The Experts below are selected from a list of 309 Experts worldwide ranked by ideXlab platform
Natalia P. Bondarenko - One of the best experts on this subject based on the ideXlab platform.
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spectral analysis of the Matrix sturm liouville operator
Boundary Value Problems, 2019Co-Authors: Natalia P. BondarenkoAbstract:The Self-Adjoint Matrix Sturm–Liouville operator on a finite interval with a boundary condition in general form is studied. We obtain asymptotic formulas for the eigenvalues and the weight matrices of the considered operator. These spectral characteristics play an important role in the inverse spectral theory. Our technique is based on an analysis of analytic functions and on the contour integration in the complex plane of the spectral parameter. In addition, we adapt the obtained asymptotic formulas to the Sturm–Liouville operators on a star-shaped graph with two different types of matching conditions.
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Spectral analysis of the Matrix Sturm–Liouville operator
Boundary Value Problems, 2019Co-Authors: Natalia P. BondarenkoAbstract:The Self-Adjoint Matrix Sturm–Liouville operator on a finite interval with a boundary condition in general form is studied. We obtain asymptotic formulas for the eigenvalues and the weight matrices of the considered operator. These spectral characteristics play an important role in the inverse spectral theory. Our technique is based on an analysis of analytic functions and on the contour integration in the complex plane of the spectral parameter. In addition, we adapt the obtained asymptotic formulas to the Sturm–Liouville operators on a star-shaped graph with two different types of matching conditions.
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Spectral data asymptotics for the Matrix Sturm-Liouville operator
arXiv: Spectral Theory, 2019Co-Authors: Natalia P. BondarenkoAbstract:The Self-Adjoint Matrix Sturm-Liouville operator on a finite interval with a boundary condition in the general form is studied. We obtain asymptotic formulas for the eigenvalues and the weight matrices of the considered operator. These spectral characteristics play an important role in the inverse spectral theory. Our technique is based on analysis of analytic functions and on the contour integration in the complex plane of the spectral parameter. In addition, we adapt the obtained asymptotic formulas to the Sturm-Liouville operators on a star-shaped graph with two different types of matching conditions.
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an inverse problem for the non self adjoint Matrix sturm liouville operator
Tamkang Journal of Mathematics, 2018Co-Authors: Natalia P. BondarenkoAbstract:The inverse problem of spectral analysis for the non-Self-Adjoint Matrix Sturm-Liouville operator on a finite interval is investigated. We study properties of the spectral characteristics for the considered operator, and provide necessary and sufficient conditions for the solvability of the inverse problem. Our approach is based on the constructive solution of the inverse problem by the method of spectral mappings. The characterization of the spectral data in the Self-Adjoint case is given as a corollary of the main result.
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An inverse spectral problem for the Matrix Sturm-Liouville operator on the half-line
Boundary Value Problems, 2015Co-Authors: Natalia P. BondarenkoAbstract:The Matrix Sturm-Liouville operator with an integrable potential on the half-line is considered. The inverse spectral problem is studied, which consists in recovering of this operator by the Weyl Matrix. The author provides necessary and sufficient conditions for a meromorphic Matrix function being a Weyl Matrix of the non-Self-Adjoint Matrix Sturm-Liouville operator. We also investigate the Self-Adjoint case and obtain the characterization of the spectral data as a corollary of our general result.
Martin Nilsson Jacobi - One of the best experts on this subject based on the ideXlab platform.
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A Robust Spectral Method for Finding Lumpings and Meta Stable States of Non-Reversible Markov Chains
Electronic Transactions on Numerical Analysis, 2010Co-Authors: Martin Nilsson JacobiAbstract:A spectral method for identifying lumping in large Markov chains is presented. The identification of meta stable states is treated as a special case. The method is based on the spectral analysis of a Self-Adjoint Matrix that is a function of the original transition Matrix. It is demonstrated that the technique is more robust than existing methods when applied to noisy non-reversible Markov chains.
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A robust spectral method for finding lumpings and meta stable states of non-reversible Markov chains
arXiv: Numerical Analysis, 2008Co-Authors: Martin Nilsson JacobiAbstract:A spectral method for identifying lumping in large Markov chains is presented. Identification of meta stable states is treated as a special case. The method is based on spectral analysis of a Self-Adjoint Matrix that is a function of the original transition Matrix. It is demonstrated that the technique is more robust than existing methods when applied to noisy non-reversible Markov chains.
Dmitry E. Pelinovsky - One of the best experts on this subject based on the ideXlab platform.
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Inertia law for spectral stability of solitary waves in coupled nonlinear Schrödinger equations
Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences, 2005Co-Authors: Dmitry E. PelinovskyAbstract:Spectral stability analysis for solitary waves is developed in the context of the Hamiltonian system of coupled nonlinear Schrodinger equations. The linear eigen- value problem for a non-Self-Adjoint operator is studied with two Self-Adjoint Matrix Schrodinger operators. Sharp bounds on the number and type of unstable eigen- values in the spectral problem are found from the inertia law for quadratic forms, associated with the two Self-Adjoint operators. Symmetry-breaking stability analysis is also developed with the same method.
Andrew Waldron - One of the best experts on this subject based on the ideXlab platform.
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Duality of Orthogonal and Symplectic Matrix Integrals and Quaternionic Feynman Graphs
Communications in Mathematical Physics, 2003Co-Authors: Motohico Mulase, Andrew WaldronAbstract:We present an asymptotic expansion for quaternionic Self-Adjoint Matrix integrals. The Feynman diagrams appearing in the expansion are ordinary ribbon graphs and their non-orientable counterparts. The result exhibits a striking duality between quaternionic Self-Adjoint and real symmetric Matrix integrals. The asymptotic expansions of these integrals are given in terms of summations over topologies of compact surfaces, both orientable and non-orientable, for all genera and an arbitrary positive number of marked points on them. We show that the Gaussian Orthogonal Ensemble (GOE) and Gaussian Symplectic Ensemble (GSE) have exactly the same graphical expansion term by term (when appropriately normalized),except that the contributions from non-orientable surfaces with odd Euler characteristic carry the opposite sign. As an application, we give a new topological proof of the known duality for correlations of characteristic polynomials. Indeed, we show that this duality is equivalent to Poincare duality of graphs drawn on a compact surface. Another application of our graphical expansion formula is a simple and simultaneous (re)derivation of the Central Limit Theorem for GOE, GUE (Gaussian Unitary Ensemble) and GSE: The three cases have exactly the same graphical limiting formula except for an overall constant that represents the type of the ensemble.Comment: 39 pages, AMS LaTeX, 49 .eps figures, references update
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duality of orthogonal and symplectic Matrix integrals and quaternionic feynman graphs
Communications in Mathematical Physics, 2003Co-Authors: Motohico Mulase, Andrew WaldronAbstract:We present an asymptotic expansion for quaternionic Self-Adjoint Matrix integrals. The Feynman diagrams appearing in the expansion are ordinary ribbon graphs and their non-orientable counterparts. We show that the 2N×2N Gaussian Orthogonal Ensemble (GOE) and N×N Gaussian Symplectic Ensemble (GSE) have exactly the same expansion term by term, except that the contributions from graphs on a non-orientable surface with odd Euler characteristic carry the opposite sign. As an application, we give a new topological proof of the known duality for correlations of characteristic polynomials, demonstrating that this duality is equivalent to Poincare duality of graphs drawn on a compact surface. Another consequence of our graphical expansion formula is a simple and simultaneous (re)derivation of the Central Limit Theorem for GOE, GUE (Gaussian Unitary Ensemble) and GSE: The three cases have exactly the same graphical limiting formula except for an overall constant that represents the type of the ensemble.
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duality of orthogonal and symplectic Matrix integrals and quaternionic feynman graphs
arXiv: Mathematical Physics, 2002Co-Authors: Motohico Mulase, Andrew WaldronAbstract:We present an asymptotic expansion for quaternionic Self-Adjoint Matrix integrals. The Feynman diagrams appearing in the expansion are ordinary ribbon graphs and their non-orientable counterparts. The result exhibits a striking duality between quaternionic Self-Adjoint and real symmetric Matrix integrals. The asymptotic expansions of these integrals are given in terms of summations over topologies of compact surfaces, both orientable and non-orientable, for all genera and an arbitrary positive number of marked points on them. We show that the Gaussian Orthogonal Ensemble (GOE) and Gaussian Symplectic Ensemble (GSE) have exactly the same graphical expansion term by term (when appropriately normalized),except that the contributions from non-orientable surfaces with odd Euler characteristic carry the opposite sign. As an application, we give a new topological proof of the known duality for correlations of characteristic polynomials. Indeed, we show that this duality is equivalent to Poincare duality of graphs drawn on a compact surface. Another application of our graphical expansion formula is a simple and simultaneous (re)derivation of the Central Limit Theorem for GOE, GUE (Gaussian Unitary Ensemble) and GSE: The three cases have exactly the same graphical limiting formula except for an overall constant that represents the type of the ensemble.
Motohico Mulase - One of the best experts on this subject based on the ideXlab platform.
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Duality of Orthogonal and Symplectic Matrix Integrals and Quaternionic Feynman Graphs
Communications in Mathematical Physics, 2003Co-Authors: Motohico Mulase, Andrew WaldronAbstract:We present an asymptotic expansion for quaternionic Self-Adjoint Matrix integrals. The Feynman diagrams appearing in the expansion are ordinary ribbon graphs and their non-orientable counterparts. The result exhibits a striking duality between quaternionic Self-Adjoint and real symmetric Matrix integrals. The asymptotic expansions of these integrals are given in terms of summations over topologies of compact surfaces, both orientable and non-orientable, for all genera and an arbitrary positive number of marked points on them. We show that the Gaussian Orthogonal Ensemble (GOE) and Gaussian Symplectic Ensemble (GSE) have exactly the same graphical expansion term by term (when appropriately normalized),except that the contributions from non-orientable surfaces with odd Euler characteristic carry the opposite sign. As an application, we give a new topological proof of the known duality for correlations of characteristic polynomials. Indeed, we show that this duality is equivalent to Poincare duality of graphs drawn on a compact surface. Another application of our graphical expansion formula is a simple and simultaneous (re)derivation of the Central Limit Theorem for GOE, GUE (Gaussian Unitary Ensemble) and GSE: The three cases have exactly the same graphical limiting formula except for an overall constant that represents the type of the ensemble.Comment: 39 pages, AMS LaTeX, 49 .eps figures, references update
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duality of orthogonal and symplectic Matrix integrals and quaternionic feynman graphs
Communications in Mathematical Physics, 2003Co-Authors: Motohico Mulase, Andrew WaldronAbstract:We present an asymptotic expansion for quaternionic Self-Adjoint Matrix integrals. The Feynman diagrams appearing in the expansion are ordinary ribbon graphs and their non-orientable counterparts. We show that the 2N×2N Gaussian Orthogonal Ensemble (GOE) and N×N Gaussian Symplectic Ensemble (GSE) have exactly the same expansion term by term, except that the contributions from graphs on a non-orientable surface with odd Euler characteristic carry the opposite sign. As an application, we give a new topological proof of the known duality for correlations of characteristic polynomials, demonstrating that this duality is equivalent to Poincare duality of graphs drawn on a compact surface. Another consequence of our graphical expansion formula is a simple and simultaneous (re)derivation of the Central Limit Theorem for GOE, GUE (Gaussian Unitary Ensemble) and GSE: The three cases have exactly the same graphical limiting formula except for an overall constant that represents the type of the ensemble.
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A generating function of the number of homomorphisms from a surface group into a finite group
arXiv: Quantum Algebra, 2002Co-Authors: Motohico MulaseAbstract:A generating function of the number of homomorphisms from the fundamental group of a compact oriented or non-orientable surface without boundary into a finite group is obtained in terms of an integral over a real group algebra. We calculate the number of homomorphisms using the decomposition of the group algebra into irreducible factors. This gives a new proof of the classical formulas of Frobenius, Schur, and Mednykh. Let S be a compact oriented or non-orientable surface without boundary, and �(S) its Euler characteristic. The subject of our study is a generating function of the number |Hom(�1(S),G)| of homomorphisms from the fundamental group of S into a finite group G. We give a generating function in terms of a non-commutative integral Eqn.(2.7) or Eqn.(3.2), according to the orientability of S. The idea of such integrals comes from random Matrix theory. Our integrals can be thought of as a generalization of real symmetric, complex hermitian, and quaternionic Self-Adjoint Matrix integrals. The graphical expansion methods for real symmetric (7, 14) and complex hermitian (4) Matrix integrals are generalized in (31) for quaternionic Self-Adjoint Matrix integrals. The technique developed in (31) is further generalized in (32) to the integrals over matrices with values in non-commutative ∗-algebras. In this article we consider 1 × 1 Matrix integrals over group algebras. Surprisingly, the graphical expansion of the integral gives a generating function of |Hom(�1(S),G)| for all closed surfaces. 1. Counting Formulas Computation of our generating functions Eqn.(2.7) and Eqn.(3.2) yields a new proof of the following classical counting formulas:
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duality of orthogonal and symplectic Matrix integrals and quaternionic feynman graphs
arXiv: Mathematical Physics, 2002Co-Authors: Motohico Mulase, Andrew WaldronAbstract:We present an asymptotic expansion for quaternionic Self-Adjoint Matrix integrals. The Feynman diagrams appearing in the expansion are ordinary ribbon graphs and their non-orientable counterparts. The result exhibits a striking duality between quaternionic Self-Adjoint and real symmetric Matrix integrals. The asymptotic expansions of these integrals are given in terms of summations over topologies of compact surfaces, both orientable and non-orientable, for all genera and an arbitrary positive number of marked points on them. We show that the Gaussian Orthogonal Ensemble (GOE) and Gaussian Symplectic Ensemble (GSE) have exactly the same graphical expansion term by term (when appropriately normalized),except that the contributions from non-orientable surfaces with odd Euler characteristic carry the opposite sign. As an application, we give a new topological proof of the known duality for correlations of characteristic polynomials. Indeed, we show that this duality is equivalent to Poincare duality of graphs drawn on a compact surface. Another application of our graphical expansion formula is a simple and simultaneous (re)derivation of the Central Limit Theorem for GOE, GUE (Gaussian Unitary Ensemble) and GSE: The three cases have exactly the same graphical limiting formula except for an overall constant that represents the type of the ensemble.