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.

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.

Flame atomic absorption spectrophotometer (FAAS) was used in this study to determine the concentrations of heavy metals such as Ca, Fe, Mn, Cd, Co, Cr, Ni, Cu, Pb and Zn in some food additives of Iraq. The order of metal contents in food additives was found to be Ca ˃ Mn ˃ Fe ˃ Cu ˃ Zn ˃ Pb ˃ Cr ˃ Ni ˃ Co ˃ Cd. The concentration level of each metal was compared with that recommended by food agriculture organisation (FAO) and world health organisation (WHO). Calibration curves were linear for all standard solutions of heavy metals in the range starting from 0.02-0.4 mg/kg for Cd to 11-100 mg/kg for Ca. The correlation coefficients values (R2) of calibrations were investigated and ranged from 0.9971 for Cr to 0.9999 for Ca. Th

In this study, dependence of gamma-ray absorption coefficient on the size of Pb particle size ranging from 200µm up to 2.5mm, using different weights of each particle size. The results show that gamma-ray attenuation coefficient is inversely proportional with the size of Pb particle size due to the reduction of the spaces between the lead particles.

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

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.

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

In recent years, there has been a rapid development in research on high performance ceramics for mechanical, electrical and medical industries. This development will be shown for alumina as a representative for oxide ceramics powders.
Dry–pressing forming technique was used to prepare different ceramic compacts for alumina grafted by polymethacrylate polymers. All Alumina compact were fired firstly at 1200 ◌ْ C, then
at 1600 ◌ْ C.
Mechanical strength was examined in different means, some
depends on compression and other depends on impact. Hardness was
also measured .The results obtained were compared with that of
Alumina compact prepared under the same condition from Alumina
especially made for pressing .

The main process, for the elimination of cholesterol from the human body, involves the alteration of cholesterol into bile acid (BA), by the liver. The farnesoid X receptor (FXR), a member of the nuclear receptor superfamily, is essential for the regulation of BA, glucose, and lipid metabolism. It is largely found in the liver, intestines, kidney, and adrenal glands, and to a smaller degree in the heart and adipose tissue. The binding locations, of the FXR, are in close proximity to formerly undisclosed target genes, with distinctive activities associated with transcriptional regulators, autophagy, apoptosis, hypoxia, inflammation, RNA processing, and a number of cellular signaling pathways. The preservation of BA homeostasis, by the FXR, e