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 applications of herbal medicine have recently acquired growing interest in range of the prophylaxis and treatment of diseases. Olibanum has been used since ancient eras and several reports studied the pharmacological characteristics of boswellic acid, particularly their effect on the inflammatory response, analgesic properties, and anti-arthritic activity mostly in cell lines, but new approaches include animal models to assess these natural derivatives effects taking into consideration of being safer than synthetic preparations.  The impact of olibanum oil on several parameters was studied in rats during this study. These included white blood cell (WBC) count, lactate dehydrogenase (LDH), and C reactive protein (CRP), as well a

Kurdish language multifunctional morphemes indicate the different functional morphological, syntactical, and semantic tasks of the morphemes. The present study discusses the multifunctional task of the Morpheme Le in Kurdish Language. The Morpheme Le has marginally been included in other studies, yet up to the present times, there has not been a research inclusively dedicated to thoroughly discuss and clarify its multifunctional aspects. The present study is divided into two chapters: Chapter one discusses the theoretical aspect of chapter two that is entirely concerned with the practical aspect of the morpheme Le. The first part of chapter one sheds light on the morphological aspect of the morpheme while part two discusses

The current research attempts to examine the relationship between social-psychological conflict and their relation to family upbringing approaches among the adolescents of intermediate stage according to sex and economical level. To do this, the researcher prepared a questionnaire to measure social-psychological conflict that consisted of (32) item divided on four dimensions, and also she prepared a questionnaire to measure family upbringing approaches which composed of (28) item divided on four dimensions. The sample was (260) male and female student from intermediate stage chosen randomly. The results revealed that there were significant differences between social-psychological conflict which went to male, there was a negative correlat

Organizations adopt a number of procedures and instructions in their field of activities in order to aid their resources development   and energies to serve their entrepreneurial orientations. This calls for preparing a range of mechanisms to mitigate the strictness and complexity of procedures. The ambiguity and severe  complexity  of procedures means acknowledging the loss in energy and this in turn  impedes the hopes while in the same time weakens the  enthusiasm in these organizations and an impedes the possibility to achieve continues innovation, thereby losing opportunities to the level of surrender to the risks and  assuming them to be unconquered obstacles.

There

The study included examination of three types of different origin and orange juice at the rate of recurring per sample, the results showed that the highest rates of acid (pH) in the A and juice were (4). And salts of calcium is 120 ppm in juice C and 86 ppm of magnesium in the juice B, for heavy metals the highest rate of lead .18 recorded ppm in juice B, 1.32 ppm of copper in juice A, 5 ppm of iron in the juice B, 1.3 ppm of zinc in the juice B, 0.05 ppm of aluminum in each of the sappy B and A, 0.02 ppm of cobalt in the juice B, 0.3 ppm of nickel in the juice B, 170.6 ppm sodium in C juice, but for the acids, organic that the highest rates were 3.2 part Millions of acid in the juice owner a, 260 ppm of the acid in the juice the ascorbi

Nominal ellipsis is a linguistic phenomenon found in English and Arabic .It is
based on leaving out a part of a nominal construction or more for the sake of good
style , compactness and connectedness .This phenomenon is found in the language of
the Glorious Qur’an .The study in hand is concerned with how translators handle
translating Qur’anic verses which contain ellipted nouns , i ,e. , to what extent the
translated Qur’anic verses are close to the original ones , and to what extent their
translations serve understanding the meanings of the glorious verses while at the
same time maintaining their beauty in style. The study aims at shedding light on
nominal ellipsis in English and Arabic .The study undertak

Transportability refers to the ease with which people, goods, or services may be transferred. When transportability is high, distance becomes less of a limitation for activities. Transportation networks are frequently represented by a set of locations and a set of links that indicate the connections between those places which is usually called network topology. Hence, each transmission network has a unique topology that distinguishes its structure. The most essential components of such a framework are the network architecture and the connection level. This research aims to demonstrate the efficiency of the road network in the Al-Karrada area which is located in the Baghdad city. The analysis based on a quantitative evaluation using graph th