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 .

To evaluate the toxicity of benzalkonium chloride in aquaculture, the hemato-serological indices of Nile tilapia Oreochromis niloticus are used as biomarkers. Following exposure to three concentrations of benzalkonium chloride BAC 0.1, 0.25, 0.50, and 1 mg/l (BAC1,2,3 and 4) in aquaria for two durations 21 and 42 days, the microbiological assay in fish aquaria, in addition to blood parameters were assessed. Except for the mean difference between BAC2 and BAC3 (P > 0.05) at 42 days, the mean values of the bacterial counts revealed a significant difference between all compared groups (0.05 ≥ P ≤ 0.01). Following exposure to the lower concentrations of BAC (1, 2 and 3), the main blood parameters of Oreochromis niloticus namely red bl

The advertising has emerged as an effective force and an effective instrument upon with all organizations and companies depend on achieving their goals. In additional to the need to use promote sales, The nature and objective of advertising go beyond the scope of specific personal communication to a broader and more effective range for consumers from multiple groups and combination play need to use as well as the need to use means of communication than com convey the message more professional, The coincides with the rapid and remarkable development of all different media technologies and as much as possible social networking sites including mobile phone companies. The advertising has emerged as an effective force and an effective instrum

This research deals with the nature of the Turkish attitude towards the events of the Arab Spring which the Arab region witnessed recently, as this attitude is characterized by hesitation and utter confusion about those events at its beginning. However, the development of events and the consequent repercussions led the Turkish decision makers of the foreign policy to reconsider their attitude towards those events for political, economic, cultural and social motives.

The report includes a group of symbols that are employed within a framework that gives a language of greater impact. This research discusses the problem of the semiotic employment of religious symbols in press reports published in the electronic press across two levels: Reading to perceive the visual message in its abstract form, and the second for re-understanding and interpretation, as this level gives semantics to reveal the implicit level of media messages through a set of semiotic criteria on which it was based to cut texts to reach the process of understanding and interpretation.

The report includes a group of symbols that are employed within a framework that gives a language of greater impact. This research discusses the p

Jurisprudential disagreements are a significant source of a vast jurisprudential wealth. Among the manifestations of these disagreements are scholarly critiques raised by some scholars against others, claiming their divergence from the legal evidence or established principles for deducing legal rulings. One such critique is presented by the narrator scholar Abu Bakr Ibn Abi Shaybah, may Allah have mercy on him, directed towards Abu Hanifah al-Nu‘man, may Allah have mercy on him. In his compilation, Ibn Abi Shaybah cited numerous hadiths and traditions that he considered conflicting with the judgments as perceived by Imam Abu Hanifah, may Allah have mercy on him. These issues cover various branches of jurisprudence, including worship, sale

The present study attempts to examine verbal/nonverbal impoliteness in the classroom interaction and outside it in one of the movies, namely, The Marva Collins. Impoliteness, which is significantly studied within pragmatics, is a negative attitude towards particular behaviors. It always presumes to have emotional concerns for at least one participant who has caused it. This study is an attempt to examine verbal/nonverbal impoliteness in The Marva Collins movie. The study aims to investigate the different types of impoliteness strategies used in the four selected scenes and find out whether the speaker’s status has anything to do with the types of impoliteness. Besides, the functions performed are also examined by following a qual