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.

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

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

CD63 is -one of the tetraspanin family proteins, which are regarded as: hallmark exosomal markers because it is absent from other types of vesicles. It is expressed in the cell membrane of cancer cells, and cytoplasm of stromal cells. Objective: To assess CD63 expression in gastric cancer (GC) patients, and detected if it could be used as a predictive marker. Furthermore, the current study aimed to find the correlation between CD63 expression and clinicopathological parameters as: gender, age, invasion depth, histopathological type, involvement of lymph nodes, grade and stages of GC (TNM). The current study is a retrospective study in the period time from (2018 to-2020); 50 randomly patients formalin-fixed paraffin embedded blocks (FFPE)

Time series analysis is the statistical approach used to analyze a series of data. Time series is the most popular statistical method for forecasting, which is widely used in several statistical and economic applications. The wavelet transform is a powerful mathematical technique that converts an analyzed signal into a time-frequency representation. The wavelet transform method provides signal information in both the time domain and frequency domain. The aims of this study are to propose a wavelet function by derivation of a quotient from two different Fibonacci coefficient polynomials, as well as a comparison between ARIMA and wavelet-ARIMA. The time series data for daily wind speed is used for this study. From the obtained results, the

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The study aims at building a mathematical model for the aggregate production planning for Baghdad soft drinks company. The study is based on a set of aggregate planning strategies (Control of working hours, storage level control strategy) for the purpose of exploiting the resources and productive capacities available in an optimal manner and minimizing production costs by using (Matlab) program. The most important finding of the research is the importance of exploiting during the available time of production capacity. In the months when the demand is less than the production capacity available for investment. In the subsequent months when the demand exceeds the available energy and to minimize the use of overti

In this research, has been to building a multi objective Stochastic Aggregate Production Planning model for General al Mansour company Data with Stochastic  demand under changing of market and uncertainty environment in aim to draw strong production plans.  The analysis to derive insights on management issues regular and extra labour costs and the costs of maintaining inventories and good policy choice under the influence medium and optimistic adoption of the model of random has adoption form and had adopted two objective functions total cost function (the core) and income and function for a random template priority compared with fixed forms with objective function and the results showed that the model of two phases wit

In this paper, we derived an estimators and parameters of Reliability and Hazard function of new mix distribution ( Rayleigh- Logarithmic) with two parameters and increasing failure rate using Bayes Method with Square Error Loss function and Jeffery and conditional probability random variable of observation. The main objective of this study is to find the efficiency of the derived of Bayesian estimator compared to the to the Maximum Likelihood of this function using Simulation technique by Monte Carlo method under different Rayleigh- Logarithmic parameter and sample sizes. The consequences have shown that Bayes estimator has been more efficient than the maximum likelihood estimator in all sample sizes with application

This paper aims to deal with the understanding of the properties of the molecular gas hydrogen in the extragalactic spirals sample. It is critical to make observations of CO (J = 1-0) line emission for spiral galaxies, particularly those with an energetic nucleus.  In the sample of spiral galaxies compiled, a carbon monoxide CO (1-0) emission line can be observed. This sample of galaxies' gas kinematics and star-forming should be analyzed statistically utilizing appropriate atomic gas HI, molecular gas H2, infrared (1μm-1000μm), visual (at λblue-optical=4400A0), and radio spectrum (at νradio=1.4 GHz and 5GHz) databases. STATISTICA is software that allows us to perform this statistical analysis. The presence of a high scale of s

Abstract