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 research deals with the lyrical introduction in the commentary of Tarfa bin al-Abd as a formative system characterized by flexibility and richness of imagination, which achieved a formative treatment and a unique construction within the structures of the structural and semantic language. I dealt with the poetic verses represented by the lyrical introduction as a formative hypothesis, basing its goal on a methodological framework distributed on the problem that was summarized by the following question: Is it possible to look at the poetic pattern within the pre-Islamic poem / hanging blinking as a model, in its plastic dimensions and to identify the stylistic treatment that achieves the formation space within the poetic text. The rese

Resumen

El presente trabajo nace de una inquietud por la enseñanza del español en Irak a nivel universitario especialmente ante las dificultades que los alumnos árabes en general, e iraquíes en particular, encuentran en su proceso de aprendizaje. Nuestra primera inclinación fue, pues, prestar una atención directa  y cercana al alumno como sujeto del aprendizaje, así como a lo que el alumno produce como resultado del mismo. En el presente trabajo pretendemos dotar al estudiante de los conocimientos lingüísticos necesarios para poder interaccionar en una variedad de situaciones y enfrentarse a problemas cotidianos, de manera que desarrolle las destrezas comunicativas que le permitan establecer una co

This research aims to solve a problem in the field of accounting and financial knowledge in the world today, that is, the problem of creative accounting. Especially after the global financial crisis and the collapse of many large companies in the world, people find that they use creative accounting methods to distinguish them from reality, showing the results of their activities and their financial status. This research discusses the concept of creative accounting, the most important methods used in financial statements and its relationship with external auditing, and procedures to limit accounting creativity. This study uses descriptive analysis methods after confirming its theoretical aspects in practice. Using the statistical

Background: Tap waters play an important role in fulfilling the people needs for drinking and domestic purposes. Contaminate the tap water with different pollutants has become an issue of great concern for 90% of people who are depended on the tap water as the main source of drinking. Pollutants can make their way easily into the delivering pipes which suffer from the leaking resulting in decreasing the quality of water. Objective: Therefore, assess the water quality for drinking purpose by calculating the water quality index is an important tool to ascertain whether the water is suitable for human consumption or not. Methods: In the present work, the water quality of the Al-Salam, western region of Baghdad city, Iraq was investigated for 7

       Metaphor is a linguistic phenomenon related to people's cultures. It is an integral part of cultural heritage. This paper tackles the use of animal-based metaphors in the field of football club titles so as to draw comparisons between those in Russian with their counterparts in Arabic. Names of animals are used to refer to some clubs and teams, where these names or titles reflect animal features such as strength, preying on victims; or animal figures are employed in the club symbols, or due to the similarity of the club shirt to the animal outer shapes in colours. For instance, "an-Nawaris", which means gulls in English, is used to refer to az-Zawraa club du

The goals of endodontic preparation were to shape and clean the space of the root canal and remove microorganisms, affected dentin and pulp, the apical foramen and the canal curve should be protected from being transported during endodontic canal preparation. The aim of this study was to evaluate the curve straightening of curved root canals and apical transportation after preparation with four rotary systems. Forty mesial roots of the lower 1st molars teeth only the mesiobuccal canals were used, these roots were immersed into cold clear acrylic , the teeth roots divided into four groups according to rotary system used for preparation of the canals (ten roots for each group):. group I: ProTaper Next rotary system, group II: IRaCe Plus rotar

This research is aimed at identifying the communicative habits and the impact of the content on the communicative process, especially the youth audience, which is one of the most important categories to which the advertisement is directed, as young people face life with passion and aspiration that make then responsive to all the influences used by the media in designing advertisements which use all the techniques and methocls to attract young people, such as relying on drama , artistic tricks, musical phrases and advertising slogans that respond to the desire of young people in entertainment.
The research aims to identify the reflection of television advertising and its impact on the development of the cognitive abilities of universi

This search includes the preparation of Schiff base ligand (SB) from condensation primary amine with vanillin. The new ligand was diagnosed by spectroscopic methods as Mass, NMR, CHN and FTIR. Ligand complexes were mixed from new (SB) and Anthranillic acid (A) with five metal (II) chlorides. The preparation and diagnosis were conducted by FTIR, CHN, UV-visible, molar conductivity, atomic absorption and magnetic moment. The octahedral geometrical shape of the complexes was proposed. The ligands and their new complexes were screened with two different types of bacteria.