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21. http://mailybaev.imec.msu.ru/papers/SeyranianEtAl2005.pdf
... Gen. 38 (2005) 1723ґ1740 doi:10.1088/0305- 4470/38/8/009 Coupling of eigenvalues of complex matrices at diabolic and exceptional points A P Seyranian, O N Kirillov and A A Mailybaev Institute of Mechanics, Moscow State Lomonosov University, Michurinskii pr. ... Coupling of eigenvalues Let us consider the eigenvalue problem Au = u (1) Coupling of eigenvalues of complex matrices at diabolic and exceptional points Table 1. ... Eigenvalues strongly couple at the point 0 in the complex plane. ...
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Ссылки http://mailybaev.imec.msu.ru/papers/SeyranianEtAl2005.pdf -- 437.1 Кб -- 14.06.2005
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22. http://mailybaev.imec.msu.ru/papers/SeyranianMailybaev2001.pdf
... Keywords. conservative system, stability b oundary, singularity, multiple eigenvalue, p erturbation. ... Because of continuous dependence of eigenvalues on parameters a boundary of the stability domain is determined by the zero eigenvalue, while all other eigenvalues are positive. ... Using the results of Arnold [1] and a perturbation technique for eigenvalues [3, 9], a classification of singularities of stability boundaries in the generic case is obtained. ...
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Ссылки http://mailybaev.imec.msu.ru/papers/SeyranianMailybaev2001.pdf -- 184.2 Кб -- 14.06.2005
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23. http://mailybaev.imec.msu.ru/papers/MailybaevSeyranian2001.pdf
... Printed in Great Britain 0021-8928/01/$-see front matter PARAMETRIC RESONANCE IN SYSTEMS WITH SMALL DISSIPATION"f A. A. MAILYBAYEV and A. P. SEYRANIAN Moscow (Received 14 December 2000) A linear oscillatory system having multiple degrees of freedom with periodic coefficients is considered. ... For an arbitrary periodic exitation matrix and a positive-definite matrix of the dissipative forces, general expressions are obtained for the domains of fundamental and combination resonances. ...
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Ссылки http://mailybaev.imec.msu.ru/papers/MailybaevSeyranian2001.pdf -- 1013.4 Кб -- 14.06.2005
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24. http://mailybaev.imec.msu.ru/papers/MailybaevSeyranian2000.pdf
... Printed in Great Britain 0021-8928/00/$-see front matter SOO21-8928(00)00122-2 ON THE BOUNDARIES OF THE PARAMETRIC RESONANCE DOMAIN-lA. ... A constructive approach is proposed which enables one, in the first approximation, to determine the stability domain in the neighbourhood of a point on its boundary using only information at this point: the values of multipliers, eigenvectors and associated vectors of the monodromy matrix and the first derivatives of the system operator with respect to...
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Ссылки http://mailybaev.imec.msu.ru/papers/MailybaevSeyranian2000.pdf -- 1108.2 Кб -- 14.06.2005
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25. http://mailybaev.imec.msu.ru/papers/MailybaevEtAl2004.pdf
Research paper Struct Multidisc Optim 27, 435 ґ 445 (2004) DOI 10.1007/s00158-004-0388-x Optimal shapes of parametrically excited beams A.A. Mailybaev, H. Yabuno, and H. Kaneko Abstract Straight elastically supported beams of variable width under the action of a periodic axial force are considered. Two shape optimization problems for reducing parametric resonance zones are studied. In the first problem, the minimal (critical) amplitude of the excitation force is maximized. ...
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Ссылки http://mailybaev.imec.msu.ru/papers/MailybaevEtAl2004.pdf -- 1418.6 Кб -- 14.06.2005
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26. http://mailybaev.imec.msu.ru/papers/MailybaevEtAl2005.pdf
Geometric phase around exceptional p oints Alexei A. Mailybaev, Oleg N. Kirillov, and Alexander P. Seyranian Institute of Mechanics, Moscow State Lomonosov University Michurinskii pr. ... We develop a general multidimensional theory of the geometric phase for (double) cycles around exceptional degeneracies in non-Hermitian Hamiltonians. ... For nonsymmetric non-Hermitian Hamiltonians of higher dimension, the geometric phase tends to for small cycles and changes as the cycle size and shape are varied. ...
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Ссылки http://mailybaev.imec.msu.ru/papers/MailybaevEtAl2005.pdf -- 99.6 Кб -- 14.06.2005
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27. http://mailybaev.imec.msu.ru/papers/Mailybaev2005.pdf
Computation of multiple eigenvalues and generalized eigenvectors for matrices dependent on parameters arXiv:math-ph/0502010 v1 2 Feb 2005 Alexei A. Mailybaev Abstract The pap er develops Newton's method of finding multiple eigenvalues with one Jordan block and corresp onding generalized eigenvectors for matrices dep endent on parameters. It computes the nearest value of a parameter vector with a matrix having a multiple eigenvalue of given multiplicity. ... m be eigenvalues of the matrix A0 . ...
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Ссылки http://mailybaev.imec.msu.ru/papers/Mailybaev2005.pdf -- 243.9 Кб -- 14.06.2005
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28. http://mailybaev.imec.msu.ru/papers/Mailybaev2001.pdf
Linear Algebra and its Applications 337 (2001) 87ґ108 www.elsevier.com/locate/laa Transformation to versal deformations of matrices Alexei A. Mailybaev Institute of Mechanics, Moscow State Lomonosov University, Michurinsky pr. ... Keywords: Versal deformation; Normal form; Transformation; Lie algebra; Jordan algebra; Reversible matrix 1. ... Arnold [1,3] defined and studied normal forms of deformations of complex matrices (called versal deformations). ... A is the Jordan normal form A = diag(J1 ,.. ...
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Ссылки http://mailybaev.imec.msu.ru/papers/Mailybaev2001.pdf -- 154.1 Кб -- 14.06.2005
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29. http://mailybaev.imec.msu.ru/papers/Mailybaev2003.pdf
... The method is based on the versal deformation theory for matrix pairs under feedback equivalence. ... Similarly, we can calculate a regular part of the uncontrollability set, corresponding to matrix pairs of J type, which is a smooth surface for a three-parameter oneinput dynamical system. Recall that, by Theorem 3.1, the surfaces corresponding to matrix pairs of J and J?i types, together with their boundaries, form the whole uncontrollability set of a generic multi-input linear dynamical system. ...
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Ссылки http://mailybaev.imec.msu.ru/papers/Mailybaev2003.pdf -- 211.1 Кб -- 14.06.2005
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30. http://mailybaev.imec.msu.ru/papers/Mailybaev1999b.pdf
... 21, No. 2, pp. 396ґ417 c 1999 Society for Industrial and Applied Mathematics TRANSFORMATION OF FAMILIES OF MATRICES TO NORMAL FORMS AND ITS APPLICATION TO STABILITY THEORY ALEXEI A. MAILYBAEV Abstract. Families of matrices smo othly dep ending on a vector of parameters are considered. ... Derivatives of these functions with resp ect to parameters are determined from a recurrent pro cedure using derivatives of the functions of lower orders and derivatives of the family of matrices. ... Theorem 2.4. ...
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Ссылки http://mailybaev.imec.msu.ru/papers/Mailybaev1999b.pdf -- 359.3 Кб -- 14.06.2005
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31. http://mailybaev.imec.msu.ru/papers/Mailybaev2000.pdf
... A constructive approach is proposed that allows one to determine, in a first approximation, the stability domain or a domain with a bounded decrement in the neighborhood of a singular or regular point of its boundary from the information available at this point (the roots and coefficients of the polynomial as well as the first derivatives of the coefficients with respect to parameters). ... The set of values of the vector p of parameters for which P(, p) is stable is called the stability domain. ...
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Ссылки http://mailybaev.imec.msu.ru/papers/Mailybaev2000.pdf -- 244.5 Кб -- 14.06.2005
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32. http://mailybaev.imec.msu.ru/papers/Mailybaev1999a.pdf
... 21, No. 1, pp. 106ґ128 c 1999 Society for Industrial and Applied Mathematics ON SINGULARITIES OF A BOUNDARY OF THE STABILITY DOMAIN ALEXEI A. MAILYBAEV AND ALEXANDER P. SEYRANIAN This paper is dedicated to V. I. Arnold on the occasion of his 60th birthday. ... ON SINGULARITIES OF A BOUNDARY OF THE STABILITY DOMAIN 115 Fig. ... ON SINGULARITIES OF A BOUNDARY OF THE STABILITY DOMAIN 119 Let us calculate the vectors hj , j = 1, 2, 3, defining collapse of a triple zero eigenvalue of the matrix A (0). ...
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Ссылки http://mailybaev.imec.msu.ru/papers/Mailybaev1999a.pdf -- 347.8 Кб -- 14.06.2005
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33. http://mailybaev.imec.msu.ru/papers/KirillovEtAl2005.pdf
... Gen. 38 (2005) 5531ґ5546 doi:10.1088/0305-4470/38/24/007 Unfolding of eigenvalue surfaces near a diabolic point due to a complex perturbation O N Kirillov, A A Mailybaev and A P Seyranian Institute of Mechanics, Moscow State Lomonosov University, Michurinskii pr. ... In the case of real symmetric matrices we study the unfolding of eigenvalue surfaces near a diabolic point under real and complex perturbations. ... A real non-symmetric perturbation of a diabolic point. c 0: Im2 + (x + )2 + (y + )2 = 2...
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Ссылки http://mailybaev.imec.msu.ru/papers/KirillovEtAl2005.pdf -- 334.3 Кб -- 14.06.2005
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34. http://mailybaev.imec.msu.ru/papers/GarciaMailybaev2003.pdf
... 24, No. 4, pp. 943ґ962 c 2003 Society for Industrial and Applied Mathematics REDUCTION TO VERSAL DEFORMATIONS OF MATRIX PENCILS AND MATRIX PAIRS WITH APPLICATION TO CONTROL THEORY M. I. GARCЄ IA-PLANAS AND A. A. MAILYBAEV Abstract. Matrix pencils under the strict equivalence and matrix pairs under the state feedback equivalence are considered. ... In this paper versal deformations of matrix pencils under the strict equivalence and pairs of matrices under the feedback equivalence are considered. ...
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Ссылки http://mailybaev.imec.msu.ru/papers/GarciaMailybaev2003.pdf -- 237.3 Кб -- 14.06.2005
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35. http://mailybaev.imec.msu.ru/papers/GrigoryanMailybaev2001.pdf
... Original Russian Text Copyright c 2001 by Grigoryan, Mailybaev On the Weierstrass Preparation Theorem S. S. Grigoryan and A. A. Mailybaev Received May 22, 2000 Abstract--An analytic function of several variables is considered. ... As an application, an explicit formula describing a bifurcation diagram locally up to second-order terms is derived for the case of a double root. Key words: Weierstrass preparation theorem, analytic function of several variables, bifurcation diagram. ... ЗЗЗ hn ! ...
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Ссылки http://mailybaev.imec.msu.ru/papers/GrigoryanMailybaev2001.pdf -- 123.8 Кб -- 14.06.2005
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