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.

In all applications and specially in real time applications, image processing and compression plays in modern life a very important part in both storage and transmission over internet for example, but finding orthogonal matrices as a filter or transform in different sizes is very complex and importance to using in different applications like image processing and communications systems, at present, new method to find orthogonal matrices as transform filter then used for Mixed Transforms Generated by using a technique so-called Tensor Product based for Data Processing, these techniques are developed and utilized. Our aims at this paper are to evaluate and analyze this new mixed technique in Image Compression using the Discrete Wavelet Transfo

The study is based on the selective binding ability of the drug compound procaine (PRO) on a surface imprinted with nylon 6 (N6) polymer. Physical characterization of the polymer template was performed by X-ray diffraction and DSC thermal analysis. The imprinted polymer showed a high adsorption capacity to trap procaine (237 µg/g) and excellent recognition ability with an imprinted factor equal to 3.2. The method was applied to an extraction column simulating a solid-phase extraction to separate the drug compound in the presence of tinoxicam and nucleosimide separately and in a mixture of them with a recovery rate more than the presence of tinoxicam and nucleosimide separately and in a mixture of them with a recovery rate of more t

The analytic solution for the unsteady flow of generalized Oldroyd- B fluid on oscillating rectangular duct is studied. In the absence of the frequency of oscillations, we obtain the problem for the flow of generalized Oldroyd- B fluid in a duct of rectangular cross- section moving parallel to its length. The problem is solved by applying the double finite Fourier sine and discrete Laplace transforms. The solutions for the generalized Maxwell fluids and the ordinary Maxwell fluid appear as limiting cases of the solutions obtained here. Finally, the effect of material parameters on the velocity profile spotlighted by means of the graphical illustrations

Background: Plantar heel pain is a clinical syndrome characterized by pain and tenderness beneath the heel which is typically worse in the morning and improves after the first few steps in the day. It is a common and frequently disabling clinical complaint that may be caused by a broad spectrum of osseous or soft tissue disorders. Objective: To evaluate the effectiveness of an operation of multiple drilling of calcaneum for resistant plantar heel pain syndrome. Methods: During the period from November 2012 to August 2016, 17 patients (17heels) were enrolled in a cohort clinical study at the orthopedic unit in AL-Sheikh Zayed and AlWassity Hospitals. Result: Drilling of the calcaneum is a simple procedure achieving 70.6% cure in resistant as