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: As human history is implicated in landscape or the natural history, it can be stated that the origins of the Caribbean writers' conflict, in general, are the colonial history of West India. That history which tells the story behind not only their fragmented identity, but also the problems connected to their language as well. Building on the arguments of the prominent Postcolonial ecoccritics such as Elizabeth DeLoughrey, George Handley, Helen Tiffin, and Graham Huggan, this research analyzes selected poems by Derek Walcott's which are bounded in his volume, Collected Poems. It shows how the Caribbean history has been erased due to the brutality of colonization offering landscape as a reliable source which has recorded that history

     The research aimed to identify the extent to which the media offices in the ministries depend on the website of the Iraqi Council of Ministers as a source of information. Such goal includes a set of sub-goals: Knowing the reasons for media offices' reliance on the information provided by the Cabinet's website; and revealing the benefit derived from relying on the Cabinet's website.

The researcher used the survey method to screen and comprehend the extent to which the media offices in the ministries depend on the website of the Iraqi Council of Ministers as a source of information.

The mechanism of comprehensive account of the limits of research wa

The applications of herbal medicine have recently acquired growing interest in range of the prophylaxis and treatment of diseases. Olibanum has been used since ancient eras and several reports studied the pharmacological characteristics of boswellic acid, particularly their effect on the inflammatory response, analgesic properties, and anti-arthritic activity mostly in cell lines, but new approaches include animal models to assess these natural derivatives effects taking into consideration of being safer than synthetic preparations.  The impact of olibanum oil on several parameters was studied in rats during this study. These included white blood cell (WBC) count, lactate dehydrogenase (LDH), and C reactive protein (CRP), as well a

The  thermal  and  electrical  performance  of  different  designs  of  air  based  hybrid photovoltaic/thermal collectors is investigated experimentally and theoretically. The circulating air is used to cool PV panels and to collect the absorbed energy to improve their performance. Four different collectors have been designed, manufactured and instrumented namely; double PV panels without cooling (model I), single duct double pass collector (model II), double duct single pass (model III), and single duct single pass (model IV) . Each collector consists of: channel duct, glass cover, axial fan to circulate air and two PV panel in parallel connection. The temperature of the upper and

Partial shading is one of the problems that affects the power production and the efficiency of photovoltaic module. A series of experimental work have been done of partial shading of   monocrystalline PV module; 50W, I_sc: 3.1A, V_oc: 22V with 36 cells in series is achieved. Non-linear power output responses of the module are observed by applying various cases of partial shading (vertical and horizontal shading of solar cells in the module). Shading a single cell (corner cell) has the greatest impact on output energy. Horizontal shading or vertical shading reduced the power from 41W to 18W at constant solar radiation 1000W/m² and steady state condition. Vertical blocking a column

Saudi Arabia’s banking sector plays an important role in the country’s development as it is among the leading sectors in the financial sector. Considering, two main Saudi banks (The National Commercial Bank and Saudi American bank), the present study aims to observe the impact of emotional intelligence on employee performance. The components of emotional intelligence affecting employee performance include self-management, relationship management, self-awareness, and social awareness. A quantitative methodology was applied to analyse the survey results of 300 respondents over the period from 2018 to 2019. The results show that there was a significant positive impact of self-management, self-awareness, and relationship manageme

The impact of management control systems (MCS) on organizations performance empirical research has been the subject of numerous studies during the past decade in developed and emerging economies. In the contemporary competitive, complex and changing global business environment, firms are being challenged to adopt business models that enable them to address the strategic uncertainties and risks they face in their business environments. The main issue of this study is that management accounting researchers argue that one of the ways firms can continually rejuvenate themselves to survive and succeed in these complex and uncertain environments is to understand the role of management control systems in Formulating a b

The choice of gate dielectric materials is fundamental for organic field effect transistors (OFET), integrated circuits, and several electronic applications. The operation of the OFET depends on two essential parameters: the insulation between the semiconductor layer and the gate electrode and the capacitance of the insulator. In this work, the electrical behavior of a pentacene-based OFET with a top contact / bottom gate was studied. Organic polyvinyl alcohol (PVA) and inorganic hafnium oxide (HfO2) were chosen as gate dielectric materials to lower the operation voltage to achieve the next generation of electronic applications. In this study, the performance of the OFET was studied using monolayer and bilayer gate insulators. To mo