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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 Jun 02 2019
Journal Name
Baghdad Science Journal
Effect of Dopant Concentration on the Structural, Optical and Sensing Properties of (SnO2)1-x(TiO2:CuO)x Sprayed Films

      Spray pyrolysis technique was subjected to synthesized (SnO2)1-x (TiO2: CuO) x Thin films on different substrates like glass and single crystal silicon using. The structure of the deposited films was studied using x-ray diffraction. A more pronounced diffraction peaks of SnO2 while no peaks of (CuO , TiO2 ) phase appear in the X-ray profiles by increasing of the content of (TiO2 , CuO) in the sprayed films. Mixing concentration (TiO2 , CuO) influences on the size of the crystallites of the SnO2 films ,the size of crystallites of the spray paralyzed oxide films change in regular manner by increasing of (TiO

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Publication Date
Fri Apr 30 2021
Journal Name
Iraqi Journal Of Science
On y-closed Dual Rickart Modules

In this paper, we develop the work of Ghawi on close dual Rickart modules and discuss y-closed dual Rickart modules with some properties. Then, we prove that, if are y-closed simple -modues and if -y-closed is a dual Rickart module, then either Hom ( ) =0 or . Also, we study the direct sum of y-closed dual Rickart modules.

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Publication Date
Sat Jan 01 2022
Journal Name
International Journal Of Research In Social Sciences & Humanities
La divergencia entre el español y el árabe al respeto de la Aspectualidad y Temporalidad “Estudio Contrastivo”

Applying grammatical rules of foreign languages regarding Time and Aspect to the Arabic language caused several problems, one of which led Orientalists to annul temporality in the Arabic language and consider it a language of aspectuality. This criterion has many fallacies, since each language differs from the other according to the syntactic and morphological norms, even in the structuring of the verbal system of each of them.

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Publication Date
Fri May 03 2019
Journal Name
Photonics
Design Investigation of 4 × 4 Nonblocking Hybrid Plasmonic Electrooptic Switch

This paper proposes a compact, plasmonic-based 4 × 4 nonblocking switch for optical networks. This device uses six 2 × 2 plasmonic Mach-Zehnder switch (MZS), whose arm waveguide is supported by a JRD1 polymer layer as a high electro-optic coefficient material. The 4 × 4 switch is designed in COMSOL environment for 1550 nm wavelength operation. The performance of the proposed switch outperforms those of conventional (nonplasmonic) counterparts. The designed switch yields a compact structure ( 500 × 70   µ m 2 ) having V π L = 12   V · µ m , 1.5 THz optical bandwidth, 7.7 dB insertion loss, and −26.5 dB crosstalk. The capability of the switch to route 8 × 40 Gbps WDM signal is demonstrated successfully.

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Publication Date
Wed Jul 17 2019
Journal Name
Aip Conference Proceedings
The correction of the line profiles for x-ray diffraction peaks by using three analysis methods

In this study used three methods such as Williamson-hall, size-strain Plot, and Halder-Wagner to analysis x-ray diffraction lines to determine the crystallite size and the lattice strain of the nickel oxide nanoparticles and then compare the results of these methods with two other methods. The results were calculated for each of these methods to the crystallite size are (0.42554) nm, (1.04462) nm, and (3.60880) nm, and lattice strain are (0.56603), (1.11978), and (0.64606) respectively were compared with the result of Scherrer method (0.29598) nm,(0.34245),and the Modified Scherrer (0.97497). The difference in calculated results Observed for each of these methods in this study.

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Publication Date
Wed Apr 09 2014
Journal Name
Chemical And Process Engineering Research
Analytical Profile of 4 - (4-Nitro Benzene Azo) - 3 - Amino Benzoic Acid on a Surface of Natural Granulated Calcined Iraqi Montmorillonite Clay Mineral, via Columnar Method

The adsorption ability of Iraqi initiated calcined granulated montmorillonite to adsorb of 4-(4-Nitrobenzeneazo) 3-Aminobenzoic Acid from aqueous solutions has been investigated through columnar method. The azo dye adsorption found to be dependent on adsorbent dosage, initial concentration and contact time. All columnar experiments were carried out at three different pH values (5.5, 7and 8) using buffer solutions at flow rate of (3 drops/ min.), at room temperature (25±2) °C. The experimental isotherm data were analyzed using Langmuir, Freundlich and Temkin equations. The monolayer adsorption capacity is 6.4066 mg Azo ligand per 1g calcined Montmorillonite. The experiments showed that highest removal rate 90.5 % for azo dye at pH 5.5.The

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Publication Date
Thu Feb 27 2020
Journal Name
Iraqi Journal Of Science
Impact of ZnO Atomic Ratio on Structural, Morphological and Some Optical Properties of (SnO2)1-x (ZnO)x Thin Films

In this work, SnO2 and (SnO2)1-x(ZnO)x composite thin films with different ZnO atomic ratios (x=0, 5, 10, 15 and 20%) were prepared by pulsed laser deposition technique on clean glass substrates at room temperature without any treatment. The deposited thin films were characterized by x-ray diffraction atomic force microscope  and UV-visible spectrophotometer to study the effect of the ZnO atomic ratio on their structural, morphological and optical properties. It was found that the crystallinety and the crystalline size vary according to ZnO atomic ratio. The surface appeared as longitudinal structures which was convert to spherical shapes with increasing ZnO atomic ratio. The optical trans

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Publication Date
Thu Apr 06 2023
Journal Name
Materials Science Forum
Study of the Effect of Ce <sup>3+</sup> on the Gas Sensitivity and Magnetic Properties of Cu<sub>x</sub>Ce<sub>0.3-X</sub>Ni<sub>0.7</sub>Fe<sub>2</sub>O<sub>4</sub> Ferrite Nanoparticles

This study includes the preparation of the ferrite nanoparticles CuxCe0.3-XNi0.7Fe2O4 (where: x = 0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3) using the sol-gel (auto combustion) method, and citric acid was used as a fuel for combustion. The results of the tests conducted by X-ray diffraction (XRD), emitting-field scanning electron microscopy (FE-SEM), energy-dispersive X-ray analyzer (EDX), and Vibration Sample Magnetic Device (VSM) showed that the compound has a face-centered cubic structure, and the lattice constant is increased with increasing Cu ion. On the other hand, the compound has apparent porosity and spherical particles, and t

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Publication Date
Thu Dec 29 2016
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
A new Spectrophotometric Method For The Determination of La (III) With 3-Hydroxy -4-(2-hydroxyPhenyl azo) Naphthalene -1- Sulfonic Acid

A simple, rapid and sensitive spectrophotometric method has been proposed for the determination of La (III) using 3-hydroxy -4-(2-hydroxy-phenyl azo) naphthalene -1- sulfonic acid as a chromogenic reagent. This method is based on the formation of a red-pink colored complex, upon the reaction of La(III) with the reagent in an alkaline medium (pH= 9.50), having a maximum absorbance at 459 nm. Beer's law is valid in the concentration range 0.512 µg.ml-1 with a Sandell's sensitivity value of 0.0188 µg.cm-2 and molar absorptivity of 7376.12 L.mol-1.cm-1. The stoichiometric composition of the chelate is 1:3. The effect of the presence of different cations as interferants in the determination of La(III) under the given optimum conditions

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Publication Date
Thu Apr 26 2018
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Minimax Shrunken Technique for Estimate Burr X Distribution Shape Parameter

      The present paper concern with minimax shrinkage estimator technique in order to estimate Burr X distribution shape parameter, when prior information about the real shape obtainable as original estimate while known scale parameter.

 Derivation for Bias Ratio, Mean squared error and the Relative Efficiency equations.

 Numerical results and conclusions for the expressions mentioned above were displayed. Comparisons for proposed estimator with most recent works were made.

 

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