A method for Approximated evaluation of linear functional differential equations is described. where a function approximation as a linear combination of a set of orthogonal basis functions which are chebyshev functions .The coefficients of the approximation are determined by (least square and Galerkin’s) methods. The property of chebyshev polynomials leads to good results , which are demonstrated with examples.

The purpose behind building the linear regression model is to describe the real linear relation between any explanatory variable in the model and the dependent one, on the basis of the fact that the dependent variable is a linear function of the explanatory variables and one can use it for prediction and control. This purpose does not cometrue without getting significant, stable and reasonable estimatros for the parameters of the model, specifically regression-coefficients. The researcher found that "RUF" the criterian that he had suggested accurate and sufficient to accomplish that purpose when multicollinearity exists provided that the adequate model that satisfies the standard assumpitions of the error-term can be assigned. It

In this paper, we designed a new efficient stream cipher cryptosystem that depend on a chaotic map to encrypt (decrypt) different types of digital images. The designed encryption system passed all basic efficiency criteria (like Randomness, MSE, PSNR, Histogram Analysis, and Key Space) that were applied to the key extracted from the random generator as well as to the digital images after completing the encryption process.

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The study aims at building a mathematical model for the aggregate production planning for Baghdad soft drinks company. The study is based on a set of aggregate planning strategies (Control of working hours, storage level control strategy) for the purpose of exploiting the resources and productive capacities available in an optimal manner and minimizing production costs by using (Matlab) program. The most important finding of the research is the importance of exploiting during the available time of production capacity. In the months when the demand is less than the production capacity available for investment. In the subsequent months when the demand exceeds the available energy and to minimize the use of overti

Transport is a problem and one of the most important mathematical methods that help in making the right decision for the transfer of goods from sources of supply to demand centers and the lowest possible costs, In this research, the mathematical model of the three-dimensional transport problem in which the transport of goods is not homogeneous was constructed. The simplex programming method was used to solve the problem of transporting the three food products (rice, oil, paste) from warehouses to the student areas in Baghdad, This model proved its efficiency in reducing the total transport costs of the three products. After the model was solved in (Winqsb) program, the results showed that the total cost of transportation is (269,

Frequency equations for rectangular plate model with and without the thermoelastic effect for the cases are: all edges are simply supported, all edges are clamped and two opposite edges are clamped others are simply supported.   These were obtained through direct method for simply supported ends using Hamilton’s principle with minimizing Ritz method to total energy (strain and kinetic) for the rest of the boundary conditions. The effect of restraining edges on the frequency and mode shape has been considered. Distributions temperatures have been considered as a uniform temperature the effect of developed thermal stresses due to restrictions of ends conditions on vibration characteristics   of a plate with different

In this research, Haar wavelets method has been utilized to approximate a numerical solution for Linear state space systems. The solution technique is used Haar wavelet functions and Haar wavelet operational matrix with the operation to transform the state space system into a system of linear algebraic equations which can be resolved by MATLAB over an interval from 0 to . The exactness of the state variables can be enhanced by increasing the Haar wavelet resolution. The method has been applied for different examples and the simulation results have been illustrated in graphics and compared with the exact solution.

We present a reliable algorithm for solving, homogeneous or inhomogeneous, nonlinear ordinary delay differential equations with initial conditions. The form of the solution is calculated as a series with easily computable components. Four examples are considered for the numerical illustrations of this method. The results reveal that the semi analytic iterative method (SAIM) is very effective, simple and very close to the exact solution demonstrate reliability and efficiency of this method for such problems.

In this paper, the speed control of the real DC motor is experimentally investigated using nonlinear PID neural network controller. As a simple and fast tuning algorithm, two optimization techniques are used; trial and error method and particle swarm optimization PSO algorithm in order to tune the nonlinear PID neural controller's parameters and to find best speed response of the DC motor. To save time in the real system, a Matlab simulation package is used to carry out these algorithms to tune and find the best values of the nonlinear PID parameters. Then these parameters are used in the designed real time nonlinear PID controller system based on LabVIEW package. Simulation and experimental results are compared with each other and showe