• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.8 no.2
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• pp.15-21
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• 2004

A Conjugate Gradiant (CG) method is proposed for unconstained optimization which is invariant to a nonlinear scaling of a strictly convex quadratic function. The technique has the same properties as the classical CG-method when applied to a quadratic function. The algorithm derived here is based on a logarithmic model and is compared to the standard CG method of Fletcher and Reeves [3]. Numerical results are encouraging and indicate that nonlinear scaling is promising and deserves further investigation.

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.91-97
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• 1993

In this article, we consider the case that S is a topologically complete subspace of $R^{k}$ , and that .GAMMA. is a set of monotone functions on S into S. It is obtained the sugficient condition for the existence of a unique invariant probability to which $P^{(n}$/(x,dy) converges exponentially fast in a metric stronger than the Kolmogorov's distance. This extends the earlier results of Bhattacharya and Lee (1988) who considered the case .GAMMA. a set of nondecreasing functions.tions.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.903-921
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• 2008

A continuous linear operator $T\;:\;X{\rightarrow}X$ is called hypercyclic if there exists an $x\;{\in}\;X$ such that the orbit ${T^nx}_{n{\geq}0}$ is dense. We consider the problem: given an operator $T\;:\;X{\rightarrow}X$, hypercyclic or not, is the restriction $T|y$ to some closed invariant subspace $y{\subset}X$ hypercyclic? In particular, it is well-known that any non-constant partial differential operator p(D) on $H({\mathbb{C}}^d)$ (entire functions) is hypercyclic. Now, if q(D) is another such operator, p(D) maps ker q(D) invariantly (by commutativity), and we obtain a necessary and sufficient condition on p and q in order that the restriction p(D) : ker q(D) $\rightarrow$ ker q(D) is hypercyclic. We also study hypercyclicity for other types of operators on subspaces of $H({\mathbb{C}}^d)$.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.42-45
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• 2003

This paper describes a new iris recognition method using shift-invariant subbands. First an iris image is preprocessed to compensate the variation of the iris image. Then, the preprocessed iris image is decomposed into multiple subbands using a shift invariant wavelet transform. The best subband among them, which have rich information for various iris pattern and robust to noises, is selected for iris recognition. The quantized pixels of the best subband yield the feature representation. Experimentally, we show that the proposed method produced superb performance in iris recognition.

• The Transactions of the Korean Institute of Electrical Engineers P
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• v.53 no.4
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• pp.175-182
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• 2004

This paper presents a new method for finding the Block Pulse series coefficients, deriving the Block Pulse integration operational matrices and generalizing the integration operational matrices which are necessary for the control fields using the Block Pulse functions. In order to apply the Block Pulse function technique to the problems of state estimation or parameter identification more efficiently, it is necessary to find the more exact value of the Block Pulse series coefficients and integral operational matrices. This paper presents the method for improving the accuracy of the Block Pulse series coefficients and derives generalized integration operational matrix and applied the matrix to the analysis of linear time-invariant system.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.813-826
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• 2005

Regarding all particles at a fixed site as a cluster, the size of the largest cluster under the zero range invariant measures is well studied by Jeon et al.[5] for the case of density one. Here, the density of the finite zero-range process is given by the ratio between the number m of particles and the number n of sites. In this paper, we study the lower density case, i.e., the case m = o(n). Especially, when m ~ $n^{\beta}$,0 < ${\beta}$ < 1, we show that there is an interesting cutoff point around $\beta$ = 1/2.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1193-1200
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• 2013

The center of the Lie group $SU(n)$ is isomorphic to $\mathbb{Z}_n$. If $d$ divides $n$, the quotient $SU(n)/\mathbb{Z}_d$ is also a Lie group. Such groups are locally isomorphic, and their Weyl groups $W(SU(n)/\mathbb{Z}_d)$ are the symmetric group ${\sum}_n$. However, the integral representations of the Weyl groups are not equivalent. Under the mod $p$ reductions, we consider the structure of invariant rings $H^*(BT^{n-1};\mathbb{F}_p)^W$ for $W=W(SU(n)/\mathbb{Z}_d)$. Particularly, we ask if each of them is a polynomial ring. Our results show some polynomial and non-polynomial cases.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.177-183
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• 2006

The purpose of this paper is to introduce an L-metrical non-linear connection $N_j^{*i}$ and investigate a conformal change in the Finsler space with $({\alpha},\;{\beta})-metric$. The (v)h-torsion and (v)hvtorsion in the Finsler space with L-metrical connection $F{\Gamma}^*$ are obtained. The conformal invariant connection and conformal invariant curvature are found in the above Finsler space.

• Korean Journal of Computational Design and Engineering
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• v.19 no.2
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• pp.119-128
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• 2014

Computing the natural-looking interpolation of different shapes is a fundamental problem of computer graphics. It is proved by some researchers that such an interpolation can be achieved by pursuing the isometry. In this paper, a novel coordinate system that is invariant under isometries is defined. The coordinate system can easily be converted from the global vertex coordinates. Furthermore, the global coordinates can be efficiently recovered from the new coordinates by simply solving two sparse least-squares problems. Since the proposed coordinate system is invariant under isometries, then transformations such as global rigid trans-formations, articulated posture deformations, or any other isometric deformations, do not change the coordinate values. Therefore, shape interpolation can be done in this framework without being affected by the distortions caused by the isometry.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.132-137
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• 2004

In this work, effects of hyper-elastic rubber material properties on the indentation load-deflection curve and subindenter deformation are first examined via [mite element (FE) analyses. An optimal data acquisition spot is selected, which features maximum strain energy density and negligible frictional effect. We then contrive two normalized functions. which map an indentation load vs. deflection curve into a strain energy density vs. first invariant curve. From the strain energy density vs. first invariant curve, we can extract the rubber material properties. This new spherical indentation approach produces the rubber material properties in a manner more effective than the common uniaxial tensile/compression tests. The indentation approach successfully measures the rubber material properties and the corresponding nominal stress.strain curve with an average error less than 3%.