• 충청수학회지
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• 제34권1호
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• pp.77-84
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• 2021

Let f : [0, 1] → [0, 1] be a multimodal map with positive topological entropy. The dynamics of the renormalization operator for multimodal maps have been investigated by Daniel Smania. It is proved that the measure of maximal entropy for a specific category of Cr interval maps is unique.

• Elastomers and Composites
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• 제37권4호
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• pp.234-243
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• 2002

A general scheme of a rubber structure is proposed. Using the thermomechanical method(TMA), some changes in the molecular and topological structures for uncured and cured, and unfilled and filled rubbers during processing are shown. In our investigations as region it is understood a complex structure, which is expressed at the thermomechanical curve(TMC) as a zone differed from others in thermal expansion properties. This zone is between the noticed temperatures of relaxation transitions, usually on the level like those determined by DMTA at 1Hz. These regions, which shares, are not stable, and differ in molecular-weight distribution(MWD) of chain fragments between the junctions. Differences in dynamics of the formation of the molecular and topological structures of a vulcanizate are dependent on the rubber formulation, mixing technology and curing time. Some of characteristics of these regions correlate with mechanical properties of vulcanizates what is shown for NR rubbers containing ENR or CPE as a polymeric additive. It is well known that the state of order influences diffusivity of low-molecular substances into the polymer matrix. Because of this, the two topological amorphous regions should influence the distribution of the ingredients and resulting in rubber compounds' heterogeneity, and related properties of cured rubber. Investigation of this problem is expected to be, in the future, one of the essential factors in determining further improvement of polymeric materials properties by compounding with additives and in reprocessing of rubber scrap.

• 대한수학회논문집
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• 제4권2호
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• pp.209-216
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• 1989

• 대한수학회지
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• 제53권4호
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• pp.795-834
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• 2016

The main purpose of this paper is to propose a scheme of a proof of the nonsimpleness of the group $Homeo^{\Omega}$ ($D^2$, ${\partial}D^2$) of area preserving homeomorphisms of the 2-disc $D^2$. We first establish the existence of Alexander isotopy in the category of Hamiltonian homeomorphisms. This reduces the question of extendability of the well-known Calabi homomorphism Cal : $Diff^{\Omega}$ ($D^1$, ${\partial}D^2$)${\rightarrow}{\mathbb{R}}$ to a homomorphism ${\bar{Cal}}$ : Hameo($D^2$, ${\partial}D^2$)${\rightarrow}{\mathbb{R}}$ to that of the vanishing of the basic phase function $f_{\underline{F}}$, a Floer theoretic graph selector constructed in [9], that is associated to the graph of the topological Hamiltonian loop and its normalized Hamiltonian ${\underline{F}}$ on $S^2$ that is obtained via the natural embedding $D^2{\hookrightarrow}S^2$. Here Hameo($D^2$, ${\partial}D^2$) is the group of Hamiltonian homeomorphisms introduced by $M{\ddot{u}}ller$ and the author [18]. We then provide an evidence of this vanishing conjecture by proving the conjecture for the special class of weakly graphical topological Hamiltonian loops on $D^2$ via a study of the associated Hamiton-Jacobi equation.

• 대한수학회지
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• 제59권1호
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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.

• 대한수학회지
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• 제33권4호
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• pp.1115-1122
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• 1996

In study of the dynamics of a map f from a topological space X to itself, a central role is played by the various recursive properties of the points of X. One such property is periodicity. A weaker property is that of being nonwandering. Intermediate recursive properties include almost periodicity and recurrence.

• 충청수학회지
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• 제31권1호
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• pp.131-135
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• 2018

In this article, we deal with notion of idempotent in dynamical systems and prove that both closure function and orbital function are idempotent functions on the systems.

• 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.

• 전자공학회논문지C
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• 제34C권7호
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• pp.82-91
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• 1997

In this paper, we analyze the dynamics of langevine competitive learning neural network based on its fokker-plank equation. From the viewpont of the stochastic differential equation (SDE), langevine competitive learning equation is one of langevine stochastic differential equation and has the diffusin equation on the topological space (.ohm., F, P) with probability measure. We derive the fokker-plank equation from the proposed algorithm and prove by introducing a infinitestimal operator for markov semigroups, that the weight vector in the particular simplex can converge to the globally optimal point under the condition of some convex or pseudo-convex performance measure function. Experimental resutls for pattern recognition of the remote sensing data indicate the superiority of langevine competitive learning neural network in comparison to the conventional competitive learning neural network.

• 한국진공학회:학술대회논문집
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• 한국진공학회 2016년도 제50회 동계 정기학술대회 초록집
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• pp.139.2-139.2
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• 2016

Electrons and phonons in chalcogenide-based materials play are important factors in the performance of an optical data storage media and thermoelectric devices. However, the fundamental kinetics of carriers in chalcogenide materials remains controversial, and active debate continues over the mechanism responsible for carrier relaxation. In this study, we investigated ultrafast carrier dynamics in an multilayered $\{Sb(3{\AA})/Te(9{\AA})\}n$ thin film during the transition from the amorphous to the crystalline phase using optical pump terahertz probe spectroscopy (OPTP), which permits the relationship between structural phase transition and optical property transitions to be examined. Using THz-TDS, we demonstrated that optical conductance and carrier concentration change as a function of annealing temperature with a contact-free optical technique. Moreover, we observed that the topological surface state (TSS) affects the degree of enhancement of carrier lifetime, which is closely related to the degree of spin-orbit coupling (SOC). The combination of an optical technique and a proposed carrier relaxation mechanism provides a powerful tool for monitoring TSS and SOC. Consequently, the response of the amorphous phase is dominated by an electron-phonon coupling effect, while that of the crystalline structure is controlled by a Dirac surface state and SOC effects. These results are important for understanding the fundamental physics of phase change materials and for optimizing and designing materials with better performance in optoelectronic devices.