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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
Tue Sep 08 2020
Journal Name
Baghdad Science Journal
Matrix Form of Deriving High Order Schemes for the First Derivative
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For many problems in Physics and Computational Fluid Dynamics (CFD), providing an accurate approximation of derivatives is a challenging task. This paper presents a class of high order numerical schemes for approximating the first derivative. These approximations are derived based on solving a special system of equations with some unknown coefficients. The construction method provides numerous types of schemes with different orders of accuracy. The accuracy of each scheme is analyzed by using Fourier analysis, which illustrates the dispersion and dissipation of the scheme. The polynomial technique is used to verify the order of accuracy of the proposed schemes by obtaining the error terms. Dispersion and dissipation errors are calculated

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Publication Date
Sat Jan 01 2022
Journal Name
Aip Conference Proceedings
Determine the hazard level and biological effects for visible laser pointers
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Publication Date
Thu Jun 30 2022
Journal Name
Journal Of Economics And Administrative Sciences
The Use of the Regression Tree and the Support Vector Machine in the Classification of the Iraqi Stock Exchange for the Period 2019-2020
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 The financial markets are one of the sectors whose data is characterized by continuous movement in most of the times and it is constantly changing, so it is difficult to predict its trends , and this leads to the need of methods , means and techniques for making decisions, and that pushes investors and analysts in the financial markets to use various and different methods in order to reach at predicting the movement of the direction of the financial markets. In order to reach the goal of making decisions in different investments, where the algorithm of the support vector machine and the CART regression tree algorithm are used to classify the stock data in order to determine

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Publication Date
Wed Feb 01 2012
Journal Name
Ibn Al-haytham Journal For Pure And Applied Science
Using Restricted Least Squares Method to Estimate and Analyze the Cobb-Douglas Production Function with Applicatio
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Publication Date
Tue Mar 06 2007
Journal Name
Iraqi J Pharm Sci,
Effect of Silibinin in Lowering the Intraocular Pressure in Normotensive Rabbits: Interaction with Pilocarpine and Cyclopentolate
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Previous data indicated the effectiveness of silibinin as intraocular pressure (IOP) - lowering agent. The present study was performed to evaluate the interaction of silibinin with pilocarpine or cyclopentolate in lowering IOP in normotensive rabbits. The effects of topically instilled silibinin hemisuccinate solution (0.75%) alone or adjunctly combined with 2% pilocarpine or 1% cyclopentolate on the IOP of normotensive rabbits were evaluated using indentation tonometry. The results showed that 0.75% solution of silibinin was found more potent than pilocarpine (2% drops) in lowering IOP of normotensive rabbits, while their combination results in longer duration of action. Moreover, the elevated IOP values produced by cyclopentolate (1%drops

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Publication Date
Sun Jan 03 2016
Journal Name
Journal Of The Faculty Of Medicine Baghdad
The Impact of Body Mass Index and Some Trace Elements in Iraqi Women with Breast Cancer
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Background: Breast cancer is a highly heterogeneous disease globally. Trace elements such as copper and zinc have a role in many biochemical reactions as micro source, their metabolism is profoundly altered in neoplastic diseases especially breast cancer which is ranked as the first of female cancersObjective: The aim of the present study is to study the impact of body mass index and some trace elements in Iraqi women with breast cancer.Patients and methods: The group of the study consisted of 25 breast cancer patients; their age range was (25–65) years recruited from the Al-Kadhimia Teaching Hospital and 25 apparently healthy women age matched, over a period of 6 months from January 2015 until June 2015. After the diagnosis was m

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Publication Date
Thu May 12 2016
Journal Name
Journal Of Biosciences
Dictyostelium discoideum RabS and Rab2 colocalize with the Golgi and contractile vacuole system and regulate osmoregulation
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Publication Date
Sun Jan 01 2023
Journal Name
Journal Of Pakistan Association Of Dermatologists
The role of epigenetics in immunosuppression in patients with infectious diseases as a fascinating applied observation
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Publication Date
Sun Jan 01 2023
Journal Name
Journal Of Medicinal And Pharmaceutical Chemistry Research
The effect of selenium nanoparticles with fenugreek extract on oxidative stress related to polycystic ovary syndrome
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In recent years, there has been growing interest in using Nanosystems in different biomedical applications. Among all metal nanoparticles, selenium nanoparticles have attracted the attention of many researchers due to its low toxicity and nutritional supplementation value. The purpose of the current study was designed to examine the possible effect of selenium nanoparticles in combination with fenugreek leaves extract (an edible herb with good medicinal properties) in the treatment of oxidative stress status-related to polycystic ovary syndrome in letrozole-induced PCOS (an imbalance of reproductive hormones that causes infertility) in adult female rats. Cold plasma was used in the preparation of selenium nanoparticles subsequently the prod

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Publication Date
Mon Aug 01 2022
Journal Name
Hiv Nursing
The Influence of Some Vitamins and Biochemical Parameters on Iraqi Females’ Patients with Malignant Breast Cancer"
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The Influence of Some Vitamins and Biochemical Parameters on Iraqi Females’ Patients with Malignant Breast Cancer"

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