• Journal of the Korean Mathematical Society
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• v.44 no.5
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• pp.1079-1092
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• 2007

This paper studies the deformation theory of a holomorphic surjective map from a normal compact complex space X to a compact $K\"{a}hler$ manifold Y. We will show that when the target has non-negative Kodaira dimension, all deformations of surjective holomorphic maps $X{\rightarrow}Y$ come from automorphisms of an unramified covering of Y and the underlying reduced varieties of associated components of Hol(X, Y) are complex tori. Under the additional assumption that Y is projective algebraic, this was proved in [7]. The proof in [7] uses the algebraicity in an essential way and cannot be generalized directly to the $K\"{a}hler$ setting. A new ingredient here is a careful study of the infinitesimal deformation of orbits of an action of a complex torus. This study, combined with the result for the algebraic case, gives the proof for the $K\"{a}hler$ setting.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.1121-1125
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• 2003

In this paper we deal with visual servoing that can control a robot arm with a camera using information of images only, without estimating 3D position and rotation of the robot arm. Here it is assumed that the robot arm is calibrated and the camera is uncalibrated. We use a pinhole camera model as the camera one. The essential notion can be show, that is, epipolar geometry, epipole, epipolar equation, and epipolar constrain. These play an important role in designing visual servoing. For easy understanding of the proposed method we first show a design in case of the calibrated camera. The design is constructed by 4 steps and the directional motion of the robot arm is fixed only to a constant direction. This means that an estimated epipole denotes the direction, to which the robot arm translates in 3D space, on the image plane.

• Proceedings of the IEEK Conference
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• 2000.09a
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• pp.671-674
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• 2000

In this paper, we present a robust global registration algorithm for multi-frame image mosaics. When we perform a pair-wise registration recovering a projective transformation between two consecutive frames, severe mis-registration among multiple frames, which are not consecutive, can be detected. It is because the concatenation of those pair-wise transformations leads to global alignment errors. To overcome those mis-registrations, we propose a new algorithm using multiple frames for constructing image mosaics. We use a graph to represent the temporal and spatial connectivity and show that global registration can be obtained through the search for an optimal path in the constructed graph. The definition of an adequate objective function characterizing the global registration provides a direct manipulation of the graph. In the presence of moving objects, especially large ones compared with low texture backgrounds, by using the likelihood ratio as the objective function, we can deal with some of the most challenging videos like basketball or soccer Moreover, the algorithm can be parallelized so it can be more efficiently implemented. Finally, we give some experimental results from real videos.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.431-440
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• 2009

In this paper, we introduce and consider a new system of relaxed cocoercive variational inequalities involving three different operators and the concept of projective nonexpansive mapping. Base on the projection technique, we suggest two kinds of new iterative methods for the approximate solvability of this system. The results presented in this paper extend and improve the main results of [S.S. Chang, H.W.J. Lee, C.K. Chan, Generalized system for relaxed co coercive variational inequalities in Hilbert spaces, Appl. Math. Lett. 20 (2007) 329-334] and [Z. Huang, M. Aslam Noor, An explicit projection method for a system of nonlinear variational inequalities with different ($\gamma,r$)-cocoercive mappings, Appl. Math. Comput. (2007), doi:10.1016/j.amc.2007.01.032].

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.259-267
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• 2002

Let X be a hemicompact space with ($K_{n}$) as an admissible exhaustion, and for each n $\in$ N, $A_{n}$ a Banach function algebra on $K_{n}$ with respect to $\parallel.\parallel_n$ such that $A_{n+1}\midK_{n}$$\subsetA_n$ and${\parallel}f{\mid}K_n{\parallel}_n{\leq}{\parallel}f{\parallel}_{n+1}$ for all f$\in$$A_{n+1}$, We consider the subalgebra A = { f $\in$ C(X) : $\forall_n\;{\epsilon}\;\mathbb{N}$ of C(X) as a frechet function algebra and give a result related to its spectrum when each $A_{n}$ is natural. We also show that if X is moreover noncompact, then any closed subalgebra of A cannot be topologized as a regular Frechet Q-algebra. As an application, the Lipschitzalgebra of infinitely differentiable functions is considered.d.

• Journal for History of Mathematics
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• v.17 no.2
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• pp.73-84
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• 2004

Stone introduced extremally disconnected spaces as the image of complete Boolean algebras under his famous duality between Bool and ZComp and they turn out to be projective objects in various categories of Hausdorff spaces and completely regular ones are exactly those X with Dedekind complete C(X, ). In the pointfree setting, extremally disconnected frame (= De Morgan frame) are those with De Morgan condition. In this paper, we investigate a historical aspect of De Morgan frame together with that of De Morgan.

• Bulletin of the Korean Mathematical Society
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• v.21 no.2
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• pp.61-66
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• 1984

It is well-known that the most interesting non-integrable almost Hermitian manifold are the nearly Kaehlerian manifolds ([2] and [3]), and that there exists a complex but not a Kaehlerian structure on Riemannian product manifolds of two normal contact manifolds [4]. The purpose of the present paper is to study nearly Kaehlerian product manifolds of two almost contact metric manifolds and investigate the geometrical structures of these manifolds. Unless otherwise stated, we shall always assume that manifolds and quantities are differentiable of class $C^{\infty}$. In Paragraph 1, we give brief discussions of almost contact metric manifolds and their Riemannian product manifolds. In paragraph 2, we investigate the perfect conditions for Riemannian product manifolds of two almost contact metric manifolds to be nearly Kaehlerian and the non-existence of a nearly Kaehlerian product manifold of contact metric manifolds. Paragraph 3 will be devoted to a proof of the following; A conformally flat compact nearly Kaehlerian product manifold of two almost contact metric manifolds is isomatric to a Riemannian product manifold of a complex projective space and a flat Kaehlerian manifold..

• Bulletin of the Korean Mathematical Society
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• v.49 no.2
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• pp.307-317
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• 2012

We say (W, {${\phi}_1,\;{\ldots}\;,{\phi}_t$}) is a polarizable dynamical system of several morphisms if ${\phi}_i$ are endomorphisms on a projective variety W such that ${\otimes}{\phi}_i^*L$ is linearly equivalent to $L^{{\otimes}q}$ for some ample line bundle L on W and for some q > t. If q is a rational number, then we have the equidistribution of small points of given dynamical system because of Yuan's work [13]. As its application, we can build a polarizable dynamical system of an automorphism and its inverse on a K3 surface and can show that its periodic points are equidistributed.

• Bulletin of the Korean Mathematical Society
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• v.49 no.2
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• pp.395-409
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• 2012

In the study of homology cobordisms, knot concordance and link concordance, the following technical problem arises frequently: let ${\pi}$ be a group and let M ${\rightarrow}$ N be a homomorphism between projective $\mathbb{Z}[{\pi}]$-modules such that $\mathbb{Z}_p\;{\otimes}_{\mathbb{Z}[{\pi}]}M{\rightarrow}\mathbb{Z}_p{\otimes}_{\mathbb{Z}[{\pi}]}\;N$ is injective; for which other right $\mathbb{Z}[{\pi}]$-modules V is the induced map $V{\otimes}_{\mathbb{Z}[{\pi}]}\;M{\rightarrow}\;V{\otimes}_{\mathbb{Z}[{\pi}]}\;N$ also injective? Our main theorem gives a new criterion which combines and generalizes many previous results.

• Journal of the Korean Mathematical Society
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• v.48 no.6
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• pp.1171-1187
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• 2011

Silverman [14] proved a height inequality for a jointly regular family of rational maps and the author [10] improved it for a jointly regular pair. In this paper, we provide the same improvement for a jointly regular family: let h : ${\mathbb{P}}_{\mathbb{Q}}^n{\rightarrow}{{\mathbb{R}}$ be the logarithmic absolute height on the projective space, let r(f) be the D-ratio of a rational map f which is de ned in [10] and let {$f_1,{\ldots},f_k|f_l:\mathbb{A}^n{\rightarrow}\mathbb{A}^n$} bbe finite set of polynomial maps which is defined over a number field K. If the intersection of the indeterminacy loci of $f_1,{\ldots},f_k$ is empty, then there is a constant C such that $ \sum\limits_{l=1}^k\frac{1}{def\;f_\iota}h(f_\iota(P))>(1+\frac{1}{r})f(P)-C$ for all $P{\in}\mathbb{A}^n$ where r= $max_{\iota=1},{\ldots},k(r(f_l))$.