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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 May 01 2021
Journal Name
Journal Of Physics: Conference Series
The substitutions of Strontium by yttrium and their effects on Bi<sub>2</sub>Sr<sub>2</sub>-<sub>x</sub>Y<sub>x</sub>Ca<sub>2</sub>Cu<sub>3</sub>O<sub>10</sub>+<sub>δ</sub> superconducting compound
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Abstract<p>Superconducting compound Bi<sub>2</sub>Sr2-<sub>x</sub>Y<sub>x</sub>Ca<sub>2</sub>Cu<sub>3</sub>O<sub>10+δ</sub> were Synthesized by method of solid state reaction, at 1033 K for 160 hours temperature of the sintering at normal atmospheric pressure where substitutions Yttrium oxide with Strontium. When Y2O3 concentration (0.0, 0.1, 0.2, 0.3, 0.4 and 0.5). All specimens of Bi<sub>2</sub>Sr<sub>2</sub>Ca<sub>2</sub>Cu<sub>3</sub>O<sub>10+δ</sub> superconducting compounds were examined. The resistivity of electrical was checked by the four point probe technique, It was found th</p> ... Show More
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Publication Date
Tue Jul 20 2021
Journal Name
Materials Science Forum
Red Laser Irradiation Effect on the Structural Properties of MawsoniteCu&lt;sub&gt;6&lt;/sub&gt;Fe&lt;sub&gt;2&lt;/sub&gt;SnS&lt;sub&gt;8&lt;/sub&gt; [CFTS] Thin Films Deposited via Semi-Computerized Spray Pyrolysis Technique
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The existing investigation explains the consequence of irradiation of violet laser on the structure properties of MawsoniteCu6Fe2SnS8 [CFTS] thin films. The film was equipped by the utilization of semi-computerized spray pyrolysis technique (SCSPT), it is the first time that this technique is used in the preparation and irradiation using a laser. when the received films were processed by continuous red laser (700 nm) with power (>1000mW) for different laser irradiation time using different number of times a laser scan (0, 6, 9, 12, 15 and 18 times) with total irradiation time (0,30,45,60,75,90 min) respectively at room temperature.. The XRD diffraction gave polycrysta

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Publication Date
Sun Jan 01 2012
Journal Name
Evidence-based Complementary And Alternative Medicine
Gelam Honey Inhibits the Production of Proinflammatory, Mediators NO,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mtext>PGE</mml:mtext></mml:mrow><mml:mtext>2</mml:mtext></mml:msub></mml:mrow></mml:math>, TNF-<b><i>α</i></b>, and IL-6 in Carrageenan-Induced Acute Paw Edema in Rats
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Natural honey is well known for its therapeutic value and has been used in traditional medicine of different cultures throughout the world. The aim of this study was to investigate the anti-inflammatory effect of Malaysian Gelam honey in inflammation-induced rats. Paw edema was induced by a subplantar injection of 1% carrageenan into the rat right hind paw. Rats were treated with the nonsteroidal anti-inflammatory drug (NSAID) Indomethacin (10 mg/kg, p.o.) or Gelam honey at different doses (1 or 2 g/kg, p.o.). The increase in footpad thickness was considered to be edema, which was measured using a dial caliper. Plasma and paw tissue were collected to analyze the production of inflammatory mediators, such as NO, PGE2

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Publication Date
Tue Dec 01 2020
Journal Name
Results In Physics
Alpha clustering preformation probability in even-even and odd-A<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e3355" altimg="si39.svg"><mml:msup><mml:mrow /><mml:mrow><mml:mn>270</mml:mn><mml:mo>−</mml:mo><mml:mn>317</mml:mn></mml:mrow></mml:msup></mml:math>(116 and 117) using cluster formation model and the mass formulae : KTUY05 and WS4
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