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The Representaion of Algebraic Integers as Sum of Units over the Real Quadratic Fields: REPRESENTAION OF ALGEBRAIC INTEGERS AS SUM OF UNITS OVER THE REAL QUADRATIC FIELDS
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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 .

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Publication Date
Sat Dec 01 2012
Journal Name
Iraqi Journal Of Science
The Effect of Metallicity on the AGB Stars Evolution by Using Synthetic Model
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Abstract: Stars whose initial masses are between (0.89 - 8.0) M☉ go through an Asymptotic Giant Branch (AGB) phase at the end of their life. Which have been evolved from the main sequence phase through Asymptotic Giant Branch (AGB). The calculations were done by adopted Synthetic Model showed the following results: 1- Mass loss on the AGB phase consists of two phases for period (P <500) days and for (P>500) days; 2- the mass loss rate exponentially increases with the pulsation periods; 3- The expansion velocity VAGB for our stars are calculated according to the three assumptions; 4- the terminal velocity depends on several factors likes metallicity and luminosity. The calculations indicated that a super wind phase (S.W) developed on the A

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Publication Date
Wed Sep 01 2010
Journal Name
Al-khwarizmi Engineering Journal
The Stress Distribution on the Zygapophyseal Joint of Lumbar Vertebra by ANSYS Program
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Zygapophyseal joints (or facet joints), are a plane synovial joint which located between the articular facet processes of the vertebral arch which is freely guided movable joints. Ten dried vertebrae were used for the lumbar region and taking (L4) as a sample to reveal stress pathways across the joints by using ANSYS program under different loading conditions which used Finite Elements Analysis model. Results obtained from the ANSYS program are important in understanding the boundary conditions for load analysis and the points of stress concentration which explained from the anatomical point of view and linked to muscle and ligament attachments. This model used as a computational tool to joint biomechanics and to prosthetic im

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Publication Date
Tue Dec 01 2020
Journal Name
Journal Of Green Engineering
Investigate the suitability of suspended sediment transport formulas in the main outfall drain
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Publication Date
Thu May 01 2025
Journal Name
Dirasat: Human And Social Sciences
The Role of Russian Writers and Intellectuals in the 1905 Revolution in Russia
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Objectives: The main objective of this study is to examine the crucial role that Russian writers and intellectuals played in catalyzing the 1905 Revolution in Russia. Specifically, the study sought to analyze how their literary works, philosophical ideas, and political writings challenged Tsarist autocracy, depicted the suffering of the masses, and inspired opposition movements. The study aimed to highlight the defiant writings that contributed to the rise of political figures and the eventual overthrow of the repressive regime. Methods: The historical narrative and analytical methods were employed, conducting a comparative analysis of prominent works by renowned authors such as Tolstoy, Gorky, and Chekhov. This analysis focused on

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Publication Date
Sun Jun 30 2024
Journal Name
Journal Of Sustainable Studies
The Scope of Resorting to Amicus Curiae at the Regional and International Levels
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The amicus curiae is one of the judicial procedures adopted in many judicial and legal systems around the world, under which a person who is not a party to the case, and without having a personal and direct interest in it, intervenes to draw the court’s attention to many factual and legal aspects

Publication Date
Wed Jan 01 2014
Journal Name
Journal Of The College Of Languages (jcl)
Females' Journey into Finding the Self in Beth Henley’s Crimes of the Heart
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Writing as a female playwright in theatre gives a deeper depiction of woman’s real- self. Beth Henley has succeeded in providing a new realist vision of women’s abilities to face their inevitable tragic fates and how to conquer their despair. In Crimes of the Heart, the playwright uses certain method to present the development of the heroines’ characters through blending the tragic events with a comic frame. In fact, Henley focuses on the simple humorous activities more that the importance of the tragic event to present her vision of how to survive and face the crisis of life.

Crimes of the Heart is a play that is concerned about three sisters whose lives are headed in distinctly different directions; howe

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Publication Date
Sun Mar 15 2020
Journal Name
Al-academy
Employing the Psychological Dimension of Sound in the Cinematic Film: أنور عبد شاطي
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         This research deals with the audio part of the cinematic film, which is the sound and its elements inside the space of the cinema picture. It also deals with the psychological side of the sound and the effects made by the sound on the audience through the carefully studied use of the film maker in employing the sound and the picture. For the importance of this element, most of the directors were aware of the seriousness that sound causes to the cinematography, and consequently working as a whole such as the  indications, meanings, symbols, metaphors ,transitions…etc. The research included the methodological framework which consists of the research problem, in which the researcher ma

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Publication Date
Sun Jan 01 2017
Journal Name
International Journal Of Science And Nature
Morphological features of the small intestine in the adult indigenous Gazelle (Gazella Subgutturosa)
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Publication Date
Sun Jan 27 2019
Journal Name
Journal Of The College Of Education For Women
Music and Singing in The Heritage of Baghdadi The 1930s is a Model
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Music and singing are always associated with the movement of society and the emergence of cultural and artistic activities other.
The social and political transformations of the 1930s helped to disseminate the study Music and music in the city of Baghdad and across Iraq This is the beginning of a new era of musical art alongside other arts.
While achieving musical arts A new step was advanced by publishing a technical study among the younger generation they were looking for to contribute to the musical field On the other hand, the city of Baghdad during the period of research many musical and musical performances Egyptian teams have provided many artistic activities and events which have had a significant impact on the development

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Publication Date
Mon Sep 04 2023
Journal Name
East European Journal Of Physics
Investigation the Structural Influences of Silver Oxide Addition in the Bioactive Phosphate Glasses
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This research investigates the impact of varying concentrations of silver oxide on the structure and morphology of phosphate bioactive glass (PBG). PBGs are gaining popularity as a potential replacement for traditional silicate glasses in biomedical applications due to their adjustable chemical resistance and exceptional bioactivity. Upon examination of the scanning electron microscope of the composites without Ag2O, it was observed that the grains tended to merge together, and the surface particles appeared to be larger than those in composites with Ag2O at concentrations of 0.25, 0.5, and 0.75 wt%. The study found that the diffraction pattern of phosphate bioactive glass composites sintered without Ag2O showed the presence of Stro

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