American Research Journal of Mathematics

Svetlana Mustafina,Rustam Ikramov

Chemical transformations typically occur according to multiphase schemes. Changes in the concentrations of the starting materials and intermediates with time are not always described with increasing or decreasing functions. A detailed study of a complex process kinetics showed that at the presence of feedback far from equilibrium there may occur vibrational modes - periodic increase or decrease in the concentration of one of the components in time. In a numerical study of oscillating reactions there appears a problem in solving a rigid system of typical differential equations. The purpose of this study is to develop an algorithm and a program to solve the direct kinetic problem and to investigate multi component chemical systems with complex nonlinear dynamics.

Isa Muslu1 AvytAsanov2SedatYanik3

TheLinear Fredholm-Stieltjes Integral Equation of the Second Kind (LFSIESK) is of wide spread use in many fields of engineering and applied mathematics. The quadrature methods are remarkable among the variety of numerical solutions to this equation.The aim of this paper is to find an approximation solution of the LFSIESK using the quadrature method the Generalized Simpson’s Method (GSM). Numerical example is presented at the end to show the efficiency and accuracy of the presented work. The software Maple 18 is used for the computations

Do Ngoc Diep1Do Thi Phuong Quynh2

 In this paper we make a clear relationship between the automorphic representations and the quantization through the Geometric Langlands Correspondence. We observe that the discrete series representation are realized in the sum of eigenspaces of Cartan generator, and then present the automorphic representations in form of induced representations with inducing quantum bundle over a Riemann surface and then use the loop group representation construction to realize the automorphic representations. The Langlands picture of automorphic representations is precised by using the Poisson summation formula.