• 대한수학회보
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• 제50권4호
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• pp.1297-1302
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• 2013

We prove that the mapping class group of a non-Haken orientable irreducible 3-manifold is finite and we show that the quotient group of the mapping class group by the rotation group is virtually torsion-free if the manifold does not have 2-sphere boundary components.

• Kyungpook Mathematical Journal
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• 제46권3호
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• pp.399-408
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• 2006

The action of mapping class groups of a handlebody on the first homology group is investigated. A homological analogy of mapping class groups of a handlebody is defined and its system of generators is given.

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 2001년도 봄 학술발표논문집 Vol.28 No.1 (A)
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• pp.670-672
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• 2001

소프트웨어 산업계에서 재사용 단위가 객체보다 더 큰 컴포넌트 기반의 개발에 관심이 집중되고 있다. 그래서 모델링 언어인 UML과 컴포넌트가 운용되는 유연하고 확장성 높은 기반 아키텍처인 EJB를 이용한 기업형 시스템 개발이 요즘 기업에서 활발해지고 있다. UML과 EJB 각각에 대한 연구는 많이 진행되었지만, UML Model을 이용한 EJB Model 구현시의 mapping 기법에 관한 연구는 아직 미흡한 실정이다. 그래서 본 논문에서는 UML Modeling을 통해 Class diagram에서 추출된 Class들이 EJB로 구현될 때 실제로 어떤 Bean으로 Mapping 되는지에 대해 제시한다.

• 한국과학교육학회지
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• 제19권3호
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• pp.479-486
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• 1999

중학교 생물의 광합성과 호흡단원에 대해 개인별 또는 협동 학습개념도를 적용한 수업결과를 전통적 강의식 수업결과와 비교하였다. 그 결과 개념도를 적용한 학습이 전통적 강의식 수업보다 효과적이었다. 공분산분석을 실시하여 개인별 개념도 작성그룹과 협동 개념도 작성그룹간(p<.008), 협동개념도 작성그룹과 전통적 강의식 학습그룹간(p<.0001)에 유의성있는 결과를 얻었다. 또한 협동개념도작성그룹이 개인별 개념도 작성그룹보다 효과적이었다(p<.04). 따라서 협동개념도 학습방법이 생물학습에 있어 가장 효과적이었다.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제13권3호
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• pp.197-206
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• 2006

This paper introduces a class of multivalued mixed quasi-variational-like ineqcalities and shows the existence of solutions to the class of quasi-variational-like inequalities in reflexive Banach spaces.

• Korean Journal of Mathematics
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• 제9권2호
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• pp.157-164
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• 2001

We construct an operad which is called the mapping class group operad. Its structure map is induced by the attachings of surfaces. The similar operad was constructed by Tillmann in order prove that ${\Gamma}^+_{\infty}$ is an infinite loop space. Our operad is rather simpler and easier to deal with.

• 대한수학회논문집
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• 제11권3호
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• pp.815-823
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• 1996

M. Kontsevich posed a problem on mapping class groups of 3-manifold that is if M is a compact 3-manifold with nonempty boundary, then BDiff (M rel $\partial$ M) has the homotopy type of a finite complex. Here, Diff (M rel $\partial$ M) is the group of diffeomorphisms of M which restrict to the identity on $\partial$ M, and BDiff (M rel $\partial$ M) is its classifying space. In this paper we resolve the problem affirmatively in the case when M is a Haken 3-manifold.

• 대한수학회보
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• 제53권2호
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• pp.601-614
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• 2016

Let $N_{g,s}$ denote the nonorientable surface of genus g with s boundary components. Recently Paris and Szepietowski [12] obtained an explicit finite presentation for the mapping class group $\mathcal{M}(N_{g,s})$ of the surface $N_{g,s}$, where $s{\in}\{0,1\}$ and g + s > 3. Following this work, we obtain a finite presentation for the subgroup $\mathcal{T}(N_{g,s})$ of $\mathcal{M}(N_{g,s})$ generated by Dehn twists.

• 대한수학회지
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• 제50권4호
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• pp.865-877
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• 2013

The disjoint union of mapping class groups of surfaces forms a braided monoidal category $\mathcal{M}$, as the disjoint union of the braid groups $\mathcal{B}$ does. We give a concrete and geometric meaning of the braidings ${\beta}_{r,s}$ in $\mathcal{M}$. Moreover, we find a set of elements in the mapping class groups which correspond to the standard generators of the braid groups. Using this, we can define an obvious map ${\phi}\;:\;B_g{\rightarrow}{\Gamma}_{g,1}$. We show that this map ${\phi}$ is injective and nongeometric in the sense of Wajnryb. Since this map extends to a braided monoidal functor ${\Phi}\;:\;\mathcal{B}{\rightarrow}\mathcal{M}$, the integral homology homomorphism induced by ${\phi}$ is trivial in the stable range.

• 대한수학회보
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• 제50권3호
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• pp.1007-1020
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• 2013

Approximate fixed point property problem for Mann iteration sequence of a nonexpansive mapping has been resolved on a Banach space independent of uniform (strict) convexity by Ishikawa [Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 59 (1976), 65-71]. In this paper, we solve this problem for a class of mappings wider than the class of asymptotically nonexpansive mappings on an arbitrary normed space. Our results generalize and extend several known results.