• East Asian mathematical journal
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• 제17권2호
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• pp.197-215
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• 2001

A generalised Taylor series with integral remainder involving a convex combination of the end points of the interval under consideration is investigated. Perturbed generalised Taylor series are bounded in terms of Lebesgue p-norms on $[a,b]^2$ for $f_{\Delta}:[a,b]^2{\rightarrow}\mathbb{R}$ with $f_{\Delta}(t,s)=f(t)-f(s)$.

• 대한기계학회논문집A
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• 제34권4호
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• pp.457-465
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• 2010

본 연구에서는 McVetty 와 Monkman-Grant 의 모델에 기초하여 만들어진 새로운 크리프 수명예측 모델인 Taylor 급수(T-S) 모델을 제안하였다. 본 모델은 회귀분석에서 발생하는 오차를 줄이기 위하여 McVetty 모델에서 sinh 함수를 Taylor 급수에 의해 변환한 후 첫 3 개항을 취한 것으로서 모델중의 상수 값은 통계학적 방법인 최대가능성 기법을 이용하여 결정되었다. T-S 모델을 이용하여 Alloy 617 의 크리프 수명을 예측한 결과 Eno, 지수함수 및 Larson-Miller(L-M) 방법에 비해 더 정확한 예측을 하는 것으로 나타났다. 또한 T-S 모델은 특정 온도에서 크리프 수명 예측을 할 수 있는 등온 T-S(IT-S) 모델로 표현될 수 있었으며, IT-S 모델은 Alloy 617 의 장시간 크리프 수명예측에서 가장 좋은 예측을 하는 것으로 나타났다.

• 응용통계연구
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• 제23권1호
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• pp.49-61
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• 2010

금융시계열 변동성의 의존성(dependency)은 멱변환된 절대수익률의 자기상관함수를 이용하여 측정할 수 있다. 이때, 절대수익률의 자기상관이 제곱수익률의 자기상관보다 더 강하게 나타나는 성질을 Taylor 성질이라고 한다. 본 논문에서는 여러 가지 국내 금융시계열 자료에 대하여 absolute-value GARCH(1,1)(AVGARCH(1,1)) 모형을 적합하고, Haas (2009)가 제안한 방법을 이용하여 Taylor 성질의 존재여부에 대하여 살펴보았다.

• Korean Journal of Mathematics
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• 제23권4호
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• pp.655-664
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• 2015

In this paper, we prove the discrete Hardy inequality through the continuous case for decreasing functions using elementary properties of calculus. Also, we prove the Carleman's inequality through limiting the discrete Hardy inequality with applications of Taylor series.

• 한국수학사학회지
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• 제31권1호
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• pp.19-35
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• 2018

Taylor's Theorem is an important theorem which is applied to several disciplines. It is usually taught in a college-level calculus course for the first time. Many students have a hard time to understand or to make applications. In this paper, we look into the history of the development of Taylor's theorem and consider a teaching strategy of the theorem.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2001년도 하계종합학술대회 논문집(2)
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• pp.129-132
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• 2001

This paper presents an efficient method to estimate the maximum SSN (simultaneous switching noise) for ground interconnection networks in CMOS systems using Taylor's series and analyzes the truncation error that has occurred in Taylor's series approximation. We assume that the curve form of noise voltage on ground interconnection networks is linear and derive a polynomial expression to estimate the maximum value of SSN using $\alpha$-power MOS model. The maximum relative error due to the truncation is shown to be under 1.87% through simulations when we approximate the noise expression in the 3rd-order polynomial.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2005년도 심포지엄 논문집 정보 및 제어부문
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• pp.125-127
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• 2005

In this paper, we propose a new scheme for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption. This scheme is applied to the sample-data representation of a nonlinear system with constant state tine-delay. The mathematical expressions of the discretization scheme are presented and the effect of the time-discretization method on key properties of nonlinear control system with state tine-delay, such as equilibrium properties and asymptotic ability, is examined. The proposed scheme provides a finite-dimensional representation for nonlinear systems with state time-delay enabling existing controller design techniques to be applied to then. The performance of the proposed discretization procedure is evaluated using a nonlinear system. For this nonlinear system, various sampling rates and time-delay values are considered.

• 제어로봇시스템학회논문지
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• 제11권1호
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• pp.1-8
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• 2005

A new discretization algorithm for nonlinear systems with delayed input is proposed. The algorithm is represented by Taylor series expansion and ZOH assumption. This method is applied to the sampled-data representation of a nonlinear system with the time-delay input. Additionally, the delay in input is time varying and its amplitude is bounded. The maximum time-delay in input is assumed to be two sampling periods. The mathematical expressions of the discretization method are presented and the ability of the algorithm is tested for some of the examples. The computer simulation proves the proposed algorithm discretizes the nonlinear system with the variable time-delay input accurately.

• Journal of Mechanical Science and Technology
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• 제17권11호
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• pp.1608-1615
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• 2003

This paper studies on the linearization of a looper system in hot strip mills, that plays an important role in regulating a strip tension or a strip width. Nonlinear dynamic equations of the looper system are analytically linearized by a static feedback linearization algorithm with a compensator. The proposed linear model of the looper is validated by a comparison with a linear model using Taylor's series. It is shown that the linear model by static feedback well describes nonlinearities of the looper system than one using Taylor's series. Furthermore, it is shown from the design of an ILQ controller that the linear model by static feedback is very useful in designing a linear controller of the looper system.

• Nonlinear Functional Analysis and Applications
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• 제29권2호
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• pp.435-450
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• 2024

This study depends on the modified conformable fractional derivative definition to generalize and proves some theorems of the classical power series into the fractional power series. Furthermore, a comprehensive formulation of the generalized Taylor's series is derived within this context. As a result, a new technique is introduced for the fractional power series. The efficacy of this new technique has been substantiated in solving some fractional differential equations.