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.

To study the removal of lead (Pb) ions from aqueous solutions, novel magnetite nanoparticles (NPs) of Ni_0.31Mg_0.15Ag_0.04Fe_2.5O₄ were synthesized by coprecipitation synthesis using metal sulfates, and then coated with Gum Arabic (GA). The prepared NPs were analyzed using various spectroscopic and analytical methods, such as X-Ray diffraction analysis (XRD), Field Emission Scanning Electron Microscopy (FE-SEM), Energy Dispersive X-ray spectroscopy (EDX), Fourier Transform Infra-Red spectroscopy (FT-IR), and Atomic Absorption Spectrophotometer (AAS). By using XRD analysis, the cubic inverse spinel structure of the prepared NPs was proven, showing average values of crystallite size, latt

In this study, the photodegradation of Congo red dye (CR) in aqueous solution was investigated using Au-Pd/TiO₂ as photocatalyst. The concentration of dye, dosage of photocatalyst, amount of H₂O₂, pH of the medium and temperature were examined to find the optimum values of these parameters. It has been found that 28 ppm was the best dye concentration. The optimum amount of photocatalyst was 0.09 g/75 mL of dye solution when the degradation percent was ~ 96 % after irradiation time of 12 hours, while the best amount of hydrogen peroxide was 7μl/75 mL of dye solution at degradation percent ~97 % after irradiation time of 10 hours, whereas pH 5 was the best value to carry out the reaction at the highest deg

In this study, the photodegradation of Congo red dye (CR) in aqueous solution was investigated using Au-Pd/TiO2 as photocatalyst. The concentration of dye, dosage of photocatalyst, amount of H2O2, pH of the medium and temperature were examined to find the optimum values of these parameters. It has been found that 28 ppm was the best dye concentration. The optimum amount of photocatalyst was 0.09 g/75 mL of dye solution when the degradation percent was ~ 96 % after irradiation time of 12 hours, while the best amount of hydrogen peroxide was 7μl/75 mL of dye solution at degradation percent ~97 % after irradiation time of 10 hours, whereas pH 5 was the best value to carry out the reaction at the highest degradation percent. In additio

The problem with research lies in hiding the Hanbali approach in building long and short travel provisions, as well as hiding some provisions relating to short travel that are not provided for by the jurists of Hanbali (in their books).

The research aims to demonstrate the approach and standards on which they based the long and short travel provisions, as well as to reflect the provisions of some of the issues that are silent on long and short travel, with evidence and significance.

The research included a preface and two researches, the researcher in the preface talked about the reality of long and short travel, in the first research on the approach of ha

To reduce the effects of discharging heated water disposed into a river flow by a single thermal source, two parameters were changed to get the minimum effect using optimization. The first parameter is to distribute the total flow of the heated water between two disposal points (double source) instead of one and the second is to change the distance between these two points. In order to achieve the solution, a two dimensional numerical model was developed to simulate and predict the changes in temperature distribution in the river due to disposal of the heated water using these two points of disposal.
MATLAB-7 software was used to build a program that could solve the governing partial equations of thermal pollution in rivers by using t

1. Anti-social behavior Baghdad University students.
2. Know the differences in anti's social behavior according to gender, specialization.
3. Know-the need for love at Bagdad University students.
4. Know the relationship between anti-social behavior and the need to love.
The research sample consisted of (100) students, the researcher numbers tools to measure anti behavior and the need to love.
The results showed that college students have an anti-social behavior is weak and they need to love and there is no correlation between them Function relationship. Researcher has shown a number of recommendations and proposals.

The current research aimed to identify the level of moral identity and social affiliation among students exposed to shock pressures, as well as to reveal the relationship between these variables. To achieve these objectives, the researcher adopted the diagnostic tool for the measure of post-traumatic stress disorder (PDS-5) scale (Foa, 2013) translated to Arabic language by (Imran, 2017). The researcher also adopted the moral identity scale built by (Al-Bayati, 2015) and the measure of social affiliation built by (Al-Jashami, 2013), which were applied to a random sample of (200) male and female students chose from al Anbar University. They were exposed to shock pressures. The results of the research showed that the sample has an average