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 .

Today, the success or failure of organizations depends to possess the wisdom of their managers promised that the key to organizational success of the business environment, making the right decisions, and create the ability to work and think towards discrimination of products and services the organization . Seek this research to investigation the relationship between the wisdom management and differentiation strategy for service operations . It was a test of that relationship in light of the results of the analysis of the data collected through the questionnaire distributed on a sample from (98) Director Mangers, head of department and head of division in  the General Establishment of Civil Aviation . The research used descriptive st

       Currently, there is no established of e-waste treatment in Thi- Qar province, while their creating is increasing every year. It has been well- known that e-waste is a source of environmental degrading and their placement in landfills increases the irreversible climate change. A research model has been developed to link three components: coercive pressure, normative influence, and mimicry, then study their effect on e-waste adopt and continuance intentions. The model was validated using data collected from a field survey of 92 managers of small enterprises in Thi-Qar province.  A questionnaire was developed to collect data. It contains five major variables, exemplify by fourteen items. Als

The subject of multi- ethnics is one of the most important subjects in the study of political
geography, as multi- ethnics and its consequent problems are global geopolitical phenomena
that started early and reached its peak with the beginning of the twentieth century, because of
major changes in the political landscape that resulted by wars and led to the collapse of many
empires and major powers, a matter which led to put new political maps according to certain
considerations of the colonial powers, especially in Africa and Asia. All these things led to
the most serious challenges based on ethnic and sectarian conflict and led to the development
of geopolitical problems. Among the examples what most countries in th

In this paper we will study some of the properties of an operator by looking at the associated S-act of this operator, and conversely. We look at some operators, like one to one operators, onto operators. On the other hand, we look at some act theoretic concepts, like faithful acts, finitely generated acts, singular acts, separated acts, torsion free acts and noetherian acts. We try to determine what properties of T make the associated S-act has any of these properties.

Abstract

Toady technology Nano since it launched human Alivia third interest and anticipation unusual and that by the decision-makers in the world's governments and its institutions and research departments productivity, especially after the US Congress enact a law (the National Initiative for Tknlojba nanotechnology in the United States of America) and the allocation of large sums of money To support this initiative, the research aims to shed light on the concept of technology nanotechnology, which is technology atheist and the twentieth century, and reflect its economic importance and in order to reach the objectives of the research has been the division of research into several axes has been allocated

This work, in fact, is an English language teaching study (henceforth, ELT) which may provide the inspiration for much –needed research on issues such as testing students' level of achievement in articulatory phonetics at the university level. It attempts to answer two questions: 1)What is college students' level of achievement in articulatory phonetics? 2- Are there any statistical significant differences in the achievement of college students in articulatory phonetics between the production and recognition testing techniques? This research falls into three sections: Section one indicates the problem, the aims, the hypotheses, the procedures, the limits and the value of the study. Section two provides a general overview of the articul

Three hundred and fifty five patients with hepatitis were investigated in this study all cases gave negative result with HBs Ag , IgM-anti HCV , IgM-anti HEV, IgM-anti HDV and anti-HIV tests . The frequency of IgM-anti HAV was 113 and the percentage was 32 % in all ages but when these patients divided into five groups dependent on ages. The highest percentage of IgM-anti HAV was (45%) in age <10 and the percentage declined with age increase till to 9% in age >41 year.