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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
Tue Jun 01 2021
Journal Name
Journal Of Planner And Development
Spatial analysis of rural services in the district of Fallujah, Zgharit village, as a model
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          The study of services in villages is one of the imperative matters that must   be focused on, because it leads to increased attention, which reduces the differences between the countryside and the urban. The extent of its.

  It is well known that community services need to be reached by a person, unlike the anchor services that reach people, here the population distribution plays an important and prominent role in signing these services, so the dispersed distribution pattern and the gathering pattern appeared in the distribution, thus an effect on the time and distance that the person walked to obtain The services are community-based. Therefore

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Publication Date
Fri Jan 23 2026
Journal Name
Journal Of Baghdad College Of Dentistry
The effect of anti-oxidant agents as neutralizers of bleaching agents on dentin bond strength
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Background: Reduction in bond strength when bonding was done immediately after intracoronal bleaching procedure has been recognized. The purpose of this study is to assess the effect of antioxidants (10% sodium ascorbate (SA), 0.1M thiourea and7% sodium bicarbonate (SB)) on reversing bonding strength of composite resin to bleached dentin. Materials and method: Sixty upper 1st premolar teeth, were selected, the crowns of the teeth were embedded in acrylic resin blocks exposing a flat dentin from the buccal surface, then divided into 6 groups (10 samples each). Bleaching for the experimental groups was performed using 35% hydrogen peroxide bleaching gel (pola–office).Group A (Negative

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Publication Date
Sun Jan 27 2019
Journal Name
Journal Of The College Of Education For Women
The Inauguration of Faisal Bin Al -husain as Iraq King (A Study of British Documents)
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Husain as a king of Iraq.
This paper deals with the British communication with faisel . then Winston Churchill's speech in British common house .then fodlowed by arriving faisal to Iraq after that the referend um faisel .
The his claims of British maneuver lastly coronation on faisal & his inauguration as a king of Iraq.

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Publication Date
Sat Jan 01 2022
Journal Name
Lecture Notes In Civil Engineering
Evaluation the Level of Service of Signalized Intersection: Al-Amreia Intersection as a Case Study
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Abstract<p>One of the main element in the network is the intersection which consider as the critical points because there are many conflict in this element. The capability and quality of operation of an intersection was assessed to provide a better understanding of the network's traffic efficiency. In Baghdad city, the capital of/Iraq the majority of the intersections are operated under the congestion status and with level of service F, therefore theses intersection are consider as high spot point of delay in the network of Baghdad city. In this study we selected Al-Ameria signalized intersection as a case study to represent the delay problem in the intersections in Baghdad. The intersection is located in the w</p> ... Show More
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Publication Date
Tue Feb 01 2022
Journal Name
Advanced Powder Technology
Functionalization of mesoporous MCM-41 for the delivery of curcumin as an anti-inflammatory therapy
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Publication Date
Thu Nov 21 2024
Journal Name
Al Rafidain Journal Of Engineering Sciences
A Review of the Effect of Crumb Rubber as an Additive on Hot Mix Asphalt
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Materials recycling has a significant economic and environmental impact; as a result, steel, aluminium, plastic, and other recyclable materials have been pushed for use in construction materials. One of these recyclable materials is the crumb rubber, has been considered as a pavement component. The general behaviour of the composite rubber-hot mix asphalt system would be varied from that of the conventional rubber free mix. In this review, desirable characteristics of hot mix asphalt are highlighted first. Also, effect of gradation and the main types of rubber are specified. Afterward, many studies that considered the crumb rubber as a waste product and its associated mixture and modifiers are reviewed. The factors affect the crumb

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Publication Date
Wed Jun 01 2022
Journal Name
Journal Of The College Of Languages
The Multifunctional Morphemes in Kurdish Language the Morpheme Le as an example
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Kurdish language multifunctional morphemes indicate the different functional morphological, syntactical, and semantic tasks of the morphemes. The present study discusses the multifunctional task of the Morpheme Le in Kurdish Language. The Morpheme Le has marginally been included in other studies, yet up to the present times, there has not been a research inclusively dedicated to thoroughly discuss and clarify its multifunctional aspects. The present study is divided into two chapters: Chapter one discusses the theoretical aspect of chapter two that is entirely concerned with the practical aspect of the morpheme Le. The first part of chapter one sheds light on the morphological aspect of the morpheme while part two discusses

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Publication Date
Tue Jun 01 2021
Journal Name
Political Sciences Journal
The European Union and the Extremist Right Phenomenon: Brexit as a Model
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The European Unit has never been affected by a serious phenomena as the phenomena of the advancing of the far right parties. Though these parties vary in their impact in their original countries, they agree on one important issue which is the deconstruction of the European unit and limiting its supernational powers. These increasing popular parties aim at more national independence in decision making away from the decisions taken by Brussels. Moreover, they criticize the financial and administrative corruption accompanied many of the rescuing procedures directed for example towards countries like Greece and Spain during the international economic crisis. This failure nourishes many of the negative feelings against the European unit which

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Publication Date
Sun Dec 01 2019
Journal Name
Iop Conference Series: Materials Science And Engineering
Place dependence as the physical environment role function in the place attachment
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Abstract<p>This research sheds light on the physical environment role in creating the place attachment, by discussing one of the important factors in the attachment creation, it is the concept place dependence, consisting of two important dimensions: the place quality and the place expectation; they contain a number of the supporter physical environment sub-indicators for place attachment. Eight physical indicators were reached; they were found to have a close relationship to the place attachment, including: the open and green spaces existence, land use diversity, diversity of housing types, dwelling / population density, accessibility, transport network development degree, transport multiple mo</p> ... Show More
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Publication Date
Fri Jun 30 2006
Journal Name
Al-kindy College Medical Journal
The Use of Spiral Computerized Tomography in the Diagnosis of Middle –Third Facial Fractures as Compared to Plain Radiography
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Background: Trauma is one of the most common
clinical problems that confront the maxillofacial
surgeon and radiologist alike. Middle third facial
fractures are diagnosed primarily on the bases of
clinical examination and plain radiographs than can
result in much preoperative speculation.
Objective: To assess the advantages of spiral
computerized tomography over conventional
radiography in the pre-surgical evaluation of middle
third facial fractures.
Methods: Thirty patients with thirty-eight facial
fractures were studied, all patients were examined
clinically, by plain radiography and then by spiral CT.
Results: Of the 38 middle-third fractures, 16
(42.1%) were zygomatic fractures, 8 (21.1%) were

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