• East Asian mathematical journal
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• v.24 no.2
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• pp.201-212
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• 2008

We characterize operators between Banach spaces sending unconditionally weakly p-summable sequences into sequences that lie in the range of a vector measure of bounded variation. Further, we describe operators between Banach spaces taking unconditionally weakly p-summable sequences into sequences that lie in the range of a vector measure.

• 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.

• Korean Journal of Mathematics
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• v.15 no.1
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• pp.13-26
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• 2007

We prove that every strong null sequence in a Banach space X lies inside the range of a vector measure of bounded variation if and only if the condition $\mathcal{N}_1(X,{\ell}_1)={\Pi}_1(X,{\ell}_1)$ holds. We also prove that for $1{\leq}p<{\infty}$ every strong ${\ell}_p$ sequence in a Banach space X lies inside the range of an X-valued measure of bounded variation if and only if the identity operator of the dual Banach space $X^*$ is ($p^{\prime}$,1)-summing, where $p^{\prime}$ is the conjugate exponent of $p$. Finally we prove that a Banach space X has the property that any sequence lying in the range of an X-valued measure actually lies in the range of a vector measure of bounded variation if and only if the condition ${\Pi}_1(X,{\ell}_1)={\Pi}_2(X,{\ell}_1)$ holds.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.779-789
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• 2011

In this paper we study the Banach space $L^1$(G) of real valued measurable functions which are integrable with respect to a vector measure G in the sense of D. R. Lewis. First, we investigate conditions for a scalarly integrable function f which guarantee $f{\in}L^1$(G). Next, we give a sufficient condition for a sequence to converge in $L^1$(G). Moreover, for two vector measures F and G with values in the same Banach space, when F can be written as the integral of a function $f{\in}L^1$(G), we show that certain properties of G are inherited to F; for instance, relative compactness or convexity of the range of vector measure. Finally, we give some examples of $L^1$(G) related to the approximation property.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.113-120
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• 2001

Using the notions of admissibility, local convexity and measure of noncompactness, we give new fixed point theorems for quasicompact or condensing multivalued mappings with domains that are not necessarily convex subsets of an arbitrary topological vector space.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.209-215
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• 2000

Let X be a locally convex space. A series of clearcut characterizations for the boundedness of vector measure $\mu{\;}:{\;}\sum\rightarrow{\;}X$ is obtained, e.g., ${\mu}$ is bounded if and only if ${\mu}(A_j){\;}\rightarrow{\;}0$ weakly for every disjoint $\{A_j\}{\;}\subseteq{\;}\sum$ and if and only if $\{\frac{1}{j^j}{\mu}(A_j)\}^{\infty}_{j=1}$ is bounded for every disjoint $\{A_j\}{\;}\subseteq{\;}\sum$.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.3
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• pp.369-374
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• 2004

A cluster merging algorithm that merges convex clusters resulted by the Fuzzy Convex Clustering(FCC) method into non-convex clusters was proposed. This was achieved by proposing a fast and reliable distance measure between two convex clusters using Support Vector Machines(SVM) to improve accuracy and speed over other existing conventional methods. In doing so, it was possible to reduce cluster number without losing its representation of the data. In this paper, results for several data sets are given to show the validity of our distance measure and algorithm.

• Proceedings of the KSRS Conference
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• v.2
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• pp.772-775
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• 2006

Muilti-dimensional feature vector matching algorithm uses multiple features such as intensity, gradient, variance, first or second derivative of a pixel to find correspondence pixels in stereo images. In this paper, we proposed a new method for adjusting automatically the weight of feature in multi-dimensional feature vector matching considering sharpeness of a pixel in feature vector distance curve. The sharpeness consists of minimum and maximum vector distances of a small window mask. In the experiment we used IKONOS satellite stereo imagery and obtained accurate matching results comparable to the manual weight-adjusting method.

• The Journal of the Acoustical Society of Korea
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• v.26 no.2E
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• pp.39-43
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• 2007

Music summarization refers to a technique which automatically extracts the most important and representative segments in music content. In this paper, we propose and evaluate a technique which provides the repeated part in music content as music summary. For extracting a repeated segment in music content, the proposed algorithm uses the weighted sum of similarity measures based on multi-level vector quantization for fixed-length summary or optimal-length summary. For similarity measures, count-based similarity measure and distance-based similarity measure are proposed. The number of the same codeword and the Mahalanobis distance of features which have same codeword at the same position in segments are used for count-based and distance-based similarity measure, respectively. Fixed-length music summary is evaluated by measuring the overlapping ratio between hand-made repeated parts and automatically generated ones. Optimal-length music summary is evaluated by calculating how much automatically generated music summary includes repeated parts of the music content. From experiments we observed that optimal-length summary could capture the repeated parts in music content more effectively in terms of summary length than fixed-length summary.

• Proceedings of the IEEK Conference
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• 2000.07a
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• pp.54-57
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• 2000

In vector quantization (VQ), mean squared difference (MSD) is a widely used distance measure between vectors. But the distance between the means of each vector elements appears as a dominant quantity in MSD. In the case of image vectors, the coincidence of edge patterns is also important when the human visual system (HVS) is considered. Therefore, we propose a new distance measure that uses the variance of differences to encode vectors and to design codebooks. It can choose more proper codewords to reduce edge degradations and make a useful codebook, which has lots of various edge codewords in place of redundant shades.