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 main factors that make it possible to get the corrosion of reinforcing steel in concrete are chloride ions and the absorption of carbon dioxide from the environment, and each of them works with a mechanism which destroys the stable immunity of rebar in the concrete. In this work the effect of carbon dioxide content in the artificial concrete solution on the corrosion behavior of carbon steel reinforcing bar (CSRB) was studied, potentiostatically using CO₂ stream gas at 6 level of concentrations;  0.03 to 2.0  weight percent, and the effect of rising electrolyte temperature was also followed  in the range 20 to 50^ᴼ C. Tafel plots and cyclic polarization procedures were obeyed to investigate the c

The study aimed at identifying the role of the Faculty of Education in the community service in light of vision of the Kingdom 2030 from the faculty members’ point of view at the University of Jeddah. The study used a descriptive method through a questionnaire administered to a sample of the faculty members.It concluded that the role of the College in serving the community is the development of the right habits in the family and the importance of establishing bridges of cooperation between the Faculty of Education and the surrounding environment and teaching special education teachers how to apply some methods of measurement to determine the needs of students with disabilities. The results also pointed out that there are no statistical

            The increase in population resulted in an increase in the consumption of water. The present work investigates the performance of a recycling solar- powered greywater treatment system for the purposes of irrigation, used to reduce the amount of waste grey water and reduce electricity consumption and reduce the costs of constructing large scale water treatment plants. The system consumes about 3814W per hour and provides water treatment about 1.4 m³ per day. The proposed system is designed to    residential, office and governmental buildings application. Tests are conducted in an office building at the Ministry of Science and Technology site in Baghdad. Laboratorial water samples testing analyses are co

The study aims to examine the reality of preparing the Arabic language teacher for non-native speakers by presenting the experience of the Arabic Language Institute at the International University of Africa. Thus, it addresses the following questions: How is it possible to invest the long scientific experiences in proposal and experiment preperations to qualify Arabic language teachers for non-native speakers? What is the reality of preparing an Arabic language teacher at the Institute? How did the Arabic Language Institute process teacher preparation? What are the problems facing the preparation of the Arabic language teachers and the most important training mechanisms used in that Institute?What problems faced the implementation of the

Lung cancer is one of the most serious and prevalent diseases, causing many deaths each year. Though CT scan images are mostly used in the diagnosis of cancer, the assessment of scans is an error-prone and time-consuming task. Machine learning and AI-based models can identify and classify types of lung cancer quite accurately, which helps in the early-stage detection of lung cancer that can increase the survival rate. In this paper, Convolutional Neural Network is used to classify Adenocarcinoma, squamous cell carcinoma and normal case CT scan images from the Chest CT Scan Images Dataset using different combinations of hidden layers and parameters in CNN models. The proposed model was trained on 1000 CT Scan Images of cancerous and non-c

The study of the future of the international system currently appears, according to scientific data and existing facts in light of the emergence of international actors from non-states and international informal institutions, to be heading towards a non-polarity system and this trend is fueled by many variables to reduce polarity, and it is expected in the future that the international system will turn into a non-polarity.

Corruption, in all its categories and forms, is regarded as the nowadays virus which has greatly spread in most institutes and society, a matter that cause a great waste of resources.

      According to the reports of international transparency Institute, Iraq is regarded as one of the greatest countries in corruption.

      Regardless of the reasons and forms of corruption, the retreat in work – values and ethics are the main reasons behind that.

      Being the main source of providing qualified staff "educators" for the working market, the high education institutes face great challenges in standing against corruption inside and outside

This research aims to know the effect of adopting IFRS 9 on the relevance of the value of the accounting information of the companies in the Iraqi Stock Exchange. Researchers relied on analyzing the financial statements of 10 listed companies for years 2016 – 2019. Researchers used the Ohlson price model to test the relationship between accounting information and value relevance. The research indicated that there is a significant relationship between the adoption of IFRS 9 and the relevance of the value of the earnings and the book value, but the earnings information is more relevance than the book value information, it is due to the interest of investors in the income statement in making investment decisions.

The electronic payment systems are considered the most important infrastructure for the work of banks, particularly after a steady and remarkable development in information and communication technology, Which created the reality of the work of the infrastructure for these systems and these systems also become one of the most important components of infrastructure for the work of banks, cause it is one of the most important channels through which the transfer of cash, financial instruments between financial institutions in general and banking in particular.

     In order to achieve the objectives of the research, the most important to identify the concept of electronic payment systems, and its divisions, and th