Gaussian Integer Solutions of the Diophantine Equation x^4+y^4=z^3 for x≠ y

Shahrina Ismail; Kamel Ariffin Mohd Atan; Diego Sejas Viscarra; Kai Siong Yow

doi:10.21123/bsj.2023.7344

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Publication Date

Sun Oct 01 2023

Journal Name

Baghdad Science Journal

Volume

20

Issue Number

5

DOI

10.21123/bsj.2023.7344

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Gaussian Integer Solutions of the Diophantine Equation x^4+y^4=z^3 for x≠ y

Algebraic properties

Diophantine equation

Gaussian integer

quartic equation

nontrivial solutions

symmetrical solutions.

Shahrina Ismail

Kamel Ariffin Mohd Atan

Diego Sejas Viscarra

Kai Siong Yow

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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

Synthesis and study the optical properties of Ge20 Bix Se80-x thin films

Optical properties

Ge20 Bix Se80-x thin films

thermal evaporation technique.

Waleed Bdaiwi

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Publication Date

Thu Dec 31 2020

Journal Name

Neuroquantology

Assessment of Some Enhancement Methods of Renal X-ray Image

Salim J.

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The study focuses on assessment of the quality of some image enhancement methods which were implemented on renal X-ray images. The enhancement methods included Imadjust, Histogram Equalization (HE) and Contrast Limited Adaptive Histogram Equalization (CLAHE). The images qualities were calculated to compare input images with output images from these three enhancement techniques. An eight renal x-ray images are collected to perform these methods. Generally, the x-ray images are lack of contrast and low in radiation dosage. This lack of image quality can be amended by enhancement process. Three quality image factors were done to assess the resulted images involved (Naturalness Image Quality Evaluator (NIQE), Perception based Image Qual

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Publication Date

Wed Jun 10 2015

Journal Name

Journal Of The College Of Basic Education

Synthesis, characterization and antimicrobial studies of 2-(4-antipyrine azo)-4-nitroaniline with some metal ions.

spectral studies

complexes

antimicrobial activity

Amer J.Jarad

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Transition metal complexes of Co(II), Ni(II), Cu(II), and Zn(II) with 2-(4-antipyrine azo)-4-nitroaniline derived from 4-aminoantipyrine and 4-nitroaniline were synthesized. Characterization of these compounds has been done on the basis of elemental analysis, electronic data, FT-IR, UV-Vis and 1HNMR, as well as magnetic susceptibility and conductivity measurements. The nature of the complexes formed were studied following the mole ratio and continuous variation methods, Beer's law obeyed over a concentration range (1×10-4 - 3×10-4 M). High molar absorbtivity of the complex solutions were observed. From the analytical data, the stoichiometry of the complexes has been found to be 1:2 (metal:ligand). On the basis of physicochemical data octa

Publication Date

Tue Dec 31 2024

Journal Name

Indian Journal Of Clinical Biochemistry

Farnesoid X Receptor-Mediated Bile Acids Regulation in Cholestasis

Bile acid synthesis

Bile acid transporters

Enterohepatic cholestasis

Extrahepatic cholestasis

Farnesoid X receptor

Thamer Abdulla

Munaf H.

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The main process, for the elimination of cholesterol from the human body, involves the alteration of cholesterol into bile acid (BA), by the liver. The farnesoid X receptor (FXR), a member of the nuclear receptor superfamily, is essential for the regulation of BA, glucose, and lipid metabolism. It is largely found in the liver, intestines, kidney, and adrenal glands, and to a smaller degree in the heart and adipose tissue. The binding locations, of the FXR, are in close proximity to formerly undisclosed target genes, with distinctive activities associated with transcriptional regulators, autophagy, apoptosis, hypoxia, inflammation, RNA processing, and a number of cellular signaling pathways. The preservation of BA homeostasis, by the FXR, e

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Publication Date

Sun Jan 01 2017

Journal Name

Journal Of The College Of Languages (jcl)

Renaissance des Briefromans Oder Der Alltag in Krisen-und Wendezeiten

Mohammad Ismail

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In der Nachwendezeit erschienen im deutschen Buchmarkt zahlreiche Werke deutscher Autoren, die einen Trend oder Tendenz markieren können. Im Mittelpunkt der vorliegenden Arbeit steht die Analyse der Struktur und des Inhalts von drei erst nach der Wende erschienen Briefromanen: Alles, alles Liebe (2000) von Barbara Honigmann (geb. 1949), Die Liebenden (2002) von Gerhard Henschel (Jahrgang 1962) und Neue Leben (2005) des im Jahre 1962 geborenen Ingo Schulze. Dieser Beitrag macht sich zur Aufgabe zu erklären, ob der Briefroman ein neuer Trend in der deutschen Literatur nach der Wende ist.

Abstract

In the after( Wende) period a large collection of literary works for German writers has been p

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Publication Date

Thu Oct 01 2020

Journal Name

Biochem. Cell. Arch

NEW ORGANOTIN(IV) COMPLEXES DERIVED FROM 3,4-DIHYDROXYBENZALDEHYDEN(4)-ETHYL-3-SEMICARBAZONE LIGAND: SYNTHESIS, CHARACTERISATION AND BIOLOGICAL ACTIVITY

Baidaa

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Two new organotin(IV) complexes Me2Snesc (C1) and Bu2Snesc (C2) have been synthesised from the reaction of the corresponding organotin(IV) chloride with the Schiff base ligand 3,4-dihydroxybenzaldehyde-4-ethylsemicarbazone (H2esc). The ligand was prepared in two steps. The first step includes the formation of 4-ethylsemicarbazide, which then reacted with 3,4-dihydroxybenzaldehyde to give the title ligand. Complex formation between the organotin(IV) moiety and the anionic form of 3,4-dihydroxybenzaldehy-4-ethylsemicarbazone occurred through the o-dihydroxy positions. The ligand and its complexes were characterised by elemental analysis, FT-IR and NMR (1H, 13C and 119Sn) spectroscopy. Accordingly, the complexes were proposed to have tetrahedr

(3)

Publication Date

Thu Apr 01 2021

Journal Name

Pakistan Journal Of Statistics

Estimation intensity radiation of chest X-ray (CXR) with application

Chest x-ray (CXR)

emissions

intensity of radiation

Sievert

Bayes

Asmaa Najm

Iqbal Mahmood

Suhad Ahmed

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In this research we assumed that the number of emissions by time (𝑡) of radiation particles is distributed poisson distribution with parameter (𝑡), where  < 0 is the intensity of radiation. We conclude that the time of the first emission is distributed exponentially with parameter 𝜃, while the time of the k-th emission (𝑘 = 2,3,4, … . . ) is gamma distributed with parameters (𝑘, 𝜃), we used a real data to show that the Bayes estimator 𝜃 ∗ for 𝜃 is more efficient than 𝜃̂, the maximum likelihood estimator for 𝜃 by using the derived variances of both estimators as a statistical indicator for efficiency

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Publication Date

Sat Jun 30 2012

Journal Name

Al-kindy College Medical Journal

Treatment of Nasopharyngeal Carcinoma by Using Deep X-Ray Therapy

Nasopharyngeal Carcinoma (NPC)

Radiotherapy (RT).

Raad . A

Wisam

Anwar S.

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Background: Nasopharyngeal carcinoma (NPC) is one of the most challenging tumors because of their relative inaccessibility and that their spread can occur without significant symptoms with few signs, but Radiotherapy (RT) has a role in treatment of it.
Objectives: To show that RT is still the modality of choice in the treatment of NPC, to study modes of presentations, commonest histopathological types and their percentages, to show differences in the sensitivities of these types to RT and to find out a 5 year survival rate(5YSR) and its relation with lymph node involvement.
Methods: This is a retrospective study of 44 patients with NPC who were treated with routine RT from 1988-2007 at the institute of radiology and nuclear medicin

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Publication Date

Tue Jan 08 2019

Journal Name

Iraqi Journal Of Physics

X- ray diffraction and dielectric properties of PbSe thin films

PbSe

vacuum deposition

conduction studies

thin films

dielectric relaxation

complex capacitance.

Bushra A.

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Lead selenide PbSe thin films of different thicknesses (300, 500, and 700 nm) were deposited under vacuum using thermal evaporation method on glass substrates. X-ray diffraction measurements showed that increasing of thickness lead to well crystallize the prepared samples, such that the crystallite size increases while the dislocation density decreases with thickness increasing. A.C conductivity, dielectric constants, and loss tangent are studied as function to thickness, frequency (10kHz-10MHz) and temperatures (293K-493K). The conductivity measurements confirm confirmed that hopping is the mechanism responsible for the conduction process. Increasing of thickness decreases the thermal activation energy estimated from Arhinus equation is

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(2)

Publication Date

Sat Sep 01 2018

Journal Name

Polyhedron

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)

The 1

3-dipolar cycloaddition “click” reaction between an azide and an alkyne to give a 1

2

3-triazole was reported by Huisgen in 1961 [1]. In 2002 the Copper(I)-catalyzed Azide-Alkyne Cycloaddition (CuAAC) to prepare a 1

2

3-triazole was reported [2]

[3]. The existence of relatively basic nitrogen atoms in the 1

2

3-triazole rings

and the possibility of introducing additional donor groups in the substituents (Fig. 1)

made the CuAAC “click” reaction an attractive method to prepare differently substituted 1

2

3-triazoles. These compounds have been used as ligands to coordinate to various metal ions that display a range of applications such as in electrochemical and photochemical studies

in supramolecular chemistry

magnetism

metal-ion sensing and catalysis [4]. The reasons for the success of the “click” reaction

is that it is easy to carry out and is widely applicable. It is not affected by a variety of functional groups

and can be carried out with a variety of Cu(I) catalysts and solvents

including aqueous conditions. The Cu(I) catalysts overcome the high activation energy barrier of the non-catalyzed Huisgen reaction by changing the mechanism of the reaction. A large variety of copper catalysts can be used for the CuAAC reaction

on condition that the maximum concentration of Cu(I) species is generated during the reaction. The pre-catalyst can be a Cu(II) salt (usually CuSO4) together with a reducing agent (often sodium ascorbate) or a Cu(I) compound in the presence of a base or amine ligand and a reducing agent to prevent oxidation to Cu(II). Some strong oxidising cupric salts or complexes such as Cu(OAc)2 also work. The solvent is very flexible from organic to aqueous

with the most commonly used combination water + an alcohol (t-BuOH

MeOH or EtOH). The key role of the solvent or solvent mixture is to solubilize the substrates and Cu(I) catalyst in order to ensure rapid reactions. Such aqueous conditions are very useful for biochemical conjugations

as well as for organic syntheses. We recently reported on the synthesis of a series of differently substituted 1

2

3-triazole chromophores

the substituted 2-(1-phenyl-1H-1

2

3-triazol-4-yl)pyridine ligands [5]

see Fig. 2 middle

with substituents R = H (L1)

CH3 (L2)

OCH3 (L3)

COOH

F

Cl

CN

CF3

O(CH2)3CH3 and N(CH3)2. These versatile ligands were found to coordinate to various first row transition metals

such as manganese

cobalt and nickel [6]. Here we extend the series to include more first row transition metal(II) coordination compounds

iron

copper and zinc

as well as a second row transition metal(II) coordination compound

cadmium

containing the 2-(1-(4-methyl-phenyl)-1H-1

2

3-triazol-1-yl)pyridine chromophore (Fig. 2 right with R = CH3). This series of seven novel coordination compounds is the first series of pyridyl-triazole based transition metal coordination compounds where seven different transition metals are coordinated to the same 1

2

3-triazole chromophore

namely 2-(1-(4-methyl-phenyl)-1H-1

2

3-triazol-1-yl)pyridine.

Kinaan M

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