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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
Mon May 01 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
Mon May 01 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
Sat Jan 05 2019
Journal Name
Iraqi Journal Of Physics
The study of the bending property of the epoxy (Ep / MgO) and (Ep/SiO2) composites in natural conditions and after immersion in chemical solution
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In this paper, a polymer-based composite material was prepared by hand Lay-up method consisting of epoxy resin as a base material reinforced by magnesium oxide powder once and silicon dioxide powder again and with different weight ratios (3, 6, 9 and 12) wt %. The three-point bending test was performed in normal conditions and after immersion in sulfuric acid. The results showed that the bending value decreased with the increase of the weighted ratio of the reinforcement material (MgO, SiO2). The Bending of samples reinforced by SiO2 was found to be less than the bending of samples reinforced by particles (MgO). For example, the bending of the SiO2 sample (0.32 mm) at the weighted ratio (3%) and for the MgO (0.18mm) sample at the weight

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Publication Date
Thu May 05 2016
Journal Name
International Journal Of Science And Research (ijsr)
Mixed-1,10-phenanthroline with Mn(II), Cu(II),Co(II), Hg(II) and Ni(II) complexes Synthesis, Antimicrobial Activity and Spectroscopic Characterization of Binuclear Schiff Base
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The M(II) complexes [M2 (phen)2 (L)(H2O)2Cl2 ] in (2:1:2 (M:L:phen) molar ratio, (where M(II) =Mn(II), Co(II), Cu(II), Ni(II) and Hg(II), phen = 1,10-phenanthroline; L = 2,2'-(1Z,1'Z)-(biphenyl-4,4'-diylbis(azan-1-yl-1-ylidene))bis(methan-1-yl-1- ylidene)diphenol] were synthesized. The mixed complexes have been prepared and characterized using 1H and13C NMR, UV/Visible, FTIR spectra methods and elemental microanalysis, as well as magnetic susceptibility and conductivity measurements. The metal complexes were tested in vitro against three types of pathogenic bacteria microorganisms: Staphylococcus aurous, Escherichia coli, Bacillussubtilis and Pseudomonasaeroginosa to assess their antimicrobial properties. From this study shows that all the

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Publication Date
Fri Mar 01 2019
Journal Name
Al-khwarizmi Engineering Journal
Parametric Study of Mixed Convective Radiative Heat Transfer in an Inclined Annulus
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The steady state laminar mixed convection and radiation through inclined rectangular duct with an interior circular tube is investigated numerically for a thermally and hydrodynamicaly fully developed flow. The two heat transfer mechanisms of convection and radiation are treated independently and simultaneously. The governing equations which used are continuity, momentum and energy equations. These equations are normalized and solved using the Vorticity-Stream function and the Body Fitted Coordinates (B.F.C) methods. The finite difference approach with the Line Successive Over-Relaxation (LSOR) method is used to obtain all the computational results. The (B.F.C) method is used to generate the grid of the problem. A computer program (Fortran

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Publication Date
Fri Mar 01 2019
Journal Name
Al-khwarizmi Engineering Journal
Parametric Study of Mixed Convective Radiative Heat Transfer in an Inclined Annulus
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The steady state laminar mixed convection and radiation through inclined rectangular duct with an interior circular tube is investigated numerically for a thermally and hydrodynamicaly fully developed flow. The two heat transfer mechanisms of convection and radiation are treated independently and simultaneously. The governing equations which used are continuity, momentum and energy equations. These equations are normalized and solved using the Vorticity-Stream function and the Body Fitted Coordinates (B.F.C) methods. The finite difference approach with the Line Successive Over-Relaxation (LSOR) method is used to obtain all the computational results. The (B.F.C) method is used to generate the grid of the problem. A computer program (Fortr

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Publication Date
Tue Jan 08 2019
Journal Name
Iraqi Journal Of Physics
Preparation and characterization of mixed SnO2:CdO thin films as gas sensor
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In this study, tin oxide (SnO2) and mixed with cadmium oxide (CdO) with concentration ratio of (5, 10, 15, 20)% films were deposited by spray pyrolysis technique onto glass substrates at 300ºC temperature. The structure of the SnO2:CdO mixed films have polycrystalline structure with (110) and (101) preferential orientations. Atomic force microscopy (AFM) show the films are displayed granular structure. It was found that the grain size increases with increasing of mixed concentration ratio. The transmittance in visible and NIR region was estimated for SnO2:CdO mixed films. Direct optical band gap was estimated for SnO2 and SnO2 mixed CdO and show a decrease in the energy gap with increasing mixing ratio. From Hall measurement, it was fou

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Publication Date
Sun Mar 01 2020
Journal Name
Baghdad Science Journal
Discussing Fuzzy Reliability Estimators of Function of Mixed Probability Distribution By Simulation
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This paper deals  with constructing mixed probability distribution  from exponential with scale parameter (β) and also Gamma distribution with (2,β), and the mixed proportions are (  .first of all, the probability density function (p.d.f) and also cumulative distribution function (c.d.f) and also the reliability function are obtained. The parameters of mixed distribution, ( ,β)  are estimated by three different methods, which are  maximum likelihood, and  Moments method,as well proposed method (Differential Least Square Method)(DLSM).The comparison is done using simulation procedure, and all the results are explained in tables.

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Publication Date
Mon Feb 01 2016
Journal Name
Journal Of Engineering
Dust Effect on the Efficiency of Silicon Mono Crystalline Solar Modules at Different Tilt Angles at Al-Jadryia Climate Conditions
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Solar energy usage in Iraq is facing many issues; one of those is the accumulation “of the dust on the surface of the solar module which” would highly lower its efficiency. The present work study the effect of dust accumulation” on installing fixed solar modules with different inclined angles 15o, 33o, 45o, 60o. Evaluation of the solar modules performance under different circumstance conditions such as rain, wind and humidity are considered in study of dust effect on solar module performance. The results show that the lowest output average efficiencies of solar modules occurs at 15o horizontally inclined angle are 7.4% , 6.7% , 8.0% , 8.1%, and 8.4% for the cor

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Publication Date
Sun Mar 03 2013
Journal Name
Baghdad Science Journal
The ability of Pisum sativum plant to use tricalcium super phosphate (TSP) in the presence and absence of mycorrhizal fungi under field conditions
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Efficiency of Pisum sativum plants in using tricalcium super phosphate (TSP) in presence and absence of mycorrhizal fungi was evaluated in the field experiment in College of Science / Al-Mustansiriyah University. The experiment comprised of (6) treatments prepared from the interaction of two levels of inoculation [non-inoculation with fungus F0 and inoculation with Glomus mosseae fungus (F1)]. And three levels of phosphorus: 0,20,40 Kg P/ha. The experimental size was (1x2)m. Irrigation and hand-weeding were done when needed. The following plant measurements were recorded: (Shoots dry weight, concentration of N and P% in addition to percentage of root infection with mycorrhizal fungi at flowering 50% of plants. The re

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