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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 May 01 2015
Journal Name
Journal Of Engineering
A Real-Coded Genetic Algorithm with System Reduction and Restoration for Rapid and Reliable Power Flow Solution of Power Systems
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The paper presents a highly accurate power flow solution, reducing the possibility of ending at local minima, by using Real-Coded Genetic Algorithm (RCGA) with system reduction and restoration. The proposed method (RCGA) is modified to reduce the total computing time by reducing the system in size to that of the generator buses, which, for any realistic system, will be smaller in number, and the load buses are eliminated. Then solving the power flow problem for the generator buses only by real-coded GA to calculate the voltage phase angles, whereas the voltage magnitudes are specified resulted in reduced computation time for the solution. Then the system is restored by calculating the voltages of the load buses in terms

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Publication Date
Sun Jul 31 2022
Journal Name
Journal Of Computational Innovation And Analytics (jcia)
PERFORMANCE MEASURE OF MULTIPLE-CHANNEL QUEUEING SYSTEMS WITH IMPRECISE DATA USING GRADED MEAN INTEGRATION FOR TRAPEZOIDAL AND HEXAGONAL FUZZY NUMBERS
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In this paper, a procedure to establish the different performance measures in terms of crisp value is proposed for two classes of arrivals and multiple channel queueing models, where both arrival and service rate are fuzzy numbers. The main idea is to convert the arrival rates and service rates under fuzzy queues into crisp queues by using graded mean integration approach, which can be represented as median rule number. Hence, we apply the crisp values obtained to establish the performance measure of conventional multiple queueing models. This procedure has shown its effectiveness when incorporated with many types of membership functions in solving queuing problems. Two numerical illustrations are presented to determine the validity of the

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Publication Date
Wed Dec 13 2017
Journal Name
Al-khwarizmi Engineering Journal
Using Activated Carbon developed from Iraqi Date Palm Seeds as Permeable Reactive Barrier for Remediation of Groundwater Contaminated with Copper
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The possibility of using activated carbon developed from date palm seeds wastes as a permeable reactive barrier (PRB) to remove copper from polluted shallow groundwater was investigated. The activated carbon has been developed from date palm seeds by dehydrating methods using concentrated sulfuric acid. Batch tests were performed to characterize the equilibrium sorption properties of new activated carbon in copper-containing aqueous solutions, while the sandy soil (aquifer) was assumed to be inert. Under the studied conditions, the Langmuir isotherm model gives a better fit for the sorption data of copper by activated carbon than other models. At a pilot scale, One-dimensional column experiments were performed, and an integrated model ba

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Publication Date
Mon Dec 01 2025
Journal Name
International Communications In Heat And Mass Transfer
Design optimization and performance analysis of a PCM-to-air heat exchanger with optimized fin configuration for building heating applications
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Publication Date
Wed Feb 01 2017
Journal Name
Journal Of Natural Gas Science And Engineering
Experimental determination of hydrate phase equilibrium for different gas mixtures containing methane, carbon dioxide and nitrogen with motor current measurements
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Hydrate dissociation equilibrium conditions for carbon dioxide + methane with water, nitrogen + methane with water and carbon dioxide + nitrogen with water were measured using cryogenic sapphire cell. Measurements were performed in the temperature range of 275.75 K–293.95 K and for pressures ranging from 5 MPa to 25 MPa. The resulting data indicate that as the carbon dioxide concentration is increased in the gas mixture, the gas hydrate equilibrium temperature increases. In contrast, by increasing the nitrogen concentration in the gas mixtures containing methane or carbon dioxide decreased the gas hydrate equilibrium temperatures. Furthermore, the cage occupancies for the carbon dioxide + methane system were evaluated using the Van der Wa

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Publication Date
Thu Oct 15 2015
Journal Name
Al Mustansyriah Journal Of Science
Comparison between (ARIMA) and (ANNs) models for estimating the relative humidity for Baghdad city
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The aim of the research is to study the comparison between (ARIMA) Auto Regressive Integrated Moving Average and(ANNs) Artificial Neural Networks models and to select the best one for prediction the monthly relative humidity values depending upon the standard errors between estimated and observe values . It has been noted that both can be used for estimation and the best on among is (ANNs) as the values (MAE,RMSE, R2) is )0.036816,0.0466,0.91) respectively for the best formula for model (ARIMA) (6,0,2)(6,0,1) whereas the values of estimates relative to model (ANNs) for the best formula (5,5,1) is (0.0109, 0.0139 ,0.991) respectively. so that model (ANNs) is superior than (ARIMA) in a such evaluation.

Publication Date
Thu Aug 01 2019
Journal Name
Journal Of Economics And Administrative Sciences
Some Estimation methods for the two models SPSEM and SPSAR for spatially dependent data
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ABSTRUCT

In This Paper, some semi- parametric spatial models were estimated, these models are, the semi – parametric spatial error model (SPSEM), which suffer from the problem of spatial errors dependence, and the semi – parametric spatial auto regressive model (SPSAR). Where the method of maximum likelihood was used in estimating the parameter of spatial error          ( λ ) in the model (SPSEM), estimated  the parameter of spatial dependence ( ρ ) in the model ( SPSAR ), and using the non-parametric method in estimating the smoothing function m(x) for these two models, these non-parametric methods are; the local linear estimator (LLE) which require finding the smoo

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Publication Date
Tue Jan 29 2019
Journal Name
Journal Of The College Of Education For Women
The Rights of the Non-Muslims During the Rule of the Prophet Mohammed and Rashidians Succession Theoretically With Historical Witnesses
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(Thimma) in Arabic means compact, and immunity. (People of Thimma) are the free non-Muslim people under Muslim rule. This includes Heavenly Religions people, i. e., Christian and Jews).
They have been called (People of Thimma) because they had paid (Jizyah: tribute) so they became safe for their souls, honor, properties at the custody of Muslims.
Islamic law had posed (Jizyah: tribute) upon the Jews and Christians who were living under Muslim rule as a reaction of not embracing Islam Faith against securing their rights and freedom.
Freedoms secured by Islam for the (People of Thimma) had been many, including the right of faith, not coercing them to be Muslim, the right to live, to possess properties, protect and secure them, the

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Publication Date
Fri Jun 12 2026
Journal Name
Revista Iberoamericana De Psicología Del Ejercicio Y El Deporte, Issn 1886-8576, Vol. 18, Nº. 4, 2023, Págs. 361-363
The Effect of a Training Curriculum in Developing the Speed Endurance and Strength Characterized By Speed for the Muscles of the Legs for Female Basketball Students
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Autorías: Mariam Liwa Abdel Fattah, Liqaa Abdullah Ali. Localización: Revista iberoamericana de psicología del ejercicio y el deporte. Nº. 4, 2023. Artículo de Revista en Dialnet.

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Scopus
Publication Date
Fri Jun 12 2026
Journal Name
Iklīl For Humanities Studies
The directions of the Federal Supreme Court in determining the parliamentary bloc with the largest number in the Iraqi constitution of 2005
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