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 .

A sensitive and accurate colorimetric method was developed for the determination of the Sitagliptin phosphate monohydrate, here and after will be named Sitagliptin, in its pure and pharmaceutical form. The suggested approach is based on boosting the sensitivity of the traditional spectrometric methods by derivatizing Sitagliptin into a colored product that absorbs the visible spectrum at 573 nm. The proposed method has effectively improved the sensitivity and the limit of detection for the analysis of Sitagliptin. A linear calibration curve was obtained over the concentration range of 0.1-10 μg/ml with a correlation coefficient of 0.9983. The calculated recovery was within the range of 98.98–100.11%. While the limit of detection LOD and

The literature shows conflicting outcomes, making it difficult to determine how e-learning affects the performance of students in higher education. The effect of e-learning was studied and data has been gathered with the utilization of a variety of qualitative and quantitative methods, especially in relation to students' academic achievements and perceptions in higher education, according to literature review that has been drawn from articles published in the past two decades (2000-2020). The development of a sense of community in the on-line environment has been identified to be one of the main difficulties in e-learning education across this whole review. In order to create an efficient online learning community, it could be claim

In this article we study the variance estimator for the normal distribution when the mean is un known depend of the cumulative function between unbiased estimator and Bays estimator for the variance of normal distribution which is used include Double Stage Shrunken estimator to obtain higher efficiency for the variance estimator of normal distribution when the mean is unknown by using small volume equal volume of two sample .

This research aims to identify the role that forensic accounting plays on the transparency and quality of the financial statements in trade bank of Iraq and the Gulf Commercial Bank in Babylon. This research came to address the problem that most financial institutions suffer from, which is represented by the lack of transparency and the quality of the financial statements issued in a manner. Annual also the manipulation and fraud in the financial data, which causes a big gap between that institutions and organizational stakeholders. According to the implementation of the research hypothesis and the objectives of the research, a questionnaire was prepared consisting of three axes, the first axis dealing with the demographic distri

The current research aims to diagnose the role of social responsibility as a contributing factor in enhancing the quality of services provided by the public sector in Iraq, where the research sought to demonstrate the relationship and impact of social responsibility dimensions (economic, legal, moral, and human) on the sector Services related to the electric field in Nineveh governorate because of its importance and its direct relationship with the citizen especially after the end of military operations in the destruction of the electricity sector by a large percentage in the city of Mosul. Nineveh Electricity Distribution Directorate / Center was chosen as a research community including (administrators and staff) of the research

    رافقت القسوة الانسان منذ القدم  وكثيرا ما تم الخلط بينها وبين العنف لشدة التقارب بينهما , وهنا يحاول البحث  ان يفصل بين كلا المفهومين ويتفرد بمفهوم القسوة, الذي سلط عليه الضوء في المسرح لأول مرة على يد الفرنسي(انطوان ارتو)  في محاولة للكشف عن المعالجة الاخراجية التي قدمها المخرج العراقي(صميم حسب الله) لمفهوم القسوة في مسرحيته الموسومة (خريف) ويتضمن البحث نبذه  (مفهوم القسوة في الفكر الانساني) وكذلك (الق

The aim of the current research is to find out the extent to which algebraic thinking skills are included in the mathematics textbook for the third intermediate grade for the academic year (2020-2021) by answering the main research question:What algebraic thinking skills are included in the mathematics textbook for middle third grade?The descriptive and analytical approach was used, and to achieve the goal of the research, a list of the main algebraic thinking skills and the sub-skills were prepared, and after analyzing the content of the mathematics textbook, the stability of the analysis was verified through the analysis over time and across individuals using the Holsti equation, and

Abstract

         Uncertainty, the deeply-rooted fact that surrounding the investment environment, especially the stock market which just prices have taken a specific trend until they moved to another one for its up or down. This means that the volatility characteristic of financial market requires the rational investor an argument led towards the adoption of planned acts to gain greater benefit in the goal of wealth maximizing. There is no possibility to achieve this goal without the burden of uncertainty and the risk of systematic fluctuations of investment returns in the financial market after the facts of  efficient diversification have pro

The features of the actor's performance in the ritual theater are of great importance and chief in theatrical work since the first emergence of the theater, as the features of the performance were embodied in all Iraqi theatrical performances, but they took personal privacy in some ritual performances because of their differences and similarities between the ritual theatrical performance and the ritual show Al-Khalis, who wanted the researcher to know the similarities and differences in the features of the ritual performance and in the theatrical performance, despite the many transformations that occurred in the theater and affected the features of the performance, but it remained an important and attractive link between the recipient, t