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.

In this paper we study multivariate integration for a weighted Korobov space for which the Fourier coefficients of the functions decay exponentially fast. This implies that the functions of this space are infinitely times differentiable. Weights of the Korobov space monitor the influence of each variable and each group of variables. We show that there are numerical integration rules which achie...

retention behavior of molecules mostly depends on their chemical structure. retention data of biologically active molecules could be an indirect relationship between their structure and biological or pharmacological activity, since the molecular structure affects their behavior in all pharmacokinetic stages. in the present paper, retention parameters (rm0) of biologically active 1,2-o-isopropyl...

Abstract We prove the existence of quasi-Jacobi form solutions for an analogue Kaneko–Zagier differential equation Jacobi forms. The transformation properties under group are derived. A special feature is polynomial dependence index parameter. results yield explicit conjectural description all double ramification cycle integrals in Gromov–Witten theory K3 surfaces.

In this paper we consider generalized eigenvalue problems for a family of operators with a polynomial dependence on a complex parameter. This problem is equivalent to a genuine non self-adjoint operator. We discuss here existence of non trivial eigenstates for models coming from analytic theory of smoothness for P.D.E. We shall review some old results and present recent improvements on this sub...

Multiple compactons in a nonlinear atomic chain equations are studied. Atoms in the chain are interacted through first-and-second interactions. Nonlinearity in the evolution equation is set to be up to cubic polynomial. The spatial and temporal dependence of the solutions are given by separating method. Multiple N−site compactons are obtained.

The main result of this paper asserts that it suffices to prove the Jacobian Conjecture for all polynomial maps of the form x + H, where H is homogeneous (of degree 3) and JH is nilpotent and symmetric. Also a 6dimensional counterexample is given to a dependence problem posed by de Bondt and van den Essen (2003).

In this paper, we provide a quantitative estimate of unique continuation (doubling property) for higher-order parabolic partial differential equations with non-analytic Gevrey coefficients. Also, a new upper bound is given on the number of zeros for the solutions with a polynomial dependence on the coefficients.

Multiple compactons in a nonlinear atomic chain equations are studied. Atoms in the chain are interacted through first-and-second interactions. Nonlinearity in the evolution equation is set to be up to cubic polynomial. The spatial and temporal dependence of the solutions are given by separating method. Multiple N−site compactons are obtained.

We define a class of generic CR submanifolds of Cn of real codimension d, 1 ≤ d ≤ n, called the Bloom-Grahammodel graphs, whose graphing functions are partially decoupled in their dependence on the variables in the real directions. We prove a global version of the Baouendi-Treves CR approximation theorem for Bloom-Graham model graphs with a polynomial growth assumption on their graphing functions.