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.

Thin films of (Cu2S)100-x( SnS2 )x at X=[ 30,40, &50)]% with thickness (0.9±0.03)µm , had been prepared by chemical spray pyrolysis method on glass substrates at 573 K. These films were then annealed under low pressure of(10-2) mbar ,373)423&473)K for one hour . This research includes , studying the the optical properties of (Cu2S)100-x-(SnS2)x at X=[ 30,40, &50)]% .Moreover studying the effect of annealing on their optical properties , in order to fabricate films with high stability and transmittance that can be used in solar cells. The transmittance and absorbance spectra had been recorded in the wavelength range (310 - 1100) nm in order to study the optical properties . It was found that these films had direct optical band

Background: Thalassemia is characterized by the decrease or absence of the synthesis of one or more globin chains of hemoglobin. Thalassemia is distributed worldwide and is characterized by; regular blood transfusion which is creating alloimmunization to erythrocyte antigens is one of the major complications of regular blood transfusions in thalassemia, particularly in patients who are chronically transfused.Objectives: The aims of this study are to understand the immune system profile as the triggering factor for thalassemia.Methods: Thirty patients aging between one year and four months and twenty two years, twenty two of them were boys and eight were girls. Twenty nine patients, their parents are relative except one and studied in the

In this study, the modified size-strain plot (SSP) method was used to analyze the x-ray diffraction lines pattern of diffraction lines (1 0 1), (1 2 1), (2 0 2), (0 4 2), (2 4 2) for the calcium titanate(CaTiO3) nanoparticles, and to calculate lattice strain, crystallite size, stress, and energy density, using three models: uniform (USDM). With a lattice strain of (2.147201889), a stress of (0.267452615X10), and an energy density of (2.900651X10-3 KJ/m3), the crystallite was 32.29477611 nm in size, and to calculate lattice strain of Scherrer (4.1644598X10−3), and (1.509066023X10−6 KJ/m3), a stress of(6.403949183X10−4MPa) and (26.019894 nm).

Lead selenide PbSe thin films of different thicknesses (300, 500, and 700 nm) were deposited under vacuum using thermal evaporation method on glass substrates. X-ray diffraction measurements showed that increasing of thickness lead to well crystallize the prepared samples, such that the crystallite size increases while the dislocation density decreases with thickness increasing. A.C conductivity, dielectric constants, and loss tangent are studied as function to thickness, frequency (10kHz-10MHz) and temperatures (293K-493K). The conductivity measurements confirm confirmed that hopping is the mechanism responsible for the conduction process. Increasing of thickness decreases the thermal activation energy estimated from Arhinus equation is

To evaluate the effectiveness of different microwave irradiation exposure times on the disinfection of dental stone samples immersed in different solutions, and its affect on the dimensional accuracy and surface porosity. Dental stone casts were inoculated with an isolate of Bacillus subtilis to examine the efficiency of microwave irradiation as a disinfection method while immersed in different solutions; water, 40% sodium chloride, or without immersion for different durations. Dimensional accuracy and surface porosity were also evaluated. Significant reduction in colony counts of Bacillus subtilis were observed after 5 minutes of microwave irradiation of immersed dental casts in water and NaCl solution. No evidence of growth was observed a