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 .

Competitive advantage is a substantial  strategic objective for organizations. It requires high levels in the quality of products and services provided to customers, continuous improvement of costing , care for creativity and innovative employees, and speed unique to the marketing and financial engineering, and business re-engineering processes. The situation in this area, requires actors to attract and develop human resources, including help in proper implementation of the strategic tasks that targeted by those institutions. According to the opinions and viewpoints of management scholars, the competitive advantage resource is the most important issue for organizations in the third millennium, which can be a

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

The marketing of banking service is considered to be one of the impotent fields which showed a universal inebriates . He research showed the comparison between the application of marketing in ideas and application for loot government and private Iraqi bank. The research comets of four parts; Mythology / the concept and the importance of Banking Marketing / Research applichlion/ Conelnion and  recommendation.

Determining risk indicators for dental implants is an essential strategy for preventing peri-implant diseases and effective diagnosis of dental implant success. To investigate the impact of certain potential factors on the osseointegrated dental implant. Eighty-four individuals were included in our study, 50 cases as a patient’s group and 34 participants as a control group. All cases were diagnosed based on certain criteria, 30 (60%) of patients had peri-implantitis, 20 (40%) with severe periimplantitis, 36(72%) were generalized, and 15 (30%) as localized peri-implantitis cases. The study has indicated that 44.7% of dental implants were in the anterior maxilla, followed by (27.3%) posterior maxilla, (17.4%) posterior mandible, and (10.4%)

 The aim of this study was to provide an overall assessment to the efficiency of the Iraq stocks exchanges (ISE) through specifying well –known models .First, Fama's efficient market hypothesis as a contrary concept to the random walk hypothesis, was performed and it has been found that ISE follows the random process, so the price of the shares can't be predicated on the basis of past information. Second,we use a multifactor model, which so named multiple regression, to explore the link between ISE  and the main economic indicators. our empirical analysis finds that every weak associations exists between major ISE measures and main economic indicators.

    In the drilling and production operations, the effectiveness of cementing jobs is crucial for efficient progress. The compressive strength of oil well cement is a key characteristic that reflects its ability to withstand forceful conditions over time. This study evaluates and improves the compressive strength and thickening time of Iraqi oil well cement class G from Babylon cement factory using two types of additives (Nano Alumina and Synthetic Fiber) to comply with the American Petroleum Institute (API) specifications. The additives were used in different proportions, and a set of samples was prepared under different conditions. Compressive strength and thickening time measurements were taken under different conditions. The amoun