in this paper, we study the boundedness and persistence of the solutions, the global stability of the unique positive equilibrium point and the rate of convergence of a solution that converges to the equilibrium $e=(bar{x}, bar{y})$ of the system of two difference equations of exponential form: begin{equation*} x_{n+1}=dfrac{a+e^{-(bx_n+cy_n)}}{d+bx_n+cy_n}, y_{n+1}=dfrac{a+e^{-(by_n+cx_n)}}{d+...

In this paper, we study the boundedness and persistence of the solutions, the global stability of the unique positive equilibrium point and the rate of convergence of a solution that converges to the equilibrium $E=(bar{x}, bar{y})$ of the system of two difference equations of exponential form: begin{equation*} x_{n+1}=dfrac{a+e^{-(bx_n+cy_n)}}{d+bx_n+cy_n}, y_{n+1}=dfrac{a+e^{-(by_n+cx_n)}}{d+...

A convenient form of kinetic equation is derived for pair annihilation of heavy stable particles relevant to the dark matter problem in cosmology. The kinetic equation thus derived extends the on-shell Boltzmann equation in a most straightforward way, including the off-shell effect. A detailed balance equation for the equilibrium abundance is further analyzed. Perturbative analysis of this equa...

The removal ofxylenol orange from aqueous solution onto the coal ash was investigated at room temperature. The results show that the adsorption capacity of xylenol orange increased as the adsorption time increased and then equilibrium established after 30 min adsorption time. The results obtained revealed that the coal ash removed about 80 % of xylenol orange from the aqueous solution withi...

le chatelier's principle is used as a very simple way to predict the effect of a change in conditions on a chemical equilibrium. . however, several studies have reported the violation of this principle, still there is no reported simple mathematical equation to express the exact condition of violation in the gas phase reactions. in this article, we derived a simple equation for the violati...

in this article, a transversely isotropic linear elastic half-space with depth wise isotropy axis of material containing a cylindrical cavity of finite length is considered to be under the effect of an arbitrary torsion force applied on the wall of the cavity. to this end, the equation of equilibrium has been written in a cylindrical coordinate system, by dividing the involved domain to two reg...

In this paper, an SIR epidemic model with an infectious period and a non-linear Beddington-DeAngelis type incidence rate function is considered. The dynamics of this model depend on the reproduction number R0. Accurately, if R0 < 1, we show the global asymptotic stability of the disease-free equilibrium by analyzing the corresponding characteristic equation and using compa...