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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 Jan 01 2021
Journal Name
Desalination And Water Treatment
Microwave induced activated carbon for the removal of metal ions in fixed-bed column study: modelling and mechanisms
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Publication Date
Fri Jul 01 2016
Journal Name
Journal Of Economics And Administrative Sciences
Using system dynamics model and the statistical indicators for Road Map of "Green government departments" project In Iraq
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Abstract                                                         

The issue of the protection of the environment is a shared responsibility between several destinations and sectors, and constitutes a main subject in which they can achieve sustainable development. In the sectors of government programs can be set up towards the establishment of the government sector to the green environment, so to be the implementati

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Publication Date
Tue Dec 31 2013
Journal Name
Al-khwarizmi Engineering Journal
Beneficiation of Iraqi Akash at Phosphate Ore Using Organic Acids for the Production of Wet Process Phosphoric Acid
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In the present work, leaching process studiedusing organic acids (acetic acid and lactic acid) to extract phosphate from the Iraqi Akashat phosphate ore by separation of calcareous materials (mainly calcite). This approach characterized by energy conservation, environmental enhancement by recovery of calcite as calcium sulfate (gypsum), keeping the physical and chemical properties of apatite. Samples were analyzed using X-ray diffraction and FTIR spectrophotometer. From the obtained experimental data it was found that using the two organic acids yields closed purity values of the produced apatite at the optimum conditions, while at different acid concentrations, it was found that the efficiency of acetic acid is higher at the low acid co

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Publication Date
Tue Mar 31 2026
Journal Name
Polymers For Advanced Technologies
Utilizing the Potential of Polyvinylidene Fluoride in Developing Durable Superhydrophobic and Antibacterial Nanocomposite Coatings for Oil/Water Separation
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ABSTRACT<p> The increasing demand for durable and multifunctional separation materials necessitates polymer‐based coatings that combine mechanical robustness with high selectivity. This study aims to develop antibacterial oil/water separation systems that effectively address challenges posed by microorganisms, which can decrease filter effectiveness and impact overall separation efficiency. Metal meshes were coated with titanium dioxide (TiO <sub>2</sub> ), octadecanethiol (ODT), and polyvinylidene fluoride (PVDF) via spray coating using four formulations: TiO <sub>2</sub> </p> ... Show More
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Publication Date
Mon Oct 02 2023
Journal Name
Imam Al-kadhim College
Awareness of environmental responsibility among chemistry students at the College of Education for Pure Sciences, Ibn al-Haytham
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Publication Date
Thu Apr 06 2023
Journal Name
International Journal Of Emerging Technologies In Learning (ijet)
The Impact of a Scenario-Based Learning Model in Mathematics Achievement and Mental Motivation for High School Students
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Publication Date
Wed May 17 2023
Journal Name
Journal Of Engineering
Development of Quality Rating Evaluation of Outgoing Product Case Study Applied at the General Company for Vegetable Oils
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Research covers the uses the method of Quality Rating Evaluation to evaluate the
quality of production through which a determination of product quality of its production in
order to determine the amount of sales hence the profits for the company. The most important
function is to satisfy consumer at reasonable prices. Methods were applied to the product
(toothpaste) in the General Company for Vegetable Oil – Almaamoon Factory .
The company's has obtained ISO-certified (ISO 9001-2008). Random samples of
final product intended for sale were collected from the store during months (February, April ,
June , October and December) for the year 2011 to determine the "quality rating " through
the applicat

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Publication Date
Sun Jan 05 2020
Journal Name
Annals Of Tropical Medicine And Public Health
[CITATION] Direct and deferred retrieval of basketball for student of the college of physical education and sport sciences
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Publication Date
Sun Mar 01 2015
Journal Name
Current Research In Microbiology And Biotechnology
Evaluation for the Cytotoxic Effect of Exotoxin A Produced by Pseudomonas aeruginosa on Mice by using Cytogenetic Parameters
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This research was conduct to evaluate the cytotoxic effect of exotoxin A (ETA) produced by Pseudomonas aeruginosa on mice in comparison with (phosphate buffer saline (PBS) as a negative control. The effect of the toxin was measured by employing the cytogenetic analysis which included (the mitotic index (MI), chromosomal aberrations (CAs), micronucleus (MN) and sperm abnormalities) parameters. In order to specify the cytotoxic effect of the toxin, three doses of ETA (125, 250 and 500 ng/ml) were used. Results showed that ETA was found to cause a significant decrease in mitotic index (MI) percentage, while significant increase in micronucleus (MN), chromosomal aberrations (CAs) and sperm abnormalities parameters in compression with control wa

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Publication Date
Tue Jun 01 2021
Journal Name
International Journal Of Nonlinear Analysis And Applications
A proposed method for cleaning data from outlier values using the robust rfch method in structural equation modeling
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