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 .

In this research The study of Multi-level  model (partial pooling model) we consider The partial pooling model which is one Multi-level  models and one of  the Most important models and extensive use and application in the analysis of the data .This Model characterized by the fact that the treatments take hierarchical or structural Form, in this partial pooling models, Full Maximum likelihood FML was used to estimated parameters of partial pooling models (fixed and random ), comparison between the preference of these Models, The application was on the Suspended Dust data in Iraq, The data were for four and a half years .Eight stations were selected randomly  among the stations in Iraq. We use Akaik′s Informa

   يهدف البحث إلى التعرف على The research aims to identify the effect ofاثر التركيب العمري للسكان على الناتج المحلي الإجمالي في العراق وتحديد الفئات العمرية من أطفال ومنتجين أي من هم في سن العمل والمسنين لأهمية ذلك لإغراض التخطيط الاقتصادي.إنeffectofeee age structure of the population on GDP in Iraq and determine the age groups of children and any of the producers wham are of working age and the elderly of the importance for the purposes of economic planning. نسبة الفئة العمرية Proportion of the age group (00- -4 4سنوات اقتربت من

Faith is a feature of the Mesopotamian population, since the ancient Mesopotamian was a believer and obedient to his God in any case, and this encouraged the emergence of some of the phenomena interpreted by historians as an integral part of the civilization and ancient history of this country, and these phenomena are the phenomena of the deification of kings for themselves, The first phenomenon was a personal endeavor for the uniqueness of power, sometimes to correct some mistakes in societies to balance the state, and civil rule is independent of religious rule, and the second was the result of divination and predictions of omen, in the case of any bad harbinger of the king, such as the occurrence of eclipse To the sun or a lunar eclip

The research sought to demonstrate the effectiveness of monetary policy in banking stability by measuring the impact of monetary policy in the composite index of banking stability in Iraq for the period 2010/2017, as the stability of the financial system is one of the main objectives that the Central Bank is keen to achieve along with other objectives to ensure the performance Effective for all economic units, this is what prompted the central banks to give more attention in ensuring the safety, durability and stability of their financial systems, and the increasing interest by the Central Bank of Iraq in the subject of financial stability stems from its responsibility in ensuring a sound and stable financial system. Maintain it and mini

This research aims at studying each of the cold and hot thermal wavelengths affecting
Iraq for a minimum climatic course of 11 years beginning from 1992 till 2002. Three stations
were selected including the parts of Iraq surface: Mosul, Baghdad and Basrah.
The wave days were also connected with the related climatic elements represented by
the wind direction and speeds and the relative humidity. It was shown that Iraq is affected by
the rates of hot thermal wave lengths greatly compared to the rates of cold wavelengths. The
results suggested that the highest rate of hot and cold wavelengths recorded over Basra station
was (3.5) days for the cold and (5) days for the hot. While the lowest rates was at Mosul
station

 This study dealt with the basics of financial inclusion in terms of concept, importance and objectives, The empowerment of women financially and bank,and then the relationship between financial inclusion and women, and determine the requirements of inclusion Financial resources for women. The analytical descriptive method was used for data, which included reviewing and analyzing information And data in economic and financial literature. The study: reached a number of conclusions, the most important of which are Financial inclusion contributes to women's financial and banking support, as there is a positive relationship between financial institutions Banking and women's access to financial and banking services, thus playing a role i

              Due to the increasing interest in the quality of auditing by writers, researchers and regulators of the auditing profession. The matter necessitated a statement of the extent to which the auditor practices professional skepticism, because of its significant impact in discovering errors and material misrepresentations contained in the financial statements in order to give the financial community confidence in them and the success of the audit process. The research aims to clarify the concept and importance of the practice of professional skepticism and its effect on the quality of the auditor's performance in Iraq. To achieve the research objectives, the two re

In this research, the focus was placed on estimating the parameters of the Hypoexponential distribution function using the maximum likelihood method and genetic algorithm. More than one standard, including MSE, has been adopted for comparison by Using the simulation method

The aim of the research is to reveal the reality of teacher performance evaluation in the Sultanate of Oman in light of some global models. The study followed a qualitative descriptive research design. Seven forms of teacher formative and summative assessments were analyzed. Besides, an analytical template was developed, consisting of six areas related to the teaching performance of teachers. These included: lesson planning and preparation, learning environment, education, professional development, student academic, and community and parental partnership. The study reached a number of results; the most notable is the lack of change of forms for more than a decade despite the rapid development of the educational system in the sultanate in