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 phenomenon of negative behavior has studied as a social and psychological phenomenon that effect on the performance and life of workers inside and outside the organization. The adoption of this phenomenon is studied in terms of the role of the internal environment of the organization in addressing this behavior, being the variables belong to the field of organizational behavior to see the results of those variables on the Iraqi organizations, since the specificities of it differ from the rest of the Arab and foreign environments. Therefore, this study focused on testing the relationship of the internal environment of the organization and its role in addressing the negative behavior of the workers.

thi

Abstract

This study aims at investigating the relationship between mindfulness and academic self-efficacy among Northern Border University students. To achieve this objective, the researcher adopted the correlative survey method for (97) students. For data collection, the researcher developed a mindfulness scale consisting of (42) items divided into seven topics, each one consisting of six items. The researcher developed an academic self-efficacy scale consisting of (20) items, adopting a five-point Likert scale. The results showed that there is a high level of mindfulness among students at the level of the seven units which formed the mindfulness scale; the conscious thinking unit showed the highest mean value o

The research seeks to examine the ability of fifth preparatory students in solving a mathematical problem in relation to system thinking. To this end, the researcher chose (140) fifth preparatory students from four-different secondary schools in Kirkuk city for the academic year (2016-2017). Two tests were adopted to collect study data: a test of (5) items about skills in solving math problem designed by (Al-raihan, 2006); and a test of system thinking skills designed by the researcher himself consisted of (14) items. It was divided into four skills (analyzing the main system to subsystems, eliminating all inner gaps of system, identifying the inner connection of system, and reorganizing the system). The findings indicated a good ability

     In this work, thin films of cadmium oxide: nickel oxide (CdO: NiO) were prepared by pulsed laser deposition at different pulse energies of Nd: YAG laser. The thin films' properties were determined by various techniques to study the effect of pulse laser energy on thin films' properties. X-ray diffraction measurements showed a mixture of both phases. The degree of crystallinity and the lattice constant increase with the laser energy increase, while the lattice strain decreases. FE-SEM images show that the substrates' entire surface is uniformly covered, without any cracks, with a well-connected structure consisting of small spherical particles ranging in size from 15 to 120 nm. Increasing the laser power causes to increase the pa

Praise be to God, who started his book with the praise of himself and prayers and peace be upon those who do not have a prophet after him and his family and companions and those who followed them with charity until the Day of Judgment. Either:
      The research examines the meanings of the formulas of the increased verbs that were mentioned in Surat Al-Baqara, at the imam of the imams of the Islamic nation, namely, Al-Fakhri Al-Razi (d. 606 AH), may God Almighty have mercy on him. With the imams of Quranic scholars.

Poly vinyl alcohol has been studied for its ability to form crystallites by using annealing method. Semicrystalline films of poly vinyl alcohol (PVA) were prepared by casting 11.5 wt. % and 13 wt. % PVA aqueous solution onto glass slides at annealing temperature range 90 -120°C and duration time 15- 60 minute. This allowed the macromolecules to form crystallites, small regions of folded and compacted chains separated by amorphous regions where single PVA chain may pass through several of these crystallites. Degree of crystallinity of PVA films (hydrogels) was determined by method of density; on the other hand the swelling behavior was conducted by the determination of water uptake, wet degree of crystallinity, gel fraction and solubilit

PVA, Starch/PVA, and Starch/PVA/sugar samples of different
concentrations (10, 20, 30 and 40 % wt/wt) were prepared by casting
method. DSC analysis was carried; the results showed only one glass
transition temperature (Tg) for the samples involved, which suggest
that starch/PVA and starch/PVA/sugar blends are miscible. The
miscibility is attributed to the hydrogen bonds between PVA and
starch. This is in a good agreement with (FTIR) results. Tg and Tm
decrease with starch and sugar content compared with that for
(PVA). Systematic decrease in ultimate strength, due to starch and
sugar ratio increase, is attributed to (PVA), which has more hydroxyl
groups that made its ultimate strength higher than that for

The Nuclear structure of 110-116Cd isotopes was studied theoretically in the framework of the interacting boson model of IBM-l and IBM-2. The properties of the lowest mixed symmetry states such as the 1+, 2+ and 3+ levels produced by the IBM-2 model in the vibrational-limit U(5) of Cd - isotopes are studied in details. This analysis shows that the character of mixed symmetry of 2+ is shared between and states in 110-114Cd – isotopes, the large shar goes to s, while in isotope, the state is declared as a mixed symmetry state without sharing. This identification is confirmed by the percentage of F-spin contribution. The electromagnetic properties of E2 and Ml operators were investigated and the results were analyzed. Various