Separation of variables in multi-Hamiltonian systems: an application to the Lagrange top

Starting from the tri-Hamiltonian formulation of the Lagrange top in a six-dimensional phase space, we discuss the reduction of the vector field and of the Poisson tensors. We show explicitly that, after the reduction on each one of the symplectic leaves, the vector field of the Lagrange top is separable in the sense of Hamilton-Jacobi.Comment: report to XVI NEEDS (Cadiz 2002): 15 pages, no figures, LaTeX. To appear in Theor. Math. Phy

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

On the integrability of stationary and restricted flows of the KdV hierarchy.

A bi--Hamiltonian formulation for stationary flows of the KdV hierarchy is derived in an extended phase space. A map between stationary flows and restricted flows is constructed: in a case it connects an integrable Henon--Heiles system and the Garnier system. Moreover a new integrability scheme for Hamiltonian systems is proposed, holding in the standard phase space.Comment: 25 pages, AMS-LATEX 2.09, no figures, to be published in J. Phys. A: Math. Gen.

Cardiac and arrhythmic complications in patients with COVID-19

In December 2019, the world started to face a new pandemic situation, the severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2). Although coronavirus disease (COVID-19) clinical manifestations are mainly respiratory, major cardiac complications are being reported. Cardiac manifestations etiology seems to be multifactorial, comprising direct viral myocardial damage, hypoxia, hypotension, enhanced inflammatory status, ACE2-receptors downregulation, drug toxicity, endogenous catecholamine adrenergic status, among others. Studies evaluating patients with COVID-19 presenting cardiac injury markers show that it is associated with poorer outcomes, and arrhythmic events are not uncommon. Besides, drugs currently used to treat the COVID-19 are known to prolong the QT interval and can have a proarrhythmic propensity. This review focus on COVID-19 cardiac and arrhythmic manifestations and, in parallel, makes an appraisal of other virus epidemics as SARS-CoV, Middle East respiratory syndrome coronavirus, and H1N1 influenza

S-ICD is effective in preventing sudden death in Arrhythmogenic Cardiomyopathy athletes during exercise

Here we describe the cases of two elite athletes, with a diagnosis of Arrhythmogenic Cardiomyopathy (ACM), in which a Subcutaneous Implantable Cardioverter Defibrillator (S-ICD) has been implanted. Both patients experienced a ventricular tachycardia during exercise and received effective S-ICD shocks that interrupted arrhythmias. This report reveals for the first time that the S-ICD is effective in reverting arrhythmias in ACM patients, even during exercise. Moreover, these cases may confirm that competition/physical activity is associated with ICD shocks

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

We discuss the Boussinesq system with $t_5$ 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