• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1996년도 Proceedings of the Korea Automatic Control Conference, 11th (KACC); Pohang, Korea; 24-26 Oct. 1996
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• pp.111-114
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• 1996

This paper proposes a robust control method using Universal Learning Network(U.L.N.) and second order derivatives of U.L.N.. Robust control considered here is defined as follows. Even if external input (equal to reference input in this paper) to the system at control stage changes awfully from that at learning stage, the system can be controlled so as to maintain a good performance. In order to realize such a robust control, a new term concerning the perturbation is added to a usual criterion function. And parameter variables are adjusted so as to minimize the above mentioned criterion function using the second order derivative of the criterion function with respect to the parameters.

• Journal of applied mathematics & informatics
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• 제6권2호
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• pp.393-406
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• 1999

Affine invariant sufficient conditions are given for two local convergence theorems involving inexact Newton-like methods. The first uses conditions on the first Frechet-derivative whereas the second theorem employs hypotheses on the second. Radius of con-vergence as well as rate of convergence results are derived. Results involving superlinear convergence and known to be true for inexact Newton methods are extended here. Moreover we show that under hypotheses on the second Frechet-derivation our radius of convergence results are derived. Results involving superlinear convergence and known to be true or inexact Newton methods are extended here. Moreover we show that under hypotheses on the second Frechet-derivative our radius of conver-gence is larger than the corresponding one in [10]. This allows a wider choice for the initial guess. A numerical example is also pro-vided to show that our radius of convergence is larger then the one in [10].

• 대한수학회논문집
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• 제29권3호
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• pp.439-449
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• 2014

In this paper, we present some inequalities for the non-tangential derivative of f(z). For the function $f(z)=z+b_{p+1}z^{p+1}+b_{p+2}z^{p+2}+{\cdots}$ defined in the unit disc, with ${\Re}\(\frac{f^{\prime}(z)}{{\lambda}f{\prime}(z)+1-{\lambda}}\)$ > ${\beta}$, $0{\leq}{\beta}$ < 1, $0{\leq}{\lambda}$ < 1, we estimate a module of a second non-tangential derivative of f(z) function at the boundary point ${\xi}$, by taking into account their first nonzero two Maclaurin coefficients. The sharpness of these estimates is also proved.

• Journal of Biosystems Engineering
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• 제22권2호
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• pp.247-255
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• 1997

This study was conducted to develop regression models predicting sugar and acid contents in intact fruits nondestructively by using the second derivative of absorbance spectrum measured with a spectrophotometer wavelength range of 400nm to 2, 400nm. The correlation analysis was made in wavelength range of 600nm to 1, 100nm and 600nm to 2, 400nm respectively, in order to examine the feasibility of using a real time spectrophotometer, which covers the former range, in predicting sugar and acid contents. The second derivative data of the spectrum were obtained by varying smoothing size and derivative size of the original absorbance spectrum. SAS statistical package program was used for the regression analysis. The sugar contents of Fuji apple, Shingo pear md Yumyung peach could be predicted with SEPs of 0.40, 1.17 and 0.77 respectively, in the spectrum range of 600 to 1, 100nm. The highest correlation coefficient of the titratible acidity of apple was -0.45 at 2, 346nm and regression models indicated determination coefficient less than 0.47.

• 한국수학교육학회:학술대회논문집
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• 한국수학교육학회 2010년도 제44회 전국수학교육연구대회
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• pp.249-259
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• 2010

This report is intended to document beliefs that engineers working as senior high school teachers have in Mexico. Documents come from the analysis of answers provided for two tasks contained in a questionnaire: one of them is marking statements as true or false in relation to the derivative function; the second one is about solving different problems: calculation of derivative of piecewise functions and the calculation of maximum and minimum of a polynomial function. Results show the strengths, quasi-logical relations and grouping which are verified in their system of beliefs and knowledge.

• 호남수학학술지
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• 제41권2호
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• pp.381-390
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• 2019

In this paper, we introduce interesting subclasses ${\mathcal{H}}^{p,q,{\beta},{\alpha}}_{{\sigma}B}$ and ${\mathcal{H}}^{p,q,{\beta}}_{{\sigma}B}({\gamma})$ of bi-univalent functions by (p, q)-derivative operator. Furthermore, we find upper bounds for the second and third coefficients for functions in these subclasses. The results presented in this paper would generalize and improve some recent works of several earlier authors.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.31-48
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• 2007

The paper deals with the solution of some fractional partial differential equations obtained by substituting modified Riemann-Liouville derivatives for the customary derivatives. This derivative is introduced to avoid using the so-called Caputo fractional derivative which, at the extreme, says that, if you want to get the first derivative of a function you must before have at hand its second derivative. Firstly, one gives a brief background on the fractional Taylor series of nondifferentiable functions and its consequence on the derivative chain rule. Then one considers linear fractional partial differential equations with constant coefficients, and one shows how, in some instances, one can obtain their solutions on bypassing the use of Fourier transform and/or Laplace transform. Later one develops a Lagrange method via characteristics for some linear fractional differential equations with nonconstant coefficients, and involving fractional derivatives of only one order. The key is the fractional Taylor series of non differentiable function $f(x+h)=E_{\alpha}(h^{\alpha}{D_x^{\alpha})f(x)$.

• 대한화학회지
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• 제37권1호
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• pp.112-118
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• 1993

수용성 발색시약인 N,N'-oxalylbis(2-pyridyl-3'-sulphobenzoylhydrazone)을 합성하여 분광광도법 및 1, 2차 미분 분광광도법에 의한 구리의 정량법을 개발하였다. 정량은 구리착물 수용액(pH 1.89)의 흡광도 및 1,2차 미분값을 379, 395, 363 그리고 421nm의 파장에서 각각 측정함으로써 수행되었다. 정량 가능한 구리의 농도 범위는 0.12~1.20${\mu}g$ /ml 였으며 이 방법을 알루미늄 합금시료의 분석에 적용하였다. 2차 미분 분광광도법으로 421nm에서 측정했을 때가 가장 좋은 결과를 나타내었다.

• Nuclear Engineering and Technology
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• 제54권5호
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• pp.1644-1651
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• 2022

This paper focuses on the power-level control of nuclear power plants (NPPs) in the presence of lumped disturbances. An adaptive second-order nonsingular terminal sliding mode control (ASONTSMC) scheme is proposed by resorting to the second-order nonsingular terminal sliding mode. The pre-existing mathematical model of the nuclear reactor system is firstly described based on point-reactor kinetics equations with six delayed neutron groups. Then, a second-order sliding mode control approach is proposed by integrating a proportional-derivative sliding mode (PDSM) manifold with a nonsingular terminal sliding mode (NTSM) manifold. An adaptive mechanism is designed to estimate the unknown upper bound of a lumped uncertain term that is composed of lumped disturbances and system states real-timely. The estimated values are then added to the controller, resulting in the control system capable of compensating the adverse effects of the lumped disturbances efficiently. Since the sign function is contained in the first time derivative of the real control law, the continuous input signal is obtained after integration so that the chattering effects of the conventional sliding mode control are suppressed. The robust stability of the overall control system is demonstrated through Lyapunov stability theory. Finally, the proposed control scheme is validated through simulations and comparisons with a proportional-integral-derivative (PID) controller, a super twisting sliding mode controller (STSMC), and a disturbance observer-based adaptive sliding mode controller (DO-ASMC).

• 전자공학회논문지SC
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• 제44권4호통권316호
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• pp.15-20
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• 2007

현재, 우리나라 당뇨병의 유병률은 빠른 속도로 증가하고 있으며 당뇨병의 유병기간이 길수록 각종 합병증이 발생하여 더욱 심각한 증상을 나타내는데, 그 중 비만 및 고혈당, 당대사장애로 인한 당뇨병성 혈관합병증과 말초 혈관 경화증이 많이 발병하고 있는 실정이다. 따라서 본 연구에서는 광혈류량 측정법(Photoplethysmography)으로 손가락 및 발가락에서 얻어진 맥파의 2차 미분분석을 통해 연령이 비슷한 정상인 50명과 당뇨병으로 확진된 50명의 말초 혈관 탄성도를 객관적으로 비교하고자 하였다. PPG 파형의 2차 미분 분석에 사용되는 평가 인자는 a, b, c, d, e 이고, b/a는 혈관의 탄성도를 의미하며 탄성도가 떨어질수록 b/a의 절대 값은 감소하게 된다. 정상인 50명의 PPG 2차 미분 b/a값은 $-1.09{\pm}0.14$, 당뇨병 환자 50명의 PPG 2차 미분 b/a값은 $-0.81{\pm}0.09$로 정상인에 비해 당뇨병 환장의 말초혈관 탄성도가 감소하였으며, Independent t-test 검정 결과 통계적으로 유의한 차이를 보였다(p<0.05). 본 연구에서는 PPG 파형의 2차 미분 분석을 통하여 정상인과 혈관합병증 발병율이 높은 당뇨병 환자의 말초혈관 탄성도를 비교하였으며, 향후 비침습적이고 간단한 방법으로 당뇨병 환자의 말초혈관 탄성도와 혈관 경화정도를 객관적으로 평가하고 진단함으로써 당뇨병 환자들의 심혈관계질환 사전예방과 치료효과 판정에 도움을 줄 것으로 기대한다.