• Title/Summary/Keyword: Dichotomy

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On The Dichotomy of Stationary and Ergodic Probability Measures

  • Park, Jeong-Soo
    • Journal of the Korean Statistical Society
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    • v.22 no.2
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    • pp.347-351
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    • 1993
  • The dichotomy of absolute continuity and singularity for a pair of stationary and ergodic measures (one of which need not be ergodic) is obtained using the ergodic decomposition theorem. The known fact that two different stationary and ergodic measures are mutually singular is obtained as a corollary of our result. An example of a pair of stationary-ergodic measures enjoying the dichotomy is presented.

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ON DICHOTOMY AND CONDITIONING FOR TWO-POINT BOUNDARY VALUE PROBLEMS ASSOCIATED WITH FIRST ORDER MATRIX LYAPUNOV SYSTEMS

  • Murty, M.S.N.;Kumar, G. Suresh
    • Journal of the Korean Mathematical Society
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    • v.45 no.5
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    • pp.1361-1378
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    • 2008
  • This paper deals with the study of dichotomy and conditioning for two-point boundary value problems associated with first order matrix Lyapunov systems, with the help of Kronecker product of matrices. Further, we obtain close relationship between the stability bounds of the problem on one hand, and the growth behaviour of the fundamental matrix solution on the other hand.

Equivalence-Singularity Dichotomies of Gaussian and Poisson Processes from The Kolmogorov's Zero-One Law

  • Park, Jeong-Soo
    • Journal of the Korean Statistical Society
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    • v.23 no.2
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    • pp.367-378
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    • 1994
  • Let P and Q be probability measures of a measurable space $(\Omega, F)$, and ${F_n}_{n \geq 1}$ be a sequence of increasing sub $\sigma$-fields which generates F. For each $n \geq 1$, let $P_n$ and $Q_n$ be the restrictions of P and Q to $F_n$, respectively. Under the assumption that $Q_n \ll P_n$ for every $n \geq 1$, a zero-one condition is derived for P and Q to have the dichotomy, i.e., either $Q \ll P$ or $Q \perp P$. Then using this condition and the Kolmogorov's zero-one law, we give new and simple proofs of the dichotomy theorems for a pair of Gaussian measures and Poisson processes with examples.

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CHARACTERIZATION OF TEMPERED EXPONENTIAL DICHOTOMIES

  • Barreira, Luis;Rijo, Joao;Valls, Claudia
    • Journal of the Korean Mathematical Society
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    • v.57 no.1
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    • pp.171-194
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    • 2020
  • For a nonautonomous dynamics defined by a sequence of bounded linear operators on a Banach space, we give a characterization of the existence of an exponential dichotomy with respect to a sequence of norms in terms of the invertibility of a certain linear operator between general admissible spaces. This notion of an exponential dichotomy contains as very special cases the notions of uniform, nonuniform and tempered exponential dichotomies. As applications, we detail the consequences of our results for the class of tempered exponential dichotomies, which are ubiquitous in the context of ergodic theory, and we show that the notion of an exponential dichotomy under sufficiently small parameterized perturbations persists and that their stable and unstable spaces are as regular as the perturbation.

A Study on the Relationship of Space and Time in Visual Tactility (시각과 시촉각에 의한 운동 측면에서 본 공간과 시간의 관계성 연구 - 연경당 외부공간을 중심으로 -)

  • Yook, Ok-Soo
    • Journal of architectural history
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    • v.20 no.1
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    • pp.77-93
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    • 2011
  • Across the culture of Western Europe, dichotomy based on the visual sense has evolved. They believed eyes and ears requiring a distance related in recognition, are more developed than any other human senses in human body. Dominant position, as a condition to using a perspective, the eye has been just concentrated in the development of optical sight. But developed a variety of modern media, highlighting the importance of the other perception, it makes dichotomy to the expansion of perception over the single function of visuality. Recently, Guille Deleuze and Merleau-Ponty try to recover the sense of tactility segregated in skin from body keeping eyes for distance. By the result, the activity can be happened by being connected to the body rather than to eye in the space between the subject and object. From the phase of recognition where the human body tries to identify the object in the space considering a time, it will be changed for the subject to the phase of structure vice versa. Visual tactility is to eliminate the distance between subject and object. If the visual tactility is to erase the distance different from the visual in dichotomy, it will be occurred to having a tension and makes new relationship to work trying to move the subjective point of view in object. Like this evidence in analysis of architecture, it can be easy to find the Korean architecture rather than western architecture in terms of emphasizing the time and space. The fact, architecture of Lee Dynasty had been preserved and consisted basic form and style over the centuries makes us assume that visual tactility was considered as well as the visual sense. This study will be intensive in terms of visual and tactile inherent in the subject and how it is being connected to the movement in the space and time.

A Critical Approach on Environmental Education Biased to Environmental Possibilism - From Clearing up the Cause to Problem-Solving Mechanism - (환경관리주의 환경교육에 대한 비판적 고찰 - 원인규명에서 해결기제로의 전환을 위하여 -)

  • Kim, Tae-Kyung
    • Hwankyungkyoyuk
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    • v.18 no.3 s.28
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    • pp.59-74
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    • 2005
  • We can't deny Korean EE has basically developed on the basis of Environmental Possibilism (Environmental management or Reformism) in lots of aspects. I would show three representative proofs here, the first, the philosophy of Korean EE has been mainly focused on dichotomy of human-techno centrism and eco-centrism with no considering other alternative environmentalism since 4th Formal Curriculum, 1981. The second, simultaneously, the concept of EE has not distinguished from it of Science education. (Furthermore, unfortunately some says EE has been a part of Science education, although there should be many differences on its contextual aspect.) And the third one is that the limit of possibilism which market economists have worried, has scarcely mentioned in various kinds of EE-related teaching materials. Possibilism is basically likely to be accompanied by science and economics-oriented approach, and in this aspect this dichotomy, human-techno centrism and eco-centrism, has come from perspectives of Economical development process and over-addicted belief to Science. So it is enough to say that Korean EE has basically developed with biased to Environmental possibilism, in other words, biased to preference to it. And I'll critically focus on these two axes of possibilism, Science and Economics and its dichotomy. Of course, we should accept there are so many same parts in its contents between EE and Science, but we should know its contextual differences for triangular position of environmentalism suitable to EE and also overcome science-dependant approach to EE. Although science-dependant approach to EE and dichotomy could provide some tools for clearing up the causes of environmental problem, especially always it has insisted fundamental causes of environmental problem originated in human faults and over-use of eco-source or over-economic development, but now it is old-fashioned discourse, furthermore it come to have unavoidable limits in the debates of problem-solving mechanism to environmental problems. The paramount important thing is to supply the ways or thoughtful mechanism for solving or coordinating the Environmental problems, not just searching for cause of it. But scientific approach and its dichotomy based on possibilism have continuously born cause & effect in EE-related discourse. So there are so much needs to transfer from continuous bearing of cause & effect to constructive alternatives at least in environmentalism of EE. Traditionally, dichotomical division in EE Environmentalism, human-techno centrism and eco-centrism, couldn't have Provided any answers to our real society, it just gives us only cause & effects of Environmental problems. And also we can't find the description on the limits of capitalism market approach to Environmental problems especially in Korean EE text books, other teaching materials and its teaching-learning process, although market approach economist has been proved its fault beyond its functional merits as Environmental management tools. So we should introduce other alternative Environmental philosophy instead of Possibilism such as eco-socialism insisted by Schmacher M. and Boochin etc, or marxist-environmentalism for relative and comparative views to market-thought such as commodification. In this aspect we need to accept Oriental philosophy based on moderation(中庸) as new another alternatives with the reflection that we have recognized monism as representative Oriental philosophical environmentalism. Fundamentally monism has done its role with providing relative concepts to Dichotomy Enlightenment, but we can't say it has been core concept for understanding of oriental environmentalism, and we can't distinguish monism from oriental philosophy itself, just because oriental thought itself was basically monism. So conceptual difference should be recognized between EE and Science education in teaching-learning process on the basis of life-philosophy(Philosophie des Lebens) from epistemology. For this transformation, we should introduce existentialism in Science education, in other words, only existential Science education based on phenomenology or interpretivism can be EE. And simultaneously we need some ways for overcoming of scientific foundationalism which has been tradition making science not stand on existentialism, formulating and featuring of almost all of natural things and its phenomenon from after enlightenment in western world, but it has malfunctioned in fixing conception of science just into essentialism itself. And we also introduce integrated approach to science and society for EE like STS. Those are ways for overcoming of Environmental possibilism in EE.

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