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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 30 2020
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
Studying the Rheological Properties of Non-Newtonian Fluids under the Effect of temperature Using Different Chemical Additives
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   This research studies the rheological properties ( plastic viscosity, yield point and apparent viscosity) of Non-Newtonian fluids under the effect of temperature using different chemical additives, such as (xanthan gum (xc-polymer), carboxyl methyl cellulose ( High and low viscosity ) ,polyacrylamide, polyvinyl alcohol, starch, Quebracho and Chrome Lignosulfonate). The samples were prepared by mixing 22.5g of bentonite with 350 ml of water and adding the additives in four different concentrations (3, 6, 9, 13) g by using Hamilton Beach mixer. The rheological properties of prepared samples were measured by using Fan viscometer model 8-speeds. All the samples were subjected to Bingham plastic model. The temperature range studi

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Publication Date
Sat Mar 01 2008
Journal Name
Al-khwarizmi Engineering Journal
Effect Of Polar Component(1-Propanol) On The Relative Volatility Of The Binary System N-Hexane - Benzene
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Vapor-liquid equilibrium data are presented for the binary systems n-hexane - 1-propanol, benzene - 1-propanol and n-hexane – benzene at 760 mm of mercury pressure. In addition ternary data are presented at selected compositions with respect to the 1-propanol in the 1-propanol, benzene, n-hexane system at 760 mmHg. The results indicate the relative volatility of n-hexane relative to benzene increases appreciably with addition of 1-propanol.

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Publication Date
Sun Jul 03 2016
Journal Name
Journal Of Educational And Psychological Researches
The Effect of Danials model in concepts Acquisition of Education Principles on Studets at college of Education .
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The research aims at identifyiny the effect of (Danials Model) in concepts Acquisition of Education Principles on Students at college at Education The total unmber of Students , is (65) male and female Students distributed in two groups . The First group is the experiemental group which is taught the (Danials Model) and is (34) Students . The second groupe is the control group which is taught the traditional method of teaching and it is (31) Students . The researcher has matcheol between the two groupe by the following variables : the age , (in monthes) their intelligence their parents a cademic leve of education . The research has constructed a test of (20) items of multiple choice test . The reliability of The test has been cal

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Publication Date
Thu Jul 18 2024
Journal Name
Journal Of Economics And Administrative Sciences
The Role Of Cognitive Sharing In Enhancing The E-Learning Quality An Analytical Study Of A Sample Of Iraqi Universities
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The world faced many communication challenges in 2020 after the Covid-19 pandemic, the most important of which was the continuation of schooling. Therefore, the research aimed to analyze the current reality of the studied universities in terms of strengths and weaknesses and measure the implementing level of quality requirements of e-learning. This research studies the impact of knowledge sharing in its dimensions (behavior, organizational culture, work teams, and technology) on the e-learning quality and its dimensions (e-learning management, educational content, evaluation ,and evaluation). After conducting the survey, there was a difference in the universities’ application of the quality requirements of e-learning, as the study

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Publication Date
Wed Mar 10 2021
Journal Name
Baghdad Science Journal
The impact of the lack of certain vitamins and minerals intake rate of hair loss in pregnant and breastfeeding women
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The research aims to identify the rates of hair loss during pregnancy and lactation and its relation to the rates get some elements motivator urged through the results of the continued failure to meet the need of daily assessments of these elements, which led to the continuation of Hair Loss

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Publication Date
Sun Feb 10 2019
Journal Name
Journal Of The College Of Education For Women
The Level of Spiritual Intelligence Among Students of Educational Psychology Course at Jerash University in The Light of Some variables
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This study aimed to determine the level of spiritual intelligence among students of educational psychology course at the Jerash University. and whether this level of varies depend on the gender of the student as well as the college type. The study sample consisted of (180) male and female students of bachelor students at the University Jerash, in the second semester of academic year2014-2015. The main results of the study were that the level of spiritual
Intelligence of Jerash University students was high. More over There were no statistically significant differences at the level of significance (0.05) due to the effect of gender, college type or academic achievement

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Publication Date
Sat Jan 22 2022
Journal Name
Research Journal Of Science
Effect of Adding Different Levels of Spirulina Algae (Spirulina Platensis) To the Diet of Japanese Quail on the Productive Performance
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This experiment was conducted at Poultry Research Station of the Animal Resources Research Department-Office Agricultural Research-Ministry of Agriculture in Iraq, during a period of 16 weeks (four periods and each period of four weeks) from 21 th April to 10 th August 2019. In this experiment 240 Japanese quail's female 9 weeks old, were used in this experiment. Females were randomly assigned to five treatments with three replicates per treatment (16 females/replicate). The experimental treatments were T1, T2, T3, T4 and T5 with an addition of Spirulina in an average of (0, 1, 2, 3, 4%) respectively in the diets of quail to study their effect on productive performance. The results of the experiment showed significant increase (P≤0.05) re

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Publication Date
Mon May 18 2026
Journal Name
Journal Of Baghdad College Of Dentistry
The Effect of Ceramic Thickness and Number of Firings on the Color of Two All-Ceramic Systems Measured by Spectrophotometer
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Background: This in vitro study was carried out to evaluate the effects of various veneering dentin ceramic thicknesses and repeated firings on the color of lithium disilicate glass-ceramic (IPS e.max Press) and zirconium-oxide (IPS ZirCAD) all-ceramic systems, measured by clinical spectrophotometers (Easyshade Advance 4.0) . Materials and methods: The 72specimens cube-shaped have the dimension of about 11 mm in width, 14 mm in length, 1mm in thickness, these cores divided into 3 groups according to the type of material each group have (24)core specimens. Each group had been divided into three sub-groups (each having 8 specimens) according to veneering with dentin ceramic thicknesses: as 0.5, 1, or 2 mm (n=8). IPS e.max press and ZirCAD c

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Publication Date
Mon May 18 2026
Journal Name
Journal Of Baghdad College Of Dentistry
Evaluation of the effect of root canal preparation size and flaring on the depth of irrigant penetration (In vitro study)
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Background: Cleaning and shaping of root canals successfully requires high volumes of irrigation solutions that can only be applied to the apical third of root canal after enlargement with instrument, so the aim of this study was to evaluate and to compare the efficiency of Maxi-I-probe (side-vented needle), in the amount of root canal irrigant penetration for five different master apical file sizes (MAF) and four different degrees of coronal and middle thirds flaring. Materials and Methods: Two hundred resin blocks with simulated root canals were used in this study and divided into 5 major groups (40 for each) based on the size of master apical files (#20, #25, #30, #35, and #40). Each major group was subdivided into 4 subgroups depending

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Publication Date
Mon May 18 2026
Journal Name
Journal Of Baghdad College Of Dentistry
In vivo histological evaluation of the effect of the topical application of estrogen hormone on wounds healing in ovariectomized rabbit
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Background: Wound healing, as a normal biological process in the human body, is achieved through four precisely and highly programmed phases: hemostasis, inflammation, proliferation, and remodeling. Growth factors released in the traumatized area promote cell migration into the wound area (chemotaxis), stimulate the growth of epithelial cells and fibroblasts (mitogenesis), initiate the formulation of new blood vessels (angiogenesis), and stimulate matrix formation and remodeling of the affected region. One of factors that effects on wound healing is a sex hormones and one of these hormones is an estrogen hormone. A wide range of cutaneous cell types (eg, fibroblast, endothelial, epithelial, and inflammatory) expressed estrogen receptors, in

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