécessaires et suffissantes à la stabilisation interne et à l’existence de factorisations do...

The Wiener index is a graph invariant that has found extensive application in chemistry. In addition to that a generating function, which was called the Wiener polynomial, who’s derivate is a q-analog of the Wiener index was defined. In an article, Sagan, Yeh and Zhang in [The Wiener Polynomial of a graph, Int. J. Quantun Chem., 60 (1996), 959969] attained what graph operations do to the Wiene...

A relativistic many-body method is developed to calculate energy and transition rates for multipole transitions in many-electron ions. This method is based on relativistic many-body perturbation theory (RMBPT), agrees with MCDF calculations in lowest order, includes all second-order correlation corrections, and includes corrections from negative-energy states. Reduced matrix elements, oscillato...

2. Soit A = {aij}1≤i≤n,1≤j≤m une matrice m × n dont les éléments sont à valeurs dans {0, 1}. Soit b = {bj}1≤j≤m un vecteur colonne dont les éléments sont à valeurs dans {−1,+1} et soit c = {ci}1≤i≤n le vecteur colonne défini par c = Ab. On pose ||c||∞ = ||Ab||∞ = max 1≤i≤n |ci| . On choisit b aléatoire: b1, . . . , bn sont des variables aléatoires indépendantes prenant les deux valeurs dans −1 ...