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.
Abstract
The current research problem includes a variety of research motivations to serve the private health sector, which is witnessing a great competition from internal and external environments. In this regard, private medical clinics are increasingly seeking to attract and retain customers through the quality of their service offerings represented by health services. Innovative and effective marketing methods to improve performance and stay in competition, by relying on the physical evidence of the product as a component of the marketing mix of services and its role in particular in packaging and supporting the health service with concrete evidence that affects the customer an
... Show MoreIn this paper we use the Markov Switching model to investigate the link between the level of Iraqi inflation and its uncertainty; forth period 1980-2010 we measure inflation uncertainty as the variance of unanticipated inflation. The results ensure there are a negative effect of inflation level on inflation uncertainty and all so there are a positive effect of inflation uncertainty on inflation level.  
... Show MoreIn this investigation, the mechanical properties and microstructure of Metal Matrix Composites (MMCs) of Al.6061 alloy reinforced by ceramic materials SiC and Al2O3 with different additive percentages 2.5, 5, 7.5, and 10 wt.% for the particle size of 53 µm are studied. Metal matrix composites were prepared by stir casting using vortex technique and then treated thermally by solution heat treatment at 530 0C for 1 hr. and followed by aging at 175 0C with different periods. Mechanical tests were done for the samples before and after heat treatment, such as impact test, hardness test, and tensile test. Also, the microstructure of the metal matrix composites was examine
... Show MoreStandards play a vital role in documenting the values of new test results in the form of tables. They are one of the basic requirements that the standardization process aims for as a complement to standardizing test procedures, and contribute to knowing the current reality of the student. The degree of readiness and level as a result of practicing different exercises for sports activities, in addition to the possibility of adopting it for comparison with his group or similar groups, classification, prediction and selection. Developing the skill of handling the football in the educational field is an important matter for achieving distinguished performance among students. This skill requires a level of accuracy, speed and control, and
... Show MoreThe research aim to the usage educational method for jump shooting and it effect on speed strength in basketball for the specialist students in College Sport of Dayla University, which used the following statistic treatment (The T.test for compatible specimens), so after statistic treatment which appears theres a tow moral differences in speed strength and jump shooting tests results to (legs & arms) for the before and after tests, and after that the conclusions we positive and the second the special drills effect immaterial speed strength to legs and arms, so the tow researches recommended to looking after the best for educational methods that used in our sport colleges in Iraq.
The indirect monetary policy tools led to financial stability for the period being studied through the use of indicators of financial stability (aggregate) to show the effect of the foreign reserves of the Central Bank of Iraq and its indirect instruments in achieving financial and economic stability, especially after the significant decline in oil prices and dependence of the Iraqi economy on Oil (rent) and lower reserves of the Central Bank of Iraq after 2014 and now compared to previous years, the goal of this research is to achieve financial stability according to selected indicators and achieve an optimal monetary policy to achieve the development goals of The economic policy in the country. Standard models were used to test
... Show MoreThe aim of the research is to evaluate the response of the researched leaders towards practicing the concept of the lens, which is its dimensions with (stakeholders, resource mobilization, knowledge development, culture management) and the nature of its relationship to tax pioneer performance represented in its dimensions (strategic direction, leadership indicators, growth, renewal and modernization, efficiency, Effectiveness) The questionnaire was approved as a main tool in collecting data and information from the sample members in the General Authority of Taxes, which number (91) Who are on (M. General Manager, Division Director, Deputy Director, Senior Division Director, Deputy Director, Second Division, Division Officer, M. D
... Show MoreBackground. The use of modern aids and technology has contributed greatly to football development, the goalkeeper is the most important position in the team, and the use of devices gave objective readings about the goalkeeper's ability in terms of skill and physical aspects. Objectives. The research aimed to prepare exercises using an electronic device to measure the knee bending angle because of its great importance in developing the skill of catching and dimensions of the high ball for football goalkeepers. Methods. The researchers used the experimental method, and the sample consisted of (4) male goalkeepers under 15 years of age, one of the research procedures was to determine the biomechanical variables affecting the development of the
... Show MoreOne of the most important phenomena facing the athlete is the anxiety of sports competition, as he faces many psychological problems during training and in competitions of psychological tension, fear and anxiety that accompany him sometimes, which leads to affecting his level, and sports competition anxiety is a special type of anxiety that occurs in the athlete It is related to the attitudes of sports competitions and that participation in sports competitions and the associated emotional experiences are among the important factors that motivate the practice of sports activity and try to advance and develop his sports level. It is assumed that when the individual begins to practice any activity, he aims to reach a level or degree of achie
... Show MoreIn this study, two types of local plants were chosen, the first is the plant golden pothos Epipremnum aureum and the second is the Iraqi Sheikh's chin plant Tribulus terrestris L, for the purpose of making a comparison between them in terms of their possession of chemical groups with antioxidant activity in order to use them as a natural alternative to using antioxidants Industrial that cause negative effects on human health, the samples were prepared using the method of water and alcohol extraction (ethanol 70%) for both plants. It revealed the presence of a number of chemical groups (tannins, carbohydrates, phenols, flavonoids, alkaloids) for both plants, the aqueous and alcoholic extracts. Coumarins are only found in the sheikh's chin pl
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