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Перегляд Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3, випуск за цей рік за назвою

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Перегляд Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3, випуск за цей рік за назвою

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  • Second-Order Approximate Symmetries of the Geodesic Equations for the Reissner-Nordström Metric and Re-Scaling of Energy of a Test Particle 
    Hussain, I.; Mahomed, F.M.; Qadir, A. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
    Following the use of approximate symmetries for the Schwarzschild spacetime by A.H. Kara, F.M. Mahomed and A. Qadir (Nonlinear Dynam., to appear), we have investigated the exact and approximate symmetries of the system of ...
  • Self-Localized Quasi-Particle Excitation in Quantum Electrodynamics and Its Physical Interpretation 
    Feranchuk, I.D.; Feranchuk, S.I. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
    The self-localized quasi-particle excitation of the electron-positron field (EPF) is found for the first time in the framework of a standard form of the quantum electrodynamics. This state is interpreted as the ''physical'' ...
  • Separation of Variables and the Geometry of Jacobians 
    Hurtubise, J. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
    This survey examines separation of variables for algebraically integrable Hamiltonian systems whose tori are Jacobians of Riemann surfaces. For these cases there is a natural class of systems which admit separations in a ...
  • Singular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular Ones 
    Langmann, E. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
    There exists a large class of quantum many-body systems of Calogero-Sutherland type where all particles can have different masses and coupling constants and which nevertheless are such that one can construct a complete (in ...
  • Singular Potentials in Quantum Mechanics and Ambiguity in the Self-Adjoint Hamiltonian 
    Fülöp, T. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
    For a class of singular potentials, including the Coulomb potential (in three and less dimensions) and V(x) = g/x² with the coefficient g in a certain range (x being a space coordinate in one or more dimensions), the ...
  • Skew Divided Difference Operators and Schubert Polynomials 
    Kirillov, A.N. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
    We study an action of the skew divided difference operators on the Schubert polynomials and give an explicit formula for structural constants for the Schubert polynomials in terms of certain weighted paths in the Bruhat ...
  • Some Conformal Invariants from the Noncommutative Residue for Manifolds with Boundary 
    Ugalde, W.J. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
    We review previous work of Alain Connes, and its extension by the author, on some conformal invariants obtained from the noncommutative residue on even dimensional compact manifolds without boundary. Inspired by recent ...
  • Some Progress in Conformal Geometry 
    Sun-Yung A. Chang; Qing, J.; Yang, P. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
    This is a survey paper of our current research on the theory of partial differential equations in conformal geometry. Our intention is to describe some of our current works in a rather brief and expository fashion. We are ...
  • Some Remarks on the KP System of the Camassa-Holm Hierarchy 
    Ortenzi, G. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
    We study a Kadomtsev-Petviashvili system for the local Camassa-Holm hierarchy obtaining a candidate to the Baker-Akhiezer function for its first reduction generalizing the local Camassa-Holm. We focus our attention on the ...
  • Some Sharp L² Inequalities for Dirac Type Operators 
    Balinsky, A.; Ryan, J. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
    We use the spectra of Dirac type operators on the sphere Sn to produce sharp L² inequalities on the sphere. These operators include the Dirac operator on Sn, the conformal Laplacian and Paenitz operator. We use the Cayley ...
  • Spectral Curves of Operators with Elliptic Coefficients 
    Eilbeck, J.C.; Enolski, V.Z.; Previato, E. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
    A computer-algebra aided method is carried out, for determining geometric objects associated to differential operators that satisfy the elliptic ansatz. This results in examples of Lamé curves with double reduction and in ...
  • Stability Analysis of Continuous Waves in Nonlocal Random Nonlinear Media 
    Molchan, M.A. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
    On the basis of the competing cubic-quintic nonlinearity model, stability (instability) of continuous waves in nonlocal random non-Kerr nonlinear media is studied analytically and numerically. Fluctuating media parameters ...
  • Stanilov-Tsankov-Videv Theory 
    Brozos-Vázquez, M.; Fiedler, B.; García-Río, E.; Gilkey, P.; Nikcevic, S.; Stanilov, G.; Tsankov, Y.; Vázquez-Lorenzo, R.; Videv, V. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
    We survey some recent results concerning Stanilov-Tsankov-Videv theory, conformal Osserman geometry, and Walker geometry which relate algebraic properties of the curvature operator to the underlying geometry of the manifold.
  • Straight Quantum Waveguide with Robin Boundary Conditions 
    Jílek, M. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
    We investigate spectral properties of a quantum particle confined to an infinite straight planar strip by imposing Robin boundary conditions with variable coupling. Assuming that the coupling function tends to a constant ...
  • SU₂ Nonstandard Bases: Case of Mutually Unbiased Bases 
    Albouy, O.; Kibler, M.R. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
    This paper deals with bases in a finite-dimensional Hilbert space. Such a space can be realized as a subspace of the representation space of SU₂ corresponding to an irreducible representation of SU₂. The representation ...
  • Symmetries and Invariant Differential Pairings 
    Eastwood, M.G. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
    The purpose of this article is to motivate the study of invariant, and especially conformally invariant, differential pairings. Since a general theory is lacking, this work merely presents some interesting examples of these ...
  • Symmetry Operators for the Fokker-Plank-Kolmogorov Equation with Nonlocal Quadratic Nonlinearity 
    Shapovalov, A.V.; Rezaev, R.O.; Trifonov, A.Yu. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
    The Cauchy problem for the Fokker-Plank-Kolmogorov equation with a nonlocal nonlinear drift term is reduced to a similar problem for the correspondent linear equation. The relation between symmetry operators of the linear ...
  • Teichmüller Theory of Bordered Surfaces 
    Chekhov, L.O. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
    We propose the graph description of Teichmüller theory of surfaces with marked points on boundary components (bordered surfaces). Introducing new parameters, we formulate this theory in terms of hyperbolic geometry. We can ...
  • The 6 Vertex Model and Schubert Polynomials 
    Lascoux, A. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
    We enumerate staircases with fixed left and right columns. These objects correspond to ice-configurations, or alternating sign matrices, with fixed top and bottom parts. The resulting partition functions are equal, up to ...
  • The Rahman Polynomials Are Bispectral 
    Grünbaum, F.A. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
    In a very recent paper, M. Rahman introduced a remarkable family of polynomials in two variables as the eigenfunctions of the transition matrix for a nontrivial Markov chain due to M. Hoare and M. Rahman. I indicate here ...

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