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.

Asthma is chronic inflammatory disease affecting 5% of world population. Characterized by eosinophilic type2 inflammation. FKBP51 immunophilin, important modular protein of glucocorticoid receptor (GR). We aimed to evaluate immunocytochemical localization of GR and FKBP51 in induced sputum cells by using immunocytochemical method and immunofluorescent ant-FKBP51 and anti –GR antibody and estimation of IgE and Type 2 inflammatory cytokine IL-5,IL-13 by ELISA technique.GR in the sputum show non-significant decrease of cytoplasmic distribution of the patient groups and highly significant increase in steroid treated patients and non-significant increase in nuclear distribution in non-steroid, FKBP51 nuclear localization show non-significant i

A new chelate complexes of Co(II),Ni(II),Zn(II) and Cd(II) were prepared by reacting these ions with the ligand 2-[4- Carboxy methyl phenyl azo]-4,5-diphenyl imidazole (4CMeI) The preparation were conducted after fixing the optimum conditions such as (pH) and concentration .UV- visible spectra of these complex solutions were studied for a range of (pH) and concentration which obey lampert-Beers Law.The structures of complexes were deduced according to mole ratio method which were obtained from the spectroscopic studies of the complex solutions .The ratios of metal: ligand obtained were (1:2) for all complexes..(UV-Vis) absorption spectra and The infrared spectra of the chelating complexes were studied ,this may indicate that coordination be

In this work, we synthesized thirteen compounds of 1-(2-furoyl)thiourea derivatives 1-13 by conversion of 2-furoyl chloride to 2-furoyl isothiocyanate by reacting it with potassium thiocyanate in dry acetone in a quite short reflux time then, in the same pot, different of (primary and secondary amines) were added individually to achieve thiourea derivatives. The products were characterized spectroscopically using (FT-IR, 1H NMR and 13C NMR) techniques. Some of them were evaluated as antioxidant agents using DPPH radical scavenging method, and all were examined theoretically as enzyme inhibitors against Bacillus pasteurii urease (pdb id: 4ubp) and  by studying  molecular docking using Autodock (4.2.6) software.

Direct agglutination test was used to evaluate the immunogenicity of three different antigens inoculated in hamsters as one , two and three doses which were: Group (1) inoculated with autoclaved killed Leishmania tropica , Group (2) inoculated with BCG vaccine alone while Group (3) inoculated with mixed antigens (autoclaved killed Leishmania "AKL"+ BCG).(4) Control animals inoculated with phosphate buffer saline. The maximum level of antibody titers were evaluated in animal inoculated with one , two or three dose of mixed antigens (320 , 640 and 1280) respectively when it compared with animals inoculated with corresponding doses of AKL antigen (80 , 160 and 320) respectively. While the minimum level of antibody titers were observed in ani

          Using sodium4-((4,5-diphenyl-imidazol-2-yl)diazenyl)-3-hydroxynaphthalene-1-sulfonate (SDPIHN) as a chromogenic reagent in presence of non-ionic surfactant (Triton x-100) to estimate the chromium(III)  ion if the wavelength of this reagent 463 nm to form a dark greenish-brown complex in wavelength 586 nm at pH=10,the complex was stable for longer than 24 hours. Beer's low, molar absorptivity 0.244×10⁴L.mol^-1.cm^-1, and Sandal's sensitivity 0.021 µg/cm² are all observed in the concentration range 1-11 µg/mL. The limits of detection (LOD) and limit of quantification (LOQ), respectively, were 0.117 µg/mL and 0.385µg/mL. (mole ratio technique, job's method) were employed to

Thiamethoxam is a synthetic organic insecticide belong to The most significant new class of pesticides created in the last thirty years is neonicotinoids. This study's objective was to determine the effect of thiamethoxam, lambda cyhalothrin and their combination on biochemical parameters, the levels of free radicals and enzymes activities liver of male.Forty Rats ( 150-170 g ) were used. animals Were separated into four groups, each with ten rats.The Gp1 was used as control, the Gp2 was used to study the effect of thiamethoxam for 3weeks, the Gp3 was employed to examine the impact of lambda cyhalothrin for 3 weeks and the Gp4 was used to research the impact of thiamethoxam and lambda cyhalothrin for 3 weeks. thiamethoxam and/or lambda cyha

Bilastine (BL) is a novel non-sedating second-generation antihistamine, and its bioavailability is about 60%. Objective: To compare the bioavailability of prepared oral self-nanoemulsions of BL (BL-SNE) with that of pure BL and marketed tablets. Methods: Four groups of Wistar rats were used in this study, each with six rats weighing between 200 and 250 g. They were treated orally using a a gavage tube. The groups were fed either with conventional tablets ("Alerbix®") after being ground and dispersed with deionized water (DIW), treated with BL-SNE or fed with pure BL powder suspension. The fourth group did not receive any medication. The concentration of BL in the rat’s plasma was measured using HPLC. We used Trandolapril as an an interna