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Abstract: In this paper we give a method for peturbation of solutions of linear homogeneous differential equation of the second order. [Copyright &y& Elsevier]

Abstract: In this paper, we give necessary and sufficient conditions for generalized solution and periodicity of the difference equation with -periodic coefficients, where , . Also, we obtain that the generalized solution is periodic with -period. [Copyright &y& Elsevier]

Abstract: In this paper, we study soft hypergroupoids. Firstly, we introduce the notion of soft hypergroupoids, and some examples are given. Also, we show that soft hypergroupoids are closely related to -subhypergroupoid. Secondly, using the notion of soft hypergroupoid, some new properties of soft hypergroupoids are obtained. Lastly, we investigate some properties of soft subhypergroupoids. [Copyright &y& Elsevier]

Abstract: This paper provides a discrete Fourier method for numerical solution of strongly coupled mixed parabolic systems which avoids solving large algebraic systems. After discretization using Crank-Nicholson difference scheme, the exact solution of the discretized problem is constructed and stability is analyzed. [Copyright &y& Elsevier]

Abstract: The scheduling problems studied in this paper concern the two-stage no-wait flowshops with parallel machines under the objective function of the minimization of the maximum completion time. A new heuristic algorithm, i.e., the minimum deviation algorithm, is developed to solve the problems. In order to evaluate the average case performance of the algorithm, we design numerical experiments to compare the effectiveness of the algorithm with that of the other approximation algorithms. Extensive simulations are conducted under different shop conditions, and the results statistically show that the minimum deviation algorithm performs well under most of the situations. [Copyright &y& Elsevier]

In this paper, we study the issues of modeling, numerical methods, and simulation with comparison to experimental data for the particle-fluid two-phase flow problem involving a solid-liquid mixed medium. The physical situation being considered is a pulsed liquid fluidized bed. The mathematical model is based on the assumption of one-dimensional flows, incompressible in both particle and fluid phases, equal particle diameters, and the wall friction force on both phases being ignored. The model consists of a set of coupled differential equations describing the conservation of mass and momentum in both phases with coupling and interaction between the two phases. We demonstrate conditions under which the system is either mathematically well posed or ill posed. We consider the general model with additional physical viscosities and/or additional virtual mass forces, both of which stabilize the system. Two numerical methods, one of them is first-order accurate and the other fifth-order accurate, are used to solve the models. A change of variable technique effectively handles the changing domain and boundary conditions. The numerical methods are demonstrated to be stable and convergent through careful numerical experiments. Simulation results for realistic pulsed liquid fluidized bed are provided and compared with experimental data. [Copyright &y& Elsevier]