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 stories of children in Iraq during the past two decades have received a number of important scientific studies. Despite tyranny of the historical study method on most of these studies, they have been and still are very important, because they have established a chronicle of this literary style that has been neglected and based not only on the academic level and serious in-depth university studies but also on the enclosed sight that doesn’t consider studied art as an innovation with its specificity and its typical technical components. While many of the public impressions and self-reflections contributed to the dominance of some of the provisions and concepts that were circulated as critical remarks and adopted by som

يصدر القضاء الدستوري احكامه على وفق اختصاصاته المتعددة ، وأخصها احكامه المعدمة للقوانين المخالفة للدستور ، لذا فإن ذاتية احكامه وصفاتها تمايزت عما سواها من الاحكام القضائية ، وامتازت عليها بخصائص العموم والالزام المطلق والبتات النهائي ؛ من هنا تقايست تلك الاحكام مع القواعد القانونية التي تسن بخصائص العموم والتجريد حتى باتت تنشر بالجريدة الرسمية ذاتها وأصبحت لا تقبل المطاعن التمييزية كونها مقترنة بقر

Background: Moringa peregrina Forssk is a well-known plant in ethnomedicine due to its widespread uses in various diseases like cough, wound healing, rhinitis, fever, and detoxification. The plant seeds contain compounds that are cytotoxic to many cancer cells. During the therapeutic use of plants via the oral route, some compounds present in the plants may be cytotoxic to normal cell lines and red blood cells. Objective: This study was the first report of investigation of the cytotoxic profile on oral cancer, CAL 27, cell line, and hemolytic activities on human erythrocytes of Moringa peregrina seeds ethanolic extract (MPSE). Methods: MPSE was screened for its cytotoxic effect against oral cancer, CAL 27, cell line using 3-(4, 5-di

Abstract

Agricultural Bank is an important source of funding Specialist His role in lending to farmers, it imposes a great job in providing the necessary head for any developmental process in the agricultural sector money. The ACB of ancient Iraqi banks, and that because of its importance to the advancement of the national economy and contribute to the development and regulation of the economic sector through the support and the assignment of the Iraqi agricultural sector in various agricultural activities because it is responsible

for the process of granting agricultural loans to farmers bank.

The aim of the internal control in the agricultural banks to

Mobile ad hoc network is nothing but the temporary network which is having the collection of mobile nodes. Routing and broadcasting are major operations of MANET network. The major operation in ad hoc mobile network is the broadcasting which sometime results to storm problem of the broadcast if the forwarding mechanism is not properly designated. Thus the challenges in the MANET are to reduce the broadcasting redundancy and under high transmission error rate provides high delivery ratio. Hence in our proposed research, we are introducing and investigating the new mechanism of broadcasting called Dual Covered Broadcast. This method takes the broadcast redundancy advantage order to improve packet delivery ratio especially under environments w

The notion of a Tˉ-pure sub-act and so Tˉ-pure sub-act relative to sub-act are introduced. Some properties of these concepts have been studied.

Catalytic removal of the S-content from thiophene is a central step in efforts aiming to reduce the environmental burdens of transportation fuels. In this contribution, we investigate the hydrodesulfurization (HDS) mechanisms of thiophene (C4H4S) over γ-Mo2N catalyst by means of density functional theory (DFT) calculations. The thiophene molecule preferentially adsorbs in a flat mode over 3-fold fcc nitrogen hollow sites. The HDS mechanism may potentially proceed either unimolecularly (direct desulfurization) or via H-assisted reactions (hydrogenation). Due to a sizable activation barrier required for the first Csingle bondS bond scission of 54.6 kcal/mol, we predict that the direct desulfurization to contribute rather very insignificant

The Atmospheric Infrared Sounder (AIRS) on EOS/Aqua satellite provides diverse measurements of Methane (CH₄) distribution at different pressure levels in the Earth's atmosphere. The focus of this research is to analyze the vertical variations of (CH₄) volume mixing ratio (VMR) time-series data at four Standard pressure levels SPL (925, 850, 600, and 300 hPa) in the troposphere above six cities in Iraq from January 2003 to September 2016. The analysis results of monthly average CH₄VMR time-series data show a significant increase between 2003 and 2016, especially from 2009 to 2016; the minimum values of CH₄ were in 2003 while the maximum values were in 2016. The vertical distribution of CH_4<

The follower of the needs of the users of accounting information notices the necessity of adopting faithful representation of information Hence, IASB adopted the economic substance approach as the basis for the Formulation and development of international accounting standards Therefore, this research discusses the reflection of the economic phenomenon in terms of its economic substance on the subject of measurement , And it should be consistent measurement method where the problem of research is concentrated in the fact that the economic units operating in the local environment to address events and economic phenomena according to the legal form , as appropriate With the requirements of the unified accounting sys