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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 Jan 01 2018
Journal Name
Materials Research Bulletin
Understanding the impacts of Al+3-substitutions on the enhancement of magnetic, dielectric and electrical behaviors of ceramic processed nickel-zinc mixed ferrites: FTIR assisted studies
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Publication Date
Sun Oct 02 2011
Journal Name
Journal Of Educational And Psychological Researches
The Effect of a consulting program for decreasing withdrawal behavior of the children with autism of kindergarten
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       unacceptable social behaviors, particularly withdrawal behavior that appears in children with autism represent a major problem hindering the process of communication with those around them and therefore the process of mergence  with them be difficult.

     The withdrawal causes a real affect deficit for children with autism limits the possibility of development of their intellectual and mental growth due to their solitude and the weakness of their focus in the acquisition of pedagogical skills and lack the necessary social skills to maintain the relations of friendship and enjoyment of them.

      withdrawal children fail to participate

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Publication Date
Mon Aug 18 2025
Journal Name
Soil And Sediment Contamination: An International Journal
Remediation Prediction of Contaminated Soil with Crude Oil Using the Optimized Remediation Method for the Iraqi Environment
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Large quantities of petroleum-contaminated soil are generated with increased global energy consumption and crude oil production. This theoretical study evaluates the treatment of 1 ton of petroleum-contaminated soil using seven methods: incineration, physical washing, chemical washing, thermal pyrolysis, Fenton-oxidation-pyrolysis, the biological treatment, and asphaltenes. Data were based on experimental results from the Nahran Bin Omar oil lake in Basra Governorate, Iraq, (2019–2021). The methods were compared by waste generation, treatment cost, and duration. Results indicate that using petroleum-contaminated soil as a raw material for asphalt manufacturing is most beneficial since it is sold as a raw material. Incineration is faster a

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Publication Date
Wed Mar 18 2020
Journal Name
Baghdad Science Journal
Mixed Micelles of Binary Mixtures of Sodium Dodecylbenzene Sulfate and Tween 80 Surfactants in Aqueous Solutions
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In the present work, the surface properties of mixed binary surfactants containing sodium dodecylbenzene sulfate (SDBS) and Tween 80 (TW80) surfactants in aqueous solutions were studied at temperature 293 K using surface tension measurements. The critical micelle concentration (cmc) magnitude for both individual surfactants and their mixtures were established the obtained results revealed  that the magnitude of cmc of the mixtures are less than the magnitude of individual surfactants and decrease with the increase in Tween 80 percent in solution which indicate the nonideal  mixing of the two surfactants. The values of molecular interaction parameters  and the mole fraction of surfactants in the micelle (X1) were calculated

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Publication Date
Thu Jun 08 2023
Journal Name
Egyptian Journal Of Chemistry
Ring Opining polymerization of caprolactone And Antibacterial activity by Mixed Ligand of Metal(II) and (III)
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Reaction of L1 [((E)-N1-(nitrobenzylidene)benzene-1,2-diamine] and L2( m-aminophenol), and one equivalent of di- or tri-valent metals(Cr(ӀӀӀ), Mn(ӀӀ), Fe(ӀӀӀ), Co(ӀӀ), Ni(ӀӀ), Cu(ӀӀ) and Zn(ӀӀ) afforded the complexes [M(L1)(L2)2]Cl, M=Cr(ӀӀӀ) and Fe(ӀӀӀ) and the complexes [M(L1)(L2)2] M= Mn(ӀӀ), Co(ӀӀ), Ni(ӀӀ), Cu(ӀӀ) and Zn(ӀӀ). The structure of the Schiff base ligand and their complexes are characterized by (C:H:N), FT.IR, UV.Vis, 1HNMR, 13CNMR and mass spectral. The presence of metal in the complexes are characterized by flame atomic absorption. The spectral data of the complexes have revealed the octahedral geometry. The (L1), (L2) and mixed ligand metal complexes were screened for their ability as cataly

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Publication Date
Fri Jun 01 2018
Journal Name
Oriental Journal Of Chemistry
Synthesis, Spectral and Biochemical Studies of New Complexes of Mixed Ligand Schiff Base and Anthranilic Acid
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In this rescrch,new mixed ligand Schiff base complexes of Mn(II),Co(II),Ni(II),Cu(II), Cd(II), and Hg(II) are formulated from the Schiff base( L)resulting from  o-phathalaldehyde(o-PA) with p-nitroaniline(p-NA)as a primary ligand and anthranilic acid as a subordinate ligand. Diagnosis of prepared Ligand and its complexes is done by spectral methods mass spectrometer;1H -NMR for ligand Schiff base FTIR, UV-Vis, molar conductance, elemental microanalyses, atomic absoption and magnetic susceptibility. The analytical studies for the all new complexes have shown octahedral geometries. The study of organicperformance  of ligand Schiff base and its complexes show various activity agansit four type of bactria two gram (+) and two gram (-) .

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Publication Date
Mon Jun 10 2019
Journal Name
Journal Of Global Pharma Technology
Mixed Ligand Schiff Base Complexes of Some Meta(II) Salts: Preparation. Spectral Characterization and Antibacterial Screening
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FH Ghanim, Journal of Global Pharma Technology, 2018

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Publication Date
Sat Dec 01 2012
Journal Name
Journal Of Economics And Administrative Sciences
Models of measurement and disclosure of fair value accounting - Applied to contribute to company garments mixed
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The research aims to provide a method to measure the fair value of the most environmentally friendly of Iraq and through the application of method of measuring the fair value of the company garments contribute to mixed as the company is of the economic units of the industrial sector and included in the Iraqi market for securities as a profit and distributes profits to shareholders since the method of measurement of the fair value based on the divided profits as toxic in a deduction of Cash Dividends cash for measuring fair value, and will also be in this research to clarify the disclosure of accounting for fair value and choose the method of disclosure most appropriate to the beneficiaries of accounting disclosure, as will be cho

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Publication Date
Tue Jun 30 2009
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
The Effect of Extraction Temperature and Solvent to Oil Ratio on Viscosity Index of Mixed-medium Lubricating Oil Fraction by Using Solvents Extraction
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In this study two types of extraction solvents were used to extract the undesirable polyaromatics, the first solvent was furfural which was used today in the Iraqi refineries and the second was NMP (N-methyl-2-pyrrolidone).
The studied effecting variables of extraction are extraction temperature ranged from 70 to 110°C and solvent to oil ratio in the range from 1:1 to 4:1.
The results of this investigation show that the viscosity index of mixed-medium lubricating oil fraction increases with increasing extraction temperature and reaches 107.82 for NMP extraction at extraction temperature 110°C and solvent to oil ratio 4:1, while the viscosity index reaches to 101 for furfural extraction at the same extraction temperature and same

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Publication Date
Thu Sep 18 2014
Journal Name
Journal Of Chemical And Pharmaceutical Research
Preparation, characterization, and antibacterial properties of mixed ligand complexes of L-aspargine and sulfamethoxazole(antibiotic) with Mn(II), Co(II), Ni(II), Cu(II), Zn(II), Cd(II) and Hg(II) ions
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The research includes the synthesis and identification of the mixed ligands complexes of M+2ions in general composition[M(Asn)2(SMX)] Where L- Aspargine (C4H8N2O3)symbolized (AsnH) as a primary ligand and Sulfamethoxazole(C10H11N3O3S) symbolized (SMX) as a secondary ligand. The ligands and the metal chlorides were brought in to reaction at room temperature in(v/v) ethanol /water as solvent containing NaOH. The reaction required the following [(metal: 2(Na+Asn-): (SMX)] molar ratios with M(II) ions, Where: M(II)=Mn(II), Co(II), Ni(II), Cu(II), Zn(II), Cd(II) and Hg(II). The UV–Vis and magnetic moment data revealed an octahedral geometry around M(II), The conductivity data show a non-electrolytic nature of the complexes. The antimicrobial a

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