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.

APDBN Rashid, Review of International Geographical Education Online (RIGEO), 2021

Regression testing being expensive, requires optimization notion. Typically, the optimization of test cases results in selecting a reduced set or subset of test cases or prioritizing the test cases to detect potential faults at an earlier phase. Many former studies revealed the heuristic-dependent mechanism to attain optimality while reducing or prioritizing test cases. Nevertheless, those studies were deprived of systematic procedures to manage tied test cases issue. Moreover, evolutionary algorithms such as the genetic process often help in depleting test cases, together with a concurrent decrease in computational runtime. However, when examining the fault detection capacity along with other parameters, is required, the method falls sh

Abstract Iraq has an important place in the regional and international balance, and the competition among countries has increased in rapprochement with Iraq, not only for its geography or its privileged location, but because it has many other components that make regional and international countries want to strengthen their relations with it (Regional and international powers). In addition to that, Iraq has become increasingly important for these international and regional powers after its victory over the terrorist organization (ISIS), which proved an important fact that Iraq represents the most important pillars in the international balance.

In this study, new derivatives of 3-C-spiro ring nucleoside analogues were synthesized. The structures of these derivatives were characterized by infrared spectroscopy,1 HNMR (some of them) and elemental analysis. The nucleoside derivatives were tested for inhibition of E-coli and were all found to be active.

methodology six sigma Help  to reduce defects by solving problems effectively, and works Lean to reduce losses through the flow of the manufacturing process and when integrating these two methodologies (Lean and six sigma), the methodology of Lean six sigma will form the entrance to the organizers of the optimization process and increase the quality and reduce lead times and costs . by focusing on the needs of the customer. this process uses statistical tools and techniques to analyze and improve processes.

 We have conducted this research in the General Company for Electrical Industries and adopted its product (machine cooling water three taps) as a sample for research. In order to determine t

Through the early childhood and after the ablactating the child learns acquired food habbits that might studying with him throughout his life. Here the parents role arises: teaching the child the sound food habits and hygienic styles and whatever beneficial to the health and with the sufficient quantities for the body. In this way the experiences the child learns at home will be of great help in his future life in choosing the suitable food after becoming more dependent in making his decisions and choices away from his parents. The results in this study showed that the averages of the children’s consumption of the high energy foods in comparison with the other highest consumption average , after that comes the con sumption of soft drills

The research aims at conducting a follow-up evaluation of a number of strategic projects implemented by the Directorate of Public Municipalities, one of the Ministry of Construction, Housing and Municipalities and Public Works. The sample included (35) varied strategic projects implemented in most Iraqi governorates. Buildings, municipal buildings, minarets, massacres, multi-story parking, paving and rehabilitation of streets and residential neighborhoods. The difference between the actual and planned times and costs of these projects was then measured and analyzed. These projects were used as a tool for collecting data and information. The questionnaire included four axes, each representing one of the parties to the project, whi