• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.177-182
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• 2018

The purpose of this paper is to present approximation of $C_0-sequentially$ equicontinuous semigroups on a sequentially complete locally convex space X.

• Journal of applied mathematics & informatics
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• v.37 no.3_4
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• pp.251-257
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• 2019

We study the orbit behaviours of recurrent, uniformly recurrent and Poisson stable points. we give conditons that a point is to be recurrent or uniformly recurrent by analyzing the behaviours of their orbits. Also, we study dynamical properties of equicontinuous points and points of characteristic $0^+$.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.707-716
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• 1999

In this pater we study the continuity of rotation numbers of liftings of circle maps with degree one. And apply our result to prove that a positively equicontinuous flow of homeomorphisms on the circle $S^1$ is topologically conjugate to a continuous flow of rotation maps.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.415-425
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• 1995

• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.47-51
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• 2019

The purpose of this paper is to present approximation of $C_0$-sequentially equicontinuous semigroups on a sequentially complete locally convex space X.

• Korean Journal of Mathematics
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• v.11 no.2
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• pp.161-167
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• 2003

The purpose of this paper is to study and characterize the notions of characteristic 0 and weakly almost periodicity in flows. In particular, we give sufficient conditions for the weakly almost periodic flow to be almost periodic.

• Communications for Statistical Applications and Methods
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• v.18 no.1
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• pp.71-77
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• 2011

In this paper, asymptotic results are investigated when a parametric transformation is applied to ARMA models. The conditions are determined to ensure the strong consistency and the asymptotic normality of maximum likelihood estimators and the correct coverage probability of the forecast interval obtained by the transformation and backtransformation approach.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.221-228
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• 2008

In this paper, we study the complexity of semigroup actions using complexity functions of open covers. The main results are as follows: (1) A dynamical system is equicontinuous if and only if any open cover has bounded complexity; (2) Weak-mixing implies scattering; (3) We get a criterion for the scattering property.

• Journal of the Korean Mathematical Society
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• v.46 no.2
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• pp.225-236
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• 2009

The equicontinuity and scattering properties of continuous semi-flows are studied on a compact metric space. The main results are obtained as follows: first, the complexity function defined by the spanning set is bounded if and only if the system is equicontinuous; secondly, if a continuous semi-flow is topologically weak mixing, then it is pointwise scattering; thirdly, several equivalent conditions for the time-one map of a continuous semi-flow to be scattering are presented; Finally, for a minimal continuous map it is shown that the "non-dense" requirement is unnecessary in the definition of scattering by using open covers.

• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.857-869
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• 2005

Let $(X,\;B,\;{\mu},\;T)$ be a dynamical system and (Y, A, v, S) be a factor. We investigate the relative sequence entropy of a partition of X via the maximal compact extension of (Y, A, v, S). We define relative sequence entropy pairs and using them, we find the relative topological ${\mu}-Kronecker$ factor over (Y, v) which is the maximal topological factor having relative discrete spectrum over (Y, v). We also describe the topological Kronecker factor which is the maximal factor having discrete spectrum for any invariant measure.