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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 corrosion protection of low carbon steel in 2.5 M HCl solution by kiwi juice was studied at different temperatures and immersion times by weight loss technique. To study the determination of the optimum conditions from statistical design in evaluation of a corrosion inhibitor, three variables, were considered as the most dominant variables. These variables are: temperature, inhibitor concentration (extracted kiwi juice) and immersion time at static conditions.

These three variables are manipulated through the experimental work using central composite rotatable Box – Wilson Experimental Design (BWED) where second order polynomial model was proposed to correlate the studied variables with the corrosion rate o

Recently, several concepts and expressions have emerged that have often preoccupied the world . around the concept of environment and sustainability. This is due to the negative and irresponsible impact of man and his innovations in various industrial and technological fieldsthat have damaged the natural environment. Architecture and cities at the broader level are some of the man made components that caused these negative impacts and in the same time affected by them. What distinguishes architectural and urban projects is the consumption of large . quantities of natural resources and production larger amounts of waste and pollution, along the life of these projects. At the end of the twentieth century and the beginning of the twenty-fir

Kurdish language multifunctional morphemes indicate the different functional morphological, syntactical, and semantic tasks of the morphemes. The present study discusses the multifunctional task of the Morpheme Le in Kurdish Language. The Morpheme Le has marginally been included in other studies, yet up to the present times, there has not been a research inclusively dedicated to thoroughly discuss and clarify its multifunctional aspects. The present study is divided into two chapters: Chapter one discusses the theoretical aspect of chapter two that is entirely concerned with the practical aspect of the morpheme Le. The first part of chapter one sheds light on the morphological aspect of the morpheme while part two discusses

The subject of  research entitled "The Mechanisms of build up the dramatic construction in the films of the world of nature - National Geographic's films as a model" emerges from the importance of the subject of the dramatic construction and its departure from its classic style due to the evolution of the visual  presentation and its instruments and the specificity and emergence of a form of television production represented by the films of the world of nature which began to occupy an important space in the map of television and television channels specialized in this subject, which drove the researcher to study the mechanisms of producing the dramatic construction in this kind of film s. This research came in three  chapt

Abstract: Microfluidic devices present unique advantages for the development of efficient drug assay and screening. The microfluidic platforms might offer a more rapid and cost-effective alternative. Fluids are confined in devices that have a significant dimension on the micrometer scale. Due to this extreme confinement, the volumes used for drug assays are tiny (milliliters to femtoliters).

 In this research, a microfluidic chip consists of micro-channels carved on substrate materials built by using Acrylic (Polymethyl Methacrylate, PMMA) chip was designed using a Carbon Dioxide (CO₂) laser machine. The CO2 parameters have influence on the width, depth, roughness of the chip. In order to have regular

Abstract Background: One of the most important methods to replace lost teeth is dental implants. In order to increase the strength of connection of the implant with the jaw bone to provide early loading after placement, implant is coated by different coating materials that achieved that purpose. The aim of this study was to evaluate the influence of coating CP Ti implant with calcium carbonate on the strength of bone-implant interface after two and six weeks of implantation in rabbit femur bone by torque removal test, histological and histomorphometric analysis. Materials and methods: Coating the surface of commercially pure titanium screws with extra pure synthetic calcium carbonate via electrophoretic deposition method (EPD) was done. The