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 .

Abstract

The present paper attempts to detect the level of (COVID-19) pandemic panic attacks among university students, according to gender and stage variables.

To achieve this objective, the present paper adopts the scale set up by (Fathallah et al., 2021), which has been applied electronically to a previous cross-cultural sample consisting of (2285) participants from Arab countries, including Iraq. The scale includes, in its final form, (69) optional items distributed on (6) dimensions:  physical symptoms (13) items, psychological and emotional symptoms (12) items, cognitive and mental symptoms (11) items, social symptoms (8) items, general symptoms (13) items and daily living practices (12) items

William Shakespeare's play Coriolanus explores the journey of power and the transformation of a skilled warrior into a statesman. This paper employs Machiavelli’s framework of pragmatic statecraft to analyse Coriolanus’s tragic failure as a political leader despite his unparalleled prowess as a Roman general. It analyses Coriolanus's political career, revealing how his military skills, while effective in warfare, do not translate into political success. The paper shows that Coriolanus’s contempt for performative politics, refusal to adopt civic diplomacy, and failure to soften aristocratic pride with populist appeal turn plebeians against him and alienate patricians. His upholding of martial honour — fostered by his mother Volumnia

The research tacklets the role of risks arising from the excessive use of derivative contracts for trading in financial crises, including the recent global financial crisis in (2008) which is known the mortgage crisis.

   In order to prove the hypothesis of the research, the risk index of derivative contracts has been chosed as expressed in the measure of (value at risk) to be the main field for testing the hypothesis of research. The duration of the contract  has been also chased  for (15) years between the years (2001- 2015), the period preceding the global financial crisis, while the second represents the period of time that followed. The research reached a number of conclusions, bu

public relations at Al-Shuhadaa Establishment: an analytical study of social networking sites and the website) came to know and monitor the contents of social networking sites for Al-Shuhadaa Establishment, the research problem was represented by the main question: (What is the effectiveness of social networking sites and the website of Al-Shuhadaa Establishment) ,This research was classified within the descriptive research, and the two researchers adopted the survey method in order to achieve the objectives of the research, and they used the tool: content analysis as a research tool, the analysis of the contents included the official website of the establishment (Instagram page), and other social networking sites that Al-Shuhadaa Establish

The city has normal natural state, and the man has a usual movement, change and search for the new .Also, the city has a usual change and transform in its time, place and quality (sizes)structures. The city has a solid memory diving into the past and the future and reflects The real present, and this memory has a timing layers change into real materialistic place making the city has accumulated overlapping circles which is hard to break u , and it broadcasts the lockup timing density ,in which there is no visual record precisely, it is just like((the social record)) that evaluates the un visual relationships between the components and parts of the city (community and form) in a visual quiet exhibition and transform change inside.

The current study aims to investigate the effect of the interaction between the use of the improve strategy in teaching mathematics and the level of academic achievement on the acquisition of algebraic concepts and habits of mind among tenth-grade students in Oman. The study adopted the experimental method, based on a quasi-experimental design with two groups: experimental and control groups and pre-post-measurement. The study sample consisted of (28) 10th-grade students as an experimental group and 26 of 10th-grade students as a control group in Al-Tufail bin Amr School in South Al Batinah. The differences in the pretest and posttest gains were analyzed using mean, standard deviation, ANCOVA, t-test, effect size (eta-square), and two-wa

The security of information represent the available  protection of  information and its component and guaranty the its safety and confidentiality. The absent or lack or stop of security of information and without maximum benefit may lead to lose confidence and make it burden on the company. So we must protect the company and information from the damages which may lead to the frailer of performance and loses of the company and its workers. So the security of information considered one of the potential  and controlling basis to protect individuals and companies from the damages. To insure the security  and confidentiality of information there are delicate,  proper and trusted ways, like FIRE WALL, PASS WORD, SYPHAR