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.

This review article summarizes our research focused on Cu(In, Ga)Se2 (CIGS) nanocrystals, including their synthesis and implementation as the active light absorbing material in photovoltaic devices (PVs). CIGS thin films were prepared by arrested precipitation from molecular precursors consisting of CuCl, InCl3, GaCl3 and Se metal onto Mo/soda-lime glass (SLG) substrates. We have sought to use CIGS nanocrystals synthesized with the desired stoichiometry to deposit PV device layers without high temperature processing. This approach, using spray deposition of the CIGS light absorber layers, without high temperature selenization, has enabled up to 1.5 % power conversion efficiency under AM 1.5 solar illumination. The composition and morphology

A polycrystalline PbxS1-x alloys with various Pb content ( 0.54 and 0.55) has been prepared successfully. The structure and composition of alloys are determined by X-ray diffraction (XRD), atomic absorption spectroscopy (AAS) and X-ray fluorescence (XRF) respectively. The X-ray diffraction results shows that the structure is polycrystalline with cubic structure, and there are strong peaks at the direction (200) and (111), the grain size varies between 20 and 82 nm. From AAS and XRF result, the concentrations of Pb content for these alloys were determined. The results show high accuracy and very close to the theoretical values. A photoconductive detector as a bulk has been fabricated by taking pieces of prepared alloys and polished chemic

A theoretical study by using computer model is presented to study the energy characteristics of the vibrational – rotational levels as a function of the vibrational and rotational quantum number, respectively. The calculations were based on the basis of a multilevel model taking into account the non-equilibrium population of the rotational levels. The computational investigation has been performed to examine the vibrational-rotational characteristics of some hydrogen halides chemical laser molecules. This program takes into account the various molecules of chemical lasers such as, Hydrogen Fluoride (HF), Deuterium Fluoride (DF), Hydrogen Chloride (HCl), and Deuterium Chloride (DCl). The practical difficulties associated with this

Aluminum oxide thin films were prepared by dc reactive sputtering technique using different mixing ratios of argon and oxygen gases (90:10, 70:30, 50:50, 30:70, and 10:90). These films were characterized to introduce their crystalline structures, surface morphology, and elemental composition. A progressive transition occurs from a predominantly amorphous to a highly crystalline Al2O3 film as the oxygen content in the Ar:O2 gas mixture is increased. Increasing the oxygen content leads to a progressive decrease in surface roughness, resulting in smoother and more uniform films with finer granular features. The oxygen-rich environments yield the smoothest surfaces, while argon-rich environments result in significantly rougher surfaces. These f

Titanium dioxide (TiO2) thin films were prepared under different pressures with values (15, 30, 60 and 120) Pa using the DC reactive magnetron homemade system with mixed gases of argon and oxygen in ratio (50:50). The result of X-ray diffraction patterns discovered that the structure of the deposited films was polycrystalline, including the phase of anatase. All the appeared peaks were matched to the planes (101), (004), (105), and (211) of diffracted states. Both the intensities and the number of the appeared peaks are declined according to the increased pressure, and the plane of (101) is be considered the preferential grown plane, it is taking a maximum texture factor. Both the lattice constant and the atomic inter-planer spacing take th

This paper presents a numerical analysis using ANSYS finite element program to simulate the reinforced concrete slabs with spherical voids. Six full-scale one way bubbled slabs of (3000mm) length with rectangular cross-sectional area of (460mm) width and (150mm) depth are tested as simply supported under two-concentrated load. The results of the finite element model are presented and compared with the experimental data of the tested slabs. Material nonlinearities due to cracking and crushing of concrete and yielding of reinforcement are considered. The general behavior of the finite element models represented by the load-deflection curves at midspan, crack pattern, ultimate load, load-concrete strain curves and failure m