• 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.51 no.4
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• pp.837-851
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• 2014

We consider ${\omega}$-chaos as defined by S. H. Li in 1993. We show that c-dense ${\omega}$-scrambled sets are present in every transitive system with two-sided limit shadowing property (TSLmSP) and that every transitive map on topological graph has a dense Mycielski ${\omega}$-scrambled set. As a preliminary step, we provide a characterization of dynamical properties of maps with TSLmSP.

• Management Science and Financial Engineering
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• v.18 no.1
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• pp.49-53
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• 2012

A novel method of transient stability analysis is presented in this paper. The proposed method extracts data points near the basin-of-attraction boundary and then builds a support vector machine (SVM) model learned from the generated data. The constructed SVM classifier has been shown to reduce dramatically the conservativeness of the estimated basin of attraction.

• Honam Mathematical Journal
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• v.40 no.2
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• pp.265-280
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• 2018

In this study, we firstly define equations of motion based on the traditional model Newtonian mechanics in terms of the Frenet frame adapted to the trajectory of the moving particle in Lie groups. Then, we compute energy on the moving particle in resultant force field by using geometrical description of the curvature and torsion of the trajectory belonging to the particle. We also investigate the relation between energy on the moving particle in different force fields and energy on the particle in Frenet vector fields.

• Journal of the Korean Society for Precision Engineering
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• v.1 no.3
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• pp.52-70
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• 1984

This paper presents a micro-computer simulation package for the various vibratory systems. The Package consists of 10 programs which describe the dynamical characteristics of the vibratory system. The programs have been written in BASIC (Appoesoft) language and programmed on the 6502 CPU with 48 KRAM. This simulation package is stored in 5 $^1/_4$ inch floppy disk. The user requires no simulation expertise on the part of designer. Through a process of disk operation, the user can easily under- stand how to use this package.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.583-599
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• 2018

In this paper, we are concerned with the existence of random dynamics for stochastic non-autonomous reaction-diffusion equations driven by a Wiener-type multiplicative noise defined on the unbounded domains.

• Bulletin of the Korean Chemical Society
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• v.6 no.5
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• pp.295-299
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• 1985

An approximate solution of the Fokker-Planck equation with the nonlinear drift term due to a Schlogl model is obtained and the result is compared with the methods proposed by Suzuki. Also the effect of nonlinearity on the correlation length at the stable steady state is studied.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.265-281
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• 2021

In the kneading theory developed by Milnor and Thurston, it is proved that the kneading matrix and the kneading determinant associated with a continuous piecewise monotone map are invariant under orientation-preserving conjugacy. This paper considers the problem for orientation-reversing conjugacy and proves that the former is not an invariant while the latter is. It also presents applications of the result towards the computational complexity of kneading matrices and the classification of maps up to topological conjugacy.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.3
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• pp.339-349
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• 2020

Let P ⋊ ℕ^x be a semidirect product of an additive semigroup P = {0, 2, 3, ⋯ } by a multiplicative positive natural numbers semigroup ℕ^x. We consider a covariant semigroup C^∗-algebra 𝓣(P ⋊ ℕ^x) of the semigroup P ⋊ ℕ^x. We obtain the condition that a state on 𝓣(P ⋊ ℕ^x) can be a ground state of the natural C^∗-dynamical system (𝓣(P ⋊ ℕ^x), ℝ, σ).

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.365-382
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• 2023

In this paper we prove the existence and uniqueness of solution of stochastic fractional neutral differential equations with Gaussian noise or Lévy noise by using the Picard-Lindelöf successive approximation scheme. Further stability results of nonlinear stochastic fractional dynamical system with Gaussian and Lévy noises are established. Examples are provided to illustrate the theoretical results.