• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제23권3호
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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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• 제25권4호
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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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• 제18권2E호
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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.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2006년도 심포지엄 논문집 정보 및 제어부문
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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.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2007년도 심포지엄 논문집 정보 및 제어부문
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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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• 제10권1호
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• pp.21-29
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• 2006

점 데이터로부터 곡선이나 곡면을 형성하는 방법은 널리 알려져 있다. 하지만 미분데이터가 주어지는 경우는 공학적으로 많지 않기 때문에 미분 데이터로부터 곡면을 형성하는 방법은 잘 사용되고 있지 않다. 여기서는 점 데이터, 1차 미분 데이터, 2차 미분 데이터 등 세 개중에 한 개 이상이 주어지면 곡면을 형성 할 수 있다. 1차 미분 데이터만 주어진 경우는 한 점에서 함수 값을 더한다. 2차 미분 데이터가 주어진 경우는 1차 함수를 추가하면 된다.

• Communications for Statistical Applications and Methods
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• 제4권2호
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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.

• 약학회지
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• 제30권2호
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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.

• 한국광학회지
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• 제25권5호
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• pp.273-278
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• 2014

일련의 국부영역으로부터 이차미분값을 획득하여 전체 형상을 복원하는 측정법을 제안하였다. 측정시 기울기가 제거된 국부형상에 대해 곡률과 이차미분이 동일시 되는 점을 이용하여, 3개의 이차미분값으로부터 직교하는 2방향을 따라 3차원형상을 복원할 수 있는 알고리즘을 구현하였다. 임의로 발생시킨 Zernike다항식의 계수로 자유곡면형상을 생성시키고, 구현된 알고리즘을 적용함으로써 검증과정을 수행하였다. 적용한 결과 최대 0.8 mm Sag를 갖는 직경 200 mm영역의 자유곡면형상에 대해 RMS 19 nm 형상복원오차를 갖고 복원됨을 확인하였다. 측정오차에 대한 복원오차 민감도를 진단하기 위해 SNR(Signal-to-Noise Ratio) 16의 가우시언 랜덤 노이즈를 부여한 후, 복원되는 형상의 오차를 진단한 결과, 197 nm의 형상복원오차가 발생함을 확인하였다.

• 한국시뮬레이션학회:학술대회논문집
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• 한국시뮬레이션학회 1999년도 추계학술대회 논문집
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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.