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In this short paper the monotonicity of functions involving the Beta function is considered to be study by using a similar method given in (2) and (4).

The paper tackled a survey of two optimization methods to study spanning tree problem by modifying the spanning tree problem to generate all of possible solutions in undirected tree graph with simulated annealing algorithm and ant colony optimization algorithm. These algorithms are two of the optimization methods to find optimal solution from many of solutions in search space. A program is written in MATLAB 6.5 language to simulate these two algorithms with spanning tree problem. The experimental results in this paper show the effectiveness and easy implementation of each algorithm to find optimal solution, and to perform significantly better than the manual method.

In this paper we consider parameter estimation in a linear regression setting with inequality linear constraints on the regression parameters. Most other research on this topic has typically been addressed from a Bayesian perspective. In this paper we apply Bayesian approach with Gibbs sampler to generate samples from the posterior distribution. However, these implementations can often exhibit poor mixing and slow convergence. This paper overcomes these limitations with a new implementation of the Gibbs sampler. In addition, this procedure allows for the number of constraints to exceed the parameter dimension and is able to cope with equality linear constraints.

In this paper, we present two gyroarea formulas (Möbius-Bretschneider’s formula and Möbius-Cagnoli’s formula) for Möbius gyroquadrilaterals in the Poincaré disc model of hyperbolic geometry.

In this paper, depending on the notion of fuzzy length space we define the Cartesian product of two fuzzy length spaces. we proved that the Cartesian product of two fuzzy length spaces is a fuzzy length space. More accurately, the Cartesian product of two complete fuzzy length spaces is proved to be a complete fuzzy length space. Furthermore, the definitions of sequentially fuzzy compact fuzzy length space, countably fuzzy compact fuzzy length space, locally fuzzy compact fuzzy length space are introduced, and theorems related to them are proved.

This paper introduces the Multistep Modified Reduced Differential Transform Method (MMRDTM). It is applied to approximate the solution for Nonlinear Schrodinger Equations (NLSEs) of power law nonlinearity. The proposed method has some advantages. An analytical approximation can be generated in a fast converging series by applying the proposed approach. On top of that, the number of computed terms is also significantly reduced. Compared to the RDTM, the nonlinear term in this method is replaced by related Adomian polynomials prior to the implementation of a multistep approach. As a consequence, only a smaller number of NLSE computed terms are required in the attained approximation. Moreover, the approximation also converges rapidly over a wide time frame. Two examples are provided for showing the ability and advantages of the proposed method to approximate the solution of the power law nonlinearity of NLSEs. For pictorial representation, graphical inputs are included to represent the solution and show the precision as well as the validity of the MMRDTM.

In this paper, for the first time we introduce a new four-parameter model called the Gumbel- Pareto distribution by using the T-X method. We obtain some of its mathematical properties. Some structural properties of the new distribution are studied. The method of maximum likelihood is used for estimating the model parameters. Numerical illustration and an application to a real data set are given to show the flexibility and potentiality of the new model.

In this paper, we shall study the existence of a new class called fractional Caputo type of order sobolev type fractional order differential Equations motion in separable Banach spaces. The class of impulsive nonlinear fractional order bilinear control differential Equations with Riemann Leovel differential initial value studied and discussed also given the important results for the almost periodic mild solution to be sTable by using Menards function and granwal fractional inequality.

In this paper, we focus on designing feed forward neural network (FFNN) for solving Mixed Volterra – Fredholm Integral Equations (MVFIEs) of second kind in 2–dimensions. in our method, we present a multi – layers model consisting of a hidden layer which has five hidden units (neurons) and one linear output unit. Transfer function (Log – sigmoid) and training algorithm (Levenberg – Marquardt) are used as a sigmoid activation of each unit. A comparison between the results of numerical experiment and the analytic solution of some examples has been carried out in order to justify the efficiency and the accuracy of our method.

This work presents the modeling of the electrical response of monocrystalline photovoltaic module by using five parameters model based on manufacture data-sheet of a solar module that measured in stander test conditions (STC) at radiation 1000W/m² and cell temperature 25 . The model takes into account the series and parallel (shunt) resistance of the module. This paper considers the details of Matlab modeling of the solar module by a developed Simulink model using the basic equations, the first approach was to estimate the parameters: photocurrent Iph, saturation current Is, shunt resistance Rsh, series resistance Rs, ideality factor A at stander test condition (STC) by an iteration process. To implement the iteration process, a numerical approach based on the Newton Raphson method has been implemented and programmed in Matlab. The second mathematical model used in Matlab/Simulink using equations for each parameter to determine the parameters at all operating conditions. The Matlab program gives the information about the behavior of the practical PV module, under different atmospheric conditions. The model accuracy was also analyzed through finding out the compatibility between the practical and the theoretical aspects at different solar radiation intensity 500, 750 and 1000 W/m2 by extracting the error ratios. The results show that there is difference between theoretical (modeled) and experimental, the best validation (less error) between five parameters model and experimental maximum power results at radiation 500, 750, 1000 W/m2 and STC was 5.5%, 19%, 18% and 12.3% in January respectively, due to the decreases in ambient temperature and thus decreases in the temperature of solar module in January led to increase in maximum output power and producing best validation between model and experimental in this month.

In this paper, the stability analysis is performed on two Galerkin finite element schemes for solving reaction-diffusion system with fast reversible reaction. Fourier (Von Neumann) method is implemented to propose time-step criteria for the consistent and the lumped schemes with four popular choices for . We have found that the two schemes are unconditionally stable when , while the consistent scheme is stable under the conditions and when . Also, the lumped scheme is stable under the conditions and when .

In this paper, we use Romberg algorithm, to find an approximation solution for a system of nonlinear Fredholm integral equations of the second kind. A comparison between this approximations and exact solutions for four numerical examples are given, depending on the least-square error and running computer time. Our numerical results are obtained by MATLAB 7.0 program and for a system of rank 2×2, 3×3 on Personal Computer P4.

In this paper, the approximate solution of a reaction-diffusion system with fast reversible reaction is obtained by using Adomian decomposition method (ADM) and variational iteration method (VIM) which are two powerful methods that were recently developed. The VIM requires the evaluation of the Lagrange multiplier, whereas ADM requires the evaluation of the Adomian polynomials. The behavior of the approximate solutions and the effects of different values of t are shown graphically.

The n-Wiener polynomials of straight hexagonal chains and the Cartesian product of a complete graph Kr and a cycle Cr are obtained in this paper. The n-diameter and the n-Wiener index of each such graphs are also determined.

Some algebraic properties of the sharp points of the joint numerical range of a matrix polynomials are the main subject of this paper. We also consider isolated points of the joint numerical range of matrix polynomials.

The aim of the project is to develop parallel approaches for Gaussian Elimination Methods that are used in linear programming to solve linear module systems. Most of these models are time-consuming when executed and processed in the sequential microprocessor computers. During the project, we try to decrease this time and increase the efficiency of the algorithm for the Gaussian Elimination Method, through developing parallel methods appropriate to be executed on MIMD type computers. In this paper, three algorithms were suggested for paralleling a developed algorithm of Gaussian Elimination Method and a comparison was made between the three algorithms and the original. As we have been able to accelerate the three parallel methods and the speedup was one of the following: Speedup = , no. of processor is (50) In general, the practical results and the suggested programs for these new algorithms proved to be better in performance than their analogues that are executed in computers of sequential processor in view of the two elements of execution time and algorithm time.

In this paper we used successive approximate method (S.A.M.) to solve Fredholm integral equation of the first kind (F.I.E.1st. K.) with symmetric kernel. And also suggested an algorithm for this method the computer programming is given for the algorithm. The method and algorithm are tested on several numerical examples. After comparing the results with exact solution see tables (1, 2), it occurred that the results are good. (in this work Matlab programming used).

This paper is devoted to drive the matrix algebraic equation for the one-dimensional nonlinear Klein-Gordon equation which is obtained from using the implicit finite difference method. The convergence analysis of the solution is discussed. Numerical computations are conducted and the solutions are stable and convergent when the sine function is used as an initial condition.

In this paper we study the existence and approximation of the periodic solutions for a system of first order nonlinear differential equations by assuming that each of the functions are measurable at t and bounded by Lebesgue integrable functions. The numerical-analytic method has been used to study the periodic solutions of ordinary differential equations which were introduced by A. M. Samoilenko.

In this paper we used Hermite polynomial with Galerkin , collocation and least square methods for solving fredholm integral equations of the first kind (F.I.E.F.K) with degenerated kernel .The algorithms and computer applications of the algorithms are given for the methods which have tested through numerical exaples and compared the results with exact solutions as indecated in tables (1,2,3,4), (used Matlab programmong in this work).