Based on Lyapunov stability theory, a partial synchronization scheme is proposed to track the signal of Hindmarsh-Rose neuron using the Coullet system via only one single controller. Summation for the series of error variables are employed to detect the degree of synchronization. Three cases are considered to verify the proposed partial synchronization scheme. To demonstrate the effectiveness of the proposed method, some simulation results are given. It is found that the arithmetic product of the gain coefficients dominate the process and speed of synchronization of the two systems. The larger arithmetic product of the two gain coefficients is used, the less time is required.

In this paper, an application of the variational iteration method (VIM) is presented. This technique provides a sequence of function which converges to the exact solution of the problem. The main property of the method is in its flexibility and ability to solve nonlinear equation accurately and conveniently. For solving the discussed inverse problem, at first we transform it into a nonlinear direct problem then use the proposed method. Numerical examples are examined to show the efficiency of the technique.

In this paper, a method is employed to approximate the solution of two-dimensional nonlinear Volterra integro-differential equations (2DNVIDEs) with supplementary conditions. First, we introduce two- dimensional Legendre polynomials, then convert 2DNVIDEs to the two-dimensional linear Volterra integro- differential equations (2DLVIDEs). Using this properties and collocation points, reduce it to the system of algebraic equations. Finally, some numerical examples are given to clarify the efficiency and accuracy of the present method.

In this paper, a Bernoulli wavelet based numerical method for the solution of Fredholm integral equations of the second kind is proposed. The method is based upon Bernoulli wavelet approximations. The Bernoulli wavelet (BW) is first presented and the resulting Bernoulli wavelet matrices are utilized to reduce the Fredholm integral equations into algebraic equations. Solving these equations using MATLAB to obtain Bernoulli coefficients. The numerical results of the proposed method through the illustrative examples is presented in comparison with the exact and existing methods (Haar wavelet method (HWM) [13], Hermite cubic splines (HCS) [11]) of solution from the literature are shown in tables and figures, which show that the validity and applicability of the technique with higher accuracy even for the smaller values of N.

In this paper an iterative method based on shifted Legendre polynomials is presented to obtain the approximate solutions of optimal control problems subject to integral equations. The operational matrices of integration and product of shifted Legendre polynomials for solving integral equation is employed. The methodology is based on the parametrization of control and state functions. This converted the problem to nonlinear optimization problem in any iteration. In addition, some numerical examples are presented to illustrate the accuracy and efficiency of the proposed method.

In this paper an optimization algorithm based on Particle Swarm Optimization algorithm is used for handwritten Persian digits recognition with General Regression Neural Network .The system uses image zoning for the digit recognition. General Regression Neural Network accuracy depends on the centers and widths of the hidden layer neuron basis functions (neuron spread). In this paper we use Particle Swarm Optimization algorithm to determine General Regression Neural Network hidden layer spread. Results show that the optimized General Regression Neural Network provides higher recognition ability compared with that of unoptimized General Regression Neural Network.

In this paper, we proposed an efficient numerical method based on uniform Haar wavelet for the numerical solutions oflinear and nonlinear Benjamin–Bona–Mahony (BBM) Equations. Such types of problems arise in various fields of science and engineering. In present study more accurate solutions have been obtained by Haar wavelet decomposition with multiresolution analysis. Three test problems are considered to check theefficiency and accuracy of the proposed method.An extensiveamount of error analysis has been carried out to obtain the convergence of the method.The numerical results are found in good agreement with exact and finite difference method (FDM), which shows that the solution using Haar wavelet method (HWM) is more effective and accurate and manageable for these equations.

The research presented in this paper was aimed to develop an CBIR system to aid in automatically detect and retrieve solar flares images based on detected edges and color features. In general, the work consists of two phases: (1) enrollment phase, which consist of feature extraction based on Conventional Color Histograms (CCH) and edge detection for sunspots and active regions on the sun using Sobel filter, (2) retrieving phase, which use the similarity measurement to retrieve most similar images from the database for a given query sample. The conducted tests were carried on 250 images and give good precision and recall rates.

The sparseness adaptive matching pursuit algorithm (SAMP) is a classical algorithm based on compressed sensing theory. Aiming at reconstructing signals with unknown sparsity, an adaptive step forward-backward matching pursuit algorithm (AFBMP) is presented. The AFBMP select matching atoms in the forward processing by using logarithmic variable steps which under the frame of sparseness adaptive matching pursuit algorithm. At the beginning of iterations, high value of step size, causing fast convergence of the algorithm is used to realize the coarse approach of signal sparse, and in the later smaller value of step size is used to realize the precise reconstruction of the sparse signal which equal to half of the previous step. Then AFBMP amend the mistakes which caused in the former stage and delete part of the false atoms in the support set using the backward strategy. Finally it realizes the signal accurately approximate. Experiments show that the AFBMP algorithm can reconstruct the unknown signal more efficiently.