• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.779-788
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• 1997

In this work, using the exact separatrix map which provides an efficient way to describe dynamics near the separatrix, we study the stochastic layer near the separatrix of a one-degree-of-freedom Hamilitonian system with time periodic perturbation. Applying the twist map theory to the exact separatrix map, T. Ahn, G. I. Kim and S. Kim proved the existence of the uniformly hyperbolic invariant set(UHIS) near separatrix. Using the theorems of Bowen and Franks, we prove this UHIS has measure zero.

• Journal of the Korean Mathematical Society
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• v.55 no.1
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• pp.17-28
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• 2018

In this paper, we enlarge the ball of convergence of a uniparametric family of secant-like methods for solving non-differentiable operators equations in Banach spaces via using ${\omega}$-condition and centered-like ${\omega}$-condition meantime as well as some fine techniques such as the affine invariant form. Numerical examples are also provided.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1249-1257
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• 2016

We prove that the Ricci operator S of an almost cosymplectic three-manifold M is invariant along the Reeb flow, that is, M satisfies ${\pounds}_{\xi}S=0$ if and only if M is either cosymplectic or locally isometric to the group E(1, 1) of rigid motions of Minkowski 2-space with a left invariant almost cosymplectic structure.

• Journal of Electrical Engineering and information Science
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• v.3 no.2
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• pp.158-162
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• 1998

We study the decentralized stabilization problem of linear time-invariant large-scale interconnected systems with delays without any system structure. We obtain sufficient stability conditions for interconnected systems which are equivalent to disturbance attenuation of some scaled system. A decentralized output-feedback controller is obtained using standard H$\infty$ control theory. The obtained controller is delay-independent. We also obtain an observer for the interconnected system.

• Journal of Institute of Control, Robotics and Systems
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• v.15 no.8
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• pp.818-822
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• 2009

In this paper, we consider a decentralized observer design problem for fault detection in large-scaled linear time-invariant systems. Since the fault detection residual is desired to be sensitive on the fault, we use the H_ index performance criterion. Sufficient conditions for the existence of such an observer is presented in terms of linear matrix inequalities. Simulation results show the effectiveness of the proposed method.

• Journal of the Korean Mathematical Society
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• v.47 no.1
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• pp.41-62
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• 2010

In this article, we discuss a Grobner basis algorithm related to the stability of algebraic varieties in the sense of Geometric Invariant Theory. We implement the algorithm with Macaulay 2 and use it to prove the stability of certain curves that play an important role in the log minimal model program for the moduli space of curves.

• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.121-131
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• 2009

In this paper we examine the relation among law-invariant coherent risk measures with the Fatou property, distortion risk measures and spectral risk measures, and give a new proof of the relation among them. It is also shown that the spectral risk measure satisfies the monotonicity with respect to stochastic dominance and the comonotonic additivity.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.10a
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• pp.404-406
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• 2002

In this paper, the method of image feature extraction is proposed. This method employ the energy field analysis, outlier removal algorithm and ring projection. Using this algorithm, we achieve rotation-translation-scale invariant feature extraction. The force field are exploited to automatically locate the extrema of a small number of potential energy wells and associated potential channels. The image feature is acquired from relationship of local extrema using the ring projection method.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.331-339
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• 2012

In this paper, let Q be the real quaternion algebra which consists of all quaternionic numbers, and let G be the Lie group of all automorphisms of the algebra Q. Assume that g is an arbitrary given left invariant Riemannian metric on the Lie group G. Then, we obtain a necessary and sufficient condition for an automorphism of the group G to be harmonic.

• Kyungpook Mathematical Journal
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• v.53 no.4
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• pp.497-505
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• 2013

The noncommutative Singer-Wermer conjecture states that every derivation on a Banach algebra (possibly noncommutative) leaves primitive ideals of the algebra invariant. This conjecture is still an open question for more than thirty years. In this note, we approach this question via some sufficient conditions for the separating ideal of ${\phi}$-derivations to be nilpotent. Moreover, we show that the spectral boundedness of ${\phi}$-derivations implies that they leave each primitive ideal of Banach algebras invariant.