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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 Dec 24 2022
Journal Name
Wasit Journal Of Pure Sciences
Synthesis of the integer FIR filters with short coefficient word length

The integer simulation and development finite impulse response (FIR) filters taking into account the possibilities of their realization on digital integer platforms are considered. The problem statement and solution of multifunctional synthesis of digital FIR filters such a problem on the basis of the numerical methods of integer nonlinear mathematical programming are given. As an several examples, the problem solution of synthesis FIR-filters with short coefficient word length  has been given. The analysis of their characteristics is resulted. The paper discusses issues of modeling and synthesis of digital FIR filters with provision for the possibilities of their implementation on digital platforms with integer computation arithme

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Publication Date
Tue Mar 14 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Spectrophotometric Method for the Determination of Tetracycline and Doxycycline by Oxidizing Coupling Reaction with 4-aminoantipyrine

 A simple,  sensitive, accurate and low cost effective spectrophotometric method has been developed for the determination of Tetracycline and Doxycycline in pure and pharmaceutical formulations. The method is based on the reaction of methyldopa with 4-aminoantipyren (4-AAP) in presence of potassium ferriecyanide (PFC) in an alkaline medium. Two optimization methods were applied to determine the optimum conditions of oxidizing coupling reaction variables; univariate and design of experiment (DOE) method. The conditions effecting the  reaction; pH, buffer Volume,   reagent concentration, oxidant concentration, type of buffer, order of addition, time of reaction and stability were optimized . Under univariate and design

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Publication Date
Sat Jan 02 2021
Journal Name
Journal Of The College Of Languages (jcl)
The problems of Google Translate: Los servicios de la traducción automática de Google y sus problemas

There are numbers of automatic translation services that internet users can choose to automatically translate a certain text, and Google translate is one of these automatic services that proposes over 51 Languages. The present paper sheds light on the nature of the translation process offered by Google, and analyze the most prominent problems faced when Google translate is used. Direct translation is common with Google Translate and often results in nonsensical literal translations, particularly with long compound sentences. This is due to the fact that Google translation system uses a method based on language pair frequency that does not take into account grammatical rules which, in turn, affects the quality of the translation. The

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Publication Date
Fri Jun 30 2023
Journal Name
Iraqi Journal Of Science
Computation of the Relationships of X-ray to Radio Luminosities of a Sample of Starburst Galaxies

      The goal of this research is to better understand the physical features of starburst galaxies. Radio and X-ray observations are good for exploring the stuff within the central regions of galaxies.  A galaxy that is undergoing a strong star formation, usually in its central area, is known as a starburst galaxy. This paper provides the results of a statistical analysis of a sample of starburst galaxies. The data used in this research have been collected from NASA Extragalactic Database (NED), and HYPERLEDA. Those data have been used to examine possible luminosity correlations of X-ray to a radio of a sample of starburst galaxies. In this research, statistical software, known as statistic-win-program, has been used to investigat

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Publication Date
Thu Dec 28 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Synthesis, Characterization and Antibacterial Activity of New Chalcones Derived from New Aldehyde; 4-[5-(4`tolyl)-1,3,4-thiadiazole-2-yl] benzaldehyde

 New chalcones of  -{ -  -   -   y  -     - hi di z  e- -y    he y  - -    e e- -  e-    -        - substituted phenyl have been prepared from condensation of  a new of  4-[5-(4`-tolyl)1,3,4-thiadiazole-2-yl] benzaldehyde (which is synthesized by the reaction of  2- amino-5- (4`-tolyl) -1,3,4-thiadiazole and benzaldehyde) with 3- or 4- substituted acetophenones in alkaline medium. The physical, CHNS analysis and spectral data of the synthesized compounds were determined. The biological activity evaluated of new compounds showed that many of these compounds possess antiba

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Publication Date
Thu Jul 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Analytical Solutions to Investigate Fractional Newell-Whitehead Nonlinear Equation Using Sumudu Transform Decomposition Method

Some nonlinear differential equations with fractional order are evaluated using a novel approach, the Sumudu and Adomian Decomposition Technique (STADM). To get the results of the given model, the Sumudu transformation and iterative technique are employed. The suggested method has an advantage over alternative strategies in that it does not require additional resources or calculations. This approach works well, is easy to use, and yields good results. Besides, the solution graphs are plotted using MATLAB software. Also, the true solution of the fractional Newell-Whitehead equation is shown together with the approximate solutions of STADM. The results showed our approach is a great, reliable, and easy method to deal with specific problems

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Publication Date
Mon Apr 10 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Studying of Structural Properties of ZnxNi1-x-yCuyFe2O4 Spinel Ferrite Using XRD Powder

ZnxNi1-x-yCuyFe2O4 spinel ferrite were prepared using solid state reaction method with (y=0.1, x=0.2, 0.3, 0.4, 0.5, 0.6 ) . X-ray diffraction with diffractometer CuKα analysis have been carried out and studied showing single phase spinel cubic with space group FD͞ 3m for all prepared samples . Lattice parameters and crystallite grain size and x-ray density(ρx-ray) bulk density and porosity ratio's were calculated and showed good agreement with the international data reported in the scientific research's.

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Publication Date
Thu Mar 01 2018
Journal Name
International Journal Of Science And Nature
EXPERIMENTAL AND THEORETICAL STUDY OF 3-BENZYL -2- MERCAPTOQUINOIZOLINE-4(3H)-ONE (BMQ) AS AN INHIBITOR OF CARBON STEEL CORROSION IN ACIDIC MEDIA

The inhibition of 3-Benzyl -2-mercaptoquinoizoline -4 (3H)-one (BMQ) on the corrosion of carbon steel in 0.5 M HCl studied by potentionstat polarization methods at 303–333 K. Results obtained show that BMQ act as inhibitor for carbon steel in HCl solution. The inhibition efficiency increase with increase in BMQ concentration. Activation parameters and Gibbs free energy for the adsorption process using Statistical Physics calculated and discussed. Quantum chemical calculations using DFT at the B3LYP/6-31G level of theory were used to calculate some electronic properties of the molecule to verify any correlation between the inhibitive effect and molecular structure of BMQ. The quantum calculations were proceeded to get data around correlati

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Publication Date
Sun Mar 07 2010
Journal Name
Baghdad Science Journal
Synthesis, characterization and antimicrobial Studies of complexes of some metal ions with 5(2-hydroxy benzylidine) -2-thio ether -1, 3, 4-thiadiazole

A new series of Fe (III) , Co (II) , Ni (II) and Cu (II) complexes of the Schiff base, 5 (2-hydroxy benzylidine) -2-thio ether -1, 3, 4-thiadiazole were prepared and characterized .The imine behaves as a bidentate. The nature of bonding and the stereochemistry of the complexes were deduced from metal analyses, infrared, electronic spectra,magnetic susceptibility and conductivity measurements, an octahedral geometry was suggested for all complexes except the copper complex has a square planar geometry .preliminary in vitro tests for antimicrobial activity show that all the prepared compounds except iron complex display good activity to gram positive Staphelococcus aures and gram negative Escherchia coli.

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Publication Date
Sat Oct 31 2020
Journal Name
International Journal Of Intelligent Engineering And Systems
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