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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
Wed Aug 06 2025
Journal Name
Innovative Infrastructure Solutions
Understanding the effectiveness of elastomeric and plastomeric polymers on the high-temperature performance of asphalt binders
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The global rise in temperature and the desert climatic conditions prevalent in Middle Eastern countries have exacerbated rutting distress in heavily trafficked highways. Conventional asphalt binders with a high-temperature performance grade (PG 70) have proven inadequate under such extreme conditions, necessitating the development of modified binders with enhanced high-temperature performance. While polymer modification using styrene-butadiene-styrene (SBS), an elastomeric polymer, and ethylene-vinyl acetate (EVA), a plastomeric polymer, has been widely studied, limited research provides a direct comparison of their effectiveness at both the binder and mixture levels under extremely high-temperature conditions. This study addresses this gap

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Publication Date
Mon Jun 05 2023
Journal Name
Al-khwarizmi Engineering Journal
A Review of the Stereo lithography 3D Printing Process and the Effect of Parameters on Quality
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Stereo lithography (SLA) three-dimensional (3D) printing process is a type of additive manufacturing techniques that uses digital models from computer-aided design to automatically produce customized 3D objects. Around 30 years, it has been widely utilized in the manufacturing, design, engineering, industrial sectors and its applications in dentistry for manufacturing prosthodontics are very important. The stereo lithography technology is highly regarded because it can produce items with excellent precision especially when selecting the best process parameters. This review article offers a useful and scientific summary of SLA three-dimensional printing technology and its brief history. The specific type of 3D printers which is SLA type b

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Publication Date
Wed May 01 2019
Journal Name
Iop Conference Series: Materials Science And Engineering
Urban renewal of the historic centre of Rusafa
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Abstract<p>The historical centers represent the present of the past, which is embodied in its buildings and spaces, which are places of continuous life bearing the history of the city with all its material and objective dimensions, making it living centers that form an essential part of the body of the city and give it a vision for another time and it represents a cultural heritage that should be preserved and maintained. The research started from the reality that indicates the great change in the land uses of the region and the deterioration of the situation and change in use in addition to the neglect of its role and historical status, the study aims to study the subject of urban renewal of he</p> ... Show More
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Publication Date
Sat Feb 02 2019
Journal Name
Journal Of The College Of Education For Women
THE EFFECT OF SPREACL of KNOWLEDGE ON ETHICS
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THE EFFECT OF SPREACL of KNOWLEDGE ON ETHICS

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Publication Date
Fri Jan 05 2024
Journal Name
Al-academy
Designs treatment of the internal spaces of pharmacies
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The pharmacy is the face for the health buildings and hospitals, The linking professional relationships and functional, it is been from the important places that most people go it, so according to that we must format its interior design in form that suitable with the need of most people use it or work in it, and this the search goal, dashing from the search subject which to hide finding designer treatment for the pharmacies interior spaces, to give share in the functional improvement performance or aesthetic. We define the search goals to share in educate the pharmacist in the effect of interior design for improvement of interior environment, in addition to the search consider as designer trying add to the other trying the interior desig

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Publication Date
Sun Dec 30 2012
Journal Name
College Of Islamic Sciences
A study of the hadiths of supplication orchestration
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A study of the hadiths of supplication orchestration

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Publication Date
Wed Mar 10 2021
Journal Name
Baghdad Science Journal
new Estimator of the parameter of negative exponential
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the main of this paper is to give a comprehensive presentation of estimating methods namely maximum likelihood bayes and proposed methods for the parameter

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Publication Date
Thu Mar 13 2025
Journal Name
Adab Al-rafidain
Guilt in The Condamned of ALtona of Sartre
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Drama "The Condamned of Altona" shows many different aspects of the 20th century. It contrasts strong, self-assured characters with weak, unsure ones to address absurdism and existentialism. Also, this piece shows the misery of the decade by showing Frantz, one of the play's heroes, taking his own life. Through suicide, disillusionment, and worry, the play depicts the upheaval of the 20th century, which was marred by numerous crises. The play's depiction of the jail and its inmates exemplifies the regret that accompanied the two world wars . Not only does guilt serve as a metaphor for the wrongs done by the Germans, but it also serves as a metaphor for the French inactivity during the occupation. And also the writers who did not devote thei

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Publication Date
Tue Jun 01 2021
Journal Name
Int. J. Nonlinear Anal. Appl.
Study of the dual ideal of ku-algebra
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In this work, we apply the notion of a filter of a KU-Algebra and investigate several properties. The paper defined some filters such as strong filter, n-fold filter and P-filter and discussed a few theorems and examples.

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Publication Date
Fri Jun 20 2025
Journal Name
Bulletin Of The Iraq Natural History Museum
INVESTIGATION OF MACROFUNGI IN THE MIDDLE OF IRAQ
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The study aimed to survey mushroom species from fields among herbs, palm trunks, and trees in central Iraq and to identify them on the basis of morphological and molecular characteristics. As a molecular identification result with polymerase chain reaction six species were recorded (with eight isolates): Agaricus bitorquis (Quéllt) Saccardo. 1887 (SHA14); Candolleomyces candolleanus (Fr.) D. Wächter & Melzer, 2020 (SHA15); Cyclocybe cylindracea (D.C.) Vizzini & Angelini, 2014 (SHA13); Leucoagaricus hesperius Vellinga, 2010 (SHA16); Volvariella sp. (SHA17), and Volvopluteus gloiocephalus (D. C.) Vizzini, Contu & Justo, 2011 (SHA10, SHA101 and SHA12), belonging to four families of Basidiomycetes: Agaricaceae, Pluteaceae,

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