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 .

The research addresses a fundamental Islamic jurisprudential Purposeful issue, which is (Sharia), and to indicate the impact of this on Islamic jurisprudence, deriving rulings and extracting purposes, and to repel the illusion that this issue is only doctrinal, and clarifying the aspects of similarities and links between them by explaining the origin of deriving the purposes of Islamic Law (Sharia) through the meanings and wisdom learned from the texts and the explanation of the rulings. The rulings of Islamic Law (Sharia) have urged bringing benefits and repelling harms, and that the path to do so is reason and its production. I began the research by defining the purposes of Islamic Law (Sharia), then defining the rule of rational right

Antimicrobial resistance (AMR) is a global concern, especially in low- and middle-income countries, threatening food production, healthcare, and life expectancy. Antimicrobial stewardship (AMS) programs can optimize antibiotic use, improve patient outcomes, lower AMR, and save healthcare costs. This observational-retrospective study in Dhi Qar Governorate aimed to assess antimicrobial prescribing patterns in Al-Nasiriya public hospitals. Dhi Qar Health Directorate comprises ten hospitals, and only one hospital was excluded from the study. The study used data from antibiotic stewardship committees, including antibiogram, antibiotic, and meropenem surveys, hospital pharmacies’ medical files, and the directorate statistics from 1/1/2

Hepatitis B and Hepatitis C viruses are the major health problem in the worldwide. In the Middle East, the prevalence of HBV in general population with the chronic infectionsis 2-5%,whereas the prevalence of HCV is about 1% in Arabian Gulf countries. World Health Organization (WHO) revealed that the risks of HBV and HCV transmissionas well as human immunodeficiency virus (HIV) through the transfusion of contaminated blood and blood products is high, because of the fragility of health services in these countries. Several viral diseases are transportby different modes like bloodtransfusion, sexual contact, and unsafe injections. The mostcommon blood-transmitted viruses are hepatitis B virus(HBV), hepatitis C virus (HCV) and humanimmunodeficie

Background In recent years, there has been a notable increase in the level of attention devoted to exploring capabilities of nanoparticles, specifically gold nanoparticles AuNPs, within context of modern times. AuNPs possess distinct biophysical properties, as a novel avenue as an antibacterial agent targeting Streptococcus Mutans and Candida Albicans. The aim of this study to create a nano-platform that has the potential to be environmentally sustainable, in addition to exhibiting exceptional antimicrobial properties against Streptococcus Mutans as well as Candida Albicans. Methods this study involved utilization of Pelargonium Graveolens leaves extract as a cost effective and environmentally sustainable app

This study was aimed to conduct one of the vertical garden systems , selecting suitable plant species that with stand the climate conditions of Baghdad city in outer space to determine the appropriate growing medium for the (LWS), and to assess the impact of spraying with potassium silicate on the resistance of the cultivated plants to heat stresses . The study carried out at at Al-Batool Park of (Al-Kadhimiya Holy City). Two experiments were carried out, each one with a different plant species, including Wedelia trilobata and Tradescantia pallida, during the winter season of 2021 and summer season of 2022. The experiments were designed using a split block design. The experiments included two factors, the first being the growing med

The present study was designed to indicate the influence of the feeding plate on the nutritional and general health problems of the isolated cleft palate infants. For this study fourteen infants were taken, their ages between one day to one week, refered from cosmetic surgery and palate center to cleft lip and palate rehabilitation center in institute of technical medical / Baghdad for feeding plate purpose . Four infants put them as normal group; all those infants were subjected during (6th) month to evaluate the body weight, feeding problem and the respiratory infection. According to tables and figures this study showed a gradual improvement in nutritional problem including (feeding problem, body weight) and health problem (such as respir

The purpose of the current research is to identify the reality and applicability of the entrepreneurial approach in its dimensions (creative, proactive, independent, risk tolerant, offensive) and its impact on the success factors of the project (organizational commitment, communication, project team, project monitoring) Access to information, treatment, storage), which is a significant and important link in the success and development of industrial projects with the possibility of studying and analyzing the provision of the appropriate environment for this.

 the research started from a problem expressed by a number of intellectual and practical questions aimed at answering them as well as To answer a