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 .

Recently, several concepts and expressions have emerged that have often preoccupied the world . around the concept of environment and sustainability. This is due to the negative and irresponsible impact of man and his innovations in various industrial and technological fieldsthat have damaged the natural environment. Architecture and cities at the broader level are some of the man made components that caused these negative impacts and in the same time affected by them. What distinguishes architectural and urban projects is the consumption of large . quantities of natural resources and production larger amounts of waste and pollution, along the life of these projects. At the end of the twentieth century and the beginning of the twenty-fir

Today, the success or failure of organizations depends to possess the wisdom of their managers promised that the key to organizational success of the business environment, making the right decisions, and create the ability to work and think towards discrimination of products and services the organization . Seek this research to investigation the relationship between the wisdom management and differentiation strategy for service operations . It was a test of that relationship in light of the results of the analysis of the data collected through the questionnaire distributed on a sample from (98) Director Mangers, head of department and head of division in  the General Establishment of Civil Aviation . The research used descriptive st

In globalization, the world became open area to competition for the attractive of investment, and the abilities of each country to win the confidence of investors depend upon the preparation to optimize circumstances.   The competitiveness is an essential means of expanding the capacity of developed to coexist in an international environment characterized by globalization. While competition describes the market structure, the behavior of investors and business, competitiveness is interested in the evaluation of business performance or countries and compare them in the conditions of competition available in these markets. Regarding Malaysia, which is depend on FDI-Export- Led Growth strategy,  it has taking on diffe

Background: Acute urinary tract infection is a common bacterial infection causing illness in infants and children. At age of seven, 8% of girls and 2% of boys will have at least one episode. Although drinking water and using home remedies are known to help to flush away bacteria and keeps them from sticking to the bladder wall, researches to test the efficacy and safety of hydrochlorothiazide's diuretic effect as adjuvant to the antibiotics in pediatric age groups are lacking, and so this research was to address this subject.

Objectives: To assess the effectiveness   and  the safety of hydrochlorothiazide as adjuvant therapy to the antibiotics in treating acute urinary tract infect

The educational sector is one of the important sectors in the world, and it is considered one of the means of community development. In addition, it is one of the means of making the country’s renaissance and devel-opment because it represents the factory of thinking minds that make change. There is no doubt that this sector is the same as any other sector. The deficit in the studied scientific planning has been prolonged, which led to its deterioration, and the problems of education remain diverse and inherited from previous time periods, where the hierarchical cluster analysis was used on postgraduate students in universities in Iraq, except for Kurdistan region, and the number of universities that were included in the study was

Heart sound is an electric signal affected by some factors during the signal's recording process, which adds unwanted information to the signal. Recently, many studies have been interested in noise removal and signal recovery problems. The first step in signal processing is noise removal; many filters are used and proposed for treating this problem. Here, the Hankel matrix is implemented from a given signal and tries to clean the signal by overcoming unwanted information from the Hankel matrix. The first step is detecting unwanted information by defining a binary operator. This operator is defined under some threshold. The unwanted information replaces by zero, and the wanted information keeping in the estimated matrix. The resulting matrix