• Title/Summary/Keyword: infinite divisibility

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REMARKS ON GAUSSIAN OPERATOR SEMI-STABLE DISTRIBUTIONS

  • Chae, Hong Chul;Choi, Gyeong Suk
    • Korean Journal of Mathematics
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    • v.8 no.2
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    • pp.111-119
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    • 2000
  • For a linear operator Q from $R^d$ into $R^d$. ${\alpha}$ > 0 and 0 < $b$ < 1, the Gaussian (Q, $b$, ${\alpha}$)-semi-stability of probability measures on $R^d$ is investigated.

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CHARACTERIZATION OF STRICTLY OPERATOR SEMI-STABLE DISTRIBUTIONS

  • Choi, Gyeong-Suk
    • Journal of the Korean Mathematical Society
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    • v.38 no.1
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    • pp.101-123
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    • 2001
  • For a linear operator Q from R(sup)d into R(sup)d and 0$\alpha$ and parameter b on the other. characterization of strictly (Q,b)-semi-stable distributions among (Q,b)-semi-stable distributions is made. Existence of (Q,b)-semi-stable distributions which are not translation of strictly (Q,b)-semi-stable distribution is discussed.

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REPRESENTATION OF OPERATOR SEMI-STABLE DISTRIBUTIONS

  • Choi, Gyeong-Suk
    • Bulletin of the Korean Mathematical Society
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    • v.37 no.1
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    • pp.135-152
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    • 2000
  • For a linear operator Q from $R^{d}\; into\; R^{d},\; {\alpha}\;>0\; and\ 0-semi-stability and the operater semi-stability of probability measures on $R^{d}$ are defined. Characterization of $(Q,b,{\alpha})$-semi-stable Gaussian distribution is obtained and the relationship between the class of $(Q,b,{\alpha})$-semi-stable non-Gaussian distributions and that of operator semistable distributions is discussed.

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Teaching and Learning Irrational Number with Its Conceptual Aspects Stressed : Consideration of Irrational Number through the Conception of 'Incommensurability' (무리수의 개념적 측면을 강조한 교육방안: '통약불가능성'을 통한 무리수 고찰)

  • 변희현;박선용
    • School Mathematics
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    • v.4 no.4
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    • pp.643-655
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    • 2002
  • In this paper we emphasize the introduction of ‘incommensurability’ on the teaching and learning the irrational number because we think of the origin of number as ‘ratio’. According to Greek classification of continuity as a ‘never ending’ divisibility, discrete number and continuous magnitude belong to another classes. That is, those components were dealt with respectively in category of arithmetic and that of geometry. But the comparison between magnitudes in terms of their ratios took the opportunity to relate ratios of magnitudes with numerical ratios. And at last Stevin coped with discrete and continuous quantity at the same time, using his instrumental decimal notation. We pay attention to the fact that Stevin constructed his number conception in reflecting the practice of measurement : He substituted ‘subdivision of units’ for ‘divisibility of quantities’. Number was the result of such a reflective abstraction. In other words, number was invented by regulation of measurement. Therefore, we suggest decimal representation from the point of measurement, considering the foregoing historical development of number. From the perspective that the conception of real number originated from measurement of ‘continuum’ and infinite decimals played a significant role in the ‘representation’ of measurement, decimal expression of real number should be introduced through contexts of measurement instead of being introduced as a result of algorithm.

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