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Calculation of singular point quantities at infinity for a type of polynomial differential systems

MATHEMATICS AND COMPUTERS IN SIMULATION 2015年 109卷 153-173页

作者： Wu, Yusen Li, Peiluan Chen, Haibo Henan Univ Sci & Technol Sch Math & Stat Luoyang 471023 Henan Peoples R China Cent South Univ Sch Math & Stat Changsha 410075 Hunan Peoples R China

The center problem at infinity is far to be solved in general. In this paper we develop a procedure to resolve it for a particular type of polynomial differential systems. The problem is solved by writing its concomitant differential equation in the complex coordinates introduced by Yirong Liu and by developing a new method of computation of the so called singular point quantities. This method is based on the transformation of infinity into the elementary origin. Finally, the investigation of center problem for the infinity of a particular family of planar polynomial vector fields of degree 5 is carried out to illustrate the main theoretical results. These involve extensive use of a Computer Algebra System, we have chosen to use Mathematica (R). (C) 2014 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

关键词： Infinity Singular point quantity Homeomorphic transformation recursive algorithm

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Maximally Flat-Frequency-Response Multiple-Resonator-Based Harmonic Analysis

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2017年第12期66卷 3387-3398页

作者： Kusljevic, Miodrag D. Tomic, Josif J. Poljak, Predrag D. TERMOELEKTRO ENEL AD Belgrade 11060 Serbia Univ Novi Sad Novi Sad 21000 Serbia Inst Chem Technol & Met Belgrade 11000 Serbia

This paper presents an improved approach to the recently proposed multiple-resonator-based method for the harmonic analysis that has been provided in the previous papers. Previously, two inherent particular cases have been considered. In these cases, reference points in which estimation is performed are located either in the middle or at the end of the observation interval. The first case exhibits a good noises and unwanted harmonics attenuation but possesses a large delay time. In the second case, the filters are able to form a zero-flat phase response about the operation frequency and hence able to provide instantaneous estimates, but with large overshoots caused by resonant frequencies at the edges of the passband, and the high level of the sidelobes, that also makes it susceptible to interharmonics and noise interference. The aim of this paper is to propose a compromised solution provided by the tradeoff between those opposite requirements by shifting this point along the observation interval. This way the frequency responses of the estimator are reshaped. A maximally flatness of the frequency response in the operation harmonic frequency is kept in all cases, but only locating the reference point in a fraction around the center of the observation interval provides flat-top frequency responses. The effectiveness of the proposed estimation technique is shown through simulations.

关键词： Discrete Fourier transform (DFT) finiteimpulse response (FIR) filter group delay harmonic analysis maximally flat (MF) filter multiple resonator (MR) recursive algorithm Taylor-Fourier transform (TFT)

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Distributed filtering over wireless sensor networks with parameter and topology uncertainties

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INTERNATIONAL JOURNAL OF CONTROL 2020年第4期93卷 910-921页

作者： Zhang, Junfeng He, Xiao Zhou, Donghua Tsinghua Univ Dept Automat BNRist Beijing 100084 Peoples R China Shandong Univ Sci & Technol Coll Elect Engn & Automat Qingdao 266590 Peoples R China

In this paper, the robust distributed filtering problem is investigated for a class of wireless sensor networks with stochastic parameter and topology uncertainties. The local filters collect information not only from itself but also from its neighbouring sensor nodes according to the network topology. A novel robust distributed filter is proposed which takes stochastic parameter and topology uncertainties into full consideration but does not depend on any specific structure of uncertainties. By proper designing of the filter gain, the trace of estimation error covariance is minimised at each time step, where the new stochastic analysis and augmentation transformation techniques are developed to handle the challenges resulting from multiplicative stochastic uncertainties and sparse topology. The corresponding recursive robust distributed filtering algorithm is also presented for real-time online applications. Finally, a simulation study is carried out to illustrate the effectiveness and applicability of our proposed method.

关键词： Wireless sensor network robust distributed filter stochastic parameter and topology uncertainties recursive algorithm

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Dynamics of serial chain systems using dual algebra

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MULTIBODY SYSTEM DYNAMICS 2022年第2期56卷 91-121页

作者： Dan, Alinjar Saha, Subir Kumar Krishna, Rama K. Indian Inst Technol Delhi Dept Mech Engn New Delhi 110016 India

Dynamic modelling of a multibody system is critical to analyse its behaviour under different circumstances. This paper proposes the dynamic modelling of a rigid multibody system in minimum coordinates with the help of Decoupled Natural Orthogonal Complement (DeNOC) matrices and dual algebra. The work brings DeNOC matrices into the dual algebra framework for the first time to solve the dynamics of a serial-chain rigid multibody system with benefits that were not explicitly available previously. The present work proposes properties of a matrix containing dual operator(s), namely, 'Duality Inducing Matrix (DIM)'. Utilizing these properties, one obtains the constrained dynamic equations of motion in minimum coordinates, and the constraint or reaction forces along the joint axes simultaneously. The latter information is useful for the calculation of the shaking forces that are typically used to optimize dynamic performance, etc. It is the unique feature of the dual algebra-based dynamics proposed in this paper. The formulation is illustrated with a simple example, namely, a spatial Revolute-Revolute manipulator even though the formulation is very generic and appropriate for any n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$n$\end{document}-link serial-chain system.

关键词： Multibody dynamics recursive algorithm Dual algebra Open-loop Equations of motion

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Convergence of the iterative algorithm for a general Hammerstein system identification

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AUTOMATICA 2010年第11期46卷 1891-1896页

作者： Bai, Er-Wei Li, Kang Univ Iowa Dept Elect & Comp Engn Iowa City IA 52242 USA Queens Univ Sch Elect Elect Engn & Comp Sci Belfast BT9 5AH Antrim North Ireland

The convergence of the iterative identification algorithm for a general Hammerstein system has been an open problem for a long time. In this paper, it is shown that the convergence can be achieved by incorporating a regularization procedure on the nonlinearity in addition to a normalization step on the parameters. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： System identification Hammerstein systems recursive algorithm

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A new algorithm for the construction of minimal acyclic DFAs

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SCIENCE OF COMPUTER PROGRAMMING 2003年第2-3期48卷 81-97页

作者： Watson, BW Univ Pretoria Dept Comp Sci ZA-0002 Pretoria South Africa

We present a semi-incremental algorithm for constructing minimal acyclic deterministic finite automata. Such automata are useful for storing sets of words for spell-checking, among other applications. The algorithm is semi-incremental because it maintains the automaton in nearly minimal condition and requires a final minimization step after the last word has been added (during construction). The algorithm derivation proceeds formally (with correctness arguments) from two separate algorithms, one for minimization and one for adding words to acyclic automata. The algorithms are derived in such a way as to be combinable, yielding a semi-incremental one. In practice, the algorithm is both easy to implement and displays good running time performance. (C) 2003 Elsevier B.V. All rights reserved.

关键词： minimal acyclic deterministic finite automata incremental algorithm recursive algorithm algorithmics

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The total distance for algebraic integers having all their conjugates in a sector

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JOURNAL OF NUMBER THEORY 2022年 239卷 445-461页

作者： Flammang, V Univ Lorraine IECL UMR CNRS 7502 Dept MathUFR MIM Site Metz3 Rue Augustin FresnelBP 45112 F-57073 Metz 2 France

Let alpha be a nonzero algebraic integer of degree d whose all conjugates alpha(1)= alpha, alpha(2),..., alpha(d) lie in a sector |arg z| <= theta, 0 < theta < 90 degrees. In 2013, K. Stulov and R. Yang defined the total distance of alpha as td(alpha) = Sigma(d)(i=1)||alpha(i)| - 1|. This paper is organized in two parts. First, we compute the greatest lower bound c(theta) of the absolute total distance of alpha, for alpha belonging to twenty one subintervals of (0, 90). Among these subintervals, eighteen are complete. Moreover, there are two sequences of seven then nine both complete and consecutive subintervals. It is the first time that these phenomena appear: such alarge number of subintervals, such a large number of complete subintervals and such a large number of complete and consecutive subintervals. These phenomena are keeping with a conjecture of G. Rhin and C. J. Smyth on the nature of the function c(theta). Secondly, using the previous results and assuming that the above conjecture is true, we give upper bounds and lower bounds for the total distance involving the Mahler measure. Mostly these bounds improve those of K. Stulov and R. Yang. All computations are done by using the method of explicit auxiliary functions. The polynomials involved in these functions are found by our recursive algorithm. (c) 2021 Elsevier Inc. All rights reserved.

关键词： Algebraic integers Total distance Mahler measure Explicit auxiliary functions recursive algorithm

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Spatial Bayesian inversion with localized likelihoods: An exact sampling alternative to MCMC

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JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH 2014年第7期119卷 5741-5761页

作者： Walker, Matthew Curtis, Andrew Univ Edinburgh Grant Inst Sch GeoSci Edinburgh Midlothian Scotland

Geoscientists often use spatially discretized cellular models of the Earth where data in each grid cell provide independent information about the model parameters of interest at that location. In Bayesian inference this information is given as a set of likelihoods describing the (unnormalized) probability of the parameters, given only the data in each cell. Preexisting information about the model parameters' values and their spatial correlations may be described by a prior probability distribution. The prior, likelihoods, and Bayes' rule together specify a posterior probability distribution that describes the resultant state of information over all model parameters. However, due to the high dimensionality of typical models, the posterior is usually only known up to a multiplicative constant and only at specific, numerically evaluated points in the model space (i.e., it is not known analytically). Markov chain Monte Carlo (MCMC) methods are typically used to produce an ensemble of correlated samples from the posterior. These ensembles are slow to converge in distribution to the posterior;indeed, they may not converge in finite time, and detecting their state of convergence is often impossible in practice. Thus, estimates of the posterior obtained in this way may be biased. We derive a recursive algorithm which samples the posterior exactly, so as to avoid these convergence issues. Its computational cost scales with the size of the parameters' sample space, the prior's spatial range of dependency, and the shortest edge dimension of the grid. We develop an approximation to the algorithm such that it may be used on large 2-D (and potentially 3-D) model grids. We apply it to synthetic seismic attribute data and obtain results which compare favorably to the results of MCMC (Gibbs) sampling-which exhibits convergence problems.

关键词： Bayesian inversion McMC spatial priors recursive algorithm high-dimensional inverse problem gridded data

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Prediction of outstanding payments in a Poisson cluster model

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SCANDINAVIAN ACTUARIAL JOURNAL 2011年第3期000卷 214-237页

作者： Jessen, Anders Hedegaard Mikosch, Thomas Samorodnitsky, Gennady Univ Copenhagen Dept Math DK-2100 Copenhagen Denmark Cornell Univ Sch Operat Res & Informat Engn Ithaca NY 14853 USA

We consider a simple Poisson cluster model for the payment numbers and the corresponding total payments for insurance claims arriving in a given year. Due to the Poisson structure one can give reasonably explicit expressions for the prediction of the payment numbers and total payments in future periods given the past observations of the payment numbers. One can also derive reasonably explicit expressions for the corresponding prediction errors. In the (a, b) class of Panjer's claim size distributions, these expressions can be evaluated by simple recursive algorithms. We study the conditions under which the predictions are asymptotically linear as the number of past payments becomes large. We also demonstrate that, in other regimes, the prediction may be far from linear. For example, a staircase-like pattern may arise as well. We illustrate how the theory works on real-life data, also in comparison with the chain ladder method.

关键词： Poisson cluster model Prediction Claims reserving Chain ladder method Panjer distributions (a, b) class recursive algorithm

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STABILIZATION VIA DYNAMIC OUTPUT-FEEDBACK - A NUMERICAL APPROACH

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1991年第5期14卷 1083-1086页

作者： SCHMITENDORF, WE SCHIRM, W UNIV STUTTGART INST SYST DYNAM & CONTROLW-7000 STUTTGART 80GERMANY

The authors present a numerical method for determining a dynamic output feedback controller. Such a controller has the capability of stabilizing systems where static output feedback fails while being simpler in structure than the control based on the separation theorem, where one first designs the controller gains assuming the complete state can be measured and then uses the same gains with an estimated state. The procedure is extended to the problem of simultaneously stabilizing several plants by a single controller.

关键词： Output Feedback Elevator Deflection Extended Kalman Filter Numerical Integration recursive algorithm Numerical algorithms Gain Scheduling Damping Ratio Mach Number Flaperon

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