the edge detour index polynomials were recently introduced for computing theedge detour indices. in this paper we nd relations among edge detour polynomials for the2-dimensional graph of tuc4c8(s) in a euclidean plane and tuc4c8(s) nanotorus.

Ordinary differential equations(ODEs) with stochastic processes in their vector field, have lots of applications in science and engineering. The main purpose of this article is to investigate the numerical methods for ODEs with Wiener and Compound Poisson processes in more than one dimension. Ordinary differential equations with Ito diffusion which is a solution of an Ito stochastic differentia...

In this paper, we present the numerical solution of ordinary differential equations (or SDEs), from each order especially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multiplicative noises). Making stochastic differe...

Two formal stochastic models are said to be bisimilar if their solutions as a stochastic process are probabilistically equivalent. Bisimilarity between two stochastic model formalisms means that the strengths of one stochastic model formalism can be used by the other stochastic model formalism. The aim of this paper is to explain bisimilarity relations between stochastic hybrid automata, stocha...

Many time-varying phenomena of various fields in science and engineering can be modeled as a stochastic differential equations, so investigation of conditions for existence of solution and obtain the analytical and numerical solutions of them are important. In this paper, the Adomian decomposition method for solution of the stochastic differential equations are improved.  Uniqueness and converg...