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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
Mon Jun 15 2026
Journal Name
Journal Of Studies And Researches Of Sport Education
The effect of rebound jumping exercises on the development of the special strength of the lower limbs among the players of the National Center for the Nurturing of Talented Sports in the high jump.
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The high bounce activity according to the fosbery way is regarded as of the difficult sports concerning its way of training and perfection due to hard technique of its performance on one hand and because it depends on the player’s ability to overcome body weight resistance against the gravity. In addition to the strong ability to control the body posture when leaving the land and flying over the barrier. This activity needs to high plosion power at the moment of bouncing and this plosion depends on the period of bouncing, so the two researchers aimed to use a mechanical bouncing platform and an electronic one through several training by one foot and both feet in different directions and positions in order to reduce the time of bouncing an

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Publication Date
Wed Jun 01 2022
Journal Name
International Journal Of Research In Social Sciences And Humanities
THE EFFECT OF SPECIAL EXERCISES IN THE DEVELOPMENT OF THE MOMENTARY BIOMECHANICAL STRENGTH OF THE SKILL OF THE TWO REAR AIR CORES ON THE PARALLEL DEVICE IN THE TECHNICAL GYMNASTICS OF THE EMERGING PLAYERS
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Gymnastics is one of the most interesting games in terms of organizing various world championships and tournaments. Their basic skills and their technical development, especially those with high difficulty levels that rely on basic and complex skills, are the basic skills of gymnastics are the main pillar to be developed and therefore high-difficulty skills will not depend on basic skills, which should reach the stage of the automatic mechanism. Retention) in order to move on to training and developing another skill for the difficulty of movements as well as the smooth flow of performance, ie the degrees of difficulty of each skill specific to your gym and The researcher used the experimental method and The research community determin

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Publication Date
Thu Nov 08 2018
Journal Name
Iraqi National Journal Of Nursing Specialties
Studying the Effect of Different Separating Medium on the Roughness of the tissue surface of Acrylic Denture Base (In Vitro Study)
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Objective: In order to evaluate the effect of different typed of Separating Medium on the roughness of the fitted
tissue surface of acrylic denture base.
Methodology: Chosen three types of separating medium (Group A Tin foil), (Group B Detery Isolant),(Group C
Cold Mould Seal),used 30 samples of hot cure acrylic resin ,10 samples for each group, after complete curing of
these samples , Profilometer device was used to measure the surface roughness of each sample in all groups.
Results: Using One Way ANOVA Test and LSD test, the results were highly significant in differences among all
groups. Although (Group A) showing lest roughness, (Group B) showing a satisfactory result of roughness, While
(Group C) Showing the hig

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Publication Date
Sun Dec 01 2019
Journal Name
Journal Of Economics And Administrative Sciences
The extent of the contribution of the determinants of organizational support in the enhancement of the mental status of banking services - A study of the views of a sample of employees in a number of banks in the city of Dohuk
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     The objective of this study is to determine the extent to which the determinants of organizational support contributed to enhancing the mental status of banking services in a number of banks in Dohuk governorate in order to diagnose the correlation between the perceived organizational support and the mental status of services. Availability in the environment of banks and to enhance the mental position from the point of view of customers as the main hypotheses focused on the nature of the relationship between the dimensions of research among them has been tested these hypotheses using statistical and descriptive methods have been The study concluded that the contribution of organizational support, which is

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Publication Date
Thu Dec 26 2024
Journal Name
Revista Electronica De Leeme
The Image of Women in the Lyrics of The Arabic Music Video: An Analytical Study of the Most-Watched Arabic Songs on YouTube in 2024
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 Several studies have indicated an unprecedented increase in the number of Arab youth who watch music videos. It is also a custom in Arab countries to broadcast songs at their happy parties such as weddings, engagements and birthdays. We see that guests and party owners interact by dancing and singing with the songs, while the viewership rates of Arab music videos have reached millions on YouTube. The researcher decided to study the image of women through the lyrics of these songs, due to their importance in shaping the image of women in the minds of young people and shaping the (self-image) of young women. Twenty songs were selected from the most watched songs on YouTube for the year 2024, and it was found that the negative qualities of t

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Publication Date
Wed Oct 04 2023
Journal Name
Journal Of Al-qadisiya In Arts And Educational Sciences
The use of the digital book and the future of the paper book
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The current research aims to know the complementary use of the paper book and the digital book by defining the paper book and the digital book and knowing the methods and methods of obtaining each of them and indicating the extent of their use and for what purpose and knowing the difficulties that researchers face in using each of them and which is better using the paper book or the digital book in preparing research Studies and for no reason. The research relied on the descriptive approach and the questionnaire as a tool for data collection, and it was distributed to professors and students of Iraqi universities. The research sample reached (219) individuals and reached a set of results, the most important of which are: Preference for the

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Publication Date
Tue Aug 03 2021
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
The relationship of the investment environment with the indicators of the national economy
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The investment environment is the incubator for all types of domestic and foreign investments, so if their determinants are encouraging, they increase the levels of investment flows and vice versa, as there is a relationship between the nature of the investment environment and the level of investment flows, and the determinants of the investment environment are numerous and the most important of which are security and political stability, and economic and financial factors that include relative stability In the exchange rate and inflation rates, the availability of banks and their development, transparency and integrity in administrative dealings and the lack of prevalence of administrative and financial corruption, and the clari

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Publication Date
Thu Mar 31 2022
Journal Name
Journal Of The College Of Education For Women
The Phonetic Connotation of the Appending Letter Alef in the Holy Qur’an
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Appending is a morphological term which means the addition of one or two letters to a structure to be similar to other structures of well-known abstractor additional nouns and verbs constructions. The goal of appending is to organize what have been expanded linguistically and collect similarities to reduce the syntactic rules. This is because the appended word exists for expanding purposes; however, it has no construction of its own. An appending was included with another construction with mentioning the additional letter. This by itself means that appending as a process is a term that helps organize rather than expand language. Scholars further noticed that the appending letter is not semantically significant, and so it differs from the

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Publication Date
Thu Mar 01 2012
Journal Name
Journal Of Economics And Administrative Sciences
Analysis of the relationship between the degree of economic freedom and foreign trade of selected developing countries for the period (1990-2005) *
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Is a high degree of economic freedom an important part in the development of the economies of developing countries in the last decade of the twentieth century and the beginning of the twentieth century and the atheist. This is because a test subject (deltoid analysis of the relationship between the degree of economic freedom and foreign trade of selected developing countries for the period
( 1990 -2005) to determine the degree of economic freedom in foreign trade promotion in Singapore and Turkey. The research recommends a number of  recommendations, the most important is the responsibility of the Ministry of Planning in Iraq that is providing the necessary data for the Fraser Institute, the aim of increasing cooperation

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Publication Date
Tue Dec 29 2020
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
The Impact of Electronic Payment systems on the Profitability of Banks: An applied research on a sample of Iraqi commercial banks
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Due to technological developments in the Iraqi banking sector, which is the use of electronic payment systems within the banking infrastructure. This has led to speed and accuracy in the completion of transactions, reduced costs, increased revenues and efficiency. This research examines the challenges and risks facing the Iraqi banking sector as a result of its use of electronic payment systems. And show its impact on the profitability of commercial banks. The research was based on the main hypothesis that there is a statistically significant moral impact relationship between electronic payment systems and the profitability of banks. Iraqi commercial banks were chosen as a research community, All Iraqi commercial banks that parti

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