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 .

This study presents the effect of laser energy on burning loss of magnesium from the holes' drilled in aluminum alloy 5052. High energy free running pulsed Nd:Glass laser of 300 µs pulse duration has been used to perform the experiments. The laser energy was varied from 1.0 to 8.0 Joules, The drilling processes have been carried out under atmospheric pressure and vacuum inside a specially designed chamber. Microhardness of the blind drilled holes has been investigated .The results indicated that the magnesium loss could be manipulated by adjusting the focusing conditions of the laser beam. Almost, the obtained holes were free of cracks with low taper and low sputter deposition. .The holes performed under atmospheric conditions have high

The changes that have occurred in the business environment and scientific and technological progress, as well as the complexity of administrative problems resulting from its practice of various activities, have led to an increase in the responsibilities entrusted to it, and for the purpose of achieving its strategic objectives, which has made the pillars of corporate governance an inevitable matter required by the nature of modern scientific management of the governorate, the success that companies seek is based on the fertile environment and the dialectical relationship between the individual and the company, and to achieve this success there must be a compatible and harmonious audit environment between the internal and external

The status of women in any society is one of the basic criteria for measuring the degree of progress that society and follow renaissance march side by sidewith men , and is no doubt that women are now of interest to the state , even if limited , which promotes public ideologies on the need for womens participation in economic infrastructure operations and social and the right to gain information and knowledge, entertainment and exercise its role in development through its president and actor in the family and raising the next generation configuration.

And affect the basic tributaries that draws them women information and ideas have a direct impact on the composition of cultural and cognitive entity woman comes satellite channels

The aim of this research is to measure and analyze the gap between the actual reality and the requirements of the environmental management system in the middle refineries company/refinery cycle according to ISO14001: 2015, as well as to measure the availability of a clean production strategy and test the relationship and impact between the availability of the requirements of the standard and a clean production strategy for the actual reality in the company.

The research problem was determined by the extent to which the requirements of the environmental management system are applied according to ISO14001: 2015 in the middle refineries company? To what extent are the required clean production strategies ava

Human beings have an innate and natural aim to achieve their self-interests and to show their ability to overcome challenges in a better way, therefore the move towards self determination is expressed by intrinsic motivation. The desire of absorbing in this task is to enjoy the task in it self and benefitting from it such a motivation is the desire rooted in human nature to judge and choose in which individual is conscious in his self, abilities and adequacy that help him in control the different  situations of life passed by him. His choices and actions are voluntary  and non-restricted to intervention or external control because control is inner and subjective, while his behavior is self-regulated with the feeling of

The expenditures of the general budget, in its operational and investment divisions, are a basic factor in the economic and social growth of any country, and its impact on various economic activities such as income, employees , and the standard of living of members of society. This was based on a basic premise: Does increasing or decreasing investment expenditures have an effect on increasing or decreasing the tax proceeds, What is the level of relationship between them? and to achieve the goal of the research, an inductive and analytical method was chosen to measure the impact of the investment budget expenditures on the tax outcome quantitatively using the financial data obtained from The General Authority for Taxes, Ministry of Financ

Situational regret and its relation to the vitality of conscience among university students The research seeks to identify situational regret and its relation to the vitality of conscience among university students, identify the significant differences in regard with students’ gender, and identify if there is a correlation between situational regret and the vitality of conscience. To do this, two scales were adopted; one to measure situational regret consisted of (31) items, which was designed by (Al-badrani, 2006), besides, costa and macrys’ (1992) scale that translated in Arabic language by (Al-qaisy, 2013). It composed of (35) items. Total of (120) male and female students were collected from three-different colleges (science, art

The study sought to highlight the importance of applying the administrative control procedures which play an important role in assessing the performance of the employees of the tax administration and specifically the companies department by setting the standards and objectives of the department on the basis of which in the implementation of its work and identify deviations and errors and find appropriate solutions and evaluate the results according to appropriate solutions, The study of the problem of research, namely the extent to which the tax administration applied to the administrative control procedures in view of its importance in evaluating the performance of its employees and the extent of their application to the legislations an

The present study discusses the problem based learning in Iraqi classroom. This method aims to involve all learners in collaborative activities and it is learner-centered method. To fulfill the aims and verify the hypothesis which reads as follow” It is hypothesized that there is no statistically significant differences between the achievements of Experimental group and control group”. Thirty learners are selected to be the sample of present study.Mann-Whitney Test for two independent samples is used to analysis the results. The analysis shows that experimental group’s members who are taught according to problem based learning gets higher scores than the control group’s members who are taught according to traditional method. This