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 .

Praise be to Allah, Lord of the Worlds, teach the pen, taught the human what he didn't know, Ihmad - Almighty - and thank him, and repent to him and ask forgiveness, which is the most forgiving, and bear witness that there is no god but Allah alone has no partner, gives and prevents, And I bear witness that Muhammad is  a slave to Allah  and his Messenger, who called for guidance and good speech and spoke, peace be upon him and his family and companions, and those who followed them until the Day of Judgment.

Money laundering is consider a crime in legal perspective and aphenomenon of negative effects in economic and Social perspective for thevarious countries of the world by the diversity of their economies to make thebadly damaged in the banking service and its reputation in some cases may leadto bankruptcy of banks, and the fact that banks is one of the most importantcircles that revolve the illicit funds, Due to its branched the banking operations,speed and overlap and increase it's complicated with the progress of bankingoperations and the use of electronic services modern here's challenges atvarious levels between the application of the legislation to combat moneylaundering and between actual fact it must find ways and means of legislat

The corrosion protection of low carbon steel in 2.5 M HCl solution by kiwi juice was studied at different temperatures and immersion times by weight loss technique. To study the determination of the optimum conditions from statistical design in evaluation of a corrosion inhibitor, three variables, were considered as the most dominant variables. These variables are: temperature, inhibitor concentration (extracted kiwi juice) and immersion time at static conditions.

These three variables are manipulated through the experimental work using central composite rotatable Box – Wilson Experimental Design (BWED) where second order polynomial model was proposed to correlate the studied variables with the corrosion rate o

Naber and toning in the modern Arab poetry Mahmoud Darwish, a model

This study seeks to examine the language context of the prominent Revolution’s poet, Moufdi Zakaria, in his anthology “ The Algerian Odyssey " )إلياذة الجزائر( in which he makes use of the Coranic terms explicitly and implicitly. Besides, it seeks to explore the content of his terms from a lexicographic and semantic point of view in their Islamic and human dimensions

Film and literature exchanges it’s influences since the early beginning of the motion pictures appearance .it was a phenomenon in other genres such as theatre ,short stories and novels .the film used out of this interaction with literature the content , themes and subjects whish were more attached to the society. based on that , the film gains it’s successes and wide spread of influences on it’s audiences who became more familiar with the motion picture style.Astrok , the French film critic wrote about “Camera the pain “ and called it as the a way of writing in the future .he was talking about the future’s role of the film .It is the importance of the film in the creation and documenting the life and its various fields.Becaus

It is well known that the spread of cancer or tumor growth increases in polluted environments. In this paper, the dynamic behavior of the cancer model in the polluted environment is studied taking into consideration the delay in clearance of the environment from their contamination. The set of differential equations that simulates this epidemic model is formulated. The existence, uniqueness, and the bound of the solution are discussed. The local and global stability conditions of disease-free and endemic equilibrium points are investigated. The occurrence of the Hopf bifurcation around the endemic equilibrium point is proved. The stability and direction of the periodic dynamics are studied. Finally, the paper is ended with a numerical simul

Every body has a size and mass that distinguishes it from others and makes it different from others. Some of these bodies are huge and large in size, and some are small and light in weight. Among these masses and bodies are some that are dealt with by their size and weight, each according to its quantity, weight, and cheapness. This is why they created quantities by which these weights and quantities could be estimated, so they used measures and weights for that. Objectives: The research aims to know some measures and weights, such as the wife’s maintenance, the amount of zakat, etc.I found it to be a widely spread topic, and widely used in the folds of jurisprudence. During my reading of jurisprudence books, I found jurists using many qu