• Title/Summary/Keyword: commensurable

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Coherent Understanding on Addition/Subtraction from the Viewpoint of Measuring (측정의 관점에서 본 덧.뺄셈의 통합적 이해)

  • Byun, Hee-Hyun
    • Journal of Educational Research in Mathematics
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    • v.19 no.2
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    • pp.307-319
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    • 2009
  • Current school mathematics introduces addition/subtraction between natural numbers, fractions, decimal fractions, and square roots, step-by-step in order. It seems that, however, school mathematics focuses too much on learning the calculation method of addition/subtraction between each stages of numbers, to lead most of students to understand the coherent principle, lying in addition/subtraction algorithm between real numbers in all. This paper raises questions on this problematic approach of current school mathematics, in learning addition/subtraction. This paper intends to clarify the fact that, if we recognize addition/subtraction between numbers from the viewpoint of 'measuring' and 'common measure', as Dewey did when he argued that the psychological origin of the concept of number was measuring, then we could find some common principles of addition/subtraction operation, beyond the superficial differences among algorithms of addition/subtraction between each stages of numbers. At the end, this paper suggests the necessity of improving the methods of learning addition/subtraction in current school mathematics.

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The General Mass Media System Theory -Based on Theories of Habermas, Luhmann, Delueze, Guattari, and Derrida (하버마스, 루만, 들뢰즈.가타리, 데리다의 이론을 통한 일반 대중매체 체계론의 제안)

  • Park, Daemin
    • Korean journal of communication and information
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    • v.67
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    • pp.119-151
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    • 2014
  • The absence of the commensurable general mass media system theory has been problematic in empirical communication studies. This study first suggests the static mass media system theory based on modified Habermas's two level society, and then develops the dynamic mass media system theory based on the boundary-agencement theory that synthesizes Luhmann's boundary theory and Delueze & Guattari's agencement theory. In the static mass media system theory, the mass media system interpenetrates other social subsystems and the life world as a part of the cultural system coordinated by generalized language media. In the dynamic mass media system theory, the mass media system is a boundary of all social subsystems. The mass media system also articulates its self-referential observations to other-referential observations from other subsystems, mediated interpenetrations between the social subsystems and the life world. Especially, performances in the mass media system deterritorizes social systems to the life world, and reterritorizes the life world to social systems. The general mass media system theory can provide commensurability for various empirical mass media system studies, and prevent biases when researchers choose research topics.

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WZ Cephei: A Dynamically Active W UMa-Type Binary Star

  • Jeong, Jang-Hae;Kim, Chun-Hwey
    • Journal of Astronomy and Space Sciences
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    • v.28 no.3
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    • pp.163-172
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    • 2011
  • An intensive analysis of 185 timings of WZ Cep, including our new three timings, was made to understand the dynamical picture of this active W UMa-type binary. It was found that the orbital period of the system has complexly varied in two cyclical components superposed on a secularly downward parabola over about 80y. The downward parabola, corresponding to a secular period decrease of $-9.{^d}97{\times}10^{-8}y^{-1}$, is most probably produced by the action of both angular momentum loss (AML) due to magnetic braking and mass-transfer from the massive primary component to the secondary. The period decrease rate of $-6.^{d}72{\times}10^{-8}y^{-1}$ due to AML contributes about 67% to the observed period decrease. The mass flow of about $5.16{\times}10^{-8}M_{\odot}y^{-1}$ from the primary to the secondary results the remaining 33% period decrease. Two cyclical components have an $11.^{y}8$ period with amplitude of $0.^{d}0054$ and a $41.^{y}3$ period with amplitude of $0.^{d}0178$. It is very interesting that there seems to be exactly in a commensurable 7:2 relation between their mean motions. As the possible causes, two rival interpretations (i.e., light-time effects (LTE) by additional bodies and the Applegate model) were considered. In the LTE interpretation, the minimum masses of $0.30M_{\odot}$ for the shorter period and $0.49M_{\odot}$ for the longer one were calculated. Their contributions to the total light were at most within 2%, if they were assumed to be main-sequence stars. If the LTE explanation is true for the WZ Cep system, the 7:2 relation found between their mean motions would be interpreted as a stable 7:2 orbit resonance produced by a long-term gravitational interaction between two tertiary bodies. In the Applegate model interpretation, the deduced model parameters indicate that the mechanism could work only in the primary star for both of the two period modulations, but could not in the secondary. However, we couldn't find any meaningful relation between the light variation and the period variability from the historical light curve data. At present, we prefer the interpretation of the mechanical perturbation from the third and fourth stars as the possible cause of two cycling period changes.