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 study Candida speices was diagnosed in 26 swab samples from patients with denture stomatitis , investigates the antagonism activity of Lactobacillus was investigated against the yeast of Candida albicans in vitro.Results revealed that The inhibition effect of Lactic Acid Bacteria against C.albicans was examined in solid medium, L.plantarum gave higher inhibition average 11mm followed by L.acidophillus with average 9 mm and, L.fermentum , L.casei with averages 7 mm. Whereas the filtrates, the highest inhibition zone were 20 and 16 mm by L. plantarum and L.acidophillus, respectively.

The study was conducted in the Tigris River in Baghdad during May 2021 until March 2022 to follow the impact of climate change, rising temperatures, and the presence of pollutants on the dynamics of phytoplankton and some physicochemical variables from four sites. The results showed that the climatic conditions during different seasons, in addition to the nature of the sampling sites, have a clear and significant impact on the studied traits and, in turn, affect the phytoplankton community. The highest average temperature (30.67 ˚C) was recorded; the pH values ranged between 8.70 & 6.75; the electrical conductivity (1208.18-770.11 µS/cm ) and the total dissolved solids (TDS) (778.95- 439.49 mg/L) were evaluated. Upon measuring

This study evaluated the structural changes of enamel treated by the Regenerate system and carbon dioxide (CO2) laser against acid challenge. Thirty human enamel slabs were prepared and assigned into three groups: Group I: untreated (control); Group II: treated with the Regenerate system; and Group III exposed to CO2 laser. All specimens were subjected to an acid challenge (pH 4.5–7.0) for 14 days. Specimens were evaluated and compared at 120 points using five Raman microspectroscopic peaks; the phosphate vibrations ν1, ν2, ν3, and ν4 at 960, 433, 1029, and 579 cm−1, respectively, and the carbonate at 1070 cm−1, followed by Vickers microhardness test. The ratio of carbonate to phosphate was correlated to the equivalent mic

The phenyl hydrazine was react readily with acetic acid chloride in [1:2] ratio in alkyl of ethanolic solution, and refluxe for five hours to produce a new ligand of (N-Carboxymethyl-N-phenyl-hydrazino)-acetic acid [H2L].

In the present work we prepared heterojunction not homogenous CdS/:In/Cu2S) by spray and displacement methods on glass substrate , CdS:In films prepared by different impurities constration. Cu2S prepared by chemical displacement method to improve the junction properties , structural and optical properties of the deposited films was achieved . The study shows that the film polycrystalline by XRD result for all film and the energy gap was direct to 2.38 eV with no effect on this value by impurities at this constration .