• Title/Summary/Keyword: discrete Laplacian

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MULTIPLE SOLUTIONS TO DISCRETE BOUNDARY VALUE PROBLEMS FOR THE p-LAPLACIAN WITH POTENTIAL TERMS ON FINITE GRAPHS

  • CHUNG, SOON-YEONG;PARK, JEA-HYUN
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.5
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    • pp.1517-1533
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    • 2015
  • In this paper, we prove the existence of at least three nontrivial solutions to nonlinear discrete boundary value problems $$\{^{-{\Delta}_{p,{\omega}}u(x)+V(x){\mid}u(x){\mid}^{q-2}u(x)=f(x,u(x)),x{\in}S,}_{u(x)=0,\;x{\in}{\partial}S}$$, involving the discrete p-Laplacian on simple, nite and connected graphs $\bar{S}(S{\cup}{\partial}S,E)$ with weight ${\omega}$, where 1 < q < p < ${\infty}$. The approach is based on a suitable combine of variational and truncations methods.

THE p-LAPLACIAN OPERATORS WITH POTENTIAL TERMS

  • Chung, Soon-Yeong;Lee, Hee-Soo
    • Communications of the Korean Mathematical Society
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    • v.26 no.4
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    • pp.591-601
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    • 2011
  • In this paper, we deal with the discrete p-Laplacian operators with a potential term having the smallest nonnegative eigenvalue. Such operators are classified as its smallest eigenvalue is positive or zero. We discuss differences between them such as an existence of solutions of p-Laplacian equations on networks and properties of the energy functional. Also, we give some examples of Poisson equations which suggest a difference between linear types and nonlinear types. Finally, we study characteristics of the set of a potential those involving operator has the smallest positive eigenvalue.

Discretization of Pressure-Poisson Equation for Solving Incompressible Navier-Stokes Equations Using Non-Staggered Grid (정규격자를 사용한 비압축성 Navier-Stokes 방정식의 수치해석을 위한 압력 Poisson 방정식의 이산화)

  • Kim Y. G.;Kim H. T.;Kim J. J.
    • 한국전산유체공학회:학술대회논문집
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    • 1998.11a
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    • pp.96-101
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    • 1998
  • Various discretiation methods of Laplacian operator in the Pressure-Poisson equation are investigated for the solution of incompressible Navier-Stokes equations using the non-staggered grid. Laplacian operators previously proposed by other researchers are applied to a Driven-Cavity problem. The computational results are compared with those of Ghia. The results show the characteristics of the discrete Laplacian operators.

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FUSESHARP: A MULTI-IMAGE FOCUS FUSION METHOD USING DISCRETE WAVELET TRANSFORM AND UNSHARP MASKING

  • GARGI TRIVEDI;RAJESH SANGHAVI
    • Journal of applied mathematics & informatics
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    • v.41 no.5
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    • pp.1115-1128
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    • 2023
  • In this paper, a novel hybrid method for multi-focus image fusion is proposed. The method combines the advantages of wavelet transform-based methods and focus-measure-based methods to achieve an improved fusion result. The input images are first decomposed into different frequency sub-bands using the discrete wavelet transform (DWT). The focus measure of each sub-band is then calculated using the Laplacian of Gaussian (LoG) operator, and the sub-band with the highest focus measure is selected as the focused sub-band. The focused sub-band is sharpened using an unsharp masking filter to preserve the details in the focused part of the image.Finally, the sharpened focused sub-bands from all input images are fused using the maximum intensity fusion method to preserve the important information from all focus images. The proposed method has been evaluated using standard multi focus image fusion datasets and has shown promising results compared to existing methods.

Inverse quantization of DCT coefficients using Laplacian pdf (Laplacian pdf를 적용한 DCT 계수의 역양자화)

  • 강소연;이병욱
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.29 no.6C
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    • pp.857-864
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    • 2004
  • Many image compression standards such as JPEG, MPEG or H.263 are based on the discrete cosine transform (DCT) and quantization method. Quantization error. is the major source of image quality degradation. The current dequantization method assumes the uniform distribution of the DCT coefficients. Therefore the dequantization value is the center of each quantization interval. However DCT coefficients are regarded to follow Laplacian probability density function (pdf). The center value of each interval is not optimal in reducing squared error. We use mean of the quantization interval assuming Laplacian pdf, and show the effect of correction on image quality. Also, we compare existing quantization error to corrected quantization error in closed form. The effect of PSNR improvements due to the compensation to the real image is in the range of 0.2 ∼0.4 ㏈. The maximum correction value is 1.66 ㏈.

DISCRETE EVOLUTION EQUATIONS ON NETWORKS AND A UNIQUE IDENTIFIABILITY OF THEIR WEIGHTS

  • Chung, Soon-Yeong
    • Journal of the Korean Mathematical Society
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    • v.53 no.5
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    • pp.1133-1148
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    • 2016
  • In this paper, we first discuss a representation of solutions to the initial value problem and the initial-boundary value problem for discrete evolution equations $${\sum\limits^l_{n=0}}c_n{\partial}^n_tu(x,t)-{\rho}(x){\Delta}_{\omega}u(x,t)=H(x,t)$$, defined on networks, i.e. on weighted graphs. Secondly, we show that the weight of each link of networks can be uniquely identified by using their Dirichlet data and Neumann data on the boundary, under a monotonicity condition on their weights.

DOUBLY NONLINEAR PARABOLIC EQUATIONS INVOLVING p-LAPLACIAN OPERATORS VIA TIME-DISCRETIZATION METHOD

  • Shin, Kiyeon;Kang, Sujin
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.6
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    • pp.1179-1192
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    • 2012
  • In this paper, we consider a doubly nonlinear parabolic partial differential equation $\frac{{\partial}{\beta}(u)}{{\partial}t}-{\Delta}_pu+f(x,t,u)=0$ in ${\Omega}{\times}[0,T]$, with Dirichlet boundary condition and initial data given. We prove the existence of a discrete approximate solution by means of the Rothe discretization in time method under some conditions on ${\beta}$, $f$ and $p$.

Distribution Approximation of the Two Dimensional Discrete Cosine Transform Coefficients of Image (영상신호 2차원 코사인 변환계수의 분포근사화)

  • 심영석
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.10 no.3
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    • pp.130-134
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    • 1985
  • In two-dimensional discrete cosine transform(DCT) coding, the measurements of the distributions of the transform coefficients are important because a better approximation yields a smaller mean square distorition. This paper presents the results of distribution tests which indicate that the statistics of the AC coefficients are well approximated to a generalized Gaussian distribution whose shape parameter is 0.6. Furthermore, from a simulation of the DCT coding, it was shown that the above approximation yields a higher experimental SNR and a better agreement between theory and simulation than the Gaussian or Laplacian assumptions.

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EXISTENCE OF POSITIVE SOLUTIONS FOR BVPS TO INFINITE DIFFERENCE EQUATIONS WITH ONE-DIMENSIONAL p-LAPLACIAN

  • Liu, Yuji
    • Journal of the Chungcheong Mathematical Society
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    • v.24 no.4
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    • pp.639-663
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    • 2011
  • Motivated by Agarwal and O'Regan ( Boundary value problems for general discrete systems on infinite intervals, Comput. Math. Appl. 33(1997)85-99), this article deals with the discrete type BVP of the infinite difference equations. The sufficient conditions to guarantee the existence of at least three positive solutions are established. An example is presented to illustrate the main results. It is the purpose of this paper to show that the approach to get positive solutions of BVPs by using multi-fixed-point theorems can be extended to treat BVPs for infinite difference equations. The strong Caratheodory (S-Caratheodory) function is defined in this paper.

A Multiresolution Digital Watermarking Based on Image Statistics (영상의 통계적 특성에 기반한 다해상도 디지털 워터마킹)

  • 한성현
    • Journal of the Institute of Electronics Engineers of Korea TE
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    • v.37 no.2
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    • pp.25-32
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    • 2000
  • Digital watermarking has been recently proposed as the means of intellectual property right protection of multimedia data. We present a novel watermarking scheme to hide a copyright information in a digital image. The method Is based on the 2D DWT(Discrete Wavelet Transform) and image statistics. Gaussian and Laplacian noises as the watermarks are added to the large wavelet coefficients at the high and middle frequency bands in the wavelet domain. Experimental results show that the proposed Laplacian watermark is stronger to several common image distortions, such as noises, JPEG coding as different qualities, Gaussian blurring, and edge enhancement.

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