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 .

In this paper, we will give another class of normal operator which is (K-N)*
quasi-n-normal operator in Hilbert space, and give some properties of this concept
as well as discussion the relation between this class with another class of normal
operators.

  Since the human being knew simulation as an expressive style of expressing himself which developed into dramatic arts that have their aesthetic uniqueness involving their own constructive techniques, the art of the theatre had a pioneering role in the development of the human awareness of himself. That’s why it was and still is in all its aesthetic manifestations a free space for the self –disclosure thus man has been simulated as he is the main theme of the existence and its main wealth. Thus the interest in the child's theatre began, because this theatrical pattern has its effectiveness in the construction of the human self and enabling it to be a productive source for a life that accommodates and elevates the human action t

Many writers and scientists hardly differentiate between the two instruments of use
(If) and (if) to convergence in the meaning, as they perform the meaning of the penalty and condition, as the answer relates to his condition, but when linguistic meditation we find a great difference in use in terms of meaning, so this research came to reveal these meanings and was extrapolated applied in Surat al-Maidah By counting the verses in which (if) and (if) the cops were given and looking at their contexts, the connotation of the cops in most places was within the context of probability, which is the origin of its use, given in twenty places of Surat al-Ma'idah, and it had multiple connotations according to the contexts of the verses received

This study included the compromised the containing Hardness and some ions of treated water in central Karbala drinking water treatment station with Iraqi and international drinking water criteria. Also, this study was attempted to focus on probable pollution sources. The Hardness and other waters salts Sulphates (SO4), Chloride ion (Cl-), Calcium ion (Ca+2), and Magnesium ion (Mg+2) tests criteria were determined on water samples taken from Al-Hussainia River water source, treated drinking water during October-November 2013 to August - September 2014.Study results revealed an increasing in Total hardness (TH), sulfate, chloride, calcium, in winter (December- January) 2014. In addition, the results showed a decrease in above mentioned cri

In this paper, a new class of harmonic univalent functions was defined by the differential operator. We obtained some geometric properties, such as the coefficient estimates, convex combination, extreme points, and convolution (Hadamard product), which are required

The current research aims to determine the intellectual security and the psychological resilience of Secondary school students and how these two variables are related to each other. The study also seeks the extent to which psychological resilience contributes to intellectual security

The research sample consisted of (420) students from the Secondary stage in the Directorate of Education of Baghdad / Rusafa III. Two scales were administered to the participants to collect the needed data. As for the analysis of data, Pearson correlation coefficient, T-test, and the Regression analysis were employed, the results revealed:

1. The members of the sample have an intellectual Security.
2. The members of the sample have

The aim of the research is to identify the economic and cultural role of contemporary interactive artworks from the public's point of view, with knowledge of the most important obstacles and proposals to improve the level of design and spread of interactive artworks. The descriptive approach was used, and the researcher used a questionnaire tool that was distributed to the audience for the events of Noor Al Riyadh (2021) and the size of the participating sample was (194) individuals from all spectrums of society. It was found through the results of the existence of public approval of the economic role of contemporary interactive artworks, as they contribute to supporting the national economy. It attracts the public to attend various paid

It is known that the oral administration of ibuprofen caused an irritation of stomach as a side effect due to its carboxylic moiety. Ibuprofen ester was synthesized by linking the carboxylic moiety of ibuprofen and the hydroxylic group of paracetamol to reduce its side effect. Study the kinetic hydrolysis of prepared ester was examined at different values of physiological pH (1.0, 5.8, 6.4 and 7.4) at 37 ± 0.1 of 1 hour period. Measurements of absorbance were carried out by UV-Visible spectrophotometer to follow the stability of ester, it showed Pseudo first order hydrolysis. The pH- apparent rate profiles of ester was exhibited a good stability at pH 1.0 and pH 5.8. Pharmacological activity in vivo of prepared ester was evaluated in re

Background: Normospermia might be a major problem to the doctor and the infertile couple because the male seminal sample has an accepted seminal parameters during the routine seminal examination and the female partner will be claimed for the infertility and she will suffered from coasty, painful, time consuming, non indicated investigations and treatments. Our purpose was to measure sperm creatine phosphokinase (CK) activity, which reflects cytoplasmic retention in immature spermatozoa and malondialdehyde in the seminal plasma which is a marker of oxidative stress in normospermic infertile males' seminal samples.
Patient and methods: Nine infertile men with aberrantly normal standard seminal analysis&nbsp