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 .

Constructional Efficiency in architecture in general is one of the most important standard success for any structure and a measure of its continuity and relevance across time and space. Given the importance of Al-Ahwaar environment that owned the spatial, environmental, economic and social elements had a prominent impact in creation of architecture patterns form to create special architectural and structural environment, which had many qualities and ingredients that contributed to its continuity and existence over the years. From the premise that man and his environment is the main goal to any architectural style,

Thus the research problem focusing on the lack of clarity of the previous literatures in its st

The importance of research is to be considered by highlighting the tax policy in Iraq which extended for successive measurement of the amount of tax receipts for respective periods, the research problem represents security, economic and political issues that Iraq suffered which were very difficult since Nineties of the last century until now that led to a lake of clarity in tax policy trends, volatility in it and finally reflected on the tax revenues increase or decrease. One of the main recommendations of the research is: (The necessity to develop a deliberate strategy for tax policy in Iraq which should take into account financial, economic, and social goals in appropriate way).

  The current research is interested in studying the symbol, due to its significant role in the architecture and arts in the holy shrines regardless of their architecture and artistic patterns, through which the symbolic and philosophical connotations insides the holy shrines are revealed. Due to the importance of the topic of the symbol, Almighty God remarked in the holy Quran (He said, "My Lord, make for me a sign." He Said, "Your sign is that you will not [be able to] speak to the people for three days except by gesture. And remember your Lord much and exalt [Him with praise] in the evening and the morning.") (Surat Al-Imran, verse 41). The research consists of two dimensions dealing with symbol and symbolism in its linguistic an

The present paper respects 'inversion' as a habit of arranging the language of modern English and Arabic poetry . Inversion is a significant phenomenon generally in modern literature and particularly in poetry that it treats poetic text as it is a violator to the ordinary text. The paper displays the common patterns and functions of inversion which are spotted in modern English and Arabic poetry in order to show aspects of similarities and differences in both languages. It concludes that inversion is most commonly used in English and Arabic poetry in which it may both satisfy the demands of sound correspondence and emphasis. English and Arabic poetic languages vary in extant to their manipulation of inverted styles as they show changeable f

The aim of the research to measure the correlation relationship between modern manufacturing systems and process design and measure the effect by adopting the regression; the research consists of two main variables, which are modern manufacturing systems and process design; it was applied in the production lines of the General Company for Construction Industries, There is a sample of managers, engineers, technicians, administrators, and some workers were selected to fill the special questionnaire with (70) forms which distributed and (65) were approved suitable for use, For data analysis the correlation coefficient was adopted to measure the relationship and regression analysis to find out the effect, Using (SPSS), So the first h

The study aimed .to identify on the melody tetrachords In the Iraqi Folklore song as mall as the melody tetracords is the basic in striation song if Iraqi Folklore so the researchers prepared their researchers from four chapters. In the first chapter of the researchers theoretical framework, included the research problem, which is determined by what is the melody tetra chords in the Iraqi Folklore songs. The research time limits were specific by year (2015-2016) then the first chapter ended with the terms mentioned in the title of research. The second chapter of the theoretical framework, included two subjects the first (Iraqi Folklore song) and the second subject included (melody tetra chords) then the third chapter deals with the resea

The Disi water samples were collected from different Disi aquifer wells in Jordan using a clean polyethylene container of 10-liter size. A hyper-pure germanium (HPGe) detector with high- resolution gamma-ray spectroscopy and a low background counting system was used for the identification of unknown gamma-rays emitting from radionuclides in the environmental samples. The ranges of specific activity concentrations of 226Ra and 228Ra in the Disi aquifer water were found to be from 0.302 ± 0.085 to 0.723 ± 0.207 and from 0.047 ± 0.010 to 0.525 ± 0.138 Bq L−1, with average values of 0.516 ± 0.090 and 0.287 ± 0.091 Bq L−1, respectively. The average combined radium (226Ra + 228Ra) activity and radium activity ratio (228Ra/226Ra) in Disi

Theoretical trends have appeared Which posed the concept of biological structures in contemporary architecture concept, Spread through the emergence of architectural production that reflect and indicate the nature of the construction structures based on the ideas and principles of biological structures in biological science: Despite the emergence of many architectural proposals that tried to explain the concept in the field of architecture, but it is not dealt with in depth and not given a comprehensive definition: So there was need to search for the concept and its beginning in the biological field as a general framework down to the field of architecture for the purpose of reducing the limits of their search framework T