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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
Fri Mar 01 2024
Journal Name
Journal Mustansiriyah Of Sports Science
Compound skill performance speed and its relationship to the motor speed of football talent centers players aged 12-14 years
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Publication Date
Thu Dec 30 2021
Journal Name
College Of Islamic Sciences
Al-Hajjaj in pre-Islamic poetry hangs Imru 'al-Qays and the Twrfa of Ibn al-Abd as a model
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The topic of (pilgrims) of the old and modern subjects at the same time, as it extends his foot and is associated with the beginning of speech and argument, a modern because it is based on studies and research (and the theory of pilgrims) from (Austin and Cyril) through (Charles Breman) to (Aristotle) ), It is worth mentioning here to mention the role of (Hazem al - Qartagni) in mentioning the value of the pilgrimage of hair and saying the use of persuasion in the hair, is palatable and acceptable. Hence our research applied these views, and we chose the pendants as a model for that matter.

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Publication Date
Mon Jun 30 2025
Journal Name
International Journal Of Sustainable Development And Planning
The Role of Sustainable Environmental Indicators in Urban Happiness: A Study of Al-Amir Neighborhood in Al-Najaf City, Iraq
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Publication Date
Wed Jan 22 2020
Journal Name
Molecules
In Vivo and In Vitro Evaluation of the Protective Effects of Hesperidin in Lipopolysaccharide-Induced Inflammation and Cytotoxicity of Cell
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(1) Background: Plant flavonoids are efficient in preventing and treating various diseases. This study aimed to evaluate the ability of hesperidin, a flavonoid found in citrus fruits, in inhibiting lipopolysaccharide (LPS) induced inflammation, which induced lethal toxicity in vivo, and to evaluate its importance as an antitumor agent in breast cancer. The in vivo experiments revealed the protective effects of hesperidin against the negative LPS effects on the liver and spleen of male mice. (2) Methods: In the liver, the antioxidant activity was measured by estimating the concentration of glutathione (GSH) and catalase (CAT), whereas in spleen, the concentration of cytokines including IL-33 and TNF-α was measured. The in vitro expe

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Publication Date
Mon May 01 2023
Journal Name
Environmental Nanotechnology, Monitoring & Management
A review study summarizes the main characterization techniques of nano-composite photocatalysts and their applications in photodegradation of organic pollutants
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Publication Date
Fri Feb 10 2023
Journal Name
Energies
Well Placement Optimization through the Triple-Completion Gas and Downhole Water Sink-Assisted Gravity Drainage (TC-GDWS-AGD) EOR Process
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Gas and downhole water sink-assisted gravity drainage (GDWS-AGD) is a new process of enhanced oil recovery (EOR) in oil reservoirs underlain by large bottom aquifers. The process is capital intensive as it requires the construction of dual-completed wells for oil production and water drainage and additional multiple vertical gas-injection wells. The costs could be substantially reduced by eliminating the gas-injection wells and using triple-completed multi-functional wells. These wells are dubbed triple-completion-GDWS-AGD (TC-GDWS-AGD). In this work, we design and optimize the TC-GDWS-AGD oil recovery process in a fictitious oil reservoir (Punq-S3) that emulates a real North Sea oil field. The design aims at maximum oil recovery us

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Publication Date
Tue Mar 28 2017
Journal Name
Archives Of Polish Fisheries
Meristic character variability among populations of Silurus triostegus Heckel, 1843 from the Euphrates, Tigris, and Shatt al-Arab Rivers, Iraq
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Abstract<p>Variation in the numbers of pectoral fin spines and rays, pelvic fin rays, gill rakers on the first gill arch, anal fin rays, and the number of vertebrae of Silurus triostegus Heckel were examined in specimens from 16 localities that span its entire distribution range in the Tigris, Euphrates, and Shatt al-Arab rivers in Iraq. The mean number of the six meristic traits increases toward high latitudes with maximum and minimum values in the north and south of Iraq. Based on cluster analysis and PCA, the Mesopotamian river samples were clearly separated into three distinct groups. The upper Tigris populations were isolated from those of the middle and southern populations of this river and from those of</p> ... Show More
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Publication Date
Fri Jan 01 2016
Journal Name
Journal Of The Electrochemical Society
Electrochemical Incineration of Oxalic Acid at Manganese Dioxide Rotating Cylinder Anode: Role of Operative Parameters in the Presence of NaCl
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A detailed experimental study was devoted to the anodic oxidation of oxalic acid using manganese dioxide rotating cylinder anode with the objective to evaluate in a systematic way the effect on the oxalic acid oxidation process of several relevant parameters, including the presence of sodium chloride, the current density (J), the rotation speed, the temperature, and the initial concentration of oxalic acid. Thin manganese dioxide film on graphite substrate has been prepared by electrochemical oxidation from MnSO4-H2SO4 electrolyte. The morphology of this electrode was investigated by XRD, SEM, EDS and AFM techniques. The results show that a firm γ-structure of MnO2 film on graphite rod can be obtained successfully. The results indicate tha

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Publication Date
Sun Dec 01 2019
Journal Name
Baghdad Science Journal
Studying the Crystal Structure, Topography, and Anti-bacterial of a Novel Titania (TiO2 NPs) Prepared by a Sol-gel Manner
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In this research, titanium dioxide nanoparticles (TiO2 NPs) were prepared through the sol-gel process at an acidic medium (pH3).TiO2 nanoparticles were prepared from titanium trichloride (TiCl3) as a precursor with Ammonium hydroxide (NH4OH) with 1:3 ratio at 50 °C. The resulting gel was dried at 70 °C to obtain the Nanocrystalline powder. The powder from the drying process was treated thermally at temperatures 500 °C and 700 °C. The crystalline structure, surface morphology, and particle size were studied by using X-ray diffraction (XRD), Atomic Force Microscopy (AFM), and Scanning Electron Microscope (SEM). The results showed (anatase) phase of titanium dioxide with the average grain size

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Publication Date
Thu Mar 01 2018
Journal Name
International Journal Of Oral And Maxillofacial Surgery
Assessment of facial asymmetry before and after the surgical repair of cleft lip in unilateral cleft lip and palate cases
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