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.

1. A missing line in the dictionary. 1 2. Laminations: general concepts 5 3. Natural extension and its regular part. 6 4. The Type Problem and affine structure on the leaves. 11 5. Post-critically finite maps. 17 6. Hyperbolic 3-laminations. 21 7. Universal orbifold laminations 25 8. Convex-cocompactness, non-recurrence and conical points 32 9. Quasi-isometries and rigidity 38 10. Further progr...

Let f ∈ Z[x], and consider the recurrence given by an = f(an−1), with a0 ∈ Z. Denote by P (f, a0) the set of prime divisors of this recurrence, i.e., the set of primes p dividing some non-zero an, and denote the natural density of this set by D(P (f, a0)). The problem of determining D(P (f, a0)) when f is linear has attracted significant study, although it remains unresolved in full generality....

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...

Applications in computational fluid dynamics (CFD) have led to the problem of finding a rational Bézier patch with a given edge parameter line k the way that the parameter lines of the other type intersect k orthogonally. This is what we call an ‘orthogonal continuation of k’. The variety of solutions to the problem is being investigated and a very geometric way for the construction of the solu...

This note presents a method for synthesizing a static state feedback controller for multiple-input linear systems over discrete sets. The method allows of a complete setting of the cyclic subspaces of the closed loop system by specifying invariant polynomials of the closed loop system. To this end, fundamentals of finite field theory and basic elements of the polynomial approach are developed t...

The dynamical inverse problem of representation theory (the Wigner problem) 1] is solved for a certain class of interactions of Hamiltonian systems. The constructed quantum dynamics describes transition processes and stationary regimes on an equal footing. Among other numerous applications the results may be useful for the description of the simultaneous quantum dynamics of the open and closed ...