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 .

It is known that the oral administration of ibuprofen caused an irritation of stomach as a side effect due to its carboxylic moiety. Ibuprofen ester was synthesized by linking the carboxylic moiety of ibuprofen and the hydroxylic group of paracetamol to reduce its side effect. Study the kinetic hydrolysis of prepared ester was examined at different values of physiological pH (1.0, 5.8, 6.4 and 7.4) at 37 ± 0.1 of 1 hour period. Measurements of absorbance were carried out by UV-Visible spectrophotometer to follow the stability of ester, it showed Pseudo first order hydrolysis. The pH- apparent rate profiles of ester was exhibited a good stability at pH 1.0 and pH 5.8. Pharmacological activity in vivo of prepared ester was evaluated in re

Background: The aim of the study was to investigate the effect of surface treatments of zirconia (grinding and sandblast with 50μm, 100 μm) on shear bond strength between zirconia core and veneering ceramic. Material and methods: Twenty-eight presintered Y-TZP ceramic specimens (IPS e.max ZirCAD, Ivoclar vivadent) were fabricated and sintered according to manufacturer’s instructions. The core specimens were divided randomly in to 4 groups, group 1: no surface treatment, group2: zirconia specimens were ground with silicon carbide paper up to1200 grit under water cooling, group3: zirconia specimens were ground and sandblast with 100 μm alumina, group 4: zirconia specimens were ground and sandblast with 50 μm alumina. Surfa

This paper shews how to estimate the parameter of generalized exponential Rayleigh (GER) distribution by three estimation methods. The first one is maximum likelihood estimator method the second one is moment employing estimation method (MEM), the third one is rank set sampling estimator method (RSSEM)The simulation technique is used for all these estimation methods to find the parameters for generalized exponential Rayleigh distribution. Finally using the mean squares error criterion to compare between these estimation methods to find which of these methods are best to the others

With the development of modern mass media and the prevalence of use continues to both researchers and practitioners their efforts to understand how the media affect Hzha on both the individual and the institutions, society and culture as a whole, which means that the need to develop models and theories explain and predict the effects of the use of such means, therefore, the study of modern technologies of communication and information as an area of ​​research has become mature to establish the intellectual base cohesive, but they are not mature enough, which calls for more research developments therefore become social networking sites online, (Facebook, and YouTube, and straining) known today as the new social media, which is witness

OBJECTIVE: Synthetic vertebral body replacement has been widely used recently to treat different spinal conditions affecting the anterior column. They arrange from trauma, infections, and even tumor conditions. In this study, we assess the functional outcome of this modality in different spinal conditions. PATIENTS AND METHODS: Thirty-six cases operated from October 2010 to December 2017. Twelve patients had spinal type A3 fractures, 11 cases with spinal tuberculosis (TB), and 13 cases with spinal tumors. They were followed clinically for a mean period of 2.4 years. RESULTS: All the cases were approached anteriorly. Seven cases had a post-operative infection. No neurological worsening reported. We had dramatic neurologic

This study is conducted to verify the efficienecy of local Ninivite rock when used in the treatment of drinking water in plants operating currently in the country in order to develop the situation of these stations to cope with the increase in population. Also, this will limit the pollutian which are increasing in the country's rivers.

(Euphrates and Tigris). These rivers are the sources to feed all water treatment plants in the country. The idea is the develop or the modify these stations by replacing part of top layer of sand filters used in these stations with Ninivite rock to operate as filters composed of two medium. The efficiency of this rock is compared with other materials used successfully worldwide in this area, such a

There is no doubt that Jane Austen is one of the most studied authors of the late 18th and early 19th centuries. Her female characters have been extensively studied and they seem to have aroused much interest as manifestations of the conduct of their time. Her heroines have realized that there were many mistakes in the rules of conduct that controlled and restricted their behaviors. Thus, they have found no fault in correcting these mistakes, by behaving naturally without acting. Elizabeth Bennet the heroine of Pride and Prejudice and Marianne Dashwood of Sense and Sensibility are the chosen examples of that kind of women.