2,043 research outputs found
Bihamiltonian geometry and separation of variables for Toda lattices
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
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
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
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
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
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
We discuss the Boussinesq system with 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
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
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 -Poisson sructures to be again a
multi-Poisson are found. It is proven that the canonical -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
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