International Journal of Industrial Mathematics
Volume:2 Issue: 2, Spring 2010

Aim of the paper is to investigate convective heat and mass transfer in the presence ofthe volumetric rate of heat generation/ absorption, which depends on local specie concentration.The main objective is to put forth the concept under rational and criticaldiscussion by the scientific community. To study such a boundary layer flow, heat andmass transfer mixed convection stagnation point flow through porous media is taken. Theresult observed satisfies the general physical laws of boundary layer flow in the presenceof the volumetric heat generation/ absorption.

The integral equations arise in many industrial fields, such as: electromagnetic fields andthermal problems. It is well-known that the problem of heat conduction with a variableheat transfer coefficient is reduced to the solution of a Volterra integral equation of second kind. In this paper, we focus on fuzzy linear Volterra integral equations of the second kind and propose a new method to solve them, namely “homotopy analysis method” (HAM). It is found that the HAM provides us with a simple way to adjust and control the convergence region of solution series by introducing an auxiliary parameter ~. The results illustrate the utility and the great potential of the HAM to solve fuzzy integral equations.

In this paper, the properties of fuzzy random variables with new meter and some extended results of monotone convergence theorem and dominated convergence theorem for fuzzy random variables are discussed. The main result is given by using Dp, q-distance defined on the set of fuzzy numbers.

In this paper, we propose a new form of the fuzzy number of right hand side vector andthen solve fuzzy linear system. We show that the solution of fuzzy linear system is alwaysfuzzy vector. We compare the result of proposed idea with other methods by some examples.

This paper studies the constrained consumable resource allocation in an uncertain projectnetwork. The project network is a directed and acyclic graph in the fuzzy environment.It is supposed that the activity duration is a positive trapezoidal fuzzy number (TFN).Parameters of the activity duration depend on the amount of resource allocated to it. Byranking the paths and activities an algorithm is developed for allocating the constrainedresource to activities in such a way that the completion time of project is decreased. Theproposed algorithm is illustrated by an example.

In this paper, we introduce a numerical method based on the Taylor polynomials for theapproximate solution of the pantograph equation with linear functional argument, withthe fuzzy initial conditions. This method is illustrated by solving two examples.

In this paper, we present a numerical method for solving fully fuzzy polynomials. Theproposed method is based on approximating fuzzy neural network. This method can alsolead to improving numerical methods. In this work, an architecture of fuzzy neural networks is also proposed to find a fuzzy root of a fuzzy polynomial (if exists) by introducing a learning algorithm. We propose a learning algorithm from the cost function for adjusting fuzzy weights. Finally, we illustrate our approach by numerical examples.

In this work, the Taylor polynomial approximation for the solution of fuzzy Fredholmintegro-difference equations with mixed argument and variable coefficients under the conditions is proposed. To do this, a Taylor matrix method is introduced. In this method,the truncated Taylor expansions of the functions are taken in the fuzzy Fredholm integrodifference equation and then their matrix forms is substituted into the mentioned equation.Hence by solving the matrix equation, unknown fuzzy Taylor coefficient can be found. Finally, the proposed method is illustrated by solving an example.