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 study aimed to investigate the employment of electronic supervision applications in developing the teaching performance of teachers in Oman. Based on the qualitative method and the study population consisted of all the teachers of the first cycle in the Governorate of Muscat. The study sample amounted to 24 female teachers. The interview was used as a tool for data collection. The study reached several results, including: There are difficulties in employing electronic supervision applications, which are weak network, density of curricula, lack of experience in applying technology, and the large number of tasks assigned to the teacher. These difficulties can also be overcome by strengthening the network, training teachers, reducing th

This research is considered one of the important researches in Maysan Governorate, as it focuses on the construction of helicopter airport project in the oil fields of the Maysan Oil Company, where the oil general companies in Maysan Governorate suffer from the cost of transporting the foreign engineering experts and the governing equipment of sustaining oil industry from Iraq's international airports to oil fields and vice versa. Private international transport companies transport foreign engineering from the oil fields to Iraqi airports and vice versa, and other international security companies take action to provide protection for foreign engineering experts during transportation. Hence, this process is very costly.

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            The objective of this study is to measure the impact of financial development on economic growth in Iraq over the period (2004-2018) by applying a fully corrected square model (FMOLS) Whereas, a set of variables represented by (credit-to-private ratio of GDP, the ratio of money supply in the broad sense of GDP, percentage of bank deposits from GDP) were chosen as indicators for measuring financial development and GDP to measure economic growth.

Major tests have been carried out, such as the stability test (Unite Root Test), the integration test (Cointegration). Results of the study showed that there

The current study aims at the extent of determining the interest of the Ministry of Higher Education and Scientific Research and its various departments in the process of strategic foresight, and whether this interest is reflected in its strategic decisions if the study relies on an exploratory and analytical approach and has targeted managers in the higher management within this ministry, and the questionnaire has also been used as a basic tool for collecting For data, the study population was (94), (89) questionnaires were distributed, (86) questionnaires were retrieved, and usable questionnaires amounted to (83). The sub-variable had the highest impact on strategic decision-making (intuition), as this research demonstrated the

The historical person study as a personality to the AL- Bazargan, one of the important
studies, is the shed light on the character had an effect of the political life in Iraq, an important
historical era involved many events, coincided with a national and historical by this personal
at the events successive positions that stage of the history of Iraq, especially if we know,
strongly his loyalty to the homeland and the earth, and intense hatred for any occupation or
colonization desecrate the land...
This was evident during his participation and his supervisor in 1920 liberal revolution
against the British occupation, and urged the need for adherence to the principles of
independence, and the emphasis on the nation

This research highlights the light on the general framework of accounting discloser in the Islamic banks, and show the types and the concepts of Cost Efficiency, In this present study, the sample included Fourteen Islamic banks, where the data was collected from the annual financial reports. Accordingly, the study in order to achieve the aims and access to the results based on the analytical method and the descriptive analysis, and conducted a Simple & Multiple Linear Regression analysis, in order to test hypotheses of the research by using of statistical analysis software (SPSS). The research has arrived to many results such as: the commitment of Islamic banks working in the Kingdome of Bahrain (Wholesale) to the requirements of the

Vehicular Ad Hoc Networks (VANETs) are integral to Intelligent Transportation Systems (ITS), enabling real-time communication between vehicles and infrastructure to enhance traffic flow, road safety, and passenger experience. However, the open and dynamic nature of VANETs presents significant privacy and security challenges, including data eavesdropping, message manipulation, and unauthorized access. This study addresses these concerns by leveraging advancements in Fog Computing (FC), which offers lowlatency, distributed data processing near-end devices to enhance the resilience and security of VANET communications. The paper comprehensively analyzes the security frameworks for fog-enabled VANETs, introducing a novel taxonomy that c