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 .

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

Experimental investigation of the influence of inserting the metal foam to the solar chimney to induce natural ventilation are described and analyzed in this work. To carry out the experimental test, two identical solar chimneys (without insertion of metal foam and with insertion of metal foam) are designed and placed facing south with dimensions of length× width× air gap (2 m× 1 m× 0.2 m). Four incline angles are tested (20^o,30^o,45^o,60^o) for each chimney in Baghdad climate condition (33.3^o latitude, 44.4^o longitude) on October, November, December 2018. The solar chimney performance is investigated by experimentally recording absorber pl

It is very necessary for the political theater to be within the space of every theatrical performance, so that the theater carries the diverse and enlightened values and cultures of this world. political theatre. In the first chapter, the researcher dealt with (the methodological framework), which includes the research problem identified by the researcher with the following question (the functional diversity of the directorial vision in the political theater)
Importance, purpose, limits and seal by defining terminology.
In the second chapter, the researcher dealt with the theoretical framework on two topics, the first (transformations of directorial vision in theatrical performance) and the second topic (aesthetic experiences i

The historical person study as a personality to the AL- Bazargan, one of the important
studies, is the shed light on the character had an effect of the political life in Iraq, an important
historical era involved many events, coincided with a national and historical by this personal
at the events successive positions that stage of the history of Iraq, especially if we know,
strongly his loyalty to the homeland and the earth, and intense hatred for any occupation or
colonization desecrate the land...
This was evident during his participation and his supervisor in 1920 liberal revolution
against the British occupation, and urged the need for adherence to the principles of
independence, and the emphasis on the nation

Purpose: To determine the effect of information technology governance (ITG) under the control objectives for information and related technologies (COBIT) on financial performance is the objective of this study. Additionally, the article seeks to look into the relationships between the factors under consideration.   Theoretical framework: Information technology and operational processes are evaluated and ensure their compliance with the instructions of the Central Bank of Iraq. Therefore, the research dealt with a conceptual framework by reviewing the literature on the importance of the COBIT framework in assessing financial performance.   Design/methodology/approach: To investigate the effect of information technology; we the valu

Background: Rehabilitation of the carious tooth to establish tooth structure integrity required cavity design that show a benign stress distribution. The aim of this study was to investigate the influence of the cavity position on the stress values in the reamining tooth structure restored with amalgam or resin composite. Materials and methods: Seven 2-D models of maxillary first premolar include class I cavity design was prepared, one sound tooth (A) 3 composite (B1, B2, and B3) and 3 amalgam (C1, C2, and C3). In design (BI and C1) the cavity position is in the mid distance between bacc-lingual cusp tip, design (B2 and C2) and (B3 and C3) shifted toward the buccal cusp and the lingual cusp for 0.5 mm respectively. One hundred N vertical

Biofilm formation is one of the biggest challenges of scientists. Role of heavy metals in forming biofilm is not clear enough. Here, the effect of lead on biofilm formation by Bacillus spp. isolated from soil in terms of biofilm formation and remove was studied. In present study, 10 isolates of Bacillus spp were isolated from soil. The ability of all isolates to form biofilm was evaluated. The effect of lead on biofilm formation was studied by adding lead (pb) before forming biofilm. In another experiment the lead was added after biofilm formation to study the effect of lead on biofilm remove. The current study, showed the ability of all studied isolates to form biofilm. Maximum biofilm formation by Bacillus spp isolate number 8 (B8) follow

In this research, (MOORA) approach based– Taguchi design was used to convert the multi-performance problem into a single-performance problem for nine experiments which built (Taguchi (L₉) orthogonal array) for carburization operation. The main variables that had a great effect on carburizing operation are carburization temperature (^oC), carburization time (hrs.) and tempering temperature (^oC). This study was also focused on calculating the amount of carbon penetration, the value of hardness and optimal values obtained during the optimization by Taguchi approach and MOORA method for multiple parameters. In this study, the carburization process was done in temperature between (850 to 950 ᵒC) for 2 to 6