• Journal of Applied and Pure Mathematics
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• v.5 no.1_2
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• pp.121-128
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• 2023

The aim of this article is to extend hesitant fuzzy minimal open and hesitant fuzzy maximal open sets in hesitant fuzzy topological space. Further, we investigate some properties with these new sets.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.745-754
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• 2016

In a graph G = (V, E), a non-empty set $S{\subseteq}V$ is said to be an open packing set if no two vertices of S have a common neighbour in G. The maximum cardinality of an open packing set is called the open packing number and is denoted by ${\rho}^{\circ}$. In this paper, we examine the effect of ${\rho}^{\circ}$ when G is modified by deleting a vertex.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.42 no.1
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• pp.117-126
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• 2022

Currently, the number of bridge structures in Korea is continuously increasing and enlarged, and the number of old bridges that have been in service for more than 30 years is also steadily increasing. Bridge aging is being treated as a serious social problem not only in Korea but also around the world, and the existing manpower-centered inspection method is revealing its limitations. Recently, various bridge damage detection studies using deep learning-based image processing algorithms have been conducted, but due to the limitations of the bridge damage data set, most of the bridge damage detection studies are mainly limited to one type of crack, which is also based on a close set classification model. As a detection method, when applied to an actual bridge image, a serious misrecognition problem may occur due to input images of an unknown class such as a background or other objects. In this study, five types of bridge damage including crack were defined and a data set was built, trained as a deep learning model, and an open set recognition-based bridge multiple damage recognition model applied with OpenMax algorithm was constructed. And after performing classification and recognition performance evaluation on the open set including untrained images, the results were analyzed.

• Journal of the Korean Society for Geothermal and Hydrothermal Energy
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• v.13 no.3
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• pp.9-15
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• 2017

In this study, set values of PICV(Pressure Independent Control Valve) were simulated according to the pressure distribution and velocity. The higher the set value and the open rate, as the lower the pressure in the neck. On the contrary, the lower the set value and open rate, as the higher the pressure in the neck. When the set value was small, the pressure was distributed sufficiently and confirmed that the pressure was generated by the VOF, confirming that it could generate a vapor pressure. When the set value 100 %, the lower corn open rate of the differential pressure was 46 % to 29 %, set value 100 % was 29 % to 19 %, and set value 6 % was 12 % to 6 % for the lower corn open rate percentile, it was limited to within 50 %. Thus, the results of this study on the correlation between open rate and differential pressure of the set value of the PICV will be beneficial to improve performance of flow control valves and contribute to their efficient operation used for a hydronic system.

• Communications of the Korean Mathematical Society
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• v.29 no.4
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• pp.555-568
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• 2014

A set with an operation defined on a family of subsets is studied. The operation is used to generalize the topological space itself. The operation defines the operation-open subsets in the set. Relations are studied among two types of the interiors and the closures of subsets. Some properties of maximal operation-open sets are obtained. Semi-open sets and pre-open sets are defined in the sets with operations and some relations among them are proved.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.401-413
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• 2012

In the present paper we construct and introduce a new topology from an old one which are independent each of the other. The members of this topology are called ${\omega}_{\delta}$-open sets. We investigate some basic properties and their relationships with some other types of sets. Furthermore, a new characterization of regular and semi-regular spaces are obtained. Also, we introduce and study some new types of continuity, and we obtain decompositions of some types of continuity.

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.749-755
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• 2008

In this paper, we introduce the relatively new notion of fuzzy ${\omega}^O$-open set. We prove that the collection of all fuzzy ${\omega}^O$-open subsets of a fuzzy topological space forms a fuzzy topology that is finer than the original one. Several characterizations and properties of this class are also given as well as connections to other well-known "fuzzy generalized open" subsets.

• Communications of the Korean Mathematical Society
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• v.26 no.2
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• pp.297-304
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• 2011

In this paper, we introduce closure operators [${\cdot}$]c and [${\cdot}$]a on a space and study some relations among [${\cdot}$]c, [${\cdot}$]a and countable tightness. We introduce the concepts of a strongly sequentially closed set and a strongly sequentially open set and show that a space X has countable tightness if and only if every strongly sequentially closed set is closed if and only if every strongly sequentially open set is open. Finally we find a generalization of the weak Fr$\'{e}$chet-Urysohn property which is equivalent to countable tightness.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.4
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• pp.565-572
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• 2016

In this paper, the concept of $PC^{\star}$-closed sets is introduced. $PC^{\star}$-closed sets contain $pre^*_I$-open and $pre^*_I$-closed sets, ${\mathcal{RPC}}_I$ and $pre^*_I$-closed sets, ${\mathcal{RPC}}_I$ and weakly $I_{rg}$-closed sets.

• Honam Mathematical Journal
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• v.29 no.3
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• pp.307-326
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• 2007

The aim of this paper is to introduce and study topological properties of semi-limit points, semi-derived, semi-interior, semi-closure, semi-border, and semi-frontier of a set using the concept of semi-open set.