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 .

Many of the dynamic processes in different sciences are described by models of differential equations. These models explain the change in the behavior of the studied process over time by linking the behavior of the process under study with its derivatives. These models often contain constant and time-varying parameters that vary according to the nature of the process under study in this We will estimate the constant and time-varying parameters in a sequential method in several stages. In the first stage, the state variables and their derivatives are estimated in the method of penalized splines(p- splines) . In the second stage we use pseudo lest square to estimate constant parameters, For the third stage, the rem

The present study was conducted with a view to determine whether focal laser therapy result in visual recovery and regression of macular edema in patients with non proliferative diabetic retinopathy and maculopathy ,and whether combined focal and scatter laser therapy in patients with proliferative diabetic retinopathy and maculopathy results in visual recovery ,regression of macular edema and regression of the risk factors. In the present work, a frequency doubled Nd: YAG laser was used for the treatment of diabetic retinopathy. The study evaluates 41 eyes of 33 diabetic patients both with Insulin Dependent Diabetes Mellitus IDDM, (n=16) and Non Insulin Dependent Diabetes Mellitus NIDDM, (n=17) with diabetic retinopathy divided into two

Background: Neonatal macrosomia is defined as a birth weight of more than 4000 g. Significant maternal and neonatal complications can result from the birth of macrosomic infants like hypoglycemia and birth injuries.Objectives: To determine the frequency of hypoglycemia in neonates with macrosomia in Amarah, IraqMethods: The study involved 146 macrosomic newborn neonates delivered in 2 maternity hospitals in Amarah, Iraq during a period from June 2011 to June 2014.Results: Hypoglycemia was observed in 16% of neonates affected by macrosomia. Maternal diabetes was the most common cause of fetal macrosomia (28%).Our results were compared with those from other parts of the world.Conclusion Macrosomia is associated with increase rate ofneonata

إن الاستخدام الفعال للأموال العامة يشكل احد الدعامات الأساسية من اجل حسن إدارة تلك الأموال و فعالية القرارات الصادرة عن السلطات المختصة ، و أن هذا الهدف لا يتحقق ما لم تكون الرقابة المالية ذات فعالية لكبح جماح حالات الفساد الإداري النظمي و تفشي ذلك في جهاز الدولة الإداري. لان ظاهرة الفساد الإداري تؤدي بجهاز الدولة الإداري إلى فقدان كيانه الموحد لصالح المنظومات الفاسدة رغم احتفاظه بكيانه الموحد شكليا، كما ت

PvcABCD are cluster of genes found in Pseudomonas aeruginosa. The research was designed to examine the relationship between the pvc genes expression and cupB gene, which plays a crucial role in the development of biofilm, and rhlR, which regulates the expression of biofilm-related genes, and to investigate whether the pvc genes form one or two operons. The aims were achieved by employing qRT-PCR technique to measure the gene expression of genes of interest. It was found that out of 25 clinical isolates, 21 isolates were qualified as P.aeruginosa. Amongst, 18(85.7%) were evaluated as biofilm producers, 10 (47.6%), 5 (23.8%), and 3 (14.2%) were evaluated as strong, moderate and weak producers respectively, while, 3 (14.2%) were considered

In this study, simply supported reinforced concrete (RC) beams were analyzed using the Extended Finite Element Method (XFEM). This is a powerful method that is used for the treatment of discontinuities resulting from the fracture process and crack propagation in concrete. The mesoscale is used in modeling concrete as a two-phasic material of coarse aggregate and cement mortar. Air voids in the cement paste will also be modeled. The coarse aggregate used in the casting of these beams is a rounded aggregate consisting of different maximum sizes. The maximum size is 25 mm in the first model, and in the second model, the maximum size is 20 mm. The compressive strength used in these beams is equal to 26 MPa.

The subje

   Addressed this research the impact of intelligence emotional dimensions of the main(self awareness, and self-management, and social awareness, and relationship management) in the performance excellence the university(performance optimization, and strategic development) this is by middling the styles decision making which are (rational and intuitive, and dependent, and spontaneous, and avoidant), and Go search of an intellectual dilemma raise fundamental questions revolve around the search was to answer those questions through a theoretical framework for search variables first and test models of the relationship and second through the impact six hypotheses President.The objective of the research to make sure the contr

Abstract

 Experimental work from Magnetic Abrasive Finishing (MAF) tests was carried out design parameters (amplitude, and number of cycle which are formed the shape of electromagnetic pole), and technological parameters (current, cutting speed, working gap, and finishing time) all have an influence on the mechanical properties of the surface layer in MAF process. This research has made to study the effect of design and technological parameters on the surface roughness (Ra), micro hardness (Hv) and material removal (MR) in working zone. A set of experimental tests has been planned using response surface methodology according to Taguchi matrix (3⁶) with three levels and six factors