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 .

Gas adsorption phenomenon on solid surface has been used as a mean in separation and purification of gas mixture depending on the difference in tendencies of each component in the gas mixture to be adsorbed on the solid surface according to its behaviour. This work concerns to study the possibilities to separate the gas mixture using adsorption-desorption phenomenon on activated carbon. The experimental results exhibit good separation factor at temperature of -40 .

Academic chemical laboratories (ACL) are considered public places  the employees come in contact with a variety of pollutants. The aim of the current study was to detect heavy metals levels in the indoor air of ACL in two universities in Baghdad city and assess their levels in the academic employees’ scalp hair as biomarkers. Air samples inside ACL were collected to detect Fe, Cd, Zn, Pb and Cu. Scalp hair samples were collected from 40 adult chemical laboratory employees aged 30-60 years, who worked 5 days/week for 6 hours a day. Personal information relating to employees such as age, duration of exposure, smoking habit and sex, was collected as a questionnaire. The results of this study concluded that academic laboratory employ

The coagulation and flocculation process using coated magnetic nanoparticles is considered one of the effective technologies for turbidity removal. This study investigates an application of magnetic nanoparticles coated with citric acid in the coagulation and flocculation process on Tigris River water in Baghdad, Iraq. Magnetic nanoparticles (MNP1) were synthesized by the co-precipitation method and coated with citric acid (MNP2). The prepared MNP1 and MNP2 were characterized by XRD, FTIR, AFM, FE-SEM, EDS, and zeta potential analysis. For coagulation process, the effect of different types of coagulants (alum, FeCl3, MNP1, MNP2), coagulant dosage (10–110 mg/l), and initial pH (3–9) were examined in this work. The best coagulant was MNP2

The study aims to identify the educational research obstacles as perceived by the faculty members at the universities of south in the west bank. As for study population, it included all (60) faculty-member in the colleges of education (bait lahem, alahliyah, al-khalil, and al-Quds almaftoha). To collect study data, the researcher used a questionnaire that consisted of (43) item; it has categorized into seven-domains: academic working conditions, academic management, resources and information, faculty members, publication, planning, and funding educational research. The findings revealed that Educational research obstacles were high with an average of (4, 39), no significant differences among sample averages and stander deviations on the

Hypercholesterolemia is a predominant risk factor for atherosclerosis and cardiovascular disease (CVD). The World Health Organization (WHO), ) recommended reducing the intake of cholesterol and saturated fats. On the other hand, limited evidence is available on the benefits of vegetables in the diet to reduce these risk factors, so this research was conducted to compare the hypolipidemic effect between the extracts of two different types of Iraqi peppers, the fruit of the genus Capsicum traditionally known as red pepper extract (RPE), and Piper nigrum as black pepper extract (BPE), respectively, in different parameters and histology of the liver of the experimental animals. The red pepper was extracted by ethyl acetate, while the black pepp

An optimization calculation is made to find the optimum properties of combined quadrupole lens which consists of electrostatic and magnetic lens. Both chromatic and spherical aberration coefficients are reduced to minimum values and the achromatic aberration is found for many cases. These calculations are achieved with the aid of transfer matrices method and using rectangular model of field distribution, where the path of charged-particles beam traversing the field has been determined by solving the trajectory equation of motion and then the optical properties for lens have been computed with the aid of the beam trajectory along the lens axis. The computations have been concentrated on determining the chromatic and spher

Every cultural achievement is a creative text, and every text is a group of signs. The Winged Bull sculpture is a sort of text that is not confined to some signs; indeed, its cultural signs go far beyond as they are open-ended, everlasting and it lends itself to various horizons of interpretation. The recipient has to combine the signs of this sculpture, which belong to different patterns, in the pursuit for perfection so that he can decode its media message.
I have tackled this sculpture by adopting a semiotic approach. The semiotic approach is a modern critical approach which is as wide as culture and as rich as knowledge. It has been linked to modernism, which in turn has been linked to modern critical approaches, because it can

The research aims to identify the effect of the inquiry wheel model on the achievement of chemistry among second-grade middle school students in public daytime middle and secondary schools. Umm Al-Qura intermediate school for girls was chosen intentionally, where students were assigned as a research sample affiliated with the Third Rusafa Directorate for the academic year (2024-2025). Two classes of the secondgrade classes were randomly selected, one of which was the first group that studied according to the inquiry wheel model, and the other was the second group that studied according to the traditional method. Equivalence was carried out between the two research groups considering chronological age in months, previous achievement in chemi

This paper aims at the analytical level to know the security topics that were used with data journalism, and the expression methods used in the statements of the Security Media Cell, as well as to identify the means of clarification used in data journalism. About the Security Media Cell, and the methods preferred by the public in presenting press releases, especially determining the strength of the respondents' attitude towards the data issued by the Security Media Cell. On the Security Media Cell, while the field study included the distribution of a questionnaire to the public of Baghdad Governorate. The study reached several results, the most important of which is the interest of the security media cell in presenting its data in differ