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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 Aug 01 2015
Journal Name
Journal Of Engineering
Determination of the Optimum Conditions in Evaluation of Kiwi Juice as Green Corrosion Inhibitor of Steel in Hydrochloric Acid
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The corrosion protection of low carbon steel in 2.5 M HCl solution by kiwi juice was studied at different temperatures and immersion times by weight loss technique. To study the determination of the optimum conditions from statistical design in evaluation of a corrosion inhibitor, three variables, were considered as the most dominant variables. These variables are: temperature, inhibitor concentration (extracted kiwi juice) and immersion time at static conditions.

These three variables are manipulated through the experimental work using central composite rotatable Box – Wilson Experimental Design (BWED) where second order polynomial model was proposed to correlate the studied variables with the corrosion rate o

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Publication Date
Fri Oct 30 2020
Journal Name
International Journal Of Agronomy
Molybdenum Induces Growth, Yield, and Defence System Mechanisms of the Mung Bean (Vigna radiata L.) under Water Stress Conditions
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Water stress has a negative impact on the yield and growth of crops worldwide and consequently has a global impact on food security. Many biochemical changes occur in plants as a response to water stress, such as activation of antioxidant systems. Molybdenum (Mo) plays an important part in activating the expression of many enzymes, such as CAT, POD, and SOD, as well as increasing the proline content. Mo therefore supports the defence system in plants and plays an important role in the defence system of mung bean plants growing under water stress conditions. Four concentrations of Mo (0, 15, 30, and 45 mg·L−1) were applied to plants, using two approaches: (a) seed soaking and (b) foliar application. Mung bean plants were subject

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Publication Date
Tue Jun 02 2026
Journal Name
University Of Kirkuk Journal For Administrative And Economic Science
Anova For Fuzzy Data With Practical in The Medical Field
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This research study Blur groups (Fuzzy Sets) which is the perception of the most modern in the application in various practical and theoretical areas and in various fields of life, was addressed to the fuzzy random variable whose value is not real, but the numbers Millbh because it expresses the mysterious phenomena or uncertain with measurements are not assertive. Fuzzy data were presented for binocular test and analysis of variance method of random Fuzzy variables , where this method depends on a number of assumptions, which is a problem that prevents the use of this method in the case of non-realized.

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Publication Date
Sun Sep 06 2009
Journal Name
Baghdad Science Journal
Effect of food on growth and fecundity Brine Shrimp Artemia spp. laboratory Conditions
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This in order to test the effect of food on growth and fecundity, two kinds of food have been used the algae Scendesmus quadricaudae and fresh water shrimp powder. For two generations, growth and productivity have been followed up. The fresh water shrimp has been noticed as a food better than algae, because it caused recording, for the two generation higher length rate for the weeks of experiment. The individuals length rate at the end of the forth week reached 9.35 and 9.48 mm for the first generation and second generation respectively. The average length weekly increase rate for the first and second generations individuals feeding on dried shrimp was higher through the first and second week compared to what was recorded when feeding alga

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Publication Date
Thu Apr 01 2021
Journal Name
Journal Of Engineering Science And Technology
Assessment Of Municipal Wastewater Treatment Using Sequencing Batch Reactor Under Real Operation Conditions
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The Sequencing Batch Reactor system (SBR) is a major component of the municipal wastewater biological treatment system and water reclamation that provides high-quality water that could be reused in restricted plants that which require large quantities of water despite the lack of water. The research aims to investigate the performance of a pilot plant SBR unit under real operation conditions that was installed and operated in Al-Rustamiya Wastewater Treatment Plant (WWTP), Baghdad, Iraq. Results showed that the BOD5/COD ratio of the raw wastewater was within the average value at 0.66 emphasizing the organic nature of the influent flow and hence the amenability to biological treatment. The results also ensured that the treatment pro

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Publication Date
Tue Nov 07 2017
Journal Name
Spe Symposium: Production Enhancement And Cost Optimisation
Wettability Alteration of Carbonate Rocks via Nanoparticle-Anionic Surfactant Flooding at Reservoirs Conditions
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Nanofluids, liquid suspensions of nanoparticles (NPs) dispersed in deionized (DI) water, brine, or surfactant micelles, have become a promising solution for many industrial applications including enhanced oil recovery (EOR) and carbon geostorage. At ambient conditions, nanoparticles can effectively alter the wettability of the strongly oil-wet rocks to water-wet. However, the reservoir conditions present the greatest challenge for the success of this application at the field scale. In this work, the performance of anionic surfactant-silica nanoparticle formulation on wettability alteration of oil-wet carbonate surface at reservoir conditions was investigated. A high-pressure temperature vessel was used to apply nano-modification of oil-wet

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Publication Date
Sun Jun 30 2013
Journal Name
Al-khwarizmi Engineering Journal
Efficiency Prediction and Performance Characterization of Photovoltaic Solar Panel at Baghdad Climate Conditions
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The performance of a solar cell under sun radiation is necessary to describe the electrical parameters of the cell. The Prova 200 solar panel analyzer is used for the professional testing of four solar cells at Baghdad climate conditions. Voltage -current characteristics of different area solar cells operated under solar irradiation for testing their quality and determining the optimal operational parameters for maximum electrical output were obtained. A correlation is developed between solar cell efficiency h and the corresponding solar cell parameters; solar irradiance G, maximum power Pmax, and production date P. The average absolute error of the proposed correlation is 5.5% for 40 data points. The results also show th

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Publication Date
Wed Nov 01 2017
Journal Name
Materials Chemistry And Physics
DFT + U and ab initio atomistic thermodynamics approache for mixed transitional metallic oxides: A case study of CoCu 2 O 3 surface terminations
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This study develops a systematic density functional theory alongside on-site Coulomb interaction correction (DFT + U) and ab initio atomistic thermodynamics approachs for ternary (or mixed transitional metal oxides), expressed in three reservoirs. As a case study, among notable multiple metal oxides, synthesized CoCu2O3 exhibits favourable properties towards applications in solar, thermal and catalytic processes. This progressive contribution applies DFT + U and atomistic thermodynamic approaches to examine the structure and relative stability of CoCu2O3 surfaces. Twenty-five surfaces along the [001], [010], [100], [011], [101], [110] and [111] low-Miller-indices, with varying surface-termination configurations were selected in this study.

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Publication Date
Wed May 24 2017
Journal Name
International Journal Of Science And Research (ijsr)
Some Properties of Mortar and Concrete Using Brick, Glass and Tile Waste as Partial Replacement of Cement
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The using of waste products as a recycled material was one of the most important studies for saving money and reduces the pollution. Mortar and concrete mixes with (10, 20 and 30)% of brick, glass and tile powder as replacement by weight of cement was investigated. The concrete mixes using brick or glass as 10%replacement of cement exhibited enhancement in compressive strength about (6, 4.7 and 2.0)% and (7.2, 5.6 and 2)% at age 7, 28 and 90 days respectively compared to reference mix. The 20% replacement of glass powder also showed an increase in the compressive strength up to (8, 6.3 and 4) %at age 7,28 and 90 days respectively compared to reference mix. Finally concrete mix using (10, 20 and 30) % tile powder as replacement of cement sho

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Publication Date
Sun Apr 17 2016
Journal Name
جلة ابن الهيثم للعلوم الصرفةم
isolation and partial purification of cell wall lipopolysaccharides of pseduomonas areuginosa and using it as Vaccine it
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