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 Turks used the Ottoman Turkish language from the thirteenth century to the twentieth century.  During this period and under the influence of Islamic civilization, a large number of words and structures were used from the Arabic and Persian languages, Therefore, many Arabic grammatical structures were used in the Ottoman Turkish language, such as the definite article simply because it was widely used.

The paper is concerned with the use of the Arabic definite article in the Ottoman Turkish language, and the aim of this contrastive study is to find out the similarities and differences between the two languages ​​in terms of meaning and structure. Since linguistic studies depend on the practical side or applied approach, two

The process of evaluating business processes, complex, repetition of procurement processes, need for raw materials and frequency of demand, which makes dealing with suppliers in the evaluation process, making the need for a process intervention in the process. Lighter on the other hand.

Many Iraqi companies suffer from problems related to suppliers, and cases of administrative and financial corruption are often raised regarding this type of contract and from this reality the necessity of researching this problem and trying to develop some solutions to reduce its impact on the companies' work, by using a method that works according to the standards adopted in Evaluation and selection of the supplier in the

The science of (- - Semiology) comes in the introduction to language sciences and linguistics that addressed the levels of language building and its phonemic signs, through which we can monitor and analyze the data of the phoneme of the actor, and the ways to build his linguistic speech, especially since (the linguist Saussure - He emphasized that linguistque is only part of the science of signs, which is particularly advanced within logic, social psychology, and general psychology, and since language is in the origin - whatever language, and at what level - it is not A separate, single and unified language, in fact, they are intertwined, multiple, varied and renewed languages due to their influence The times and its development and the

Luqman's story stated that human instinct, if I was brought up properly, reaches wisdom and inflicts the right to everything. It is to go to worship God and adhere to the satisfaction of morals and high morals that are ordered to meet among human beings in this life, because this worship educates in the soul the most beautiful morals needed by human beings of honesty, honesty and modesty, and the work of good and virtues, and distancing the soul from evil and vices.

The military presence in the Gulf region after the British withdrawal from it in 1971 was one of the most important pillars of the American strategy to climb the ladder of global leadership, as the geostrategic features that the region enjoyed provided factors of controlling energy sources and global trade routes. The United States of America guarantees Western Europe and Japan the process of access to energy sources and the exclusion of its opponents from the region, especially the Soviet Union, and the growing American military presence in the Gulf after the invasion of Iraq in 2003. On the other hand, the region experiences many contradictions, some of which threaten its security, such as the exacerbation of disputes between its count

Urban planning task and the control of constructional planning and urban management for cities considers the main tasks that the government takes care off. The paper discusses the concept of power from historical view of ancient Islamic cities to discover the strategies of urban management that the Islamic city adopt and to employ it in contemporary cities ,the more problems that modern cities suffer from which appears through poorness of urban context ,belongs to the loss of balance exists between the different faces of power that takes the tasks of urban management .therefore enhancement of urban environment is being through re-back that balance in administrative structures that make the cities go ahead . So the attention has b

In light of the increasing interest in Child-rearing in nurseries and kindergartens and the most important experiences gained by the child at this stage that form the basis for the subsequent stages of her/his physical mental and social growth.

The significance of the research concentrates the need to asses the affecting variables on the child growth to create opportunities for her/him to have intact rearing.

The research also aims to classify these variables at each age level and highlight its moral role.

The problem of the research is the lack of clarity of different variables impact of the child growth in different age levels in nurseries and kindergart

Gaining the relationship between the central government and local governments is great importance especially after the expanded functions of the central government and became unable to carry out their works without all that delegate or transfer parts of its powers to lower levels.

The aims of the research is  to determine the relationship of the central government with the local government in accordance with the principle of administrative decentralization with the presentation of the competent authorities, the control of local governments, according to the Provincial Council Act No. 21 of 2008 amended.

The research has a problem that has been the relationship of the central