• 충청수학회지
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• 제32권4호
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• pp.509-524
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• 2019

Let Act(G, X) be the set of all continuous actions of a finitely generated group G on a compact metric space X. In this paper, we study the concepts of topologically stable points and continuous shadowable points of a group action T ∈ Act(G, X). We show that if T is expansive then the set of continuous shadowable points is contained in the set of topologically stable points.

• 충청수학회지
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• 제28권4호
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• pp.647-651
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• 2015

Let (X, d) be a compact metric space, and let $f:X{\rightarrow}X$ be a continuous map. We consider that if a positively continuum-wise expansiveness continuous map f has the positively shadowing property in the nonwandering set, then the topological entropy is positive.

• 대한수학회논문집
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• 제25권2호
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• pp.257-262
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• 2010

Let f be a $C^2$-diffeomorphism on a closed surface which satisfies the Axiom A. Then f is in the $C^2$-interior of the set of all diffeomorphisms having the inverse shadowing property with respect to the class of the continuous methods if and only if f satisfies the strong transversality condition.

• 대한수학회논문집
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• 제21권2호
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• pp.355-361
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• 2006

We prove that if a continuous surjective map f on a compact metric space X has the average shadowing property, then every point x is chain recurrent. We also show that if a homeomorphism f has more than two fixed points on $S^1$, then f does not satisfy the average shadowing property. Moreover, we construct a homeomorphism on a circle which satisfies the shadowing property but not the average shadowing property. This shows that the converse of the theorem 1.1 in [6] is not true.

• 충청수학회지
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• 제35권2호
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• pp.171-176
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• 2022

In this article, we investigate the transitivity and chain transitivity on multi-valued dynamical systems. For compact-valued continuous dynamics, we prove that the notion of transitivity is expressed by the notions of the shadowing property and chain transitivity under locally maximal condition.

• 대한수학회논문집
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• 제35권4호
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• pp.1309-1318
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• 2020

In this paper we extend the concept of topological stability from continuous maps to the corresponding induced maps and prove that a continuous map is topologically stable if and only if its induced map also is topologically stable.

• Nuclear Engineering and Technology
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• 제55권3호
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• pp.1084-1096
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• 2023

On-the-fly(OTF) generation of Spectral Superhomogenization(SSPH) factors is analyzed in the multigroup(MG) whole core calculation employing pin-wise continuous energy(CE) slowing-down solutions. The motivation for the work is to avoid the huge computing time required for the generation of a parametrized SSPH factor library(PSSL) which is used to resolve the angular dependency of MG resonance cross sections, and also to exploit the advantage of flexible choice of a MG structure by using CE slowing-down solutions. Two pin-wise CE slowing-down methods, the equivalent Dancoff cell method and the shadowing effect correction method, are evaluated with the OTF SSPH method. The effectiveness of the OTF SSPH method is examined for various simplified and realistic core problems with various MG structures. It is demonstrated that the computing time overhead of this method is negligible whereas the solution accuracy is considerably enhanced.

• 대한수학회논문집
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• 제34권3호
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• pp.951-965
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• 2019

Let $f:X{\rightarrow}X$ be a continuous map on a compact metric space (X, d) and for an arbitrary $x{\in}X$, $${\mathcal{SC}}_d(x,f):=\{y{\mid}x{\text{ can be strong }}d-{\text{chain to }}y\}$$. We give an example to show that ${\mathcal{SC}}_d(x,f)$ is dependent on the metric d on X but it is a closed and f-invariant set. We prove that if ${\mathcal{SC}}_d(x,f){\supseteq}{\Omega}(f)$ or f has the asymptotic-average shadowing property, then ${\mathcal{SC}}_d(x,f)=X$. Also, we show that if f has the shadowing property, then ${\lim}\;{\sup}_{n{\in}{\mathbb{N}}}\{f^n\}={\mathcal{SC}}_d(f)$ where ${\mathcal{SC}}_d(f)=\{(x,y){\mid}y{\in}{\mathcal{SC}}_d(x,f)\}$. For each $n{\in}{\mathbb{N}}$, we give an example in which ${\mathcal{SCR}}_d(f^n){\neq}{\mathcal{SCR}}_d(f)$. In spite of it, we prove that if $f^{-1}:(X,d){\rightarrow}(X,d)$ is an equicontinuous map, then ${\mathcal{SCR}}_d(f^n)={\mathcal{SCR}}_d(f)$ for all $n{\in}{\mathbb{N}}$.

• Nonlinear Functional Analysis and Applications
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• 제27권4호
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• pp.709-730
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• 2022

We consider the nonlinear matrix equation (NMEs) of the form 𝓤 = 𝓠 + Σ^k_i=1 𝓐^*_iℏ(𝓤)𝓐_i, where 𝓠 is n × n Hermitian positive definite matrices (HPDS), 𝓐₁, 𝓐₂, . . . , 𝓐_m are n × n matrices, and ~ is a nonlinear self-mappings of the set of all Hermitian matrices which are continuous in the trace norm. We discuss a sufficient condition ensuring the existence of a unique positive definite solution of a given NME and demonstrate this sufficient condition for a NME 𝓤 = 𝓠 + 𝓐^*₁(𝓤²/900)𝓐₁ + 𝓐^*₂(𝓤²/900)𝓐₂ + 𝓐^*₃(𝓤²/900)𝓐₃. In order to do this, we define 𝓕𝓖_w-contractive conditions and derive fixed points results based on aforesaid contractive condition for a mapping in extended Branciari b-metric distance followed by two suitable examples. In addition, we introduce weak well-posed property, weak limit shadowing property and generalized Ulam-Hyers stability in the underlying space and related results.

• 한국재난정보학회 논문집
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• 제9권4호
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• pp.439-448
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• 2013

2013년 3월 22일부터 시행된 개정 <경범죄처벌법>은, 제3조 제1항 제41호에 "지속적괴롭힘"이라는 표제로 "상대방의 명시적 의사에 반하여 지속적으로 접근을 시도하여 면회 또는 교제를 요구하거나 지켜보기, 따라다니기, 잠복하여 기다리기 등의 행위를 반복"하는 것을 스토킹 행위로 규정하였다. 이러한 스토킹 행위의 가해자에게는 <경범죄처벌법 시행령>에 따라 8만원의 범칙금이 부과되고 있다. 그러나 나날이 교묘해지고 다양해지는 스토킹 범죄의 심각성에 비해 현행 <경범죄처벌법>의 적용이 과연 실효성이 있는가의 문제가 존재한다. 스토킹을 직접적으로 규제하고 있는 현행 <경범죄처벌법>이 가지는 한계점을 극복하고 스토킹 범죄에 보다 적절히 대응하여야 할 것이다.