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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 Feb 03 2019
Journal Name
Iraqi Journal Of Physics
Morphology and electrical properties of Cu X Zn1-XO thin films prepared by PLD technique

Cu X Zn1-XO films with different x content have been prepared by
pulse laser deposition technique at room temperatures (RT) and
different annealing temperatures (373 and 473) K. The effect of x
content of Cu (0, 0.2, 0.4, 0.6, 0.8) wt.% on morphology and
electrical properties of CuXZn1-XO thin films have been studied.
AFM measurements showed that the average grain size values for
CuXZn1-xO thin films at RT and different annealing temperatures
(373, 473) K decreases, while the average Roughness values increase
with increasing x content. The D.C conductivity for all films
increases as the x content increase and decreases with increasing the
annealing temperatures. Hall measurements showed that there are
two

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Publication Date
Tue Sep 19 2023
Journal Name
Bulletin Of The Chemical Society Of Ethiopia
Exploring the biological activity of organotin carboxylate complexes with 4-sulfosalicylic acid

ABSTRACT. 4-Sulfosalicylic acid (SSA) was used as a ligand to prepare new triphenyltin and dimethyl-tin complexes by condensation with the corresponding organotin chloride salts. The complexes were identified by different techniques, such as infrared spectra (tin and proton), magnetic resonance, and elemental analyses. The 119Sn-NMR was studied to determine the prepared complexes' geometrical shape. Two methods examined the antioxidant activity of (SSA) and prepared complexes; Free radical scavenging activity (DPPH) and CUPRRAC methods. Tri and di-tin complexes gave high percentage inhibition than ligands with both methods due to tin moiety; the triphenyltin carboxylate complex was the best compared with the others. Also, antibacter

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Publication Date
Tue Mar 30 2021
Journal Name
Iraqi Journal Of Science
Electrochemical Polymerization and Biological Activity of 4-(Nicotinamido)-4-Oxo-2-Butenoic Acid as An Anticorrosion Coating on A 316L Stainless Steel Surface

In this study, poly4-(nicotinamido)-4-oxo-2-butenoic acid (PNOE) was prepared by the electro polymerization of 4-(nicotinamido)-4-oxo-2-butenoic acid (NOE) monomer on a 316 stainless steel (St.St) which acts as an anticorrosion coating.  Fourier transforms infrared (FTIR), atomic force microscopy (AFM), scanning electron microscopy (SEM), and cyclic voltammetry were used to diagnose the structure and the properties of the prepared polymer layer. The corrosion behavior of the uncoated and coated 316  St.St were evaluated by using an electro chemical polarization technique in 0.2 M hydrochloric acid  solution as a corrosive medium at a temperature range of 293 to 323 K. Nano materials, such as nano ZnO and graphene were adde

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Publication Date
Fri Apr 21 2023
Journal Name
Technologies And Materials For Renewable Energy, Environment And Sustainability: Tmrees22fr
Study of the x-ray diffraction lines of calcium titanate nanoparticle using SSP method and Scherrer method

In this study, the modified size-strain plot (SSP) method was used to analyze the x-ray diffraction lines pattern of diffraction lines (1 0 1), (1 2 1), (2 0 2), (0 4 2), (2 4 2) for the calcium titanate(CaTiO3) nanoparticles, and to calculate lattice strain, crystallite size, stress, and energy density, using three models: uniform (USDM). With a lattice strain of (2.147201889), a stress of (0.267452615X10), and an energy density of (2.900651X10-3 KJ/m3), the crystallite was 32.29477611 nm in size, and to calculate lattice strain of Scherrer (4.1644598X10−3), and (1.509066023X10−6 KJ/m3), a stress of(6.403949183X10−4MPa) and (26.019894 nm).

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Publication Date
Fri May 24 2024
Journal Name
Molecular Crystals And Liquid Crystals
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Publication Date
Mon Sep 25 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Synthesis,Charaterization and Biological Activity Studies of Some Transtion and Non transition Metalcomplexes with(4 – Dithiocarbamato-N-(5- methylisoxazole-3-yle)- ion-ligand)

This work involves the preparation of the ligand [KL] :-                    Â­Â­Â­Â­Â­Â­

K[4-(N-(5-methylisoxazol-3-yl) sulfamyl) phenylcarbamodithioate] from the reaction of sulfamethoxazole  with Carbon disulfide  in the presence of  potassium hydroxide under reflux (4 hours) using methanol as asolvent. The prepared ligand was characterized using FT-IR, UV-Vis, 1H,13C–NMR spectroscopy, molar conductivity and melting point,  Complexes for the above ligand [KL] with some bivalent transition and non-transition metals (Mn +2, Co+2  , Ni+2  ,

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Publication Date
Mon Oct 25 2021
Journal Name
Iraqi Journal Of Science
Synthesis of Some New Bis- 2, 3-Dihydroquinazolin-4(1H)-one Derivatives from Dapsone Drug and Investigating their Liquid Crystalline Properties and Antibacterial Activities

     During this paper, new Schiff's base derivatives [F1-F5] were prepared through the reaction of dapsone drug with different substituted benzaldehyde compounds. Schiff's bases were then converted into 2,3-dihyroquinazolin-4(1H)-one derivatives [F6-F10] through the reaction with 2-amino benzoic acid in ethanol. The synthesized compounds were identified by their physical properties using UV-Vis, FT-IR and 1H-NMR analyses. The liquid crystalline properties of some prepared compounds revealed smectic and nematic phases. Using two separate bacterial species, Pseudomonas aeruginosa (Gram -ve) and Staphylococcus  aureus<

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Publication Date
Fri Jul 01 2022
Journal Name
Structures
Reliability analysis of deteriorated post-tensioned concrete bridges: The case study of Ynys-y-Gwas bridge in UK

Concrete structures are exposed to aggressive environmental conditions that lead to corrosion of the embedded reinforcement and pre-stressing steel. Consequently, the safety of concrete structures may be compromised, and this requires a significant budgets to repair and maintain critical infrastructure. Prediction of structural safety can lead to significant reductions in maintenance costs by maximizing the impact of investments. The aim of this paper is to establish a framework to assess the reliability of existing post-tensioned concrete bridges. A time-dependent reliability analysis of an existing post-tensioned involving the assessment of Ynys-y-Gwas bridge has been presented in this study. The main cause of failure of this bridge was c

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Publication Date
Sun Mar 01 2020
Journal Name
Journal Of Mechanical Science And Technology
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Publication Date
Tue Dec 25 2018
Journal Name
Journal Of Engineering Science And Technology
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