The first geometric-arithmetic index was introduced in the chemical theory as the summation of 2 du dv /(du  dv ) overall edges of the graph, where du stand for the degree of the vertex u. In this paper we give the expressions for computing the first geometric-arithmetic index of hexagonal systems and phenylenes and present new method for describing hexagonal system by corresponding a simple g...

This paper presents an analytical view of variance reduction by control variate technique for pricing arithmetic Asian options as a financial derivatives. In this paper, the effect of correlation between two random variables is shown. We propose an efficient method for choose suitable control in pricing arithmetic Asian options based on the control variates (CV). The numerical experiment shows ...

Let φ : V → V be a self-morphism of a quasiprojective variety defined over a number field K and let P ∈ V (K) be a point with infinite orbit under iteration of φ. For each prime p of good reduction, let mp(φ, P ) be the size of the φ-orbit of the reduction of P modulo p. Fix any ǫ > 0. We show that for almost all primes p in the sense of analytic density, the orbit size mp(φ, P ) is larger than...

This paper studies geometric and spectral properties of S-adic shifts and their relation to continued fraction algorithms. Pure discrete spectrum for S-adic shifts and tiling properties of associated Rauzy fractals are established under a generalized Pisot assumption together with a geometric coincidence condition. These general results extend the scope of the Pisot substitution conjecture to t...

a graph that contains a hamiltonian cycle is called a hamiltonian graph. in this paper wecompute the first and the second geometric – arithmetic indices of hamiltonian graphs. thenwe apply our results to obtain some bounds for fullerene.

Arboreal Galois groups sit naturally as subgroups of tree (or graph) automorphism groups, while dynatomic Galois groups are naturally subgroups of certain wreath products. A fundamental problem is to determine general conditions under which these dynamically generated Galois groups have finite index in the natural geometric groups that contain them. This is a dynamical analog of Serre’s theorem...

Let K be a number field, let φ(x) ∈ K(x) be a rational function of degree d > 1, and let α ∈ K be a wandering point such that φ(α) = 0 for all n > 0. We prove that if the abc-conjecture holds for K, then for all but finitely many positive integers n, there is a prime p of K such that vp(φ (α)) > 0 and vp(φ (α)) 0 for all positive integers m < n. Under appropriate ramification hypotheses, we can...

the treatise entitled “arithmetic in astronomy”, which is edited and commented upon in this paper, is part of an old manuscript collection preserved in the national library of bosnia and herzegovina. at the end of this treatise there are some phrases in arabic which show that the treatise was originally part of a persian book written by ʿalī al-qūshchī. this manuscript is, in fact, an abridged ...