• East Asian mathematical journal
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• v.17 no.2
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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 $f_{\Delta}(t,s)=f(t)-f(s)$.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.4
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• pp.457-465
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• 2010

In this study, a Taylor series (T-S) model based on the Arrhenius, McVetty, and Monkman-Grant equations was developed using a mathematical analysis. In order to reduce fitting errors, the McVetty equation was transformed by considering the first three terms of the Taylor series equation. The model parameters were accurately determined by a statistical technique of maximum likelihood estimation, and this model was applied to the creep data of alloy 617. The T-S model results showed better agreement with the experimental data than other models such as the Eno, exponential, and L-M models. In particular, the T-S model was converted into an isothermal Taylor series (IT-S) model that can predict the creep strength at a given temperature. It was identified that the estimations obtained using the converted ITS model was better than that obtained using the T-S model for predicting the long-term creep life of alloy 617.

• The Korean Journal of Applied Statistics
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• v.23 no.1
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• pp.49-61
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• 2010

The time series dependencies of Financial volatility are frequently measured by the autocorrelation function of power-transformed absolute returns. It is known as the Taylor property that the autocorrelations of the absolute returns are larger than those of the squared returns. Hass (2009) developed a simple method for detecting the Taylor property in absolute-value-GAROH(1,1) (AVGAROH(1,1)) model. In this article, we fitted AVGAROH(1,1) model for various Korean financial time series and observed the Taylor property.

• Korean Journal of Mathematics
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• v.23 no.4
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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.

• Journal for History of Mathematics
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• v.31 no.1
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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.

• Proceedings of the IEEK Conference
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• 2001.06b
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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.

• Proceedings of the KIEE Conference
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• 2005.05a
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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.

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.1
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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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• v.17 no.11
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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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• v.29 no.2
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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.