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 .

This research aimed at identifying the factors that affecting in the recruitment of a teaching staff for the Massive Open Online Courses (MOOCs) in university teaching at the University of Khartoum. The descriptive method was followed. The questionnaire was used as a tool for data collection,, which was distributed directly to a sample of (181) respondent of the teaching staff members of the senate at University of Khartoum from those who were attend at the senate meeting No. (409) which was held on 22 August 2016 Of (272). The researcher followed for the distribution the chance method, where each questionnaire was distributed to each of a teaching staff from different faculties at the University of Khartoum, according to his willingness

The study aims to analyze computer textbooks content for preparatory stage according to the logical thinking. The researcher followed the descriptive analytical research approach (content analysis), and adopted an explicit idea during the analysis process. One of the content analysis tools which was designed based on mental processes employed during logical thinking has utilized to figure out the study results. The findings revealed that logical thinking skills formed (52%) in fourth preparatory textbook and (47%) in fifth preparatory textbook.     

It is no secret to everyone that the Arab individual suffers from poor self-awareness and political awareness, which made the state and the importance of its existence and preserving its institutions not among his interests, which made researchers wonder about the possibility of strengthening it and the extent of its impact on the future of building the contemporary Arab state. So, the study attempts to addressing the issue of community awareness and its impact on building the state through a clear intellectual vision that blended what is social and political to define the concept of community awareness and highlight its importance and role as a basic pillar in shaping and building modern Arab countries in the Arab world and ways to enha

The summary:

This research paper presents a standard economic study. This study aims to build an economic standard form of the investment effect in Human Capital on Economic Growth in Algeria. The study showed that there is an inverse relationship between the investment and human capital. This is expressed by expending on education and economic growth. This contradicts with the economic theory. Such matter could be explained by that expending on education does not contribute in the economic growth. This refers to that the education sector result does not employee or save jobs. Thus, it does not contribute in growth; in addition, the Algerian economy depends on petrol in the first class. This means the ab

Is the subject of environmental analysis of the important issues that should occupy the attention of the departments of banks in general and banks in particular, the research sample, regardless of their size and the nature of its activity, So if the current era and witnessing rapid developments and changes, making the banking environment is more complex and interconnected than ever, And it became not possible for banks to be aware and understand the external environment variables without an analysis of the various constituent elements and influential heavily in its financial and administrative,Therefore research aims to find out the relationship between the external environment and banking facilities analysis application on the Rafidain

This paper deals with a method called Statistical Energy Analysis that can be applied to the mechanical and acoustical systems like buildings, bridges and aircrafts …etc. S.E.A as a tool can be applied to the resonant systems in the circumstances of high frequency or/and complex structure». The parameters of S.E.A such as coupling loss factor, internal loss factor, modal density and input power are clarified in this work ; coupled plate sub-systems and explanations are presented for these parameters. The developed system is assumed to be resonant, conservative, linear and there is an equipartition of energy between all the resonant modes within a given frequency band in a given sub-system. The aim of th

I found that it does not meet some of the requirements, including browsing and organizing structural elements, which is something in which the researcher found a scope for research, and from here she can formulate the problem of her research with the following question: Is there an actual need to develop user interface designs in the websites of Iraqi colleges of fine arts? The research included four chapters (the first chapter - the research problem - the second chapter (theoretical framework), which included three sections, the first is to identify the user interface, the second topic is the structural elements, and the third topic includes the rules of interface design and the dimensions of interaction), as well as the third chapter i

  After the internal audit as a tool of internal control in any organization, and helps in the evaluation of all internal control activities, as a tool to ensure compliance with the plans and policies to achieve the goals of the institution as much as possible of the efficiency, effectiveness, and should have the Internal Audit full independence and is linked to senior management, and aims to get the credibility and accuracy of information and data, and keep abreast of modern developments.

  The practical side includes the preparation of the questionnaire, which included a set of questions that fit the hypothesis of the research, was Tozeiha the research sample consisting of employees of the Internal Audit Department an

Purpose: studying and analyzing the nature of uncertainty as part of strategy formulation, through analyzing the uncertainty faced by managers in the modern business environment characterized by high complexity and dynamism, though developing of an idea about the uncertainty cases and how enable the mind to understand these cases.

Methodology: It was the use of inductive and analytical approach, in order to study the accumulation of knowledge towards development areas that could contribute to strengthening the strategy formulation.

Findings: Mentoring the future will not make the success for business organization but thought business organization ability to developing share mental