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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
Fri Aug 02 2024
Journal Name
Engineering, Technology & Applied Science Research
Effects of utilizing Crumb Rubber as Aggregate in Asphalt Mixtures
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Experts have given much attention on the use of waste in asphalt paving because of its significance from a sustainability perspective. This paper evaluated the performance properties of asphalt concrete mixes modified with Crumb Rubber (CR) as a partial replacement for two grade sizes of fine aggregate (2.36, and 0.3 mm) at six replacement rates: 0%, 2%, 4%, 6%, 8%, and 10% by weight. Asphalt concrete mixes were prepared at their Optimum Asphalt Content (OAC) and then tested for their engineering properties. Marshall properties, fatigue, rutting, ideal CT index test, Scanning Electron Microscopy (SEM), and Energy-Dispersive X-ray (EDX) spectroscopy were deployed to examine the crystalline structure and elemental composition of the C

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Publication Date
Tue Jun 11 2019
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Preparation and Characterization of Etodolac as a Topical Nanosponges Hydrogel
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Nanosponges (NS) of etodolac(ETO) was prepared using the emulsion solvent diffusion method ; the effects of drug: polymer ratio, the effect of level concentration of internal phase and stirring time and other variables that effect on the physical characteristics of NS were investigated and characterized, The selected formula was lyophilized then incorporated into hydrogel ; which also evaluated .The results show that the formulation that contain Drug: PVA:EC in ratio 1:3:2 is the best with smallest particle size 40.2±0.098 with polydispersibility0.005 and in vitro release 97.6±0.11%, , ETO NS Carbopol hydrogel produced a significant(p<0.05) improvement of the in vitro release than pure ETO hydrogel.

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Publication Date
Fri Sep 30 2022
Journal Name
College Of Islamic Sciences
TYPES OF THINKING ACCORDING TO IBN AL-QAYYIM (Analytical Thinking as a Model)
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The human intellect and his ability to complex thinking is a characteristic that Allah has given him above all his creatures. Islam came to encourage the utilization of the mind by thought, contemplation and consideration of the kingdom of Allah, His signs and religion, and He gave us a set of legislation that preserves the mind and protects it from falling into error or deviation.

This research deals with one of the most important components of civilizations in general and Islamic civilization in particular, which is thinking and what is related to it. It is an essential and influential component in man's dealing with life around him and the for

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Publication Date
Sun Dec 03 2017
Journal Name
Baghdad Science Journal
CFIA-Turbidimetric and Photometric Determination of Vitamin B9 (Folic acid) Using LEDs as a Source of Irradiation and Two Solar Cells as an Energy Transducer
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A specific, sensitive and simple method was used for the determination of: vitamin B9 (Folic acid) in pure and pharmaceutical formulations using continuous flow injection analysis. The method is based on formation of ion pair compound between folic acid and ammonium molybdate in an aqueous medium to obtain a gray precipitate complex, using homemade; Ayah-6SX1-ST-2D solar cell CFI Analyzer. Optimum parameters was studied to increase the sensitivity for developed method. The linear range for the calibration graph was 0.01-0.6 mMol.L-1 of vitamin B9 and LOD was 131.994 ng/sample with correlation coefficient ( r ) of 0.9810, RSD% was lower than 0.1%, (n=9) for the determination of vitamin B9 at concentration (0.07and 0.5) mMol.L-1 respectiv

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Publication Date
Sun Oct 19 2025
Journal Name
Lecture Notes In Networks And Systems
Using Artificial Intelligence in Analyzing Historical Documents: The Egyptian Libyan Border as a Model (1911–1951)
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Publication Date
Sun Mar 15 2020
Journal Name
Al-academy
Shapes as an Alternative to the Word in Designing Textbooks: سحر علي سرحان-منى محمد غلام
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Shapes have differed in terms of their temporality, tools, technical variations, aesthetic functions and dimensions. The beginnings started with manual primitive techniques that have played an a significant artistic role in the ancient civilizations, then developed with the technological development and the digital technologies that encompassed various programs and specialist means in the graphic design, so that its visual outputs in the textbook that is considered a communication means that has an effect and attracts the recipient. That is what made the researcher search and investigate this topic describing the research problem as follows: What are the shapes as alternatives to the words in the design of the textbook? The research obje

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Publication Date
Sun Feb 03 2019
Journal Name
Journal Of The College Of Education For Women
What came as a language in the book to explain Ibn Aqeel on Alfiya Ibn malek
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It is found in the book "Ibn Aqeel: Alfiya Ibn Malek" that there are some linqustical aspected are related to the native tribal speakers like Tamim or Tie or some others. Sometimes in the book he said "some Arabian said without mentioning the name of the tribe.
As weel, he hasn’t mentioned the accent but he does mention the language. In the book, he has brought back the most important and the biqqest Arabian tribes suchas tribes of Hegaz, Tamim, Hatheyal, son of Anber, Tie, Rabia Bin Wael, Bani Katham, Au there, Bani AL Harth, Bani Kalb, Bani Hgim, Zabid, Hamedan, Alia Qais, Bani Ameer and many others. However, the most mentioned tribes were Hegaz and Tami.
Hence, the importance of the book expiain Ibn Aqeel by mentioning these A

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Publication Date
Wed Feb 22 2023
Journal Name
Iraqi Journal Of Science
Isolation and Identification the Cyanobacterium: Scytonema hofmanni var. calcicolum as New Record in Iraqi Drinking Water.
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The aim of this study was to isolate and identify the cyanobacterium Scytonema hofmanni Var. calcicolum from the domestic drinking tanks as a new record in Iraqi drinking water. Scytonema hofmanni var. calcicolum, a filamentous freshwater cyanobacterium (blue-green alga). This alga was isolated from the walls of the domestic plastic water tanks in Al- karkh/ Baghdad city on July 2014. The sampling was performed by collecting three samples from this tanks, the three examined samples microscopically revealed the dominance of this cyanobacterium as unialgal in the studied samples. The results showed this alga has the ability to tolerate high temperature up to 42 Cº and very low light intensity inside the tanks which up to 10 μE/m²/s.

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Publication Date
Sun Dec 02 2018
Journal Name
Journal Of The College Of Education For Women
Poverty and its Relations to Some Social Variables (Children in the Primary Stage as a Model)
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The phenomenon of poverty is one of the most important phenomena facing the world at large. Despite the tremendous technological progress witnessed by mankind and despite the unprecedented high levels of world economic production, poverty remains the greatest challenge facing the world. Statistics and studies have shown that poverty is caused by several problems: (health, social, economic, educational, etc.) These problems are obstacles to the ability to obtain employment opportunities, which leads in the beginning to the growth phenomenon of unemployment, and ultimately to the growth of poverty.

The results of a range of research in the field of psychology have confirmed that children from poor homes suffer from a high level of

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Publication Date
Wed Sep 27 2023
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Assessing the reliability of serum macrophage migration inhibitory factor as a marker for diabetic nephropathy prediction in type 2 diabetes patients and the effect of ACE inhibitors on its level
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Abstract Diabetic nephropathy (DN) is a prevalent chronic microvascular diabetic complication. As inflammation plays a vital role in the development and progress of DN the macrophages migration inhibitory factor (MIF), a proinflammatory multifunctional cytokine approved to play a critical function in inflammatory responses in various pathologic situations like DN. This study aimed To assess serum levels of MIF in a sample of Iraqi diabetic patients with nephropathy supporting its validity as a marker for predicting nephropathy in T2DM patients. In addition, to evaluate the nephroprotective effect of angiotensin-converting enzyme (ACE) inhibitors in terms of their influence on MIF levels. This is a case-control study involving ninety

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