• Title, Summary, Keyword: Laplacian

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QUANTUM EXTENSIONS OF FOURIER-GAUSS AND FOURIER-MEHLER TRANSFORMS

  • Ji, Un-Cig
    • Journal of the Korean Mathematical Society
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    • v.45 no.6
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    • pp.1785-1801
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    • 2008
  • Noncommutative extensions of the Gross and Beltrami Laplacians, called the quantum Gross Laplacian and the quantum Beltrami Laplacian, resp., are introduced and their basic properties are studied. As noncommutative extensions of the Fourier-Gauss and Fourier-Mehler transforms, we introduce the quantum Fourier-Gauss and quantum Fourier- Mehler transforms. The infinitesimal generators of all differentiable one parameter groups induced by the quantum Fourier-Gauss transform are linear combinations of the quantum Gross Laplacian and quantum Beltrami Laplacian. A characterization of the quantum Fourier-Mehler transform is studied.

LAPLACIAN SPECTRA OF GRAPH BUNDLES

  • Kim, Ju-Young
    • Communications of the Korean Mathematical Society
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    • v.11 no.4
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    • pp.1159-1174
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    • 1996
  • The spectrum of the Laplacian matrix of a graph gives an information of the structure of the graph. For example, the product of non-zero eigenvalues of the characteristic polynomial of the Laplacian matrix of a graph with n vertices is n times of the number of spanning trees of that graph. The characteristic polynomial of the Laplacian matrix of a graph tells us the number of spanning trees and the connectivity of given graph. in this paper, we compute the characteristic polynomial of the Laplacian matrix of a graph bundle when its voltage lie in an abelian subgroup of the full automorphism group of the fibre; in particular, the automorphism group of the fibre is abelian. Also we study a relation between the characteristic polynomial of the Laplacian matrix of a graph G and that of the Laplacian matrix of a graph bundle over G. Some applications are also discussed.

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A NEW DETAIL EXTRACTION TECHNIQUE FOR VIDEO SEQUENCE CODING USING MORPHOLOGICAL LAPLACIAN OPERATOR (수리형태학적 Laplacian 연산을 이용한 새로운 동영상 Detail 추출 방법)

  • Eo, Jin-Woo;Kim, Hui-Jun
    • Journal of IKEEE
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    • v.4 no.2
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    • pp.288-294
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    • 2000
  • In this paper, an efficient detail extraction technique for a progressive coding scheme is proposed. The existing technique using the top-hat transformation yields an efficient extraction scheme for isolated and visually important details, but yields an inefficient results containing significant redundancy extracting the contour information. The proposed technique using the strong edge feature extraction property of the morphological Laplacian in this paper can reduce the redundancy, and thus provides lower bit-rate. Experimental results show that the proposed technique is more efficient than the existing one, and promise the applicability of the morphological Laplacian operator.

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Upper and lower solutions for a singular p-Laplacian system

  • Kim, Chan-Gyun;Lee, Eun-Kyoung
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.11 no.4
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    • pp.89-99
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    • 2007
  • In this paper, we define the upper and lower solutions for a p-Laplacian system with singular nonlinearity at the boundaries. And we prove the theorem for the upper and power solutions method.

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Analysis on the Regularization Parameter in Image Restoration (영상복원에서의 정칙화 연산자 분석)

  • 전우상;이태홍
    • Journal of Korea Multimedia Society
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    • v.2 no.3
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    • pp.320-328
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    • 1999
  • The Laplacian operator is usually used as a regularization operator which may be used as any differential operator in the regularization iterative restoration. In this paper, several kinds of differential operator and 1-H operator that has been used in our lab as well, as a regularization operator, were compared with each other. In the restoration of noisy motion-blurred images, 1-H operator worked better than Laplacian operator in flat region, but in the edge the Laplacian operator operated better. For noisy gaussian-blurred image, 1-H operator worked better in the edge, while in flat region the Laplacian operator resulted better. In regularization, smoothing the noise and resorting the edges should be considered at the same time, so the regions divided into the flat, the middle, and the detailed, which were processed in separate and compared their MSE. Laplacian and 1-H operator showed to be suitable as the regularization operator, while the other differential operators appeared to be diverged as iterations proceeded.

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THE NORMALIZED LAPLACIAN ESTRADA INDEX OF GRAPHS

  • Hakimi-Nezhaad, Mardjan;Hua, Hongbo;Ashrafi, Ali Reza;Qian, Shuhua
    • Journal of applied mathematics & informatics
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    • v.32 no.1_2
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    • pp.227-245
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    • 2014
  • Suppose G is a simple graph. The ${\ell}$-eigenvalues ${\delta}_1$, ${\delta}_2$,..., ${\delta}_n$ of G are the eigenvalues of its normalized Laplacian ${\ell}$. The normalized Laplacian Estrada index of the graph G is dened as ${\ell}EE$ = ${\ell}EE$(G) = ${\sum}^n_{i=1}e^{{\delta}_i}$. In this paper the basic properties of ${\ell}EE$ are investigated. Moreover, some lower and upper bounds for the normalized Laplacian Estrada index in terms of the number of vertices, edges and the Randic index are obtained. In addition, some relations between ${\ell}EE$ and graph energy $E_{\ell}$(G) are presented.