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 .

The aim of the research is to measure the relationship and effect of the application of total production maintenance TPM in the operational strategy, as it is considered one of the most important strategies for the process of restoring production losses because of inefficient equipment. Competitive edge in the global market by upgrading the operational strategies of OS in the application of TPM in those institutions that apply both H-OS-oriented and P-OS-oriented strategies where the strategy has been identified as a critical success factor. The aim of this study is to attempt to consider the application of comprehensive productive maintenance in industrial establishments

The international standing has an impact on the strategic importance of the country in its relations with other regional and international countries. The strategic position of Taiwan has an impact on the US-Chinese relations, as it is one of the most important issues that raise dispute between the two countries. The while the Chinese consider Taiwan is an ancient legacy of their republic, and an integral part of it, the Americans consider it as an area linking the U.S. to the Asia-Pacific region, through which it intends to help its allies (Japan and South Korea). Moreover, Taiwan has huge economic importance as it is one of the largest manufacturers of electronic chips and semiconductors. This fact represents one of the most important issu

Objectives: To determine the effectiveness of post-abortion family planning counseling program on nurses and midwives' practices and to predict the variables which may effect on their practices Methodology: A quasi experimental study was conducted from 23th April 2017 to 14th March 2018 in three governorates in Middle Euphrates of Iraq: (Holy Karbala, Al - Najef Al Ashraf and Babylon) on nurses and midwives who work at maternity hospitals. Systematic random sampling was used to select 122 nurses and midwives, (60) of them for study group and (62) for control group. A checklist is an instrument that evaluate the practices which included 50 items. Validity of content was determined through reviewing it by (16) experts and reliability of to

The research aims at considering the reality of cognitive bias and organizational inertia as determinants of strategic change in a sample of companies listed in Amman Stock Market. To achieve objectives of the research, a model consisting of two independent variables has been designed, namely:

(1) The cognitive bias resulting from (escalating commitment, analogy, previous assumptions, representative generalization, command and control, convergent thinking), and (2) Organizational inertia due to (Icarus discrepancy, power distribution, rooted organizational culture), and a dependent variable, strategic change in (leadership patterns, strategy, the organization per se). 

From the model two main hypotheses were derived;

The subject of multi- ethnics is one of the most important subjects in the study of political
geography, as multi- ethnics and its consequent problems are global geopolitical phenomena
that started early and reached its peak with the beginning of the twentieth century, because of
major changes in the political landscape that resulted by wars and led to the collapse of many
empires and major powers, a matter which led to put new political maps according to certain
considerations of the colonial powers, especially in Africa and Asia. All these things led to
the most serious challenges based on ethnic and sectarian conflict and led to the development
of geopolitical problems. Among the examples what most countries in th

This work, in fact, is an English language teaching study (henceforth, ELT) which may provide the inspiration for much –needed research on issues such as testing students' level of achievement in articulatory phonetics at the university level. It attempts to answer two questions: 1)What is college students' level of achievement in articulatory phonetics? 2- Are there any statistical significant differences in the achievement of college students in articulatory phonetics between the production and recognition testing techniques? This research falls into three sections: Section one indicates the problem, the aims, the hypotheses, the procedures, the limits and the value of the study. Section two provides a general overview of the articul