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 .

Human interferon as is the case in all kinds of interferon has complex effects but all share their impact on preventing the proliferation of viruses and preventing or reducing human Alantervjørn conversion occurs if the cell is in preventing the growth of the virus when interferon Balnmstqubl connects

The objectives of research to identify the maximum consumption of oxygen index (VO2max) predictable by knowing the concentration of lactic acid after the maximum physical effort and determine the percentage contribution of the concentration of lactic acid in the maximum consumption of oxygen index (VO2max) and find the equations of predictive indicator under study suppose the researchers that there is a statistically significant correlation between reduction index Aqsa for the consumption of oxygen and the concentration of lactic acid after the maximum physical effort and physical effort maximum influence constant variable under study and the researchers used the descriptive style of one group were identified variables of the maximum consum

تكمن أهمية ألبحث : تأثير تمرينات تأهيلية مصاحبة لجهاز التحفيز الكهربائي للعضلات العاملة في تخفيف الالآم أسفل الظهر للنساء بعمر (25-35) سنة والتعرف على مدى تأثير تلك التمرينات في تخفيف الألأم أسفل الظهر. وتكمن مشكلة البحث نتيجة للتقدم التكنولوجي حيث أصبحت حركة الفرد تقل شيئا فشيئا مما جعله أكثر عرضة للإصابات مما أدى الى ارتفاع نسبة عدد المصابات بالالآم أسفل الظهر وما لتلك الالام من تأثيراتها السلبية على حيا

Abstract

The pressures of life have become a tangible phenomenon in all societies in varying degrees. This disparity determines several factors, including the nature of societies, the level of their urbanization, the intensity of interaction, the intensity of conflict, and the increasing rate of change in those societies. many people name The modern era in which we live the “era of pressures", where one of the most important of these changes is the “new Coronavirus 19-COVID”, which has spread widely throughout the world, as the pandemic, has affected all aspects of daily life, including the educational and academic process, academic activities have been suspended in universities, which caused sudden change

Production of fatty acid esters (biodiesel) from oleic acid and 2-ethylhexanol using sulfated zirconia as solid catalyst for the production of biodiesel was investigated in this work.

       The parameters studied were temperature of reaction (100 to 130°C), molar ratio of alcohol to free fatty acid (1:1 to 3:1), concentration of catalyst (0.5 to 3%wt), mixing speed (500 to 900 rpm) and types of sulfated zirconia (i.e modified, commercial, prepared  catalyst according to literature and reused catalyst). The results show the best conversion to biodiesel was 97.74% at conditions of 130°C, 3:1, 2wt% and 650 rpm using modified catalyst respectively. Also, modified c

The study aimed to identify the level of health awareness and health education among mothers zones, urban and rural areas as well as to identify the differences between them and to achieve this study was conducted on a sample of (121) or been Akhittarhn randomly, aged (20 - 43 years) and applied them to a questionnaire to measure the health awareness, which formed from a group of paragraphs, and after the collection of data was treated using the statistical software (SAS), where research showed many of the results are:
1/ Reached the age group ranging between (20-30 years), the highest rate for the present, where was (40.51%), while in the countryside matched by age group (31-40 years old) in terms of (54.76%)./ It turns out that the