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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 Mar 02 2026
Journal Name
Актуальные проблемы обучения русскому языку Xiii
ARABIC PHONO-GRAMMAR AND ITS RUSSIAN EQUIVALENTS AS A NEW APPROACH IN FL TEACHING (RUSSIAN AND ARABIC IN RUSSIAN AND ARABIC CLASSROOMS)
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Central and Eastern European Online Library - CEE journals, documents, articles, periodicals, books available online for download, Zeitschrfitendatenbank, Online Zeitschriften, Online Zeitschriftendatenbank

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Publication Date
Wed Jan 01 2020
Journal Name
Materials Chemistry And Physics
Natural dye extracted from Areca catechu fruits as a new sensitiser for dye-sensitised solar cell fabrication: Optimisation using D-Optimal design
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Publication Date
Mon Aug 01 2022
Journal Name
Engineering, Technology & Applied Science Research
Castellated Beams with Fiber-Reinforced Lightweight Concrete Deck Slab as a Modified Choice for Composite Steel-Concrete Beams Affected by Harmonic Load
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The behavior investigation of castellated beams with fiber-reinforced lightweight concrete deck slab as a modified choice for composite steel-concrete beams affected by harmonic load is presented in this study. The experimental program involved six fixed-supported castellated beams of 2140mm size. Three types of concrete were included: Normal Weight Concrete (NWC), Lightweight Aggregate Concrete (LWAC), and Lightweight Fiber-Reinforced Aggregate Concrete (LWACF). The specimens were divided into two groups: the first comprised three specimens tested under harmonic load effect of 30Hz operation frequency for 3 days, then the residual strength was determined through static load application. The second group included three specimens ide

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Publication Date
Sun Jan 02 2022
Journal Name
Journal Of Medicinal And Chemical Sciences
Microwave synthesis schiff Base from Drug and 1,10-phenanthroline/8_Hydroxy quinoline as a Co- ligand with complexes:cytotoxic, Antimicrobial, and DNA Interaction Efficacy
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Publication Date
Thu Dec 13 2018
Journal Name
Iraqi National Journal Of Nursing Specialties
Evaluation of Women's Knowledge and Personal Preference about The Place of Delivery in Baghdad City
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Objective: The study aim to evaluate of women's knowledge and personal preference about the place
of delivery in Baghdad City
Methodology:
descriptive study conducted in baghdad city on the mothers for the period from the 14th of December,
2015 to the 14th of April 2016. The sample of study included 500 mothers who were attending to
primary health care centers have been chosen sample of 26 primary health care center by a multi-stage
Simple random sampling Data was collected through a constructed questionnaire, validity Data was
analyzed by using of descriptive and inferential data analysis methods .
Results: The results indicated that approximately (29.4%) of the mothers in the age group (20-24) and
the average

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Publication Date
Sun Jul 01 2018
Journal Name
Journal Of Educational And Psychological Researches
Analysis of computer textbooks content for intermediate stage according to the theory of multiple intelligence
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The purpose of current study is to analyze the computer textbooks content for intermediate stage in Iraq according to the theory of multiple intelligence. By answering the following question “what is the percentage of availability of multiple intelligence in the content of the computer textbooks on intermediate stage (grade I, II) for the academic year (2017-2018)? The researcher followed the descriptive analytical research approach (content analysis), and adopted an explicit idea for registration. The research tool was prepared according the Gardner’s classification of multiple intelligence. It has proven validity and reliability. The study found the percentage of multiple intelligence in the content of computer textbooks for the in

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Publication Date
Mon Aug 01 2016
Journal Name
Journal Of Economics And Administrative Sciences
The effects of human error in the banking risks - Empirical study in a number of Iraqi private banks
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Abstract

This research aims to study human error effects in the banking risks in the private banks  through the measurement and testing of human error effect in every kind of banking risks types and stand on the most closely associated with the risks in order to focus on them and make appropriate processors have with respect to and increase the availability of skills and expertise required to carry out banking operations of error-free manner.

Find dealt with human error in terms of meaning and understandable, classifications and types, causes and consequences and its approaches and theories. Also addressed placed banking risks in terms of meaning and concept, species and entr

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Publication Date
Wed Mar 10 2021
Journal Name
Baghdad Science Journal
THE EFFECT OF CHEMICAL AND BIOLOGICAL TREATMENTS ON IMPROVING THE NUTRITIVE VALUE OF CORN COBS AND WILD REED
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This study was conducted in Animal Resources Department , College of Agriculture to estimate the effect of chemical and biological treatments to improve the nutritive value of poor quality roughages ( corn cobs and wild reed ) . The feeds were treated chemically with 4% NaoH solution ,whereas Aspergillus niger was used to ferment corn cobs and wild reed samples . The chemical analysis showed that protein percentages of corn cobs and wild reed was increased significantly (P<0.05) from 6.05% to 10.51% and 17.70% and from 3.10 %to 6.50% and 9.96% for both chemical and biological treatments respectively. The crude fiber percentages decreased significantly (P<0.05) from 29.19% and 26.10% to 23.60% and 20.10% for chemical treatment and was 20

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Publication Date
Sat Dec 05 2020
Journal Name
Iop Conference Series: Materials Science And Engineering, Volume 1067
The effect of cyclic loading on the nonlinear response of structural concrete members with arbitrary cross-sectional shapes
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Publication Date
Sun Dec 27 2020
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
Evaluation the profitability of public commercial banks using liquidity indicators: A comparison of the Rafidain and Rasheed study
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The issue of liquidity, profitability, and money employment, and capital fullness is one of the most important issues that gained high consideration by other authors and researchers in their attempts to find out the real relationship and how can balance be achieved, which is the main goal of each deposits.

For the sake of comprising the study variables, the research has formed the problem of the study which refers to the bank capability to enlarge profits without dissipation in liquidity   of the bank which will negatively reflect on the bank's fame as well as the customers' trust. For all these matters, the researcher has proposed a set of aims, the important of which is the estimation of the bank profitability; liquid

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