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 importance of this research is due to its importance goals, Which are about the attempt of researchers to investigate the probability of depending on businesses^, environments to transform organizations^, performance in away that enhance the leading  role of organizations  in their environments , and through views of a number of the staff working in the foundation of technical institutes in Mosul.  .

     After deciding the methodology of the study that ,in one hand ,performs the goals of the study , and achieving a suitable theoretical framework to present the concepts of businesses^, environments and the leadin

The chemical properties of chemical compounds and their molecular structures are intimately connected. Topological indices are numerical values associated with chemical molecular graphs that help in understanding the physicochemical properties, chemical reactivity and biological activity of a chemical compound. This study obtains some topological properties of second and third dominating David derived (DDD) networks and computes several K Banhatti polynomial of second and third type of DDD.

The research is based on the basic idea that companies today are moving towards a new trend towards protecting the environment coupled with the increasing wareness of the pollution damage caused by these companies due to their operations and activities in the environment. The two main reasons that led the researchers to choose this subject is the need to adapt the companies themselves in response to successive developments, The great development was that companies moved from the sole economic responsibility of the business to social responsibility by emphasizing socially responsible profit. The problem of research is the knowledge of the availability of the dimensions of the green processing series in Kirkuk Cement Factory The re

The research problem lies in the ambiguity of the usage of propaganda contents by two main media outlets (the Russian RT and American Alhurra) in their news coverage of the Syrian crisis through their websites and the methods used by them to convince users taking into account the mutual propaganda conflict between the United States and Russia in the war against Syria. The objectives of the research can be represented by the following: investigating the contents of American and Russian electronic propaganda towards Syrian crisis.
• Identifying the contents that received most of the coverage in the Syrian crisis by the two news outlets.
• Identifying the terms and phrases that have been most used by the websites of RT and Alhurr

This research aims at answering many questions raised by the research problem concerning the view of the organizations under consideration for the concept of smart leadership and its most important dimensions, as well as the view of crisis management and its concept and most important methods through research objectives that define and clarify the smart leadership with its dimensions and methods of crisis management.

For the purpose of reaching the results of the research and testing the assumptions about the relationship between smart leadership and methods of crisis management, the researcher adopted a questionnaire, designed especially to be a criterion for the research, as the main tool for data coll

Abstract

This research aims to study human error effects in the banking risks in the private banks  through the measurement and testing of human error effect in every kind of banking risks types and stand on the most closely associated with the risks in order to focus on them and make appropriate processors have with respect to and increase the availability of skills and expertise required to carry out banking operations of error-free manner.

Find dealt with human error in terms of meaning and understandable, classifications and types, causes and consequences and its approaches and theories. Also addressed placed banking risks in terms of meaning and concept, species and entr

This study focuses on the impact of technology on creating a dystopian world as presented by the English playwright Caryl Churchill in her play A Number (2002). This dramatic work came as a reaction to the most crucial and valuable turning point in the scientific achievements of human engineering, namely, the cloning of the sheep called Dolly. Therefore, A Number is a play that presents an analytical stage for imagining the biotechnological and scientific future. This dramatic vignette captures the playwright’s fears towards the abnormal progress of technology and science and how far such technological progress affects human relationships and identity. It also portrays how technological progress results in the feeling of a lack of

Liquefied petroleum gas (LPG), Natural gas (NG) and hydrogen were all used to operate spark ignition internal combustion engine Ricardo E6. A comparison of CO emissions emitted from each case, with emissions emitted from engine fueled with gasoline as a fuel is conducted.

The study was accomplished when engine operated at HUCR for gasoline n(8:1), was compared with its operation at HUCR for each fuel. Compression ratio, equivalence ratio and spark timing were studied at constant speed 1500 rpm.

CO concentrations were little at lean ratios; it appeared to be effected a little with equivalence ratio in this side, at rich side its values became higher, and it appeared to be effected by equivalence ratio highly, the results s