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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
Mon Apr 19 2021
Journal Name
Turkish Journal Of Computer And Mathematics Education (turcomat)
The Impact Of Innovative Matrix Strategy And The Problem Tree Strategy On The Mathematical Proficiency Of Intermediate Grade Female Students
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The research aims to know the impact of the innovative matrix strategy and the problem tree strategy in teaching mathematics to intermediate grade female students on mathematical proficiency. To achieve the research objectives, an experimental approach and a quasi-experimental design were used for two equivalent experimental groups. The first is studied according to the innovative matrix strategy, the second group is studied according to the problem tree strategy. The research sample consisted of (32) female students of the first intermediate grade, who were intentionally chosen after ensuring their equivalence, taking into several factors, most notably (chronological age, previous achievement, and intelligence test). The research tools con

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Publication Date
Tue Oct 01 2019
Journal Name
Journal Of Economics And Administrative Sciences
Determination of the lot size using the Wagner-Whitin algorithm under the Constraint Theory / Case Study of Diyala Public Company
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         International companies are striving to reduce their costs and increase their profits, and these trends have produced many methods and techniques to achieve these goals. these methods is heuristic and the other Optimization.. The research includes an attempt to adapt some of these techniques in the Iraqi companies, and these techniques are to determine the optimal lot size using the algorithms Wagner-Whitin under the theory of constraints. The research adopted the case study methodology to objectively identify the problem of research, namely determining lot size optimal for each of the products of electronic measurement laboratory in Diyala and in light of the bottlenecks in w

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Publication Date
Thu Jun 30 2011
Journal Name
Al-khwarizmi Engineering Journal
The Effect of the Solution Heat Treatment on the Mechanical Properties of Aluminum-Copper Alloy (2024-T3) Using Rolling Process
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The effect of solution heat treatment on the mechanical properties of Aluminum-Copper alloy. (2024-T3) by the rolling process is investigated. The solution heat treatment was implemented by heating the sheets to 480 C° and quenching them by water; then forming by rolling for many passes. And then natural aging is done for one month. Mechanical properties (tensile strength and hardness) are evaluated and the results are compared with the metal without treatment during the rolling process. ANSYS analysis is used to show the stresses distribution in the sheet during the rolling process.  It has been seen that good mechanical properties are evident in the alloy without heat treatment due to the strain hardening and also the mechanical

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Publication Date
Mon Jan 01 2018
Journal Name
Journal Of The College Of Languages (jcl)
‘There is no place like home’: A Comparative Study of the Meaning of Home in The Wonderful Wizard of Oz and Peter and Wendy
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The Wonderful Wizard of Oz and Peter and Wendy present universal ideas that exist in all times, despite being written in the beginning of the 20th century. Among the most significant ones is the concept of “home”. The article discusses the essentiality of the idea of “home” where the identity of an individual shapes, and where one’s spiritual, psychological, and physical being develop. It also studies the attitudes of each protagonist towards the concept of ‘home’ based on their understanding of it and according to their gender differences. The characters in both stories tread on the path of perplexity between leaving their homes and returning to them. Peter’s world is the world of imagination while Doro

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Publication Date
Wed Mar 02 2022
Journal Name
Journal Of Educational And Psychological Researches
Awareness Level of the Hidden Curriculum among Field Education Students at College of Education, Ha'il University
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The study aimed to identify the awareness level of hidden curriculum among field education students, College of Education, Hail University. To identify the different awareness level of hidden curriculum among field education students depending on specialization variable, and grade variable in curriculum and instruction course, a descriptive survey method was used. The study sample consisted of (182) students: 78 students in Islamic Culture major, 46 primary major and 58 in physical education. To achieve the study objectives, a hidden curriculum awareness scale was designed included (36) items. The study results showed: the awareness level of hidden curriculum among students of field education, Education College, Hail University, achieved

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Publication Date
Sun Sep 06 2009
Journal Name
Baghdad Science Journal
Study and Analysis the Mathematical Operations of Fuzzy Logic
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The last decade of this 20th century provides a wide spread of applications of one of the computer techniques, which is called Fuzzy Logic. This technique depends mainly on the fuzzy set theory, which is considered as a general domain with respect to the conventional set theory. This paper presents in initiative the fuzzy sets theory and fuzzy logic as a complete mathematics system. Here it was explained the concept of fuzzy set and defined the operations of fuzzy logic. It contains eleven operations beside the other operations which related to fuzzy algebra. Such search is considered as an enhancement for supporting the others waiting search activities in this field.

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Publication Date
Thu Aug 03 2023
Journal Name
Journal Of Legal Sciences
Subjective Objective Conditions for the Possibility of Punishment
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Objective conditions for the possibility of punishment are legal or material facts –positive or negative that depart from the activity of the offender. The legislator comments on their subsequent verification on the formation of some crimes the possibility of.The application of punishment to the offender , but although they are facts of an object nature that approach and overlap with many systems and cases , they are distinguished by a certain subjectivity that differentiates them from each case that may seem similar or approach them. To clarify the ambiguity that may surround these conditions , Which may lead to confusion between them and what be similar to other cases due to the common effect that they have in common , which is the f

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Publication Date
Mon Jul 28 2025
Journal Name
Retos
The effect of the beehive strategy on deliberate thinking and learning the setting skill of volleyball among female students at the College of Physical Education and Sports Sciences for Woman
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Objective: Develop a deliberate thinking scale for the setting skill in volleyball for second-year female students in the College of Physical Education and Sports Sciences for Woman. Research methodology: The researchers used the experimental approach, employing a two-group approach (pre-test and post-test), to suit the nature of the research. The research community comprised (65) second-year female students from the College of Physical Education and Sports Sciences for Woman at the University of Baghdad for the academic year 2024-2025. The research sample was randomly selected, with (15) students in Section A, the experimental group, and (15) students in Section B, the control group. This group represented (46%) of the students. Th

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Publication Date
Sun Jun 01 2014
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
Suggested Model for The Work of the Certified Fraud Examiner & His Role in Reducing The Incidents of Fraud and Corruption: An Applied Study in The Federal Board of Supreme Audit
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Is hardly day expire without hearing the news either Abuse Managementthe accounting standards or the existence of serious misstatements by someauditors.Which caused the demanding of many companies in the recent republication of the financial statements and the re-announcement of its financialresults. Such acts raise questioning about the role that should be played by theauditors, prompting agencies responsible for setting auditing standards to takeTo throw increasingly responsibility on the auditors in order to interest risksfraud The Risks of Fraud in their review of the financial statements.also The Public Company Accounting Oversight Board in the U.S.called about the need of owning the Certified Public Accountants those whoaudits for

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Publication Date
Fri Jan 01 2021
Journal Name
Journal Of Economics And Administrative Sciences
Evaluating The Performance of Public Companies in The Light of Financial Indicators Case study of the General Company for Drugs and Medical Supplies/ Samarra – Iraq For the period (2014-2019)
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The research aimed to evaluate the financial performance of the Public Company for the manufacture of medicines and medical supplies / Samarra - Iraq to know the strengths and weaknesses that affect its performance, as well as to compare its performance in the years between (2017-2019), which are characterized by security stability with its performance in previous years (2014 -2016) which is characterized by security instability, to assess the extent of its ability to achieve growth in performance, by answering the main question, what is the evaluation of the performance of the Public Company for the manufacture of medicines and medical supplies / Samarra - Iraq in the light of financial indicators?

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