• Title, Summary, Keyword: Taylor series

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A study on understanding of Taylor series (테일러급수의 이해에 대한 연구)

  • Oh, Hye-Young
    • Communications of Mathematical Education
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    • v.31 no.1
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    • pp.71-84
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    • 2017
  • Taylor series has a complicated structure comprising of various concepts in college major mathematics. This subject is a strong tool which has usefulness and applications not only in calculus, analysis, and complex analysis but also in physics, engineering etc., and other study. However, students have difficulties in understanding mathematical structure of Taylor series convergence correctly. In this study, after classifying students' mathematical characteristic into three categories, we use structural image of Taylor series convergence which associated with mathematical structure and operation acted on that structure. Thus, we try to analyze the understanding of Taylor series convergence and present the results of this study.

TDOA Measurement Based Taylor Series Design Method Considering Height Error for Real-Time Locating Systems (실시간 위치추적 시스템에서 높이 오차를 고려한 TDOA 측정치 기반 테일러 급수 설계 방법)

  • Kang, Hee-Won;Hwang, Dong-Hwan;Park, Chan-Sik
    • Journal of Institute of Control, Robotics and Systems
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    • v.16 no.8
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    • pp.804-809
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    • 2010
  • This paper proposes a Taylor-series design method which reduces the height error of the tag when readers are arranged at the same height in 3-dimensional space. The proposed method consists of two steps. Firstly, the planar position is estimated by the Taylor-series method using the TDOA measurement. Next, the height is estimated from the estimated planar position. In order to show the validity of the proposed method, computer simulations were performed for the static case and linear trajectory of the tag. Results show that the proposed method gives convergent estimated position and better height estimate than the Taylor series method.

APPLICATIONS OF TAYLOR SERIES FOR CARLEMAN'S INEQUALITY THROUGH HARDY INEQUALITY

  • IDDRISU, MOHAMMED MUNIRU;OKPOTI, CHRISTOPHER ADJEI
    • 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.

NEW BOUNDS FOR A PERTURBED GENERALIZED TAYLOR'S FORMULA

  • Cerone, P.;Dragomir, S.S.
    • 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 $f_{\Delta}(t,s)=f(t)-f(s)$.

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Taylor Series-Based Long-Term Creep-Life Prediction of Alloy 617 (Taylor 급수를 이용한 617 합금의 장시간 크리프 수명 예측)

  • Yin, Song-Nan;Kim, Woo-Gon;Park, Jae-Young;Kim, Soen-Jin;Kim, Yong-Wan
    • 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.

Evidence of Taylor Property in Absolute-Value-GARCH Processes for Korean Financial Time Series (Absolute-Value-GARCH 모형을 이용한 국내 금융시계열의 Taylor 성질에 대한 사례연구)

  • Baek, J.S.;Hwang, S.Y.;Choi, M.S.
    • 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.

Exploring Teaching Way Using GeoGebra Based on Pre-Service Secondary Teachers' Understanding-Realities for Taylor Series Convergence Conceptions (테일러급수 수렴에 대한 예비중등교사의 이해실태와 GeoGebra를 활용한 교수방안 탐색)

  • Kim, Jin Hwan
    • School Mathematics
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    • v.16 no.2
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    • pp.317-334
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    • 2014
  • The purpose of this study is to grasp pre-service secondary teachers' understanding-realities for Taylor series convergence conceptions and to examine a teaching way using GeoGebra based on the understanding-realities. In this study, most pre-service teachers have abilities to calculate the Taylor series and radius of convergence, but they are vulnerable to conceptual problems which give meaning of the equality between a given function and its Taylor series at any point. Also they have some weakness in determining the change of radius of convergence according to the change of Taylor series' center. To improve their weakness, we explore a teaching way using dynamic and CAS functionality of GeoGebra. This study is expected to improve the pedagogical content knowledge of pre-service secondary mathematics teachers for infinite series treated in high school mathematics.

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Taylor Series Discretization Method for Input-Delay Nonlinear Systems

  • Zhang, Zheng;Chong, Kil-To
    • Proceedings of the KIEE Conference
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    • pp.152-154
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    • 2007
  • Anew discretization method for the input-driven nonlinear continuous-time system with time delay is proposed. It is based on the combination of Taylor series expansion and first-order hold assumption. The mathematical structure of the new discretization scheme is explored. The performance of the proposed discretization procedure is evaluated by case studies. The results demonstrate that the proposed discretization scheme can assure the system requirements even though under a large sampling period. A comparison between first order hold and zero-order hold is simulated also.

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NORM CONVERGENT PARTIAL SUMS OF TAYLOR SERIES

  • YANG, JONGHO
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.5
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    • pp.1729-1735
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    • 2015
  • It is known that the partial sum of the Taylor series of an holomorphic function of one complex variable converges in norm on $H^p(\mathbb{D})$ for 1 < p < ${\infty}$. In this paper, we consider various type of partial sums of a holomorphic function of several variables which also converge in norm on $H^p(\mathbb{B}_n)$ for 1 < p < ${\infty}$. For the partial sums in several variable cases, some variables could be chosen slowly (fastly) relative to other variables. We prove that in any cases the partial sum converges to the original function, regardlessly how slowly (fastly) some variables are taken.