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Gaussian Integer Solutions of the Diophantine Equation x^4+y^4=z^3 for x≠ y

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
Mon Aug 01 2022
Journal Name
Baghdad Science Journal
An Analytic Solution for Riccati Matrix Delay Differential Equation using Coupled Homotopy-Adomian Approach

An efficient modification and a novel technique combining the homotopy concept with  Adomian decomposition method (ADM) to obtain an accurate analytical solution for Riccati matrix delay differential equation (RMDDE) is introduced  in this paper  . Both methods are very efficient and effective. The whole integral part of ADM is used instead of the integral part of homotopy technique. The major feature in current technique gives us a large convergence region of iterative approximate solutions .The results acquired by this technique give better approximations for a larger region as well as previously. Finally, the results conducted via suggesting an efficient and easy technique, and may be addressed to other non-linear problems.

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Publication Date
Sun Mar 02 2014
Journal Name
Baghdad Science Journal
Exploiting the diazotization reaction of 4- minoacetophenone for Methyldopa determination.

Based on the diazotization reaction of 4-aminoacetophenone with sodium nitrite in acid medium to form diazonium salt, which was coupled with Methyldopa to form a violet reddish soluble azo dye with maximum absorbance at 560 nm,a batch procedure had been developed for the estamination of Methyldopa. Under optimum experimental parameters affecting on the development and stability of the colored product, Beer´s law obeyed in the range (0.5-45) ?g.ml-1 with a correlation coefficient (0.9979).The proposed method was successfully applied to the determination of Methyldopa in either pure form and in commercial brands of pharmaceuticals, no interference was observed from common excipients in the formulations. The analytical results obtained by app

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Publication Date
Thu Jun 01 2017
Journal Name
Journal Of The College Of Languages (jcl)
Realismo y tradicionessocioculturales en “Bodas de sangre”

Resumen

El trabajo se investiga en el realismo y la tradición social que incluye la tragedia Bodas de sangre, del autor español Federico García Lorca. A lo largo de estas páginas se da la luz sobre los temas, acciones, oraciones y palabras que pertenecen a la realidad de la vida española en general y sobre todo en territorio andaluz, en el que ocurren los sucesos de la obra.  Así como las tradiciones sociales que el dramaturgo español contemporáneo abundando a lo largo de su texto, y que han sido tomadas de la herencia popular.

    Literariamente, esta obra se clasifica como Tragedia Moderna, por la razón de que incorpora los elementos necesarios de d

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Publication Date
Tue Jan 01 2013
Journal Name
Journal Of The College Of Languages (jcl)
LA ENSEÑANZA Y EL APRENDEZAJEDELLÉXICO ESPAÑOL ENIRAK

El tema de esta investigación está directamente relacionado con el papel del léxico en la enseñanza-aprendizaje del español como segunda lengua en el sistema de enseñanza universitariairaquí, donde se llevó a cabo la investigación empírica y la propuesta de criterios de la selección de léxico español.

Este estudio se ha centrado concretamente en los alumnos irakíes de nivel elemental que estudian elespañol como segunda lengua extranjera. Con el fin de conocer los estilos de enseñanza-aprendizaje del vocabulario practicado en las aulas, de determinar las faltas en la selección léxica y realizar propuestas de mejorar la competencia  léxica,  hemos efectuado el an

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Publication Date
Thu Sep 01 2022
Journal Name
Iraqi Journal Of Physics
X-Ray Emission Spectroscopy Analysis for Near-Asteroid Belt of Atmospheric of the Comets

         According to Chandra Survey Observatory Near-Asteroid Belt Comets, the solar wind's contact with the comet produces a variety of spectral characteristics. The study of X-ray spectra produced by charge exchange is presented here. The spectrum of a comet can reveal a lot about its composition. This study has concentrated on the elemental abundance in six different comets, including 17P/Holmes, C/1999T1, C/2013A1, 9p/Temple1, and 103p/Hartley2 (NEAT). Numerous aspects of the comet's dynamics allow it to behave in a unique manner as it gets closer to the Near-Asteroid Belt. These characteristics are being examined, and some studies are still ongoing. The computations allow us to observe, for instance, how the composition of

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Publication Date
Wed Dec 01 2021
Journal Name
Baghdad Science Journal
Analytical Solutions for Advanced Functional Differential Equations with Discontinuous Forcing Terms and Studying Their Dynamical Properties

This paper aims to find new analytical closed-forms to the  solutions of the nonhomogeneous functional differential equations of the nth order with finite and constants delays and various initial delay conditions in terms of elementary functions using Laplace transform method. As well as, the definition of dynamical systems for ordinary differential equations is used to introduce the definition of dynamical systems for delay differential equations which contain multiple delays with a discussion of their dynamical properties: The exponential stability and strong stability

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Publication Date
Thu Jun 30 2011
Journal Name
Al-khwarizmi Engineering Journal
Effect of Lanthanum Addition on the Microstructure of Mg-4Al Alloy

 This research was to determine the effect of rare earth metal (REM) on the as-cast microstructure of Mg-4Al alloy. The rare earth metal used here is Lanthanum to produce Mg-4Al-1.5La alloy. The microstructure was characterized by optical microscopy. The phases of this alloy were identified by X-ray diffraction. The microstructure of Mg-4Al consists of α-Mg and grain boundaries with precipitated phase particles. With the addition of Lanthanum, three distinct phases were identified in the X-ray diffraction patterns of the as cast Mg-4Al-1.5La:  Mg, Al11La3, Al4La. The Mg17Al12 phase was not detected. The addition of Lanthanium increases the hardness and dec

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Publication Date
Sun Mar 06 2011
Journal Name
Baghdad Science Journal
The Calculation of the partical distribution function g(r12,r1) for Carbon Ion cases (C+2,C+3,C+4) in the position space

The aim of this work is study the partical distribution function g(r12,r1) for Carbon ion cases (C+2,C+3,C+4) in the position space using Hartree-Fock's Wave function, and the partitioning technique for each shell which is represented by Carbon Ions [C+2 (1s22s2)], [C+3 (1s22s)] and [C+4 (1s2)]. A comparision has been made among the three Carbon ions for each shell. A computer programs (MATHCAD ver. 2001i) has been used texcute the results.

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Publication Date
Thu May 28 2020
Journal Name
Iraqi Journal Of Science
Designing A Zener Diode Using Ag2O(1-X)Zno(X)/Psi Structures Deposited by Laser Induced Plasma Technique

In this paper Zener diode was designed by mixing three mixing ratios of Ag2O(1-x)ZnO(x), where x is 0.5, 0.3, and 0.1, that are deposited on a p-type porous silicon using laser induced plasma technique at room temperature (RT). The results of the Zener diode showed a decrease in knee and Zener voltage when the mixing ratio of Ag2O(1-x)ZnO(x) structure was increased. Nanofilms of 200nm thickness were prepared from pure ZnO and Ag2O as well as Ag2O(1-x)ZnO(x) with three maxing ratios and deposited on glass slides at RT to analyze the structure and optical properties. The structures of Ag2O and Ag2O

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Publication Date
Tue Nov 19 2024
Journal Name
Al–bahith Al–a'alami
News Coverage in the Iraqi Electronic Press for Internal Crises: (An Analytical Study of Al-Zaman and Al-Sabah Electronic Newspapers for the period from 1/ 3/ 2013 to 31/ 3/ 2013)

 

The research study focused on the need to clarify the relationship between the Websites of Iraqi Newspapers and their roles in covering the internal crises in Iraq. The selection of Iraqi websites for the newspapers Al-Zaman and Al-Sabah was adopted as one of the most important media with a wide audience; and as a model of hot news and continuous coverage of those sites since 2003 so far. As a result, this necessitated the emergence of new types of methods of editing and writing news stories related to Iraq.

Consequently, the enormous and rapidly changing amount of Iraq news, the process of preparing and creating news has become a complex industry

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