• International Journal of Fuzzy Logic and Intelligent Systems
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• 제10권3호
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• pp.242-246
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• 2010

It is well-known that the space $E^n$ of fuzzy numbers(i.e., normal, upper-semicontinuous, compact-supported and convex fuzzy subsets)in the n-dimensional Euclidean space $R^n$ is separable but not complete with respect to the $L_p$-metric. In this paper, we introduce the space $F_p(R^n)$ that is separable and complete with respect to the $L_p$-metric. This will be accomplished by assuming p-th mean bounded condition instead of compact-supported condition and by removing convex condition.

• Journal of Communications and Networks
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• 제14권5호
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• pp.546-553
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• 2012

Compact routing intends to achieve good tradeoff between the routing path length and the memory overhead, and is recently considered as a main alternative to overcome the fundamental scaling problems of the Internet routing system. Plenty of studies have been conducted on compact routing, and quite a few universal compact routing schemes have been designed for arbitrary network topologies. However, it is generally believed that specialized compact routing schemes for peculiar network topologies can have better performance than universal ones. Studies on complex networks have uncovered that most real-world networks exhibit power-law degree distributions, i.e., a few nodes have very high degrees while many other nodes have low degrees. High-degree nodes play the crucial role of hubs in communication and inter-networking. Based on this fact, we propose two highest-degree landmark based compact routing schemes, namely HDLR and $HDLR^+$. Theoretical analysis on random power-law graphs shows that the two schemes can achieve better space-stretch trade-offs than previous compact routing schemes. Simulations conducted on random power-law graphs and real-world AS-level Internet graph validate the effectiveness of our schemes.

• 대한수학회지
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• 제47권5호
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• pp.899-924
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• 2010

In the paper we introduce averages of each type and use these averages to construct examples of weakly compact operators on the space C ($\Omega$) for which the necessary and sufficient conditions that they be compact, absolutely summing or nuclear are distinct. A great number of concrete examples, in various situations, are given.

• 한국산학기술학회논문지
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• 제18권2호
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• pp.501-513
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• 2017

본 연구는 도시농업의 이론, 패러다임, 유형을 통해 개발현황을 분석하고 공간형태에 관한 적용빈도와 개발 키워드를 도출하는데 그 목적을 둔다. 분석결과, 첫째, 거리(Distance)에 의한 도시공간은 자가생산방식, 공동생산방식 그리고 국가 사회운영방식을 통한 공간형태의 디멘존(Dimension)이 결정된다. 둘째, 형태(Shape)에 의한 단지공간은 광활한 토지를 활용하기 위한 플랫형(Flat), 협소하고 환경의 질이 열약한 공간을 극복하기 위한 컴팩트형(Compact) 그리고 플랫과 컴팩트 사이에서의 유기적인 활용울 위한 융합형(Fusion of Flat Compact)을 통해 공간형태의 아이덴티티(Identity)가 결정된다. 셋째, 위치(Location)에 의한 건축과 실내공간은 지상공간, 옥상공간, 벽면공간, 베란다, 실내공간, 실내인프라 공간을 통해 공간형태의 유틸리티(Utility)가 결정된다. 도시농업의 공간형태에 대한 개념들은 유기적인 연관성을 갖고 있으며 향후 진화를 통해 공간은 지속적으로 발전될 것이다. 도시농업의 공간형태는 다양한 융합과정을 통해 새로운 창조공간을 계속해서 만들어 나갈 것이며, 그것은 새로운 도시농업의 개발 트렌드가 될 것이다. 제도적 기준을 통해 계획된 도시농업은 최적의 생산환경과 도시경관 구축을 가능하게 할 것이며, 또한 국가별 문화와 환경적 특성에 따라 탄력적으로 변화하는 공간은 다양한 형태로 도시농업이 진화하는 발판이 될 수 있을 것이라 예측된다.

• 한국수학사학회지
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• 제11권2호
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• pp.83-90
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• 1998

Observing that for any compact space X, the minimal basically disconnected cover ${\bigwedge}Λ_X$ : ${\bigwedge}Λ_X{\leftrightarro}$ is ${\sigma}Z^#$-irreducible, we will show that the projective objects in the category of compact spaces and ${\sigma}Z^#$-irreducible maps are precisely basically disconnected spaces.

• 대한수학회보
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• 제39권1호
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• pp.133-140
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• 2002

On compact complex hyperbolic manifolds of complex dimension two, we show that the dimension of the space of infinitesimal deformations of self-dual conformal structures is smaller than that of the deformation obstruction space and that every self-dual metric with covariantly constant Ricci tensor must be a standard one upto rescalings and diffeomorphisms.

• 대한수학회지
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• 제35권2호
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• pp.371-386
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• 1998

Let G be a compact Lie group and M a semialgebraic G space in some orthogonal representation space of G. We prove that if G is finite then M has an equivariant semialgebraic triangulation. Moreover this triangulation is unique. When G is not finite we show that M has a semialgebraic G CW complex structure, and this structure is unique. As a consequence compact semialgebraic G space has an equivariant simple homotopy type.

• 대한수학회논문집
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• 제10권4호
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• pp.931-941
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• 1995

The definitions and techniques, which deals with homotopic harmonic maps from a compact Riemannian manifold into a compact metric space, developed by N. J. Korevaar and R. M. Schoen [7] can be applied to more general situations. In this paper, we prove that for a complicated domain, possibly noncompact Riemannian manifold with infinitely generated fundamental group, the existence of homotopic harmonic maps can be proved if the initial map is simple in some sense.

• 대한수학회지
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• 제47권2호
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• pp.299-309
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• 2010

The Weyl group of a compact connected Lie group is a reflection group. If such Lie groups are locally isomorphic, the representations of the Weyl groups are rationally equivalent. They need not however be equivalent as integral representations. Turning to the invariant theory, the rational cohomology of a classifying space is a ring of invariants, which is a polynomial ring. In the modular case, we will ask if rings of invariants are polynomial algebras, and if each of them can be realized as the mod p cohomology of a space, particularly for dihedral groups.

• 대한수학회보
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• 제42권2호
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• pp.327-335
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• 2005

For a compact and orientable minimal real hypersurface $M\;in\;QP^n$, we prove that if the minimum of the sectional curvatures of Mis 3/(4n - 1), then M is isometric to the geodesic minimal hypersphere $M_{0,n-1}^Q$.