The method of operational matrices is based on the Bernoulli and Shifted Legendre polynomials which is used to solve the Falkner-Skan equation. The nonlinear differential equation converting to a system of nonlinear equations is solved using Mathematica®12, and the approximate solutions are obtained. The efficiency of these methods was studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as increases. Moreover, the obtained approximate solutions are compared with the numerical solution obtained by the fourth-order Runge-Kutta method (RK4), which gives a good agreement.
Abstract
Praise be to Allah, The Lord of the worlds, and peace be upon
Muhammad the master of former and latter people, and peace be upon His
relatives, companions and those who followed Him to Judgment day.
After recognizing the prescription which is called (Al- Fadhaly's Thesis in
parsing of "There is no god but God") as it is related with the word of the
investigation of this issue attracted me, as being related with the idea of the
only one God that is mentioned in the prophetic speech, which is said by
Anas- God satisfies him- Who said, Said the Messenger Muhammad peace
be upon him " Goes out of the Hell who said: there is no god but God, and in
his heart a hair weight of charity, and goes out of the He
Background: Malignant lymphoma is a term that describes primary tumors of the lymphoreticular system, almost all of which arise from lymphocytes.MMP-1 is the most ubiquitously expressed interstitial collagenase, a subfamily of MMPs that cleaves stromal collagens. It is also called collagenase-1.TIMPs which inhibits MMP activity and thereby restrict extracellular matrix breakdown, TIMP-1 is a stromal factor that has a wide spectrum of functions in different tissues. Material and Methods: This study was performed on (68) formalin-fixed, paraffin-embedded blocks, histopathologically diagnosed as lymphoma (head and neck lesions). Immunohistochemical staining of MMP1and TIMP1 was performed on each case of the study sample. Results: The expressio
... Show MoreEvaluation is one of the most important elements of teaching process. The recent trends in evaluation and educational reform movements have called for using alternative evaluation, which focuses on performance evaluation. Authentic assessment is usually described as formative, in which students participate in their acquisition, in addition to the fact that students are productive and active, which is reflected in the students' achievement and skill level. The study aims to reveal the degree of knowledge and use of alternative assessment tools by primary school teachers in Gaza -Palestine. To meet the objective of the study, the researchers used the descriptive-analytical method and the questioner as a study tool. The study sample c
... Show MoreThe paper studies the description of the colloquial and popular vocabulary used by wholesales tradesmen in Varonech before the Bolshevik Revolution . The vocabulary were used in the personal letters written by the poet and sent to famous poets and critics like Belenisky, kryvesky and Malsheve. And some were sent to his father and his sister. Not only did these letter bear the personal taste, but they represented a literary product reflecting on the poet's impressions, views, ambitions, and opinion in arts, poetry, prose, and theatre. The researcher used about thirty instances of various levels of grammar, style and phonology, all representing colloquial vocabulary used commonly at the time of Alexi 
... Show MoreBackground: Peripheral giant cell lesion (PGCL) and central giant cell lesion (CGCL) of the jaws have a distinct clinical behavior.Giant cell tumour (GCT) is a benign locally aggressive neoplasm affects the long bones. Both lesions are characterized histologically by multinucleated giant cells in a background of ovoid to spindle-shaped mesenchymal cells. The WW domain-containing oxidoreductase (WWOX) gene is located at 16q23.1–16q23.2, a region that spans the second most common human fragile site, FRA16D, at 16q23.2.The Ki-67 antigen is a nuclear protein that is associated with and may be necessary for cellular proliferation.Ki-67 protein is present during all active phases of the cell cycle (G1, S, G2, and mitosis), but is absent fr
... Show MoreThis study aimed to identify the employment of the social networking platform «Twitter» in the 2016 presidential campaign led by the Republican candidate, Donald Trump; and analyse his tweets through his personal account on «Twitter» for the period from: 10/ 8/2016 to: 11/ 8/2016 which represents the last month of the election campaign.
The study belongs to the type of descriptive studies using the analytical method through an analysis index that includes sub-categories and other secondary categories. The research has adopted the ordinary unit of information material (tweet) as an analysis unit for this purpose.
... Show MoreBACKGROUND: Idiopathic immune thrombocytopenia purpura is an autoimmune bleeding disorder that accounts for approximately one-third of clinical hemorrhagic diseases. Pathophysiologically, it involves a complicated imbalance in the immune system. OBJECTIVES: This study focuses on evaluating the levels of the immunomodulatory cytokines interleukin (IL)-35, interleukin-10, and transforming growth factor-β (TGF)-β in patients with refractory idiopathic immune thrombocytopenia undergoing treatment with romiplostim. MATERIALS AND METHODS: A cross-sectional study encompassed 78 individuals with idiopathic immune thrombocytopenia and conducted measurements of different immunomodulatory cytokines in response to different responses of idiopath
... Show MoreThe media, especially the satellite channels in our time, are one of the most important pillars of daily life, public and private, for society and people, and are considered by sociologists and sociologists as one of the most important factors of social upbringing and the most important, as a result of the technological and technological development of the media as well as increasing their numbers and vertical and horizontal expansion locally, As well as entering into the lives of individuals and people and leading them to important sites within their interests and preferences, not to mention the long time spent exposure to those media and benefit from the programs offered or broadcast. , The problem of this research is that there is a l
... Show MoreThe relationship between pollution levels in river sediment and fluctuating asymmetry of resident silurid fish species,