INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS
Year:2013 | Volume:5 | Issue:4|Papers Count:16

In this paper we propose a method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. The proposed approach is based on an Unsupervised Combined Artificial Neural Networks (UCANN) method. Firstly, The trial solutions of the differential equations are written in the form of feed-forward neural networks containing adjustable parameters (the weights and biases), results are then optimized with the combined neural network. The proposed method is tested on series of Lane-Emden differential equations and the results are reported. Afterward, these results are compared with the solution of other methods demonstrating the efficiency and applicability of the proposed method.  

In this paper, the homotopy analysis method (HAM) is considered to obtain the solution of the Schrodinger equation with a power law nonlinearity. For this purpose, a theorem is proved to show the convergence of the series solution obtained from the proposed method. Also, an example is solved to illustrate the efficiency of the mentioned algorithm and the h-curve is plotted to determine the region of convergence.

The aim of this study is to investigate the effects of outside board on firm value in Tehran Stock Exchange (TSE) from the perspective of information transaction costs. To do so, a sample of 96 firms listed in TSE is selected to be studied during the period of 2003-2012. Tobin q ratio is used to measure firm's value and bid-ask spread for information transaction costs. In addition to these variables, four control variables are adapted namely firm's characteristic, age, size and duality. The results of the study show that there is not a significant relationship between outside board and firm's value. Investigating the relationship between outside board and firm's value, the results indicate that only in food and non-metal industries, there is a negative relationship between outside board and firm's performance. Therefore, it can be concluded that not in all of industries outside board affects firm's value. Further, results do not prove the effects of outside board on information transaction cost. In addition, the results do not support that information transaction cost affect firm's value. Finally, the results also suggest that independence and presence of outside board of director member does not affect firm's value in firms with lower information transaction cost.

In the real world there are groups which composed of independent units. The conventional data envelopment analysis (DEA) model treats groups as units, ignoring the operation of individual units within each group. The current paper, investigates parallel system network approach proposed by Kao and modifies it. As modified Kao' model is more eligible to recognize efficient groups, a new ranking method is proposed based on a model which calculates efficiencies with additional constraint that made model share constant inefficiency among groups. To show advantages, modifies model is applied to efficiency calculation of both artificial and real groups and results is compared with conventional DEA model and parallel system network model as well. Finally it is shown by tow numerical and empirical examples that efficient groups recognized by modified model how can be ranked according to proposed ranking model.

We introduce an implicit method for finding a common element of the set of solutions of systems of equilibrium problems and the set of common fixed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. Then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition for a minimization problem and is also a common fixed point for a sequence of nonexpansive mappings and a representation of nonexpansive mappings.

The SST Decomposition Method for solving system of linear equations make it possible to obtain the values of roots of the system with the specified accuracy as the limit of the sequence of some vectors. In this topic we are going to consider vectors as fuzzy vectors. We have considered a numerical example and tried to find out solution vector X~ in fuzzified form using method of SST Decomposition.

In this paper, We interpret a fuzzy differential equation by using the strongly generalized differentiability concept. Utilizing the Generalized characterization Theorem. Then a novel hybrid method based on learning algorithm of fuzzy neural network for the solution of differential equation with fuzzy initial value is presented. Here neural network is considered as a part of large field called neural computing or soft computing. The model finds the approximated solution of fuzzy differential equation inside of its domain for the close enough neighborhood of the fuzzy initial point. We propose a learning algorithm from the cost function for adjusting of fuzzy weights.

This paper intends to offer a new iterative method based on artificial neural networks for finding solution of a fuzzy equations system. Our proposed fuzzified neural network is a five-layer feed-back neural network that corresponding connection weights to output layer are fuzzy numbers. This architecture of artificial neural networks, can get a real input vector and calculates its corresponding fuzzy output. In order to find the approximate solution of the fuzzy system that supposedly has a real solution, first a cost function is defined for the level sets of the fuzzy network and target output. Then a learning algorithm based on the gradient descent method is used to adjust the crisp input signals. The present method is illustrated by several examples with computer simulations.

Fuzzy linear programming problem occur in many fields such as mathematical modeling, Control theory and Management sciences, etc. In this paper we focus on a kind of Linear Programming with fuzzy numbers and variables namely Fully Fuzzy Linear Programming (FFLP) problem, in which the constraints are in inequality forms. Then a new method is proposed to fine the fuzzy solution for solving (FFLP). Numerical examples are providing to illustrate the method.

In the linear system Ax=b the points x are sometimes constrained to lie in a given subspace S of column space of A. Drazin inverse for any singular or nonsingular matrix, exist and is unique. In this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of Drazin inverse in solving such systems is investigated. Constrained linear system arise in electrical network theory.

Solitons are ubiquitous and exist in almost every area from sky to bottom. For solitons to appear, the relevant equation of motion must be nonlinear. In the present study, we deal with the Korteweg-de Vries (KdV), Modified Korteweg-de Vries (mKdV) and Regularised Long Wave (RLW) equations using Homotopy Perturbation method (HPM). The algorithm makes use of the HPM to determine the initial expansion coefficients using the initial value and boundary conditions. The physical structures of the nonlinear dispersive equation have been investigated for different parameters involved. It is shown how the nature of the waves look like in a simple way by considering the value of a certain single combination of constant parameters. The proposed scheme is standard, direct and computerized, which allow us to do complicated and tedious algebraic calculations. The ease of using this method to determine shock or solitary type of solutions, shows its power.