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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
Sun Apr 30 2023
Journal Name
Iraqi Journal Of Science
Synthesis and characterization of 4-(((3-mercapto-5-phenyl-4H-1,2,4-triazole-4-yl)imino)methyl)-2-methoxyphenol and its complexes with Zr(IV), Cd(II) and Sn(II) ions

A series of coordination compounds of Zr(IV), Cd(II) and Sn(II) ions with 4-(((3-mercapto-5-phenyl-4H-1,2,4-triazole-4-yl)imino)methyl)-2-methoxyphenol, as a ligand has been successfully prepared in alcoholic medium. The prepared complexes were characterized quantitatively and qualitatively by using: elemental analysis CHNS, FT-IR spectroscopy, UV-visible spectroscopy, 1H and 13CNMR, atomic absorption measurements, magnetic susceptibility, thermal analysis)TG and DTG) and conductivity measurements. This ligand coordinates as a bidentate that to the metal ions through sulphur and nitrogen of (azomethine group) atoms. According to the spectral data, Cd(II)- and Sn(II)-complexes have coordination of 6 with octahedral geometry while the Zr(I

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Publication Date
Tue Nov 19 2024
Journal Name
Al–bahith Al–a'alami
The Responsibility of the Iraqi Journalism in Promoting Political Culture in Society: (An Analytical Study in Newspapers: Al-Sabah, Al-Ittihad, Al-Aalam for 2/ 3/ 2013 - 31/ 3/ 2013)

 

This study comes as: The responsibility of the Iraqi newspapers in promoting  the political culture inside society, an analytical study in newspapers: Al-Sabah, Al-Ittihad, Al-Aalam for 2/ 3/ 2013 to 31/ 3/ 2013 to spot light on the extent to which the three mentioned newspapers are compliance with the promotion  of the political culture inside society which is seen as one of the essential requirements for the success and promotion of the democratic process inside society.

The study aims to: finding out the extent to which these newspapers are compliance with their responsibility in the promoting the political culture inside society; knowing the nature of their role in pr

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Publication Date
Tue Aug 04 2020
Journal Name
Indonesian Journal Of Pharmacy
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Publication Date
Thu Aug 01 2013
Journal Name
Ibn Al- Haitham Journal For Pure And Applied Science
Synthesis and Characterization of Heterocyclic Compounds Derived From 4- Hydroxy and 4-Amino Acetophenone

Two series of Schiff Bases [VI]n and thiazolidin-4-one derivatives[VII]n were synthesized by many steps starting from cyclization of 4- hydroxyacetophenon with thiourea in iodine to yield 1,3-thiazole compound which was reacted with pentoxy bromide in anhydrous potassium carbonate to converted compound[II] and this reacted with Phenol to yield azo compound[III]. The azo compound reacted with ethyl chloro acetate in basic medium to get a new easter compound[IV] which is converted to their acid hydrazid[V]. The later compound condensation with n-alkoxy benzaldehyde to give new Schiff bases[VI]n . Imine group undergoes addition cyclization with thioglycolic acid to get thiazolidinone compounds[VII]n .Also, two new series of Schiff Bases [XII]n

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Publication Date
Mon Apr 24 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Synthesis and Characterization of Heterocyclic Compounds Derived From 4- Hydroxy and 4-Amino Acetophenone

 Two series of Schiff Bases [VI]n and thiazolidin-4-one derivatives[VII]n were synthesized by many steps starting from cyclization of 4- hydroxyacetophenon with thiourea in iodine to yield 1,3-thiazole compound which was reacted with pentoxy bromide in anhydrous potassium carbonate to converted compound[II] and this reacted with Phenol to yield azo compound[III]. The azo compound reacted with ethyl chloro acetate in basic medium to get a new easter compound[IV]  which is converted to their acid hydrazid[V]. The later compound condensation with n-alkoxy benzaldehyde to give new Schiff bases[VI]n . Imine group undergoes addition cyclization with thioglycolic acid to get thiazolidinone compounds[VII]n .Also, two new series of Schi

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Publication Date
Thu Dec 01 2022
Journal Name
Journal Of Solid State Chemistry
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Publication Date
Mon Dec 30 2019
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
Synthesis and Characterization of Nano Y Zeolite Using MWCNT as Media for Crystal Growth

   The present research was conducted to synthesis Y-Zeolite by sol-gel technique using MWCNT (multiwalled carbon nanotubes) as crystallization medium to get a narrow range of particle size distribution with small average size compared with ordinary methods. The phase pattern, chemical structure, particle size, and surface area were detected by XRD, FTIR, BET and AFM, respectively. Results shown that the average size of Zeolite with and without using MWCNT were (92.39) nm and (55.17) nm respectively .Particle size range reduced from (150-55) nm to (130-30) nm. The surface area enhanced to be (558) m2/g with slightly large pore volume (0.231) km3/g was obtained. Meanwhile, degree of crystallization decrease

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Publication Date
Sun Apr 01 2018
Journal Name
Journal Of The Faculty Of Medicine Baghdad
Conversion of sleeve Gastrectomy to Roux-en-Y Gastric bypass for weight loss failure

Background: Obesity is a global health issue. Laparoscopic sleeve gastrectomy has progressively become the most popular procedure among the surgical community as a definitive bariatric operation. The increasing number of surgeries performed will be likely be followed by increasing reports of patients experiencing weight loss failure.
Objectives: To determine the effectiveness of conversion from laparoscopic sleeve gastrectomy to Roux-en-Y gastric bypass in cases with weight loss failure.
Patient &methods: The retrospective review of patients who had operated with laparoscopic sleeve gastrectomy from October 2009 to January 2016 at Saint Raphael hospital, 21 patients includ

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Publication Date
Fri Feb 01 2019
Journal Name
Journal Of Physics: Conference Series
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Publication Date
Mon Oct 01 2007
Journal Name
Journal Of The Faculty Of Medicine Baghdad
the role of interferon - gamma( IFN-Y) In infectious mononucleosis like syndrome

Background: infection monomcleosis is caused by the ubiquitous Epstein-Barr virus.

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