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 United States government allowed Native Americans to abandon their reservations in the 1950s and 1960s. The historical, social, and cultural backgrounds shaped the forms and themes of works by American Indian writers who urged people to refuse their culture's sense of shame. Moreover, their behavior corresponded with the restoration of individuals to their rituals after disappointment, loss of sense of life, and mental illness performed from the influence of mainstream American society. Among these writers, N. Scott Momaday and Leslie Marmon Silko participate in similar interest in portraying characters caught between indigenous beliefs and white mainstream standards.  

      The construction of

Aims of this research to determine asbestos fibers levels in surrounding air of some crowded sites of Baghdad city were monitored in summer 2020. Collection of samples was conducted by directing air flow to a mixed cellulose ester membrane filter mounted on an open‑faced filter holder using sniffer a low flow sampling pump, samples of air were collected from five studied areas selected in some heavy traffic areas of Baghdad city, (Al-Bayaa and Al-Shurta tunnel, Al-Jadriya, and Al-Meshin commercial complex, control), then analyzed to determine concentrations of asbestos fibers. Counting of asbestos on the filters was carried out through using both scanning electron microscope SEM and an energy dispersive X‑ray system EDS to count

A study of taxonomic quality of algae attaching Three concert bridges built on the Tigris River within city of Baghdad including Al-Jadriyah Bridge in Al-Jadriyah area and the Bab Al-Mu'adam Bridge in Al-Shalajiya area, while the third site included Al-Muthanna Bridge in north of Baghdad city, for the period from Autumn 2021 and Winter 2022. The study identified 114 species of 32 Genus in which the predominance of Bacillariophceae (74 species, 14 Genus) Followed by Cyanophyceae (30species, 12 Genus) and 10 species (6 Genus) of Chlorophyceae. The study showed an increase in species of Bacillariophceae, Cyanophyceae which has the ability to secretion gelatinous substances that enable it to stick to solid stand, the number of the larges

Purpose: The present study seeks to examine various history stages in which undergone by the concept of scenarios, and development of this concept to integration with the strategic management practices:
Methodology: The current study relied on a literature review and approach in providing total picture of different stages undergone by this concept.
The main results: the scenarios did not reach maturity in their quest for integration with strategic management, and still need a great effort for the maturation of this thought in the framework of strategic management, and through it can contribute in creating important knowledge evolution.
Originality and value: providing a contemporary model linking the roots of this concept and cu

           English has for long been one of the most widely used media of communication globally, especially in the Malaysian universities. It has been termed as a Lingua Franca because it is shared with other languages which are considered first languages by different speakers. For this reason, English as a Lingua Franca (ELF) has attracted a number of researchers to investigate its variety via other languages in various communities. The objective of this paper is therefore to establish the strategies which are employing by the international students at the National University of Malaysia/ UniversitiKebangsaan Malaysia (UKM) as an example of one of the Malaysian universities; when they e

Abstract              
          Agricultural investment is one of the main requirements in most economies of the world for its importance in the development of the agricultural sector through the agricultural and technological infrastructure and agricultural research, as well as its impact on most economic, social and service activities, especially if managed and employed scientifically, which generates income and productive capacities and services and new commodities, Unemployed as agricultural investments in Iraq fell significantly after 2003 due to economic, political, social

In this study, the specimens of land snails Polygyra cereolus (Megerle v on Mühlfeld t , 181 8
(Gastropoda, Stylommatophora, are collected between March and April 2021
from gardens and nurseries in Baghdad province, this species was recorded as a new record to
Iraq molluscan fauna. Description of the most important characteristics, measurements of the
shell are presented with digital p photographs, subsequently, this study represents the first record
of the Polygyridae in Iraq.

Background: The skull offers a high resistance of adverse environmental conditions over time, resulting in the greater stability of the dimorphic features as compared to other skeletal bony pieces. Sex determination of human skeletal considered an initial step in its identification. The present study is undertaken to evaluate the validity of 3D reconstructed computed tomographic images in sex differentiation by using craniometrical measurements at various parts of the skull. Materials and Method: 3D reconstructed computed tomographic scanning of 100 Iraqi subject, (50 males and 50 females) were analyzed with their age range from20-70 years old. Craniometrical linear measurements were located and marked on both side of the 3D skull images.