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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 Sep 01 2018
Journal Name
Journal Of Pharmaceutical Sciences And Research
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Publication Date
Sat Dec 17 2022
Journal Name
Iraqi Journal Of Laser
PDF Study the Effect of Gold Film Thickness on the Sensitivity of the U Shape Fiber Sensor by the Occurrence of LSPR Phenomenon: Saffana Z. Maseer*, Bushra R. Mahdi

Abstract: In this paper, a U-shaped probe with a curvature diameter of half a centimeter was implemented using plastic optical fibers. A layer of the outer shell of the fibers was removed by polishing to a D-section. The sensor was tested by immersing it in a sodium chloride solution with variable refractive index depending on solution concentrations ranging from 1.333 to 1.363. In this design, the sensor experienced a decrease in its intensity as the concentration of the solution increased. The next step The sensor was coated with a thin layer of gold with a thickness of 20 nm, and the sensor was tested with the same solutions which resulted in a shift in wavelengths where the shift in wavelength was 5.37 nm and sensiti

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Publication Date
Wed Mar 10 2021
Journal Name
Baghdad Science Journal
studies of human interferon a B and Y activities on diffrent cell

Human interferon as is the case in all kinds of interferon has complex effects but all share their impact on preventing the proliferation of viruses and preventing or reducing human Alantervjørn conversion occurs if the cell is in preventing the growth of the virus when interferon Balnmstqubl connects

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Publication Date
Sun Oct 23 2016
Journal Name
Oriental Journal Of Chemistry
Synthesis and Antioxidant Ability of Some 4-(((4-(5-(Aryl)-1,3,4-Oxadiazol-2-Yl)Benzyl)Oxy)Methyl)-2,6-Dimethoxyphenol

A series of new 4-(((4-(5-(Aryl)-1,3,4-oxadiazol-2-yl)benzyl)oxy)methyl)-2,6-dimethoxy phenol (6a-i) were synthesized from cyclization of 4-(((4-hydroxy-3,5-dimethoxy benzyl)oxy)methyl)benzohydrazide with substituted carboxylic acid in the presences of phosphorusoxy chloride.The resulting compounds were characterized by IR, 1H-NMR, 13C-NMR, and HRMS data. 2,2-Diphenyl-1-picrylhydrazide (DPPH) and ferric reducing antioxidant power (FRAP) assays were used to screen their antioxidant properties. Compounds 6i and 6h exhibited significant antioxidant ability in both assay. Furthermore, type of substituent and their position of the aryl attached 1,3,4-oxadiazole ring at position five are play an important roles in enhancing or declining the antio

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Publication Date
Sat Jan 20 2024
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Synthesis of New Bismaleimide Homopolymer and Copolymers Derived from 4, 4ˉ-Bis[4-(N-maleimidyl) Phenyl Schiff Base] Tolidine

Polyimides are widely used in high-temperature plastics, adhesives, dielectrics, photoresists, nonlinear optical materials, separation membrane materials, and Langmuir-Blodgett (LB) films. They are commonly regarded as the most heat-resistant polymers. This work involved the synthesis of a new bismaleimide homopolymer and copolymer by performing many steps. The synthesis of compound (1) (bis [4-(amino phenyl) Schiff base] tolidine) via condensation of o-tolidine with two moles of 4-aminoacetophenone. Secondly, compound (1) was combined with maleic anhydride to form compound (2) (4, 4ˉ-bis[4-(N-maleamic acid) phenyl Schiff base] toluidine). Thirdly, a dehydration reaction was carried out affording compound (3) (4,4ˉ-bis [4-(N-maleimidyl

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Publication Date
Fri Jun 01 2007
Journal Name
Journal Of The College Of Languages (jcl)
TECHNIQES OF SURREALISM: A STUDY IN TWO NOVELS BY THOMAS PYNCHON, V. AND THE CRYING OF LOT 49

Surrealism is a twentieth-century literary and artistic movement oriented toward the liberation of the mind. Surrealism is a reaction to the philosophy of rationalism which was believed to be the cause of the disaster of World War I. It emphasizes the expression of the imagination as revealed in dreams and presented without conscious control, the unexpected juxtapositions of objects, the withdrawal of the self, and the exploitation of chance effects.
Surrealism began in Paris in the early 1920s, as Europe emerged from the devastation of World War I. A group of writers, artists, and filmmakers, led by the poet André Breton, adopted the word surréaliste (meaning, roughly, "super-real") as a label for their artistic activities. Influen

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Publication Date
Wed Nov 08 2023
Journal Name
Technologies And Materials For Renewable Energy, Environment, And Sustainability: Tmrees23fr
Analysis of x-ray diffraction lines of cuprous oxide nanoparticles by using variance analysis method

In this study, the results of x-ray diffraction methods were used to determine the Crystallite size and Lattice strain of Cu2O nanoparticles then to compare the results obtained by using variance analysis method, Scherrer method and Williamson-Hall method. The results of these methods of the same powder which is cuprous oxide, using equations during the determination the crystallite size and lattice strain, It was found that the results obtained the values of the crystallite size (28.302nm) and the lattice strain (0.03541) of the variance analysis method respectively and for the Williamson-Hall method were the results of the crystallite size (21.678nm) and lattice strain (0.00317) respectively, and Scherrer method which gives the value of c

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Publication Date
Mon Jun 17 2019
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Analysis of Different Types of Tea Leaves by X-Ray Flourescence Technique

Samples of tea leaves (Green tea, Gugarate tea and Black tea used commonly in Iraq) are dried, grinded, pressed and submitted for the elemental analysis by x-ray fluorescence technique (XRF). The concentrations of major, minor and trace elements are determined. The major elements were Na, Mg, Al, K, Si, Ca, Mn, Fe, S and P. Of these elements, Ca, concentration in Gugarate tea leaves is three times, it's level in the other types of tea. Titanium, Cl, Rb and Sr are found as minor elements, while other elements such as Cu, Zn, V, Cr, Co, ...etc are found as trace elements. Of these trace elements considerable concentration values are found for some toxic elements Hg, Cd, Pb and As. Green tea contains 1.1 ppm Hg and 4.4 ppm Pb. Gugarate tea

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Publication Date
Sun Oct 01 2023
Journal Name
Baghdad Science Journal
Nonlinear Ritz Approximation for the Camassa-Holm Equation by Using the Modify Lyapunov-Schmidt method

 

          In this work, the modified Lyapunov-Schmidt reduction is used to find a nonlinear Ritz approximation of Fredholm functional defined by the nonhomogeneous Camassa-Holm equation and Benjamin-Bona-Mahony. We introduced the modified Lyapunov-Schmidt reduction for nonhomogeneous problems when the dimension of the null space is equal to two.  The nonlinear Ritz approximation for the nonhomogeneous Camassa-Holm equation has been found as a function of codimension twenty-four.

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Publication Date
Wed Apr 01 2020
Journal Name
Biochem. Cell. Arch.
SYNTHESIS, SPECTROSCOPIC IDENTIFICATION AND ANTIMICROBIAL ACTIVITY OF MIXED LIGAND COMPLEXES OF NEW LIGAND [3-((4- ACETYL PHENYL)AMINO)-5,5-DIMETHYLCYCLOHEX-2-EN-1-ONE] (HL* ) WITH 3-AMINO PHENOL

This work includes the synthesis and identification of ligand {3-((4-acetylphenyl)amino)-5,5-dimethylcyclohex2-en-1-one} (HL* ) by the treatment of 5,5-dimethylcyclohexane-1,3-dione with 4-aminoacetophenone under reflux. The ligand (HL* ) was identified via FTIR, Mass spectrum, elemental analysis (C.H.N.), 1H and 13C-NMR spectra, UV-Vis spectroscopy, TGA and melting point. The complexes were synthesized from ligand (HL* ) mixed with 3-aminophenol (A) and metal ion M(II), where M(II) = (Mn, Co, Ni, Cu, Zn and Cd) at alkaline medium to produce complexes of general formula [M(L* )(A)] with (1:1:1) molar ratio. These complexes were detected via FT-IR spectra, UV-Vis spectroscopy as well as elemental analysis (A.A) and melting point, conductivit

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