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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
Sat Jan 01 2005
Journal Name
Journal Of The College Of Languages (jcl)
Ser y Estar

Ser y Estar

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Publication Date
Thu Oct 01 2015
Journal Name
Journal Of Educational And Psychological Researches
القيادة التربوية في ضوء نظريتي x-yوعلاقتها بالروح المعنوية لمديري المدارس الإعدادية

This study aimed to identify the educational leadership in the light of my theory xy and its relationship to the morale of the managers of the junior high school as the study population consisted of directors of junior high school in the city of Baghdad of six directorates education for the academic year 2013-2014 AD The number of managers (211) as director, and amounted to a sample Search of (150) director and director of the research community overall rate (71%) and represent this community fully representative sample, two tools were used in the study: the first measure of educational leadership in the light of my theory xy and the second tool to gauge morale.

Results concluded that the

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Publication Date
Sun Jun 01 2014
Journal Name
Baghdad Science Journal
The Effect of annealing temperature on the optical properties of (Cu2S)100-x( SnS2 )x thin films

Thin films of (Cu2S)100-x( SnS2 )x at X=[ 30,40, &50)]% with thickness (0.9±0.03)µm , had been prepared by chemical spray pyrolysis method on glass substrates at 573 K. These films were then annealed under low pressure of(10-2) mbar ,373)423&473)K for one hour . This research includes , studying the the optical properties of (Cu2S)100-x-(SnS2)x at X=[ 30,40, &50)]% .Moreover studying the effect of annealing on their optical properties , in order to fabricate films with high stability and transmittance that can be used in solar cells. The transmittance and absorbance spectra had been recorded in the wavelength range (310 - 1100) nm in order to study the optical properties . It was found that these films had direct optical band

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Publication Date
Wed Oct 26 2022
Journal Name
Research Journal Of Chemistry And Environment
Synthesis, Antioxidant ability and Docking study for new 4, 4'-((2-(Aryl)-1H-benzo [d] imidazole-1, 3 (2H)-diyl) bis (methylene)) diphenol

New series of 4,4'-((2-(Aryl)-1H-benzo[d]imidazole1,3(2H)-diyl)bis(methylene))Diphenol(3a-g) was successfully synthesized from cyclization of the reduction product of bis Schiff bases (2) with aryl aldehydes bearing phenolic hydroxyl in the presence of acetic acid. The structure of these compounds was identified from FT-IR, 1H NMR, 13C NMR and EIMs. The Antioxidant capability was screened by DPPH and FRAP assays. Both assays showed antioxidant capability more than BHT as well. Compounds 3b and 3c showed antioxidant capacity slightly less than ascorbic acid. The docking study for theses compound was carried out as III DNA polymerase inhibitor. The results of docking demonstrated that the increase in hinderances around phenolic hy

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Publication Date
Wed Oct 05 2022
Journal Name
Research Journal Of Chemistry And Environment
Synthesis, Antioxidant ability and Docking study for new 4, 4'-((2-(Aryl)-1H-benzo [d] imidazole-1, 3 (2H)-diyl) bis (methylene)) diphenol

New series of 4, 4'-((2-(Aryl)-1H-benzo [d] imidazole-1, 3 (2H)-diyl) bis (methylene)) Diphenol (3a-g) was successfully synthesized from cyclization of the reduction product of bis Schiff bases (2) with aryl aldehydes bearing phenolic hydroxyl in the presence of acetic acid. The structure of these compounds was identified from FT-IR, 1H NMR, 13C NMR and EIMs. The Antioxidant capability was screened by DPPH and FRAP assays. Both assays showed antioxidant capability more than BHT as well. Compounds 3b and 3c showed antioxidant capacity slightly less than ascorbic acid. The docking study for theses compound was carried out as III DNA polymerase inhibitor. The results of docking demonstrated that the increase in hinderances around phenolic hydr

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Publication Date
Wed Mar 01 2023
Journal Name
Baghdad Science Journal
Traveling Wave Solutions of Fractional Differential Equations Arising in Warm Plasma

This paper aims to study the fractional differential systems arising in warm plasma, which exhibits traveling wave-type solutions. Time-fractional Korteweg-De Vries (KdV) and time-fractional Kawahara equations are used to analyze cold collision-free plasma, which exhibits magnet-acoustic waves and shock wave formation respectively. The decomposition method is used to solve the proposed equations. Also, the convergence and uniqueness of the obtained solution are discussed. To illuminate the effectiveness of the presented method, the solutions of these equations are obtained and compared with the exact solution. Furthermore, solutions are obtained for different values of time-fractional order and represented graphically.

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Publication Date
Tue Jan 08 2019
Journal Name
Iraqi Journal Of Physics
Effect of concentrations ratios of NiO on the efficiency of solar cell for (CdO)1-x(NiO)x thin films

CdO:NiO/Si solar cell film was fabricated via deposition of CdO:NiO in different concentrations 1%, 3%, and 5% for NiO thin films in R.T and 723K, on n-type silicon substrate with approximately 200 nm thickness using pulse laser deposition. CdO:NiO/n-Si solar cell photovoltaic properties were examined under 60 mW/cm2 intensity illumination. The highest efficiency of the solar cell is 2.4% when the NiO concentration is 0.05 at 723K.

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Publication Date
Mon Oct 01 2012
Journal Name
Iraqi Journal Of Physics
The effect of sulfide content(x) on the electrical properties of (ZnSx Se1-x) thin films

Thin films of ZnSxSe1-x with different sulfide content(x)
(0, 0.02, 0.04, 0.06, 0.8, and 0.1), thickness (t) (0.3, 0.5, and 0.7 μm) and annealing temperature (Ta) (R.T 373 and 423K) were fabricated by thermal evaporating under vacuum of 10-5 Toor on glass substrate. The results show that the increasing of sulfide content (x)and annealing temperature lead to decrease the d.c conductivity σDC of and concentration of charge carriers (nH) but increases the activation energy (Ea1,Ea2), while the increasing of t increases σDC and nH but decrease (Ea1,Ea2). The results were explained in different terms

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Publication Date
Sat Aug 31 2019
Journal Name
Iraqi Journal Of Physics
A Study of the Spectroscopic Performance of Laser Produced CdTe(x):S(1-x) Plasma

Abstract

In this work, the plasma parameters (electron temperature (Te), electron density( ne), plasma frequency (fp) and Debye length (λD)) have been studied by using the spectrometer that collect the spectrum of Laser produce CdTe(X):S(1-X) plasma at X=0.5 with different energies. The results of electron temperature for CdTe range 0.758-0.768 eV also the electron density 3.648 1018 – 4.560 1018 cm-3  have been measured under vacuum reaching 2.5 10-2 mbar .Optical properties of CdTe:S were determined through the optical transmission method using ultraviolet visible spectrophotometer within the r

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Publication Date
Fri Nov 29 2019
Journal Name
Iraqi Journal Of Physics
Gas Sensing of (SnO2)1-x(ZnO)x Composite Associating with Electrical Properties

Abstract

Semiconductor-based gas sensors were prepared, that use n-type tin oxide (SnO2) and  tin oxide: zinc oxide composite (SnO2)1-x(ZnO)x at different x ratios using pulse laser deposition at room temperature. The prepared thin films were examined to reach the optimum conditions for gas sensing applications, namely X-ray diffraction, Hall effect measurements, and direct current conductivity. It was found that the optimum crystallinity and maximum electron density, corresponding to the minimum charge carrier mobility, appeared at 10% ZnO ratio. This ratio appeared has the optimum NO2 gas sensitivity for 5% gas concentration at 300 °C working temperat

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