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 .

Abstract

     My research dealt with the phenomenon of  repeated translation.

First Section deals with identifying repeated translation from both linguistic and terminological sides . Section two display the reasons and factors that stand behind this phenomenon while section three sheds light on the positive and negative sides of the phenomenon understudy and in  the last section , the researcher sets several recommendations which lead to prevent the widespread of repeated translation phenomenon .

چکیده

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Andalusian women enjoyed much historical news in the fluorescence of Andalusia, describing it as beautiful and good cohabitation, as the men were involved in conquests, including those who were wives of the caliphs, including scientists, singers, and adept writers Hassan and tongue, in addition to the acquisition of masters in slave markets in Cordoba, Seville and many cities, In addition, Andalusian women enjoy freedom in their relationship with men and have been reflected in the historical fluorescence of Andalusia, such as the book of the history of Ibn Abdul Malik bin Habib al-Alberi (d. And the collar of the dove repented in intimacy and thousands of Ibn Hazm al-Qurtubi (d. 456 AH / 1065 CE), the book of Hilla al-Sayra of Ibn al-Wel

A new Species of the Cerambycinae belonging to the genus Hesperophanes was found new to the fauna of Iraq and Science. H. testaceus was studied in details and the male genitalia were illustrated. Type's paratypes and the locality of this newly described Species were mentioned.

Targeted Search:

-scale preparation of teaching and professional competencies required for university professor from the perspective of students from different disciplines.

-scale application prepared by the researcher for the students to see how their preference for these competencies to their professors.

-limited Search: Find determined to present the following

-students of both sexes in the University of Baghdad.

2013 -      2012

The research aims to identify the most important areas of voluntary work available to women in society, stand on the most important controls that push women to work in voluntary areas in society. The research also seeks to stand on the most prominent obstacles to the voluntary work of women in society. The research contained four main chapters: Chapter I: Definition of research, Chapter 2: Objectives, areas, controls and effects of volunteer work, Chapter 3: Voluntary Work of Women in the Celestial Religions, and lastly, Chapter 4: Theories, Constraints, and Recommendations for Voluntary Work for Women.The researcher suggested several recommendations: 1-establishing a unit responsible for planning,

This paper deals with aesthetic and a sitting position in contemporary Iraqi sculpture and studied this situation, an analytical study to reveal how to employ them in aesthetically pleasing work of art has been research in a sitting position to a lack of technical library for such research, this study includes four chaptersChapter I contains the research problem and its importance in terms of the released address and its objectives in the detection of this situation, how to employ the HDL research is to detect how the aesthetic of the Employment sit position and limits Find business is bronze and stone-dimensional exclusively carried out from 2000 to 2009 AD.Chapter II included the Framework theory and previous studies and with three Inv

To develop a petrol engine so that it works under the bi-engine pattern (producer gas-petrol) without any additional engine modifications, a single-point injection method inside the intake manifold is a simple and inexpensive method. Still, it leads to poor mixing performance between the air and producer gas. This deficiency can cause unsatisfactory engine performance and high exhaust emissions. In order to improve the mixing inside the intake manifold, nine separate cases were modelled to evaluate the impact of the position and angle orientation inside the intake manifold on the uniformity and spread of the mixture under AFR=2.07. A petrol engine (1.6 L), the maximum engine speed (8000 rpm), and bi-engine mode (petrol-producer ga

This study calculated the surface roughness length (Z_o), zero-displacement length (Z_d) and height of the roughness elements (Z_H) using GIS applications. The practical benefit of this study is to classify the development of Baghdad, choose the appropriate places for installing wind turbines, improve urban planning, find rates of turbulence, pollution and others. The surface roughness length (Z_o) of Baghdad city was estimated based on the data of the wind speed obtained from an automatic weather station installed at Al-Mustansiriyah University, the data of the satellite images digital elevation model (DEM), and the digital surface model (DSM), utilizing Remote Sensing Techniques. The study area w