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 current study is descriptive; it focuses on studying the contemporary geopolitical problem, and sectarian differences in Caucasus. Nagorno-Karabakh is considered an important disputed region nowadays. Many parties and states participated in this dispute, especially after the conflict had developed into an open war between Armenia and Azerbaijan. Thus, the study aims to examine the causes of the conflict in this region, analyze the international positions on this conflict, and find if Armenia was able to occupy this region. The methodology adopted by the researchers is the functional approach, and the theory of power analysis that Cohen created for analyzing all strengths that drove each of the parties t

Iraq has confronted a huge political transformations after 2003 which resembled and presented rapid changes from totalitarian regime into democracy's system , this phenomenon has become a feature embodied in a new political system, specifically is being a price for previous deprivation and despotism .So that, the nature of political work has been changed as a result of practicing new democratic values ,but the real challenges appeared by depending on the conformity and political compromise in dealing with all of crises and problems in the political life .
The future of political work in this nascent democracy could be prepared according to fulfillment an active doings values stretched on national unity and forgiveness from one side ,t

Abstract

This study aims to find the relationships between social capital (social network, social trust, shared goals) and knowledge sharing (knowledge Donating, knowledge collecting) as independent variables and their impact on improving the quality of educational services (academic staffs quality, Quality of teaching methods and study curriculums). This research is an important, because it attempts to identify the relationship between social capital and the knowledge sharing and their effect on improving the quality of educational service for universities. The study problem was determined in several questions related to the nature of the correlation relationship - the impact between the different independent variables (

Of the new concepts introduced by the decree of the amendment of the French Civil Code No. 131-2016 issued on 10 February 2016, which raised a debate in jurisprudence both at the level of French jurisprudence or the Arab, the concept of (the content of the contract), which seems to have emerged from the appearance of new legal articles ( 1162-1171) is the cornerstone of the contract and the contract in the contract, the two pillars which, over the course of 200 years and a half, have been one of the main pillars of the codification of Napoleon. Is that the decree of amendment has already abandoned these two pillars, or most of what he did is a change in terminology while preserving the content of these two pillars implicitly, this is what w

This paper presents a vibration suppression control design of cantilever beam using two piezoelectric ‎patches. One patch was used as ‎an actuator element, while the other was used as a sensor. The controller design was designed via the balance realization reduction method to elect the reduced order model that is most controllable and observable. ‎the sliding mode observer was designed to estimate six states from the reduced order model but three states are only used in the control law. Estimating a number of states larger than that used is in order to increase the estimation accuracy. Moreover, the state ‎estimation error is proved bounded. An ‎optimal LQR controller is designed then using the ‎estimated states with the slid

The research aims to employ one of the most important strategies for recovery from the crisis of the Covid-19 pandemic, which ravaged the economies of the entire world and its various sectors, including the banking sector, through financial technology that is based on digital transformation to achieve financial sustainability and the creation of innovative financial value chains in light of the decline in the banking sector as a result of The negative effects of the Covid-19 pandemic, be guided by the relevant international accounting standards to control the risks associated with financial technology. To recover from the Covid-19 crisis, the research came out with a set of recommendations, most notably financial technology from

Patients with decompensated cirrhosis have typically prescribed a combination of therapeutic and prophylactic medications. Polypharmacy increases the probability of medication errors and drug related problems. Clinical pharmacists are highly effective at identifying, resolving, and preventing clinically important drug-related problems in their patients' care. The objectives of the study were the identification and classification of drug-related problems, as well as the discussion of these problems with health care providers (physicians, pharmacists, and nurses) and patients. Reduce their incidence as effectively as possible and educate all research participants on the significance of following their prescribed drug regimen

Coronavirus disease (COVID-19) is an acute disease that affects the respiratory system which initially appeared in Wuhan, China. In Feb 2019 the sickness began to spread swiftly throughout the entire planet, causing significant health, social, and economic problems. Time series is an important statistical method used to study and analyze a particular phenomenon, identify its pattern and factors, and use it to predict future values. The main focus of the research is to shed light on the study of SARIMA, NARNN, and hybrid models, expecting that the series comprises both linear and non-linear compounds, and that the ARIMA model can deal with the linear component and the NARNN model can deal with the non-linear component. The models

The current study aims to examine the level of problems faced by university students in distance learning, in addition to identify the differences in these problems in terms of the availability of internet services, gender, college, GPA, interactions, academic cohort, and family economic status. The study sample consisted of (3172) students (57.3% females). The researchers developed a questionnaire with (32) items to measure distance learning problems in four areas: Psychological (9 items), academic (10 items), technological (7 items), and study environment (6 items). The responses are scored on a (5) point Likert Scale ranging from 1 (strongly disagree) to 5 (strongly agree). Means, standard deviations, and Multivariate Analysis of Vari