• Title, Summary, Keyword: limit set

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A NOTE ON MINIMAL SETS OF THE CIRCLE MAPS

  • Yang, Seung-Kab;Min, Kyung-Jin
    • 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.

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A Historical Study on the Interaction of the Limit-the Infinite Set and Its Educational Implications (극한과 무한집합의 상호작용과 그 교육적 시사점에 대한 역사적 연구)

  • Park, Sun-Yong
    • Journal for History of Mathematics
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    • v.31 no.2
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    • pp.73-91
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    • 2018
  • This study begins with the awareness of problem that the education of mathematics teachers has failed to link the limit and the infinite set conceptually. Thus, this study analyzes the historical and reciprocal development of the limit and the infinite set, and discusses how to improve the education of these concepts and their relation based on the outcome of this analysis. The results of the study confirm that the infinite set is the historical tool of linking the limit and the real numbers. Also, the result shows that the premise of 'the component of the straight line is a point.' had the fundamental role in the construction of the real numbers as an arithmetical continuum and that the moral certainty of this premise would be obtained through a thought experiment using an infinite set. Based on these findings, several proposals have been made regarding the teacher education of awakening someone to the fact that 'the theoretical foundation of the limit is the real numbers, and it is required to introduce an infinite set for dealing with the real numbers.' in this study. In particular, by presenting one method of constructing the real numbers as an arithmetical continuum based on a thought experiment about the component of the straight line, this study opens up the possibility of an education that could get the limit values psychologically connected to the infinite set in overcoming the epistemological obstacle related to the continuum concept.

MP2 Basis Set Limit Binding Energy Estimates of Hydrogen-bonded Complexes from Extrapolation-oriented Basis Sets

  • Park, Young-Choon;Lee, Jae-Shin
    • Bulletin of the Korean Chemical Society
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    • v.28 no.3
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    • pp.386-390
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    • 2007
  • By use of a simple two-point extrapolation scheme estimating the correlation energies of the molecules along with the basis sets specifically targeted for extrapolation, we have shown that the MP2 basis set limit binding energies of large hydrogen-bonded complexes can be accurately predicted with relatively small amount of computational cost. The basis sets employed for computation and extrapolation consist of the smallest correlation consistent basis set cc-pVDZ and another basis set made of the cc-pVDZ set plus highest angular momentum polarization functions from the cc-pVTZ set, both of which were then augmented by diffuse functions centered on the heavy atoms except hydrogen in the complex. The correlation energy extrapolation formula takes the (X+1)-3 form with X corresponding to 2.0 for the cc-pVDZ set and 2.3 for the other basis set. The estimated MP2 basis set limit binding energies for water hexamer, hydrogen fluoride pentamer, alaninewater, phenol-water, and guanine-cytosine base pair complexes of nucleic acid by this method are 45.2(45.9), 36.1(37.5), 10.9(10.7), 7.1(6.9), and 27.6(27.7) kcal/mol, respectively, with the values in parentheses representing the reference basis set limit values. A comparison with the DFT results by B3LYP method clearly manifests the effectiveness and accuracy of this method in the study of large hydrogen-bonded complexes.

ON POINTS OF ZERO CHARACTERISTIC PROPERTIES IN DYNAMICAL SYSTEMS

  • Koo, Ki-Shik
    • Communications of the Korean Mathematical Society
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    • v.19 no.2
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    • pp.329-336
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    • 2004
  • In this paper, we study relationships between zero characteristic properties and minimality of orbit closures or limit sets of points. Also, we characterize the set of points of zero characteristic properties. We show that the set of points of positive zero characteristic property in a compact spaces X is the intersection of negatively invariant open subsets of X.

ON ORDINALS

  • Chung, Se Hwa
    • Journal of the Chungcheong Mathematical Society
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    • v.24 no.4
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    • pp.675-686
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    • 2011
  • The aim of this paper is two fold: One of them is to introduce a formal definition of ordinals which is equivalent to Neumann's definition without assuming the axiom of regularity. The other is to introduce the weak transfinite set and show that the weak transfinite set is a transfinite limit ordinal.

CONFORMAL DENSITY OF VISIBILITY MANIFOLD

  • Kim, Hyun-Jung
    • Bulletin of the Korean Mathematical Society
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    • v.38 no.1
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    • pp.211-222
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    • 2001
  • In this paper, we prove the existence and uniqueness of a $\delta(\Gamma)$-conformal density on the limit set of $\Gamma$ acting on visibility manifold H for a Fuchsian group $\Gamma$.

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ON ω-LIMIT SETS AND ATTRACTION OF NON-AUTONOMOUS DISCRETE DYNAMICAL SYSTEMS

  • Liu, Lei;Chen, Bin
    • Journal of the Korean Mathematical Society
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    • v.49 no.4
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    • pp.703-713
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    • 2012
  • In this paper we study ${\omega}$-limit sets and attraction of non-autonomous discrete dynamical systems. We introduce some basic concepts such as ${\omega}$-limit set and attraction for non-autonomous discrete system. We study fundamental properties of ${\omega}$-limit sets and discuss the relationship between ${\omega}$-limit sets and attraction for non-autonomous discrete dynamical systems.

ON THE SOME PROPERTIES OF THE LIMITS SETS

  • Yeom, Seung-Wha;Min, Kyung-Jin
    • The Pure and Applied Mathematics
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    • v.3 no.2
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    • pp.123-129
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    • 1996
  • In this paper, we investigate the properties of various limit sets. In particular, we study the relationship between the recurrent set and special $\gamma$-limit set. And also we show that if $\chi$ is not almost periodic, then $\chi$ is special a-limit.

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