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 aim of this paper is to know the persuasive methods and public relations strategies in building the reputation of the United Arab Emirates, since the UAE is progressing among the international indicators in good reputation. The researcher used the survey method, using the content analysis tool, to analyze the publications of the UAE Ministry of Foreign Affairs and International Cooperation for the period from 10/1/2021 to 12/31/2021.The researcher reached a set of results, the most important of which are: The UAE Foreign Ministry relied on public relations strategies in order to build a good reputation for the country, as it focused on the media strategy and gave little importance to the consensus-building strategy, as well as focuse

ABSTRACT

The research aims to identify the role of scientific planning of inventory by determining the quantity of economic demand and the number of times of purchase and associated annual total costs to achieve a sufficient and appropriate level of inventory . The research was based on the case study methodology. Materials of increasing demand in the Institute of Technical Management and knowledge of the degree of conformity of the procurement plan with the standard indicators adopted in a scientific method ,its include economic order quantity and number of purchasing times .
one of The main results  of the research was  the existence of a large difference between the quantity of the economic purchase of ea

The aim of the research: To identify the trends of students of the College of Physical Education and Sports Sciences towards modern teaching methods. To determine the type of strategies used that students prefer in practical lessons. In light of the research results, the researcher adopted the descriptive method because it is appropriate for the study. The research community is represented by students of the College of Physical Education and Sports Sciences (fourth stage), amounting to (320) students. Conclusions: The research results indicate that students of the College of Physical Education and Sports Sciences have positive and strong attitudes towards using modern teaching methods, and they realize their reality in improving interaction

Mishrif Formation is the main reservoir in oil-fields (North Rumaila, South Rumaila, Majnoon, Zubair and West Qurna) which located at Basrah southern Iraq. The Inductively coupled plasma-Mass spectrometer (ICP-MS) was used for the water chemistry analysis and Scanning Electron Microprobe (SEM) for the purpose of mineralogy diagnosis. A weak acidic water of salinity six-time greater than seawater plays a role in generating the formation pressure and controlling the fluid flow. The potentiometric subsurface maps were modeled and the direction of super-pressure sites that are of a great importance in the oil exploration were marked to pay attention during future drilling.

Records of two regionalized variables were processed for each of porosity and permeability of reservoir rocks in Zubair Formation (Zb-109) south Iraq as an indication of the most important reservoir property which is the homogeneity,considering their important results in criterion most needed for primary and enhanced oil reservoirs.The results of dispersion treatment,the statistical incorporeal indications,boxes plots,rhombus style and tangents angles of intersected circles indicated by confidence interval of porosity and permeability data, have shown that the reservoir rocks of Zubair units (LS),(1L) and (DJ) have reservoir properties of high quality,in contrast to that of Zubair units (MS) and (AB)which have reservoir properties of less q

This research worked on identifying the effect of increasing the volume of indebtedness by companies listed on the Iraq Stock Exchange on the trading volume of those companies, and this research included some theoretical concepts related to both debt financing and trading volume, and it represents the research community of the joint-stock companies listed in The Iraq Stock Exchange (the banking sector). As for the research sample, it was deliberately chosen represented by companies with continuous trading without stopping, which reached 10 joint-stock companies, and the period of research was extended during the period 2011-2015, and a set of indicators and financial methods were used In measuring research v

 هدف البحث التعرف الى اسباب سلوك التنمر لدى طلاب الصف الاول المتوسط من وجهة نظر المدرسين والمدرسات واساليب تعديله، واستعمل الباحثان المنهج الوصفي واختيار عينة عشوائية من المدرسين والمدرسات في متوسطة أرض الرافدين ومتوسطة الرحمن للبنين وكان عددهم (46) مدرساً ومدرسة بواقع (32) مدرساً و(14) مدرسة، واعتمد الباحثان الاستبانة أداة للتعرف الى اسباب سلوك التنمر واساليب تعديله، واشارت نتائج البحث الى تنوع اسباب التن