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 .

Twitter data analysis is an emerging field of research that utilizes data collected from Twitter to address many issues such as disaster response, sentiment analysis, and demographic studies. The success of data analysis relies on collecting accurate and representative data of the studied group or phenomena to get the best results. Various twitter analysis applications rely on collecting the locations of the users sending the tweets, but this information is not always available. There are several attempts at estimating location based aspects of a tweet. However, there is a lack of attempts on investigating the data collection methods that are focused on location. In this paper, we investigate the two methods for obtaining location-based dat

Now-a-days the Flexible AC Transmission Systems (FACTS) technology is very effective in improving the power flow along the transmission lines and makes the power system more flexible and controllable. This paper deals with the most robust type of FACTS devices; it’s a Unified Power Flow Controller (UPFC). Many cases have been taken to study how the system behaves in the presence and absence of the UPFC under normal and contingency conditions. The UPFC is a device that can be used to improve the bus voltage, increasing the loadability of the line and reduce the active and reactive power losses in the transmission lines, through controlling the flow of real and reactive power. Both the magnitude and the phase angle of th

The aim of this study was to identify the level of critical thinking skills among fourth-grade middle school students and to determine the performance level of the underhand volleyball pass, with the assumption that there is a positive relationship between critical thinking and skill performance. The study population included 281 students from Basra Preparatory School for Girls under the Second Baghdad Education Directorate for the 2024/2025 academic year, of whom 275 students were intentionally selected as the research sample (97.865% of the population). The experimental procedure involved applying a critical thinking scale and a technical performance test for the underhand pass on 25 students per day over 11 days, from February 9

We investigate mathematical models of the Hepatitis B and C viruses in the study, considering vaccination effects into account. By utilising fractional and ordinary differential equations, we prove the existence of equilibrium and the well-posedness of the solution. We prove worldwide stability with respect to the fundamental reproduction number. Our numerical techniques highlight the biological relevance and highlight the effect of fractional derivatives on temporal behaviour. We illustrate the relationships among susceptible, immunised, and infected populations in our epidemiological model. Using comprehensive numerical simulations, we analyse the effects of fractional derivatives and highlight solution behaviours. Subsequent investigatio

The novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) caused a pandemic of coronavirus disease 2019 (COVID-19) which represents a global public health crisis. Based on recent published studies, this review discusses current evidence related to the transmission, clinical characteristics, diagnosis, management and prevention of COVID-19. It is hoped that this review article will provide a benefit for the public to well understand and deal with this new virus, and give a reference for future researches.

Stenography is the art of hiding the very presence of communication by embedding secret message into innocuous looking cover document, such as digital image, videos, sound files, and other computer files that contain perceptually irrelevant or redundant information as covers or carriers to hide secret messages.

In this paper, a new Least Significant Bit (LSB) nonsequential embedding technique in wave audio files is introduced. To support the immunity of proposed hiding system, and in order to recover some weak aspect inherent with the pure implementation of stego-systems, some auxiliary processes were suggested and investigated including the use of hidden text jumping process and stream ciphering algorithm. Besides, the suggested

The study aims to indicate the role of strategic financial accounting  in the service investors  to take appropriate decisions in the future, Through what is provided by the strategic accounting, the future of information and data that enable the investor to make future investment decisions appropriate، If no longer traditional financial accounting putting meet all existing and prospective investors Requirements، That reliance on historical data and information already signed and neglected aspect of future, From this point it was to highlight the role of strategic financial accounting to contribute in this area.

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  The problem of the study represented in the gap between what banks possess of Information Technology and Knowledge Management and what they need to help them in decision making and problem solving and achieving High Business Value. It formed a focus and fundamental point for this study in its analysis and interpretation. This was done by a scientific methodology and five chapters.

  The study aimed at analyzing the use of partnering Information Technology with Knowledge Management to achieve High Business Value at commercial banks in Jordan. Data were collected from 116 managers, experts, and advisors working for 16 Jordanian banks through a questionnaire de