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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 30 2016
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
Determination of the Optimum Conditions for the Production of Gamma Alumina (ɤ-Al2O3) By the Precipitation Method of the Sodium Aluminate Solution
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Design of experiments (DOE) was made by Minitab software for the study of three factors used in the precipitation process of the Sodium Aluminate solution prepared from digestion of α-Al2O3  to determine the optimum conditions to a produce Boehmite which is used in production of ɤ-Al2O3 during drying and calcination processes, the factors are; the temperature of the sodium aluminate solution, concentration of HCl acid added for the precipitation and the pH of the solution at which the precipitation was ended. The design of the experiments leads to 18 experiments.

   The results show that the optimum conditions for the precipitation of the sodium aluminate solution which

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Publication Date
Fri Dec 01 2023
Journal Name
Political Sciences Journal
The Future of the Russian- Ukrainian War and the Extent of its Reflection on the Security of Eastern European Countries after 2022
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Wars represent one of the most serious threats to the world order; It is considered a violation of international laws and norms, and humanitarian principles. From this point comes the study of the importance of the topic entitled (The Future of the Russian-Ukrainian war and the extent of its Reflection on the security of Eastern European countries after the year 2022). This study is based on reviewing future possibilities (scenarios) of war. The Russian-Ukrainian war, which was launched by the Russian government led by Russian President Vladimir Putin in February 2022, is still ongoing at the time of writing this research. This chapter includes three possibilities (scenarios). The first possibility deals with the development of the war t

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Publication Date
Thu Aug 01 2019
Journal Name
Journal Of Economics And Administrative Sciences
Analysis of the sustainability of the public debt in light of the volatile oil revenues in Iraq for the period (2005-2015)
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Abstract

This study deals with the fluctuations of oil revenues and its effect on the public debt. This can be studied through the indicators of debt sustainability, the financial, and economic indicators which express the risk of debt. The study focuses on clarification of the public debt path and its management both domestic and foreign. The sustainability of debt takes an important role according the macroeconomic variables. This study stresses the relationship between the rental economy in Iraq and the risk of the public debt, it is very important to work high oil prices, and on investigating during high work to establish a fund to support the budget deficit. This will reduce future risks arising from the use of publi

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Publication Date
Tue Sep 15 2020
Journal Name
Al-academy
The Impact of Elements of the Ancient Iraqi Heritage in the Gallery of the Iraqi Natural History Museum: محمود حسين عبد الرحمن
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  The research addresses the most important elements of the ancient Iraqi heritage represented by architecture and plastic arts being the direct means that preserved the heritage due to the ease of preserving them and the speed of circulating them and diversity of their topics. Through the features of these elements, the research problem has been defined in the form of questions including: what are the most important elements of the ancient Iraqi heritage? What are the plastic arts? What are the most important topics adopted? What is the concept of palm in the ancient Iraqi heritage? What is the evidence for that?
Has it been employed in the Iraqi contemporary art? What is the evidence for that? How to employ it in the arts and t

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Publication Date
Tue Dec 11 2018
Journal Name
Iraqi National Journal Of Nursing Specialties
Impact of spastic cerebral palsy upon the quality of life of children under the age of 12 years in Erbil City: parents’ reports
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Objectives: This study aims to assess the quality of life of cerebral palsy children less than 12 years old reported by
parents in Erbil city/Iraq.
Methodology: A descriptive study was conducted during 2014, to describe the quality of life of cerebral palsy
children. One hundred mothers have cerebral palsy children were participated in this study. The study took place at
Helena Center for handicapped children in Erbil City. Questionnaire was used to collect data, which consists of two
main parts. The first part is divided into two sections; section one was described the mothers’ demographic
characteristics, while the second section was for identifying the demographical characteristics of cerebral palsy
children. Th

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Publication Date
Fri Jan 01 2021
Journal Name
Review Of International Geographical Education Online
Measuring The Efficiency of The Departments of The College of Administration and Economics / University of Baghdad Using the Method of Data Envelopment Analysis (DEA), A Comparative Study
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The research aims at the possibility of measuring the technical and scale efficiency (SE) of the departments of the College of Administration and Economics at the University of Baghdad for a period lasting 8 years, from the academic year 2013-2014 to 2018-2019 using the method of Applied Data Analysis with an input and output orientation to maintain the distinguished competitive position and try to identify weaknesses in performance and address them. Nevertheless, the research problem lies in diagnosing the most acceptable specializations in the labor market and determining the reasons for students’ reluctance to enter some departments. Furthermore, the (Win4DEAp) program was used to measure technical and scale efficiency (SE) and rely on

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Scopus
Publication Date
Fri Nov 05 2021
Journal Name
Review Of International Geographical Education Online
Measuring The Efficiency of The Departments of The College of Administration and Economics / University of Baghdad Using the Method of Data Envelopment Analysis (DEA), A Comparative Study
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Publication Date
Sun Feb 03 2019
Journal Name
Journal Of The College Of Education For Women
The Role of the Family in investment Effect of the Mates in Evaluating the Childs Acceptance (2-5 years) of rich foods and inhancemenl rein for cement of the social love concepts: The Role of the Family in investment Effect of the Mates in Evaluating the Childs Acceptance (2-5 years) of rich foods and inhancemenl rein for cement of the social love concepts
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Abstract:
The aim of the present research is to evaluate the child’s nutritional
method (2-5 years old) which is based on his resistance of the food highly rich
with nutritional elements and his acceptance of the food of a low nutritional
value in addition to his having forbidden food with other mates and making
use of all mates when having food, in establishing the sound social values and
affection since child hood. The required statistical equation have been used
by the researcher namely (Z test).
The sample of the present study consists of (26) children who were selected
intentionally and randomly from the kindergartens of Al-Bayaa region and the
college of Education for women. The questionnaires were d

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Publication Date
Thu Mar 30 2006
Journal Name
College Of Islamic Sciences
The Messenger’s approach to preaching (the Meccan stage in light of the Qur’an and Sunnah)
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First: People’s need for advocacy:

Calling for a legal necessity for all people, regardless of their races, colours, tongues, and culture, to explain the truth, spread fear, bring benefits, ward off evil, regulate a person’s relationship with his Lord, and his relationship with creatures, so that he knows his money and what he owes.

All of creation is in dire need of the call to God’s religion with insight due to their inability to reach out to goodness, righteousness, guidance, and success on their own. Man is limited in thinking in this universe, limited in his resolve, unable to know what will improve his affairs in the two worlds. His need for religion is one of the necessities of his life, and one of the comple

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Publication Date
Sun Oct 02 2016
Journal Name
Journal Of Educational And Psychological Researches
The Effect of Driver and Posner Models in correcting Alternative Perceptions in Educational Psychology Material for the Students at the Institute of Fine Arts
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To achieve the goals, the researcher followed the design of equal and   independent groups of partial control and post-test . The research has chosen the Institute of Fine Arts in the area Almansour area as deliberate sample where three sections of students have been chosen and the   number of students is (69) students. The researcher conducted equivalence in the variables (age, and IQ , and the overall rate for grade III). in diagnostic phase,  (21) concepts of alternative    image out of (46) concepts have been identified in addition to the goals of formulation of acquisition concepts according to the three processes (definition, discrimination and application). Achievement test has been

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