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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
Fri Jan 01 2010
Journal Name
Journal Of The College Of Education, Al-mustansiriya University
Synthesis and ldentification of metal complexes of 1- phenyl -3, (2'(S'phenyl amine)'l, 3, 4-thiad iazole'Z'yl) phenyl thiourea.

Complexes of 1-phenyl-3-(2(-5-(phenyl amino)-1,3,4- thiadiazole-2-yl)phenyl) thiourea have been prepared and characteized by elemental analysis, Ff-[R, and u.v./ visible spectra moreover, determination of metal content M%o by flame atomic absorption spectroscopy, molar conductance in DMSO solution and magnetic moments (peffl. The result showed that the ligand (L) was coordinated to Mn*2, Ni*2, Ct*2,2n*2,Cd*2, and Hg*2 ions through the nitrogen atoms and sulpher atoms. From the result obtained, rhe following general formula [MLClz] has been given for the prepared complexes with an octahedral geometry around the metal ions for all complexes. where M= Mn*2, Ni*2, cu*2, zn*z, cd*z, and Hg*2 l= l-phenyl-3-(2-(5-(phenyl amino)-1, 3,

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Publication Date
Sun Jan 26 2020
Journal Name
Iraqi Journal Of Science
Proving the Equality of the Spaces Q_b^r (A),Q_b^l (A) and BL(X) where X is a Complex Banach Space

Cabrera and Mohammed proved that the right and left bounded algebras of quotients  and  of norm ideal  on a Hilbert space  are equal to  Banach algebra of all bounded linear operators on . In this paper, we prove that  where  is a norm ideal on a complex Banach space .

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Publication Date
Fri Jan 01 2016
Journal Name
Al-mustansiriyah Journal Of Science
Synthesis and Characterization of Some New Metal Complexes of Ligand [N-(3-acetylphenylcarbamothioyl)-4-chlorobenzamide]

A new ligand [N-(3-acetylphenylcarbamothioyl)-4-chlorobenzamide] (CAD) was synthesized by reaction of 4-Chlorobenzoyl isothiocyanate with 3-amino acetophenone, The ligand was characterized by elemental micro analysis C.H.N. S., FT-IR, UV-Vis and 1H,13C- NMR spectra, some transition metals complexes of this ligand were prepared and characterized by FT-IR, UV-Vis spectra, conductivity measurements, magnetic susceptibility and atomic absorption, From obtained results the molecular formula of all prepared complexes were [M(CAD)2(H2O)2]Cl2 (M+2 =Mn, Co, Ni, Cu, Zn, Cd and Hg),the proposed geometrical structure for all complexes were octahedral.

Publication Date
Sat Dec 30 2023
Journal Name
Wasit Journal For Pure Sciences
A Review of Modern Methods of Synthesis 1, 3, 4-Oxadiazole as a Bioactive Compounds

ABSTRACT: Oxadiazole ring is a heterocyclic molecule with an oxygen and two nitrogen atoms spread throughout its five-membered structure. There are four different isomers that have been discovered, Because of their wide applications in a range of sectors, including medications . Some of these biological activity are; anticonvulsant capacity, anticancer as well, antibacterial, antiviral, antifungal,  antimalarial, antitubercular, anti-asthmatic, antidepressant, antidiabetic, antioxidant, antiparkinsonian, analgesic and  anti-inflammatory, are just some of the therapeutic uses that have drawn attention to drug candidates containing an oxadiazole moiety. This review, we will examine the various methods of oxadiazole synthesis. The mo

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Publication Date
Sun May 14 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
A Complete (k,r)-Cap in PG(3,p) Over Galois Field GF(4)

   The aim of this paper is to construct the (k,r)-caps in the projective 3-space PG(3,p) over Galois field GF(4). We found that the maximum complete (k,2)-cap which is called an                       ovaloid  , exists in PG(3,4) when k = 13. Moreover the maximum (k,3)-caps, (k,4)-caps and   (k,5)-caps. 

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Publication Date
Sun Dec 05 2010
Journal Name
Baghdad Science Journal
Study the structure of Hg1-x Cdx Te alloy

A study carried out to prepare Hg1-xCdxTe compound and to see the effect on increasing the percentage of x on the compound structure by using x-ray diffraction and atomic absorption for 0

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Publication Date
Tue Jun 01 2021
Journal Name
Journal Of Interdisciplinary Mathematics
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Publication Date
Sun Mar 01 2020
Journal Name
Plant Archives
Thermodynamic and kinetic analysis of Basic green-4 dye Removal from aqueous solutions using adsorption technique

In this work, a local sunflower husk (SFH) was used as a natural surface for removing Basic Green-4 (BG4) dye, as a watersoluble pollutant. The effect of initial concentration, contact time, the mass of surface of the dye with the SFH as well as the medium temperature was studied. The application of Langmuir, Freundlich isotherms on the collected data of the adsorption process found to harmonize to Freundlich equation more than that of Langmuir. However, the adsorbed mass of BG4 dye showed a direct increase with the increase of SFH mass and equilibrium was achieved within a 60min window. The interaction of BG4 with SFH surface was spontaneous and exothermic. The empirical kinetic outcomes at ambient temperatures were applied to pseudo 1st a

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Publication Date
Mon Oct 01 2018
Journal Name
Data In Brief
Chemical and structural data of (1, 2, 3-triazol-4-yl) pyridine-containing coordination compounds

The data presented in this paper are related to the research article entitled “Novel dichloro(bis{2-[1-(4-methylphenyl)-1H-1,2,3-triazol-4-yl-κN3 ]pyridine-κN})metal(II) coordination compounds of seven transition metals (Mn, Fe, Co, Ni, Cu, Zn and Cd)” (Conradie et al., 2018) [1]. This paper presents characterization and structural data of the 2-(1-(4-methyl-phenyl)-1H-1,2,3-triazol-1-yl)pyridine ligand (L2 ) (Tawfiq et al., 2014) [2] as well as seven dichloro(bis{2- [1-(4-methylphenyl)-1H-1,2,3-triazol-4-yl-κN3 ]pyridine-κN})metal (II) coordination compounds, [M(L2 )2Cl2], all containing the same ligand but coordinated to different metal ions. The data illustrate the shift in IR, UV/VIS, and NMR (for diamagnetic complexes) peaks wh

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Publication Date
Wed Mar 10 2021
Journal Name
Baghdad Science Journal
SYNTHESIS AND ANTIMICROBIAL ACTIVITY OF SOME (2-AMINO-5-THIOL-1, 3, 4-THIADIAZOLE DERIVATIVES

Five derivatives of thiadiazole were prepared with aldehydes and alkyl halides, compoundA: 2-amino-5-thiol-1,3,4- thiadiazole, compound B :2-(o-hydroxybenzylidine)amino-5-thiol-1,3,4-thiadiazole, compoundC: 2(2-butan-lidine)amino-5-thiol-1,3,4-thiadiazole, compound E: 2- amino-5-(2-Propanylthio)-1,3,4-thiadiazol) and compound F:2(o-chlorobenzylamino)-5-(2-propanyl thio)-1,3,4 thiadiazol. All prepared compounds were diagnosed by (IR) and (UV) Spectroscopy. All of those compounds were screened for their anti-microbial activity in vitro. The results show that most of the compounds A, B, C exhibited moderate to good activity against Gram-positive bacteria and the same compound exhibit low to moderate activity on most gram-negative bacte

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