INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS
Year:2009 | Volume:1 | Issue:4|Papers Count:8

In this paper, the model of the equations of generalized thermoelastic diffusion for a homogeneous isotropic elastic half-space under the dependence of the modulus of elasticity on the reference temperature is established. The modulus of elasticity is taken as a linear function of the reference temperature. The formulation is applied to the generalized thermoelasticity theory under the Lord-Shulman and the classical dynamical coupled theories. Also the normal mode analysis is used to obtain the exact expressions for the displacement components, temperature distribution and thermal stress. Finally the variations of the considered variables are represented graphically and comparison is made with the results predicted by two theories and with the case where the modulus of elasticity is independent of temperature.

This work uses the thermal non-equilibrium model to study free convection boundary-layer flow of a micropolar fluid along a cylinder of elliptic cross-section embedded in porous me-dia. The transformed conservation equations of the non-similar boundary layers are solved numerically by an efficient, iterative, tri-diagonal implicit finite difference method. The numerical results are compared and found to be in excellent agreement with previously published results on special cases of the problem. The obtained results are displayed graphically to illustrate the influence of the different physical parameters on the linear and angular velocities and the fluid- and solid-phase temperatures, as well as the local skin-friction coefficient, wall couple stress coefficient and the local Nusselt numbers for fluid and solid phases.

Data envelopment analysis is a technique for measuring the relative efficiency of a set of decision making units with common data, but in this paper we explain a new method for evaluating of decision making units with fuzzy data.We solve CCR and BCC models with fuzzy inputs and outputs by distance minimization that this method is better than other methods for ranking of fuzzy numbers and then we put in order efficient and inefficient decision making units.

In recent years, many authors have focused on hyperconvex space and obtained a lot of valuable results (see [1, 2, 3, 5]). In this paper we develop some of those results for modular hyperconvex spaces. As a consequence we show that Ar (Xr) Í er (Xr) Í Hr (Xr) where, Ar (Xr), er (Xr), and Hr (Xr) are modular admissible subsets, modular externally hyperconvex subsets and modular hyperconvex subsets in Xr, respectively.

In this article, it is attempted to develop a method for solving an arbitrary general fuzzy linear system by using the weighted metric. Using the distance between two fuzzy numbers, the best and nearest approximation fuzzy symmetric vector can be obtained. Defuzzifi-cation can replace then × n fuzzy linear system with two n × n crisp linear systems. Consequently, to obtain the best approximate solution forn × n fuzzy linear system the researcher must solve twon × n crisp linear systems. First considering the existing and uniqueness of fuzzy solution ton×n fuzzy linear system is done. Then numerical examples are presented to illustrate the proposed model.

In this paper, we present a method for ranking decision making units (DMUs) with interval data in data envelopment analysis that is different from the other methods. In this method we use a new pair of interval DEA models that are constructed on the basis of interval arithmetic, which differ from the existing DEA models that work with interval data in fact it is a linear CCR model without a need for extra variable alternations and uses a fixed and unified production frontier (i.e. the same constraint set) to measure the efficiencies of decision making units (DMUs) with interval input and output data. This methodology exerts an appropriate minimum weight restriction on all input and output weights which is called maxmin weight. New linear programming (LP) model constructs proportion with each efficient unit for determining maximin weight. Choosing a maxmin weight, all efficient units put in order as fully or partially. One numerical example is inspected using the proposed ranking methodology to illustrate its ability in discriminating between DEA efficient unit with interval data.

Analytical Hierarchy Process is a method of solving a Multiple Attribute Decision Mak-ing. This method is based on the pairwise comparisons between the alternatives. These comparisons form a matrix named pairwise comparison matrix or judgment matrix. The weights of mentioned alternatives will be determined from this mentioned above matrix. In the case of consistency of the judgments, the cited weights are reliable and trusty. On the other hand, if the consistency of the judgment matrix is not acceptable, the result sufficient level of trust. In this case it is requested that the decision maker revise the judg-ment. In this paper we propose a method to approximate a consistent judgment matrix from an inconsistent one without the revision of the judgments. This method is based on decreasing the effects of the mistakes made by the decision maker.

In this paper we introduce a homotopy perturbation method (HPM) to solve non-linear system of third-order boundary value problems. Using the HPM, it is possible to find the exact solution in some cases or an approximate solution in convergent series forms. This method is a powerful devise for solving a wide variety of problems, without any discretization, linearizetion or small perturbations. Some examples are presented, and obtained results ensure that this method is very effective, simple and has less the numerical computation.