• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.95-108
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• 2020

The aim of this paper is to show that for the one-sided symbolic system, there exist an uncountable distributively chaotic set contained in the set of irregularly recurrent points and an uncountable distributively chaotic set in a sequence contained in the set of proper positive upper Banach density recurrent points.

• Communications of the Korean Mathematical Society
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• v.25 no.1
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• pp.97-104
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• 2010

The article is devoted to exhibit some general properties of strong chain recurrent set and strong chain transitive components for a continuous map f on a compact metric space X. We investigate the relation between the weak shadowing property and strong chain transitivity. It is shown that a continuous map f from a compact metric space X onto itself with the average shadowing property is strong chain transitive.

• The Pure and Applied Mathematics
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• v.5 no.1
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• pp.13-16
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• 1998

For continuous maps f of the circle to itself, we show that (1) every $\omega$-limit point is recurrent (or almost periodic) if and only if every $\omega$-limit set is minimal, (2) every $\omega$-limit set is almost periodic, then every $\omega$-limit set contains only one minimal set.

• 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 $0^+$.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.1029-1038
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• 2000

In this paper, we show that if x is a positively Lyapunov stable point of an expansive homeomorphism with the pseudo-orbit-tracing-property, then x is a periodic point or its positive limit set consists of only one periodic orbit, and their periods are predictable. We give a necessary and sufficient condition that a basic set is to be a sink or source. Also, we consider some dynamical properties of basic sets.

• 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.

• Communications for Statistical Applications and Methods
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• v.27 no.1
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• pp.37-46
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• 2020

Recurrent event data frequently occur in clinical studies, demography, engineering reliability and so on (Cook and Lawless, The Statistical Analysis of Recurrent Events, Springer, 2007). Sometimes, two or more different but related type of recurrent events may occur simultaneously. In this study, our interest is to estimate the covariate effect on bivariate recurrent event times with zero inflations. Such zero inflation can be related with susceptibility. In the context of bivariate recurrent event data, furthermore, such susceptibilities may be different according to the type of event. We propose a joint model including both two intensity functions and two cure rate functions. Bivariate frailty effects are adopted to model the correlation between recurrent events. Parameter estimates are obtained by maximizing the likelihood derived under a piecewise constant hazard assumption. According to simulation results, the proposed method brings unbiased estimates while the model ignoring cure rate models gives underestimated covariate effects and overestimated variance estimates. We apply the proposed method to a set of bivariate recurrent infection data in a study of child patients with leukemia.

• Journal of Institute of Control, Robotics and Systems
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• v.10 no.12
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• pp.1295-1304
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• 2004

In this paper, the Bayesian recurrent neural network is proposed to predict time series data. A neural network predictor requests proper learning strategy to adjust the network weights, and one needs to prepare for non-linear and non-stationary evolution of network weights. The Bayesian neural network in this paper estimates not the single set of weights but the probability distributions of weights. In other words, the weights vector is set as a state vector of state space method, and its probability distributions are estimated in accordance with the particle filtering process. This approach makes it possible to obtain more exact estimation of the weights. In the aspect of network architecture, it is known that the recurrent feedback structure is superior to the feedforward structure for the problem of time series prediction. Therefore, the recurrent neural network with Bayesian inference, what we call Bayesian recurrent neural network (BRNN), is expected to show higher performance than the normal neural network. To verify the proposed method, the time series data are numerically generated and various kinds of neural network predictor are applied on it in order to be compared. As a result, feedback structure and Bayesian learning are better than feedforward structure and backpropagation learning, respectively. Consequently, it is verified that the Bayesian reccurent neural network shows better a prediction result than the common Bayesian neural network.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.157-163
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• 2020

Conley introduced attracting sets and repelling sets for a flow on a topological space and showed that if f is a flow on a compact metric space, then 𝓡(f) = ⋂{A_U ∪ A*_U |U is a trapping region for f}. In this paper we introduce chain recurrent set, trapping region, attracting set and repelling set for a flow f on a TVS-cone metric space and prove that if f is a flow on a compact TVS-cone metric space, then 𝓡(f) = ⋂{A_U ∪ A*_U |U is a trapping region for f}.

• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.575-586
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• 2007

We introduce here notions of chain recurrent sets, attractors and its basins for general dynamical systems and prove important properties including (i) the chain recurrent set CR(f) of f on a metric space (X, d) is the complement of the union of sets B(A) -A as A varies over the collection of attractors and (ii) genericity of general dynamical systems.