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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
Fri May 15 2026
Journal Name
Journal Of Physical Education
The impact of a training field in Lake Al-Razzaza to develop the strength of the legs and arms for young boxers
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Publication Date
Mon Sep 12 2022
Journal Name
Communications In Mathematical Biology And Neuroscience
The influence of fear on the dynamic of an eco-epidemiological system with predator subject to the weak Allee effect and harvesting
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In this paper, an eco-epidemiological prey-predator system when the predator is subjected to the weak Allee effect, and harvesting was proposed and studied. The set of ordinary differential equations that simulate the system’s dynamic is constructed. The impact of fear and Allee’s effect on the system's dynamic behavior is one of our main objectives. The properties of the solution of the system were studied. All possible equilibrium points were determined, and their local, as well as global stabilities, were investigated. The possibility of the occurrence of local bifurcation was studied. Numerical simulation was used to further evaluate the global dynamics and understood the effects of varying parameters on the asymptotic behavior of t

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Publication Date
Tue Sep 05 2023
Journal Name
Pakistan Heart Journal
The Effect of Dynamic Lactic Training According to the Target Time to Develop the Achievement of 800m Runners Under 20 Years Old
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MA Mahde, HAA Kadhim, HN Tarish…, Pakistan Heart Journal, 2023 - Cited by 4

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Publication Date
Wed Sep 15 2021
Journal Name
Al-academy
Representations of the body in the works of the artist Ali Al-Najjar (analytical study): رحاب حسين حسن-سلام ادور يعقوب اللوس
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The twentieth century witnessed developments, transformations and artistic revolutions, including what was witnessed in Arab art, especially contemporary Iraqi plastic art, and as a result, research and studies have increased that dealt with its topics in different ways, which has become a presence that gave it its own language and unique discourse, especially the body, thus opening the way for its employment in composition, to become a form. It denotes interpretable meanings through its various formal representations, which are artistic, cultural and cognitive products. The modernity of the Iraqi formation in the body has passed through different roles, so it started to deal with the body as a representation that reflects the real envir

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Publication Date
Wed Nov 07 2018
Journal Name
Iraqi National Journal Of Nursing Specialties
Quality of Life among Adult Patients with Peptic Ulcer in the City of Sulaimani
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Objectives: To assess the quality of life for adult patients with peptic ulcers in the city of Sulaimani.
Methodology: A descriptive study, using the assessment approach was conducted on patients with peptic ulcer
disease from January 12th, 2009 to September 30th, 2009. A purposive "non-probability" sample of (100) paƟents
(males and females) with peptic ulcers who attended Kurdistan Center for Gastroenterology and Hepatology were
selected for the study. A questionnaire was adapted from the World Health Organization quality of life questionnaire
(1998) for the purpose of the study. It is comprised of (3) parts that included sociodemographic characteristics form,
medical history form and adult peptic ulcers patients' qu

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Publication Date
Wed Jun 30 2021
Journal Name
Journal Of Economics And Administrative Sciences
A proposed model for disclosing the role of the collective intelligence system in improving joint auditing
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This research aims to present a proposed model for disclosure and documentation when performing the audit according to the joint audit method by using the questions and principles of the collective intelligence system, which leads to improving and enhancing the efficiency of the joint audit, and thus enhancing the confidence of the parties concerned in the outputs of the audit process. As the research problem can be formulated through the following question: “Does the proposed model for disclosure of the role of the collective intelligence system contribute to improving joint auditing?”   

The proposed model is designed for the disclosure of joint auditing and the role

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Publication Date
Mon Dec 01 2014
Journal Name
Journal Of Economics And Administrative Sciences
The role of financial reporting for non-current assets impairment in enhancing the relevance accounting information
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  This research deals with the financial reporting for the non-current assets impairment from the viewpoint of international accounting standards, especially IAS 36 "Impairment of assets”. The research problem focused on the non-compliance with the requirements of IAS 36 which would negatively affect the accounting information quality, and its characteristics, especially the relevance of accounting information, that confirms the necessity of having such information for the three sub-characteristics in order to be useful for the decisions of users represented

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Publication Date
Wed Nov 02 2022
Journal Name
Res Militaris
Cultural Activities The Iraqi Ministry of Culture, Tourism and Antiquilies
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It’s an attempt to identify the cultural activities of the Ministry of Culture, Tourism and Antiquities, which are provided by the Ministry of Culture, Tourism and Antiquities and the departments affiliated with the Ministry of Culture only, not tourism and antiquities. The most important results areIs that the Ministry of Culture, Tourism and Antiquities has many cultural activities such as (festivals, exhibitions, conferences, fashion shows, concerts, musical evenings, theatrical and cinematic performances) in addition to literary series and cultural magazines, which are directed to the public in general, whether it is elite or not, and this shows the extent The importance of cultural activities published by the Ministry of Culture, Tou

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Publication Date
Mon Feb 13 2023
Journal Name
Journal Of Educational And Psychological Researches
The Degree of Practicing Citizenship Values by Bisha University Students
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Abstract

 

The study aims to identify the degree of citizenship values practiced by Bisha University students and identify the impact of gender, college, and academic level, on the degree of the practice of University students for citizenship values. The researcher used the descriptive-analytical method including a questionnaire of (44) items. To process the data, the researcher applied the computational averages, standard deviations, percentages, and T-test. The questionnaire was implemented on a sample of (600) of the 2 and 8 levels during the second semester of the academic year (2020-2019) at Bisha University. The study findings revealed that the degree of the pra

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Publication Date
Fri May 15 2026
Journal Name
Al–bahith Al–a'alami
Verses of Monks in the Holy Quran Study and Analysis
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Tafsir, ‘interpretation’ is one of the most important sciences the Muslims need. Because Allah, Almighty, revealed the Qur’an to be a way of life for the Muslims in which the healing of what is in the chest, including their goodness and their peasant. Allah says:
“O people, an admonition has indeed come to you from your Lord and a healing for what is in the hearts; and a guidance and a mercy for the believers.”
In order to achieve the goal for which God revealed the Quran must be understood and managed verses:” This is a Book that We have revealed to you abounding in good, that they may ponder over its verses, and that those who have understanding may be mindful.”
The Prophet (PBUH) and his companions understood t

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