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 .

This research was carried out to reveal the the technique of the recitation in this story including a preface, introduction, two chapters and the conclusion. the introduction consisted of the problem, significance , purpose and limitations of research. The preface included two paragraphs. The first included a meta-recitation of terminology and semantic. The second paragraph devoted to show the cultural identity of Hussein Rahim. The first chapter aimed to reveal the reality and the imaginary in the story of Na'lat Al Hakawaty (storyteller's curse). The second chapter aimed to study the strange arguments in the story. The research concluded the conclusion by presenting the results for attaching them with the margins, and the references

The factors influencing the financial market are rapidly becoming more complex. The impact of non-financial factors on the performance of a company’s common stock can increase in ways that were not previously expected. This study investigated how brand capital affects the risk of stock prices in Iraqi private banks listed on the Iraq Stock Exchange failing by identifying the likelihood of a crash caused by a negative deviation in the distribution of returns on ordinary shares. As a result, the current study’s concept is to review an analytical knowledge framework of the nature of that relationship, its changes, and its impact on the pricing of ordinary shares of the banks of the researched sector for the years 2009 to 2017, as w

تم التطرق في هذا البحث الى دور الذكاء الاصطناعي والتكنولوجيا الحديثة في العملية التدريبية بما يخدم أهدافه والاستفادة منه من خلال المخرجات الجيدة، حيث ان توظيف التكنولوجيا في تدريب رياضة المبارزة يسهل العملية التدريبية على المدرب واللاعب ويساهم في تقليل الجهد المبذول والوقت المستغرق ، وهدفت الدراسة الى التعرف على تأثير الجهاز المصنع في ضبط المسافة بين القدمين لدى عينة البحث  ،استخدم المنهج التجريبي بت

     The present work aimed to examine the nature and degree of the cross-correlations among three different ionospheric indices: these are Optimum Working Frequency (OWF), Highest Probable Frequency (HPF), and Best Usable Frequency (BUF). VOCAP and ASASPS models were adopted to determine the datasets of the selected ionospheric indices. The determination was made for different transceiver stations that provide certain HF connection links during the minimum and maximum years of solar cycle 24, 2009 and 2014, respectively. Matlab program was implemented to produce the geodesic parameters for the selected transceiver stations. The determination was made for different path lengths (500, 1000, 1500, and 2000) Km and bearings (0o, 45

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

This study synthesized nanocomposite photocatalyst materials from a mixture of Cu₂O nanoparticles, ZnO nanoparticles, and graphene oxide (GO) through coprecipitation and hydrothermal methods. This study aims to determine the optimum composition of Cu₂O/ZnO/GO nanocomposites in degrading methylene blue. The nanocomposite was synthesized in two steps:  1  the synthesis of Cu₂O and ZnO nanoparticles through the coprecipitation method and the preparation of GO through the modified Hummer method.  2  The preparation of Cu₂O and ZnO nanoparticles mixtures with GO through the hydrothermal method to form Cu₂O/ZnO/GO nanocomposites. The adsorption-photocatalysis process of methylene blue

The settlement rate and pore water pressure dissipation rate are mainly controlled by the permeability of soil. Both laboratory and field tests show that the permeability is varied during the loading and consolidation process. It is known that consolidation process is accompanied by decrease in void ratio which leads to decrease in the coefficient of permeability. The importance of the decrease of the coefficient of permeability on the time rate of settlement and pore water pressure needs to be investigated.
This paper takes into account the change in coefficient of permeability during consolidation and studies its effect on consolidation characteristics of a clay layer. The finite element method is used in the analysis and the packag

Medication safety and effectiveness can be improved through interprofessional collaboration. The goals of this study were to measure the degree of physician–pharmacist collaboration within Iraqi governmental healthcare settings and to investigate factors influencing this collaboration.