Asian Research Journal of Mathematics

Aims/ Objectives: To prove the existence of a pullback Absorbing set.
Study Design: Ornstein-Uhlenbeck process.
Place and Duration of Study: College of Management, Shanghai University of Engineering Science.
Methodology: A transformation of addition involved with an Ornstein-Uhlenbeck process is used.
Results: In this paper, pullback absorbing property for the stochastic reversible Selkov system in an innite lattice with additive noises is proved.

By applying the classical Holder's inequality, Young's inequality, Minkowski's inequality and some other analytical tools, we establish some inequalities involving the Chaudhry-Zubair extension of the gamma function. The established results serve as generalizations of some known results in the literature.

We study the qualitative behavior of a predator-prey model, where the carrying capacity of the predators environment is proportional to the number of prey. The considered system is given by the following rational difference equations:

$$x_{n+1}=\dfrac{x_{n} y_{n-2}}{y_{n-1} + y_{n-2}},\quad y_{n+1}=\dfrac{y_{n} x_{n-2}}{\pm x_{n-1} \pm x_{n-2}},\quad
n=0,1,\cdots,$$

where the initial conditions x-2; x-1; x₀; y-2; y-1; y₀ are arbitrary positive real numbers. Also, we give specic form of the solutions of some special cases of this equation. Some numerical examples are given to verify our theoretical results.

Presented here is a numerical integrator, with sixth order of convergence, for solving oscillatory problems. Dispersion and dissipation errors are taken into account in the course of deriving the method. As a result, the method possesses dissipation of order infinity and dispersive of order six. Validity and effectiveness of the method are tested on a number of test problems. Results obtained show that the new method is better than its equals in the scientific literature. 

In this paper the concept of total outer independent monophonic domination number of a graph is introduced. A monophonic set SÍV  is said to be total outer independent monophonic domination set if <S> has no isolated vertex and <V-S> is an independent set.