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.

Polycrystalline Cadmium Oxide (CdO) thin films were prepared
using pulsed laser deposition onto glass substrates at room
temperature with different thicknesses of (300, 350 and 400)nm,
these films were irradiated with cesium-137(Cs-137) radiation. The
thickness and irradiation effects on structural and optical properties
were studied. It is observed by XRD results that films are
polycrystalline before and after irradiation, with cubic structure and
show preferential growth along (111) and (200) directions. The
crystallite sizes increases with increasing of thickness, and decreases
with gamma radiation, which are found to be within the range
(23.84-4.52) nm and (41.44-4.974)nm before and after irradiation for

This paper reports the effect of Mg doping on structural and optical properties of ZnO prepared by pulse laser deposition (PLD). The films deposited on glass substrate using Nd:YAG laser (1064 nm) as the light source. The structure and optical properties were characterized by X-ray diffraction (XRD) and transmittance measurements. The films grown have a polycrystalline wurtzite structure and high transmission in the UV-Vis (300-900) nm. The optical energy gap of ZnO:Mg thin films could be controlled between (3.2eV and 3.9eV). The refractive index of ZnO:Mg thin films decreases with Mg doping. The extinction coefficient and the complex dielectric constant were also investigate.

In this work, As60Cu40-xSex thin films were synthesized, and the pulsed laser deposition method was used to study the effected partial replacement of copper with selenium. The electrical characteristics and optical characteristics, as indicated by the absorbance and transmittance as a function of wavelength were calculated. Additionally, the energy gap was computed. The electrical conductivity of the DC in the various conduction zones was calculated by measuring the current and voltage as a function of temperature. Additionally, the mathematical equations are used to compute the energy constants, electron hopping distance, tail width, pre-exponential factor, and density of the energy states in variation zones (densities of the energ

The electronic properties and Hall effect of thin amorphous Si1-xGex:H films of thickness (350 nm) have been studied such as dc conductivity, activation energy, Hall coefficient under magnetic field (0.257 Tesla) for measuring carrier density of electrons and holes and Hall mobility as a function of germanium content (x = 0–1), deposition temperature (303-503) K and dopant concentration for Al and As in the range (0-3.5)%. The composition of the alloys and films were determined by using energy dispersive spectroscopy (EDS) and X-ray photoelectron spectroscopy (XPS).
This study showed that dc conductivity of a-Si1-xGex:H thin films is found to increase with increasing Ge content and dopant concentration, whereas conductivity activati

The effect of annealing temperature (Ta) on the electrical properties like ,D.C electrical conductivity (σ DC), activation energy (Ea),A.C conductivity σa.c ,real and imaginary (ε1,ε2) of dielectric constants ,relaxation time (τ) has been measured of ZnS thin films (350 nm) in thickness which were prepared at room temperature (R.T) using thermal evaporation under vacuum . The results showed that σD.C increases while the activation energy values(Ea) decreases with increasing of annealing temperature.(Ta) from 303- 423 K .
The density of charge carriers (nH) and Hall mobility (μH) increases also with increasing of annealing temperature Hall effect measurements showed that ZnS films were n-type converted to p-type at high annealin

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.

In this research study the effect of irradiation by (CW) CO2 laser on some optical properties of (Cds) doping by Ni thin films of (1)µm thickness has been prepared by heat evaporation method. (X-Ray) diffraction technique showed the prepared films before and after irradiation are ploy crystalline hexagonal structure, optical properties were include recording of absorbance spectra for prepared films in the range of (400-1000) nm wave lengths, the absorption coefficient and the energy gap were calculated before and after irradiation, finally the irradiation affected (CdS) thin films by changing its color from the Transparent yellow to dark rough yellow and decrease the value absorption coefficient also increase the value of energy gap.