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Publication Date
Sun Apr 26 2020
Journal Name
Iraqi Journal Of Science
Volume
61
Issue Number
4
DOI
10.24996/ijs.2020.61.4.22
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ijs-1830
Some Properties of the Essential Fuzzy and Closed Fuzzy Submodules
Fuzzy Module
Closed Fuzzy
essential fuzzy submodule
Hassan K.
Hatam Y.
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In this paper, we introduce and study the essential and closed fuzzy submodules of a fuzzy module X as a generalization of the notions of essential and closed submodules. We prove many basic properties of both concepts.

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Background: With the increasing demands for adult orthodontics, a growing need arises to bond attachments to porcelain surfaces. Optimal adhesion to porcelain surface should allow orthodontic treatment without bond failure but not jeopardize porcelain integrity after debonding.The present study was carried out to compare the shear bond strength of metal bracket bonded to porcelain surface prepared by two mechanical treatments and by using different etching systems (Hydrofluoric acid 9% and acidulated phosphate fluoride 1.23%). Materials and Methods: The samples were comprised of 60 models (28mm *15mm*28mm) of metal fused to porcelain (feldspathic porcelain). They were divided as the following: group I (control): the porcelain surface left u

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CONVERGENCES VIA ẛـ PREـ gـ OPEN SET
: Ideal
separation axioms
ẛ ـpre ـg ـopen set
ẛ ـpre ـg ـclosed set
ẛـpre ـgـ Convergent
ẛ ـpre ـg ـopen function
ẛ ـpre ـg ـcotinuous function.
Ahmed A.
R. B.
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   The main aim of this paper is to use the notion  which was introduced in [1], to offered new classes of separation axioms in ideal spaces. So, we offered new type of notions of convergence in ideal spaces via the set. Relations among several types of separation axioms that offered were explained.

 

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