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\

preparation process of performance evaluation in organizations is of extreme importance, and under development in organizations and the opening of markets and technological developments in the industry and heightened competition among industrial organizations imposed systems are built for performance give a clear picture about performance and competition,  And centered research problem in answering the following questions: Is performance evaluation system is available in Wasit State Company for Textile Industries(Research sample ), This research aims to assess the performance of policies and programs in the company, according to guide performance evaluation of programs and policies prepared by the Dutch Cou

This study presents a linguistic analysis of how Russian and American mainstream media and official statements deployed speech acts of accusation during the 2022 Russian invasion of Ukraine. Using Speech Act Theory (Austin, 1962; Searle, 1976) as the framework. The study analyzes 50 texts of English-language official statements and media headlines from both sides. In this research utterances are categorized into assertives, expressives, directives, commissives, and declarations, and analyzes their pragmatic force in shaping narratives. The analysis reveals contrasts in tone and rhetorical strategy: U.S. officials and media overwhelmingly use assertive accusations and expressive condemnations to morally indict Russia, while Russian counterpa

In this research the relation between skin resistances and standard penetration test of over consolidated
clay soils has been studied. The research includes doing boreholes at Babil governorate in Iraq to get
undisturbed samples and standard penetration test. Determination skin friction from direct shear test between
smooth concrete and soil was explored in laboratory for design purposes and correlated with standard
penetration test values. In many foundation design problems, the shear strength between soil and
foundation materials were estimated or correlated without any direct methods for measurement.
Twelve strain controlled direct shear tests were performed simulate the shear strength interaction
between smooth c

Personality regard as one of the human soul pillars that has been built throughout the life of people, starting from the fertilizing process to different stages of people ages. Over time, numerous scientific studies have shown that fetus has the ability to hear and feel and he is being stereotyped since the first stages of formation. Accordingly, the process of forming human personality set up since that date. Besides, the socialization means that take different resources to enhance human personality such as holy Quran, school, social media, and social environment. The emergence of social media made the world as a small village which gives the chance for all people, over the world, to obtain the knowledge easily and limitless. Thus, the

Abstract:

               The research aims to achieve defining the concept of environmental quality and associated costs. Studying the impact of environmental quality costs on the performance of economic units. Measuring the relationship between environmental quality and environmental performance of the units. Where the research problem is represented in the weak awareness of some economic units of the importance of environmental quality costs and their impact on evaluating environmental performance, and this leads to neglecting environmental considerations and not improving environmental performance effectively, which negatively affects the en

Background and purpose: Animal model helps researchers to evaluate new treatment plan for human and understand pathological mechanism involved in a development of disease. The use of rats as an animal model for Alzheimer's research has become a favorite among researchers. Rats are capable in mimicking Alzheimer disease due to their intelligence and quick adaptation to nature. At present there are several methods that can be used to induce Alzheimer's animals, but each method has advantages and disadvantages. We need to learn other methods that can provide many advantages and few disadvantages. The Amyloid-beta 42 (Aβ-42) and Reactive Oxygen Species (ROS) are thought to play an important role in the pathology of Alzheimer’s disease. Th

Objectives: to compare health of mothers and neonatal among age groups, to find out the correlation between
age groups and mother and neonatal health.
Methodology: A descriptive study was carried out at delivery rooms of three teaching hospitals in Baghdad city
from Feb. 28th through May. 28th
, 2013. A purposive (non-probability) sample of 300 laboring women was selected
from delivery rooms categorized into three groups, group 1 (≤19) years, group 2 their age between (20-35) years
old and group 3 their age (≥35) years. The data were collected through the use of constructing questionnaire, an
interview technique with mothers and reviewing their medical records as means of data collection; The
questionnaire con

In this study, the modified size-strain plot (SSP) method was used to analyze the x-ray diffraction lines pattern of diffraction lines (1 0 1), (1 2 1), (2 0 2), (0 4 2), (2 4 2) for the calcium titanate(CaTiO3) nanoparticles, and to calculate lattice strain, crystallite size, stress, and energy density, using three models: uniform (USDM). With a lattice strain of (2.147201889), a stress of (0.267452615X10), and an energy density of (2.900651X10-3 KJ/m3), the crystallite was 32.29477611 nm in size, and to calculate lattice strain of Scherrer (4.1644598X10−3), and (1.509066023X10−6 KJ/m3), a stress of(6.403949183X10−4MPa) and (26.019894 nm).