Algorithms using the second order of B -splines [B (x)] and the third order of B -splines [B,3(x)] are derived to solve 1' , 2nd and 3rd linear Fredholm integro-differential equations (F1DEs). These new procedures have all the useful properties of B -spline function and can be used comparatively greater computational ease and efficiency.The results of these algorithms are compared with the cubic spline function.Two numerical examples are given for conciliated the results of this method.

       In the present paper, by making use of the new generalized operator, some results of third order differential subordination and differential superordination consequence for analytic functions are obtained. Also, some sandwich-type theorems are presented.

in this paper the collocation method will be solve ordinary differential equations of retarted arguments also some examples are presented in order to illustrate this approach

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

Oscillation criterion is investigated for all solutions of the first-order linear neutral differential equations with positive and negative coefficients. Some sufficient conditions are established so that every solution of eq.(1.1) oscillate. Generalizing of some results in [4] and [5] are given. Examples are given to illustrated our main results.

The results shows existence of metals such as copper, iron, Cadmium, lead and zinc in most of examined samples , the highest concentration are up to (2.26, 40.82, 282.5, 31.02, 19.26, 4.34) Part per million) ppm) in pasta hot (Zer brand), Indomie with chicken, granule (Zer brand), brand (Zer brand), and rice (mahmood brand) respectively, with presence nickel in spaghetti( Zer brand), granule, Zer brand with concentration reached to 4.34 ppm and 1.06 ppm respectively.
The results of cereals group and its products show that two kinds of fungi, Aspergillus spp. and Penicillin spp. were found in rice (Mahmood brand) with numbers got to 1.5×103 Colony Forming Unit/ gram (c.f.u./g),while Bacillus cereus and Staphylococcus aureus were isola

The aim of this research is to estimate the parameters of the linear regression model with errors following ARFIMA model by using wavelet method depending on maximum likelihood and approaching general least square as well as ordinary least square. We use the estimators in practical application on real data, which were the monthly data of Inflation and Dollar exchange rate obtained from the (CSO) Central Statistical organization for the period from 1/2005 to 12/2015. The results proved that (WML) was the most reliable and efficient from the other estimators, also the results provide that the changing of fractional difference parameter (d) doesn’t effect on the results.

This study emphasizes the infinite-boundary integro-differential equation. To examine the approximate solution of the problem, two modified optimization algorithms are proposed based on generalized Laguerre functions. In the first technique, the proposed method is applied to the original problem by approximating the solution using the truncated generalized Laguerre polynomial of the unknown function, optimizing coefficients through error minimization, and transforming the integro-differential equation into an algebraic equation. In contrast, the second approach incorporates a penalty term into the objective function to effectively enforce boundary and integral constraints. This technique reduces the original problem to a mathematical optimi