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 .

Background: Different diagnostic definition and criteria have been recommended by different expert groups for the diagnosis of metabolic syndrome, however, it’s prevalence in the same population could differ depending on the definition used yielding different results. In Iraq, there is a lack of research comparing these different diagnostic definitions. Objective: To find out the most suitable metabolic syndrome definition to be used for Iraqi people.  Methods: 320 participants were recruited for this study, 53.4% men and 46.6% women, aged between 25-85 years, visiting Baghdad Teaching Hospital, the prevalence of metabolic syndrome according to different definitions were compared and the agreement was assessed by the Kappa st

       Despite the multiplicity of institutions contributing to the decision-making process in the United States of America, they interact to crystallize positions regarding international and strategic situations. The formulation of the national security policy depends on a number of institutions that complement each other in order to achieve an advanced security situation. Thus, the decision reflects the process of interaction of the existing regulatory institutions. This is because the essence of the national security and achieving its requirements also stems from the existence of a coherent system of shared beliefs and principles in the American society. Besides, these elements are the bases for achieving

The Security Council has an active role in addressing international crises and dealing with their causes. The Libyan crisis is one of the most important real tests of the Security Council and its role in maintaining international peace and security, as the Council has proven so far an ineffective role in resolving the crisis and dealing withtheir causes, which has prolonged its duration and increased its complexities and dangerous repercussions, perhaps the most prominent of which is the threat of the recently achieved cease-fire and the formation of a new transitional government led by Abdel Hamid al-Dabaiba, the growing significant obstacles facing the political process, foremost of which is the continued presence of foreign forces , m

The current research aims to identify the level of strategic orientation and its dimensions (vision, mission, goals, and values) in the Iraqi National Security Service (INSS). The researchers followed the descriptive analytical approach as one of the forms of analysis and organized scientific interpretation to describe a specific phenomenon or problem, adopting the form questionnaire being the main source in collecting data and preparing for this. Based on the program of the Statistical Package of Social Sciences (SPSS 26) to analyze the data and come up with the final research results to identify the opinions of the intended sample on the subject of research, and the questionnaire of (20) paragraphs included the search variable, and was

Iraq suffers from lack of water resources supply because the headwaters of the rivers located outside its borders and the influence of upstream countries on the quantities of flowing water, in addition to the increase of pressure on available water as a result of population increase and not adopting the principle of rationalization where misuse and wastage and lack of strategic vision to treat and manage water use in accordance with the economic implications fall.  This is reflected fallout on water security and subsequently on national and food security, while the issue of using water resources is development top priority in different countries in the world because of the importance of water effect on the security of indivi

Fast economical developments in the US. in second half of nineteenth century contained many social results, such as increasing of stealing and killing crimes and expand of Labor strikes, which resulted in violence actions, and presented acceptable reason for emergence specialist security agencies, first of them "Pinkerton Agency". which played important role in all of that, besides that .. its role in American Civil War such as discovering an attempt to kill elected republican president Abraham Lincoln. This research studied all that aspects, focused on period of 1850 - 1899 of agency's history.

            The article describes a certain computation method of -arcs to construct the number of distinct -arcs in  for . In this method, a new approach employed to compute the number of -arcs and the number of distinct arcs respectively. This approach is based on choosing the number of inequivalent classes } of -secant distributions that is the number of 4-secant, 3-secant, 2-secant, 1-secant and 0-secant in each process. The maximum size of -arc that has been constructed by this method is . The new method is a new tool to deal with the programming difficulties that sometimes may lead to programming problems represented by the increasing number of arcs. It is essential to reduce the established number of -arcs in each cons

In recent years, there has been growing interest in using Nanosystems in different biomedical applications. Among all metal nanoparticles, selenium nanoparticles have attracted the attention of many researchers due to its low toxicity and nutritional supplementation value. The purpose of the current study was designed to examine the possible effect of selenium nanoparticles in combination with fenugreek leaves extract (an edible herb with good medicinal properties) in the treatment of oxidative stress status-related to polycystic ovary syndrome in letrozole-induced PCOS (an imbalance of reproductive hormones that causes infertility) in adult female rats. Cold plasma was used in the preparation of selenium nanoparticles subsequently the prod

Improving the quality of health services in the health sector is an important and necessary matter that must be taken care of and improved, and this study seeks to demonstrate the role of quality costs in improving the quality of health services and achieving a high level of quality to satisfy the beneficiaries and to provide health services of good quality, and the research concluded that the main point of service provision Good health is the costs of prevention and evaluation (costs of quality conformity) and attention to it, and that technical competition contributes greatly to the development of the level of quality, as well as the use of health and medical staff with competent expertise, and that the costs of internal failure and th