• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.139-152
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• 2003

In this paper, we characterize a vector-valued convex set function by its epigraph. The concepts of a vector-valued set function and a vector-valued concave set function we given respectively. The definitions of the conjugate functions for a vector-valued convex set function and a vector-valued concave set function are introduced. Then a Fenchel duality theorem in multiobjective programming problem with set functions is derived.

• Honam Mathematical Journal
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• v.25 no.1
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• pp.163-172
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• 2003

In this paper we study the property of harmonic vector fields. We call a vector fields ${\xi}$ harmonic if it is a harmonic map from the manifold into its tangent bundle with the Sasaki metric. We show that the characteristic polynomial of operator $A={\nabla}{\xi}\;in\;S^{2n+1}\;is\;(x^2+1)^n$.

• Journal of the Korean Statistical Society
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• v.36 no.3
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• pp.367-372
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• 2007

Classification as a tool to extract information from data plays an important role in science and engineering. Among various classification methodologies, support vector machine has recently seen significant developments. The central problem this paper addresses is the accuracy of support vector machine. In particular, we are interested in the situations where fast rates of convergence to the Bayes risk can be achieved by support vector machine. Through learning examples, we illustrate that support vector machine may yield fast rates if the space spanned by an adopted kernel is sufficiently large.

• Proceedings of the IEEK Conference
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• 2003.07e
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• pp.2044-2047
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• 2003

In this paper, we propose efficient motion vector refinement algorithm for frame-rate reduction transcoding. The proposed algorithm is to set the search range for motion refinement based on the incoming motion vector. The algorithm calculates the importance of motion vector of the skipped frame and then selects two motion vector to set search range. Through this process, we determine the accuracy of incoming motion vector and set the search range lot refinement adaptively by means of the accuracy. In experiments, we show efficiency of our algorithm to reduce the search points for refinement.

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.605-613
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• 2007

Main interest of the present paper is to investigate the criticality of characteristic vector fields on almost cosymplectic manifolds. Killing critical characteristic vector fields are absolute minima. This paper contains some examples of non-Killing critical characteristic vector fields.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1699-1718
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• 2017

We give a construction of the second Chern number of a vector bundle over a smooth projective surface by means of adelic transition matrices for the vector bundle. The construction does not use an algebraic K-theory and depends on the canonical ${\mathbb{Z}}-torsor$ of a locally linearly compact k-vector space. Analogs of certain auxiliary results for the case of an arithmetic surface are also discussed.

• East Asian mathematical journal
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• v.26 no.3
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• pp.389-395
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• 2010

In this paper, a class of g-demi-pseudomonotone mappings is introduced and the solvability of a class of generalized vector F-complementarity problems with the mappings in Banach spaces is considered.

• Journal of the Korean Mathematical Society
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• v.40 no.2
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• pp.287-305
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• 2003

Second order necessary optimality condition for properly efficient solutions of a twice differentiable vector optimization problem is given. We obtain a nonsmooth version of the second order necessary optimality condition for properly efficient solutions of a nondifferentiable vector optimization problem. Furthermore, we prove a second order necessary optimality condition for weakly efficient solutions of a nondifferentiable vector optimization problem.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.85-89
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• 2003

Let V be a localizing infinite-dimensional complex Banach space. Let X be a flag manifold of finite flags either of finite codimensional closed linear subspaces of V or of finite dimensional linear subspaces of V. Let E be a holomorphic vector bundle on X with finite rank. Here we prove that E is uniform, i.e. that for any two lines $D_1$ R in the same system of lines on X the vector bundles E$\mid$D and E$\mid$R have the same splitting type.

• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.133-145
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• 2006

We study Riemannian or pseudo-Riemannian manifolds which admit a closed conformal vector field. Subject to the condition that at each point $p{\in}M^n$ the set of conformal gradient vector fields spans a non-degenerate subspace of TpM, using a warped product structure theorem we give a complete description of the space of conformal vector fields on arbitrary non-Ricci flat Einstein spaces.