• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.821-829
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• 2013

Let f be a diffeomorphism of a closed $C^{\infty}$ manifold M, and let ${\Lambda}{\subset}M$ be a closed f-invariant set. We show that if $f{\mid}_{\Lambda}$ is robustly chain transitive with shadowing, then ${\Lambda}$ is the hyperbolic homoclinic class.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.257-271
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• 2016

In this paper, we compute the trace field of C(2, s), the complement of two component chain link with s left half twists in ${\mathbb{S}}^3$, for every s. As a result, for every $n{\in}{\mathbb{N}}{\backslash}\{1\}$, we can find $s{\in}{\mathbb{Z}}$ such that the degree of the trace field of C(2, s) is n. We also prove that if for fixed p, the degree of the trace field of C(p, s) runs over ${\mathbb{N}}{\backslash}\{1\}$, then p is contained in {1, 2, 4, 8}.

• Journal of the Korean Mathematical Society
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• v.59 no.1
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• pp.105-127
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• 2022

It is known that the maximal invariant set of a continuous iterative dynamical system in a compact Hausdorff space is equal to the intersection of its forward image sets, which we will call the first minimal image set. In this article, we investigate the corresponding relation for a class of discontinuous self maps that are on the verge of continuity, or topologically almost continuous endomorphisms. We prove that the iterative dynamics of a topologically almost continuous endomorphisms yields a chain of minimal image sets that attains a unique transfinite length, which we call the maximal invariance order, as it stabilizes itself at the maximal invariant set. We prove the converse, too. Given ordinal number ξ, there exists a topologically almost continuous endomorphism f on a compact Hausdorff space X with the maximal invariance order ξ. We also discuss some further results regarding the maximal invariance order as more layers of topological restrictions are added.

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.127-144
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• 2009

Let f be a diffeomorphism of a compact $C^{\infty}$ manifold, and let p be a hyperbolic periodic point of f. In this paper we introduce the notion of $C^1$-stable inverse shadowing for a closed f-invariant set, and prove that (i) the chain recurrent set $\cal{R}(f)$ of f has $C^1$-stable inverse shadowing property if and only if f satisfies both Axiom A and no-cycle condition, (ii) $C^1$-generically, the chain component $C_f(p)$ of f associated to p is hyperbolic if and only if $C_f(p)$ has the $C^1$-stable inverse shadowing property.

• Communications of the Korean Mathematical Society
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• v.14 no.1
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• pp.1-12
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• 1999

The faithful bi-module \ulcornerM\ulcorner with its endomorphism ring End\ulcorner(M) such that M\ulcorner is flat (in other words, End\ulcorner(M)-flat, or endo-flat)and with a commutative ring R containing an identity has been studied in this paper. The chain conditions of a faithful endo-flat module \ulcornerM relative to those of the endomorphism ring End\ulcorner(M) having the zero annihilator of each non-zero endomorphism are studied.

• Proceedings of the IEEK Conference
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• 2000.09a
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• pp.375-378
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• 2000

In this paper, we propose a novo] content-based image retrieval system using both Hidden Markov Model(HMM) and an improved chain code. The Gaussian Mixture Model(GMM) is applied to statistically model a color information of the image, and Deterministic Annealing EM(DAEM) algorithm is employed to estimate the parameters of GMM. This result is used to segment the given image. We use an improved chain code, which is invariant to rotation, translation and scale, to extract the feature vectors of the shape for each image in the database. These are stored together in the database with each HMM whose parameters (A, B, $\pi$) are estimated by Baum-Welch algorithm. With respect to feature vector obtained in the same way from the query image, a occurring probability of each image is computed by using the forward algorithm of HMM. We use these probabilities for the image retrieval and present the highest similarity images based on these probabilities.

• Journal of Acupuncture Research
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• v.20 no.3
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• pp.104-116
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• 2003

목적 : 시스테인 단백분해 효소인 cathepsin는 인간과 생쥐의 항원제시세포에서 II형 주적합항원 불변사슬(MHC class II invariant chain)의 분해에 관여한다. 본 연구는 녹용 약침액이 류마티스 관절염 생쥐 모델의 골조직(연골과 활액) 유래 cathepsin 활성에 미치는 영향을 검정하였다. 방법 : 관절염 동물모델은 BALb/c계 생쥐를 생후 3일에 흉선 적출(3d-Tx)을 하여 만들었다. 동물모델의 골조직, 임파절세포, 비장 등을 녹용처치군과 대조군으로 나누어 cathepsin의 활성도 및 자가항원 특이(C-II-specific) T-세포의 활성도를 비교 분석하였다. 결과 : 각 장기에서 cathepsin S의 활성은 녹용약침 처치군에서 농도 의존적으로 유의성 있게 억제되었고, T-세포 특이 자가항원반응은 녹용약침 처치군의 임파절 세포에서 유의성있게 억제되었다. 그리고 T-세포 특이 자가항원 반응의 불활성화에는 녹용 10~20ug/ml의 용량으로 충분하였다. 결론 : 이러한 실험결과는 녹용 약침액이 cathepsin S를 선택적으로 억제시켜 류마티스 관절염과 같은 자가면역 질환에 유효한 치료약물로 사용될 수 있음을 시사한다.

• Journal of the Korean Mathematical Society
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• v.46 no.2
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• pp.363-447
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• 2009

The author previously defined the spectral invariants, denoted by $\rho(H;\;a)$, of a Hamiltonian function H as the mini-max value of the action functional ${\cal{A}}_H$ over the Novikov Floer cycles in the Floer homology class dual to the quantum cohomology class a. The spectrality axiom of the invariant $\rho(H;\;a)$ states that the mini-max value is a critical value of the action functional ${\cal{A}}_H$. The main purpose of the present paper is to prove this axiom for nondegenerate Hamiltonian functions in irrational symplectic manifolds (M, $\omega$). We also prove that the spectral invariant function ${\rho}_a$ : $H\;{\mapsto}\;\rho(H;\;a)$ can be pushed down to a continuous function defined on the universal (${\acute{e}}tale$) covering space $\widetilde{HAM}$(M, $\omega$) of the group Ham((M, $\omega$) of Hamiltonian diffeomorphisms on general (M, $\omega$). For a certain generic homotopy, which we call a Cerf homotopy ${\cal{H}}\;=\;\{H^s\}_{0{\leq}s{\leq}1}$ of Hamiltonians, the function ${\rho}_a\;{\circ}\;{\cal{H}}$ : $s\;{\mapsto}\;{\rho}(H^s;\;a)$ is piecewise smooth away from a countable subset of [0, 1] for each non-zero quantum cohomology class a. The proof of this nondegenerate spectrality relies on several new ingredients in the chain level Floer theory, which have their own independent interest: a structure theorem on the Cerf bifurcation diagram of the critical values of the action functionals associated to a generic one-parameter family of Hamiltonian functions, a general structure theorem and the handle sliding lemma of Novikov Floer cycles over such a family and a family version of new transversality statements involving the Floer chain map, and many others. We call this chain level Floer theory as a whole the Floer mini-max theory.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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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 $n{\in}{\mathbb{N}}$.

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.541-550
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• 2003

We consider the generalized autoregressive model with conditional heteroscedasticity process(GARCH). It is proved that if (equation omitted) β/sub i/ < 1, then there exists a unique invariant initial distribution for the Markov process emdedding the given GARCH process. Geometric ergodicity, functional central limit theorems, and a law of large numbers are also studied.