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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
Wed Jul 01 2020
Journal Name
Plant Archives
Investigating the ability to use natural iraqi material ⇜crushed porcelanite rocks⇝ in greywater filtration, and compare it with sand filter
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Publication Date
Thu Jul 09 2026
Journal Name
Journal Of Physical Education
The Effect of Exercises With Aiding Devices Using Consistent Style on Developing Motor Response Speed in Female Basketball Players U14
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Publication Date
Sat Jan 01 2022
Journal Name
Ieee Transactions On Robotics
Lidar-Level Localization With Radar? The CFEAR Approach to Accurate, Fast, and Robust Large-Scale Radar Odometry in Diverse Environments
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Publication Date
Sat Sep 01 2018
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
The role of risk management programs in Dealing With risks at international airports: An Applied research at Baghdad International Airport
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The objective of the research is to identify the efficiency of risk management in various names at Baghdad International Airport in the face of various risks (financial - technical - human - natural ..) facing the sample of the search of the General Establishment of Civil Aviation and the Iraqi Airways Company where the researcher identified the hypothesis that summarizes There is a significant significant correlation between risk management, risk management and risk review and assessment. The researcher used the means of research from observation and interviews with the relevant officials in this field, as well as used the questionnaire and distributed a sample of 170 employees in the field of risk management (SMS Department) in Iraqi A

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Publication Date
Sat Oct 01 2022
Journal Name
Case Studies In Thermal Engineering
Comparative assessment of the performance and combustion attributes of a free piston linear generator fuelled with CNG and CNG-CO2
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Publication Date
Fri Mar 01 2019
Journal Name
Archives Of Plastic Surgery
Surgical outcomes of 14 consecutive bilateral cleft lip patients treated with a modified version of the Millard and Manchester methods
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Background Bilateral cleft lip deformity is much more difficult to correct than unilateral cleft lip deformity. The complexity of the deformity and the sensitive relationships between the arrangement of the muscles and the characteristics of the external lip necessitate a comprehensive preoperative plan for management. The purpose of this study was to evaluate the repair of bilateral cleft lip using the Byrd modification of the traditional Millard and Manchester methods. A key component of this repair technique is focused on reconstruction of the central tubercle.

Methods Fourteen patients with mean age of 5.7 months presented with bilateral cleft lip deformity and were operated on using a mod

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Publication Date
Mon Jul 30 2018
Journal Name
Journal Of Pharmacy And Biological Sciences
Histological study of the embryogenesis of metencephalon in pre-implantation of albino rat's embryos after maternal treated with silver nanoparticles
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Cerebellum is the most important and critical part of the central nervous system, cerebellum is very sensitive to the abnormal changes during the embryological development in its histological structure, the exposure to any infection during embryogenesis produce abnormalities in the cerebellum and behavioral of offspring. In this study we tried to study the ontogenesis of the cerebellum in the embryos of the albino rats and detection the effect of the AgNPs on the ontogenesis of the rat cerebellum after exposure of AgNPs during pregnancy. we used 60 female pregnant rats divided in to three group, each contain 20 female, (G1) treated with 2mg/kg /day suspension of silver nanoparticles (Ag NPs) (G2) treated with 20mg/kg/day AgNPs from first da

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Publication Date
Mon Jan 01 2024
Journal Name
Revista Española De Cirugía Oral Y Maxilofacial
The correlation of alveolar trabecular bone microstructure with bone density measured by cone-beam computed tomography (CBCT) and implant stability
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Publication Date
Fri Jan 06 2023
Journal Name
Journal Of Advanced Biotechnology And Experimental Therapeutics
Evaluation of oxidative stress activity and the levels of homocysteine, vitamin B12, and DNA methylation among women with breast cancer
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Breast cancer (BC) is the most common malignant tumor in women and the leading cause of cancer deaths worldwide. This work was conducted to estimate the roles of oxidative stress, vitamin B12, homocysteine (HCY), and DNA methylation in BC disease progression. Sixty BC patients (age range 33–80 years) and 30 healthy controls were recruited for this study. Patients with BC were split to group 1 consisted of stage II BC women (low level), and group 2 consisted of patients in stages III and IV (high level). Malondialdehyde (MDA), glutathione peroxidase 3 (GPX3), HCY, and vitamin B12 levels in the study groups were measured. Also, the 5-methylcytosine (5mC) global DNA methylation levels were evaluated. The results showed a significant

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Publication Date
Mon Nov 01 2010
Journal Name
Iraqi Journal Of Physics
Preparation of Xerogel Films Doped with R6G Laser Dye using spin coating technique and Study the Spinning parameters Baha T.
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Spin coating technique has been applied in this work to prepared Xerogel films doped with Rhodamine 6G laser dyes. The solid host of laser dye modifies its spectroscopic properties with respect to liquid host. During the spin coating process the dye molecules suffer from changing their environment. The effects of three parameters were studied here: the spinning speed, multilayer coating and formaldehyde addition

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