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Fuzzy Real Pre-Hilbert Space and Some of Their Properties
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In this work, two different structures are proposed which is fuzzy real normed space (FRNS) and fuzzy real Pre-Hilbert space (FRPHS). The basic concept of fuzzy norm on a real linear space is first presented to construct  space, which is a FRNS with some modification of the definition introduced by G. Rano and T. Bag. The structure of fuzzy real Pre-Hilbert space (FRPHS) is then presented which is based on the structure of FRNS. Then, some of the properties and related concepts for the suggested space FRN such as -neighborhood, closure of the set  named , the necessary condition for separable, fuzzy linear manifold (FLM) are discussed. The definition for a fuzzy seminorm on  is also introduced with the prove that a fuzzy seminorm on  is FRNS. The relationship between the -convergent sequence, -Cauchy sequence and -completeness is then investigated in this work. The structure of FRPHS with some important properties concerning on this space are introduced and proved. In addition, the property of orthogonality with some important properties for these spaces is included, for example the annihilator of the set . The relation between FRPHS and FRNS is investigated in the present work. Finally, after introducing the structure of FRPHS, it leads naturally to the definition of the most important class of FRPHS, namely the fuzzy real Hilbert space (FRHS).

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Publication Date
Tue Mar 15 2022
Journal Name
Journal Of Baghdad College Of Dentistry
Effect of Resin Infiltration and Microabrasion on the Microhardness of the Artificial White Spot Lesions (An in Vitro Study)
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Background: White spot lesion is the first visible sign of dental caries that is characterized by demineralized lesion underneath an intact surface. Several studies demonstrated that they could be treated using noninvasive techniques like the use of fluoride or casein phospho-peptide and amorphous calcium phosphate. Improvement in aesthetic outcomes by covering the demineralized enamel is one of the advantages of the use of resin infiltration and opal-ustre microabrasion, which are two new techniques that had been used for treatment of white spot lesion. The purpose of this study was to evaluate the impact of resin infiltration and microabrasion in the microhardness of the artificial white spot lesions at various depths. Material and method

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Publication Date
Thu Nov 14 2019
Journal Name
Advances In Intelligent Systems And Computing
The Application of Bus Rapid Transit System in the City of Baquba and Its Impact on Reducing Daily Trips
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Publication Date
Fri Feb 10 2023
Journal Name
Dentistry Journal
The Role of Social Media in Communication and Learning at the Time of COVID-19 Lockdown—An Online Survey
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This study aimed to assess orthodontic postgraduate students’ use of social media during the COVID-19 lockdown. Ninety-four postgraduate students (67 master’s students and 27 doctoral students) were enrolled in the study and asked to fill in an online questionnaire by answering questions regarding their use of social media during the COVID-19 lockdown. The frequency distributions and percentages were calculated using SPSS software. The results showed that 99% of the students used social media. The most frequently used type of social media was Facebook, 94%, followed by YouTube, 78%, and Instagram, 65%, while Twitter and Linkedin were used less, and no one used Blogger. About 63% of the students used elements of social media to l

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Publication Date
Tue May 13 2025
Journal Name
Energies
Thermal and Thermo-Hydraulic Performance of a Semi-Circular Solar Air Collector Utilizing an Innovative Configuration of Metal Foams
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The enhancement of the thermal and thermo-hydraulic performance of a semi-circular solar air collector (SCSAC) is numerically investigated using porous semi-circular obstacles made of metal foam with and without longitudinal porous Y-shaped fins. Two 10 and 40 PPI porous material samples are examined. Three-dimensional models are built to simulate the performance of SCSAC: model (I) with clear air passage; model (II) with only metal foam obstacles, and model (III) with metal foam obstacles as well as porous Y-fins. COMSOL Multiphysics software version 6.2 based on finite element methodology is employed. A conjugate heat transfer with a (k-ε) turbulence model is selected to simulate both heat transfer and fluid flow across the entir

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Publication Date
Sun Mar 01 2015
Journal Name
Spectrochimica Acta Part A: Molecular And Biomolecular Spectroscopy
Effect of solvents on the extraction of natural pigments and adsorption onto TiO2 for dye-sensitized solar cell applications
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Publication Date
Sat Jan 01 2022
Journal Name
Journal Of The Mechanical Behavior Of Materials
Impact of eccentricity and depth-to-breadth ratio on the behavior of skirt foundation rested on dry gypseous soil
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Abstract<p>Gypseous soils are considered one of the most problematic soils. The skirted foundation is an alternative technology that works to improve the bearing capacity and reduce settlement. This paper investigates the use of square skirted foundations resting on gypseous soil subjected to concentric and eccentric vertical load with eccentricity values of 4, 8, and 17 mm in 16 experimental model tests. To obtain the results by using this type of foundation, a small-scale physical model was designed to obtain the load–settlement behavior of the square skirted foundation; the dimension of the square footing is 100 mm × 100 mm with 1 mm thickness, the skirt depth (<italic>D</italic></p> ... Show More
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Publication Date
Mon Apr 03 2023
Journal Name
Journal Of Educational And Psychological Researches
Typical Effect of Flower and Coscroff on Expressive the Development of Lateral Thinking among the Literary Fifth Grade Students
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Abstract

The current research aims to identify the typical effect of Flower and Coscroft on expressive performance and the development of lateral thinking among literary fifth-grade students. To achieve the research objective, the researcher chose a sample of (90) female students from the fifth literary grade, with two experimental groups and a control group. The research groups are of six subjects. The research found that the two experimental groups have more expressive performance than the control group. Students of the first experimental group outperformed the students of the second experimental group in expressive performance and lateral thinking tests. In light of the findings of the research, the researcher

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Publication Date
Mon Jun 03 2024
Journal Name
Functional Foods In Health And Disease
A comparative study of the effect of extracts extracted from Ocimum basilicum leaves using organic extract and essential oil
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Background: Medicinal plants that possess antimicrobial and antioxidant properties have garnered significant attention for their role in maintaining food quality, improving safety, and impeding spoilage. They also can aid in controlling food contamination risks and augmenting the nutritional value of foods. Objective: The study aimed to obtain botanical extracts possessing antimicrobial capabilities and use them to inhibit the growth of molds and yeasts. Additionally, these extracts are aimed at prolonging product shelf life by harnessing their antioxidant attributes. Methods: Several microorganisms, including E. coli and Pseudomonas, were subjected to testing. Ethanolic alcohol, chloroform, and essential oil extracts were prepared;

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Publication Date
Thu Dec 01 2016
Journal Name
Journal Of Hazardous Materials
Hierarchical porous structured zeolite composite for removal of ionic contaminants from waste streams and effective encapsulation of hazardous waste
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Publication Date
Wed Jun 01 2022
Journal Name
Heliyon
Modification of SBA-15 mesoporous silica as an active heterogeneous catalyst for the hydroisomerization and hydrocracking of n-heptane
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