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Matrix Theory (matrix + theory)
Kinds of Matrix Theory Selected AbstractsIntegrable operators and canonical differential systemsMATHEMATISCHE NACHRICHTEN, Issue 1-2 2007Lev Sakhnovich Abstract In this article we consider a class of integrable operators and investigate its connections with the following theories: the spectral theory of the non-self-adjoint operators, the Riemann-Hilbert problem, the canonical differential systems, the random matrices theory and the limit values of the multiplicative integral. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Generalized probabilistic approach of uncertainties in computational dynamics using random matrices and polynomial chaos decompositionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2010Christian Soize Abstract A new generalized probabilistic approach of uncertainties is proposed for computational model in structural linear dynamics and can be extended without difficulty to computational linear vibroacoustics and to computational non-linear structural dynamics. This method allows the prior probability model of each type of uncertainties (model-parameter uncertainties and modeling errors) to be separately constructed and identified. The modeling errors are not taken into account with the usual output-prediction-error method, but with the nonparametric probabilistic approach of modeling errors recently introduced and based on the use of the random matrix theory. The theory, an identification procedure and a numerical validation are presented. Then a chaos decomposition with random coefficients is proposed to represent the prior probabilistic model of random responses. The random germ is related to the prior probability model of model-parameter uncertainties. The random coefficients are related to the prior probability model of modeling errors and then depends on the random matrices introduced by the nonparametric probabilistic approach of modeling errors. A validation is presented. Finally, a future perspective is introduced when experimental data are available. The prior probability model of the random coefficients can be improved in constructing a posterior probability model using the Bayesian approach. Copyright © 2009 John Wiley & Sons, Ltd. [source] A method for fast simulation of multiple catastrophic faults in analogue circuitsINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 3 2010Micha, Tadeusiewicz Abstract The paper offers an efficient method for simulation of multiple catastrophic faults in linear AC circuits. The faulty elements are either open circuits or short circuits. The method exploits the well-known Householder formula in matrix theory to find the node voltages deviations due to the perturbations of some circuit elements. The main achievement of the paper is a systematic method for performing the simulation of all combinations of the multiple catastrophic faults. The method includes two new procedures enabling us to find very efficiently the node impedance matrix of the nominal circuit and inverses of some matrices corresponding to different fault combinations. The procedures are the crucial point of this approach and make it very efficient. Consequently, the amount of the computing power needed to carry out all the simulations is significantly reduced. Numerical examples illustrating the proposed approach are provided. Copyright © 2008 John Wiley & Sons, Ltd. [source] Multi-vehicle coordination for double-integrator dynamics under fixed undirected/directed interaction in a sampled-data settingINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 9 2010Yongcan Cao Abstract This paper studies the convergence of two coordination algorithms for double-integrator dynamics under fixed undirected/ directed interaction in a sampled-data setting. The first algorithm guarantees that a team of vehicles achieves coordination on their positions with a zero final velocity while the second algorithm guarantees that a team of vehicles achieves coordination on their positions with a constant final velocity. We show necessary and sufficient conditions on the sampling period, the control gain, and the communication graph such that coordination is achieved using these two algorithms under, respectively, an undirected interaction topology and a directed interaction topology. Tools like matrix theory, bilinear transformation, and Cauchy theorem are used for convergence analysis. Coordination equilibria for both algorithms are also given. Simulation results are presented as a proof of concept. Copyright © 2009 John Wiley & Sons, Ltd. [source] Stability and coexistence in a lawn community: mathematical prediction of stability using a community matrix with parameters derived from competition experimentsOIKOS, Issue 2 2000Stephen H. Roxburgh Community matrix theory has been proposed as a means of predicting whether a particular set of species will form a stable mixture. However, the approach has rarely been used with data from real communities. Using plant competition experiments, we use community matrix theory to predict the stability and competitive structuring of a lawn community. Seven species from the lawn, including the six most abundant, were grown in boxes, in conditions very similar to those on the lawn. They were grown alone (monocultures), and in all possible pairs. The species formed a transitive hierarchy of competitive ability, with most pairs of species showing asymmetric competition. Relative competitive ability (competitive effect) was positively correlated with published estimates of the maximum relative growth rate (RGRmax) for the same species. A seven-species community matrix predicted the mixture of species to be unstable. Simulations revealed two topological features of this community matrix. First, the matrix was closer to the stability/instability boundary than predicted from a range of null (random) models, suggesting that the lawn may be close to stability. Second, the tendencies of the lawn species to compete asymmetrically, and to be arranged in competitive hierarchies, were found to be positively associated with stability, and hence may be contributing factors to the near-stability seen in the matrix. The limitations of using competition experiments for constructing community matrices are discussed. [source] Transition between Airy1 and Airy2 processes and TASEP fluctuationsCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 11 2008Alexei Borodin We consider the totally asymmetric simple exclusion process, a model in the KPZ universality class. We focus on the fluctuations of particle positions, starting with certain deterministic initial conditions. For large time t, one has regions with constant and linearly decreasing density. The fluctuations on these two regions are given by the Airy1 and Airy2 processes, whose one-point distributions are the GOE and GUE Tracy-Widom distributions of random matrix theory. In this paper we analyze the transition region between these two regimes and obtain the transition process. Its one-point distribution is a new interpolation between GOE and GUE edge distributions. © 2007 Wiley Periodicals, Inc. [source] Averages of characteristic polynomials in random matrix theoryCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 2 2006A. Borodin We compute averages of products and ratios of characteristic polynomials associated with orthogonal, unitary, and symplectic ensembles of random matrix theory. The Pfaffian/determinantal formulae for these averages are obtained, and the bulk scaling asymptotic limits are found for ensembles with Gaussian weights. Classical results for the correlation functions of the random matrix ensembles and their bulk scaling limits are deduced from these formulae by a simple computation. We employ a discrete approximation method: the problem is solved for discrete analogues of random matrix ensembles originating from representation theory, and then a limit transition is performed. Exact Pfaffian/determinantal formulae for the discrete averages are proven using standard tools of linear algebra; no application of orthogonal or skew-orthogonal polynomials is needed. © 2005 Wiley Periodicals, Inc. [source] | |||||||||||||