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.
To obtain the approximate solution to Riccati matrix differential equations, a new variational iteration approach was proposed, which is suggested to improve the accuracy and increase the convergence rate of the approximate solutons to the exact solution. This technique was found to give very accurate results in a few number of iterations. In this paper, the modified approaches were derived to give modified solutions of proposed and used and the convergence analysis to the exact solution of the derived sequence of approximate solutions is also stated and proved. Two examples were also solved, which shows the reliability and applicability of the proposed approach.
This paper is concerned with the blow-up solutions of a system of two reaction-diffusion equations coupled in both equations and boundary conditions. In order to understand how the reaction terms and the boundary terms affect the blow-up properties, the lower and upper blow-up rate estimates are derived. Moreover, the blow-up set under some restricted assumptions is studied.
The main objective of this paper is to find the order and its exponent, the general form of all conjugacy classes, Artin characters table and Artin exponent for the group of lower unitriangular matrices L(3,? p ), where p is prime number.
In this study, the ability of pistachio shells, as an unconventional adsorbent, to recover thallium cations from contaminated aqueous solutions was investigated. To achieve the objective of the study, practical experiments were conducted using a batch-mode adsorption unit under various operating conditions. The results obtained showed that the pistachio shells have the ability to remove thallium cations with a high efficiency exceeding 86% at room temperature. The results indicated that the maximum treatment efficiency was achieved at values of 7, 350 rpm, 86 ppm, 5 g, 150 min of pH, agitation speed, initial concentration of thallium, dosage of pistachio shell used, and contact time, respectively. Morphological results confirmed tha
... Show MoreThe reaction of(2-oxo-2H-chromen-3-Carbonyl chloride)(k1) with hydrazine in boiling ethanol gives the hydrazide(K2).When compound (k2) reacts with various aromatic aldehydes ,the corres ponding Schiff bases(k3–k4) achieve new series of thiazotidines (k5–k6) and azetidinones (k7–k8) obtained from the reactions of appropriate Schiff bases with mercapto acetic acid and chloro acetyl chloride respectively. All the compounds are characterized by FT-IR,1H-NMR and GC-Ms.
The reaction of methyldopa with o-vanillin in refluxing ethanol afforded Schiff base and characterized through physical analysis with a number of spectra also the study of biological activity. The geometry of the Schiff base was identified through using (C.H.N) analysis, Mass, 1H-NMR, FT-IR, UV-Vis spectroscopy. Metal complexes of Cr3+, Mn2+, Co2+, Ni2+, Cu2+, Zn2+, Cd2+ and Hg2+ with Schiff base have been prepared in the molar ratio 2:1 (Metal:L), (L = Schiff base ligand) except Hg2+ at molar ratio 1:1 (Hg:L). The prepared complexes were characterized by using Mass, FT-IR and UV-Vis spectral studies, on other than magnetic properties and flame atomic absorption, conductivity measurements. According to the results a dinuclear octahe
... Show MoreThe reaction of methyldopa with o-vanillin in refluxing ethanol afforded Schiff base and characterized through physical analysis with a number of spectra also the study of biological activity. The geometry of the Schiff base was identified through using (C.H.N) analysis, Mass, 1H-NMR, FT-IR, UV-Vis spectroscopy. Metal complexes of Cr3+, Mn2+, Co2+, Ni2+, Cu2+, Zn2+, Cd2+ and Hg2+ with Schiff base have been prepared in the molar ratio 2:1 (Metal:L), (L = Schiff base ligand) except Hg2+ at molar ratio 1:1 (Hg:L). The prepared complexes were characterized by using Mass, FT-IR and UV-Vis spectral studies, on other than magnetic properties and flame atomic absorption, conductivity measurements. According to the results a dinuclear octahedral geo
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