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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
Sat Feb 21 2026
Journal Name
Journal Of Al-turath University College
The role of the Prophet ( peace be upon him and progeny) in the field of the Administration Regulation and applying Shura Principle Council in Islamic State Administration
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Publication Date
Fri Oct 30 2020
Journal Name
Journal Of Economics And Administrative Sciences
The effect of some short-term debt instruments on the money supply and its effect on the production of wheat crop in Iraq during the period (1990_2018).
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The research aims to show the effect of some short-term debt instruments (central treasury transfers, cash credit granted to the government by commercial banks) on the production of the wheat crop in Iraq, through its effect on money supply during the period (1990-2018), As the study includes two models according to the statistical program (Eviews9), the first model included measuring the effect of short-term debt instruments on money supply, and the second measuring the extent of the money supply's impact on Wheat crop production, as the results of the standard analysis showed that the short-term debt instruments used in the model were Significant effect on wheat crop production indirectly through its effect on money supply, As

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Publication Date
Wed Jan 10 2024
Journal Name
Annals Of Applied Sport Science
The Effect of an Electronic Device Designed to Measure the Knee Bending Angle in Developing the Skill of Catch and Clearance the High Ball for Football Goalkeepers
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Background. The use of modern aids and technology has contributed greatly to football development, the goalkeeper is the most important position in the team, and the use of devices gave objective readings about the goalkeeper's ability in terms of skill and physical aspects. Objectives. The research aimed to prepare exercises using an electronic device to measure the knee bending angle because of its great importance in developing the skill of catching and dimensions of the high ball for football goalkeepers. Methods. The researchers used the experimental method, and the sample consisted of (4) male goalkeepers under 15 years of age, one of the research procedures was to determine the biomechanical variables affecting the development of the

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Publication Date
Wed Mar 23 2022
Journal Name
Journal Of Educational And Psychological Researches
The Effectiveness of the (PEOE) Model in Teaching Science to Develop the Skills of Generating and Evaluating Information and the Scientific Sense among Intermediate First Grade Students
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The research aimed mainly to discover the effectiveness of the (PEOE) model in teaching science to develop the skills of generating and evaluating information and the emotional side of the scientific sense of the intermediate first grade students. An experimental approach with a quasi-experimental design called pre-test and post-test control design was used. The research sample consisted of (60) students, who were selected in a random cluster method, (30) students in the experimental group studied the unit "The Nature of Material" using the (PEOE) model, and (30) students in the control group studied according to the prevailing method of teaching. The research materials and tools were represented in: a teacher's guide for teaching the un

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Publication Date
Thu Dec 31 2020
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
Electronic payment methods used for salary resettlement and its impact on improving the mental image of customers: an applied study of the opinions of a sample of (private) commercial banks 'customers contracting with the Ministry of Higher Education and Scientific Research to localize employees' salaries
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The research seeks to identify the contemporary events that face the use of electronic payment methods to localize the salaries of state employees and its impact in enhancing the mental image of customers, and to achieve this purpose from the fact that a questionnaire was designed and distributed to an optional sample of (31) individual customers (employees) dealing With the researched private banks, it has been analyzed and reached a number of conclusions and recommendations, the most prominent of which is the lack of modernity of electronic payment methods by customers, which is reflected in the mental image of customers and the achievement of their satisfaction, in the Emiratization project for salaries needs an advanced leade

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Publication Date
Thu Dec 01 2022
Journal Name
Baghdad Science Journal
The Approximation of Weighted Hölder Functions by Fourier-Jacobi Polynomials to the Singular Sturm-Liouville Operator
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      In this work, a weighted H lder function that approximates a Jacobi polynomial which solves the second order singular Sturm-Liouville equation is discussed. This is generally equivalent to the Jacobean translations and the moduli of smoothness. This paper aims to focus on improving methods of approximation and finding the upper and lower estimates for the degree of approximation in weighted H lder spaces by modifying the modulus of continuity and smoothness. Moreover, some properties for the moduli of smoothness with direct and inverse results are considered.

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Publication Date
Sat Jul 01 2023
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
Compliance auditing according to the INTOSAI standards and its effect on the quality of audit reports: applied research
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                The main objective of the audit process is to enable the auditor to express his neutral technical opinion as to whether the financial statements have been prepared in accordance with the financial reporting framework and fairly express the financial position, the result of the activity and the cash flows. A wrong opinion works to burden the beneficiary parties with great damages, and then the presence of any error or bias from the auditor when applying the rules of professional ethics (such as violating professional confidentiality and conflict of interest and moving away from impartiality and objectivity) negatively affects the performance of his

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Publication Date
Wed May 29 2019
Journal Name
Iraqi Journal Of Physics
Analysis the effect of economic conditions on the vegetative change in Baghdad using GIS and remote sensing techniques
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The study of vegetative change of cities is one of the most important studies related to human life because of its direct correlation with the temporal conditions that occur. These include the economic problems that force people to move and look for job opportunities in the city, which leads to an increase in the population density of cities, especially for cities with an important economic and administrative location as in the capital city of Baghdad. In this study, the effect of the increasing in population density was analyzed on the urban planning of Baghdad city. The decreasing in vegetation was due to the increasing of urban areas on the outskirts of the city, which led to an increase in its area. Moreover, urban cities increased t

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Publication Date
Sun Apr 02 2017
Journal Name
Journal Of Educational And Psychological Researches
Impact of modeling strategy in deductive thinking and the attitvde towards mathematics among students in the highschool stage
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    The current research aims to identify the Impact of  strategy of modeling in the of deductive thinking and the attitvde towards mathematics among students in the high school stage

 through check the following hypotheses:       

1.There is no difference statistically significant at the level (0.05) between the scores  mean of the experimental group students who have studied according to the modeling strategy and scores of control group students who have studied according to ordinary method in deductive thinking. 

2.

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Publication Date
Mon Nov 19 2018
Journal Name
Arab Science Heritage Journal
المجتمع المجتمع المدني في الفكر السياسي الإسلامي مقاربة فكرية مع نظريات الحكم الأساسية في الإسلام
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   This research is entitled (civil society in Islamic political thought) which is an intellectual approach with theories of governance in Islam) to be as an attempt to clarify the confusion between mandatory and governorship text basis, and the extent of the nation’s movement within the framework of guiding to translate requirements of the responding towards the civil state project through civil visions according to the Islamic perspective.

      In other words, It is the relationship of man and society in one hand and with an authority with other hand , according to an attempt vision that is to emphasize that Islamic religion can manage modern society and can prove legal philosophical reason

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