Zeitschrift für Angewandte und Computermathematik

In this paper we study a family of nonlinear Elliptic problems in two dimensions, we give some estimates for the solutions of this problem, and we decompose it on two problems, the first is the Poisson's equation and the second is the Liouville equation.

nvironments. If we carrying the produce from sources to destination by the means of unlike conveyances then due to insurgency, land slide and bad road, there are some risks or difficulties to transport the items. By this motive we initiate “Safety Factors” in transportation problem. Due to this reason desired total safety factor is being introduced. Also our objective is to evaluate the solution of STP using expected value model. Here we develop six models where first three models are formulated taking crisp unit transportation cost but the remaining three models are formulated taking hybrid unit transportation cost. To build up the different models we consider breakability and safety factor which is taken as crisp, fuzzy and hybrid for assorted models. All the fuzzy and hybrid models are reduced into its crisp equivalent using expected value modeling. Finally by Generalized Reduced Gradient (GRG) method using LINGO.13 optimization software and Genetic Algorithm we solve the mathematical models and put a enlarge discussion on it.

In this paper, a new type of chaos synchronization in discrete-time is proposed when the scaling functions in Q-S synchronization are replaced by two suitable matrices. This new synchronization type allows us to study synchronization between different dimensional discrete chaotic systems in different dimensions. By using Lyapunov stability theory and nonlinear controllers, new results are derived. Numerical simulations are used to verify the effectiveness of the theoritical results and the proposed schemes derived in this paper.