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 .

Computer systems and networks are being used in almost every aspect of our daily life; as a result the security threats to computers and networks have also increased significantly. Traditionally, password-based user authentication is widely used to authenticate legitimate user in the current system0T but0T this method has many loop holes such as password sharing, shoulder surfing, brute force attack, dictionary attack, guessing, phishing and many more. The aim of this paper is to enhance the password authentication method by presenting a keystroke dynamics with back propagation neural network as a transparent layer of user authentication. Keystroke Dynamics is one of the famous and inexpensive behavioral biometric technologies, which identi

Accurate emotion categorization is an important and challenging task in computer vision and image processing fields. Facial emotion recognition system implies three important stages: Prep-processing and face area allocation, feature extraction and classification. In this study a new system based on geometric features (distances and angles) set derived from the basic facial components such as eyes, eyebrows and mouth using analytical geometry calculations. For classification stage feed forward neural network classifier is used. For evaluation purpose the Standard database "JAFFE" have been used as test material; it holds face samples for seven basic emotions. The results of conducted tests indicate that the use of suggested distances, angles

The research dealt with the subject of measuring the competitive performance of the National Insurance Company and some of its branches (Basra, Ninwa, Kirkuk and Babil), Depending on the Revenue Growth Index at the activity level, and the Revealed Comparative Advantage Index RCAIAt the branch level,To measure the competitiveness of the company And some branches, As the problem of research in the lack of adoption by some companies in the insurance service sector on scientific indicators to measure their competitive performance, The aims of the research is to measure the competitiveness of the National Insurance Company, as well as the competitiveness of its branches according to the scientific method, One of the main Conclusions of the re

The federal state is usually based on a number of regions because it is based on the multiplicity of political entities. The federal experiments were based on the existence of two or more regions and each federal system has its own peculiarities. Administrative authority between the federal government and local elected bodies of local people of absolute relative independence does not threaten the entity of the state according to the Constitution and the law and on a regional or reformer basis and exercise its powers within the legal scope prescribed The relationship between the federal authority and the Kurdistan region is the first level of the relationship on the real level, especially since no other region in Iraq has been formed exce