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.

The aim of this work is synthesis of _Eoly (Vinyl-4-AminoBenzoate) (PVAB) from reaction of _Eoly Vinyl Alkohol PVA with 4-aminobenzoyl chloride in alkaline media. We also prepare the metal complexes of poly (vinyl- 4-aminobenzoate) and antimicrobial properties were evaluated by dilute method against five pathogenic bacteria (Escherichia coli, Shigella dysentery, Klebsiella pneumonae, Staphylococcus aureus, Staphylococcus Albus) and two fungal (Aspergillus Niger, Yeast). All polymer metal complexes showed different activities against the various microbial isolates. The polymer metal complexes showed higher activity than the free polymer.

A novel ligand ((1E)-(2-(4-fluorobenzylidene)amino)methyl) phenyl)diazenyl)-1,3,7-trimethyl-3,7-dihydro-1H-purine-2,6-dione (4-FADPD) was synthesized via the azotization reaction of 2-aminobenzylamine with caffeine, and the resultant compound was condensed with 4-fluorobenzaldehyde to form a newly azo-Schiff base ligand. Its complexes with Cu(II), Ag(I), and Au(III) were synthesized. The results of multi-identifications, including XRD, elemental analysis (C.H.N), UV-vis spectroscopy, FTIR, and 1H-NMR, were used to propose the suggested structures using molar conductivity measurements. These data were utilized to propose appropriate geometric configurations for all complexes. The azo-Schiff base ligand coordinates toward the Cu(II) i

Abstract:

Background: Retinol binding protein 4 (RBP4), an adipokine that participate in a lipid metabolism or insulin resistance through a complex regulatory network. Recently, RBP4 was reported to be associated with many cardiovascular diseases (CVDs) risk factors in patients of type 2 diabetes mellitus (T2DM). This study aims to study the correlation of  serum RBP4 with some markers of glycemic control, dyslipidemia, hypertension and obesity in T2DM Iraqi patients.

Subjects and Methods: one hundred fifty participants were enrolled in this coss-sectional study, 120 of participants were T2DM patients and 30 were apparently healthy individuals to serve as control gro

This search include the synthesis of some new 1,3-oxazepine derivatives have been prepared, starting from reaction of L-ascorbic acid with dry acetone in presence of dry hydrogen chloride afforded the acetal (I). Treatment of the latter with p-nitrobenzoyl chloride in dry pyridine yielded the ester (II) which was dissolved in (65%) acetic acid in absolute ethanol yielded the glycol (III). The reaction of the glycol (III) with sodium periodate in distilled water at room temperature produced the aldehyde (IV). The compound (V) [2-amino-5-mercapato-1,3,4-thiadiazole] was prepared through the reaction of thiosemicarbazide with carbon disulphide (CS2) in entity of anhydrous (Na2CO3) in (abs. ethanol ). Compound (VI) [2-(5-mercapto-1,3,4-thiadiaz

In the cuurent article, the photophysical properties of 3,6-bis(5-bromothiophen-2-yl)-2,5-bis(2-ethylhexyl)-2,5-dihydropyrrolo[3,4-c]pyrrole-1,4-dione were investigated. The visible absorption bands at 527, 558 and 362 nm in propylene carbonate and the compound was found to be fluorescent in solution and in the plastic film with emission wavelengths between 550- 750 nm. The Stokes Shift of P.C., acetonitrile, diethyl ether, Tetrahydrofuran THF, cyclohexane, dibutyl ether, and dichloromethane DCM  are 734, 836, 668, 601, 601, 719, and 804 cm^-1 in respectively. The Stokes Shift Δ was less in THF and cyclohexane, than the solvents, which indicates that the energy loss is less between the excitation and fluorescence states. The

A series of novel hybrid molecules containing 1,3,4-oxadiazole and 1,3,4-thiadiazole moieties bearing an ibuprofen moiety were designed, synthesized, and evaluated for their in vitro antibacterial activity against Gram-positive and Gram-negative bacteria. A carboxylic acid compound with a 1,3,4-thiadiazole unit was synthesized via the coupling reaction of 5-(1-(4-isobutylphenyl) ethyl)-1,3,4-thiadiazol-2-amine with benzoic acid. This compound was then used as the starting material to make several new 1,3,4-oxadiazole derivatives through ring closure reactions, after first converting it to its ester (methyl 4-(5-(1-(4-isobutylphenyl)ethyl)-1,3,4-thiadiazol-2-yl) benzoate) and then to the acid hydrazide (4-(5-(1-(4-isobutylphenyl) eth

This work includes the synthesis and identification of ligand {3-((4-acetylphenyl)amino)-5,5-dimethylcyclohex2-en-1-one} (HL* ) by the treatment of 5,5-dimethylcyclohexane-1,3-dione with 4-aminoacetophenone under reflux. The ligand (HL* ) was identified via FTIR, Mass spectrum, elemental analysis (C.H.N.), 1H and 13C-NMR spectra, UV-Vis spectroscopy, TGA and melting point. The complexes were synthesized from ligand (HL* ) mixed with 3-aminophenol (A) and metal ion M(II), where M(II) = (Mn, Co, Ni, Cu, Zn and Cd) at alkaline medium to produce complexes of general formula [M(L* )(A)] with (1:1:1) molar ratio. These complexes were detected via FT-IR spectra, UV-Vis spectroscopy as well as elemental analysis (A.A) and melting point, conductivit

This work includes the synthesis and identification of ligand {3-((4-acetylphenyl)amino)-5,5-dimethylcyclohex2-en-1-one} (HL* ) by the treatment of 5,5-dimethylcyclohexane-1,3-dione with 4-aminoacetophenone under reflux. The ligand (HL* ) was identified via FTIR, Mass spectrum, elemental analysis (C.H.N.), 1H and 13C-NMR spectra, UV-Vis spectroscopy, TGA and melting point. The complexes were synthesized from ligand (HL* ) mixed with 3-aminophenol (A) and metal ion M(II), where M(II) = (Mn, Co, Ni, Cu, Zn and Cd) at alkaline medium to produce complexes of general formula [M(L* )(A)] with (1:1:1) molar ratio. These complexes were detected via FT-IR spectra, UV-Vis spectroscopy as well as elemental analysis (A.A) and melting point, conductivit

The research included the preparation of cyclic compounds from thiazoles, imidazoles and oxazepines from the reaction of cyclization starting material that acts Schiff bases, which is a raw material in the formation of cyclic compounds from Schiff's(B1) by reaction of 4- aminobenzenesulfonylamide with 4-hydroxyacetophenone which can used to synthesized two lines. The first introducing the preparation of pyrazoles [B4, B5] from ester [B2], which derived to acid hydrazide[B3] with hydrazine hydrate and final pyrazoles obtained by the reaction with diethylmalonate and acetylacetone. The second including prepared the new 1,3-oxazepine1,5-dione derivatives[B6,B7,B8] from adding different anhydrides to the base[B1] as a seven membered ring ; te