• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.10 no.3
• /
• pp.242-246
• /
• 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
• /
• v.14 no.5
• /
• pp.546-553
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.47 no.5
• /
• pp.899-924
• /
• 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.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.18 no.2
• /
• pp.501-513
• /
• 2017

This study analyzed the situation of urban agriculture development through theories, paradigms, and typology to determine the application frequency and development keywords about space forming. The results showed that urban space by distance determines "Dimension of space forming" through self-production, public-production, and nation-social operation. Second, the complex space by shape determine "Identity of space forming" through "Flat Shape" for using the widespread land, "Compact Shape" for overcoming the small and poor land, and "Fusion of Flat Compact Shape" for systematic use between Flat and Compact. Third, building and interior space according to location determine the "Utility of space forming" through land, roof, wall, veranda, interior, and infrastructure space. The concepts about space forming of urban agriculture have an organic correlation and will be developed sustainably by the evolved cases from now on. In addition, space forming of urban agriculture produces new creation space by various fusion processes and will be a development trend of new urban agriculture.

• Journal for History of Mathematics
• /
• v.11 no.2
• /
• pp.83-90
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.39 no.1
• /
• pp.133-140
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.35 no.2
• /
• pp.371-386
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• v.10 no.4
• /
• pp.931-941
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.47 no.2
• /
• pp.299-309
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.2
• /
• pp.327-335
• /
• 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 $M_{0,n-1}^Q$.