• Kyungpook Mathematical Journal
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• 제45권4호
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• pp.539-547
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• 2005

The class of b-open sets in the sense of $Andrijevi{\acute{c}}$ ([3]), was discussed by El-Atik ([9]) under the name of ${\gamma}-open$ sets. This class is closed under arbitrary union. The aim of this paper is to use ${\Lambda}-sets$ and ${\vee}-sets$ due to Maki ([15]) some topologies are constructed with the concept of b-open sets. $b-{\Lambda}-sets,\;b-{\vee}-sets$ are the basic concepts introduced and investigated. Moreover, several types of near continuous function based on $b-{\Lambda}-sets,\;b-{\vee}-sets$ are constructed and studied.

• Korean Journal of Mathematics
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• 제25권3호
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• pp.437-453
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• 2017

A new class of sets, called generalized (${\Lambda}$, b)-closed sets, has been introduced and studied. Also, several properties of generalized (${\Lambda}$, b)-closed sets are investigated. Some characterizations of ${\Lambda}_b$-regular spaces and ${\Lambda}_b$-normal spaces are discussed.

• Korean Journal of Mathematics
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• 제26권4호
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• pp.709-727
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• 2018

Here we have studied the ideas of $g^*$-closed sets, $g{\bigwedge}_{{\tau}^-}$ sets and ${\lambda}^*$-closed sets and investigate some of their properties in the spaces of A. D. Alexandroff [1]. We have also studied some separation axioms like $T_{\frac{\omega}{4}}$, $T_{\frac{3\omega}{8}}$, $T_{\omega}$ in Alexandroff spaces and also have introduced a new separation axiom namely $T_{\frac{5\omega}{8}}$ axiom in this space.

• 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.

• 한국지반공학회논문집
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• 제29권10호
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• pp.39-48
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• 2013

본 논문에서는 표준관입시험(SPT) 중에 발생하는 관입거동을 표현하기 위한 이론식을 유도하여 나타내었다. 이를 위하여 에너지보존법칙을 도입하고 SPT 항타거동을 소형강관말뚝이 관입되는 것과 같이 모형화 하였다. 이론식에는 쉽게 결정하기 어려운 쌍곡선 매개변수(m과 ${\lambda}$)를 포함하여 3종류의 입력정수 항으로 구성되어 있다. 최적화된 m과 ${\lambda}$값은 3점에서의 측정값을 사용하여 시행착오법으로 구하였다. 체계적으로 측정된 기존의 자료로부터 얻어진 관입곡선과 예측 관입곡선을 비교한 결과 좋은 일치를 보여 주어서 본 이론식의 적용성이 입증되었다. 본 이론식에 의하면, 주어진 깊이에서 m값이 증가할수록 ${\lambda}$값은 감소하고 관입곡선의 곡률과 N값은 증가하였다. 일반적으로 예측 관입곡선은 예비타 부분을 넘어서면서 거의 직선적으로 변하였으며, 이러한 경향은 모래가 조밀할수록 현저하였다. 그러므로 제안방법은 불충분하게 측정된 관입곡선으로부터 30cm 관입에 해당하는 N값을 외삽법으로 구할 수 있다. 이와 유사한 결과는 역시 간단한 직선식을 이용하여 구할 수 있다.

• 대한수학회지
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• 제36권4호
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• pp.787-811
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• 1999

Let M be the maximal ideal space of the Banach algebra $H^{\infty}$ of bounded analytic functions on the open unit disc $\triangle$. For a positive singular measure ${\mu}\;on\;{\partial\triangle},\;let\;{L_{+}}^1(\mu)$ be the set of measures v with $0\;{\leq}\;{\nu}\;{\ll}\;{\mu}\;and\;{{\psi}_{\nu}}$ the associated singular inner functions. Let $R(\mu)\;and\;R_0(\mu)$ be the union sets of $\{$\mid$\psiv$\mid$\;<\;1\}\;and\;\{$\mid${\psi}_{\nu}$\mid$\;<\;0\}\;in\;M\;{\setminus}\;{\triangle},\;{\nu}\;\in\;{L_{+}}^1(\mu)$, respectively. It is proved that if $S(\mu)\;=\;{\partial\triangle}$, where $S(\mu)$ is the closed support set of $\mu$, then $R(\mu)\;=\;R0(\mu)\;=\;M{\setminus}({\triangle}\;{\cup}\;M(L^{\infty}(\partial\triangle)))$ is generated by $H^{\infty}\;and\;\overline{\psi_{\nu}},\;{\nu}\;{\in}\;{L_1}^{+}(\mu)$. It is proved that %d{\theta}(S(\mu))\;=\;0$ if and only if there exists as Blaschke product b with zeros $\{Zn\}_n$ such that $R(\mu)\;{\subset}\;{$\mid$b$\mid$\;<\;1}\;and\;S(\mu)$ coincides with the set of cluster points of $\{Zn\}_n$. While, we proved that $\mu$ is a sum of finitely many point measure such that $R(\mu)\;{\subset}\;\{$\mid${\psi}_{\lambda}$\mid$\;<\;1}\;and\;S(\lambda)\;=\;S(\mu)$. Also it is studied conditions on \mu for which $R(\mu)\;=\;R0(\mu)$.