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 influence of different thickness (500, 1000, 1500, and 2000) nm on the electrical conductivity and Hall effect measurements have been investigated on the films of copper indium gallium selenide CuIn1-xGaxSe2 (CIGS) for x= 0.6.The films were produced using thermal evaporation technique on glass substrates at R.T from (CIGS) alloy. The electrical conductivity (σ), the activation energies (Ea1, Ea2), Hall mobility and the carrier concentration are investigated and calculated as function of thickness. All films contain two types of transport mechanisms of free carriers, and increases films thickness was fond to increase the electrical cAnductivity whereas the activation energy (Ea) would vary with films thickness. Hall Effect analysis resu

Abstract : Tin oxide SnO2 films were prepared by atmospheric chemical vapor deposition (APCVD) technique. Our study focus on prepare SnO2 films by using capillary tube as deposition nozzle and the effect of these tubes on the structural properties and optical properties of the prepared samples. X-ray diffraction (XRD) was employed to find the crystallite size. (XRD) studies show that the structure of a thin films changes from polycrystalline to amorphous by increasing the number of capillary tubes used in sample preparation. Maximum transmission can be measured is (95%) at three capillary tube. (AFM) where use to analyze the morphology of the tin oxides surface. Roughness and average grain size for different number of capillary tubes have b

In the present work, pulsed laser deposition (PLD) technique was applied to a pellet of Chromium Oxide (99.999% pure) with 2.5 cm diameter and 3 mm thickness at a pressure of 5 Tons using a Hydraulic piston. The films were deposited using Nd: YAG laser λ= (4664) nm at 600 mJ and 400 number of shot on a glass substrate, The thickness of the film was (107 nm). Structural and morphological analysis showed that the films started to crystallize at annealing temperature greater than 400 oC. Absorbance and transmittance spectra were recorded in the wavelength range (300-
4400) nm before and after annealing. The effects of annealing temperature on absorption coefficient, refractive index, extinction coefficient, real and imaginary parts of d

The semiconductor ZnO is one of II – VI compound group, it is prepare as thin films by using chemical spray pyrolysis technique; the films are deposited onto glass substrate at 450 °C by using aqueous zinc chloride as a spray solution of molar concentration 0.1 M/L. Sample of the prepared film is irradiating by Gamma ray using CS 137, other sample is annealed at 550°C. The structure of the irradiated and annealed films are analyzed with X-ray diffraction, the results show that the films are polycrystalline in nature with preferred (002) orientation. The general morphology of ZnO films are imaged by using the Atomic Force Microscope (AFM), it constructed from nanostructure with dimensions in order of 77 nm.
The optical properties o

Applications of superconductor compounds were considered as modern and important topics, especially these which are exposures to one of the nuclear radiation kinds. So, we gone to investigate the influence of fast neutrons irradiation on electrical and structural characteristics of HgxSb1-xBa2Ca2Cu3O8+δ superconducting compound at (x = 0.7) in ratio. The superconducting specimens were synthesized using solid state technique. Specimens were exposure to the nuclear radiation using fast neutrons with doses (0, 9.06 x1010, 15.3 x 1010 and 18.17 x 1010) n/cm2 respectively. Electrical and X-ray diffraction properties of superconductor specimens before and after irradiation were investigated under standard conditions. Results of X-ray diffraction

In this research we prepared CdS thin films by Spray pyrolysis method on a glass substrates and we study its structural , optical , electrical properties .The result of (X-Ray ) diffraction showed that all thin films have a polycrystalline structure , The relation of the transmission as a function of wavelength for the CdS films had been studied , The investigated of direct energy gap of the CdS its value is (2.83 eV). In Hall effect measurement of the CdS we find the charge carriers is p – type and Hall coefficient 1157.33(cm3/c) ,Hall mobility 6.77(cm2/v.s)

The paper reports the influence of annealing temperature under vacuum for one hour on the some structural and electrical properties of p-type CdTe thin films were grown at room temperature under high vacuum by using thermal evaporation technique with a mean thickness about 600nm. X-ray diffraction analysis confirms the formation of CdTe cubic phase at all annealing temperature. From investigated the electrical properties of CdTe thin films, the electrical conductivity, the majority carrier concentration, and the Hall mobility were found increase with increasing annealing temperatures.

NiO0.99Cu0.01 films have been deposited using thermal evaporation
technique on glass substrates under vacuum 10-5mbar. The thickness
of the films was 220nm. The as -deposited films were annealed to
different annealing temperatures (373, 423, and 473) K under
vacuum 10-3mbar for 1 h. The structural properties of the films were
examined using X-ray diffraction (XRD). The results show that no
clear diffraction peaks in the range 2θ= (20-50)o for the as deposited
films. On the other hand, by annealing the films to 423K in vacuum
for 1 h, a weak reflection peak attributable to cubic NiO was
detected. On heating the films at 473K for 1 h, this peak was
observed to be stronger. The most intense peak is at 2θ = 37