• Journal of the Chungcheong Mathematical Society
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• v.17 no.2
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• pp.137-145
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• 2004

We give characterization of ${\Omega}$-stable diffeomorphisms via the notions of weak inverse shadowing. More precisely, it is proved that the $C^1$ interior of the set of diffeomorphisms with the weak inverse shadowing property with respect to the class $\mathcal{T}_h$ coincides with the set of ${\Omega}$-stable diffeomorphisms.

• YAKHAK HOEJI
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• v.41 no.3
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• pp.298-304
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• 1997

Molecular mechanics and conformation search methods were carried oyt to investigate the relationship between conformations and thromboxane synthetase ingibitory activities of om ega-pyridylalkenoic acids. The initial geometries of ${\omega}$-pyridylalkenoic acids and heme part of cytochrome P-450 were obtained from MM+ geometry optimization. The bond lenths and angles were not varied by step during the conformation searching. Stable conformers of some ${\omega}$-pyridylalkenoic acids were obtained by comformational search method. The distances were 8.5~10.8 ${\AA}$- between N atom at 3-position of pyridine ring and C atom at carboxylic group of stable ${\omega}$-pyridylalkenoic acids. The conformations of ${\omega}$-pyridylalkenoic acids and heme part complex were determined by same method. In theses structures, benzene ring and ethylene group in ${\omega}$-pyridylalkenoic acids are making the structure more rigid and increase inhbitory activity. The electron donating groups in C atom shich is connected to pyridine ring also increase activity.

• Journal of the Chungcheong Mathematical Society
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• v.5 no.1
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• pp.65-74
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• 1992

In this note, we show that the ${\omega}$-limit mapping is continuous and the Lipschitz constants vary continuously if the flow (x, ${\pi}$) is Lipschitz stable. Moreover we analyse the ${\omega}$-limit sets under the generalized locally Lipschitz stable flows.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2001.05a
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• pp.207-212
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• 2001

In this paper, a method to be able to decide the possible maximum gain of P, PI control for the retarded processes under stable condition is proposed. At first, adjustable parameter set causing stability limit are obtained based on the frequency domain condition which makes the roots of transfer function locate on the $j\omega$ axis. And the cut-in frequency $\omega{_p}$ to bring the parameter set to P control from PI control is derived by an equation with 2 parameters L and $T_m$ given, then $\omega{_p}$ is used to compute the maximum gain with stable condition. For the calculation, the controlled process of first order system with time delay element is introduced and all parameters are presumed to be time invariant.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.249-254
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• 2000

We give an easy proof of the fact that every noncommutative torus $A_{\omega}$ is stably isomorphic to the noncommutative torus $C(\widehat{S\omega}){\;}\bigotimes{\;}A_p$ which hasa trivial bundle structure. It is well known that stable isomorphism of two separable $C^{*}-algebras$ is equibalent to the existence of eqivalence bimodule between the two stably isomorphic $C^{*}-algebras{\;}A_{\omega}$ and $C(\widehat{S\omega}){\;}\bigotimes{\;}A_p$.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.165-171
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• 2014

Let M be a manifold with a volume form ${\omega}$ and $f:M{\rightarrow}M$ be a diffeomorphism of class 𝒞$^1$ that preserves ${\omega}$. We prove that if M is almost bounded for the diffeomorphism f, then M is chain recurrent. Moreover, we get that Lagrange stable volume-preserving manifolds are also chain recurrent.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.519-525
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• 2008

Let f be a diffeomorphisms of a compact $C^{\infty}$ manifold, and let p be a hyperbolic periodic point of f. In this paper, we prove that if generically, f is tame diffeomorphims then the following conditions are equivalent: (i) f is ${\Omega}$-stable, (ii) f has the $C^1$-stable shadowing property (iii) f has the $C^1$-stable inverse shadowing property.

• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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• pp.199-209
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• 1994

In this paper, we show that a persistent dynamical system is structurally stable with respect to $E_{\alpha}$(X) for every ${\alpha}$ > 0 if it is expansive. Also, we prove that a homeomorphism$ f:{\Omega}(f){\rightarrow}{\Omega}(f)$ has the semi-shadowing property then so does $f:\overline{C(f)}{\rightarrow}\overline{C(f)}$.

• Journal of Advanced Marine Engineering and Technology
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• v.25 no.5
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• pp.1086-1090
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• 2001

In this paper, a method deciding the permissible gains of the P and PT controllers for a retarded process under stable condition is proposed. For analysis, the controlled process is assumed to be first-order system with time delay. At first, the adjustable parameter sets causing stability limit are obtained based on the frequency domain condition which makes the roots of the characteristic equation locate on the imaginary axis. And the cut-in frequency ${\omega}_p$ to bring the parameter set to P control from PI control is derived is derived in terms of L and $T_m$ then ${\omega}_p$ is used to compute the maximum gain with stable condition. The results indicate that the permissible controller gains can be described by a unique if parameters L and $T_m$ are know.

• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1131-1142
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• 2018

A notion of measure expansivity for homeomorphisms was introduced by Morales recently as a generalization of expansivity, and he obtained many interesting dynamic results of measure expansive homeomorphisms in [8]. In this paper, we introduce a concept of weak measure expansivity for homeomorphisms which is really weaker than that of measure expansivity, and show that a diffeomorphism f on a compact smooth manifold is $C^1$-stably weak measure expansive if and only if it is ${\Omega}$-stable. Moreover we show that $C^1$-generically, if f is weak measure expansive, then f satisfies both Axiom A and the no cycle condition.