2,043 research outputs found

    Bihamiltonian geometry and separation of variables for Toda lattices

    Get PDF
    We discuss the bihamiltonian geometry of the Toda lattice (periodic and open). Using some recent results on the separation of variables for bihamiltonian manifolds, we show that these systems can be explicitly integrated via the classical Hamilton-Jacobi method in the so-called Darboux-Nijenhuis coordinates.Comment: 12 pages, Latex with amsmath and amssymb. Report of talks given at NEEDS9

    Quasi-BiHamiltonian Systems and Separability

    Full text link
    Two quasi--biHamiltonian systems with three and four degrees of freedom are presented. These systems are shown to be separable in terms of Nijenhuis coordinates. Moreover the most general Pfaffian quasi-biHamiltonian system with an arbitrary number of degrees of freedom is constructed (in terms of Nijenhuis coordinates) and its separability is proved.Comment: 10 pages, AMS-LaTeX 1.1, to appear in J. Phys. A: Math. Gen. (May 1997

    On a class of dynamical systems both quasi-bi-Hamiltonian and bi-Hamiltonian

    Full text link
    It is shown that a class of dynamical systems (encompassing the one recently considered by F. Calogero [J. Math. Phys. 37 (1996) 1735]) is both quasi-bi-Hamiltonian and bi-Hamiltonian. The first formulation entails the separability of these systems; the second one is obtained trough a non canonical map whose form is directly suggested by the associated Nijenhuis tensor.Comment: 11 pages, AMS-LaTex 1.

    The quasi-bi-Hamiltonian formulation of the Lagrange top

    Full text link
    Starting from the tri-Hamiltonian formulation of the Lagrange top in a six-dimensional phase space, we discuss the possible reductions of the Poisson tensors, the vector field and its Hamiltonian functions on a four-dimensional space. We show that the vector field of the Lagrange top possesses, on the reduced phase space, a quasi-bi-Hamiltonian formulation, which provides a set of separation variables for the corresponding Hamilton-Jacobi equation.Comment: 12 pages, no figures, LaTeX, to appear in J. Phys. A: Math. Gen. (March 2002

    Relationship of hyperglycaemia, hypoglycaemia, and glucose variability to atherosclerotic disease in type 2 diabetes

    Get PDF
    Objective: Type 2 diabetes mellitus (T2DM) is known to be associated with increased cardiovascular risk. The aim of this study was therefore to investigate the independent effects of hyperglycaemia, hypoglycaemia, and glucose variability on microvascular and macrovascular disease in T2DM. Methods. Subjects with T2DM of 7.8mmol/L (β=15.83, p=0005) was the sole independent predictor of albuminuria in generalised linear regression. Conclusions. This study demonstrates that hypoglycaemia is associated with the occurrence of atherosclerotic disease while hyperglycaemia is associated with microvascular disease in a Caucasian population with T2DM of recent duration.peer-reviewe

    Applications of Information Theory to Analysis of Neural Data

    Full text link
    Information theory is a practical and theoretical framework developed for the study of communication over noisy channels. Its probabilistic basis and capacity to relate statistical structure to function make it ideally suited for studying information flow in the nervous system. It has a number of useful properties: it is a general measure sensitive to any relationship, not only linear effects; it has meaningful units which in many cases allow direct comparison between different experiments; and it can be used to study how much information can be gained by observing neural responses in single trials, rather than in averages over multiple trials. A variety of information theoretic quantities are commonly used in neuroscience - (see entry "Definitions of Information-Theoretic Quantities"). In this entry we review some applications of information theory in neuroscience to study encoding of information in both single neurons and neuronal populations.Comment: 8 pages, 2 figure

    Reduction of bihamiltonian systems and separation of variables: an example from the Boussinesq hierarchy

    Full text link
    We discuss the Boussinesq system with t5t_5 stationary, within a general framework for the analysis of stationary flows of n-Gel'fand-Dickey hierarchies. We show how a careful use of its bihamiltonian structure can be used to provide a set of separation coordinates for the corresponding Hamilton--Jacobi equations.Comment: 20 pages, LaTeX2e, report to NEEDS in Leeds (1998), to be published in Theor. Math. Phy

    Generalized Lenard Chains, Separation of Variables and Superintegrability

    Full text link
    We show that the notion of generalized Lenard chains naturally allows formulation of the theory of multi-separable and superintegrable systems in the context of bi-Hamiltonian geometry. We prove that the existence of generalized Lenard chains generated by a Hamiltonian function defined on a four-dimensional \omega N manifold guarantees the separation of variables. As an application, we construct such chains for the H\'enon-Heiles systems and for the classical Smorodinsky-Winternitz systems. New bi-Hamiltonian structures for the Kepler potential are found.Comment: 14 pages Revte

    The local structure of n-Poisson and n-Jacobi manifolds

    Get PDF
    N-Lie algebra structures on smooth function algebras given by means of multi-differential operators, are studied. Necessary and sufficient conditions for the sum and the wedge product of two nn-Poisson sructures to be again a multi-Poisson are found. It is proven that the canonical nn-vector on the dual of an n-Lie algebra g is n-Poisson iff dim(g) are not greater than n+1. The problem of compatibility of two n-Lie algebra structures is analyzed and the compatibility relations connecting hereditary structures of a given n-Lie algebra are obtained. (n+1)-dimensional n-Lie algebras are classified and their "elementary particle-like" structure is discovered. Some simple applications to dynamics are discussed.Comment: 45 pages, latex, no figure
    • …
    corecore