• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.05a
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• pp.14-17
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• 2003

By Mazur's theorem, the convex hull of a relatively compact subset a Banach space is also relatively compact. But this is not true any more in the space of fuzzy numbers endowed with the Hausdorff-Skorohod metric. In this paper, we establish a necessary and sufficient condition for which the convex hull of K is also relatively compact when K is a relatively compact subset of the space F(R$\^$k/) of fuzzy numbers of R$\^$k/ endowed with the Hausdorff-Skorohod metric.

• Korean Journal of Plant Tissue Culture
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• v.27 no.3
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• pp.233-238
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• 2000

To obtain a basic information of the development of Genus Viola, morphological and histological observation of in vitro calli and cells in Viola culture cells were investigated. There were two callus types obtained by long term subculture of wild viola (Viola partrinii DC. ) petiole callus. One was friable callus - soft and pale green in color and small cells in size, and the other was compact callus - compact and deep bluish green in color, large cells in size. In scanning electron microscopic observation, friable callus was composed of voculated cell around small. cell clump, while compact callus was composed of cells filled with protoplasm Somatic embryogenesis was observed from suspension culture of the compact callus.

• Korean System Dynamics Review
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• v.11 no.2
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• pp.5-28
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• 2010

The purpose of this paper is to review relationship between spatial characteristics of compact city and urban sustainabiliy from system dynamics perspective using causal loop analysis. It has been argued that spatial characteristics of compact city, high population density and mixed land use, are positively related to urban sustainability. However, research results that are not consistent with pros of compact city argument have been accumulated too. It is especially true when spatial characteristics of compact city are examined with regard to each dimension of sustainablility: economic, social, and environmental sustainability. Reviewing each dimension of sustainability with regard to spatial characteristics based on causal loop analysis, this paper provides more clear understanding on relationship between compact city and sustainability. Also this paper provides a base for system dynamics simulation for future study.

• Kyungpook Mathematical Journal
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• v.28 no.1
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• pp.23-34
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• 1988

A version of Ascoli's Theorem (equating compact and equicontinuous sets) is presented in the context of convergence spaces. This theorem and another, (involving equicontinuity) are applied to characterize compact subsets of quasi-multipliers of a $C^*$-algebra B, and to characterize the compact subsets of the state space of B. The classical Ascoli Theorem states that, for pointwise pre-compact families F of continuous functions from a locally compact space Y to a complete Hausdorff uniform space Z, equicontinuity of F is equivalent to relative compactness in the compact-open topology([4] 7.17). Though this is one of the most important theorems of modern analysis, there are some applications of the ideas inherent in this theorem which arc not readily accessible by direct appeal to the theorem. When one passes to so-called "non-commutative analysis", analysis of non-commutative $C^*$-algebras, the analogue of Y may not be relatively compact, while the conclusion of Ascoli's Theorem still holds. Consequently it seems plausible to establish a more general Ascoli Theorem which will directly apply to these examples.

• Journal of the Korean Mathematical Society
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• v.47 no.5
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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.

• East Asian mathematical journal
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• v.23 no.2
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• pp.151-158
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• 2007

In this paper we introduce the concept of fuzzy ${\beta}-compact^*$ spaces. Besides giving some interesting properties of fuzzy ${\beta}-compact^*$ spaces we also give a characterization on fuzzy $\beta$-compact spaces by making use of newly introduced concept of fuzzy $\beta$-filters.

• Korean Journal of Mathematics
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• v.10 no.2
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• pp.103-116
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• 2002

We characterize operators between Banach spaces sending compact sets into sets that lie in the range of a vector measure. Further, we describe operators between Banach spaces taking compact sets into sets that lie in the range of a vector measure of bounded variation.

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.309-317
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• 2003

In this paper we study the relation of Euler characteristic with respect to cohomology with compact support in F$_{p}$-coefficient for the fibration of ENR's and generalize some properties on proper G-spaces for locally compact Lie group G.G.

• Kyungpook Mathematical Journal
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• v.32 no.1
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• pp.31-43
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• 1992

• The Bulletin of The Korean Astronomical Society
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• v.37 no.1
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• pp.48.2-48.2
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• 2012

We present preliminary results of a statistical study on the nuclear activity of compact group galaxies. What triggers Active Galactic Nuclei (AGN) is still a puzzling problem. One of the suggested AGN triggering mechanisms is galaxy-galaxy interaction. Many simulations have shown that gas can be supplied to the center of galaxies during galaxy encounters. In this regard, compact groups of galaxies are an ideal laboratory for studying the connection between galaxy interaction and nuclear activity because of their high densities and low velocity dispersions. We study the environmental dependence of the activity in galactic nuclei using 59 compact groups in the SDSS DR6. Using the emission line data, we classify galaxies in the compact groups. We find that 19% of the compact group galaxies are pure star-forming nuclei, 10% as transition objects, and only 7% of the galaxies in compact groups show the nuclear activity. The AGN fraction of compact group is higher than galaxy clusters, but lower than field environment. Implications of this result will be discussed.