In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

Our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

The importance of government Expenditure policy in economy come from its role leading to the mitigation and adjustment of fluctuations in macroeconomic variables caused by imbalance between aggregate demand and aggregate supply,  It is associated with the efficient management of government Expenditure to reinforcement the relationship between government Expenditure and the overall economic system .

Regarding the Iraqi economy,the increasing in financial rentier after the political change in 2003 has led to finance the budgets Characterized by consumption,The government Expenditure employed to encourage government employment in services jobs, and find different channels for the distribution of

The aim of the research is to test the effect of outsourcing human resources activities (independent variable) with its dimensions (outsourcing of staffing, outsourcing of training and development, outsourcing of wages and compensation, outsourcing of human resources information systems) on organizational winning (dependent variable) with its dimensions (the culture of winning, successful organizational change, continuous improvement, and adoption of risk). The research problem was the questions posed by the researcher, the most important of which is the extent to which the research sample realizes the importance of applying outsourcing to human resources activities and its role in organizational vi

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The study aims to indicate the role of the mechanisms and principles of corporate governance in the activation of social responsibility reports, and increase disclosure, to achieve sustainability, legitimacy, and integrity of the business. Through the presentation of the conceptual framework for corporate governance and social responsibility, identify the key dimensions of social responsibility and the statement of the relationship between the mechanisms of governance and social responsibility reports in accordance with these dimensions. To prove the hypothesis research has selected a sample of listed companies in the Iraqi market for securities,

In this study; a three-dimensional model was created to simulate groundwater in Al-Haydariyah area of the governorate of Al-Najaf. A solid model was created to utilize the cross sections of 25 boreholes in the research region, and it was made out of two layers: sand and clay. The steady-state calibration was employed in six observation wells to calibrate the model and establish the hydraulic conductivity, which was 17.49 m/d for sand and 1.042 m/d for clay, with a recharge rate of 0.00007 m/day. The wells in the research region were reallocated with a distance of 1500 m between each well, resulting in 140 wells evenly distributed throughout the study area and with a discharge of 5 l/s, and the scenarios were run for 1000

This paper presents a numerical simulation of the flow around elliptic groynes by using CFD ‎software. The flow was simulated in a flume with 4m long, 0.4m wide, ‎and 0.175m ‎high ‎‎with a constant bed slope. Moreover, the first Groyne placed at 1m from the flow ‎‎inlet with a ‎constant the Groyne height of 10cm and a 1cm thickness, and the ‎width of Groynes equals ‎7cm‎. A submergence ratio of the elliptic Groynes of 75% was assumed, corresponding to a discharge of ‎0.0057‎m³/sec. The CFD ‎model showed a good ability to simulate the flow ‎around ‎Groynes with ‎ good accuracy. The results of ‎CFD software showed that when using double elliptic Groy

The research aims to measure, assess and evaluate the efficiency of the directorates of Anbar Municipalities by using the Data Envelopment Analysis method (DEA). This is because the municipality sector is consider an important sector and has a direct contact with the citizen’s life. Provides essential services to citizens. The researcher used a case study method, and the sources of information collection based on data were monthly reports, the research population is represented by the Directorate of Anbar Municipalities, and the research sample consists of 7 municipalities which are different in terms of category and size of different types. The most important conclusion reached by the research i

Sports risk has become a threat to the sports sector in general and the impact on an efficient player and the old stadiums in particular. So have such a thing fertile ground of global insurance companies to exploit it optimally exploited through the development and marketing of insurance lids for the provision of protection for athletes of different risks they may face, which contributed to the growth and development of the performance of these companies and helped in the emergence of sports insurance specialist firms. And through the insurance process in the field of sports and where the insurance is a type of social solidarity. The main problem is this spirit manifested search in question is whether to embrace sports institutions sport