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bsj-4152
Representation 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
Tue Jan 31 2017
Journal Name
Journal Of Engineering
The Effect of The Utilitarian Need For the High Water Tanks Towers to Sustain Life in the City
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      The service system has become a necessity of life in modern cities to be the most basic necessities of modern humans, they constitute a major base, which is based on the sustainability of life in the city and a standard measured through the degree of well-being and progress of civilized peoples and their interaction with the surrounding environment, making the services sector as a need not be an option, whenever the cities widened in population and space whenever provision of services and upgrading the quality and quantity more pressing, which made the subject of the services takes the biggest area of the trends and thinking of urban planners and those who in charge of drawing the cities policies. Consideri

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Publication Date
Sun Oct 01 2023
Journal Name
Baghdad Science Journal
The Necessary and Sufficient Optimality Conditions for a System of FOCPs with Caputo–Katugampola Derivatives
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The necessary optimality conditions with Lagrange multipliers  are studied and derived for a new class that includes the system of CaputoKatugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left CaputoKatugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time  and the final state  are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.

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Publication Date
Tue Feb 05 2019
Journal Name
Journal Of The College Of Education For Women
Study the positive effects of “Whatsup” application in the educational process
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Limited importance of research in a stand on the most important difficulties faced by both faculty and parents to communicate with each process to follow up on their children, and the analysis and inventory of the obstacles that hinder the educational process, and work to develop a vision of how to address these constraints and the important role of technology in the treatment of problems of the society so as to develop frameworks future to minimize the errors and the problems they face, and the development outlook for future generations in order to promote the educational level, especially that Iraq is going through a change in conditions in all sectors. Through the questionnaire, which includes questions set that was made on a sample o

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Publication Date
Mon Jun 30 2025
Journal Name
مجلة ميسان للدراسات الاكاديمية
The poetic image in the Diwan of Al-Oqaisher Al-Asadi
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Publication Date
Tue May 17 2016
Journal Name
J. Of College Of Education For Women
The Sufferings Of Afro-American Maids in Kathryn Stockett's The Help
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Publication Date
Wed Jan 01 2025
Journal Name
Journal Of Animal Health And Production
The Control and Preventative Measures for the Health Problems of Pets
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Publication Date
Thu Apr 14 2022
Journal Name
Plos One
The passage of time in Iraq during the covid-19 pandemic
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The covid-19 global pandemic has influenced the day-to-day lives of people across the world. One consequence of this has been significant distortion to the subjective speed at which people feel like time is passing. To date, temporal distortions during covid-19 have mainly been studied in Europe. The current study therefore sought to explore experiences of the passage of time in Iraq. An online questionnaire was used to explore the passage of time during the day, week and the 11 months since the first period of covid-19 restrictions were imposed in Iraq. The questionnaire also measured affective and demographic factors, and task-load. The results showed that distortions to the passage of time were widespread in Iraq. Participants co

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Publication Date
Fri Jan 01 2021
Journal Name
دراسات قانونية
The Legal Nature of the Build-Operate- transfer-Ownership Contract (B.O.T.)
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The legal nature of the Build-Operate-Transfer-Ownership Contract (B.O.T) The Build, Operate, and Transfer of Ownership Contract (BOT) has emerged as the most successful and safest method for involving the private sector in public sector services. The major infrastructure projects that are built through the BOT contract are no longer financed by the state and its budget, but the private sector has played a major role in financing These projects, especially developing countries that need to establish infrastructure or modernize their existing infrastructure, especially in the areas of transport, communications, services, electricity, water ..... and other public utilities.

Publication Date
Tue May 30 2006
Journal Name
Baghdad University
Unpublished Cuneiform Texts From The Reign Of The King Ammi Şaduqa
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The cuneiform texts considered one of the most important resources which play an important role help us to know how was the economic , politic and religious manner and every thing have relation of the history of Mesopotamia which contain many of information that enrich our knowldgement every side of Mesopotamia civilization since using writing as away to register the science and human knowldgement . The city of Sippar (Abu –Habba ) was one of most important city of ancient Mesopotamia which mentioned as one of first five Mesopotamian cities found before floating and it exposed through excavating rich one of them tablet which some of it dated to old Babylon period . The king Ammi-Saduqa has a big share of tablet we study number of thi

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Publication Date
Fri Apr 01 2016
Journal Name
Astronomy Reports
Ionized gas in the circumgalactic vicinity of the M81 galaxy group
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