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The operational matrices for Elliptic Partial Differential Equations with mixed boundary conditions
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Abstract<p>The purpose of this research is to implement the orthogonal polynomials associated with operational matrices to get the approximate solutions for solving two-dimensional elliptic partial differential equations (E-PDEs) with mixed boundary conditions. The orthogonal polynomials are based on the Standard polynomial (<italic>x<sup>i</sup> </italic>), Legendre, Chebyshev, Bernoulli, Boubaker, and Genocchi polynomials. This study focuses on constructing quick and precise analytic approximations using a simple, elegant, and potent technique based on an orthogonal polynomial representation of the solution as a double power series. Consequently, a linear partial differential equation is transformed into a linear algebraic system which is solved by the Mathematica®12. Approximate solutions can be found if the answers are polynomials in and of itself. Three applications involving well-known linear problems Laplace, Poisson, and Helmholtz equations have been solved by using the proposed methods, and a comparison of the approaches has been provided. Furthermore, the computation of the error norm <italic>L<sub>∞</sub> </italic> has been done to show the accuracy of the suggested approaches. The results clearly demonstrate how precise, efficient, and dependable the proposed methods are in obtaining rough solutions to the problem. Bernoulli was one of the best methods in most examples.</p>
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Publication Date
Sat Nov 15 2025
Journal Name
Journal Of Physical Education
The Effect of Increasing Rehabilitation Program Using Electric Stimulation On Rehabilitating Knee Joint Working Muscles Due to ACL Tear In Athletes
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Publication Date
Fri Jan 01 2021
Journal Name
Aip Conference Proceedings
Comparison effect of violet and red laser irradiation on the structural properties of mawsonite Cu6Fe2SnS8 [CFTS] thin films deposited via (SCSPT)
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Publication Date
Fri Oct 30 2020
Journal Name
Journal Of Economics And Administrative Sciences
The role of internal marketing in achieving customer satisfaction An exploratory study of a sample of private bank managers in Baghdad
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This study examined the effect of elements of internal marketing activities on customer satisfaction through an exploratory study of banking services in the city of Baghdad, if the research problem crystallized by asking a group of questions, the most important (is there a correlation and impact between the dimensions of internal marketing and customer satisfaction, this study aims to determine The effect of internal communication, training and internal market research on customer satisfaction, represented by the quality of service, loyalty and market share, and embodied the objective of this study to identify the level of availability of internal marketing activities and programs in the research banks, data were collected using

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Publication Date
Tue Nov 01 2022
Journal Name
Journal Of Engineering
Influence of Fire-Flame Duration and Temperature on the Behavior of Reinforced Concrete Beam Containing Water Absorption Polymer Sphere; Numerical Investigation
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One of the most important parameters determining structural members' durability and strength is the fire flame's influence and hazard. Some engineers have advocated using advanced analytical models to predict fire spread impact within a compartment and considering finite element models of structural components to estimate the temperatures within a component using heat transfer analysis. This paper presented a numerical simulation for a reinforced concrete beam’s structural response in a case containing Water Absorbing Polymer Spheres (WAPS) subjected to fire flame effect. The commercial finite element package ABAQUS was considered. The relevant geometrical and material parameters of the reinforced concrete beam model a

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Publication Date
Sat Sep 01 2018
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
Conceptual visions of standard capital measurement Measures and determinants of disclosure to create Sustainable competition In light of the knowledge economy
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  This century is witnessing changes in various fields,which have become a challenge to the enterprises in the contemporary business environment, the most important of which is the importance of measurement and disclosure of the role of knowledge capital in the transition to the knowledge economy, which is no longer the land and labor and physical capital resources the basic. Knowledge-based capital has emerged that provides the enterprise with an area of ​​excellence and enhances its position to achieve competitive advantage. The research tackled the concept, objectives, components and importance of knowledge capital, which is fundamental in knowledge management, creating value added and enhancing competitiveness, as well as an

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Publication Date
Wed Jun 01 2022
Journal Name
Baghdad Science Journal
Investigating the Effect of Drugs of Chloramphenicol and Gentamicin on Acanthamoeba genotype T3 Causing keratitis Isolated from Environmental samples in vitro
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This study is an investigation of the drugs effect on some pathogenic Acanthamoeba isolated from Iraqi waters, where the problem of environmental adaptation that characterizes this organism in addition to being a reservoir for many pathogenic microorganisms that take shelter in it to escape disinfectants and medicines is sometimes difficult to treat it with traditional treatments.  Twenty water samples were collected from different water regions in Iraq, namely the Dokan Lake, Tigris River, Euphrates River and Najaf Sea, 5 samples from each source.  Acanthamoeba was isolated from water samples on NNA and PYG media, using an inverted microscope with an electron microscope to determine their phenotypic features. PCR and

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Publication Date
Sun Jan 01 2017
Journal Name
South Asian Journal Of Life Sciences
Comparison the Effect of Fungi (Beauveria bassiana) and Bacteria Bacillus thuringiensis (israelensis) on a Cumulative Mortality of Culex Quinquefasciatus (Diptera: Culicidae)
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Publication Date
Fri Mar 01 2019
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
Management skills and their reflection in the settlement of insurance compensation: Applied Study in National Insurance Company and Iraqi Insurance Company
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The environment contemporary works for the insurance companies have seen a number of technological developments and changes rapidly in light of the intense competition in the insurance market, and this affects human behavior in the workplace, and to director in his work needs to be a set of managerial skills. so we find compensation activity in companies insurance needs a high managerial skills, so that compensation, director of the settlement procedure successfully. So research aims to test two hypotheses two major belongings variables search using some statistical methods to extract the results and interpretation and analysis (such as arithmetic mean, standard deviation, percentages, Alpha Cronbach's coefficient, Pearson correlation co

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Crossref
Publication Date
Tue Oct 25 2022
Journal Name
Aip Conference Proceedings
Consequence of violet laser irradiation on the optical properties of mawsoniteCu6Fe2SnS8 [CFTS] thin films deposited via semi-computerized spray pyrolysis technique
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Publication Date
Wed Dec 11 2019
Journal Name
Journal Of The College Of Education For Women
Social Aspects in the Kingdom of Mali Through Ibn Battuta's book Tuhfat Alnuddar in Garaeb Al Amsar Wa Ajaeb Al Asfar
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Social Aspects in the Kingdom of Mali Through Ibn Battuta's book Tuhfat   Alnuddar  in  Garaeb  Al Amsar  Wa  Ajaeb  Al  Asfar 

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