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 .

الخلاصة
یعد والت وتمن شاعرا استثنائیا سواء أكان ذلك في المكانة التي یحتلھا في الأدب الأمریكي او في نمط
اع t ذا الإیق t لة ھ t ة وص t وافقي خاص t اع الت t تخدامھ الإیق t ي اس t دي ف t ر تقلی t عرا غی t الشعر الذي یكتبھ. لقد كتب وتمن ش
ل t ة للتوص t ف الطبیع t وافقي لوص t اع ا لت t ن الإیق t تخدم وتم t ر ، اس t بوحدة الكون الذي عبر عنھ في شعره.وبمعنى آخ
نص t ل ال t جام داخ t رابط وانس t یج مت t ھ نس t ق انظم t دف لخل t ھ تھ t اھره أدبی t واف

The intensification of competition in the business environment has forced research organizations to develop marketing dynamics that help them to sense and conceptualize market opportunities and uncertainties. Then, the marketing capabilities of the organization are restructured and developed according to mechanisms such as speed, timing, and frequency of application. The problem of most organizations is their lack of interest in capabilities  Marketing dynamics, which represent the most important factor in enhancing their marketing performance, so the objective of the research is to identify the most important capabilities that banks should pay attention to and evaluate their role in determining the strategic direction of th

The education sector, before and after 2003, inherited a heavy legacy. Successive governments are trying hard to reduce the effects of that legacy by filling the shortage in school buildings. The best example of this is the shortage in public schools in Wasit governorate, as this governorate lacks a number of factors that make education in it. Vulnerable due to the lack of schools, where we find in most government schools that the number of students in one class is more than 50 male and female students, as most parents resorted to registering their children in private schools, so we will address in this research to some predictive methods to find solutions Where we dealt with the traditional trend methods represented by the exponential smoo

The study aimed to evaluate the antimicrobial activity using different concentrations of aqueous and alcoholic extracts of dried lemongrass leaves. Chemical phytochemical tests were performed for aqueous and alcoholic extracts of lemongrass. Antimicrobials activity was tested using agar disc diffusion method against Escherichia coli and Staphylococcus aureus. The results of the study showed that the aqueous extract of dried lemon leaves was highly effective (P≤0.05) against S. aureus, as the inhibition diameter was 22 mm for 50 dilution, while the inhibition diameter decreased to 15 mm for concentration 100. As for the alcoholic extract only, the diameter of inhibition decreased significantly (P≤0.0

A field experiment was carried out at the research station of the College of Agriculture - Wasit University / Kut, during the fall season 2021 in soil with texture (sandy mixture) using the RCBD design in the arrangement of splintered plates and with three replications, to study the effect of spraying different combinations of organic emulsion (Appetizer) and NPK nano fertilizer with urea fertilizer on the growth of synthetic cultivars of yellow corn. The main panels included three synthetic varieties of yellow corn (Fajr1, Sumer and Baghdad3), which symbolized by (V1,V2,V3) in sequence, while the secondary panels included five fertilization treatments in which mineral fertilizer (urea) was used 46% nitrogen with the full recomme

  The life insurance marketing faces many difficulties because it is not a current tangible commodity, so it needs a planning for promotional activities and data about prospective applicants according to many factors such as age and residence area ​​, marital status and profession to determine the group wich need insurance covers.                                                                    &nb

The increasing rates of consumption of cigarettes harmful, to health in the world in general, and in Iraq in particular, and because of the costs borne by individuals, and the state as a result of addressing its damage, as well as Iraq's commitment, to international conventions against cigarettes, and demands of the World Health Organization, to raise prices to reduce consumption. Therefore, the tax Selectivity is one of the most important ways of regulating the consumption of this commodity on the one hand and increasing the tax revenue on the other. The research aims to shed light on the issue of selective tax on cigarettes and the impact of their application in increasing tax revenues and identify the effectiveness of the application

This study has been carried out in the animal field of the college of agricultural engineering sciences, university of Baghdad, for the period from 12/15/2021 to 1/26 /2022 for 42 d, to investigate the effect of adding different levels of ellagic acid to the diet of broilers, on some physiological characteristics &  oxidation indicators in meat compared to vitamin C in meat,  225 Ross 308 chicks were used, divided randomly to five treatments such us: T1: control group without additives to diet, &  the other T2, T3, T4 was added  ellagic  acid (