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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

A relation spectrum inheriting taylor series:muscle synergy and coupling for hand

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Frontiers of Information Technology & Electronic Engineering 2022年第1期23卷 145-157页

作者： Gang LIU Jing WANG Institute of Robotics and Intelligent Systems Xi’an Jiaotong UniversityXi’an710049China

There are two famous function decomposition methods in math:the taylor series and the Fourier *** Fourier series developed into the Fourier spectrum,which was applied to signal decomposition and ***,because the taylor series function cannot be solved without a definite functional expression,it has rarely been used in *** developed a taylor series using our proposed dendrite net(DD),constructed a relation spectrum,and applied it to decomposition and analysis of models and ***,knowledge of the intuitive link between muscle activity and finger movement is vital for the design of commercial prosthetic hands that do not need user ***,this link has yet to be understood due to the complexity of the human *** this study,the relation spectrum was applied to analyze the muscle—finger *** single muscle actuates multiple fingers,or multiple muscles actuate one single finger ***,the research was focused on muscle synergy and muscle coupling for the *** main contributions are twofold:(1)The findings concerning the hand contribute to the design of prosthetic hands;(2)The relation spectrum makes the online model human-readable,which unifies online performance and offline *** is available at https://***/liugang1234567/Gang-neuron.

关键词： taylor series Relation spectrum Dendrite net(DD) Prosthetic hands Machine learning Engineering

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

An Accurate Near-Field Distance Estimation Differential Algorithm

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Chinese Journal of Electronics 2022年第5期31卷 851-859页

作者： ZHAO Yan TAO Haihong CHANG Xin National Key Laboratory of Radar Signal Processing Xidian Univercity The 54th Research Institute China Electronics Technology Group Corporation School of Electronic Engineering Xidian University

The triangular geometry is the basis of near field array accurate distance estimation *** Fisher expression of traditional distance estimation is derived by utilizing the taylor series. To improve convergence rate and estimation accuracy, a novel iterative distance estimation algorithm is proposed with differential equations based on the triangular geometry. Firstly, its convergence performance is analysed in detail. Secondly,the selection of the initial value and the number of iterations are respectively studied. Thirdly, compared with the traditional estimation algorithms by utilizing the Fisher approximation, the proposed algorithm has a higher convergence rate and estimation accuracy. Moreover, its pseudocode is presented. Finally, the experiment results and performance analysis are provided to verify the effectiveness of the proposed algorithm.

关键词： iterative methods iterative distance estimation convergence performance triangular geometry Fisher expression approximation theory convergence near-field distance estimation Fisher approximation taylor series differential equations estimation theory

Numerical method of slope failure probability based on Bishop model

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Journal of Central South University of Technology 2008年第1期15卷 100-105页

作者：苏永华赵明华张月英 Institute of Geotechnical Engineering Hunan University

Based on Bishop's model and by applying the first and second order mean deviations method, an approximative solution method for the first and second order partial derivatives of functional function was deduced according to numerical analysis theory. After complicated multi-independent variables implicit functional function was simplified to be a single independent variable implicit function and rule of calculating derivative for composite function was combined with principle of the mean deviations method, an approximative solution format of implicit functional function was established through taylor expansion series and iterative solution approach of reliability degree index was given synchronously. An engineering example was analyzed by the method. The result shows its absolute error is only 0.78% as compared with accurate solution.

关键词： Bishop mechanical model failure probability of slope mean deviation method implicit function taylor series dump of open-pit

Artificial perturbation for solving the Korteweg-de Vries equation

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2006年第12期7卷 2079-2082页

作者： KHELIL N. BENSALAH N. SAIDI H. ZERARKA A. Laboratory of Physics and Applied Mathematics University Med Khider BP 145 07000 Biskra Algeria

A perturbation method is introduced in the context of dynamical system for solving the nonlinear Korteweg-de Vries (KdV) equation. Best efficiency is obtained for few perturbative corrections. It is shown that, the question of convergence of this approach is completely guaranteed here, because a limited number of term included in the series can describe a sufficient exact solution. Comparisons with the solutions of the quintic spline, and finite difference are presented.

关键词： Perturbation taylor series Quintic spline Korteweg-de Vries (KdV) equation

Adomian Decomposition Method Using Integrating Factor

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Communications in Theoretical Physics 2013年第8期60卷 159-164页

作者： Yinwei Lin Tzon-Tzer Lu Cha'o-Kuang Chen Department of Mechanical Engineering National Cheng Kung University Department of Applied Mathematics National Sun Yat-sen University

This paper proposes a new Adomian decomposition method by using integrating *** models are solved by this method to get more reliable and efficient numerical *** can also solve ordinary differential equations where th... 详细信息

关键词： Adomian decomposition integrating factor nonlinearity analytic solution taylor series erroranalysis