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 .

Objective: To assess the Impact of Socio-economic status on age at menarche among secondary school students at
AL-Dora city in Baghdad, Iraq.
Methodology: This is a cross sectional study with multi-stage sampling was carried out during the period from the
3
th of December2013 to 12th of March 2014. The Sample comprised of 1760 girls, 1510 girls from urban area and
250 from rural area was included in the study. In first stage, selection of schools was done, and one class was
selected randomly from each level of Education, The data collection through a special questionnaire which Contain
the age of girl by year, class level, birth order, number of household, number of rooms, residency (urban/rural),
education level

            This research aims to know the role and impact of participation in the capabilities of human resources programs, and for the purpose of measuring it has been determined the dimensions of these two variables by relying on standards for this purpose, was chosen as the Ministry of Higher Education and Scientific Research / device supervision and scientific calendar as one of the important departments in the ministry and includes a large number of individuals at different organizational levels for the purpose of answering a questionnaire prepared for the purpose of measurement and access to the results and the achievement of the objectives of the research and which ha

The aim of this study to identity using Daniel's model and Driver’s model in learning a kinetic chain on the uneven bars in the artistic gymnastics for female students. The researchers used the experimental method to design equivalent groups with a preand post-test, and the research community was identified with the students of the third stage in the college for the academic year 2020-2021 .The subject was, (3) class were randomly selected, so (30) students distributed into (3) groups). has been conducted pretesting after implementation of the curriculum for (4) weeks and used the statistical bag of social sciences(SPSS)to process the results of the research and a set of conclusions was reached, the most important of which is t

Abstract:

There is a close relationship between rigidity and distort structure of production and productivity and inflation rates. The effects of this relationship are distorted the contribution rate of the productive sectors and the disproportionate of exchange rate in foreign trade.

raising the general level of prices is one of the way that have been used by previous governments (inflationary financing or deficit financing) in order to speed up the process of capital formation, depending on the availability of economic resources idle.

The fabricating inflation for development does not represent a true understanding of the nature of the

This study attempts to test the interactive role played by organizational agility in enhancing the effect of organizational anomie on the behavior of planned human resources. The study of organizational anomie has increased because of the moral and legal pressures facing the organization by the external environment within its framework. To adapt to all external developments faced by these organizations, the behavior of human resources planned reflects the ability of individuals to control their behavior in different situations and situations that face them in the work.

The problem of the research indicates that there is a clear lack of understanding of what is meant by the variables studied in the sample

Acid treatment is a widely used stimulation technique in the petroleum industry. Matrix acidizing is regarded as an effective and efficient acidizing technique for carbonate formations that leads to increase the fracture propagation, repair formation damage, and increase the permeability of carbonate rocks. Generally, the injected acid dissolves into the rock minerals and generates wormholes that modify the rock structure and enhance hydrocarbon production. However, one of the key issues is the associated degradation in the mechanical properties of carbonate rocks caused by the generated wormholes, which may significantly reduce the elastic properties and hardness of rocks. There have been several experimental and simulation studies regardi

A condense study was done to compare between the ordinary estimators. In particular the maximum likelihood estimator and the robust estimator, to estimate the parameters of the mixed model of order one, namely ARMA(1,1) model.

Simulation study was done for a varieties the model.  using: small, moderate and large sample sizes, were some new results were obtained. MAPE was used as a statistical criterion for comparison.