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 .

four coordinated complexes for divalent metal ions : Mn, Fe, Co, Ni, Cu and Cd have been synthesized using bidentate Schiff base ligand type (NN)formed by the condensation of o-phenylenediamine , p- methylbenzadehyde and furfural in methanol. The ligand was reacted with divalent metal chloride forming complexes of the types :[M(L)Cl2] where : MII=Mn, Fe, Ni, Cu, and Cd . These new compounds were characterized by elemental analysis, spectroscopic methods (FT-IR, U.V-Vis, 1HNMR (for ligand only and atomic absorption) , magnetic susceptibility, chloride content along with conductivity measurement. These studies revealed that the geometry for all complexes about central metal ion is tetrahedral.

The purpose of this paper is to identifying the level of skill self-esteem of the young tennis players in the Governorate of Baghdad, identifying some aspects of attention (acuteness, concentration, and diversion of attention) among the young tennis players of the Baghdad governorate, and identify the skills of serve and serve spiking in tennis by young tennis players in Baghdad governorate. The researchers used the descriptive approach in the correlative relations style for its suitability and the research problem. the research sample was chosen in a deliberate way from the youth team players in tennis for the Governorate of Baghdad and the participants in the 2021-2022 sports season, whose number is (20) male players and (4) young playe

Background: Porcelain veneers are under a great deal of stress which may lead to clinical failure as fracture or dettachment. This study examined whether different finishing lines and lingual shoulder preparations in the incisal area of the maxillary central incisor affect the bond of the porcelain veneers. Materials and methods: A two- dimensional finite element model was made. Location and magnitude of maximum Von Mises stresses were calculated in porcelain veneer. Six types of preparations were drawn as:incisal overlap of 0.5mm, 1mm and 1.5mm depth and lingual shoulder, and incisal overlap of 0.5mm, 1mm and 1.5mm depth without shoulder preparation. Results: Stress formation is maximum in the incisal edge region. All the lingual shoulder

This experiment was carried out at the Field of Poultry, Department of Animal Resources, College of Agriculture, University of Baghdad, during the period from 1/5/2011 until 5/7/2011 to study the effect of adding arginine to laying hens diet on certain blood traits. A total of 100 Brown Lohmann laying hen chickens, 38 weeks of age, were randomly distributed into four treatment groups, with 25 hens for each treatment. Treatment groups were: T1: bird-fed diet with no additional arginine (control group); T2, T3, and T4: bird-fed diet supplemented with 0.4, 0.7, and 0.9%, respectively. Therefore, the total amounts of arginine in the four treatments (T1, T2, T3, and T4) become 1.1, 1.5, 1.8, and 2.0%, respectively. Results of this experiment rev

Background: Diabetes mellitus is a chronic disease with an increasing prevalence worldwide and characterized by an increase in oxidative stress and inflammation. The most important factor that is responsible for oxidative stress and production of reactive oxygen species (ROS) is hyperglycemia. The major targets of ROS are proteins. The most common and widely used biomarker of severe oxidative protein damage is protein carbonyl content.

The study was designed to assess the serum level of protein carbonyl as a marker of protein oxidation in patients with type 2 diabetes mellitus and to evaluate the effect of age, body weight, waist circumference, diabetic control and disease duration on the level

The current research aims to :
•know the level of social intelligence of the sample as a whole .
. •taraf statistically significant differences in social intelligence between disadvantaged and
non-disadvantaged peers .
To achieve these objectives, the selected sample of Talbhalmrahlh medium and specifically
students of the second grade average, were chosen randomly stratified's (360) students
included sex (male, female) and (deprived of the Father and the non-deprived) for the
academic year (2013-2014) for the province of Baghdad on both sides (Rusafa-Karkh (
As applied to them measurements of social intelligence, which is prepared by the researcher,
having achieved _khasaúsma of psychometric (valid and re

حضر الليكاند (L) 1-فنيل-3-بردين-2-يل مثيل-ثايويوريا من تفاعل 2-أمينو مثيل بردين مع فنيل ايزوثايوسيانيت وبنسبة 1: 1 وشخص الليكاند بواسطة التحليل الدقيق للعناصر (C, H, N), الأشعة تحت الحمراء، الأشعة فوق البنفسجية–المرئية وطيف الرنين النووي المغناطيسي كما حضرت وشخصت معقدات أملاح بعض ايونات العناصر الثنائية التكافؤ (Co, Ni, Cu, Cd and Hg). استخدمت تقنية الأشعة تحت الحمراء، الأشعه فوق البنفسجية-المرئية, التوصيلية الكهربائية و الا

In this work, an important sugar alkynyl ether has been synthesized in two subsequent steps starting from commercially available D-galactose (3). This kind of compounds is highly significant in the synthesis of biologically active molecules such as 1,2,3-triazole and isoxazoles. In the first step, galactose (3) was reacted with acetone in the presence of anhydrous copper (II) sulfate to produce 1,2:3,4-di-O-isopropylidene-α-D-galactose (4) in good yield. The latter was reacted with excess of 3-bromoprop-1-yne in DMF in the presence of NaOH pellets to afford the target molecule 5 in a very good yield. The temperature of this step is crucial in determining the reaction yi