• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.3
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• pp.179-202
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• 2019

This paper presents second derivative generalized extended backward differentiation formulas (SDGEBDFs) based on the second derivative linear multi-step formulas of Cash [1]. This class of second derivative linear multistep formulas is implemented as boundary value methods on stiff problems. The order, error constant and the linear stability properties of the new methods are discussed.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.4
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• pp.224-261
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• 2021

The interest in implicit-explicit (IMEX) integration methods has emerged as an alternative for dealing in a computationally cost-effective way with stiff ordinary differential equations arising from practical modeling problems. In this paper, we introduce implicit-explicit second derivative linear multi-step methods (IMEX SDLMM) with error control. The proposed IMEX SDLMM is based on second derivative backward differentiation formulas (SDBDF) and recursive SDBDF. The IMEX second derivative schemes are constructed with order p ranging from p = 1 to 8. The methods are numerically validated on well-known stiff equations.

• The Journal of the Acoustical Society of Korea
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• v.18 no.2E
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• pp.31-38
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• 1999

This paper focuses on extracting formants from transfer function, derived from linear prediction analysis of speech signal. The second derivative of the log magnitude spectrum of the transfer function, the first and third derivatives of the phase spectrum of the transfer function in the z-plane are discussed. Their resolutions of detecting formants are analyzed and some comparisons are given. Theoretical analyses and experimental results show that the third derivative of the phase spectrum decays more rapidly around the formant locations than the first derivative of the phase spectrum and the second derivative of the log magnitude spectrum. Compared with the second derivative of the log spectrum and the first derivative of the phase spectrum, the third derivative of the phase spectrum has higher resolution in frequency domain and provides more accurate formant extraction.

• Proceedings of the KIEE Conference
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• 2006.04a
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• pp.42-44
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• 2006

Up to the present, finger replantation patients have complained about various symptoms because of blood circulatory failure. Objective evaluation methods for the level of the blood circulatory failures in fingers were needed other than patient's subjective symptoms and complaints. Photoplethysmogram(PPG) measured from fingers is very useful for evaluation of vascular aging and sclerosis level since the PPG signal represents characteristics of peripheral vascular. Several researchers have reported that second derivative of the finger PPG waveform was useful to evaluate vascular compliance and developed various analysis methods for vascular compliance. However, vascular compliance study for finger replantation patient was never evaluated by using second derivative of PPG. Therefore, we aimed to objectively compare and to assess normal and replanted finger vascular compliance using the second derivative of PPG waveform in this study. The evaluated factors of second derivative of PPG are 'a', 'b', 'c', 'd', 'e' and b/a represents vascular compliance. Study found out that when vascular compliance is decreased, b/a is increased, the absolute value of b/a is decreased. For 43 finger replantation patients, the average vascular compliance of replanted finger is lower than the normal finger statistically(p=0.001). we suggested an objective evaluation of finger vascular compliance for finger replantation patients and effect of surgical operation.

• Proceedings of the KIEE Conference
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• 2007.04a
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• pp.67-69
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• 2007

Recently, the prevalence rate of diabetes in Korea has been increasing rapidly due to high growth of economy and changes in dietary lifestyle. Vascular complication is one of diabetic complications which have frequently occurred by obesity, hyperglycemia and impaired glucose metabolism. Photoplethysmogram(PPG) measured from finger and toe is very useful for evaluation of vascular aging and sclerosis level since the PPG signal represents characteristics of peripheral vascular. Several researchers have reported that second derivative of the finger PPG waveform was useful to evaluate vascular compliance and developed various analysis methods for vascular compliance. However, peripheral vascular compliance study for diabetic patient was never evaluated by using second derivative of PPG. Therefore, we aimed to objectively compare and to assess normal and diabetic group vascular compliance using the second derivative of PPG waveform in this study. The evaluated factors of second derivative of PPG are 'a', 'b', 'c', 'd', 'e' and b/a represents vascular compliance. Study found out that when vascular compliance is decreased, b/a is increased, the absolute value of b/a is decreased. The average vascular compliance of 50 diabetic patients with neuropathy is statistically lower than the normal group(p<0.05). We suggest an objective evaluation of peripheral vascular compliance for diabetic patients and prevention of vascular complication.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.10 no.1
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• pp.21-29
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• 2006

The method to construct a surface from point data are widely known. But the way to make a surface from derivative data is not usually used since derivative data in engineering appears very often. In this paper, if more than one types of data among three possible data such as point data, first derivative data, second derivative data are given, we can construct a surface. If only first derivative data are given, we add a function value at the one point. If only second derivative data are given, we add a linear function.

• Communications for Statistical Applications and Methods
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• v.4 no.2
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• pp.515-522
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• 1997

In this paper, we find the second derivative of mean busy cycle with respect to a parameter of inter-arrival time distribution. We show that this derivative can be estimated from single sample path. We do the similar thing for the mean number of arrivals during busy cycle.

• YAKHAK HOEJI
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• v.30 no.2
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• pp.100-103
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• 1986

The second derivative absorption spectra of acetaminophen in commercial tablet forms were measured without prior separation from other pharmaceutical adjuvants. The second derivative spectra of acetaminophen were found to have no influence on the characteristic absorbance band of it. A plot of 25 sets of the ordinate (Z) values with various acetaminophen concentrations mixed in other additives gave a straight line (correlation coefficient, 0.9999) and the slope was 2.901${\times}10^{-2}Z$ value/($\mu\textrm{g}$/ml). The procedures were sufficiently sensitive, precise and economical for the assay of tablets of acetaminophen.

• Korean Journal of Optics and Photonics
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• v.25 no.5
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• pp.273-278
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• 2014

We present an algorithm for surface reconstruction from the second-derivative data for free-form aspherics, which uses a subaperture scanning system that measures the local surface profile and determines the three second-derivative values at those local sampling points across the free-form surface. The three second-derivative data were integrated to get a map of x- and y-slopes, which went through a second Southwell integration step to reconstruct the surface profile. A synthetic free-form surface 200 mm in diameter was simulated. The simulation results show that the reconstruction error is 19 nm RMS residual difference. Finally, the sensitivity to noise is diagnosed for second-derivative Gaussian random noise with a signal to noise ratio (SNR) of 16, the simulation results proving that the suggested method is robust to noise.

• Proceedings of the Korea Society for Simulation Conference
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• 1999.10a
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• pp.294-298
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• 1999

In this paper, through simulations, we find the second derivative SPA(Smoothed Perturbation Analysis) estimates of mean busy cycle with respect to a given parameter in a Markov renewal process which is generated by two exponential distributions. We compare these SPA estimates with the traditional SD(symetric difference) estimates.