In this paper, a new technique is offered for solving three types of linear integral equations of the 2^nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree  and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those

This paper presents a modified training method for Recurrent Neural Networks. This method depends on the Non linear Auto Regressive (NARX) model with Modified Wavelet Function as activation function (MSLOG) in the hidden layer. The modified model is known as Modified Recurrent Neural (MRN). It is used for identification Forward dynamics of four Degrees of Freedom (4-DOF) Selective Compliance Assembly Robot Arm (SCARA) manipulator robot. This model is also used in the design of Direct Inverse Control (DIC). This method is compared with Recurrent Neural Networks that used Sigmoid activation function (RS) in the hidden layer and Recurrent Neural Networks with Wavelet activation function (RW). Simulation results shows that the MRN model is bett

             It is the regression analysis is the foundation stone of knowledge of statistics , which mostly depends on the ordinary least square method , but as is well known that the way the above mentioned her several conditions to operate accurately and the results can be unreliable , add to that the lack of certain conditions make it impossible to complete the work and analysis method and among those conditions are the multi-co linearity problem , and we are in the process of detected that problem between the independent variables using farrar –glauber test , in addition to the requirement linearity data and the lack of the condition last has been resorting to the

In this paper, The transfer function model in the time series was estimated using different methods, including parametric Represented by the method of the Conditional Likelihood Function, as well as the use of abilities nonparametric are in two methods  local linear regression and cubic smoothing spline method, This research aims to compare those capabilities with the nonlinear transfer function model by using the style of simulation and the study of two models as output variable and one model as input variable in addition t

Slag of aluminum is a residue which results during the melting process of primary and secondary aluminum production. Salt slag of aluminum is hazardous solid waste according to the European Catalogue for Hazardous Wastes. Hence, recovery of aluminum not only saves the environment, but also has advantages of financial and economic returns. In this research, aluminum was recovered and purified from the industrial wastes generated as waste from both of State Company for Electrical and Electronic Industries (Baghdad/AlWaziriya) and General Company for Mechanical Industries (Babylon/-Al-Escandria). It was found that these wastes contain tiny proportions of other elements such as iron, copper, nickel, titanium, lead, and potassium. Wastes were

 The transfer function model the basic concepts in the time series. This model is used in the case of multivariate time series. As for the design of this model, it depends on the available data in the time series and other information in the series so when the representation of the transfer function model depends on the representation of the data In this research, the transfer function has been estimated using the style nonparametric represented in two method  local linear regression and cubic smoothing spline method The method of semi-parametric represented use semiparametric single index model, With four proposals, , That the goal of this research is comparing the capabilities of the above mentioned m

In this paper, a computational method for solving optimal problem is presented, using indirect method (spectral methodtechnique) which is based on Boubaker polynomial. By this method the state and the adjoint variables are approximated by Boubaker polynomial with unknown coefficients, thus an optimal control problem is transformed to algebraic equations which can be solved easily, and then the numerical value of the performance index is obtained. Also the operational matrices of differentiation and integration have been deduced for the same polynomial to help solving the problems easier. A numerical example was given to show the applicability and efficiency of the method. Some characteristics of this polynomial which can be used for solvin

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