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 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.

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

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

Time is an essential element of contracts، as there is an independent in many parts of each contract، but the time dimension has a significant impact on the provisions of all contracts and is not limited to a particular range of contracts، and French and Arab jurists alike have called for this dimension to be given special attention، and as a result the French legislator has introduced the term duration of the contract، to try to limit the temporal elements، to clarify their provisions and to distinguish between them in decree131/2 016، but for our Arab country it did not receive the appropriate answer. The problem of duration in contracts relates to the lack of clarity of the idea، and then to confuse the various time terms in the

Ephedra alata. is a plant that widely available around the world and long used in folk medicine as a natural medication, was employed in the current work to prepare extracts rich in alkaloids and to test their cytotoxic potential. Alkaloids-rich and crude extracts of E.alata were compared to pure ephedrine medication for mitosis on Allium cepa. test system. Alkaloids and crude aqueous extracts of A. cepa root tips were examined for a total of five hours at five different concentrations compared to ephedrine standard. Mitotic index, phase index, and chromosomal aberration as part of the study. IC50 values of 35 mg/ml were found for each extract, indicating a sub-lethal influence on cell viability. (Toxic and sublethal effects are thought to