• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11b
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• pp.1182-1188
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• 2001

The objective of this paper is to show the effectiveness of the wavelet transform by means of its capability to estimate the Lipschitz exponent. In particular, we show that the magnitude of the Lipschitz exponent can be used as a useful tool estimating the damage extent. An effective method based on the Lipschitz exponent is proposed and we present the results investigated both numerically and experimentally. The continuous wavelet transform by a Mexican hat wavelet having two vanishing moments is utilized for the estimation of the Lipschitz exponent.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.713-732
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• 2017

Let ${\Omega}{\in}L^s(S^{n-1})$ for s > 1 be a homogeneous function of degree zero and b be BMO functions or Lipschitz functions. In this paper, we obtain some boundedness of the $Calder{\acute{o}}n$-Zygmund singular integral operator $T_{\Omega}$ and its commutator [b, $T_{\Omega}$] on Herz-type Hardy spaces with variable exponent.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.745-765
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• 2021

Let Ω be a proper open subset of ℝⁿ and p(·) : Ω → (0, ∞) be a variable exponent function satisfying the globally log-Hölder continuous condition. In this article, the author introduces the "geometrical" variable Hardy spaces H^p(·)_r (Ω) and H^p(·)_z (Ω) on Ω, and then obtains the grand maximal function characterizations of H^p(·)_r (Ω) and H^p(·)_z (Ω) when Ω is a strongly Lipschitz domain of ℝⁿ. Moreover, the author further introduces the "geometrical" variable local Hardy spaces h^p(·)_r (Ω), and then establishes the atomic characterization of h^p(·)_r (Ω) when Ω is a bounded Lipschitz domain of ℝⁿ.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.10A
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• pp.1011-1020
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• 2002

The current paper presents an effective deblocking algorithm for block-based coded images using singularity detection in a wavelet transform. In block-based coded images, the local maxima of a wavelet transform modulus detect all singularities, including blocking artifacts, from multiscale edges. Accordingly, the current study discriminates between a blocking artifact and an edge by estimation the Lipschitz regularity of the local maxima and removing the wavelet transform modulus of a blocking artifact that has a negative Lipschitz regularity exponent. Experimental results showed that the performance of the proposed algorithm was objectively and subjectively superior.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1471-1493
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• 2022

The goal of this paper is to establish the boundedness of bilinear Calderón-Zygmund operator BT and its commutator [b₁, b₂, BT] which is generated by b₁, b₂ ∈ BMO(ℝⁿ) (or ${\dot{\Lambda}}_{\alpha}$(ℝⁿ)) and the BT on generalized variable exponent Morrey spaces 𝓛^p(·),𝜑(ℝⁿ). Under assumption that the functions 𝜑₁ and 𝜑₂ satisfy certain conditions, the authors proved that the BT is bounded from product of spaces 𝓛^{p₁(·),𝜑₁}(ℝⁿ)×𝓛^{p₂(·),𝜑₂}(ℝⁿ) into space 𝓛^p(·),𝜑(ℝⁿ). Furthermore, the boundedness of commutator [b₁, b₂, BT] on spaces L^p(·)(ℝⁿ) and on spaces 𝓛^p(·),𝜑(ℝⁿ) is also established.

• Journal of the Institute of Convergence Signal Processing
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• v.8 no.3
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• pp.143-148
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• 2007

The many studies have been proceeding to express accurately the feature of a sudden signal and a uncertain system in the image processing field. It is well know that Fourier Transform is widely used for frequency analysis of any signal. However, The frequency transform domain is not used for expressing the sudden signal change and non-stationary signal at the time-axis by this method. This paper describes of image analysis by discrete wavelet transform. Wavelet modulus maxima on transformed plane gives the Lipschitz exponent expression, which is useful to examine the characteristics of signal or the edge of an image. It is possible to reconstruct the original image only using the few maxima points. The fractal analysis is applied as an examples. The visualized image of oil flow on a ship model is analyzed. The fractal variable is obtained by the maxima analysis and the good results on the exprement is obtained by the visualized image analysis.

• Journal of the Institute of Convergence Signal Processing
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• v.11 no.2
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• pp.157-162
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• 2010

In this paper we propose a fractal analysis based on the discrete wavelet transform. It is well known that Fourier Transform is widely used for frequency analysis of random signal. However, the frequency domain is not used for expressing the sudden signal change and non-stationary signal at the time-axis by this method. Maximum value in the wavelet modules can be expressed by the Lipschitz exponent, which is useful to represent the characteristics of signal or the edge of an image. It is possible to reconstruct the original image only by using the few maximum points. The v possible image It iusing oil was acquired to interpret the maximum value. ufter that, it was applied to the v possible image of a ship model. In addition, the fractal dimens by by the conlapse process of the sediment particle was examined. In this paper, the fractal dimens by has been obtained by the maximum value and the experiment obtained from the visualized image also acquired the same result as existing methods.

• Interaction and multiscale mechanics
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• v.3 no.4
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• pp.321-331
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• 2010

A new technique is proposed for bridge structural damage detection based on spatial wavelet analysis of the time history obtained from vehicle body moving over the bridge, which is different from traditional detection techniques based on the bridge response. A simply-supported Bernoulli-Euler beam subjected to a moving spring-mass unit is established, with the crack in the beam simulated by modeling the cracked section as a rotational spring connecting two undamaged beam segments, and the equations of motion for the system is derived. By using the transfer matrix method, the natural frequencies and mode shapes of the cracked beam are determined. The responses of the beam and the moving spring-mass unit are obtained by modal decomposition theory. The continuous wavelet transform is calculated on the displacement time histories of the sprung-mass. The case study result shows that the damage location can be accurately determined and the method is effective.