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Gaussian Integer Solutions of the Diophantine Equation x^4+y^4=z^3 for x≠ y
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The investigation of determining solutions for the Diophantine equation  over the Gaussian integer ring for the specific case of  is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.

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Publication Date
Sun Sep 03 2017
Journal Name
Baghdad Science Journal
Kinetic and Mechanistic Studies for the Gas-phase Reaction of Ozone with 2, 3-Dimethyl-2-Butene and 1, 3-Butadiene
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The reactions of ozone with 2,3-Dimethyl-2-Butene (CH3)2C=C(CH3)2 and 1,3-Butadiene CH2=CHCH=CH2 have been investigated under atmospheric conditions at 298±3K in air using both relative and absolute rate techniques, and the measured rate coefficients are found to be in good agreement in both techniques used. The obtained results show the addition of ozone to the double bond in these compounds and how it acts as function of the methyl group substituent situated on the double bond. The yields of all the main products have been determined using FTIR and GC-FID and the product studies of these reactions establish a very good idea for the decomposition pathways for the primary formed compounds (ozonides) and give a good information for the effe

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Publication Date
Sat Apr 30 2022
Journal Name
Pakistan Journal Of Medical And Health Sciences
Evaluation of Cytotoxic T-Lymphocyte Antigen 4 Polymorphism and Soluble Immune Checkpoint Level Among A Sample of Sars-Cov-2 Iraqi Patients
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Objective: To Evaluate the Roley of Cytotoxic T-Lymphocytek antigen 4 Polymorphism and soluble immune checkpoint level (PD-1,PDL-1 and CTLA-4 ) in SARS-Cov-2 patients. Methods: Fromt October 2020 to April 2021, the currentk study was conducted in Baghdad-Iraq. Ninety patients with Confirmatory SARS-Cov-2 by PCR were inclusion in the study, and they were seeking treatment at Medical City in Baghdad's Teaching Hospital (BTH). Patients with SARS-Cov-2 were divided into two groups: those with Sever SARS-Cov-2 symptom and those with mild - moderate SARS-Cov-2 symptoms (cross sectional study. Patients with another form of autoimmune illness, malignant, diabetes, under the age of 18 and pregnant women were excluded. Results: Data rega

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Publication Date
Wed Jan 01 2025
Journal Name
Journal Of Interdisciplinary Mathematics
Double INEM-transform integral for solving second order partial differential equation
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In this study, a brand-new double transform known as the double INEM transform is introduced. Combined with the definition and essential features of the proposed double transform, new findings on partial derivatives, Heaviside function, are also presented. Additionally, we solve several symmetric applications to show how effective the provided transform is at resolving partial differential equation.

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Publication Date
Thu Oct 20 2022
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Iterative Method for Solving a Nonlinear Fourth Order Integro-Differential Equation
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This study presents the execution of an iterative technique suggested by Temimi and Ansari (TA) method to approximate solutions to a boundary value problem of a 4th-order nonlinear integro-differential equation (4th-ONIDE) of the type Kirchhoff which appears in the study of transverse vibration of hinged shafts. This problem is difficult to solve because there is a non-linear term under the integral sign, however, a number of authors have suggested iterative methods for solving this type of equation. The solution is obtained as a series that merges with the exact solution. Two examples are solved by TA method, the results showed that the proposed technique was effective, accurate, and reliable. Also, for greater reliability, the approxim

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Publication Date
Sat Jan 01 2022
Journal Name
Proceeding Of The 1st International Conference On Advanced Research In Pure And Applied Science (icarpas2021): Third Annual Conference Of Al-muthanna University/college Of Science
Efficient approach for solving high order (2+1)D-differential equation
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Publication Date
Mon Jan 04 2021
Journal Name
Iium Engineering Journal
RELIABLE ITERATIVE METHODS FOR SOLVING 1D, 2D AND 3D FISHER’S EQUATION
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In the present paper, three reliable iterative methods are given and implemented to solve the 1D, 2D and 3D Fisher’s equation. Daftardar-Jafari method (DJM), Temimi-Ansari method (TAM) and Banach contraction method (BCM) are applied to get the exact and numerical solutions for Fisher's equations. The reliable iterative methods are characterized by many advantages, such as being free of derivatives, overcoming the difficulty arising when calculating the Adomian polynomial boundaries to deal with nonlinear terms in the Adomian decomposition method (ADM), does not request to calculate Lagrange multiplier as in the Variational iteration method (VIM) and there is no need to create a homotopy like in the Homotopy perturbation method (H

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Publication Date
Sun Sep 01 2024
Journal Name
Partial Differential Equations In Applied Mathematics
Perturbation iteration transform method for solving fractional order integro-differential equation
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Publication Date
Thu Feb 29 2024
Journal Name
Iraqi Journal Of Science
Finding the Exact Solution of Kepler’s Equation for an Elliptical Satellite Orbit Using the First Kind Bessel Function
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     In this study, the first kind Bessel function was used to solve Kepler equation for an elliptical orbiting satellite. It is a classical method that gives a direct solution for calculation of the eccentric anomaly. It was solved for one period from (M=0-360)° with an eccentricity of (e=0-1) and the number of terms from (N=1-10). Also, the error in the representation of the first kind Bessel function was calculated. The results indicated that for eccentricity of (0.1-0.4) and (N = 1-10), the values of eccentric anomaly gave a good result as compared with the exact solution. Besides, the obtained eccentric anomaly values were unaffected by increasing the number of terms (N = 6-10) for eccentricities (0.8 and 0.9). The Bessel

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Publication Date
Wed Mar 01 2023
Journal Name
Journal Of Photochemistry And Photobiology A: Chemistry
Multipurpose properties the Z-scheme dimanganese copper oxide/cadmium sulfide nanocomposites for photo- or photoelectro-catalytic, antibacterial applications, and thiamine detection process
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Publication Date
Tue Jun 12 2007
Journal Name
Iraqi Journal Of Laser
Nonlinear Optical Properties of CdS Thin Film Nanoparticles Using z-Scan Technique
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In the present work, a z-scan technique was used to study the nonlinear optical properties, represented by the nonlinear refractive index and nonlinear absorption coefficients of nanoparticles cadmium sulfide thin film. The sample was prepared by the chemical bath deposition method. Several testing were done including, x-ray, transmission and thickness of thin film. z-Scan experiment was performed at two wavelengths (1064 nm and 532 nm) and different energies. The results showed the effect of self-focusing in the material at higher intensities, which evaluated n2 to be (0.11-0.16) cm2/GW. The effect of two-photon absorption was studied, which evaluated β to be (24-106) cm/GW. In addition, the optical limiting behavior has been studied.

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