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 .

In this research was the study of the educational values ​​when Shafei, contained in hair Shafi'i, and that what the role of these values ​​in the education of generations, and the possibility of their application in the educational curriculum. Find addressed Shafei life and his time. The values ​​derived from his hair, as well as quoting from the Koran and influenced by it, which is evident in the hair, governance and eating Alomthal.okzlk Find the importance of this thought in modern education, so as to realism and ease of application. It is the search results, the Shafi'i put thought educationally integral based on the Koran rise to the level of theory. Find and conclusions: that education in its present situation

Background: Tear of MCL of the knee is a frequent problem among knee ligaments injuries.Injuries to the MCL are usually caused by contact on the outside of the knee and are accompanied by sharp pain on the inside of the knee. Contrary to most other knee ligaments the medial collateral ligament (MCL) has an excellent ability to heal, being fairly large and well vascularised structure. The vast majority of isolated medial ligament injuries heal without significant long-term problems

Objectives: is to compare between the early clinical examination, and assessment under general anesthesia (GA), and to find out the best methods to assess the MCL tear especially in suspected cases.

Type

The research seeks to identify the proposed scenarios to predict and ward off monetary credit risks that the bank is exposed to in the future, using the banking stress tests model, and showing their impact on capital adequacy and profitability ratio,To achieve this purpose, Sumer Commercial Bank was taken as a case study, and mathematical equations were used to extract the results. Low percentage of profits and returns, strictness in the process of granting credit and financing operations in order to reduce credit risks.

هدفت هذه الدراسة إلى التعرف على درجة استخدام معلمات الرياضيات لأدوات التقويم البديل من وجهة نظرهن، وتحديد إذا كانت توجد فروق ذات دلالة إحصائية تعزى لمتغير سنوات الخبرة التدريسية، ولتحقيق أهداف الدراسة تم استخدام المنهج الوصفي. وتكونت عينة الدراسة من 37 معلمة من معلمات الرياضيات في الحلقة الثانية من التعليم الأساسي في محافظة ظفار في سلطنة عُمان. وتم بناء استبانة مكونة من (21) فقرة موزعة على (4) محاور تمثل أدوات

Studying the past for its importance and connection with the present is reflected in a relative scale in the light of data and thought of the predecessors of a great nation like the Mesopotamia, where its civilization flourished and rose since the ancient times, which inspires the present with inherited meanings that might be an entity or recognized symbols in the establishment of a vision, system or architectural building. The researcher has crystallized the description of the past to enhance the vision of the present within what is required by the interior design specialty about the historical origins of education and the design of schools in the Mesopotamia, in addition to its ethnic and environmental specificity and the moral content

Globally, the COVID-19 pandemic’s development has presented significant societal and economic challenges. The carriers of COVID-19 transmission have also been identified as asymptomatic infected people. Yet, most epidemic models do not consider their impact when accounting for the disease’s indirect transmission. This study suggested and investigated a mathematical model replicating the spread of coronavirus disease among asymptomatic infected people. A study was conducted on every aspect of the system’s solution. The equilibrium points and the basic reproduction number were computed. The endemic equilibrium point and the disease-free equilibrium point had both undergone local stability analyses. A geometric technique was used

The research aims to identify the most important variables affecting shooting from jumping high and compare them for the two foot the weak and strong, where the researchers adopted the descriptive method, and the sample was chosen by the intentional method, which consists of (4) players from the Iraqi Sports Army Club, where these variables were studied and their impact on The accuracy of aiming at the two men, and the researchers concluded that most of the players have more accuracy in aiming at the strong leg than at the weak leg, which leads to the loss of many real opportunities during the match because of the players changing the situation or wasting the available opportunity when the position of correction is an opportunity for the w

The study was conducted to investigate the effect of salinity of irrigation water on seeds quality and seedling growth characters for three oat cultivars (Shifaa, Hamel and Pimula) . It was carried oat in seed technology laboratory, field crops department, College of Agriculture, Baghdad University of Aljadiriya for period of tow years. Seeds of three oat cultivars (Shifaa, Hamel and Pimula) taken from a field experiment conducted during 2014-2015 and 2015-2016 irrigated with three salinity water levels (3, 6 and 9 dS.m-1 ) in addition to river water with salinity level of 1.164 dS.m-1 as control. Seeds were tested in laboratory experiments to estimate their quality, and completely randomized design with three replicates was used. Statistic

The purpose of this paper is to apply different transportation models in their minimum and maximum values by finding starting basic feasible solution and finding the optimal solution. The requirements of transportation models were presented with one of their applications in the case of minimizing the objective function, which was conducted by the researcher as real data, which took place one month in 2015, in one of the poultry farms for the production of eggs