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 research aims to study the elements of attraction in television advertising and determine their relationship to consumer preferences, the extent to which the sample (250) watches television advertisements, and the motives for viewing. Males and females, and the statistical program spss was used to analyze the results using percentages, arithmetic mean, correlation coefficients ch2, Pearson’s coefficient and Alpha Cronbach for the stability of the test, and the research came to the conclusion that the percentage of watching television advertisements is good motivated by the identification of new goods and services in the market, as advertisements sometimes achieve consumer preferences, and the most prominent The forms that a

الموازنة العراقية قبل عام 2003 تعاني من مشكله العجز فعلي بسبب انخفاض كمية تصدير النفط وانخفاض ايرادات الدولة ولكن بعد عام 2003 وبعد تحسن الوضع المالي للبلد (زيادة ايرادات الدولة) بسبب فك الحصار عن العراق وزيادة كميات النفط المصدرة اصبحت المشكلة التي تعاني منها الموازنة العامة هي العجز المخطط من عام (2004- 2018) .وبسبب الاعتماد على الايرادات النفطية نلاحظ في حالة زيادة اسعار النفط تزداد ايرادات الدولة فيزداد الت

1. S. Eliot is one of the important founders of the modernist movement in literature, a cutting-edge poet of the first order. After his 1927 conversion to Anglicanism, he began calling himself a conservative, royal, and a classicist.

"Ash Wednesday" is the first long poem written by him after his conversion. It deals with the struggle that ensues when one who has lacked faith acquires it. It is richly but ambiguously allusive, and deals with the aspiration to move from spiritual barrenness to hope for human salvation.

"Ash Wednesday" not only struggles with an approach to faith but with an approach to a language capable of expressing it. Eliot's style is different from that that predates his conve

The main idea of this paper is to define other types of a fuzzy local function and study the advantages and differences between them in addition to discussing some definitions of finding new fuzzy topologies. Also in this research, a new type of fuzzy closure has been defined, where the relation between the new type and different types of fuzzy local function has been studied

The objectives of research to identify the maximum consumption of oxygen index (VO2max) predictable by knowing the concentration of lactic acid after the maximum physical effort and determine the percentage contribution of the concentration of lactic acid in the maximum consumption of oxygen index (VO2max) and find the equations of predictive indicator under study suppose the researchers that there is a statistically significant correlation between reduction index Aqsa for the consumption of oxygen and the concentration of lactic acid after the maximum physical effort and physical effort maximum influence constant variable under study and the researchers used the descriptive style of one group were identified variables of the maximum consum

يتناول البحث الحالي احد الاساليب المعروفة والمستخدمة في تحليل الاسهم بصورة منفردة او ضمن (قطاعاتها الصناعية) الا وهو اسلوب تحليل القوة النسبية.

ولاثبات فرضية البحث تم اختيار سوق العراق للاوراق المالية لكي يكون مجتمعا للبحث، ومن ثم اختيار عينة عمدية مؤلفة من ثلاثة عشر سهما من اسهم الشركات المدرجة في هذه السوق لتكون ميدانا للبحث.

توصل البحث الى عدد من الاستنتاجات، الا ان اكثر

Polymer electrolytes were prepared using the solution cast technology. Under some conditions, the electrolyte content of polymers was analyzed in constant percent of PVA/PVP (50:50), ethylene carbonate (EC), and propylene carbonate (PC) (1:1) with different proportions of potassium iodide (KI) (10, 20, 30, 40, 50 wt%) and iodine (I₂) = 10 wt% of salt. Fourier Transmission Infrared (FTIR) studies confirmed the complex formation of polymer blends. Electrical conductivity was calculated with an impedance analyzer in the frequency range 50 Hz–1MHz and in the temperature range 293–343 K. The highest electrical conductivity value of 5.3 × 10^-3 (S/cm) was observed for electrolytes with 50 wt% KI concentration at room

The research aims to achieve several goals، which are to reveal the issues that the social marketing campaigns organized by the community police in the Iraqi Ministry of Interior focus on، and to identify the communication methods that are used in the social marketing campaigns، as well as to reveal the audience groups that are targeted by the social marketing campaigns organized by them. Community police، as well as identifying the slogans that community police used in their campaigns، and revealing the extent to which community police use new ideas in social marketing campaigns ،The researcher adopted the survey method، relying on content analysis in form and content، to analyze the publications related to social marke