A new method based on the Touchard polynomials (TPs) was presented for the numerical solution of the linear Fredholm integro-differential equation (FIDE) of the first order and second kind with condition. The derivative and integration of the (TPs) were simply obtained. The convergence analysis of the presented method was given and the applicability was proved by some numerical examples. The results obtained in this method are compared with other known results.

تتحقق اهداف الدول عبر توظيف امكانياتها ومواردها ، وهذا التوظيف يقترن بوسائل مختلفة باختلاف الامكانيات المتاحة. وتتفاوت هذه الوسائل ما بين الاكراه والترغيب ، واحياناً من الممكن استخدام كلا الوسيلتين ، وتندرج هذه الوسائل من حيث تصنيفها ضمن نوعين رئيسين هما: القوة الصلبة ]القوة العسكرية والاقتصادية[ والقوة الناعمة ]استخدام جميع ادوات الترغيب وتسخيرها من اجل ان تُعجب بها الدول الاخرى وتنصاع

The research aims to measure the net nominal protection coefficients for the products table eggs and poultry meat and the extent of its impact on domestic production volume for the period of 1990- 2013 has been the use of mathematical formulas simplified in the calculation of the transaction process with a view to the extent of support and protection offered by the state pricing policy for products Resources Sector Animal in Iraq and reach search Highlights and most important, there are volatile price state policy with regard to eggs and poultry meat, as it ranged net nominal protection coefficients between the larger and less than the right one, which means that values are unstable to support local producers or consumers, and can be The

Nowadays, the power plant is changing the power industry from a centralized and vertically integrated form into regional, competitive and functionally separate units. This is done with the future aims of increasing efficiency by better management and better employment of existing equipment and lower price of electricity to all types of customers while retaining a reliable system. This research is aimed to solve the optimal power flow (OPF) problem. The OPF is used to minimize the total generations fuel cost function. Optimal power flow may be single objective or multi objective function. In this thesis, an attempt is made to minimize the objective function with keeping the voltages magnitudes of all load buses, real outp

In this paper,the homtopy perturbation method (HPM) was applied to obtain the approximate solutions of the fractional order integro-differential equations . The fractional order derivatives and fractional order integral are described in the Caputo and Riemann-Liouville sense respectively. We can easily obtain the solution from convergent the infinite series of HPM . A theorem for convergence and error estimates of the HPM for solving fractional order integro-differential equations was given. Moreover, numerical results show that our theoretical analysis are accurate and the HPM can be considered as a powerful method for solving fractional order integro-diffrential equations.

Porous Silicon (PS) layer has been prepared from p-type silicon by electrochemical etching method. The morphology properties of PS samples that prepared with different current density has been study using atom force measurement (AFM) and it show that the Layer of pore has sponge like stricture and the average pore diameter of PS layer increase with etching current density increase .The x-ray diffraction (XRD) pattern indicated the nanocrystaline of the sample. Reflectivity of the sample surface is decrease when etching current density increases because of porosity increase on surface of sample. The photolumenses (PL) intensity increase with increase etching current density. The PL is affected by relative humidity (RH) level so we can use

In this work, an analytical approximation solution is presented, as well as a comparison of the Variational Iteration Adomian Decomposition Method (VIADM) and the Modified Sumudu Transform Adomian Decomposition Method (M STADM), both of which are capable of solving nonlinear partial differential equations (NPDEs) such as nonhomogeneous Kertewege-de Vries (kdv) problems and the nonlinear Klein-Gordon. The results demonstrate the solution’s dependability and excellent accuracy.

     In this article, a new efficient approach is presented to solve a type of partial differential equations, such (2+1)-dimensional differential equations non-linear, and nonhomogeneous. The procedure of the new approach is suggested to solve important types of differential equations and get accurate analytic solutions i.e., exact solutions. The effectiveness of the suggested approach based on its properties compared with other approaches has been used to solve this type of differential equations such as the Adomain decomposition method, homotopy perturbation method, homotopy analysis method, and variation iteration method. The advantage of the present method has been illustrated by some examples.

Throughout this paper R represents a commutative ring with identity and all R-modules M are unitary left R-modules. In this work we introduce the notion of S-maximal submodules as a generalization of the class of maximal submodules, where a proper submodule N of an R-module M is called S-maximal, if whenever W is a semi essential submodule of M with N ⊊ W ⊆ M, implies that W = M. Various properties of an S-maximal submodule are considered, and we investigate some relationships between S-maximal submodules and some others related concepts such as almost maximal submodules and semimaximal submodules. Also, we study the behavior of S-maximal submodules in the class of multiplication modules. Farther more we give S-Jacobson radical of rings