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 .

Hypoxic training, which in turn is one of the methods adopted in sports training methods, especially in activities that depend on the aerobic system in its performance, which includes training with a lack of oxygen by reducing its molecular pressure, since this method targets functional organs and works temporary responses during training and permanent responses After training as an adaptation to these devices as a result of training in this way, the study aimed to identify the effect of hypoxic exercises using the training mask and the extent of the change in some biochemical indicators, in addition to that to identify the effect of these exercises on the indicator of energy expenditure and )VMA) and the achievement of the effectiveness of

Background: Antibiotic resistance is a problem leading to difficulty in treating microbial infections thatmay occur due to many causes. For the important pharmacist role as a reference for the information and theability to access to medications, they are vital members in lowering the development of antibiotic resistance,and also they support the proper use and control of antibioticsmisuse. Our goal is comparing the knowledge,attitude, practice of undergraduate and postgraduate pharmacy students and their perceptions about thecausing factors of antibiotic resistance in Iraq.Method: A cross sectional study was conducted involving the final year bachelor and postgraduate (masterand Philosophical doctor) students from different private

The bourgeoisie groups derived great advantages from the system upon which the Fatimids built up their Regime out the land-tax and other taxes against a fixed sum . The surpulus revenue was the prophet of the farmers . A striking feature of the Fatimid was freedom of enterprise .All sectors of economic life were free-crafts , industry and trade . The government interfered in the trade in victuals only so far to in order to guarantee the supply of wheat to the big towns
The Egyptian Bourgeoisie enjoyed also the great prosperity which was produced among other reasons by the inflationary system of Fatimid economy .
The maintenance of gold dinar being almost pure and of full weight was only possible because Egypt steadily received cons

The study attempts to identify 1) the habits of playing video games among students, 2) the effect of playing video games on students’ academic achievement, 3) the statistically significant differences among students in regard of (gender, time of playing video games, number of hours). To this end, a five-likert scale questionnaire included four questions was applied to (250) male and female students chosen randomly from the second-intermediate stage at Al-Karakh side secondary schools. The findings revealed that students play games only on holidays and less than an hour daily, which means playing games does not affect their academic achievement. Additionally, the findings found there is a significant difference between male and female i

those affected by technological development risks within the scope of medical works. The unprecedented technological development the world witnesses nowadays has been providing brilliant medical service to the human being including examination, diagnosis and the treatment or follow up. However, such works hide behind potential risks threatening people's lives and such risks my be discovered within the limits of now – how and technical knowledge prevailing the time of rendering the medical service. Also this the question is raised on how to keep up between the safety of the patients and such risks are being unknown by the provider and questioning them contradicts the justices. subsequently, can the patients (affected) acquire the compensat

      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

The new sustainable development goals set by the UN include a goal of making cities inclusive, safe, sustainable, and resilient. Cities are growing at huge rates, and conditions of deteriorating QOL̛s are increasing in the form of poor access to services, and slums are remarkable, especially in the cities of the Middle East; hence, the research problem can arise from a lack of knowledge regarding the in determination of a way to assess the resilience of cities to develop mechanisms that will improve the quality of urban life. In this study, a tool called CRF has been applied for the assessment of the city's resilience principles of health and quality of life, economics and social, infrastructure and environmental systems, and the principle

The banking sector is currently facing great challenges resulting from intense competition in the financial environment, and this is what makes the supreme audit bodies and the Central Bank audit as the highest supervisory authority on banks in order to achieve profit and not be exposed to loss, and this requires identifying the banking strengths and risks that constitute points Weakness that affects the future performance and the life of the bank, which requires special supervisory care, and from this point of view, the research aims to use the CAMELS model as a control tool in banks, through the use of its six indicators: capital adequacy, asset quality, management quality, profits, liquidity And sensitivity to market risks, th

Background: The gene encoding a disintegrin and metalloproteinase domain 33 (ADAM33) is known to be associated with asthma in different ethnic groups. In Iraq, among the Arab ethnic background, this association has not yet been highlighted. Methods: One hundred and ninety-two asthmatics were examined; 118 males and 74 females (mean age 38.23 ± 9.13 years). The control group was 183; 110 males and the rest were females. The SNP of rs2280091 A/G (T1) was studied here to determine adam33 genotyping status using polymerase chain reaction–restriction fragment length polymorphism (PCR–RFLP). The level of total IgE was measured using enzyme-linked immunosorbent assay (ELISA). Results: Significant differences (p = 0.004) in the frequencies of