• Korean Journal of Mathematics
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• 제7권1호
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• pp.111-116
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• 1999

In this paper, we introduce the concepts of quasi retract ideals and quasi retract topological semigroups which are weaker than those of retract ideals and retract topological semigroups, respectively. We prove that every $n$-th power ideal of a commutative power cancellative power ideal topological semigroup is a quasiretract ideal.

• 호남수학학술지
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• 제36권3호
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• pp.519-530
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• 2014

To study a deformation of a digital space from the viewpoint of digital homotopy theory, we have often used the notions of a weak k-deformation retract [20] and a strong k-deformation retract [10, 12, 13]. Thus the papers [10, 12, 13, 16] firstly developed the notion of a strong k-deformation retract which can play an important role in studying a homotopic thinning of a digital space. Besides, the paper [3] deals with a k-deformation retract and its homotopic property related to a digital fundamental group. Thus, as a survey article, comparing among a k-deformation retract in [3], a strong k-deformation retract in [10, 12, 13], a weak deformation k-retract in [20] and a digital k-homotopy equivalence [5, 24], we observe some relationships among them from the viewpoint of digital homotopy theory. Furthermore, the present paper deals with some parts of the preprint [10] which were not published in a journal (see Proposition 3.1). Finally, the present paper corrects Boxer's paper [3] as follows: even though the paper [3] referred to the notion of a digital homotopy equivalence (or a same k-homotopy type) which is a special kind of a k-deformation retract, we need to point out that the notion was already developed in [5] instead of [3] and further corrects the proof of Theorem 4.5 of Boxer's paper [3] (see the proof of Theorem 4.1 in the present paper). While the paper [4] refers some properties of a deck transformation group (or an automorphism group) of digital covering space without any citation, the study was early done by Han in his paper (see the paper [14]).

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제5권1호
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• pp.40-45
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• 2005

The concept of a intuitionistic fuzzy topology (IFT) was introduced by Coker 1997. The concept of a fuzzy retract was introduced by Rodabaugh in 1981. The aim of this paper is to introduce a new concepts of fuzzy continuity and fuzzy retracts in an intuitionistic fuzzy topological spaces and establish some of their properties. Also, the relations between these new concepts are discussed.

• 대한수학회지
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• 제44권6호
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• pp.1479-1503
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• 2007

In this paper, we study a strong k-deformation retract derived from a relative k-homotopy and investigate its properties in relation to both a k-homotopic thinning and the k-fundamental group. Moreover, we show that the k-fundamental group of a wedge product of closed k-curves not k-contractible is a free group by the use of some properties of both a strong k-deformation retract and a digital covering. Finally, we write an algorithm for calculating the k-fundamental group of a dosed k-curve by the use of a k-homotopic thinning.

• 대한기계학회논문집A
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• 제36권1호
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• pp.91-96
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• 2012

착륙장치 접개 작동기는 항공기 이착륙 시 착륙장치를 항공기 동체 내로 접어 올리거나 동체 밖으로 펼쳐 내려주는 역할을 한다. 접개 작동기 내부에는 착륙장치 펼침 상태에서 외란에 의해 착륙장치가 접히게 되는 것을 방지하기 위한 별도의 잠금장치가 장착된다. 이 잠금장치는 작동기 내부에 공급되는 유압을 통해 작동기 내부 구성품과 기계적으로 구속됨으로써 작동기 잠금 기능을 수행하게 된다. 착륙장치 접힘/펼침에 따라 잠금장치의 잠김/풀림이 반복되므로, 잠금장치는 항공기 운용 중 반복되는 동일 하중을 받게 되며, 이로 인한 피로 파괴의 가능성이 존재하게 된다. 본 논문에서는 잠금장치에 대한 피로해석 과정 및 결과를 제시하고, 피로시험을 통해 그 결과의 타당성을 검증하였다.

• 호남수학학술지
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• 제33권1호
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• pp.51-60
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• 2011

The aim of the paper is to develop an identification method for digital spaces and to study its digital homotopic properties related to a strong k-deformation retract.

• 대한수학회지
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• 제47권5호
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• pp.1031-1054
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• 2010

Let $\mathbb{Z}^n$ be the Cartesian product of the set of integers $\mathbb{Z}$ and let ($\mathbb{Z}$, T) and ($\mathbb{Z}^n$, $T^n$) be the Khalimsky line topology on $\mathbb{Z}$ and the Khalimsky product topology on $\mathbb{Z}^n$, respectively. Then for a set $X\;{\subset}\;\mathbb{Z}^n$, consider the subspace (X, $T^n_X$) induced from ($\mathbb{Z}^n$, $T^n$). Considering a k-adjacency on (X, $T^n_X$), we call it a (computer topological) space with k-adjacency and use the notation (X, k, $T^n_X$) := $X_{n,k}$. In this paper we introduce the notions of KD-($k_0$, $k_1$)-homotopy equivalence and KD-k-deformation retract and investigate a classification of (computer topological) spaces $X_{n,k}$ in terms of a KD-($k_0$, $k_1$)-homotopy equivalence.

• Korean Journal of Mathematics
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• 제16권2호
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• pp.215-231
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• 2008

Let E be a uniformly convex Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm, C a nonempty closed convex subset of E, and $T:C{\rightarrow}{\mathcal{K}}(E)$ a multivalued nonself-mapping such that $P_T$ is nonexpansive, where $P_T(x)=\{u_x{\in}Tx:{\parallel}x-u_x{\parallel}=d(x,Tx)\}$. For $f:C{\rightarrow}C$ a contraction and $t{\in}(0,1)$, let $x_t$ be a fixed point of a contraction $S_t:C{\rightarrow}{\mathcal{K}}(E)$, defined by $S_tx:=tP_T(x)+(1-t)f(x)$, $x{\in}C$. It is proved that if C is a nonexpansive retract of E and $\{x_t\}$ is bounded, then the strong ${\lim}_{t{\rightarrow}1}x_t$ exists and belongs to the fixed point set of T. Moreover, we study the strong convergence of $\{x_t\}$ with the weak inwardness condition on T in a reflexive Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm. Our results provide a partial answer to Jung's question.

• 호남수학학술지
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• 제30권2호
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• pp.207-217
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• 2008

Digital geometry has strongly contributed to the study of a discrete topological space $X{\subset}{\mathbf{Z}}^n$ with k-adjacency of ${\mathbf{Z}}^n$. As a survey-type article, we review various utilities of digital geometry.

• 대한수학회지
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• 제32권1호
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• pp.33-40
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• 1995

A space Y is called finitely dominated if there is a finite complex K such that Y is a retract of K in the homotopy category, i.e., we require maps $i : Y \longrightarrow K and r : K \longrightarrow Y with r \circ i \simeq idy$. The following questions are very classical in topology.