In this paper, the homotopy perturbation method (HPM) is presented for treating a linear system of second-kind mixed Volterra-Fredholm integral equations. The method is based on constructing the series whose summation is the solution of the considered system. Convergence of constructed series is discussed and its proof is given; also, the error estimation is obtained. Algorithm is suggested and applied on several examples and the results are computed by using MATLAB (R2015a). To show the accuracy of the results and the effectiveness of the method, the approximate solutions of some examples are compared with the exact solution by computing the absolute errors.

Industrial machining workshops generate substantial quantities of aluminum wire offcuts and filings that cannot be re-entered into bulk metal recycling circuits, posing both a resource management challenge and a potential environmental burden. This study demonstrates a closed-loop valorization route in which this low-grade aluminum waste is converted into nanostructured aluminum oxide (Al2O3) nanoparticles (NPs) by two scalable synthesis pathways (i) chemo-thermal calcination of precipitated Al(OH)₃ at 1000 °C and 1200 °C for 1 and 4 h, and (ii) direct chemical precipitation via AlCl3/Na2CO3 reaction, and then deployed as a functional additive in water-based drilling fluids (WBDFs) used by the oil and gas industry. Comprehensive chara

In this research PbS and PbS:Cu films were prepered with thicknesses (0.85±0.05)?m and (0.55±0.5)?m deposit on glass and silicon substrate respectively using chemical spray pyrolysis technique with a substrate temperature 573K, from lead nitrate salt, thiourea and copper chloride. Using XRD we study the structure properties for the undoped and doped films with copper .The analysis reveals that the structure of films were cubic polycrystalline FCC with a preferred orientation along (200) plane for the undoped films and 1% doping with copper but the orientation of (111) plane is preferred with 5% doping with the rest new peaks of films and appeared because of doping. Surface topography using optical microscope were be checked, it was found

This research was conducted to study the histological structure of the eye in the tree frog (Hyla arborea savignyi) and showed that it is composed of the eyeball and the lens and optic nerve. Appeared eyeball is surrounded by three Tunica from the inside to the outside are Tunica Interna, Tunica vasculosa, Tunica fibrosa. The tunica interna consists of the retina that consists of 10 layers are from outer to inner pigment epithelial layer, rods and cones layer, external limiting membrane, outer nuclear layer, outer plexiform layer, inner nuclear layer, inner plexiform layer , ganglion cells layer , nerve fibers layer, internal limiting membrane .The vascular tunic or Uvea consists of the choroid, ciliary body , and iris . The fibrous coat co

The study is done in the period between (February 20 and October 20) by using ten adult quail Coturnix coturnix (Linnaeus, 1758). The sections are preparing by paraffin method then stain in Harris haematoxylin-eosin. The histological aspects of spinal cord in quail (Coturnix coturnix) the white matter is in the outer part, while the gray matter is arranged in from of X represents its internal part, the dorsal region is called the dorsal horns while the ventral region is called the ventral horns and the central canal cavity, the spinal cord areas appeared as follows: The medial column, column of von Lenhossek, lateral column, dorsal magnocellular column and marginal paragriseal, columns are also called Hoffmann’s nuclei.

The research topic (The dramatic structure transformations in the Iraqi Feature Film) studies the dramatic structure and its transformations in the Iraqi feature film. The research determined the research problem and the need for it in addition to the aims and the limits of the study as well as its importance. The theoretical framework consists of the following themes: the dramatic transformations mechanism and dramatic data in the Iraq film 1957-2003 then the dramatic values transformations and the performance contradictions in the Iraqi film.
The research, after concluding the theoretical framework, came up with a number of indicators of the theoretical framework that have been used as a tool to analyze the sample. The research proc

  The sentence is one building unit in a music that has a full  meaning which in the end takes a long silence .The sentence bases made the sentences with  intransitive verb ( non connection ) and the sentences are   made with general verb (connection ) .The sentence parts :Verbal sentence –supportive sentence , sentence without a verb .

The method of divide the sentence into these syntax  units ( face division ) or (analysis and to each of the syntax units resulted from dividing the sentence to sections made to the end the characterizes the  smaller syntax units ,the words .The method of analyze the surface structure of Persian language sentence  is exchange method.   &nbsp

is divided into two chapter:Chapter one to ensure asyslematic framework for research amd included aresearch problem and also inchuded on the importance of research and the need for him as well as to clarify. The second chapter inchuded a theoretical framework: theoretical framework has been divided into two section. The first topic: poetics transformations The second topic: poetics and scale of rheloric in the film After the comp of the theoretical framework; so the researcher analyzed the film (Antichrist) has arrived ataset of resuits was including