The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.

Suffer most of the industrial sector companies from high Kperfi magnitude of the costs of industrial indirect, lack of equitable distribution of these costs on the objectives of cost, increased competition, and the lack of proper planning in line and changes faced by the industrial sector (general) and sample (private), as well as the difficulty in re- directing efforts to improve profitability and in-depth analysis of activities, and to identify untapped resource activities, then link these activities to the final products  The research aims to apply the technology review and evaluate programs with the method (ABC) through the application stages of planning, scheduling and control and a comparison to get to the products of dev

In this research Bi2S3 thin films have been prepared on glass substrates using chemical spray pyrolysis method at substrate temperature (300oC) and molarity (0.015) mol. Structural and optical properties of the thin films above have been studied; XRD analysis demonstrated that the Bi2S3 films are polycrystalline with (031) orientation and with Orthorhombic structure. The optical properties were studied using the spectral of the absorbance and transmission of films in wavelength ranging (300-1100) nm. The study showed that the films have high transmission within the range of the visible spectrum. Also absorption coefficient, extinction coefficient and the optical energy gap (Eg) was calculated, found that the film have direct ener

The inverse problem is important method in the design of electrostatic lenses which is used in this work, with new technique by suggesting an axial electrostatic potential distribution using polynomial functions of the third order. The paraxial-ray equation is solved to obtain the trajectory of particles that satisfy the suggested potential function.In this work design of immersion electrostatic lens operated under zero magnification condition. The electrode shape of sthe electrostatic lens was the dermined from the solution of laplace equation and plotted in two deimensions . The results showed low values of spherical and chromatic aberrations , which are considered as good criteria for good desigh.

In this paper the variable structure control theory is utilized to derive a discontinuous controller to the magnetic levitation system. The magnetic levitation system model is considered uncertain, which subjected to the uncertainty in system parameters, also it is open-loop unstable and strongly nonlinear. The proposed variable structure control to magnetic levitation system is proved, and the area of attraction is determined. Additionally, the chattering, which induced due to the discontinuity in control law, is attenuated by using a non-smooth approximate. With this approximation the resulted controller is a continuous variable structure controller with a determined steady state error according to the selected control

The design of the Graphic has recently taken a great variety in the curricula and design methods that have led to its applications for career advancement and aesthetic quality. This is due to the communicative role that it plays in the movement of human beings and their aspirations. Among these applications are the designs of magazine covers in different variations. The design of the cover is based on a structural system that requires awareness and skill from the designer, especially since the organizational structure in the design of the envelope is limited in both vocabulary and space, and in the neighborhood Many have the image of sovereignty and sometimes the other head line, and can lead color values ​​are other.

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Designed Mirrors double and triple package adoption concept heap where they were changing the thickness of the layers within periodic basis of the pile and different ratios (p: q) in addition to change the refractive index of materials within periodic basis and its impact on sites Dhour tops high reflectivity study included spectral region visible and infrared, depending on NdharahFeatured matrix adjusted fall of light close to the vertical arrangement multilayer dielectric materials and thin films homogeneous and uniform

This research aims to study and reveal the influence of Bauhaus principles in contemporary graphic design. The researcher determined the objective/spatial/temporal limit: Study of the Bauhaus influence in the design of the graphic poster in Germany in 2020. The theoretical framework in the first section dealt with (the emergence and factors of the emergence of the Bauhaus school and its characteristics), while the second topic dealt with (the intellectual, functional and aesthetic data of the Bauhaus School), after which the indicators that resulted from the theoretical framework were produced.

He mentioned four previous studies, one of them was discussed in detail. In the third chapter he defined the methodology, society, and sam