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 .

       Metaphor is a linguistic phenomenon related to people's cultures. It is an integral part of cultural heritage. This paper tackles the use of animal-based metaphors in the field of football club titles so as to draw comparisons between those in Russian with their counterparts in Arabic. Names of animals are used to refer to some clubs and teams, where these names or titles reflect animal features such as strength, preying on victims; or animal figures are employed in the club symbols, or due to the similarity of the club shirt to the animal outer shapes in colours. For instance, "an-Nawaris", which means gulls in English, is used to refer to az-Zawraa club du

The research seeks to identify the comprehensive electronic banking system and the role of the auditor in light of the customer's application of electronic systems that depend on the Internet in providing its services, as a proposed audit program has been prepared in accordance with international auditing controls and standards based on the study of the customer's environment and the analysis of external and internal risks in the light of financial and non-financial indicators, the research reached a set of conclusions, most notably, increasing the dependence of banks on the comprehensive banking system for its ability to provide new and diverse banking services, The researcher suggested several recommendations, the most important of whi

This paper presents a study of the application of gas lift (GL) to improve oil production in a Middle East field. The field has been experiencing a rapid decline in production due to a drop in reservoir pressure. GL is a widely used artificial lift technique that can be used to increase oil production by reducing the hydrostatic pressure in the wellbore. The study used a full field model to simulate the effects of GL on production. The model was run under different production scenarios, including different water cut and reservoir pressure values. The results showed that GL can significantly increase oil production under all scenarios. The study also found that most wells in the field will soon be closed due to high water cuts. Howev

Polycystic ovary syndrome (PCOS) is the main cause of female infertility. The role of insulin resistance in the development of polycystic ovary is actively discussed here. The study included patients with PCOS without insulin resistance (n = 48) and with insulin resistance (n = 39). The comparison groups were patients with no history of PCOS: a control group without insulin resistance (n = 46) and a group of patients with insulin resistance (n = 45). The following parameters were determined in patients: FSH, LH, TSH, T3_f, T4_f, PRL, E2, 17-OHd, Pr, AMH, Test total, Test_f, DHEAS, DHEAS_s, SHBG, ACTH, cortisol, IRI, IGF-1, C-peptide, and glucose level. The HOMA-IR index and the LH / FSH ratio and t

Today, the prediction system and survival rate became an important request. A previous paper constructed a scoring system to predict breast cancer mortality at 5 to 10 years by using age, personal history of breast cancer, grade, TNM stage and multicentricity as prognostic factors in Spain population. This paper highlights the improvement of survival prediction by using fuzzy logic, through upgrading the scoring system to make it more accurate and efficient in cases of unknown factors, age groups, and in the way of how to calculate the final score. By using Matlab as a simulator, the result shows a wide variation in the possibility of values for calculating the risk percentage instead of only 16. Additionally, the accuracy will be calculate

Objective: Detection the level of YKL-40 biochemical marker and vitamin D level in sera of Iraqi uterine cancer
females' patients.
Methodology: This study included 90 female volunteers, 30 of them were healthy volunteers who were
considered as a control group, while sixty serum samples were collected from women patients suffering from
uterine tumors (30 malignant and 30 fibroid benign tumors), benign cases were considered as a disease
control group for malignant tumors. The average age of those females was 30-75 years, which matched the
control group. All the samples were collected from Azady hospital in Kirkuk and the gynecologic department at
Medical City in Baghdad during October /2012 to May /2013. All the serum