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...

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...

we consider the class of polynomial differential equation x&= , 2(,)(,)(,)nnmnmpxypxypxy++++2(,)(,)(,)nnmnmyqxyqxyqxy++&=++. for where and are homogeneous polynomials of degree i. inside this class of polynomial differential equation we consider a subclass of darboux integrable systems. moreover, under additional conditions we proved such darboux integrable systems can have at most 1 limit cycle.

in this paper, we introduce the new notion of strongly j-clean rings associatedwith polynomial identity g(x) = 0, as a generalization of strongly j-clean rings. we denotestrongly j-clean rings associated with polynomial identity g(x) = 0 by strongly g(x)-j-cleanrings. next, we investigate some properties of strongly g(x)-j-clean.

An analytical method is developed for the reconstruction of velocity profiles using measured potential distributions obtained around the boundary of a multi-electrode electromagnetic flow meter (EMFM). The method is based on the Discrete Fourier Transform (DFT), and is implemented in Matlab. The method assumes the velocity profile in a section of a pipe as a superposition of polynomials up to 6...

For a polynomial p(z) of degree n, having all zeros in |z|< k, k< 1, Dewan et al [K. K. Dewan, N. Singh and A. Mir, Extension of some polynomial inequalities to the polar derivative, J. Math. Anal. Appl. 352 (2009) 807-815] obtained inequality between the polar derivative of p(z) and maximum modulus of p(z). In this paper we improve and extend the above inequality. Our result generalizes certai...

Introduction: Impact craters on the Moon (and other bodies) form and degrade over time resulting in a change in crater shape and hence an overall evolution in lunar topography. Modeling of crater erosion (e.g. [1, 2, 3]) enables the tracking of crater shape evolution with time and can be used to estimate the relative age of a particular crater. Intuitively, crater degradation results from the c...

The derivation of the mean velocity profile for a given vorticity distribution over pipe cross-section is presented in this paper1. and are axisymmetric, which means that radius only variable. importance vortex field flow analysis discussed paper. polynomial function with four free parameters chosen distribution. Free determined using boundary conditions. There also two exponents polynomial. Th...

let g be a simple graph and (g,) denotes the number of proper vertex colourings of gwith at most  colours, which is for a fixed graph g , a polynomial in  , which is called thechromatic polynomial of g . using the chromatic polynomial of some specific graphs, weobtain the chromatic polynomials of some nanostars.