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The Riemann Problem, Complete Integrability and Arithmetic Applications : proceedings of a seminar held at the Institut des hautes études scientifiques, Bures-sur-Yvette, France, and at Columbia University, New York, U.S.A., 1979-1980 / edited by D. Chudnovsky and G. Chudnovsky.

By: Contributor(s): Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag) ; 925.Publication details: Berlin ; New York : Springer-Verlag, 1982.Description: 1 online resource (vi, 373 pages) : illustrationsContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783540391524
  • 3540391525
Subject(s): Genre/Form: Additional physical formats: Print version:: Riemann Problem, Complete Integrability and Arithmetic Applications.DDC classification:
  • 515.35 22
LOC classification:
  • QA3 .L28 no. 925 QA379
Other classification:
  • SI 850
  • MAT 329f
  • MAT 309f
Online resources:
Contents:
Continuous exponents of spin correlation functions of inhomogeneous layered ising models -- to holonomic quantum fields -- Planar ising ferromagnet: correlation functions and the inverse scattering method -- Infinite component?-models and instanton solutions -- Infinite component two-dimensional completely integrable systems of KdV type -- The representation of an arbitrary, two-dimensional completely integrable system as the common action of two commuting one-dimensional Hamiltonian flows -- Self-duality of Yang-Mills fields and of gravitational instantons -- On proving the nonintegrability of a Hamiltonian system -- Classical solutions in nonlinear Euclidean field theory and complete integrability -- Hamiltonian structure of isospectral deformation equations. Elliptic curve case -- Quantum Hamiltonians associated with finite-dimensional Lie algebras and factorized s-matrices -- Classical and quantum operator nonlinear schrodinger equation. I -- Trace identities for the Schröedinger operator and the WKB method -- Zeta functions of the quartic (and homogeneous anharmonic) oscillators -- On trace formula -- Resolvent and trace identities in the one dimensional case -- The devil's stair case transformation in incommensurate lattices -- The convergence of padé approximants and their generalizations -- Note on generalized jacobi polynomials -- Multidimensional hermite interpolation and Padé approximation -- Hermite-padé approximations to exponential functions and elementary estimates of the measure of irrationality of? -- Criteria of algebraic independence of several numbers -- Rational approximation for non-linear ordinary differential equations.
Action note:
  • digitized 2011 HathiTrust Digital Library committed to preserve
Summary: Seminar on the Riemann Problem, Complete Integrability and Arithmetic Applications.
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Includes bibliographical references and index.

Continuous exponents of spin correlation functions of inhomogeneous layered ising models -- to holonomic quantum fields -- Planar ising ferromagnet: correlation functions and the inverse scattering method -- Infinite component?-models and instanton solutions -- Infinite component two-dimensional completely integrable systems of KdV type -- The representation of an arbitrary, two-dimensional completely integrable system as the common action of two commuting one-dimensional Hamiltonian flows -- Self-duality of Yang-Mills fields and of gravitational instantons -- On proving the nonintegrability of a Hamiltonian system -- Classical solutions in nonlinear Euclidean field theory and complete integrability -- Hamiltonian structure of isospectral deformation equations. Elliptic curve case -- Quantum Hamiltonians associated with finite-dimensional Lie algebras and factorized s-matrices -- Classical and quantum operator nonlinear schrodinger equation. I -- Trace identities for the Schröedinger operator and the WKB method -- Zeta functions of the quartic (and homogeneous anharmonic) oscillators -- On trace formula -- Resolvent and trace identities in the one dimensional case -- The devil's stair case transformation in incommensurate lattices -- The convergence of padé approximants and their generalizations -- Note on generalized jacobi polynomials -- Multidimensional hermite interpolation and Padé approximation -- Hermite-padé approximations to exponential functions and elementary estimates of the measure of irrationality of? -- Criteria of algebraic independence of several numbers -- Rational approximation for non-linear ordinary differential equations.

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Seminar on the Riemann Problem, Complete Integrability and Arithmetic Applications.

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