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 research work is "The passive voice as a grammatical phenomenon in four selected textbooks". The research deals with the grammatical phenomenon passive in German. The research consists of two parts, the theoretical and the empirical part. The present research work is divided into 3 sections:

The first section includes the definition of passive, passive types, process passive, state passive, passive with modal verbs, and other types of passive. The second section provides illustrations of the four selected textbooks. The third chapter presents the passive voice in textbooks, namely German language teaching for foreigners by Dora Schulz and Heinz Griesbach, Delfin von Aufderstrasse H. and others, Em von Balme, M. and others and

Recently, several concepts and expressions have emerged that have often preoccupied the world . around the concept of environment and sustainability. This is due to the negative and irresponsible impact of man and his innovations in various industrial and technological fieldsthat have damaged the natural environment. Architecture and cities at the broader level are some of the man made components that caused these negative impacts and in the same time affected by them. What distinguishes architectural and urban projects is the consumption of large . quantities of natural resources and production larger amounts of waste and pollution, along the life of these projects. At the end of the twentieth century and the beginning of the twenty-fir

This study aimed to identify the employment of the social networking platform «Twitter» in the 2016 presidential campaign led by the Republican candidate, Donald Trump; and analyse his tweets through his personal account on «Twitter»  for the period from: 10/ 8/2016 to: 11/ 8/2016 which represents the last month of the election campaign.

The study belongs to the type of descriptive studies using the analytical method through an analysis index that includes sub-categories and other secondary categories. The research has adopted the ordinary unit of information material (tweet) as an analysis unit for this purpose.

This research addresses: Sharh Usul Al-Bazdawi "Explanation of the Fundamentals for Al-Bazdawi", by studying and investigating, from the beginning of prohibition chapter to its end. The researcher conducted a study about this book stating its significance and introducing the compiler and the commentator. The researcher as well mentioned that the prohibition has a special formula and requires repetition, and he went on explaining that prohibition according to Hanafis does not require absolute corruption of the prohibited matter unless based on an evidence, and that what is condemned as wrong act for itself is considered void and what is condemned as wrong act for external reasons is considered corrupt accor

EMS in accordance with ISO 14001: 2015 is considered an entry point to reduce environmental impacts, especially the effects resulting from the oil industry, which is the main source of environmental pollution and waste of natural resources, since the second revision of the standard took place in September 2015. The problem of the research was manifested in the weakness in understanding the correct guidelines that must be followed in order to obtain and maintain the standard. The purpose of this research was to give a general picture of what is behind ISO14001:2015 and how it is possible to create a comprehensive base for understanding its application by seeking the gap between the actually achieved reality, standards requirements

Vitamins play an important role in the human health, and thus they are the kind of major nutrients in the body. Chemical products perform numerous physiological functions and can jeopardize health jointly in their absence and surplus. Therefore, it is necessary to establish methods for observation vitamin levels in various molds. In this review paper, the most methods of determination used are high performance liquid chromatography (HPLC), spectrophotometric and potentiometric techniques by listed the value of : slope, linear range, correlation coefficient, detection limit, the max of wavelength and PH and compared with these methods.

The purpose of this paper is to identifying the level of analytical thinking and its relationship to the skills of response and simple response to the foil weapon for students of the College of Physical Education and Sports Sciences, University of Basra. Achieving the objectives of the research requires the use of a research method, and accordingly, the researchers used the descriptive method using the survey method .The two researchers identified the research community with the students of the third stage - College of Physical Education and Sports Sciences / University of Basra / for the academic year (2021-2022). Their number is (45) students and the two researchers chose the entire research community to represent th

In this research thin films from SnO2 semiconductor have been prepared by using chemical pyrolysis spray method from solution SnCl2.2H2O at 0.125M concentration on glass at substrate temperature (723K ).Annealing was preformed for prepared thin film at (823K) temperature. The structural and sensing properties of SnO2 thin films for CO2 gas was studied before and after annealing ,as well as we studied the effect temperature annealing on grain size for prepared thin films .