• Journal of the Chungcheong Mathematical Society
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• v.35 no.1
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• pp.77-83
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• 2022

In this paper we investigate the topological stability of induced homeomorphisms on a hyperspace. More precisely, we show that an expansive induced homeomorphism on a hyperspace is topologically stable. We also give examples and a diagram about implications to illustrate our results.

• Bulletin of the Korean Mathematical Society
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• v.32 no.1
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• pp.93-102
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• 1995

In [6], we introduce a hyperbolic homeomorphism on a compact metrizable space and show that a hyperbolic homeomorphism is topologically stable. The purpose of this paper is to study a necessary and sufficient condition for a homeomorphism to be hyperbolic. We get the following theorem.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.1
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• pp.61-66
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• 2017

In this paper, we introduce the notion of persistent actions of finitely generated groups on compact metric spaces and give a necessary condition for a persistent dynamical system to be topologically stable.

• Journal of the Chungcheong Mathematical Society
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• v.3 no.1
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• pp.1-11
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• 1990

The purpose of this paper is to study the chain recurrent sets under persistent dynamical systems, and give a necessary condition for a persistent dynamical system to be topologically stable. Moreover, we show that the various recurrent sets depend continuously on persistent dynamical system.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.439-449
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• 2021

In this paper, we introduce the notions of expansiveness, shadowing property and topological stability for group actions on metric spaces and give a version of Walters's stability theorem for group actions on locally compact metric spaces. Moreover, we show that if G is a finitely generated virtually nilpotent group and there exists g ∈ G such that if Tg is expansive and has the shadowing property, then T is topologically stable.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.1
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• pp.91-101
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• 2022

We study some properties of nonwandering set Ω(𝜙) and chain recurrent set CR(𝜙) for an expansive flow which has the POTP on a compact TVS-cone metric spaces. Moreover we shall prove a spectral decomposition theorem for an expansive flow which has the POTP on TVS-cone metric spaces.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.457-478
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• 2014

In this paper, a 3D autonomous system, which has only stable or non-hyperbolic equilibria but still generates chaos, is presented. This system is topologically non-equivalent to the original Lorenz system and all Lorenz-type systems. This motivates us to further study some of its dynamical behaviors, such as the local stability of equilibrium points, the Lyapunov exponent, the dissipativity, the chaotic waveform in time domain, the continuous frequency spectrum, the Poincar$\acute{e}$ map and the forming mechanism for compound structure of its special cases. Especially, with the help of the Project Method, its Hopf bifurcation of codimension one is in detailed formulated. Numerical simulation results not only examine the corresponding theoretical analytical results, but also show that this system possesses abundant and complex dynamical properties not solved theoretically, which need further attention.

• Bulletin of the Korean Chemical Society
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• v.32 no.9
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• pp.3372-3376
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• 2011

We have studied the relative stability and atomic structures of five $C_{20}X_2$ regioisomers obtained as diadducts of a $C_{20}$ cage (X = H, F, Cl, Br, and OH). All the regioisomers are geometric isomers, i.e., they differ in their spatial arrangement. Full-geometry optimizations of the regioisomers have been performed using the hybrid density-functional (B3LYP/6-31G(d, p)) method. Our results suggest that the cis-1 regioisomer (the 1,2-diadduct) is the most stable and that the second most stable is the trans-2 (1,13-diadduct) regioisomer, implying that the long-range interaction between the two adducts and the resonance effect are more pronounced than the diadduct-induced strain in the $C_{20}$ cage. The HOMO and LUMO characteristics of each regioisomer with the same symmetry of structural regioisomers except $C_{20}(OH)_2$ are topologically same. This suggests that by using an entirely different set of characteristic chemical reactions for each regioisomer, we can distinguish between the five regioisomers for each $C_{20}$ diadduct derivative.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.11
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• pp.2893-2912
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• 2013

The design of geometrically invariant watermarking is one of the most challenging work in digital image watermarking research area. To achieve the robustness to geometrical attacks, the inherent characteristic of an image is usually used. In this paper, a geometrically invariant image watermarking scheme using connected objects and gravity center is proposed. First, the gray-scale image is converted into the binary one, and the connected objects according to the connectedness of binary image are obtained, then the coordinates of these connected objects are mapped to the gray-scale image, and the gravity centers of those bigger objects are chosen as the feature points for watermark embedding. After that, the line between each gravity center and the center of the whole image is rotated an angle to form a sector, and finally the same version of watermark is embedded into these sectors. Because the image connectedness is topologically invariant to geometrical attacks such as scaling and rotation, and the gravity center of the connected object as feature points is very stable, the watermark synchronization is realized successfully under the geometrical distortion. The proposed scheme can extract the watermark information without using the original image or template. The simulation results show the proposed scheme has a good invisibility for watermarking application, and stronger robustness than previous feature-based watermarking schemes against geometrical attacks such as rotation, scaling and cropping, and can also resist common image processing operations including JPEG compression, adding noise, median filtering, and histogram equalization, etc.

• Journal of Korea Foundry Society
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• v.33 no.5
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• pp.215-225
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• 2013

The alloys required for fossil power plants are altered from stainless steel that has been used below $600^{\circ}C$ to Ni-based alloys that can operate at $700^{\circ}C$ for Hyper Super Critical (HSC) steam turbine. The IN740 alloy (Special Metals Co. USA) is proposed for improved rupture strength and corrosion resistance at high temperature. However, previous studies with experiments and simulations on stable phases at about $700^{\circ}C$ indicated the formation of the eta phase with the wasting of a gamma prime phase, which is the most important reinforced phase in precipitation hardened Ni alloys, and this resulted in the formation of precipitation free zones to decrease the strength. On the basis of thermodynamic calculation, the new Ni-based superalloy named LESS 1 (Low Eta Sigma Superalloy) was designed in this study to improve the strengthening effect and structure stability by depressing the formation of topologically close packed phases, especially sigma and eta phases at high temperature. A thermal exposure test was carried out to determine the microstructure stability of LESS 1 in comparison with IN740 at $800^{\circ}C$ for 300 hrs. The experimental results show that a needle-shaped eta phase was formed in the grin boundary and it grew to intragrain, and a precipitation free zone was also observed in IN740, but these defects were entirely controlled in LESS 1.