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.

In this work, we focused on studying 1,4-naphthoquinones and their derivatives, and knowing the methods of preparing them using different auxiliary agents and forming derivatives containing heterocyclic rings, active groups and saturated rings containing heterogeneous elements . In addition, due to their strong antibacterial, antifungal and anticancer activity, 1,4-naphthoquinone compounds biological importance and are considered a source of various pharmaceutical compounds.

The adsorption process of reactive blue 49 (RB49) dye and reactive red 195 (RR195) dye from an aqueous solutions was explored using a novel adsorbent produced from the sunflower husks encapsulated with copper oxide nanoparticle (CSFH). Primarily, the features of a CSFH, such as surface morphology, functional groups, and structure, were characterized. It was determined that coating the sunflower husks with copper oxide nanoparticles greatly improved the surface and structural properties related to the adsorption capacity. The adsorption process was successful, with a removal efficiency of 97% for RB49 and 98% for RR195 under optimal operating conditions, contact time of 180 min, pH of 7, agitation speed of 150 rpm, initial dye concentration

Rosemary (Rosmarinus officinalis L.) is one of the most economically important species of the family Lamiaceae. Rosemary extract was examined by applying 2.2-diphenyl-1- picrylhydrazyl (DPPH) radical-scavenging assays. The result proved that rosemary extract had a higher antioxidant activity by absorption at a wavelength of 517a nm by using three different concentrations (0.5, 1.0 and 3) mg/ml which performed the absorbance at (2. 314, 0. 211 and 0.296) nm in comparison with control (21.8, 92.2 and 90) nm respectively. Results obtained using chemical detection of the phytochemicals indicated the presence of flavonoids, phenols, saponins, Steroids and cardiac in rosemary water extract. Water extracts of R. officinalis leaves were inves

Numerical Investigation was done for steady state laminar mixed convection and thermally and hydrodynamic fully developed flow through horizontal rectangular duct including circular core with two cases of time periodic boundary condition, first case  on the rectangular wall while keeping core wall constant and other on both the rectangular duct and core walls. The used governing equations are continuity momentum and energy equations. These equations are normalized and solved using the Vorticity-Stream function and the Body Fitted Coordinates (B.F.C.) methods. The Finite Difference approach with the Line Successive Over Relaxation (LSOR) method is used to obtain all the computational results the (B.F.C.) method is used to generate th

The present work involved four steps: First step include reaction of acrylamide ,N-?-Methylen-bis(acryl amide) and N-tert Butyl acryl amide with poly acryloyl chloride in the presence of triethyl amine (Et3N) as catalyst, the second step include homopolymerization of all products of the first step by using benzoyl peroxide(BPO) as initiator in (80-90)Co in the presence of Nitrogen gas(N2). In the third step the poly acrylimide which prepare in second step was convert into potassium salt by using alcoholic potassium hydroxide solution. Fourth step include Alkylation of the prepared polymeric salts in third step by react it with different alkyl halides(benzyl chloride, allylbromide , methyl iodide) by using DMF as solvent for(10-12) hours.

A new derivative of PAM, acrylamide was copolymerized with succinic anhydride, and the reaction product reacted with three dyes, anthocyanin, bromophenol, and thymol. The prepared polymers were characterized by X-ray diffraction, FT-IR and UV-visible spectroscopy, proton nuclear magnetic resonance spectrometry, and thermal analysis. FT-IR spectroscopy showed the disappearance of two bands near 3450 and 3380 cm-1 for the stretching vibrations of the primary amine which indicates for the formation of amides. The UV-photolysis of aqueous solutions of different concentrations of the polymers was studied. Polyacrylamide-g-succinic anhydride showed an increase in polymerization under light. An increase of ~ 50% was observed for a 200 mg/L

Background: The PMMA polymer denture base materials are low mechanical properties, adaptation of the denture base to underlying tissue is important for retention and stability of denture. The aim of the study was toevaluate the effect of mixtureZrO2-Al2O3 nanoparticles on impact strength, transverse strength, hardness, roughness, denture base adaptation of heat cured acrylic resin denture base material. Materials and methods: One hundred (100) specimens were prepared, the specimens were divided into five groups (20 specimens to each) according to the test type, each group was subdivided in to two subgroups (control and experimental) each subgroup consist of 10 specimens, the experimental group included mixture of 2% (ZrO2-Al2O3ratio2:1) b