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.

This study aims at evaluating the performance of MA students in the College of Education for Women in using the digital transformation and identifying the significant difference in performance evaluation according to the variable of academic qualification (Master or PHD). In order to achieve the aim of the research the researcher prepared a questionnaire of 20 items, and this happens after the researcher's getting acquaintance of the literature of previous studies related to the variable of the research. The apparent validity of the items was examined by exposing them to 10 juries specialized in education, psychology and evaluation and measurement. The stability of the items was examined via two methods, the test-repetition and half-divisio

The high carbon dioxide emission levels due to the increased consumption of fossil fuels has led to various environmental problems. Efficient strategies for the capture and storage of greenhouse gases, such as carbon dioxide are crucial in reducing their concentrations in the environment. Considering this, herein, three novel heteroatom-doped porous-organic polymers (POPs) containing phosphate units were synthesized in high yields from the coupling reactions of phosphate esters and 1,4-diaminobenzene (three mole equivalents) in boiling ethanol using a simple, efficient, and general procedure. The structures and physicochemical properties of the synthesized POPs were established using various techniques. Field emission scanning elect

Indexes of topological play a crucial role in mathematical chemistry and network theory, providing valuable insights into the structural properties of graphs. In this study, we investigate the Resize graph of G2(3), a significant algebraic structure arising from the exceptional Lie group (G2) over the finite field F3. We compute several well-known topological indices, including the Zagreb indices, Wiener index, and Randić index, to analyze the graph's connectivity and complexity. Our results reveal intricate relationships between the algebraic structure of G2(3) and its graphical properties, offering a deeper understanding of its combinatorial and spectral characteristics. These findings contribute to the broader study of algebraic graph t

SAIs has a pivotal role in enhancing public sector performance through its quest to achieve the greatest possible efficiency and effectiveness in its, so  it has to adopt applied framework for abilities building, the research aims to shed light on the role of SAIs and the nature of their  work,  and  the definition for its abilities building, and to prepare a proposal for abilities building applied to work with the SAI in the Republic of Iraq (of the Federal Board of Supreme Audit ),the Researchers reached conclusions, namely: abilities building is the outcome of the interaction between the reality of all of the employees of the SAI and the institution itself and the environment and the specific requirements of the de

In this work, we carried out an experimental study of thedusty
plasma by taking the dust material Fe₃O₄ with radius of the any grain
0.1μm - 0.5μm. In experiment we use air in the vacuum chamber
system under different low pressure (0.1-1) Torr. The results
illustrated that the present of dust particles in the air plasma did not
effect on Paschen minimum which is 0.5 without dust and with Fe₃O₄
dusty grains.
The effect of Fe3O4 dust particles on plasma parameters can be
notice in direct current system in glow discharge region. The plasma
parameters which were studied in this work represent plasma
potential, floating potential,electron saturation current, temperatu

Soil improvement has developed as a realistic solution for enhancing soil properties so that structures can be constructed to meet project engineering requirements due to the limited availability of construction land in urban centers. The jet grouting method for soil improvement is a novel geotechnical alternative for problematic soils for which conventional foundation designs cannot provide acceptable and lasting solutions. The paper's methodology was based on constructing pile models using a low-pressure injection laboratory setup built and made locally to simulate the operation of field equipment. The setup design was based on previous research that systematically conducted unconfined compression testing (U.C.Ts.). Th