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.

Cu X Zn1-XO films with different x content have been prepared by
pulse laser deposition technique at room temperatures (RT) and
different annealing temperatures (373 and 473) K. The effect of x
content of Cu (0, 0.2, 0.4, 0.6, 0.8) wt.% on morphology and
electrical properties of CuXZn1-XO thin films have been studied.
AFM measurements showed that the average grain size values for
CuXZn1-xO thin films at RT and different annealing temperatures
(373, 473) K decreases, while the average Roughness values increase
with increasing x content. The D.C conductivity for all films
increases as the x content increase and decreases with increasing the
annealing temperatures. Hall measurements showed that there are
two

A thin CdS Films have been evaporated by thermal evaporation technique with different thicknesses (500, 1000, 1500 and 2000Å) and different duration times of annealing (60, 120 180 minutes) under 573 K annealing temperature, the vacuum was about 8 × 10-5 mbar and substrate temperature was 423 K. The structural properties of the films have been studied by X- ray diffraction technique (XRD). The crystal growth became stronger and more oriented as the film thickness (T) and duration time of annealing ( Ta) increases.

Copper oxide thin films were deposited on glass substrate using Successive Ionic Layer Adsorption and Reaction (SILAR) method at room temperature. The thickness of the thin films was around 0.43?m.Copper oxide thin films were annealed in air at (200, 300 and 400°C for 45min.The film structure properties were characterized by x-ray diffraction (XRD). XRD patterns indicated the presence of polycrystalline CuO. The average grain size is calculated from the X-rays pattern, it is found that the grain size increased with increasing annealing temperature. Optical transmitter microscope (OTM) and atomic force microscope (AFM) was also used. Direct band gap values of 2.2 eV for an annealed sample and (2, 1.5, 1.4) eV at 200, 300,400oC respect

Background: Bone mineral density has been assessed using Dual-Energy X-Ray Absorptiometry. Bone mineral density is measured according to the results of the Dual-Energy X-Ray Absorptiometry examination of the vertebral column and pelvis. Although diabetes mellitus type II (DM) is known to affect bone mineral density, at the present time this particular relationship is not clear. Objective: The aim of current study was to evaluate the effects of type II diabetes mellitus on bone mineral density of the upper and lower limbs as well as gender differences. Patients and Methods: This study involved 165 patients complaining of bone pain (85 males and 80 females), 85 patients of who suffered from diabetes, involving both genders. In addition,

Thin films of Mn2O3 doped with Cu have been fabricated using the simplest and cheapest chemical spray pyrolysis technique onto a glass substrate heated up to 250 oC. Transmittance and absorptance spectra were studied in the wavelength range (300 -1100) nm. The average transmittance at low energy was about 60% and decrease with Cu doping, Optical constants like refractive index, extinction coefficient and dielectric constants (εr), (εi) are calculated and correlated with doping process.

ZnO nanostructures were synthesized by hydrothermal method at different temperatures and growth times. The effect of increasing the temperature on structural and optical properties of ZnO were analyzed and discussed. The prepared ZnO nanostructures were characterized by X-ray diffraction (XRD), UV–Vis. absorption spectroscopy (UV–Vis.), Photoluminescence (PL), and scanning electron microscopy (SEM). In this work, hexagonal crystal structure prepared ZnO nanostructures was observed using X-ray diffraction (XRD) and the average crystallite size equal 14.7 and 23.8 nm for samples synthesized at growth time 7 and 8 hours respectively. A nanotubes-shaped surface morphology was found using scanning electron microscopy (SEM). The optic

Zinc oxide (ZnO) nanoparticles were synthesized using a modified hydrothermal approach at different reaction temperatures and growth times. Moreover, a thorough morphological, structural and optical investigation was demonstrated using scanning electron microscopy (SEM), x-ray diffraction (XRD), ultra-violate visible light spectroscopy (UV-Vis.), and photoluminescence (PL) techniques. Notably, SEM analysis revealed the occurrence of nanorods-shaped surface morphology with a wide range of length and diameter. Meanwhile, a hexagonal crystal structure of the ZnO nanoparticles was perceived using XRD analysis and crystallite size ranging from 14.7 to 23.8 nm at 7 and 8 ℎ𝑟𝑠., respectively. The prepared ZnO samples showed good abso

In this study, the Halder-Wagner method was used for an analysisX-ray lines of Tio2 nanoparticles. Where the software was used to calculate the FWHM and integral breath (β) to calculate the area under the curve for each of the lines of diffraction. After that, the general equation of the halder- Wagner method is applied to calculate the volume (D), strain (ε), stress (σ), and energy per unit(u). Volume (β). Where the value of the crystal volume was equal to (0.16149870 nm) and the strain was equal to (1.044126), stress (181.678 N / m2), and energy per unit volume (94.8474 J m-3).The results obtained from these methods were then compared with those obtained from each of the new paradigm of the HalderWagner method, the Shearer developm

New series of metal ions complexes have been prepared from the new ligand 1,5- Dimethyl-4- (5-oxohexan-2- ylideneamino) -2-phenyl- 1H-pyrazol-3 (2H)-one derived from 2,5-hexandione and 4-aminophenazone. Then, its V(IV), Ni(II), Cu(II), Pd(II), Re(V) and Pt(IV) complexes prepared. The compounds have been characterized by FT-IR, UV-Vis, mass and 1H and 13C-NMR spectra, TGA curve, magnetic moment, elemental microanalyses (C.H.N.O.), chloride containing, Atomic absorption and molar conductance. Hyper Chem-8 program has been used to predict structural geometries of compounds in gas phase, the heat of formation, (binding, total and electronic energy) and dipole moment at 298 K.