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.

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

 
      The process of soil classification in Iraq for industrial purposes is important topics that need to be extensive and specialized studies. In order for the advancement of reality service and industrial in our dear country, that a lot of scientific research touched upon the soil classification in the agricultural, commercial and other fields. No source and research can be found that touched upon the classification of land for industrial purposes directly. In this research specialized programs have been used such as geographic information system software The geographical information system permits the study of local distribution of phenomena, activities and the aims that can be determined in the loca

The results of previous scientific studies showed that knowledge is something and application is something else, that's why teachers' preparation programs focused, in the present time, on special standards for knowledge and performance, i.e., who has knowledge is not necessary able to apply it in his life or in his field of work, which led to the existence of a gap between knowledge and application. Based on that, those interested in (teachers' preparation) reconsidered their work evaluation, thus the concept of competency appeared at the end of the sixties of the past century to address the negative in teachers' preparation.
The following contains a number of competency features in teachers' preparation programs:
Teachers' effec

Software cost management is a significant feature of project management. As such, it needs to be employed in a project or line of work. Software cost management is integral to software development failures, which, in turn, cause software failure. Thus, it is imperative that software development professionals develop their cost management skills to deliver successful software projects. The aim of this study is to examine the impact of cost management success factors with project management factors and three agile methodologies – Extreme Programming (XP), Scrum and Kanban methodologies which are used in the Pakistani software industry. To determine the results, the researchers applied quantitative approach through an extensive survey on

The reconciliation of tax reconciliation is one of the legal methods used by the financial authority in Iraq, which is done with the taxpayer

The research dealt with the weakness of tax revenues for many reasons, including tax evasion, which led to the search for ways to reduce evasion to increase the tax revenue, and settlement reconciliation one of these means .

The research proceeded from the premise that the use of a more broadly settled settlement would govern the tax evasion of taxpayers.

The researchers used a series of studies and previous research, books and other sources related to the subject of research, and this was done through the theoretical framework, and the practical aspect that included the fin

The important factor in the success of construction projects is its ability to objective estimate of the cost of the project and adapt to the changes of the external environment, which is affected by a lot of elements and the requirements of the competitive environment. The faces of those projects are several problems in order to achieve particular goals. To overcome these difficulties has been the development of research in the last two decades and turn the focus on the role of the cost of project management, by providing information and assist management in planning and control of the budget among the main elements of the project, namely, (time-cost-quality),The research aims at the possibility of developing and implementing mechanisms

Based on previous research results that recognized the role of paternalistic leadership in promoting a positive work climate, this study explored the impact of a toxic work environment on the mental health and well-being of employees. We used the quantitative methodology to collect and analyze data. A sample of 108 participants from Iraqi internet service provider (ISPs) companies represented the purposive study sample. We targeted employees who experienced the COVID-19 pandemic. All data was collected through an electronic questionnaire (Google and Microsoft Forms). The research model was tested using structural equation modeling (SEM). The results showed a negative effect of the toxic workplace on the mental health of employees. T

The research aims to reach a set of objectives concerning creation a clear vision about conceptual, philosophical and practical dimension of relations, and effects between knowledge management, costumer orientation and competitiveness to construct a framework of a pragmatic model as a solution to research problem and its questions which the main one is about the role of knowledge management and costumer orientation in competitiveness of business organizations. To achieving this goal, it was necessary to make, in priory, a review and discussion to the theoretical dimension of research variables to have a clear vision about constructing hypostatical research model implying a set of hypotheses which, by proving them in companies studied, repr

Sports management is a fundamental pillar that supports sports institutions and plays a pivotal role in achieving advanced levels of success in talent development. The Talent Development Project is one of the key strategic initiatives of the Ministry of Youth and Sports. This study compares department heads with effective managerial competence to those with ineffective competence to highlight differences in performance quality. Through this comparison, the urgent need to assess the administrative performance skills of the heads of sports talent departments becomes evident, particularly their ability to lead and manage the Sports Talent Development Project. The objective is to identify strengths and weaknesses, establish a clear framework fo