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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
Thu Jun 01 2006
Journal Name
Journal Of The College Of Languages (jcl)
The Image of the Anti- Hero in James Joyce's Ulysses
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The hero traditionally has such admirable traits as courage, fortitude,
chivalry and patriotism. In the literary works, the hero is the leading
character and the pivot around which all the characters and the events
revolve. The characteristics of the hero usually reflect the cultural values
of his time. Because, in each age, Man's attitudes towards himself and the
world change, different images of the hero emerge.
In Greek Mythology, the hero is frequently favoured by the gods;
therefore, he is himself semi-divine. The Greek hero is of princely birth
and is endowed with good physique, exceptional strength, skill in
athletics and battle, energy and eloquence, like Odysseus who is the hero
of the Odyssey, long

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Publication Date
Sun Dec 16 2018
Journal Name
Al-academy
The Aesthetics of the Digital Sound Effects in Television Drama
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The sound effects in TV dramas achievements have become very important not only in terms of function and implementation, but at a greater and wider level in terms of artistic and aesthetic values, which are produced and employed in the most important world artistic achievements of drama, using the latest and most prominent technologies and equipment and according to the expressive and dramatic values expressed by these modern digital sound effects. Therefore, the researcher chose the aesthetic effect of digital sound effects in television drama to identify the aesthetic aspects provided by digital sound effects by employing them and their accompaniment for the image.

The researcher, therefor, divided this study into the methodolo

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Publication Date
Wed Jan 01 2020
Journal Name
Technologies And Materials For Renewable Energy, Environment And Sustainability: Tmrees20
Studying the effect of the annealing on Ag2Se thin film
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Publication Date
Sun Jun 26 2022
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
The role of banking effort tests in the face of monetary credit risk and its impact on the profits and adequacy of the bank’s capital : / a case study of Sumer Commercial Bank for the period from 2015 to 2020
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The research seeks to identify the proposed scenarios to predict and ward off monetary credit risks that the bank is exposed to in the future, using the banking stress tests model, and showing their impact on capital adequacy and profitability ratio,To achieve this purpose, Sumer Commercial Bank was taken as a case study, and mathematical equations were used to extract the results. Low percentage of profits and returns, strictness in the process of granting credit and financing operations in order to reduce credit risks.

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Publication Date
Fri Apr 12 2019
Journal Name
Journal Of Economics And Administrative Sciences
The relationship between social capital and knowledge sharing and their impact on improving the educational service quality: an analytical study of the views of a sample of academic staffs in the government universities in the Kurdistan Region of Iraq
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Abstract

This study aims to find the relationships between social capital (social network, social trust, shared goals) and knowledge sharing (knowledge Donating, knowledge collecting) as independent variables and their impact on improving the quality of educational services (academic staffs quality, Quality of teaching methods and study curriculums). This research is an important, because it attempts to identify the relationship between social capital and the knowledge sharing and their effect on improving the quality of educational service for universities. The study problem was determined in several questions related to the nature of the correlation relationship - the impact between the different independent variables (

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Publication Date
Sun Dec 01 2019
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
Study of the imperatives of promoting financial inclusion in Iraq: Opportunities and challenges
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The aim of the research is to provide an analytical study to promote financial inclusion in Iraq by clarifying the opportunities and challenges of the economic and demographic situation in Iraq, studying the structure of the financial system and introducing non-bank financial institutions operating in Iraq, and using the descriptive approach. Analytical in the study of the phenomenon of research, the research reached a number of conclusions, the most prominent of which were:

  • Iraqi society is a young society.
  • The majority of the population is 70 percent. They live almost in urban areas.
  • The coverage of bank branch networks is concentrated in only four provinces, leaving other provinces outside financial

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Publication Date
Thu Mar 30 2023
Journal Name
Journal Of Economics And Administrative Sciences
The Role of Electronic Customer Trust Building Tools On Excellent Performance An analytical study of the opinions of a sample of individuals in the administrative and leadership positions in the Northern Cement Company
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The current study aims to overcome the conflicts facing the company in its way of staying and continuing to maintain its performance excellent in light of the intense competition, which made it seek to find strong ways and links with its customers through electronic communication using electronic platforms, and this put confidence and safety in The place of suspicion and fear of not fulfilling credibility or violating the privacy, so this research comes to answer about the question:  “Can the company achieve an excellent performance by relying on the customer's electronic confidence?”.

The study followed the descriptive and analytical approaches by providing a virtual model and testing the zero hypotheses, which stipulat

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Publication Date
Fri Jun 03 2022
Journal Name
Journal Ofxi'an University Of Architecture & Technology
Extent of mathematics teachers' appreciation of the mathematical problem `multiple solutions
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Aims to find out the (Extent of mathematics teachers' appreciation of the mathematical problem `multiple solutions) Research sample consisted of (100) mathematics teachers distributed on the General Directorates of Education in Baghdad (Rusafa 1/2/3) and (Karkh 1/2/ 3) There was two research approach which are: The first - two different answers of students to the same issue where teachers must assess each answer and explain which one the teacher will accept and why? The second - Different solutions of students' to the same issue, including wrong answers , Teachers should correct the answers and give them final grades (0-10). Descriptive and analytical Approch was used in this research methodology And zero hypotheses, which are as f

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Publication Date
Sat Dec 30 2023
Journal Name
Journal Of The College Of Education For Women
The Effect of Barman's Model on acquiring the Concepts of Fiqh of Worship among Students of Departments of Qur'anic Sciences
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The current research seeks to identify the impact of Barman's model on acquisition of the concepts of jurisprudence of worship among students of the departments of Qur'anic sciences. To achieve the research objectives, the researcher relied on the experimental method through a design with partial control by relying on two experimental groups receiving teaching by using the Barman model and a control group receives teaching through the normal method. After applying the experiment, the study reached the following results: Students of the Department of Qur’anic Sciences in general need educational programs linked to the curriculum and built on scientific foundations, according to their needs and problems (psychological, cognitive, and soc

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Publication Date
Tue Feb 17 2026
Journal Name
Sciences Journal Of Physical Education
Individual analysis of kinetic response variables according to the measurement of the H7 system for the best jumping players in the national basketball team 2021
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