مجله بین المللی محاسبات و مدل سازی ریاضی
سال چهارم شماره 4 (Autumn 2014)

This paper analyzes renewal input state dependent queue with $N$- policy wherein the server takes exactly one vacation. Using the supplementary variable technique and recursive method, we derive the steady state system length distributions at various epochs. Various performance measures has been presented. Finally, some numerical computations in the form of graphs are presented to show the parameter effect on various performance measures.

In this paper, a fault diagnosis system based on discrete wavelet transform (DWT) and artificial neural networks (ANNs) is designed to diagnose different types of fault in gears and bearings. DWT is an advanced signal-processing technique for fault detection and identification. Five features of wavelet transform RMS, crest factor, kurtosis, standard deviation and skewness of discrete wavelet coefficients of normalized vibration signals has been selected. These features are considered as the feature vector for training purpose of the ANN. A wavelet selection criteria, Maximum Energy to Shannon Entropy ratio, is used to select an appropriate mother wavelet and discrete level, for feature extraction. To ameliorate the algorithm, various ANNs were exploited to optimize the algorithm so as to determine the best values for ‘‘number of neurons in hidden layer” resulted in a high-speed, meticulous three-layer ANN with a small-sized structure. The diagnosis success rate of this ANN was 100% for experimental data set. Some experimental set of data has been used to verify the effectiveness and accuracy of the proposed method. To develop this method in general fault diagnosis application, three different examples were investigated in cement industry. In first example a MLP network with well-formed and optimized structure (20:15:7) and remarkable accuracy was presented providing the capability to identify different faults of gears and bearings. In second example a neural network with optimized structure (20:15:4) was presented to identify different faults of bearings and in third example an optimized network (20:15:3) was presented to diagnose different faults of gears. The performance of the neural networks in learning, classifying and general fault diagnosis were found encouraging and can be concluded that neural networks have high potential in condition monitoring of the gears and bearings with various faults.

In this paper, we use Petrov-Galerkin elements such as continuous and discontinuous Lagrange-type k-0 elements and Hermite-type 3-1 elements to find an approximate solution for linear Fredholm integro-differential equations on $[0,1]$. Also we show the efficiency of this method by some numerical examples.

In this paper, we propose an algorithm base on decomposition technique for solvingthe mixed integer linear multiplicative-linear bilevel problems. In actuality, this al-gorithm is an application of the algorithm given by G. K. Saharidis et al for casethat the rst level objective function is linear multiplicative. We use properties ofquasi-concave of bilevel programming problems and decompose the initial probleminto two subproblems to names RMP and SP. The lower and upper bound providedfrom the RMP and SP are updated in each iteration. The algorithm converges whenthe dierence between the upper and lower bound is less than an arbitrary tolerance.Finally, we give some numerical examples are presented in order to show the eciencyof algorithm.

In this study, we introduce the classes of $\phi$-strongly pseudocontractive mappings in the intermediate sense and generalized $\Phi$-pseudocontractive mappings in the intermediate sense and prove the existence of fixed points for those maps. The results generalise the results of several authors in literature including Xiang [Chang He Xiang, Fixed point theorem for generalized $\Phi$-pseudocontractive mappings, Nonlinear Analysis 70 (2009) 2277-2279].

By using the trigonometric uniform splines of order 3 with a real tension factor, a numericalmethod is developed for solving a linear second order boundary value problems (2VBP) withDirichlet, Neumann and Cauchy types boundary conditions. The moment at the knots isapproximated by central finite-difference method. The order of convergence of the methodand the theory is illustrated by solving test examples. Experimental results demonstrate thatour method is more effective for the problems where the exact solution is trigonometric orhyperbolic.

In this paper, we present a computational method for solving boundary integral equations with loga- rithmic singular kernels which occur as reformulations of a boundary value problem for the Laplacian equation. The method is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis. This approach utilizes the non-uniform Gauss-Legendre quadrature rule for approximating logarithm-like singular integrals and so reduces the solution of boundary integral equations to the solution of linear systems of algebraic equations. The properties of CAS wavelets are used to make the wavelet coe±cient matrices sparse, which eventually leads to the sparsity of the coe±cient matrix of the obtained system. Finally, the validity and e±ciency of the new technique are demonstrated through a numerical example.

In this work, we analyse a pair of two-dimensional coupled reaction-diusion equations known as the Gray-Scott model, in which spot patterns have been observed. We focus on stationary patterns, and begin by deriving the asymptotic scaling of the parameters and variables necessary for the analysis of these patterns. A complete bifurcation study of these solutions is presented. The main mathematical techniques employed in this analysis of the stationary patterns is the Turing instability theory. This paper addresses the question of how popula- tion diusion aects the formation of the spatial patterns in the Gray-Scott model by Turing mechanisms. In particular, we present a theoretical analysis of results of the numerical simulations in two dimensions. Moreover, there is a critical value for the system within the linear regime. Below the critical value the spatial patterns are impermanent, whereas above it stationary spot patterns can exist over time. We have observed the formation of spatial patterns during the evolution, which are sparsely isolated ordered spot patterns that emerge in the space. In this research we focuse on three areas: rst, the biology; second, the mathematics and third, the application. We use these spatial patterns to understand the nature of disease spread and that means to understand the mechanism of interaction of the populations. There remains uncertainty in the mechanisms surrounding the genesis of how epidemics spread in their spatial enveronment. The role of mathematical modelling in understanding the spread and control of epidemics can never be over emphised.