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taylor series AND ORTHOGONALITY OF THE OCTONION ANALYTIC FUNCTIONS

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Acta Mathematica Scientia 2001年第3期21卷 323-330页

作者：李兴民彭立中 Department of Mathematics Guangzhou Normal University Guangzhou 510405 China Department of Mathematics Beijing University Beijing 100871 China

The taylor series of the Octonion analytic function is given. And the orthogonal formula for the Octonion analytic functions is also obtained.

关键词： Octonion O-analytic function taylor series orthogonality

SOME REMARKS ON HOLOMORPHIC FUNCTIONS AND taylor series IN C^n

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Acta Mathematica Scientia 2008年第4期28卷 721-726页

作者：余家荣 School of Mathematics and Statistics Wuhan University

Some previous results on convergence of taylor series in C^n [3] are improved by indicating outside the domain of convergence the points where the series diverges and simplifying some proofs. These results contain the Cauchy-Hadamard theorem in C. Some Cauchy integral formulas of a holomorphic function on a closed ball in C^n are constructed and the taylor series expansion is deduced.

关键词： Polar coordinates taylor series holomorphic functions

Stability and Accuracy Analysis for taylor series Numerical Method

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Tsinghua Science and Technology 2004年第1期9卷 51-56页

作者：赵丽滨姚振汉王寿梅 Department of Engineering Mechanics Tsinghua University Beijing 100084 China Solid Mechanics Research Center Beihang University Beijing 100083 China

The taylor series numerical method (TSNM) is a time integration method for solving problems in structural dynamics. In this paper, a detailed analysis of the stability behavior and accuracy characteristics of this method is given. It is proven by a spectral decomposition method that TSNM is conditionally stable and belongs to the category of explicit time integration methods. By a similar analysis, the characteristic indicators of time integration methods, the percentage period elongation and the amplitude decay of TSNM, are derived in a closed form. The analysis plays an important role in implementing a procedure for automatic searching and finding convergence radii of TSNM. Finally, a linear single degree of freedom undamped system is analyzed to test the properties of the method.

关键词： structural dynamics time integration taylor series stability accuracy

Slow growing random taylor series

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Progress in Natural Science:Materials International 1997年第4期 25-33页

作者：孙道椿 China Department of Mathematics Wuhan 430072 Wuhan University

The slow growth random taylor series of a class general enough in unit disk has been studied, and it is proved that every point on unit circumference is almost surely a singular point, and that if the random variables... 详细信息

关键词： random variable slow growth taylor series singular point.

Study on Coded Permutation Entropy of Finite Length Gaussian White Noise Time series

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Chinese Journal of Electronics 2024年第1期33卷 185-194页

作者： Huihui SUN Xiaofeng ZHANG School of Physics and Information Technology Shaanxi Normal University

As an extension of permutation entropy(PE), coded permutation entropy(CPE) improves the performance of PE by making a secondary division for ordinal patterns defined in PE. In this study, we provide an exploration of the statistical properties of CPE using a finite length Gaussian white noise time series theoretically. By means of the taylor series expansion, the approximate expressions of the expected value and variance of CPE are deduced and the Cramér-Rao low bound(CRLB) is obtained to evaluate the performance of the CPE estimator. The results indicate that CPE is a biased estimator, but the bias only depends on relevant parameters of CPE and it can be easily corrected for an arbitrary time series. The variance of CPE is related to the encoding patterns distribution,and the value converges to the CRLB of the CPE estimator when the time series length is large enough. For a finitelength Gaussian white noise time series model, the predicted values can match well with the actual values, which further validates the statistic theory of CPE. Using the theoretical expressions of CPE, it is possible to better understand the behavior of CPE for most of the time series.

关键词： Time series analysis White noise Predictive models taylor series Entropy Encoding Time measurement

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Design of a Multifrequency Signal Parameter Estimation Method for the Distribution Network Based on HIpST

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Energy Engineering 2024年第3期121卷 729-746页

作者： Bin Liu Shuai Liang Renjie Ding Shuguang Li Tongliao Power Supply Company State Grid East Inner Mongolia Electric Power Co.Ltd.Tongliao028000China School of Electrical Engineering Northeast Electric Power UniversityJilin132012China

The application of traditional synchronous measurement methods is limited by frequent fluctuations of electrical signals and complex frequency components in distribution ***,it is critical to find solutions to the issues of multifrequency parameter estimation and synchronous measurement estimation accuracy in the complex environment of distribution *** utilizing the multifrequency sensing capabilities of discrete Fourier transform signals and taylor series for dynamic signal processing,a multifrequency signal estimation approach based on HT-IpDFT-STWLS(HIpST)for distribution networks is ***,by introducing the Hilbert transform(HT),the influence of noise on the estimation algorithm is ***,signal frequency components are obtained on the basis of the calculated signal envelope spectrum,and the interpolated discrete Fourier transform(IpDFT)frequency coarse estimation results are used as the initial values of symmetric taylor weighted least squares(STWLS)to achieve high-precision parameter estimation under the dynamic changes of the signal,and the method increases the number of discrete ***,the accuracy of this proposed method is verified by simulation *** show that this proposed method can accurately achieve the parameter estimation of multifrequency signals in distribution *** approach provides a solution for the application of phasor measurement units in distribution networks.

关键词： Discrete fourier transform taylor series hilbert transform multifrequency signal parameter estimation

Maximum Correntropy High-Order Extended Kalman Filter

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Chinese Journal of Electronics 2022年第1期31卷 190-198页

作者： SUN Xiaohui WEN Chenglin WEN Tao School of Automation Hangzhou Dianzi University School of Automation Guangdong University of Petrochemical Technology School of Electronic and Information Engineering Beijing Jiaotong University

In this paper, a novel maximum correntropy high-order extended Kalman filter(H-MCEKF) is proposed for a class of nonlinear non-Gaussian systems presented by polynomial form. All high-order polynomial terms in the state model are defined as implicit variables and regarded as parameter variables; the original state model is equivalently formulated into a pseudo-linear form with original variables and parameter variables; the dynamic relationship between each implicit variable and all variables is modeled, then an augmented linear state model appears by combing with pseudo-linear state model; similarly, the nonlinear measurement model can be equivalently rewritten into linear form; once again, the statistical characteristics of non-Gaussian modeling error are described by mean value and variance based on their finite samples; combing original measurement model with predicted value regarded as added state measurement, a cost function to solve the state estimation based on maximum correntropy criterion(MCC) is constructed; on the basis of this cost function, the state estimation problem can be equivalently converted into a recursive solution problem in the form of Kalman filter, in which the filter gain matrix is solved by numerical iteration though its fixed-point equation; illustration examples are presented to demonstrate the effectiveness of the new algorithm.

关键词： Kalman filters Random variables taylor series Mathematical models State estimation Nonlinear filters Measurement uncertainty

ON A GENERALIZED taylor THEOREM： A RATIONAL PROOF OF THE VALIDITY OF THE HOMOTOPY ANALYSIS METHOD

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Applied Mathematics and Mechanics(English Edition) 2003年第1期24卷 53-60页

作者： LIAOShi－jun SchoolofNavalArchitecture＆OceanEngineering ShanghaiJiaotongUniversityShanghai200030China

A generalized taylor series of a complex function was derived and some related theorems about its convergence region were given. The generalized taylor theorem can be applied to greatly enlarge convergence regions of approximation series given by other traditional techniques. The rigorous proof of the generalized taylor theorem also provides us with a rational base of the validity of a new kind of powerful analytic technique for nonlinear problems, namely the homotopy analysis method.

关键词： taylor series convergence and summability of series homotopy analysis method perturbation

Discretization of Nonlinear Non-affine Time Delay Systems Based on Second-order Hold

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International Journal of Automation and computing 2014年第3期11卷 320-327页

作者： Yuan-Liang Zhang School of Mechanical Engineering Huaihai Institute of Technology Jiangsu Province Research and Development Institute of Marine Resources

When calculating the sampled-date representation of nonlinear systems second-order hold(SOH) assumption can be applied to improving the precision of the discretization results. This paper proposes a discretization method based on taylor series and the SOH assumption for the nonlinear systems with the time delayed non-affine input. The mathematical structure of the proposed discretization method is explored. This proposed discretization method can provide a precise and finite dimensional discretization model for the nonlinear time-delayed non-affine system by keeping the truncation order of the taylor series. The performance of the proposed discretization method is evaluated by doing the simulation using a nonlinear system with the time-delayed non-affine *** input signals, time-delay values and sampling periods are considered in the simulation to investigate the proposed *** simulation results demonstrate that the proposed method is practical and easy for time-delayed nonlinear non-affine *** comparison between SOH assumption with first-order hold(FOH) and zero-order hold(ZOH) assumptions is given to show the advantages of the proposed method.

关键词： Nonlinear system non-affine input discretization taylor series second-order hold(SOH).