• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.187-198
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• 2017

We obtain some necessary and sufficient conditions for the boundedness of the composition operators between weighted Bergman spaces of logarithmic weights. In terms of the conditions for the boundedness, we compute the essential norm of the composition operators.

• 한국지구물리탐사학회:학술대회논문집
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• 2007.06a
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• pp.130-134
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• 2007

Classical full waveform inversion for velocity estimation defines the objective function as the $l^2$ -norm of differences between the modeled and the observed wavefields. Although widely used, the results of this method have been less than satisfactory. A moderate improvement of this method is to define the objective function as the $l^2$ -norm of differences between the logarithms of the modeled and observed wavefields. In this paper we propose new objective functions of waveform inversion. They produce better results in sub-salt imaging than those of the classical and the logarithmic objective functions. One objective function defines the residual as the difference between $L^{th}$ power of the modeled wavefields and that of the observed wavefields. Another defines the residual as the difference between the integral of the $L^{th}$ power of the modeled wavefields and that of the observed wavefields. We apply these new objective functions to the synthetic SEG/EAGE salt model, and show that our new waveform inversion algorithms provide more accurate results than those of the classical and logarithmic waveform inversion methods.

• 한국지구물리탐사학회:학술대회논문집
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• 2007.06a
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• pp.118-123
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• 2007

A robust objective function in the frequency domain is applied to the acoustic full waveform inversion. The proposed objective function is defined as $l_1$-norm of residual wavefields in the frequency domain. Generally, the full waveform inversion is extremely sensitive to a number of factors such as parameterization, initial model, noise and so on. The numerical tests were performed for checking the sensitivity to attenuation and several noises. For the comparison with other objective functions, the conventional least-squares method and the logarithmic method were tested under the same condition. The synthetic data examples show that the proposed algorithm is more robust than the well-known methods.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.941-958
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• 2000

Euler method is generalized to solve the system of nonlinear differential equations. The generalization is carried out by taking a special constant matrix S so that exp(tS) can be exactly computed. Such a matrix S is extracted from the Jacobian matrix of the given problem. Stability of the generalized Euler process is discussed. It is shown that the generalized Euler process is comparable to the fourth order Runge-Kutta method. We also exemplify that the important qualitative and geometric features of the underlying dynamical system can be recovered by the generalized Euler process.

• The Journal of Internal Korean Medicine
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• v.30 no.3
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• pp.510-524
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• 2009

Objective : This study was designed to find the correlation between Sasang Constitution and heart rate variability(HRV). Method : There were 665 subjects (280 men and 385 women), between 39 and 72 years old. in a rural community. Sasang Constitution was diagnosed by a Sasang constitutional specialist using PSSC (Phonetic System for Sasang Constitution), face and tongue photo and checkup-list. A structured-questionnaire was used to assess the general characteristics. HRV was recorded using SA-2000 (medi-core). HRV was assessed by time domain and by frequency domain analysis. Metabolic syndrome was defined on the basis of clustering of risk factors, when three or more of the following cardiovascular risk factors were included : blood pressure, fasting blood sugar, triglyceride HDL-cholesterol, and abdominal obesity (waist). Because of the skewness of the data, logarithmic transformation was performed on the absolute units of the spectral components of HRV, and the resulting logarithmic values and normalized units were compared between the groups by a logistic regression. The 95% confidence interval (CI) of the odds ratio was used and calculated from the data laid out for a cross sectional study. Results : 1. Odds ratios of Taeeumin and Soeumin in female adults below 60 years old were significantly lower than that of Soyangin in LF norm and LF/HF ratio. Odds ratios of Taeeumin and Soeumin in female adults below 60 years old were significantly higher than that of Soyangin in HF norm. 2. There was no significant correlation between HRV and Sasang Constitution in female adults from 60 years old and over. 3. There was no significant correlation between HRV and Sasang Constitution in male adults. Conclusion : There is a statistically significant correlation between the HRV and Sasang Constitution. There is a tendency of increase in the sympathetic activity in Soyangin. There is a tendency of decrease in the parasympathetic activity in Taeeumin and Soeumin.