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.

This research is presenting a study of optical and structural properties of (Fe2O3)1-x(MgO)x composites synthesized as thin film that can be used as a gas sensor. Pulsed laser deposition technique was used to prepare thin films of (Fe2O3)1-x(MgO)x. The pattern of X-ray diffraction of the composites powder showed the consistency of iron oxide (α-Fe2O3) hematite phase along with the planes (104) and (110) as preferred planes for crystal growth where the intensities of which varied with MgO content. The crystal size of the thin film material was varied in between (26.8-35.1) nm. The diffraction pattern of the pulsed laser deposited thin films was absent from any diffraction peaks. The maximum transparency obtained of hematite

Extension of bandwidth for high reflectance zone for the spectral region (8-14pm) was studied adapting the concept of contiguous and overlapping high reflectance stacks. Computations was carried out using the modified characteristic matrix theory restricted to near-normal incidence of light on dielectric , homogenous and isotropic symmetrical stack. Certain precautions must be taken in the choice of stacks to avoid deep —reflectance minima from developing within the extended high reflectance region. Results illustrate that the techniques of extending the high reflectance regions are applicable not only to mirrors , but also to short-and long-edge filter and to narrow band pass filters.

Spin coating technique used to prepare ZnPc, CdS and ZnPc/CdS blend thin films, these films annealed at 423K for 1h, 2h and 3h. Optical behavior of these films were examined using UV-Vis. and PL. The absorption spectrum of ZnPc shows a decreasing in absorption with the increase of annealing time while CdS spectrum give a clearly absorption peak at~510 nm. Energy gap of ZnPc increases from 1.41 to 1.52 eV by increasing the annealing time. E_g of CdS decrease by increasing annealing time, from 2.3 eV to 2.2 eV. The intensities of the peaks obtained from PL spectra were strongly dependent on annealing time and confirmed the results obtained from UV-Vis. D.C. conductivity measurement showed that all the thin films have two differen

The study of properties of space of entire functions of several complex variables was initiated by Kamthan [4] using the topological properties of the space. We have introduced in this paper the sub-space of space of entire functions of several complex variables which is studied by Kamthan.

A study was carried out to analysis of some heavy metals in nine different types of vinegar, belong to Grape, Apple, Synthetic White, Date, Hawthorn, Garlic, Cactus, Pomegranate and Ginger vinegar, which are locally available in Iraqi folk medicine markets. The concentrations of heavy metals in the studied samples including, Cr, Mg, Mn, Zn, Fe, Cd, Ni, Pb and Ag, were determining by using flame atomic absorption spectrophotometry. All data were subjected to statistical analysis by calculating accuracy, precision and correlation coefficient for each concentrations level. The results indicate that Ni was recorded the highest concentration in all studied samples except, Ginger and cactus vinegar, each one receded the highest concentration valu

Three types of medical commercial creams Silvazine, Cinolon Tar and Hydroquinon Domina were incorporated in this study. The medical creams were taken directly and placed uniformly on the glass slide. Each type of pharmaceutical was weighed at 1 mg and dispersed on an area of 1x1 cm. This process ensures same thickness for all samples. The creams were analyzed by using double-beam UV/visible spectrophotometer Metertech SP8001. The absorption spectrum for each of samples was measured against wavelength range of 300–700 nm.

Catalytic microwave-assisted pyrolysis of biomass is gaining popularity as an alternative to fossil fuels due to health, environmental, climate, and economic issues. This study conducted a catalytic pyrolysis process of the Albizia plant's branches using an Iraqi clay catalyst (bentonite) focusing on the variables including the biomass-particle size, experimental time, microwave power level, and the catalyst-to-biomass ratio. The physical and chemical properties of the resulting biofuel were analyzed presented by HHV, acidity, density, viscosity, GC-MS, FTIR for bio-oil and SEM, EDX, BET, HHV, FTIR for biochar. The study revealed that addition of bentonite as a catalyst led to enhanced production of biogas produced from 5% to 45% an