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 study aimed to identify the awareness degree of teacher students in the department of Arabic language and their supervisors at Al-aqsa University for their future roles in the age of knowledge. To achieve this objective, descriptive- analytical approach was used. The instruments of this study were two questionnaires: first one consist of (20) item for teacher students, and the second consist of (27) item for educational supervisors which covered three roles: professional, technological, and humanitarian. The sample was (120) student selected randomly, and (39) supervisors of Arabic language. The result revealed that the mean of degree awareness of teacher students and their supervisors of future role are (3.857), (3.472) respectively

    Language contains various kinds of grammatical rules that are used to express thoughts and feelings. The present paper studies some of the German language grammatical rules as being the most important basics needed to master and develop the art of writing for the German language learners. Writing is one of the productive language learning skills that transform thoughts into a written form. Hence, constant exercising on the use of the language to master the grammatical rules enables German language learners to develop their creative writing skills.

     The present study discusses the importance of grammatical exercises in developing the language learning abilities. The study provides a gener

     In the present investigation two different types of fiber reinforced polymer composites were prepared by hand lay-up method using three different parameters (curing temperature, pressing load and fiber volume fraction). These composites were prepared from the polyester resin as the matrix material reinforced with glass fibers as first group of samples and mat Kevlar fibers as the second group, both with different volume fractions (4%, 8%, and 12%) of fibers. They were then tested by tensile strength and impact strength. The main objective in this study is to use Taguchi method for predicting the better parameters that give the better tensile and impact strength to the composites, and then preparing composites at

The Flanagan Aptitude Classification Tests (FACT) assesses aptitudes that are important for successful performance of particular job-related tasks. An individual's aptitude can then be matched to the job tasks. The FACT helps to determine the tasks in which a person has proficiency. Each test measures a specific skill that is important for particular occupations. The FACT battery is designed to provide measures of an individual's aptitude for each of 16 job elements.

The FACT consists of 16 tests used to measure aptitudes that are important for the successful performance of many occupational tasks. The tests provide a broad basis for predicting success in various occupational fields. All are paper and pen

 Political terminology differs from any other type of terminology not only in the presence of political terminology, but also in content, structure, functions and the recipient who perceives it. Taking this into account, it is inappropriate to consider the semantic difficulties of translating Russian-language political terms solely at the semantic level. In our opinion, it is inextricably linked with the lexical, syntactic and grammatical levels. If we combine all 4 levels, then the following translation techniques can be distinguished: lexical borrowing (transcription / transliteration, tracing); modulation; generalization / concretization; omission / addition; descriptive translation; conversion [Komissarov 2013]. One of the most

Multilevel models are among the most important models widely used in the application and analysis of data that are characterized by the fact that observations take a hierarchical form, In our research we examined the multilevel logistic regression model (intercept random and slope random model) , here the importance of the research highlights that the usual regression models calculate the total variance of the model and its inability to read variance and variations between levels ,however in the case of multi-level regression models, the calculation of  the total variance is inaccurate and therefore these models calculate the variations for each level of the model, Where the research aims to estimate the parameters of this m

LandSat Satellite ETM+ image have been analyzed to detect the different depths of regions inside the Tigris river in order to detect the regions that need to remove sedimentation in Baghdad in Iraq Country. The scene consisted of six bands (without the thermal band), It was captured in March ٢٠٠١. The variance in depth is determined by applying the rationing technique on the bands ٣ and ٥. GIS ٩. ١ program is used to apply the rationing technique and determined the results.

The best means and ways to develop an athlete's physical and skill capabilities, and among these means is the use of training aids that help develop some bio-kinetic abilities, and prepared exercises have had an important role in improving athletic performance in badminton, where the player must possess physical fitness, explosive power, and strength. Characterized by speed as well as accuracy, awareness, and focus while playing on the court, the badminton player must be physically fit through a continuous movement of small and large muscles to achieve good performance, which requires special physical abilities and skills, and the most important of these bio-kinetic abilities are agility, coordination, and measuring the coordination

This study is concerned with the comparison of the results of some tests of passing and dribbling of the basketball of tow different years between teams of chosen young players in Baghdad. Calculative methods were used namely (Arithmetic mean, Value digression and T.test for incompatible specimens). After careful calculative treatments, it has been that there were abstract or no abstract differences in the find results of chestpass, highdribble and cross-over dribble. The clubs were: (Al-Khark, Air defence, Police and Al-Adamiyah) each one separate from the other for the year (2000-2001). After all that many findings were reached such as the lack of objective valuation (periodical tests) between one sport season and the other. In the light