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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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... Show MoreIn this study the new azo compounds (3compounds) for nitrogen bases (Adenine and Cytosine) are synthesized through two reaction steps (formation of diazonium salt and coupling reaction). The compounds have been characterized by FTIR, melting point, and ultra-violate (UV) spectra. All synthesized compounds have been estimated in vitro for their antimicrobial activities against two species of bacteria(E.coli, S.aureus)and one kind of fungi ( Aspergillus flavus) .The results show that these compounds have very good antibacterial and antifungal activities especially compounds 1 and 3.To study the effect of these compounds were making some physiological tests on rats are made ,the results of hematological study showed decreasing level of
... Show MoreA new series of ?-D-glucose as Schiff bases derivatives is synthesized and characterized with studying their bioactivity. Hydroxyl groups at C (1,2&5,6) sugar moiety are converted into acetal form through a reaction with dry acetone using phosphoric acid and anhydrous zinc chloride as catalysts producing 1,2:5,6-di-O-isopropyledine ?-D-glucofuranose(I). The five memberd ring acetal of C(5,6) is hydrolyzed with acetic acid (65%)and a reaction of the new product with sodium periodate is carried on to get an aldehyde moiety which is used to produce a new series of Schiff bases through reacting with different amino compounds such as 4-amino antipyrene . The suggested chemical structures of the prepared compounds are confirmed by using UV., FT
... Show MoreThe aim of this study is to investigate the kinetics of copper removal from aqueous solutions using an electromembrane extraction (EME) system. To achieve this, a unique electrochemical cell design was adopted comprising two glass chambers, a supported liquid membrane (SLM), a graphite anode, and a stainless-steel cathode. The SLM consisted of a polypropylene flat membrane infused with 1-octanol as a solvent and bis(2-ethylhexyl) phosphate (DEHP) as a carrier. The impact of various factors on the kinetics constant rate was outlined, including the applied voltage, initial pH of the donor phase solution, and initial copper concentration. The results demonstrated a significant influence of the applied voltage on enhancing the rate of c
... Show MoreTwo series of bent and liner core mesogen containing 1,2,4-traizole ring [VI]a,g and series were synthesized by many steps starting from esterification of isophthalic acid and terephathalic acid with methanol to yield diester compound [I]a,b which was converted to their acid hydrazide [II]a,b and the acid hydrazide reacted with ammonium thiocyanate or diester reacted with thiosemicarbazide to yield compounds [III]a,b. Then cyclization by 4% NaOH to yielded 1,2,4 traizole-3- thiol compounds [IV]a,b , afterword adding hydrazine hydrate to yield compounds [V]a,b. These compounds condensated with different substituted aldehyde to give new Schiff bases[VI]a,b ,[VII]a,b . Also , reaction acid hydrazide [II]a,b with aldehyde [VII] to yielded Schif
... Show MoreNitrogen-comprising heterocyclic compounds and their derivatives have empirically been invaluable as therapeutic agents. Fundamentally, 4-chloro-6-nitro-2-amino-1,3-benzothiazole 1 was synthesized via bromination of 2-chloro-4-nitro aniline with ammonium thiocyanate. This new heterocyclic haloorganoamino-1,3-benzothiazole derivative, was a starting material, which condensed and tethered with three different aromatic aldehyde pendant arm in presence of ethanol and glacial acetic acid isolating an interesting sequence of tridentate Schiff bases 2-4. These compounds were used for complexation reactions in 1:1 (metal: ligand) stoichiometry to obtain heteroleptic Al(III), Ni (II) and K(I) benzothiazole chelat
... Show MoreCoupling reaction of 2-amino benzoic acid with the 8-hydroxy quinoline gave the azo ligand (H2L): 5-(2-benzoic acid azo )-8-hydroxy quinoline.Treatment of this ligand with some metal ions (CoII, NiII and CuII ) in ethanolic medium with a (1:2) (M:L) ratio yielded a series of neutral complexes with general Formula[M(HL)2],where: M=Co(II), Ni(II) and Cu(II), HL=anion azo ligand (-1).The prepared complexes were characterized using flame atomic absorption,FT-IR and UV-Vis spectroscopic methods as well as magnetic susceptibility and conductivity measurements.