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 .

Abstract

The aim of the research is to identify the role of ethical leadership in achieving comprehensive quality standards in public education schools in the Al-Ardha governorate. To achieve this goal, the descriptive approach was used, the researcher developed a questionnaire consisting of (35) items, divided into two sections: the first one is related to ethical leadership includes (17) items, and the second section relates to total quality management includes (18) items. The research sample consisted of (405) teachers from the stages of public education. The results showed that the level of ethical leadership practice (ethical personal characteristics, ethical administrative features, teamwork, and human rela

This study focuses on  in the (D.N.A) as an evidence In proving criminals materials, it has shown the biological sign effect and its role in proving the criminal materials, and then its role to create the judge believes therefore ; this study has been made in tow chapters,intermediate chapter: the type of biological signs and its relation with proving evidences, in the first chapter the biological sign has been limited through its meaning that could reach by using the exact meaning of the sign and biology, accordingly it has been defined as ( a mark that can be sensed and examined where the main source is the human body, and related to one of the human biology actions starting from its anatomy, physiology, or it can be resulted fro

The main aim of this research is to: 1) identify the Transformational Leadership of the Managers of higher School in ALkut district and its relationship with organizational Loyalty. 2) Clarify the relationship between Transformational Leadership and organizational Loyalty. Regarding the research methodology, the researcher used the descriptive method because it meets this research. The two research tools were a questionnaire and the statistical program (spss). The results revealed that there is a strong positive relationship between Transformational Leadership and organizational Loyalty, which means that when the managers have a Transformational Leadership leads to having organizational loyalty.

The aim of the research is to determine the extent to which young people watch television sports programs and the impact of viewing on the level of sports culture among young people and the impact of demographic variables on youth over the viewing of sports programs, The study was conducted on a sample of (200) male and female students from the faculties of the University of Baghdad, where a questionnaire form composed of several axes and questions was prepared to measure the effectiveness of sports programs in youth culture, The statistical program used spss to empty data and extract results by frequency, percentages, correlations, The research reached several results, the most important of which is that there is a strong influence of s

Background: Chronic Obstructive Pulmonary Disease (COPD) represents one of the major causes of chronic morbidity where, airflow limitation is caused by a mixture of small airways disease and parenchyma destruction.
Objective: to correlate the clinical characteristics of patients with COPD with imaging classification into phenotypes.
Patients and Methods: Thirty patients with stable COPD were examined by chest CT. Bronchial wall thickness is evaluated by measuring the wall area percentage by identifying the trunk of the apical bronchus of the right upper lobe, while the extent of emphysema was assessed using the percentage of lung voxels with X-ray attenuation values less than -950 HU {automatically calculated by special software}.<

The aim of the research is to demonstrate the impact of the dimensions of the marketing vigilance represented by (environmental scanning, diagnostic capacity, validity and decision-making) and to attract deposits represented by (customer relationship management strategy, distribution strategy (location), promotion strategy), as the research was applied in each of Banks (Assyria International, Iraqi Middle East Investment, Business Bay, Iraqi Investment, Babel, Al Mansour Investment), and the questionnaire was adopted as a main tool for collecting data and information from a sample of (110) who are in the position (department manager, department manager, assistant Section Director, Division Officer, Unit Officer), and the statistical prog

DEMs, thus, simply regular grids of elevation measurements over the land surface.The aim of the present work is to produce high resolution DEM for certain investigated region (i.e. Baghdad University Campus\ college of science). The easting and northing of 90 locations, including the ground-base and buildings of the studied area, have been obtained by field survey using global positioning system (GPS). The image of the investigated area has been extracted from Quick-Bird satellite sensor (with spatial resolution of 0.6 m). It has been geo-referenced and rectified  using 1^st order polynomial transformation. many interpolation methods have been used to estimate the elevation such as ordinary Kriging, inverse distance weight

The business process re-engineering is one of the popular concepts at this time because its provide a radical solution for the problems that companies faces. This method appeared because the changes of competition and costumers 'desires at the two last decades. The markets become wider because of the globalization so the companies must change its way to stay a life.

        The research aim is to concentrate on the  BPR  because it's a  philosophy aims to re-organize the company's business process to achieve the competitive advantage, the research also aims to a plicate  the BPR using cost management technique  in the State Company of Vegetable Oils Industry.

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Backgrounds: Despite advances in management of diabetes mellitus, it remains one of the major causes of morbidity and mortality, yet diabetic nephropathy is one of the main complications of diabetes mellitus. .Microalbuminuria is the beginning to the renal complications of diabetes mellitus; it is a significant index of early detection as well as monitoring the progression of diabetic nephropathy.