• Title/Summary/Keyword: Generalization operator

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Characterization of Some Classes of Distributions Related to Operator Semi-stable Distributions

  • Joo, Sang Yeol;Yoo, Young Ho;Choi, Gyeong Suk
    • Communications for Statistical Applications and Methods
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    • v.10 no.1
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    • pp.177-189
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    • 2003
  • For a positive integer m, operator m-semi-stability and the strict operator m-semi-stability of probability measures on R^d$ are defined. The operator m-semi-stability is a generalization of the definition of operator semi-stability with exponent Q. Characterization of strictly operator na-semi-stable distributions among operator m-semi-stable distributions is given. Translation of strictly operator m-semi-stable distribution is discussed.

Characterization of some classes of distributions related to operator semi-stable distributions

  • Joo, Sang-Yeol;Choi, Gyeong-Suk
    • Proceedings of the Korean Statistical Society Conference
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    • 2002.11a
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    • pp.221-225
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    • 2002
  • For a positive integer m, operator m-semi-stability and the strict operator m-semi-stability of probability measures on $R^{d}$ are defined. The operator m-semi-stability is a generalization of the definition of operator semi- stability with exponent Q. Translation of strictly operator m-semi-stable distribution is discussed.

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A GENERALIZATION OF STONE'S THEOREM IN HILBERT $C^*$-MODULES

  • Amyari, Maryam;Chakoshi, Mahnaz
    • The Pure and Applied Mathematics
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    • v.18 no.1
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    • pp.31-39
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    • 2011
  • Stone's theorem states that "A bounded linear operator A is infinitesimal generator of a $C_0$-group of unitary operators on a Hilbert space H if and only if iA is self adjoint". In this paper we establish a generalization of Stone's theorem in the framework of Hilbert $C^*$-modules.

Comparative Study of Map Generalization Algorithms with Different Tolerances (임계치 설정에 따른 지도 일반화 기법의 성능 비교 연구)

  • Lee, Jae-Eun;Park, Woo-Jin;Yu, Ki-Yun
    • Proceedings of the Korean Society of Surveying, Geodesy, Photogrammetry, and Cartography Conference
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    • 2010.04a
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    • pp.19-21
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    • 2010
  • In this study, regarding to the generalization of the map, we analyze how the different tolerances influence on the performances of linear generalization operators. For the analysis, we apply the generalization operators, especially two simplification algorithms provided in the commercial GIS software, to 1:1000 digital topographic map for analyzing the aspect of the changes in positional error depending on the tolerances. And we evaluate the changes in positional error with the quantitative assessments. The results show that the analysis can be used as the criteria for determining proper tolerance in linear generalization.

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SOME CLASSES OF OPERATORS RELATED TO (m, n)-PARANORMAL AND (m, n)*-PARANORMAL OPERATORS

  • Shine Lal Enose;Ramya Perumal;Prasad Thankarajan
    • Communications of the Korean Mathematical Society
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    • v.38 no.4
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    • pp.1075-1090
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    • 2023
  • In this paper, we study new classes of operators k-quasi (m, n)-paranormal operator, k-quasi (m, n)*-paranormal operator, k-quasi (m, n)-class 𝒬 operator and k-quasi (m, n)-class 𝒬* operator which are the generalization of (m, n)-paranormal and (m, n)*-paranormal operators. We give matrix characterizations for k-quasi (m, n)-paranormal and k-quasi (m, n)*-paranormal operators. Also we study some properties of k-quasi (m, n)-class 𝒬 operator and k-quasi (m, n)-class 𝒬* operators. Moreover, these classes of composition operators on L2 spaces are characterized.

ROUGH ISOMETRY AND THE SPACE OF BOUNDED ENERGY FINITE SOLUTIONS OF THE SCHRODINGER OPERATOR ON GRAPHS

  • Kim, Seok-Woo;Lee, Yong-Hah;Yoon, Joung-Hahn
    • Communications of the Korean Mathematical Society
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    • v.25 no.4
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    • pp.609-614
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    • 2010
  • We prove that if graphs of bounded degree are roughly isometric to each other, then the spaces of bounded energy finite solutions of the Schr$\ddot{o}$dinger operator on the graphs are isomorphic to each other. This is a direct generalization of the results of Soardi [5] and of Lee [3].