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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 Jan 11 2022
Journal Name
3rd International Scientific Conference Of Alkafeel University (iscku 2021)
Elimination of the broadening in X-ray diffraction lines profile for nanoparticles by using the analysis of diffraction lines method
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In this research, the results of the Integral breadth method were used to analyze the X-ray lines to determine the crystallite size and lattice strain of the zirconium oxide nanoparticles and the value of the crystal size was equal to (8.2nm) and the lattice strain (0.001955), and then the results were compared with three other methods, which are the Scherer and Scherer dynamical diffraction theory and two formulas of the Scherer and Wilson method.the results were as followsScherer crystallite size(7.4nm)and lattice strain(0.011968),Schererdynamic method crystallite size(7.5 nm),Scherrer and Wilson methodcrystallite size( 8.5nm) and lattice strain( 0.001919).And using another formula for Schearer and Wilson methodwe obtain the size of the c

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Publication Date
Wed Jun 20 2018
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Synthesis, Characterization and Antimicrobial Evaluation with DFT Study of New Two-Amino-4-(4-Chlorophenyl) Thiazole Derivatives
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2-amino-4-(4-chloro phenyl)-1,3-thiazole (1) was synthesized by refluxing thiourea with para-chloro phenacyl bromide in absolute methanol. The condensation of amine compound (1)  with phenylisothiocyanate in the presence of pyridine will  produce 1-(4-(4-chlorophenyl)thiazol-2-yl)-3-phenylthiourea(2), which is  upon treatment with 2,4 dinitrophenyl hydrazine by conventional method, afforded 1- ( 4 - ( 4 – chlorophenyl ) thiazol – 2 – yl ) – 3 - phenylhydrazonamide,N' - ( 2 , 4 -dinitrophenyl) ,(3).The characterization of the titled compounds were performed utilizing FTIR spectroscopy, 1HNMR and CHNS elemental analysis, and by me

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Publication Date
Wed Feb 01 2023
Journal Name
Baghdad Science Journal
Synthesis, Theoretical Study, and Biological Evaluation of Some Metal Ions with Ligand "Methyl -6-[2-(4-Hydroxyphenyl) -2-((1-Phenylethylidene) Amino) Acetamido] -2,2-Dimethyl-5—Oxo-1-Thia-4-Azabicyclo [3.2.0] Heptane-3-Carboxyylate
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Schiff base (methyl 6-(2- (4-hydroxyphenyl) -2- (1-phenyl ethyl ideneamino) acetamido) -3, 3-dimethyl-7-oxo-4-thia-1-azabicyclo[3.2.0] heptane-2-carboxylate)Co(II), Ni(II), Cu (II), Zn (II), and Hg(II)] ions were employed to make certain complexes. Metal analysis M percent, elemental chemical analysis (C.H.N.S), and other standard physico-chemical methods were used. Magnetic susceptibility, conductometric measurements, FT-IR and UV-visible Spectra were used to identified. Theoretical treatment of the generated complexes in the gas phase was performed using the (hyperchem-8.07) program for molecular mechanics and semi-empirical computations. The (PM3) approach was used to determine the heat of formation (ΔH˚f), binding energy (ΔEb

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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
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          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
Fri Mar 28 2014
Journal Name
Advances In Life Science And Technology
Synthesis and Characterization of Novel Schiff Bases, N-Acyl and Diazetines Derived from 3-((5-hydrazinyl-4-phenyl-4H-1,2,4- triazol-3-yl)methyl)-1H-indole
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This work involves synthesis of some new heterocyclic compounds including 1, 3-diazetine. The new Schiff bases [VI] ad derived from 3-((5-hydrazinyl-4-phenyl-4H-1, 2, 4-triazol-3-yl) methyl)-1H-indole [V] which was synthesized by refluxing 5-((1H-indol-3-yl) methyl)-4-phenyl-4H-1, 2, 4-triazole-3-thiol [IV] with hydrazine hydrate in absolute ethanol and this amino compound [V] condensation with different aromatic aldehydes in absolute ethanol to yielded a new Schiff bases [VI] ad. N-acyl compounds [VII] ad were synthesized by addition reaction of acetyl chloride to imine group of Schiff bases in dry benzene. The new diazetine derivatives [VIII] ad synthesized by the reaction of N-acyl compounds [VII] ad with sodium azide in dimethylformamid

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Publication Date
Sun Jun 05 2016
Journal Name
Baghdad Science Journal
Preparation and Spectroscopic Studies of Some Metal Ion Complexes of 2-((4-Formyl-3-Hydroxynaphthalen-2-yl) Diazenyl) Benzoic Acid
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New azo ligand 2-((4-formyl-3-hydroxynaphthalen-2-yl) diazenyl) benzoic acid (H2L) was synthesized from the reaction of 2-aminobenzoic acid and2-hydroxy-1-naphthaldehyde. Monomeric complexes of this ligand, of general formulae [MII(L)(H2O)] with (MII = Mn, Co, Ni, Cu, Zn, Pd, Cd and Hg ) were reported. The compounds were isolated and characterized in solid state by using 1H-NMR, FT-IR, UV–Vis and mass spectral studies, elemental microanalysis, metal content, magnetic moment measurements, molar conductance and chloride containing. These studies revealed tetrahedral geometries for all complexes except PdII complex is Square planar. The study of complexes formation via molar ratio of (M:L) as (1:1). Theoretical treatments of compounds in gas

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Publication Date
Sat Sep 01 2018
Journal Name
Journal Of Pharmaceutical Sciences And Research
Farnesoid X receptor is an exciting new perspective target for treatment of diverse pathological disorders: Review
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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
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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
Tue Jul 01 2025
Journal Name
Russian Journal Of Physical Chemistry A
Electrochemical and Theoretical Study of the Corrosion Inhibition of Carbon Steel Using 3-Allyl-2-mercaptoquinazolin-4(3H)-one in an Acidic Environment
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This study investigates the corrosion inhibition performance of a newly synthesized quinazolinone derivative, AMQ, on mild steel in a hydrochloric acid medium. The inhibition efficiency was evaluated using potentiodynamic polarization at varying inhibitor concentrations (100–250 ppm) and temperatures (303– 333 K). The results showed that AMQ exhibited effective corrosion inhibition, with the highest efficiency of 74% observed at 250 ppm and 323 K. Density Functional Theory (DFT) calculations were conducted to study the electronic properties of AMQ and its adsorption behavior. The thermodynamic parameters, including activation energy, enthalpy, and Gibbs free energy, were calculated, indicating spontaneous adsorption of AMQ onto the meta

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Publication Date
Sat Nov 15 2025
Journal Name
Baghdad Science Journal
Determination of Ni (II) by Forming a New Complex N-(4-(dimethyl amino) benzylidene)-3, 5-Dinitrobenzohydrazide Nickel (II) Chloride
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In this research, the theme for employing a simple and sensitive method is to employ a new Schiff base ligand (N’-(4- (dimethyl amino) benzylidene)-3, 5-dinitrobenzohydrazide) to estimate Ni (II) to form orange complex (N-(4-(dimethyl amino) benzylidene)-3, 5-dinitrobenzohydrazide nickel (II) chloride) in acid medium (hydrochloric acid), it gives an absorption peak at the wavelength 485 nm. The preferred conditions were studied to form the complex and obtain the highest absorbance including concentration of Schiff base ligand, the best medium for complex formation, effects of addition sequence on complex formation, the effect of temperature on the absorbance of the complex formed, and the setting time of the formed complex. The obtained r

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