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 research, silver nanoparticles (AgNPs) were manufactured using aqueous extract of mushroom Pleurotus ostreatus. Anticancer potential of AgNPs was investigated versus human breast cancer cell line (MCF-7). Cytotoxic response was assessed by MTT assay. AgNPs showed inhibition effect at the following concentrations 12.5, 25, 50, 100 and 200 µg/ml versus MCF-7 cell line, and all treatments had a positive result. The MCF-7 cells were inhibited up to 85.14 % at the concentration 200 μg/ml of AgNPs which reduced cells viability to 14.86%, while 12.5 μg/ml of AgNPs caused 24.23% cells inhibition with reduction of cells viability to 75.77%.

In this research, the X-ray diffraction pattern was used, which was obtained experimentally after preparation of barium oxide powder. A program was used to analyze the X-ray diffraction lines of barium oxide nanoparticles, and then the particle size was calculated by using the Williamson-Hall method, where it was found that the value of the particle size is 25.356 nm. Also, the dislocation density was calculated, which is equal to1.555 x1015 (lines/nm2), and the value of the unit cell number was also calculated, as it is equal to 23831.

Green synthesis is depending on preparation of nano composited SiO₂/V₂O₅ by using the modified sol-gel method depending on rice husk ash as a source for the extraction of silica gel and the product powder of nano composited SiO₂/V₂O₅ characterization by many techniques such as X-ray diffraction spectroscopy (XRD), field emission scanning electron microscopy (FESEM), and N₂ adsorptions/desorption isotherms (BET). This study also includs the biological effectiveness of SiO₂/V₂O₅ and its effect on inhibiting bacterial growth after the prepared nanomaterial was applied to wound dressings, which gave a promising result for its use as

The Voluntary Obedience has great importance for the modern taxes systems and its management and this is meant the taxpayer whom in charge to pay of his taxes obligations voluntarily , he is very known of himself whereas he prepared his finishing accountings and present them as samples prepared by taxes management and settle the tax sum directly according to specified income , which has an impact to find end to tax evasion as result lead to increase the tax income and achieve the justice for the taxpayer and the state treasury

In the present study, chitosan Schiff base has been prepared from chitosan reaction with p-chloro benzaldehyde. The AuNPs and AgNPs were manufactured by extract of onion peels as a reducing agent. The AuNPs and AgNPs that have been synthesized were characterized through UV-vis spectroscopy, XRD analyses and SEM microscopy. The polymer blends of the chitosan / PEG has been prepared by using the approach of solution casting. Chitosan Schiff base / PEG Au and Ag nanocomposites were synthesized, nanocomposites and polymer blends have been characterized by FTIR which confirm the formation of Schiff base by revealing a new band of absorption at 1693 cm-1 as a result of the (C=N) imine group. FESEM, DSC and TGA confirm the thermal stability

Anchusa strigosa - prickly alkanet from Boraginaceae grows in roadsides, and fields of a broad range of habitats from mediterranean woodlands, to steppe vegetation, to true desert. It is commonly known as" him him" or "lisan al thawr". Anchusa can withstand hard weather conditions and hence is widely cultivated. The color of its flowers can range from pure white to deep cobalt blue. Various parts of A. strigosa are used in traditional medicine for treating several diseases or symptoms, such as abdominal pain, bronchitis, cough, and diarrhea. The goal of this study was to examine the cytotoxic effect of the crude extract of A. strigosa roots and leaves and their fractions against various tumor cell lines: adenoc

Alloys of GaxSb1-x system with different Ga concentration (x=0.4, 0.5, 0.6) have been prepared in evacuated quartz tubes. The structure of the alloys were examined by X-ray diffraction analysis (XRD) and found to be polycrystalline of zincblend structure with strong crystalline orientation (220). Thin films of GaxSb1-x system of about 1.0 μm thickness have been deposited by flash evaporation method on glass substrate at 473K substrate temperature (Ts) and under pressure 10-6 mbar. This study concentrated on the effect of Ga concentration (x) on some physical properties of GaxSb1-x thin films such as structural and optical properties. The structure of prepared films for various values of x was polycrystalline. The X-ray diffraction analy