• 대한수학회논문집
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• 제25권4호
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• pp.623-628
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• 2010

Nakaoka and Oda ([1] and [2]) introduced the notion of maximal open sets and minimal closed sets in topological spaces. In this paper, we introduce new classes of sets called maximal $\theta$-open sets, minimal $\theta$-closed sets, $\theta$-semi maximal open and $\theta$-semi minimal closed and investigate some of their fundamental properties.

• 대한수학회보
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• 제47권5호
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• pp.1025-1036
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• 2010

A new class of generalized open sets in a topological space, called e-open sets, is introduced and some properties are obtained by Ekici [6]. This class is contained in the class of $\delta$-semi-preopen (or $\delta-\beta$-open) sets and weaker than both $\delta$-semiopen sets and $\delta$-preopen sets. In order to investigate some different properties we introduce two strong form of e-open sets called e-regular sets and e-$\theta$-open sets. By means of e-$\theta$-open sets we also introduce a new class of functions called strongly $\theta$-e-continuous functions which is a generalization of $\theta$-precontinuous functions. Some characterizations concerning strongly $\theta$-e-continuous functions are obtained.

• 대한수학회논문집
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• 제26권1호
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• pp.135-149
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• 2011

Using (r, s)-preopen sets [14] and pre-${\omega}_t$-closures [6], a new kind of covering property $P^t_{({\omega}_r,s)}$-closedness is introduced in a bitopological space and several characterizations via filter bases, nets and grills [30] along with various properties of such concept are investigated. Two new types of cluster sets, namely pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets and (r, s)t-${\theta}_f$-precluster sets of functions and multifunctions between two bitopological spaces are introduced. Several properties of pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets are investigated and using the degeneracy of such cluster sets, some new characterizations of some separation axioms in topological spaces or in bitopological spaces are obtained. A sufficient condition for $P^t_{({\omega}_r,s)}$-closedness has also been established in terms of pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets.

• 충청수학회지
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• 제25권3호
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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.

• Kyungpook Mathematical Journal
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• 제47권2호
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• pp.155-164
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• 2007

It is the objective of this paper to study further the notion of ${\Lambda}_s$-semi-${\theta}$-closed sets which is defined as the intersection of a ${\theta}$-${\Lambda}_s$-set and a semi-${\theta}$-closed set. Moreover, introduce some low separation axioms using the above notions. Also we present and study the notions of ${\Lambda}_s$-continuous functions, ${\Lambda}_s$-compact spaces and ${\Lambda}_s$-connected spaces.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제6권3호
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• pp.255-263
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• 2006

In this paper, we introduce the concepts of ${\gamma}$-fuzzy feebly open and ${\gamma}$-fuzzy feebly closed sets in Sostak's fuzzy topological spaces and by using them, we explain the notions of ${\gamma}$-fuzzy F-closed spaces. Also, we give some characterization of ${\gamma}$-fuzzy F-closedness in terms of fuzzy filterbasis and ${\gamma}$-fuzzy feebly-${\theta}$-cluster points.

• 대한수학회지
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• 제36권4호
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• pp.649-662
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• 1999

A random vector =(X1,…, Xn) is conditionally weakly associated if and only if for every pair of partitions 1=(X$\pi$(k+1),…,X$\pi$(k)), 2=(X$\pi$(k+1),…,X$\pi$(n)) of P(1$\in$A│2$\in$B, $\theta$$\in$I) $\geq$P$\in$A│$\theta$$\in$I whenever A and B are open upper sets and $\pi$ is any permutation of {1,…,n}. In this note we develop some concepts of conditional positive dependence, which are weaker than conditional weak association but stronger than conditional positive orthant dependence, by requiring the above inequality to hold only for some upper sets and applying the arguments in Shaked (1982).

• 대한수학회지
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• 제56권1호
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• pp.91-111
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• 2019

We give a direct proof of the sharp two-sided estimates, recently established in [4, 9], for the Dirichlet heat kernel of the fractional Laplacian with gradient perturbation in $C^{1,1}$ open sets by using Duhamel's formula. We also obtain a gradient estimate for the Dirichlet heat kernel. Our assumption on the open set is slightly weaker in that we only require D to be $C^{1,{\theta}}$ for some ${\theta}{\in}({\alpha}/2,1]$.

• 충청수학회지
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• 제33권2호
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• pp.271-285
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• 2020

In this paper, we have introduced a new type of covering property ${\beta}^t_{({\omega}_r,s)}$-closedness, stronger than $P^t_{({\omega}_r,s)}$-closedness [3] in terms of (r, s)-β-open sets [9] and β-ω_t-closures in bitopological spaces along with its several characterizations via filter bases and grills [15] and various properties. Further grill generalizations of ${\beta}^t_{({\omega}_r,s)}$-closedness (namely, ${\beta}^t_{({\omega}_r,s)}$-closedness modulo grill) and associated concepts have also been investigated.

• 암석학회지
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• 제18권2호
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• pp.115-135
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• 2009

경상분지 북동부 일대의 제3기 결정질 응회암에서 분포하는 미세균열의 전반적인 분포특성을 규명하였다. 포항시 흥해읍 및 청하면 지역에서 채취한 6개 암석시료의 수평면 상에서 발달하는 108조의 미세균열은 영상처리를 통하여 구별하였다. 이들 108조의 미세균열은 38장의 영상에서 뚜렷한 선상배열을 보여 주었다. 결정질 응회암에 대한 방향각(${\theta}$)-빈도수(N) 관계도의 전 영역은 미세균열의 분포상에 의하여 20개의 영역으로 분류할 수가 있다. 관계도에서 미세균열의 여러 조는 수직상의 일반적인 절리의 방향과 일치하는 강한 배향성을 보여 준다. 따라서 관계도의 각 영역내에서 빈도가 높은 방향각으로부터 거시적인 수직상 절리의 잠재성을 추측할 수가 있다. 관계도에서 나타난 이러한 절리의 형태는 강화군 석모도의 중생대 화강암의 경우와 거의 동일하다. 결정질 응회암에서 도출한 미세균열의 방향을 종합한 장미도에서, 빈도등급에 따른 미세균열의 우세한 조들의 방향성은 암체에 작용한 최대 압축 주응력의 대표적인 방향성을 시사한다. 한편 결정질 응회암의 미세균열의 방향성에 대하여 경상분지 남서부의 불국사 화강암류에서 분포하는 열린 미세균열 그리고 국내 중생대 화강암류의 석산에서 발달하는 수직 결의 방향성과 비교하였다. 광역 분포도에서 상기한 결정질 응회암 및 불국사 화강암류의 미세균열 조 그리고 수직 결 사이의 분포형이 일치한다는 사실은 결정질 응회암에서 내재하는 미세균열의 계는 국내 중생대 화강암류에서도 광역적으로 발달함을 시사한다.