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Gaussian Integer Solutions of the Diophantine Equation x^4+y^4=z^3 for x≠ y
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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
Tue Jun 20 2023
Journal Name
Baghdad Science Journal
Numerical Solutions for the Nonlinear PDEs of Fractional Order by Using a New Double Integral Transform with Variational Iteration Method
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This paper considers a new Double Integral transform called Double Sumudu-Elzaki transform DSET. The combining of the DSET with a semi-analytical method, namely the variational iteration method DSETVIM, to arrive numerical solution of nonlinear PDEs of Fractional Order derivatives. The proposed dual method property decreases the number of calculations required, so combining these two methods leads to calculating the solution's speed. The suggested technique is tested on four problems. The results demonstrated that solving these types of equations using the DSETVIM was more advantageous and efficient

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Publication Date
Wed Mar 18 2020
Journal Name
Baghdad Science Journal
Solving Linear Volterra – Fredholm Integral Equation of the Second Type Using Linear Programming Method
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In this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree  and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those methods i

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Publication Date
Sun Jan 01 2023
Journal Name
Technologies And Materials For Renewable Energy, Environment And Sustainability: Tmrees22fr
Investigate the structural properties of Tl1-xHgxSr2Ca2Cu3O8+δ compound by using Scherrer modified equation
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Publication Date
Sun Jun 30 2013
Journal Name
Al-khwarizmi Engineering Journal
Al-Khriet Agricultural Waste Adsorbent, for Removal Lead and Cadmium Ion from Aqueous Solutions
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The availability of low- cost adsorbent namely Al-Khriet ( a substance found in the legs of Typha  Domingensis) as an agricultural waste material, for the removal of lead and cadmium from aqueous solution was investigated. In the batch tests experimental parameters were studied, including adsorbent dosage between (0.2-1) g, initial metal ions concentration between (50-200) ppm (single and binary) and contact time (1/2-6) h. The removal percentage of each ion onto Al-Khriet reached equilibrium in about 4 hours. The highest adsorption capacity was for lead (96%) while for cadmium it was (90%) with 50 ppm ions concentration, 1 g dosage of adsorbent and pH 5.5. Adsorption capacity in the binary mixture were reduce at about 8% for lead a

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Publication Date
Wed May 01 2024
Journal Name
Journal Of Water Process Engineering
Rational assembly of Z-scheme FeTiO3/Fe-doped g-C3N4 photocatalytic heterojunctions: Photodegradation behavior and mechanism insight
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Expanded use of antibiotics may increase the ability of pathogenic bacteria to develop antimicrobial resistance. Greater attention must be paid to applying more sustainable techniques for treating wastewater contaminated with antibiotics. Semiconductor photocatalytic processes have proven to be the most effective methods for the degradation of antibiotics. Thus, constructing durable and highly active photocatalytic hybrid materials for the photodegradation of antibiotic pollutants is challenging. Herein, FeTiO3/Fe-doped g-C3N4 (FTO/FCN) heterojunctions were designed with different FTO to FCN ratios by matching the energy level of semiconductors, thereby developing effective direct Z-type heterojunctions. The photodegradation behaviors of th

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Publication Date
Sat Aug 01 2020
Journal Name
Key Engineering Materials
Effect of Coefficient of Variation on the Reliability of Collapse Potential's Equation Predicted by ANNs
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In this paper, the Reliability Analysis with utilizing a Monte Carlo simulation (MCS) process was conducted on the equation of the collapse potential predicted by ANN to study its reliability when utilized in a situation of soil that has uncertainty in its properties. The prediction equation utilized in this study was developed previously by the authors. The probabilities of failure were then plotted against a range of uncertainties expressed in terms of coefficient of variation. As a result of reliability analysis, it was found that the collapse potential equation showed a high degree of reliability in case of uncertainty in gypseous sandy soil properties within the specified coefficient of variation (COV) for each property. When t

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Publication Date
Fri Aug 01 2014
Journal Name
International J. Of Math. Sci. & Engg. Appls.
NEUTRAL DELAY DIFFERENTIAL EQUATION WITH ONE LARGE DELAY
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Publication Date
Thu Jan 01 2015
Journal Name
Finite Difference Methods,theory And Applications
Determination of the Time-Dependent Thermal Conductivity in the Heat Equation with Spacewise Dependent Heat Capacity
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Publication Date
Wed Mar 10 2021
Journal Name
Baghdad Science Journal
The Influence of The Kind of Feeding on The Average of Body Growth for The Infant of The Age (3-6) Months in Baghdad.City
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This paper was conducted to identifying the body growth averages for the infants of the age (3-6) months and their relation with brest (natural ) or artificial feeding The results showed that the higher percentage was for the infants with the natural feeding in comparison with those of the artificial or mixed feeding. Also there was a clear increase in the average of the body growth for those with the natural feeding and such results were closer to the standard criterion. While the averages of body growth for those with the artificial or mixed feeding were low. In addition, it was clear that the averages of body growth of the i

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Publication Date
Sat Apr 01 2017
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Synthesis of 3 - 3 - gem - di - C -Nitromethyl Nucleoside Analogues of Possible Biological Activity
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Synthesis of new nucleoside analogues of the type : 3¢ , 3¢ - gem – di – C – nitromethly , expected to have useful application in the chemotherapeutic treatment of AIDS , cancer and microbial infections. The synthesis involved the condensation of the appropriate sugar derivative ( i.e . 3¢ , 3¢ –  gem – di – C – nitromethly – 1–  ribofuranose ) with nitrogen bases , such as , uracil and theophllin following a multi step scheme starting from diacetone golucose (1) (scheme 1) .The prepared compound were identified by spectroscopic methods ; ir , mass , 1H and 13C nmr.

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