• 대한수학교육학회지:학교수학
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• 제19권1호
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• pp.95-116
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• 2017

지수함수의 미분에 대한 경험이 없는 학생들을 대상으로 자연상수 e를 구성하는 과정과 자연상수 e에 대한 이해를 기반으로 지수함수 $y=2^x$의 x=0에서 미분계수를 구하는 일련의 과정을 교수실험을 통하여 관찰하였다. 본 연구의 목적은 학생들의 반응을 일반화하는 것에 있는 것이 아니라, 실험에 참여한 학생들의 다양한 반응 분석을 통하여 미적분 관련 수학적 개념 지도에 대한 시사점을 찾아 제시하고자 하였다. 본 연구와 같이 학습자의 이해 방식과 구성 방식에 대한 연구 자료의 축적은 이후 미적분 관련 학습 모델을 제시하는데 중요한 기초 자료가 될 것으로 기대된다.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권4호
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• pp.387-392
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• 2008

In this note, an alternative proof and extensions are provided for the following conclusions in [6, Theorem 1 and Theorem 3]: The functions $\frac1{x^2}-\frac{e^{-x}}{(1-e^{-x})^2}\;and\;\frac1{t}-\frac1{e^t-1}$ are decreasing in (0, ${\infty}$) and the function $\frac{t}{e^{at}-e^{(a-1)t}}$ for a $a{\in}\mathbb{R}\;and\;t\;{\in}\;(0,\;{\infty})$ is logarithmically concave.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 춘계학술대회논문집C
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• pp.386-391
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• 2001

This paper presents a new two-point approximation method based on the exponential intervening variable. To avoid the lack of definition of the conventional exponential intervening variables due to zero- or negative-valued design variables the shifting level into each exponential intervening variable is introduced. Then a new quadratic approximation, whose Hessian matrix has only diagonal elements of different values, is proposed in terms of these intervening variables. These diagonal elements are computed in a closed form, which correct the typical error in the approximate gradient of the TANA series due to the lack of definition of exponential type intervening variables and their incomplete second-order terms. Also, a correction coefficient is multiplied to the pre-determined quadratic term to match the value of approximate function with that of the original function at the previous point. Finally, the authors developed a sequential approximate optimizer, solved several typical design problems used in the literature and compared these optimization results with those of TANA-3. These comparisons show that the proposed method gives more efficient and reliable results than TANA-3.

• 한국지반공학회논문집
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• 제25권10호
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• pp.67-76
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• 2009

국내 풍화암 터널현장에서 수집한 RMR 평점, RMR* 평점 그리고 천단침하량의 자료를 이용하여 통계적 분석을 실시하였으며, 분석된 자료를 이용하여 회귀분석, 지수함수, 그리고 인공신경망(ANN)으로 천단침하량을 예측하였다. 예측 결과, ANN, 지수함수에 의한 근사함수, 그리고 회귀분석의 천단침하량 예측 순으로 실측치에 근접하였다. 회귀분석으로 추정된 천단침하량의 범위는 매우 넓게 분포하였으며, 계측치에 비하여 과대한 침하량을 예측하였다. 또한 모든 방법에서 RMR 평점을 사용한 예측이 RMR* 평점을 사용하여 예측한 결과보다 계측 침하량에 더 가까운 예측을 하였다.

• 대한기계학회논문집
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• 제6권3호
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• pp.247-255
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• 1982

The heat diffusion equation for an annular fin is analyzed by Laplace transformation. The fin has a uniform thickness, with its end insulated, and three different temperature profiles at the base such as step change, harmonic and exponential functions. The exact solutions for the temperature and heat flux of the fins are obtained with the infinite series. The series solutions converge rapidly for large values of dimensionless time, but slowly for small values. Therefore some approximate solutions are presented here to fine the temperature distribution and heat flux for small values of dimensionless time. Furthermore a simple approximate heat flux, .OMEGA.=1.13c.tau.$^{1}$2/ is found in the range of .tau. .leg. o.1/c for the exponential function at the base.

• 한국수학교육학회지시리즈A:수학교육
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• 제40권1호
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• pp.113-123
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• 2001

We investigated an irrational constant e and compared its computational methods using spreadsheet. Such methods are based on classical definition, infinite series, continued fraction, infinite product exponential function and accelerated classical method. This kind of work is focused on experimental mathematics using computers in math class. This approach will be helpful for mathematics teachers to teach constant e in their classroom.

• International Journal of Reliability and Applications
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• 제7권2호
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• pp.111-125
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• 2006

This paper introduces different vectors of the reliability equivalence factors of a series system consists of n independent and nonidentical components. The failure rates of the system components are assumed to be constant. The reliability function and mean time to failure are used as performances to derive the reliability equivalences of the system. The results presented here generalize those available in the literatures. Numerical study is given to explain how one can utilize the theoretical results obtained.

• 대한수학회지
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• 제48권4호
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• pp.775-795
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• 2011

The disturbance attenuation problem for a class of discretetime switched linear systems with exponential uncertainties via switched state feedback and switched dynamic output feedback is investigated, respectively. By using Taylor series approximation and convex polytope technique, exponentially uncertain discrete-time switched linear system is transformed into an equivalent switched polytopic model with additive norm bounded uncertainty. For such equivalent switched model, one designs its switching strategy and associated state feedback controllers and dynamic output feedback controllers so that whole switched model is asymptotical stabilization with H-in nity disturbance attenuation base on switched Lyapunov function and LMI approach. Finally, two numerical examples are presented to illustrate our results.

• 대한안전경영과학회:학술대회논문집
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• 대한안전경영과학회 2008년도 추계학술대회
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• pp.153-160
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• 2008

This paper presents the log likelihood function for integrated models for ALT such as exponential-general Eyring, Weibull-temperature and specific heat, lognormal-temperature and specific heat. Additionally this paper estimates the system reliability and mean time to failure(MTTF) for series, parallel, k of n, and standby system using ALT linkage parameter. Lastly this study designs three variable reliability acceptance sampling(RAS) plans such as type I, II censored test, sequential test by the use of integrated models for ALT.

• Journal of Mechanical Science and Technology
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• 제15권9호
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• pp.1257-1267
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• 2001

For efficient mechanical system optimization, a new two-point approximation method is presented. Unlike the conventional two-point approximation methods such as TPEA, TANA, TANA-1, TANA-2 and TANA-3, this introduces the shifting level into each exponential intervening variable to avoid the lack of definition of the conventional exponential intervening variables due to zero-or negative-valued design variables. Then a new quadratic approximation whose Hessian matrix has only diagonal elements of different values is proposed in terms of these shifted exponential intervening variables. These diagonal elements are determined in a closed form that corrects the typical error in the approximate gradient of the TANA series due to the lack of definition of exponential type intervening variables and their incomplete second-order terms. Also, a correction coefficient is multiplied to the pre-determined quadratic term to match the value of approximate function with that of the previous point. Finally, in order to show the numerical performance of the proposed method, a sequential approximate optimizer is developed and applied to solve six typical design problems. These optimization results are compared with those of TANA-3. These comparisons show that the proposed method gives more efficient and reliable results than TANA-3.