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 .

All foreign language teachers highlight the difficulties students face during learning. The aim of this work is to explain the most complex problems of teaching foreign language grammar to Spanish language students at the University of Baghdad. Its methodology is based on an assessment of a group of intermediate-level students in the Faculty of Languages ​​at the University of Baghdad. Furthermore, the responses are analyzed, and the errors are described. We conclude that the best method for teaching the passive voice to students is based on an analysis from syntactic and morphological perspectives. We present the main distinguishing characteristics of the Spanish language to students and offer some recommendations for learning Spanish

This research is an attempt to study and evaluate the maintenance function at Factory 7 - The State General Company for Leather Industries, and to design a computerized preventive maintenance system to design and to analyze preventive  maintenance.  To accomplish the objectives of this research, data were gathered and analyzed according to the reliability engineering criteria for the period 2/1– 30/6/2005, then a preventive maintenance plan was designed for each machine of the sample study using the computerized system designed in this research. A Monte Carlo Simulation methodology was used for the purpose of evaluating the performance of the preventive maintenance plan of each machine for one year. The simulation res

هدفت الدراسة إلى قياس النشاط الكهربائي (المعدل والقمة) للعضلة الصدرية العظيمة لجهتي اليمين واليسار في تمرين الضغط على المسطبة المستوية باستعمال الأثقال الحرة وجهاز سميث، والتعرف على الفروق في النشاط الكهربائي للعضلة الصدرية العظيمة اليمين واليسار في تمرين الضغط على المسطبة المستوية باستعمال الأثقال الحرة وجهاز سميث وفي الشدد (50% و 75% و100%). واستعمل الباحث المنهج التجريبي بأسلوب المقارنة. وتم اختيار عينة

المقدمة:

تعد الخطوة الأولى او خطوة البداية من اهم التحديات التي تواجه الاقتصاديين وصناع القرار في العراق لإعادة تنظيم الاقتصاد العراقي وإعادة اعمار ما دمرته الحروب والسياسات الاقتصادية السابقة على حد سواء، فالتخلف ضارب إطنابه في كل مكان، فهناك تخلف في القطاعات الرئيسية المختلفة كالقطاع الزراعي والصناعي وهناك تدمير في البنية التحتية نتيجة الحرب وما قبلها واختلال في الإنتاج ومعدلات ع

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Humanity has Suffered Greatly from the Economic crisis and instability, Before the Emergence of the rule of the Capitalist System, However, the reaons were Different. But almost Completely Contradictory. At a time When the Causes of the Crisis was due to the time Factor is the product of failure of productie forces, Bears modern Crises resoled by the progress that is in the embrace of the abundance, and as far as lies in the nature and content of the capitalist system itselfas a system based on the creation of productive capacities in excess unable to accomplish through demand by the chaos of production based,  on the logic of the market on one hand, and the nature of the output and direction. On the other hand the relations

The research aims to measure the extent of the impact of Earnings quality in the continuity of the company for a sample of private commercial banks listed on the Iraq Stock Exchange. The research sample included (15) of the listed commercial banks that continue to issue their financial statements for the period from (2009-2018).The research relied on three main models of measurement and on four steps. The first step is to measure the Persistence (Earnings Quality) by Depending the sustainability model. While the second step included measuring the Predictability of accounting profits by deriving the square root of the disparity of the estimation error from the first model Persistence (Earnings Quality), and the third step included