In this paper, three approximate methods namely the Bernoulli, the Bernstein, and the shifted Legendre polynomials operational matrices are presented to solve two important nonlinear ordinary differential equations that appeared in engineering and applied science. The Riccati and the Darcy-Brinkman-Forchheimer moment equations are solved and the approximate solutions are obtained. The methods are summarized by converting the nonlinear differential equations into a nonlinear system of algebraic equations that is solved using Mathematica®12. The efficiency of these methods was investigated by calculating the root mean square error (RMS) and the maximum error remainder (𝑀𝐸𝑅n) and it was found that the accuracy increases with increasi

Original Research Paper Mathematics 1-Introduction : In the light of the progress and rapid development of the applications of research in applications fields, the need to rely on scientific tools and cleaner for data processing has become a prominent role in the resolution of decisions in industrial and service institutions according to the real need of these methods to make them scientific methods to solve the problem Making decisions for the purpose of making the departments succeed in performing their planning and executive tasks. Therefore, we found it necessary to know the transport model in general and to use statistical methods to reach the optimal solution with the lowest possible costs in particular. And you know The Transportatio

The aim of the research is to investigate the effect of cold plasma on the bacteria grown on texture of sesame paste in its normal particle and nano particle size. Starting by using the image segmentation process depending on the threshold method, it is used to get rid of the reflection of the glass slides on which the sesame samples are placed.  The classification process implemented to separate the sesame paste texture from normal and abnormal texture. The abnormal texture appears when the bacteria has been grown on the sesame paste after being left for two days in the air, unsupervised k-mean classification process used to classify the infected region, the normal region and the treated region. The bacteria treated with cold plasma, t

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

The energy expectation values for Li and Li-like ions ( , and ) have been calculated and examined within the ground state and the excited state in position space. The partitioning technique of Hartree-Fock (H-F) has been used for existing wave functions.

An experimental and numerical study was carried out to investigate the heat transfer by natural convection in a three dimensional annulus enclosure filled with porous media (silica sand) between two inclined concentric cylinders with (and without) annular fins attached to the inner cylinder under steady state condition. The experiments were carried out for a range of modified Rayleigh number (0.2 ≤Ra*≤ 11) and extended to Ra*=500 for numerical study and for annulus inclination angle of (δ = 0˚, 30˚, 60˚ and 90˚). The numerical study was to give the governing equation under assumptions that used Darcy law and Boussinesq’s approximation and then it was solved numerically using finite difference approximation. It was found that t