• 충청수학회지
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• 제6권1호
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• pp.113-130
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• 1993

In this paper, we introduce certain subgroups $E^{Rel}_n$ (X, Y, K, G) of the relative homotopy groups ${\sigma}_n$(X, Y, K, G) of a transformation group and examine the algebraic properties of these groups.

• 충청수학회지
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• 제5권1호
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• pp.9-21
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• 1992

We define a certain subgroup $E_n$ (X, K, G) of the relative homotopy groups of a transformation group ${\sigma}_n$(X, K, G). The algebraic properties of these groups are examined.

• 자연과학논문집
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• 제8권2호
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• pp.17-20
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• 1996

Fiber의 dimension이 일일 때, Equivariant Serre problem이 실 대수 범주에서 맞다는 것을 보였다. 즉 실 표현공간 위에서의 equivariant line bundle은 실 표현공간과 어떤 G-module의 product bundle과 동치임을 보였다.

• 호남수학학술지
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• 제34권4호
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• pp.495-504
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• 2012

Let G be a semialgebraic group and M a proper semi-algebraic G-set which is locally complete. In this paper we show that the orbit space M/G has a semialgebraic structure such that the orbit map is semialgebraic.

• 대한전자공학회논문지
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• 제12권2호
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• pp.11-17
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• 1975

이 논문은 한글문자의 자동인식을 위한 기초적인 연구로서 기본문자의 구조에 대해서 검토하였다. 기본문자를 구조, 선분구조 및 물자 graph의 node와의 연결곤계 들 구조를 세가지 측면에서 집합 및 군론에 의한 대수적인 분석을 하고 또 그들의 각 구조의 복잡성에 대한 계릉을 고찰하였다. 나아가서 10개의 모음은 한 요소의 Affine 변환에 의한 연속회전으로 이루어지는 회전변환군 속에서 다수의 동치관계가 존재한다는 것을 기술하므로써, 한글문자의 인식에 있어서는 topological 골격외에 기하적 성질이 특히 중요하다는 것을 아울러 지적 하였다. The paper examined the character structure as a basic study for the recognition of Korean characters. In view of concave structure, line structure and node relationship of character graph, the algebraic structure of the basic Korean characters is are analized. Also, the degree of complexities in their character structure is discussed and classififed. Futhermore, by describing the fact that some equivalence relations are existed between the 10 vowels of rotational transformation group by Affine transformation of one element into another, it could be pointed out that the geometrical properting in addition to the topological properties are very important for the recognition of Korean characters.

• Korean Journal of Mathematics
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• 제5권1호
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• pp.49-54
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• 1997

In this paper we study the generalized Reidemeister number $R({\varphi},{\psi})$ for a self-map $({\varphi},{\psi}):(X,G){\rightarrow}(X,G)$ of a transformation group (X, G), as an extension of the Reidemeister number $R(f)$ for a self-map $f:X{\rightarrow}X$ of a topological space X.

• Korean Journal of Mathematics
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• 제7권2호
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• pp.151-158
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• 1999

Let (X, G) be a transformation group and ${\sigma}(X,x_0,G)$ the fundamental group of (X, G). In this paper, we prove that the Reidemeister number $R(f_G)$ for an endomorphism $f_G:(X,G){\rightarrow}(X,G)$ is a homotopy invariant. In particular, when any self-map $f:X{\rightarrow}X$ is homotopic to the identity map, we give some calculation of the lower bound of $R(f_G)$. Finally, we discuss commutativity and product formula for the Reidemeister number $R(f_G)$.

• 대한수학회지
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• 제41권4호
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• pp.629-646
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• 2004

Let G be a compact semialgebraic group and M a semi-algebraic G-set. We prove that there exists a semialgebraic slice at every point of M. Moreover M can be covered by finitely many semialgebraic G-tubes. As an application we give a different proof that every semialgebraic G-set admits a semi algebraic G-embedding into some semialgebraic orthogonal representation space of G, which has been proved in [15].

• Korean Journal of Mathematics
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• 제5권2호
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• pp.177-183
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• 1997

Let ${\sigma}(X,x_0,G)$ be the fundamental group of a transformation group (X,G). Let $R({\varphi},{\psi})$) be the generalized Reidemeister number for an endomorphism $({\varphi},{\psi}):(X,G){\rightarrow}(X,G)$. In this paper, our main results are as follows ; we prove some sufficient conditions for $R({\varphi},{\psi})$ to be the cardinality of $Coker(1-({\varphi},{\psi})_{\bar{\sigma}})$, where 1 is the identity isomorphism and $({\varphi},{\psi})_{\bar{\sigma}}$ is the endomorphism of ${\bar{\sigma}}(X,x_0,G)$, the quotient group of ${\sigma}(X,x_0,G)$ by the commutator subgroup $C({\sigma}(X,x_0,G))$, induced by (${\varphi},{\psi}$). In particular, we prove $R({\varphi},{\psi})={\mid}Coker(1-({\varphi},{\psi})_{\bar{\sigma}}){\mid}$, provided that (${\varphi},{\psi}$) is eventually commutative.

• 대한수학회보
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• 제49권1호
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• pp.109-126
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• 2012

In 2003, Marques-Smith and Sullivan described the join ${\Omega}$ of the 'natural order' $\leq$ and the 'containment order' $\subseteq$ on P(X), the semigroup under composition of all partial transformations of a set X. And, in 2004, Pinto and Sullivan described all automorphisms of PS(q), the partial Baer-Levi semigroup consisting of all injective ${\alpha}{\in}P(X)$ such that ${\mid}X{\backslash}X{\alpha}\mid=q$, where $N_0{\leq}q{\leq}{\mid}X{\mid}$. In this paper, we describe the group of automorphisms of R(q), the largest regular subsemigroup of PS(q). In 2010, we studied some properties of $\leq$ and $\subseteq$ on PS(q). Here, we characterize the meet and join under those orders for elements of R(q) and PS(q). In addition, since $\leq$ does not equal ${\Omega}$ on I(X), the symmetric inverse semigroup on X, we formulate an algebraic version of ${\Omega}$ on arbitrary inverse semigroups and discuss some of its properties in an algebraic setting.