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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 May 14 2026
Journal Name
Al-anbar University Journal Of Law And Political Sciences
The reasons for the fall of sanctions in the decisions and customs provisions in Iraqi law
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Publication Date
Mon Feb 04 2019
Journal Name
Journal Of The College Of Education For Women
The Effectiveness Of the Poetic Text Between the Presence and Absence in Abu Firas al_Hamdani Romyate
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Abu Firas al- Hamdani is one of the most prominent abbasid poets Who characterized their poetry with high artistic quality especially in his Romyate which blended the quality of feelings of grief, sorrow, longing and nostalgia that makes sensitive self conflict that stems with time from one hand and with place on the other hand. Because we are dealing with a poet lived west spatial coercive which it has been hurt him within a time conflict swinging between despair and some times patience and hope other times between the present and his painful reality also between the past and the beautiful times.
This researcher is to stand on this Romyat by monitoring effectiveness of the poetic text based on conflict between the presenc

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Publication Date
Sun Apr 01 2018
Journal Name
Journal Of Economics And Administrative Sciences
The history of rational thought for the investment by human capital and the investing in it.
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The investment however "was its description and meaning, it remains a resident" in the composition of capital assets located in the forefront of the creation of productive assets, and this means that the investment in the productive sectors is a priority in achieving capital accumulation, on any other investment that takes place with the stages of advanced development of formation , not forgetting "to humans and investment humans as head of real money product, the source of the economic surplus and accumulation, and the source of producing values, and if human labor was the source of value, and the human was the source of work, therefore humanitarian work on different levels and skills presents capital", so the investment in huma

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Publication Date
Sat Oct 02 2021
Journal Name
International Journal Of Nonlinear Analysis And Applications
Using the wavelet analysis to estimate the nonparametric regression model in the presence of associated errors
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Abstract The wavelet shrink estimator is an attractive technique when estimating the nonparametric regression functions, but it is very sensitive in the case of a correlation in errors. In this research, a polynomial model of low degree was used for the purpose of addressing the boundary problem in the wavelet reduction in addition to using flexible threshold values in the case of Correlation in errors as it deals with those transactions at each level separately, unlike the comprehensive threshold values that deal with all levels simultaneously, as (Visushrink) methods, (False Discovery Rate) method, (Improvement Thresholding) and (Sureshrink method), as the study was conducted on real monthly data represented in the rates of theft crimes f

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Publication Date
Sat Dec 31 2016
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
Experimental Work to Study the Behavior of Proppant Inside the Hydraulic Fractures and the Plugging Time
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Experiments were conducted to study the behavior of the solid particles (proppant) inside the hydraulic fracture during the formation stimulation, and study the effect of the proppant concentration on the hydraulic fracturing process, which lead to bridge and screen-out conditions inside the fractures across the fracture width that restricts fracturing fluid to flow into the hydraulic fracture. The research also studies the effect of the ratio between the fracture size and the average particles diameter “proppant", on fracture bridging. In this study two ratios were considered β= 2 and 3 ,where β=Dt / Dp where: Dt= hydraulic fracture size (width) and Dp=Average particles diameter.

This work pr

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Publication Date
Sun May 10 2015
Journal Name
Al-academy
Impediments to the use of the Iraqi musical instruments in the orchestra: احسان شاكر محسن زلزلة
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The diversity of ideas and freedom of expression among the authors, who are looking for what's new serve the goals of musical expression and aesthetic, which calls for the use of traditional instruments with the formation of the great instrumental music and well-known orchestra, is a major challenge from several quarters, the failure of some of those musical instruments or limited potential or method performed by costly sometimes prevents the use of a permanent in this great configuration, had to be the emergence of some of the problems faced by the author and musician on the one hand and the receiver on the other hand, which must be looking for the perfect, some of these musical instrument are used systematically follows the work of the

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Publication Date
Fri Dec 31 2021
Journal Name
Political Sciences Journal
The application of smart power in the regional power struggle in the Middle East after 2011
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Receipt date:12/7/2020 accepted date:24/1/2021 Publication date:31/12/2021

 Creative Commons License This work is licensed under a Creative Commons Attribution 4.0 International License.

The constant characteristic of international relations is the constant change due to political, economic and military developments in addition to technology, and this in turn has led to many transformations in the concept of power, its uses, and the elements that form power and its distribution, and according to those variables, the concept of power has shifted from hard to soft, up to smart powe

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Publication Date
Wed Feb 01 2023
Journal Name
South Asian Journal Of Social Sciences And Humanities
The Impact of the Sustainable Strategy on Strategic Performance: Field Study in the Iraqi Tourism Sector
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The tourism industry, with its two sides (recreational and religious), is one of the important investment fields in Iraq, it is represented Iraq as the second economic source after the oil sector. So a need for serious efforts to develop the tourism sector and maintain its sustainability. This paper will be one of the important contributions in this field; the paper aims to explore the extent of the impact of the sustainable strategy on the level of overall performance in the Iraqi tourism sector. The field of research was some Iraqi tourist institutions at Iraqi tourism, Which covers the field of study on the one side, and can be studied on the other side, for the developing study methodology and organizing its main parts, the research pap

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Publication Date
Sun Feb 28 2021
Journal Name
Journal Of Economics And Administrative Sciences
Evaluating the Efficiency of the Municipal Sector in Anbar Governorate, using the Non-Parametric Approach (DEA).
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The research aims to measure, assess and evaluate the efficiency of the directorates of Anbar Municipalities by using the Data Envelopment Analysis method (DEA). This is because the municipality sector is consider an important sector and has a direct contact with the citizen’s life. Provides essential services to citizens. The researcher used a case study method, and the sources of information collection based on data were monthly reports, the research population is represented by the Directorate of Anbar Municipalities, and the research sample consists of 7 municipalities which are different in terms of category and size of different types. The most important conclusion reached by the research i

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Publication Date
Wed Sep 15 2021
Journal Name
Al-academy
The impact of e-learning on the cognitive level in the Corona crisis: أسماء غازي عبد
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E-learning is a necessity imposed by the Corona pandemic, which has disrupted various educational institutions in the world, but some of these institutions have not been affected and education has continued with them, due to their flexible educational system that was able to employ technology in the continuity of the educational process in the so-called e-learning, because It has characteristics that make it the most suitable alternative to avoid the consequences of the Corona pandemic and its damage to the educational process, as e-learning is one of the modern methods that contribute to enhancing the effectiveness of the learner, and enabling him to assume greater responsibility compared to traditional education, so the learner becomes

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