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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
Wed Jan 01 2020
Journal Name
Cogent Engineering
On the computational aspects of Charlier polynomials
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Publication Date
Sun Dec 12 2021
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
The Acute Toxicity of Rutin in Mice
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Acute toxicity is a step to evaluate the toxicity of a substance. Rutin is one of the flavonoid compounds with a variety of pharmacological effects. The aim of the study is to calculate the lethal dose that affect fifty percent of the mice used in the experiment (LD50). Thirty Swiss albino male and 30 non-pregnant female mice have been divided equally and randomly into 5 treated groups and one control group (n=5)  Rutin has been administered with  concentrations 5, 2.5.1.25,0.625 and 0.312 g/kg administered as a single dose intraperitoneally (IP) while the control group received 1% DMSO (IP).  Animals were observed for any morbidity and mortality for 14 days. After 14 days the animal blood collected for biochemical and hem

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Publication Date
Wed Mar 15 2023
Journal Name
Al-academy
The Role of Context in Graphic Design
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The need for an intellectual understanding of the context from many aspects' dictates understanding the ways through which the graphic designer walks in simulating the intent of the design process and elevating it to levels of communicative perception that leads to communicating the idea to the recipient, and it is thus a need closely related to the context, if it is historical. Culturally or socially, and between the mechanisms of selecting and operating the elements and units of the graphic and design achievement. On this basis, the role of context in graphic design can be studied.

The research included four chapters, the first chapter of the research problem and the need for it, and the aim of the research was (discovering the

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Publication Date
Sat Mar 07 2026
Journal Name
Al–bahith Al–a'alami
INDICATEURS OF THE EXCELLENT PUBLIC RELATION PRACTICE
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« This paper presents the indicators of the development of excellent public relations in the institutions of higher education that are possible for three contextual variables: institutional, professional, professional, and effective communication. Therefore, the study used six indicators to measure the excellent public relations in institutions of higher education and scientific research. These indicators are based on the theory of excellence in public relations . Research Objectives: The aim of the research paper is to uncover the institutional, professional, and professional indicators of effective communication of excellent public relations in higher education institutions. Resea

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Publication Date
Thu May 18 2023
Journal Name
College Of Islamic Sciences
Lamentation in the poetry of Hafez Ibrahim
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Elegy is one of the foundations of the Arab poetic heritage, and it is one of the main sections of poetry. Man has found in him his desire to express his innermost self at an hour filled with pain, and an outlet from which his anguish and grief come out in an expressive form that liberates tears and reproaches death.
Lamentation is an evolving purpose that grows with the growth of society and life and records the change that takes place in every stage of history. It is an important result of the poet's collision with life and events.
That is why I chose the lamentation poetry of Hafiz Ibrahim, due to the importance of this art to him, and it is the art in which he excelled the poets of his time.
I have divided this research into

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Publication Date
Tue Apr 01 2014
Journal Name
Journal Of Economics And Administrative Sciences
Financial markets liquidity and their impact in the return of common stocks
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    The research aimed to study the financial markets liquidity and returns of common stocks , Take the research  the theoretical concepts  associated with each of the liquidity of financial markets and returns of common stocks , As well as the use of mathematical methods in the practical side to measure market liquidity and Stocks  Return, the community of research in listed companies in Iraqi stock exchange that have been trading on its stock and number 85 joint-stock company, The research was based to one premise, there is a statistically significant effect for the liquidity of the Iraqi stock exchange on returns  of common stocks  to traded companies in which , Using th

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Publication Date
Wed Dec 30 2020
Journal Name
Al-kindy College Medical Journal
The immediate and late results for balloon angioplasty of native coarctation of aorta in pediatrics age group
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Background: percutaneous balloon dilation of corotation of aorta is a less invasive and alternative to surgical repair for patients with discrete coaction of aorta and although the used of balloon angioplasty in patients with recurrent postoperative coarctation gained a wide consensus, the use this technique for native coarctation is still controversial in children less one years. 

Objective: to evaluate the immediate and late result of balloon dilation of native coarctation of aorta in infant and children.

Type of the study: A prospective study. 

Subjects & Methods: The study was done on forty-five patients who were referred for cardiac catheterization and balloon

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Publication Date
Mon Jun 30 2025
Journal Name
Modern Sport
Attitudes of Female Physical Education and Sports Science Teachers Toward the Use of AI Applications
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The integration of arti cial intelligence (AI), whether through devices or software, has become a critical tool in analyzing and evaluating technical performance. AI signi cantly contributes to enhancing athletic performance by enabling accurate data analysis and supporting educators in developing effective training programs and interactive curricula. This study addresses a noticeable gap in the literature regarding the attitudes and inclinations of educators toward AI in physical education and sport sciences—a gap often attributed to limited awareness and lack of access to moderntechnologies.Theprimaryaimofthestudyistoexaminethetendenciesandperceptionsoffemaleinstructorsin physical education and sport sciences toward the use of AI

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Publication Date
Wed Aug 11 2021
Journal Name
Nauchforum
ROLE OF METAPHOR IN PUPPET IMPLEMENTATION (ON THE EXAMPLE OF D. RUBINA'S NOVEL «PETRUSHKA'S SYNDROME»)
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The article examines metaphors as one of the fundamental means used by D. Rubina when writing the novel “Parsley Syndrome” to form images of dolls as equal heroes of the work. The author of the article continues research related to the work of Dina Ilinichna Rubina, a representative of modern Russian prose.

Publication Date
Tue Jun 30 2015
Journal Name
Iraqi Journal Of Market Research And Consumer Protection
Isolation and identification of Bacillus stearothermophilus and study the inhibition effect of squeezed grape waste extract on it.: Isolation and identification of Bacillus stearothermophilus and study the inhibition effect of squeezed grape waste extract on it.
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The aim of this study was to know the inhibition activity of squeezed grape waste extract on Bacillus stearpthermophilus by using three different tempretures degree 40, 60 and 80c, in order to reduce the time exposure of food for preservation. This study include two branchs: First: isolation and identification of Bacillus stearothermophilus from soil, 5 sample were collected from the soil of the college agriculture/Baghdad university. Samples were cultured on nutrient agar, microscopic and culturing tests were conducted and many biochemical tests were done. The isolates were cultivated at 55 c and 65 c for differentiate it from Bacillus coagulans which is can't grow at 65 co. The c

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