• Journal of the Korean Mathematical Society
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• v.29 no.1
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• pp.175-190
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• 1992

• 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.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.525-531
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• 2007

We newly introduce the concept of summable in measure and investigate on some its properties. In addition to this, we consider a size of given series by means of we are giving Lebesgue measure to an associated series.

• Journal of the Korean Mathematical Society
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• v.32 no.1
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• pp.103-108
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• 1995

It is a well-known classical result of Mazur and Ulam that an isometry T from a real Banach space X onto a real Banach space Y with T(0) = 0 is automatically linear[5].

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.315-330
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• 2007

In this paper, some hybrid fixed point theorems are proved which are further applied to first and second order neutral functional differential equations for proving the existence results for the extremal solutions under the mixed Lipschitz, compactness and monotonic conditions.

• Communications of the Korean Mathematical Society
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• v.19 no.3
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• pp.557-567
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• 2004

We prove the sufficient conditions for optimality in differential inclusion problem by using the value function. For this purpose, we assume at first that the value function is locally Lipschitz. Secondly, without this assumption, we use the viability theory.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.101-111
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• 2001

We investigate the property of h-stability, which is an important extension of the notions of exponential stability and uniform Lipschitz stability in variation for nonlinear Volterra difference systems.

• East Asian mathematical journal
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• v.26 no.3
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• pp.365-370
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• 2010

A local convergence result is provided for the continuous analog of Newton's method in a Banach space setting. The radius of convergence is larger, the error bounds tighter, and under the same or weaker hypotheses than before [12].

• Journal of Korea Society of Industrial Information Systems
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• v.11 no.5
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• pp.62-66
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• 2006

We investigate various $\Phi(t)-stability$ of comparison differential equations and we abtain necessary and/or sufficient conditions for the uniform asymptotic and exponential asymptotic stability of the nonlinear differential equation x'=f(t, x).