Relevant bibliographies by topics / Liouville systems

Academic literature on the topic 'Liouville systems'

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Published: 14 March 2023

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Journal articles on the topic "Liouville systems"

1

Chetverikov, V. N. "Liouville systems and symmetries." Differential Equations 48, no. 12 (December 2012): 1639–51. http://dx.doi.org/10.1134/s0012266112120099.

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Wang, Guofang. "Moser-Trudinger inequalities and Liouville systems." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 328, no. 10 (May 1999): 895–900. http://dx.doi.org/10.1016/s0764-4442(99)80293-6.

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Lin, Chang-Shou. "Liouville Systems of Mean Field Equations." Milan Journal of Mathematics 79, no. 1 (June 2011): 81–94. http://dx.doi.org/10.1007/s00032-011-0149-4.

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Zhuo, Ran, and FengQuan Li. "Liouville type theorems for Schrödinger systems." Science China Mathematics 58, no. 1 (November 21, 2014): 179–96. http://dx.doi.org/10.1007/s11425-014-4925-9.

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Demskoi, D. K. "One Class of Liouville-Type Systems." Theoretical and Mathematical Physics 141, no. 2 (November 2004): 1509–27. http://dx.doi.org/10.1023/b:tamp.0000046560.84634.8c.

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Battaglia, Luca, Francesca Gladiali, and Massimo Grossi. "Nonradial entire solutions for Liouville systems." Journal of Differential Equations 263, no. 8 (October 2017): 5151–74. http://dx.doi.org/10.1016/j.jde.2017.06.009.

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Chipot, M., I. Shafrir, and G. Wolansky. "On the Solutions of Liouville Systems." Journal of Differential Equations 140, no. 1 (October 1997): 59–105. http://dx.doi.org/10.1006/jdeq.1997.3316.

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Chipot, M., I. Shafrir, and G. Wolansky. "On the Solutions of Liouville Systems." Journal of Differential Equations 178, no. 2 (January 2002): 630. http://dx.doi.org/10.1006/jdeq.2001.4105.

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Borisova, Galina. "Sturm - Liouville systems and nonselfadjoint operators, presented as couplings of dissipative and antidissipative operators with real absolutely continuous spectra." Annual of Konstantin Preslavsky University of Shumen, Faculty of mathematics and informatics XXIII C (2022): 11–21. http://dx.doi.org/10.46687/wxfc2019.

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This paper is a continuation of the considerations of the paper [1] and it presents the connection between Sturm-Liouville systems and Livšic operator colligations theory. An usefull representation of solutions of Sturm - Liouville systems is obtained using the resolvent of operators from a large class of nonselfadjoint nondissipative operators, presented as couplings of dissipative and antidissipative operators with real spectra. A connection between Sturm-Liouville systems and the inner state of the corresponding open system of operators from the considered class is presented.
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Rynne, Bryan P. "The asymptotic distribution of the eigenvalues of right definite multiparameter Sturm-Liouville systems." Proceedings of the Edinburgh Mathematical Society 36, no. 1 (February 1993): 35–47. http://dx.doi.org/10.1017/s0013091500005873.

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This paper studies the asymptotic distribution of the multiparameter eigenvalues of a right definite multiparameter Sturm–Liouville eigenvalue problem. A uniform asymptotic analysis of the oscillation number of solutions of a single Sturm–Liouville type equation with potential depending on a general parameter is given; these results are then applied to the system of multiparameter Sturm–Liouville equations to give the asymptotic eigenvalue distribution for the system as a function of a “multi-index” oscillation number.
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Dissertations / Theses on the topic "Liouville systems"

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Battaglia, Luca. "Variational aspects of singular Liouville systems." Doctoral thesis, SISSA, 2015. http://hdl.handle.net/20.500.11767/4857.

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I studied singular Liouville systems on compact surfaces from a variational point of view. I gave sufficient and necessary conditions for the existence of globally minimizing solutions, then I found min-max solutions for some particular systems. Finally, I also gave some non-existence results.
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Jevnikar, Aleks. "Variational aspects of Liouville equations and systems." Doctoral thesis, SISSA, 2015. http://hdl.handle.net/20.500.11767/4847.

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Holtz, Susan Lady. "Liouville resolvent methods applied to highly correlated systems." Diss., Virginia Polytechnic Institute and State University, 1986. http://hdl.handle.net/10919/49795.

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Altundag, Huseyin. "Inverse Sturm-liouville Systems Over The Whole Real Line." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612693/index.pdf.

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In this thesis we present a numerical algorithm to solve the singular Inverse Sturm-Liouville problems with symmetric potential functions. The singularity, which comes from the unbounded domain of the problem, is treated by considering the limiting case of the associated problem on the symmetric finite interval. In contrast to regular problems which are considered on a finite interval the singular inverse problem has an ill-conditioned structure despite of the limiting treatment. We use the regularization techniques to overcome the ill-posedness difficulty. Moreover, since the problem is nonlinear the iterative solution procedures are needed. Direct computation of the eigenvalues in iterative solution is handled via psoudespectral methods. The numerical examples of the considered problem are given to illustrate the accuracy and convergence behaviour.
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Aldrovandi, Ettore. "Liouville Field Theory, Drinfel'd-Sokolov Linear Systems and Riemann Surfaces." Doctoral thesis, SISSA, 1992. http://hdl.handle.net/20.500.11767/4292.

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Alici, Haydar. "A General Pseudospectral Formulation Of A Class Of Sturm-liouville Systems." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612435/index.pdf.

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In this thesis, a general pseudospectral formulation for a class of Sturm-Liouville eigenvalue problems is consructed. It is shown that almost all, regular or singular, Sturm-Liouville eigenvalue problems in the Schrö
dinger form may be transformed into a more tractable form. This tractable form will be called here a weighted equation of hypergeometric type with a perturbation (WEHTP) since the non-weighted and unperturbed part of it is known as the equation of hypergeometric type (EHT). It is well known that the EHT has polynomial solutions which form a basis for the Hilbert space of square integrable functions. Pseudospectral methods based on this natural expansion basis are constructed to approximate the eigenvalues of WEHTP, and hence the energy eigenvalues of the Schrö
dinger equation. Exemplary computations are performed to support the convergence numerically.
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Schirmer, Sonja G. "Theory of control of quantum systems /." view abstract or download file of text, 2000. http://wwwlib.umi.com/cr/uoregon/fullcit?p9963453.

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Thesis (Ph. D.)--University of Oregon, 2000.
Typescript. Includes vita and abstract. Includes bibliographical references (leaves 98-99). Also available for download via the World Wide Web; free to University of Oregon users. Address: http://wwwlib.umi.com/cr/uoregon/fullcit?p9963453.
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Medeira, Cléber de. "Resolubilidade global para uma classe de sistemas involutivos." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-15062012-162546/.

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Estudamos a resolubilidade global de uma classe de sistemas involutivos com n campos vetoriais suaves definidos no toro de dimensão n + 1. Obtemos uma caracterização completa para o caso desacoplado desta classe em termos de formas de Liouville e da conexidade de todos os subníveis e superníveis, no espaço de recobrimento minimal, de uma primitiva global da 1-forma associada ao sistema. Além disso, apresentamos uma situação especial na qual o sistema não é globalmente resolúvel e usamos isso para obter alguns resultados em um caso com acoplamento mais forte
We study the global solvability of a class of involutive systems with n smooth vector fields on the torus of dimension n + 1. We obtain a complete characterization for the uncoupled case of this class in terms of Liouville forms and of the connectedness of all sublevel and superlevel sets of the primitive of a certain 1-form in the minimal covering space. Also, we exhibit a special situation where the system is not globally solvable and we use this to obtain some results in a more general case
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McAnally, Morgan Ashley. "Generalized D-Kaup-Newell integrable systems and their integrable couplings and Darboux transformations." Scholar Commons, 2017. https://scholarcommons.usf.edu/etd/7423.

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We present a new spectral problem, a generalization of the D-Kaup-Newell spectral problem, associated with the Lie algebra sl(2,R). Zero curvature equations furnish the soliton hierarchy. The trace identity produces the Hamiltonian structure for the hierarchy. Lastly, a reduction of the spectral problem is shown to have a different soliton hierarchy with a bi-Hamiltonian structure. The first major motivation of this dissertation is to present spectral problems that generate two soliton hierarchies with infinitely many commuting conservation laws and high-order symmetries, i.e., they are Liouville integrable. We use the soliton hierarchies and a non-seimisimple matrix loop Lie algebra in order to construct integrable couplings. An enlarged spectral problem is presented starting from a generalization of the D-Kaup-Newell spectral problem. Then the enlarged zero curvature equations are solved from a series of Lax pairs producing the desired integrable couplings. A reduction is made of the original enlarged spectral problem generating a second integrable coupling system. Next, we discuss how to compute bilinear forms that are symmetric, ad-invariant, and non-degenerate on the given non-semisimple matrix Lie algebra to employ the variational identity. The variational identity is applied to the original integrable couplings of a generalized D-Kaup-Newell soliton hierarchy to furnish its Hamiltonian structures. Then we apply the variational identity to the reduced integrable couplings. The reduced coupling system has a bi-Hamiltonian structure. Both integrable coupling systems retain the properties of infinitely many commuting high-order symmetries and conserved densities of their original subsystems and, again, are Liouville integrable. In order to find solutions to a generalized D-Kaup-Newell integrable coupling system, a theory of Darboux transformations on integrable couplings is formulated. The theory pertains to a spectral problem where the spectral matrix is a polynomial in lambda of any order. An application to a generalized D-Kaup-Newell integrable couplings system is worked out, along with an explicit formula for the associated Bäcklund transformation. Precise one-soliton-like solutions are given for the m-th order generalized D-Kaup-Newell integrable coupling system.
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Liard, Thibault. "Observation et contrôle de quelques systèmes conservatifs." Thesis, Paris 6, 2016. http://www.theses.fr/2016PA066364/document.

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Dans cette thèse, nous nous intéressons à la contrôlabilité interne et à son coût pour une ou plusieurs équations aux dérivées partielles conservatives. ?Dans la première partie, nous introduisons et détaillons deux méthodes permettant d'estimer le coût du contrôle (et par dualité, de la constante d'observabilité) de l'équation des ondes avec potentiel $l^{\infty}$ en dimension un d'espace. La première utilise la propagation des ondes le long des caractéristiques en s'appuyant sur le rôle symétrique de la variable de temps et d'espace. La deuxième méthode repose sur la décomposition spectrale de l'équation des ondes et sur l'utilisation des inégalités d'ingham. L'estimation de la constante d'observabilité se ramène alors à l'étude d'un problème d'optimisation faisant intervenir les vecteurs propres du laplacien-dirichlet avec potentiel. Nous fournissons ensuite des propriétés qualitatives sur le minimiseurs ainsi qu'une estimation du minimum ne dépendant que de la mesure de l'ensemble d'observation. ?Dans la deuxième partie, nous étudions la contrôlabilité de certains systèmes d'équations avec un nombre de contrôles réduits, autrement dit le nombre de contrôles est plus petit que le nombre d'équations. En particulier, nous caractérisons exactement les données initiales qui peuvent être contrôlées pour des systèmes d'équations couplées de type schrödinger et nous énonçons une condition nécessaire et suffisante de type kalman pour des systèmes d'équations des ondes couplées. La preuve repose sur une méthode de contrôle fictif combinée à la résolution algébrique d'un système sous-déterminé et sur certains résultats de régularité
In this work, we focus on the internal controllability and its cost for some linear partial differential equations. In the first part, we introduce and describe two methods to provide precise estimates of the cost of control (and by duality, of the observability constant) for general one dimensional wave equations with potential. The first one is based on a propagation argument along the characteristics relying on the symmetrical roles of the time and space variables. The second one uses a spectral decomposition of the solution of the wave equation and ingham's inequalities. This relates the estimation of the observability constant to the study of an optimal problem involving dirichlet eigenfunctions of laplacian with potential. We provide some qualitative properties of the minimizers, and also precise bounds on the minimum. In the second part, we are concerned with the controllability of some systems of equations by a reduced number of controls (i.e. the number of controls is less that the number of equations). In particular, in the case of coupled systems of schrödinger equations, we exactly characterize the initial conditions that can be controlled and we give a necessary and sufficient condition of kalman type for the controllability of coupled systems of wave equations. The proof relies on the fictitious control method coupled with the proof of an algebraic solvabilityproperty for some related underdetermined system, as well as on some regularity results
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Books on the topic "Liouville systems"

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Mingarelli, Angelo B. (Angelo Bernardo), 1952-, ed. Multiparameter eigenvalue problems: Sturm-Liouville theory. Baca Raton, FL: CRC Press, 2010.

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Atkinson, F. V., and Angelo B. Mingarelli. Multiparameter Eigenvalue Problems: Sturm-Liouville Theory. Taylor & Francis Group, 2010.

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Atkinson, F. V., and Angelo B. Mingarelli. Multiparameter Eigenvalue Problems: Sturm-Liouville Theory. Taylor & Francis Group, 2010.

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Atkinson, F. V., and Angelo B. Mingarelli. Multiparameter Eigenvalue Problems. Taylor & Francis Group, 2010.

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Atkinson, F. V., and Angelo B. Mingarelli. Multiparameter Eigenvalue Problems. Taylor & Francis Group, 2019.

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Mann, Peter. Autonomous Geometrical Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0022.

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This chapter examines the structure of the phase space of an integrable system as being constructed from invariant tori using the Arnold–Liouville integrability theorem, and periodic flow and ergodic flow are investigated using action-angle theory. Time-dependent mechanics is formulated by extending the symplectic structure to a contact structure in an extended phase space before it is shown that mechanics has a natural setting on a jet bundle. The chapter then describes phase space of integrable systems and how tori behave when time-dependent dynamics occurs. Adiabatic invariance is discussed, as well as slow and fast Hamiltonian systems, the Hannay angle and counter adiabatic terms. In addition, the chapter discusses foliation, resonant tori, non-resonant tori, contact structures, Pfaffian forms, jet manifolds and Stokes’s theorem.
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Nolte, David D. The Tangled Tale of Phase Space. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805847.003.0006.

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This chapter presents the history of the development of the concept of phase space. Phase space is the central visualization tool used today to study complex systems. The chapter describes the origins of phase space with the work of Joseph Liouville and Carl Jacobi that was later refined by Ludwig Boltzmann and Rudolf Clausius in their attempts to define and explain the subtle concept of entropy. The turning point in the history of phase space was when Henri Poincaré used phase space to solve the three-body problem, uncovering chaotic behavior in his quest to answer questions on the stability of the solar system. Phase space was established as the central paradigm of statistical mechanics by JW Gibbs and Paul Ehrenfest.
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Nitzan, Abraham. Chemical Dynamics in Condensed Phases. Oxford University Press, 2006. http://dx.doi.org/10.1093/oso/9780198529798.001.0001.

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This text provides a uniform and consistent approach to diversified problems encountered in the study of dynamical processes in condensed phase molecular systems. Given the broad interdisciplinary aspect of this subject, the book focuses on three themes: coverage of needed background material, in-depth introduction of methodologies, and analysis of several key applications. The uniform approach and common language used in all discussions help to develop general understanding and insight on condensed phases chemical dynamics. The applications discussed are among the most fundamental processes that underlie physical, chemical and biological phenomena in complex systems. The first part of the book starts with a general review of basic mathematical and physical methods (Chapter 1) and a few introductory chapters on quantum dynamics (Chapter 2), interaction of radiation and matter (Chapter 3) and basic properties of solids (chapter 4) and liquids (Chapter 5). In the second part the text embarks on a broad coverage of the main methodological approaches. The central role of classical and quantum time correlation functions is emphasized in Chapter 6. The presentation of dynamical phenomena in complex systems as stochastic processes is discussed in Chapters 7 and 8. The basic theory of quantum relaxation phenomena is developed in Chapter 9, and carried on in Chapter 10 which introduces the density operator, its quantum evolution in Liouville space, and the concept of reduced equation of motions. The methodological part concludes with a discussion of linear response theory in Chapter 11, and of the spin-boson model in chapter 12. The third part of the book applies the methodologies introduced earlier to several fundamental processes that underlie much of the dynamical behaviour of condensed phase molecular systems. Vibrational relaxation and vibrational energy transfer (Chapter 13), Barrier crossing and diffusion controlled reactions (Chapter 14), solvation dynamics (Chapter 15), electron transfer in bulk solvents (Chapter 16) and at electrodes/electrolyte and metal/molecule/metal junctions (Chapter 17), and several processes pertaining to molecular spectroscopy in condensed phases (Chapter 18) are the main subjects discussed in this part.
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Book chapters on the topic "Liouville systems"

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Hassani, Sadri. "Sturm-Liouville Systems." In Mathematical Physics, 563–602. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-01195-0_19.

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Laurent-Gengoux, Camille, Anne Pichereau, and Pol Vanhaecke. "Liouville Integrable Systems." In Grundlehren der mathematischen Wissenschaften, 329–51. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-31090-4_12.

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Arutyunov, Gleb. "Liouville Integrability." In Elements of Classical and Quantum Integrable Systems, 1–68. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-24198-8_1.

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Hassani, Sadri. "Sturm-Liouville Systems: Formalism." In Mathematical Physics, 507–23. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-642-87429-1_19.

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Hassani, Sadri. "Sturm-Liouville Systems: Examples." In Mathematical Physics, 524–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-642-87429-1_20.

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Poliakovsky, A., and G. Tarantello. "On Singular Liouville Systems." In Analysis and Topology in Nonlinear Differential Equations, 353–85. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-04214-5_22.

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Klyatskin, Valery I. "Indicator Function and Liouville Equation." In Understanding Complex Systems, 95–114. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-07587-7_3.

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Cossali, Gianpietro Elvio, and Simona Tonini. "Sturm–Liouville Problems." In Drop Heating and Evaporation: Analytical Solutions in Curvilinear Coordinate Systems, 149–81. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-49274-8_5.

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Kang, Jing, Xiaochuan Liu, Peter J. Olver, and Changzheng Qu. "Liouville correspondences for integrable hierarchies." In Nonlinear Systems and Their Remarkable Mathematical Structures, 102–34. Boca Raton: Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003087670-4.

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Marinca, Vasile, Nicolae Herisanu, and Bogdan Marinca. "Cylindrical Liouville-Bratu-Gelfand Problem." In Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems, 343–54. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-75653-6_27.

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Conference papers on the topic "Liouville systems"

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KRICHEVER, IGOR. "Algebraic versus Liouville integrability of the soliton systems." In XIVth International Congress on Mathematical Physics. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812704016_0006.

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Soolaki, Javad, Omid Solaymani Fard, and Akbar Hashemi Borzabadi. "Fuzzy fractional variational problems under Jumarie's Riemann-Liouville H-differentiability." In 2015 4th Iranian Joint Congress on Fuzzy and Intelligent Systems (CFIS). IEEE, 2015. http://dx.doi.org/10.1109/cfis.2015.7391703.

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Pfister, Felix M. J., and Sunil K. Agrawal. "Analytical Dynamics of Unrooted Multibody-Systems With Symmetries." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/mech-5869.

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Abstract The objectives of this paper are to (i) exploit the structure of Euler-Liouville equations for multibody systems and separate the external and internal aspects of motion, (ii) specialize these equations to systems with special mass and geometric properties such as holonomoids and orthotropoids, (iii) apply the results to special orthotropoids, the spheroidal linkages of Wohlhart, and write their equations of motion in a simple and elegant manner.
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Santhanam, Balu. "On a Sturm-Liouville framework for continuous and discrete frequency modulation." In 2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers. IEEE, 2009. http://dx.doi.org/10.1109/acssc.2009.5469748.

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Ge, Fudong, YangQuan Chen, and Chunhai Kou. "The Adjoint Systems of Time Fractional Diffusion Equations and Their Applications in Controllability Analysis." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46696.

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This paper is devoted to the construction of the adjoint system for the case of time fractional order diffusion equations. We first obtain the equivalent integral equation of the abstract fractional state-space system of both Caputo and Riemann-Liouville type by utilizing the Laplace transform and the semigroup theory. Then the adjoint system of time fractional diffusion equation is introduced and used to analyze the duality relationship between observation and control in a Hilbert space. The new introduced notations can also be used in many fields of modelling and control of real dynamic systems.
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Takahashi, Futoshi. "Singular extremal solutions to a Liouville-Gelfand type problem with exponential nonlinearity." In The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications (Madrid, Spain). American Institute of Mathematical Sciences, 2015. http://dx.doi.org/10.3934/proc.2015.1025.

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Lei Wang, Chao Lv, and Qiming Zhao. "Uniqueness of positive solutions for singular Sturm-Liouville like nonlocal boundary value problems." In 2010 International Conference on Intelligent Computing and Integrated Systems (ICISS). IEEE, 2010. http://dx.doi.org/10.1109/iciss.2010.5655453.

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Mozyrska, Dorota, and Malgorzata Wyrwas. "Solutions of fractional linear difference systems with Riemann-Liouville-type operator via transform method." In 2014 International Conference on Fractional Differentiation and its Applications (ICFDA). IEEE, 2014. http://dx.doi.org/10.1109/icfda.2014.6967410.

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Razi, Mani, Peter Attar, and Prakash Vedula. "Uncertainty Quantification for Multidimensional Dynamical Systems Based on Adaptive Numerical Solution of Liouville Equation." In 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2013. http://dx.doi.org/10.2514/6.2013-1536.

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Fan, Wentao, Faisal R. Al-Osaimi, and Nizar Bouguila. "A novel 3D model recognition approach using Pitman-Yor process mixtures of Beta-Liouville Distributions." In 2016 IEEE International Symposium on Circuits and Systems (ISCAS). IEEE, 2016. http://dx.doi.org/10.1109/iscas.2016.7538965.

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