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Relevant bibliographies by topics / Isospectral transformations

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Academic literature on the topic 'Isospectral transformations'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 February 2022

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Journal articles on the topic "Isospectral transformations"

1

Duarte, Pedro, and Maria Joana Torres. "Eigenvectors of isospectral graph transformations." Linear Algebra and its Applications 474 (June 2015): 110–23. http://dx.doi.org/10.1016/j.laa.2015.01.038.

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Bunimovich, L. A., and B. Z. Webb. "Isospectral compression and other useful isospectral transformations of dynamical networks." Chaos: An Interdisciplinary Journal of Nonlinear Science 22, no. 3 (September 2012): 033118. http://dx.doi.org/10.1063/1.4739253.

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Chou, Tian, and Zhang Youjin. "Backlund transformations for the isospectral and non-isospectral MKdV hierarchies." Journal of Physics A: Mathematical and General 23, no. 13 (July 7, 1990): 2867–77. http://dx.doi.org/10.1088/0305-4470/23/13/024.

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Krajewska, Agnieszka, Alexander Ushveridze, and Zbigniew Walczak. "Anti-Isospectral Transformations in Quantum Mechanics." Modern Physics Letters A 12, no. 17 (June 7, 1997): 1225–34. http://dx.doi.org/10.1142/s0217732397001242.

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In this letter we demonstrate that there exists a remarkable class of quantum models admitting Z2 anti-isospectral transformations which change the form of the potential and invert the sign of a certain finite set of energy levels. These transformations help one to construct interesting classes of non-monic polynomials which are mutually orthogonal on two different intervals with two different weight functions.

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Guliyev, Namig J. "Essentially isospectral transformations and their applications." Annali di Matematica Pura ed Applicata (1923 -) 199, no. 4 (November 27, 2019): 1621–48. http://dx.doi.org/10.1007/s10231-019-00934-w.

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WANG, QINMOU, UDAY P. SUKHATME, WAI-YEE KEUNG, and TOM D. IMBO. "SOLITONS FROM SUPERSYMMETRY." Modern Physics Letters A 05, no. 07 (March 20, 1990): 525–30. http://dx.doi.org/10.1142/s0217732390000603.

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Supersymmetry transformations constitute a new, powerful technique of generating families of isospectral potentials. We show that isospectral families of reflectionless potentials provide surprisingly simple expressions for the pure multi-soliton solutions of the KdV and other nonlinear evolution equations.

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Gottlieb, H. P. W. "Transformations between isospectral membranes yield conformal maps." IMA Journal of Applied Mathematics 70, no. 6 (December 1, 2005): 748–52. http://dx.doi.org/10.1093/imamat/hxh067.

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Rosenhouse, Avia, and Jacob Katriel. "Isospectral transformations in relativistic and nonrelativistic mechanics." Letters in Mathematical Physics 13, no. 2 (February 1987): 141–46. http://dx.doi.org/10.1007/bf00955203.

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FENG, QIAN, YI-TIAN GAO, XIANG-HUA MENG, XIN YU, ZHI-YUAN SUN, TAO XU, and BO TIAN. "N-SOLITON-LIKE SOLUTIONS AND BÄCKLUND TRANSFORMATIONS FOR A NON-ISOSPECTRAL AND VARIABLE-COEFFICIENT MODIFIED KORTEWEG-DE VRIES EQUATION." International Journal of Modern Physics B 25, no. 05 (February 20, 2011): 723–33. http://dx.doi.org/10.1142/s0217979211058043.

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A non-isospectral and variable-coefficient modified Korteweg–de Vries (mKdV) equation is investigated in this paper. Starting from the Ablowitz–Kaup–Newell–Segur procedure, the Lax pair is established and the Bäcklund transformation in original variables is also derived. By a dependent variable transformation, the non-isospectral and variable-coefficient mKdV equation is transformed into bilinear equations, by virtue of which the N-soliton-like solution is obtained. In addition, the bilinear Bäcklund transformation gives a one-soliton-like solution from a vacuum one. Furthermore, the N-soliton-like solution in the Wronskian form is constructed and verified via the Wronskian technique.

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BINDING, PAUL A., PATRICK J. BROWNE, and BRUCE A. WATSON. "TRANSFORMATIONS BETWEEN STURM–LIOUVILLE PROBLEMS WITH EIGENVALUE DEPENDENT AND INDEPENDENT BOUNDARY CONDITIONS." Bulletin of the London Mathematical Society 33, no. 6 (November 2001): 749–57. http://dx.doi.org/10.1112/s0024609301008177.

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Explicit relationships are given connecting ‘almost’ isospectral Sturm–Liouville problems with eigen-value dependent, and independent, boundary conditions, respectively. Application is made to various direct and inverse spectral questions.

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Dissertations / Theses on the topic "Isospectral transformations"

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李達明 and Tad-ming Lee. "Isospectral transformations between soliton-solutions of the Korteweg-de Vries equation." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1994. http://hub.hku.hk/bib/B29866261.

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Lee, Tad-ming. "Isospectral transformations between soliton-solutions of the Korteweg-de Vries equation /." [Hong Kong : University of Hong Kong], 1994. http://sunzi.lib.hku.hk/hkuto/record.jsp?B1359753X.

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Kong, Cho-wing Otto, and 江祖永. "K-DV solutions as quantum potentials: isospectral transformations as symmetries and supersymmetries." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1990. http://hub.hku.hk/bib/B3120921X.

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Webb, Benjamin Zachary. "Isospectral graph reductions, estimates of matrices' spectra, and eventually negative Schwarzian systems." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/39521.

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This dissertation can be essentially divided into two parts. The first, consisting of Chapters I, II, and III, studies the graph theoretic nature of complex systems. This includes the spectral properties of such systems and in particular their influence on the systems dynamics. In the second part of this dissertation, or Chapter IV, we consider a new class of one-dimensional dynamical systems or functions with an eventual negative Schwarzian derivative motivated by some maps arising in neuroscience. To aid in understanding the interplay between the graph structure of a network and its dynamics we first introduce the concept of an isospectral graph reduction in Chapter I. Mathematically, an isospectral graph transformation is a graph operation (equivalently matrix operation) that modifies the structure of a graph while preserving the eigenvalues of the graphs weighted adjacency matrix. Because of their properties such reductions can be used to study graphs (networks) modulo any specific graph structure e.g. cycles of length n, cliques of size k, nodes of minimal/maximal degree, centrality, betweenness, etc. The theory of isospectral graph reductions has also lead to improvements in the general theory of eigenvalue approximation. Specifically, such reductions can be used to improved the classical eigenvalue estimates of Gershgorin, Brauer, Brualdi, and Varga for a complex valued matrix. The details of these specific results are found in Chapter II. The theory of isospectral graph transformations is then used in Chapter III to study time-delayed dynamical systems and develop the notion of a dynamical network expansion and reduction which can be used to determine whether a network of interacting dynamical systems has a unique global attractor. In Chapter IV we consider one-dimensional dynamical systems of an interval. In the study of such systems it is often assumed that the functions involved have a negative Schwarzian derivative. Here we consider a generalization of this condition. Specifically, we consider the functions which have some iterate with a negative Schwarzian derivative and show that many known results generalize to this larger class of functions. This includes both systems with regular as well as chaotic dynamic properties.

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Passey, Jr David Joseph. "Growing Complex Networks for Better Learning of Chaotic Dynamical Systems." BYU ScholarsArchive, 2020. https://scholarsarchive.byu.edu/etd/8146.

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This thesis advances the theory of network specialization by characterizing the effect of network specialization on the eigenvectors of a network. We prove and provide explicit formulas for the eigenvectors of specialized graphs based on the eigenvectors of their parent graphs. The second portion of this thesis applies network specialization to learning problems. Our work focuses on training reservoir computers to mimic the Lorentz equations. We experiment with random graph, preferential attachment and small world topologies and demonstrate that the random removal of directed edges increases predictive capability of a reservoir topology. We then create a new network model by growing networks via targeted application of the specialization model. This is accomplished iteratively by selecting top preforming nodes within the reservoir computer and specializing them. Our generated topology out-preforms all other topologies on average.

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Serier, Frédéric. "Problèmes spectraux inverses pour des opérateurs AKNS et de Schrödinger singuliers sur [0,1]." Phd thesis, Université de Nantes, 2005. http://tel.archives-ouvertes.fr/tel-00009719.

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Deux opérateurs sont étudiés dans cette thèse: l'opérateur de Schrödinger radial, issu de la mécanique quantique non relativiste; puis le système AKNS singulier, adaptation de l'opérateur de Dirac radial provenant de la mécanique quantique relativiste. La première partie consiste en la résolution du problème direct associé à chacun des deux opérateurs: détermination des valeurs et vecteurs propres, ainsi que leur dépendance vis à vis des potentiels. La présence de fonctions de Bessel due à la singularité explicite induit des difficultés lors de la détermination d'asymptotiques. La seconde partie porte sur la résolution de ces problèmes spectraux inverses. À l'aide d'opérateurs de transformations nous évitons les difficultés induites par la singularité. Ils nous permettent de développer une théorie spectrale inverse pour les opérateurs singuliers considérés. Précisément, nous construisons une application spectrale bien adapté à l'étude de la stabilité du problème inverse ainsi qu'à l'étude des ensembles isospectraux. Un résultat d'injectivité est aussi obtenu pour les opérateurs AKNS et de Dirac singuliers avec potentiels réguliers.

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Books on the topic "Isospectral transformations"

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Bunimovich, Leonid, and Benjamin Webb. Isospectral Transformations. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-1375-6.

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Isospectral Transformations: A New Approach to Analyzing Multidimensional Systems and Networks. Springer, 2014.

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Webb, Benjamin, and Leonid Bunimovich. Isospectral Transformations: A New Approach to Analyzing Multidimensional Systems and Networks. Springer, 2016.

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Webb, Benjamin, and Leonid Bunimovich. Isospectral Transformations: A New Approach to Analyzing Multidimensional Systems and Networks. Springer, 2014.

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Book chapters on the topic "Isospectral transformations"

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Tian, Chou, and Youjin Zhang. "Bäcklund Transformations for the Isospectral and Non-Isospectral KdV Hierarchies." In Nonlinear Physics, 35–41. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-84148-4_5.

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Bunimovich, L. A., and B. Z. Webb. "Improved Estimates of Survival Probabilities via Isospectral Transformations." In Ergodic Theory, Open Dynamics, and Coherent Structures, 119–35. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-0419-8_7.

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Nakamura, Yoshimasa. "Applications of Transformation Theory for Nonlinear Integrable Systems to Linear Prediction Problems and Isospectral Deformations." In Algebraic Analysis, 505–15. Elsevier, 1988. http://dx.doi.org/10.1016/b978-0-12-400466-5.50010-x.

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Conference papers on the topic "Isospectral transformations"

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Friswell, Michael I., Seamus D. Garvey, and Uwe Prells. "Structure Preserving Transformations and Isospectral Flows for Second Order Systems." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48453.

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When the dynamics of any general second order system are cast in a state-space format, the initial choice of the state-vector usually comprises one partition representing system displacements and another representing system velocities. Coordinate transformations can be defined which result in more general definitions of the state-vector. This paper discusses the general case of coordinate transformations of state-space representations for second order systems. It identifies one extremely important subset of such coordinate transformations — namely the set of structure-preserving transformations for second order systems — and it highlights the importance of these. It shows that one particular structure-preserving transformation results in a new system characterised by real diagonal matrices and presents a forceful case that this structure-preserving transformation should be considered to be the fundamental definition for the characteristic behaviour of general second order systems — in preference to the eigenvalue-eigenvector solutions conventionally accepted. The regular λ-matrix λ2M + λD + K with M,D,K ∈ Rn×n defines a second-order system. A one-parameter trajectory of such a system {M(t),D(t),K(t)} is an isospectral flow (or more correctly an equivalence flow) if the eigenvalues and the dimensions of the associated eigenspaces are the same for all parameter values t ∈ R. This paper presents the general form for real isospectral flows of real-valued second order systems.

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Zhang, Yuanyuan. "Bilinear Backlund Transformation for a Non-Isospectral KdV Equation." In 2009 International Conference on Computational Intelligence and Software Engineering. IEEE, 2009. http://dx.doi.org/10.1109/cise.2009.5367193.

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