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 .

Abstract

The research aims to investigate the private sector attitudes toward operational contracting in special education schools. The research adopted the qualitative approach by using personal interviews with a sample of (45) private school owners and managers in Oman. The results of the research revealed that there is an agreement among the majority of respondents on the ability of the private sector to manage special education schools, the advantages of the partnership, as well as the need for guarantees to support this partnership. The government should fully assume it. The role of the private sector remains to raise the operational efficiency of schools. Opinions vary about the level of powers granted to t

Praise be to Allah, Lord of the Worlds, teach the pen, taught the human what he didn't know, Ihmad - Almighty - and thank him, and repent to him and ask forgiveness, which is the most forgiving, and bear witness that there is no god but Allah alone has no partner, gives and prevents, And I bear witness that Muhammad is  a slave to Allah  and his Messenger, who called for guidance and good speech and spoke, peace be upon him and his family and companions, and those who followed them until the Day of Judgment.

Constitute a planning problem on the basis of personal experience and self-governance in the service organizations away from quantitative scientific method in planning an anchor and a platform, who made a recent research study, analysis and interpretation through scientific methodology adopted which formed its contents, The research aims to identify the true reality of production planning in service organizations, specifically in the Baghdad Hotel as a society to look, in order to assess the best strategy through the standard cost of the strategies of tracking and settlement to cope with developments on services demand changes, Search results confirmed that the settlement rates of production strategy is the best strategy in accordance wi

Recently, several concepts and expressions have emerged that have often preoccupied the world . around the concept of environment and sustainability. This is due to the negative and irresponsible impact of man and his innovations in various industrial and technological fieldsthat have damaged the natural environment. Architecture and cities at the broader level are some of the man made components that caused these negative impacts and in the same time affected by them. What distinguishes architectural and urban projects is the consumption of large . quantities of natural resources and production larger amounts of waste and pollution, along the life of these projects. At the end of the twentieth century and the beginning of the twenty-fir

The research aims to test the correlation relationships between wise leadership, and the business model, and to demonstrate its influence (wise leadership) on the business model. Therefore, two main hypotheses were put forward. The research was applied to a sample consisting of (87) managers and deputy managers, some of them are members on the board of directors of the researched company. The questionnaire was adopted as a basic tool for collecting data, in addition to personal interviews. A number of statistical methods were used to analyze the data and obtain results. The researcher showed a set of results, including: There is a significant correlation between wise leadership and business model. There is an influence of wise leadership on

The research aims to diagnose the shortcomings and weaknesses in applying the dimensions of the quality of work life and the extent of their impact on employees’ attitudes and behaviors, and thus their relationship to enhancing their core competencies. The scientific value of the research stems from highlighting the importance of the dimensions of the quality of professional life in improving the productive efficiency of workers in the public sector and raising the level of organizational performance. Because the quality of working life plays an important role in enhancing the core competencies of employees in the public sector, it can also be an incentive or a disincentive for any employee by adapting to the economic and social condition

The research aims to diagnose the shortcomings and weaknesses in applying the dimensions of the quality of work life and the extent of their impact on employees’ attitudes and behaviors, and thus their relationship to enhancing their core competencies. The scientific value of the research stems from highlighting the importance of the dimensions of the quality of professional life in improving the productive efficiency of workers in the public sector and raising the level of organizational performance. Because the quality of working life plays an important role in enhancing the core competencies of employees in the public sector, it can also be an incentive or a disincentive for any employee by adapting to the economic and social condit

يهدف البحث إلى تشخيص أوجه القصور ونقاط الضعف في تطبيق أبعاد جودة الحياة الوظيفية ومدى تأثيرها على اتجاهات وسلوكيات الموظفين، وبالتالي علاقتها بتعزيز مقدراتهم الجوهرية. وتنبع القيمة العلمية للبحث من إبراز أهمية أبعاد جودة حياة العمل في تحسين الكفاءة الإنتاجية للعاملين في القطاع العام ورفع مستوى الأداء التنظيمي. ولأن جودة الحياة العملية تلعب دوراً مهماً في تعزيز المقدرات الأساسية للموظفين في القطاع الع