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 aimed to identify the extent to which the media offices in the ministries depend on the website of the Iraqi Council of Ministers as a source of information. Such goal includes a set of sub-goals: Knowing the reasons for media offices' reliance on the information provided by the Cabinet's website; and revealing the benefit derived from relying on the Cabinet's website.

The researcher used the survey method to screen and comprehend the extent to which the media offices in the ministries depend on the website of the Iraqi Council of Ministers as a source of information.

The mechanism of comprehensive account of the limits of research wa

In this study, a review of variety of processes that are used in the treatment produced water prior to reuse or to responsible disposal are presented with their environmental issues and economical benefits. Samples of produced water from five locations in Rumaila oilfield/in south of Iraq were taken and analyzed for their contents of brine, some heavy metals, total suspended solids and oil and grease. Moreover, two samples of water were treated using reverse osmosis technique which showed its ability to treat such contaminated water. The results showed that the environmental impact of produced water arises from its chemical composition; i.e., its salt content, its heavy metals, and hydrocarbon contents.

         Over the last few decades, many instructors have been trying all kinds of teaching methods, but without benefit. Nevertheless, in the 1986, a new technique is appeared which called K-W-L technique, it  is specified for reading comprehension passages because reading  skill is not easy matter for students for specific purposes (ESP).therefore, the K-W-L technique is a good one for thinking and experiences. To fulfill the aims and verify the hypothesis which reads as follows" it is hypothesized that there are no significant differences between the achievements of students who are taught according to K-W-L technique and those who are taught according to the traditional method

This thesis aims to show the effects of the development of the traditional manual system of the tax accounting process to the electronic system by the activation of the tax identification numbers (TINs) mechanism. The impact of this development is facilitating the tax accounting process, tax fraudand thus increasing the tax outcome.To prove the research hypothesis, an electronic system was designed based on income tax report, estimation note of individuals, in additional to using Adobe Dreamweaver application to write PHP, HTML, Javascript, and CSS web languages to implement  the proposed system. The research reached a set of conclusions, the most important of which is; not enough the communication methods between the Genera

Metalloendo peptidase is a neutral endopeptidase that cleaves peptides at the amino side of hydrophobic residues and inactivates several peptide hormones, including atrial natriuretic factor, giucagon, enkephalin, substance p, neurotensin, oxytocin, and bradykinin. It is also a major enzyme for the degradation of beta-amyloid. This study aimed to measure enzyme activity and compare it with other biochemical changes in sera patients with diabetic nephropathy. The study included 35 pathological samples of people with diabetic nephropathy, 24 samples from males and 11 samples from females, as well as the same number of healthy people as a comparison group of 15 males, 20 females, with the ages of both groups of patients with diabetic nephropat

This paper studies the main characteristics of the traditional urban configuration of Arab cities, as an important built heritage, discussing the approach adopted with such configuration at the local level, and examines its ability to preserve the character of the city, as well as, its responsiveness to the recent  requirements of its society that constantly change; in order to reach the appropriate procedures to deal with the traditional urban configuration of the Iraqi city to achieve a vital cultural communication with the vernacular built heritage, by dealing with the Form-Moral Values structure. Due to its importance within other traditional Iraqi cities, the research chose Al-Kadhimiya as a case study, so it discusses and compares

The study highlighted the transformation of value systems and educational patterns between past and present, especially with the introduction of modern variables and means, such as mobile phones, the internet, social media, and others. These factors have contributed both positively and negatively to the study. The study highlights the integral role of the school in collaboration with the family in guiding and educating children. It also emphasizes the active role of the school in developing students' abilities and skills, either attracting them to school or vice versa. This includes an examination of the essential skills required in education and their role in achieving a state of psychological well-being and systematically developing child

In this study, Titanium Dioxide Nanoparticles were synthesized by an easy and eco-friendly technique (green synthesis) using green tea leaves (Camillia sinensis), Nanoparticles were analyzed using structural and optical analysis, the X-ray pattern showed that Titanium Dioxide NPs had a tetragonal structure with (Face Centered Tetragonal) FCT crystal structure, the UV-visible recorded an absorbance peak near 350 nm and calculated energy band gap was 3.5 eV, all measurements were proved the purity and Nano size of prepared Nanoparticles. Biochemical parameters evaluation also mentioned in this research, these analyzes showed that Titanium Dioxide nanoparticles in particular dose (50 mg/kg) have the ability to reduce blood glucose