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 .

Background: Because of the disturbance in the pituitary gland, growth hormone (GH) secretion will be increased and, as a result, insulin-like growth factor 1 (IGF-1) secretion will be increase as well, leading to a chronic and rare disease called acromegaly disease. One of the most serious complications of acromycaly is diabetes. Insulin resistance, which causes diabetes, occurs in the body because of increased growth hormone secretion Objective: The aim of this work is to estimate some biochemical parameters. These parameters were not studied extensively in the literature such as BALP and LOX and the possibility of using LOX as a new biomarker for acromyalgic patients with diabetic. Patients and Methods: The study was performed on (25) mal

The objective of this research was to investigate the effect of replacing fat(shortening) with different percentages of tahena on the quality properties (physiochemical and sensory ) of shortened cake.The percentages of moisture,protein ,fat and ash of cake increased significantly(p<0.05) as the replacement was increased .The highest increase percentages were 10,48,5,and 90 %,respectivly, at 100% replacement .Carbohydrate,however,decreased by 10%at 100% replacement .these findings may indicate improvement of cake nutritional value.Standing height,as an indicator of cake volume, also increased significantly by 4% at the 50% replacement then it decreased by 4% 100% replacement level. Basic formula (control) has signific

Background: Complete analysis of facial profile should also include an evaluation of soft tissue morphology. Materials and Method:The sample consisted of 90 Iraqi adults (45 males and 45 females) aged 18-25 years from Baghdad city divided into 3 groups according to the ANB angle with 30 subjects in each group (15 males and 15 females) for class I, II and III. Lateral cephalometric radiograph was taken for each subject and 8 angular and 5 linear measurements were identified and determined, t-test, ANOVA and LSD test were used to compare between both genders and between different classes. Results:Showed that females had greater angular measurements and smaller linear measurements with more lip prominence than males in all classes, there was m

The objective of this study was to evaluate the alteration in levels of gonado trophins hormones i.e.,Leutizing (LH),Follicular(FSH) in sera of patients with thyroid disorders and molecular binding study of (LH ,FSH) with their antibodies The study was conducted at the specialized center for endocrinology and diabetes from January / 2009 to March / 2010.Two hundreds and twenty three Iraqi subjects, 109 patients with thyroid disorders at age range between (40-50) years and 114 healthy individuals as control group were included in this study.The majority of patients were female with hyperthyroidism and (49.54 % ) were at age range between(40 - 50) years. The levels of hormones(LH,FSH.tri iodothyronine(T3).thyroxine(T4), thy

The investment environment is the incubator for all types of domestic and foreign investments, so if their determinants are encouraging, they increase the levels of investment flows and vice versa, as there is a relationship between the nature of the investment environment and the level of investment flows, and the determinants of the investment environment are numerous and the most important of which are security and political stability, and economic and financial factors that include relative stability In the exchange rate and inflation rates, the availability of banks and their development, transparency and integrity in administrative dealings and the lack of prevalence of administrative and financial corruption, and the clari

The first aim of the present study was performed to assay the activity of arginase in sera of women with uterine fibroid.. This study consisted of(50) women with uterine fibroid as patient's group and (30) healthy women as control group. The age ranged between (30-55) years for the two groups. The results showed that highly significant increas (P< 0.0001) in the arginase activity in sera of women with uterine fibroid (7.99± 0.23) I.U/L is found when compared with healthy group (0.52±0.02) I.U/L. The second aim was performed to isolate arginase from sera of women with uterine fibroids. The purification is done by addition of ammonium sulfate, dialysis, gel filtration chromatography by using sephadex G-50 and ion exchange chromatography by