Some Remarks on the KP System of the Camassa-Holm Hierarchy

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 differences with the standard KdV-KP case.Comment: This is a contribution to the Proc. of workshop on Geometric Aspects of Integrable Systems (July 17-19, 2006; Coimbra, Portugal), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Lithium-Ion/Supercapacitors Storage System Powered Microcar: Development and Testing☆

Abstract The use of SuperCapacitors together with the lead-acid battery storage on electric vehicles have the advantage of improving the vehicle range and life-cycle of the lead-acid batteries. An urban City car, was tested on cycle ECE15, (the urban part of the type approval procedure of vehicles, the NEDC) and an automatic tool and procedure to run it on the dynamometer chassis has been developed. The results of the experimentation show the advantages in adoption of hybrid storage (Li-Ion + UC) systems in terms of range are lower (+5%) than those obtained with lead-acid + UC (+50%)

Heisenberg ferromagnetism as an evolution of a spherical indicatrix: localized solutions and elliptic dispersionless reduction

A geometrical formulation of Heisenberg ferromagnetism as an evolution of a curve on the unit sphere in terms of intrinsic variables is provided and investigated. Given a vortex filament moving in an incompressible Euler fluid with constant density (under the local induction approximation hypotheses), the solutions of the classical Heisenberg ferromagnet equation are represented by the corresponding spherical (or tangent) indicatrix. The equations for the time evolution of the indicatrix on the unit sphere are given explicitly in terms of two intrinsic variables, the geodesic curvature and the arc-length of the curve. Notably, by considering the evolution with respect to slow variables and neglecting the dispersive terms, a novel elliptic dispersionless reduction of the Heisenberg ferromagnet model is obtained. The length of the spherical indicatrix is proved not to be conserved. Finally, a totally explicit algorithm is provided, allowing to construct a solution of the Heisenberg ferromagnet equation from a solution of Nonlinear Schrodinger equation, and, remarkably, viceversa, allowing to construct a solution of Nonlinear Schrodinger equation from a solution of the Heisenberg ferromagnet equation. As expected from the Zakharov-Takhtajan gauge equivalence, in the reflectionless case such a two-way map between solutions is shown to preserve the Inverse Scattering Transform spectra, and thus the localization

Solutions and Singularities of the Semigeostrophic Equations via the Geometry of Lagrangian Submanifolds

Using Monge-Amp\`ere geometry, we study the singular structure of a class of nonlinear Monge-Amp\`ere equations in three dimensions, arising in geophysical fluid dynamics. We extend seminal earlier work on Monge-Amp\`ere geometry by examining the role of an induced metric on Lagrangian submanifolds of the cotangent bundle. In particular, we show that the signature of the metric serves as a classification of the Monge-Amp\`ere equation, while singularities and elliptic-hyperbolic transitions are revealed by the degeneracies of the metric. The theory is illustrated by application to an example solution of the semigeostrophic equations.Comment: 22 pages, 5 figure

Robot-Assisted Colonic Resections for Cancer

Minimally invasive surgery for colon cancer, if compared with open surgery, has shown similar oncologic outcomes, and it has become the standard management for malignant colonic disease. Its benefits appear yet in early post-operative period such as less postoperative pain, earlier recovery of gastrointestinal functions and shorter hospital stay. Robotic surgery was born in the attempt to overcome the intrinsic limitations of laparoscopic technique. It offers the possibility to have a tridimensional magnified view of surgical field and to use wristed instrument to perform an accurate dissection and lymphadenectomy. It provides the possibility to rotate at 360 degrees the instruments, facilitating considerably the performance of intracorporeal ileo-colic anastomosis in right colectomy. We want to illustrate the feasibility and technique to carry out right and left colectomy in a robotic-assisted way and its advantages with respect to laparoscopic surgery

The continuous classical Heisenberg ferromagnet equation with in-plane asymptotic conditions. I. Direct and inverse scattering theory

We develop the direct and inverse scattering theory of the linear eigenvalue problem associated with the classical Heisenberg continuous equation with in-plane asymptotic conditions. In particular, analyticity of the scattering eigenfunctions and scattering data, and their asymptotic behaviours are derived. The inverse problem is formulated in terms of Marchenko equations, and the reconstruction formula of the potential in terms of eigenfunctions and scattering data is provided

Advantages of retrofitting old electric buses and minibuses

Abstract Old electric buses and minibuses equipped with obsolete energy storage systems are today circulating on the roads all over the world. A minibus prototype equipped with Ion-Lithium batteries developed in the ENEA Casaccia Research Centre demonstrated that an old minibus can be retrofitted by replacing the old lead acid batteries pack with a new pack assembled with LiFePO4 electrochemistry. The new batteries provide sufficient power to the electric motor, an amount of energy to cover nearly 30 kilometers with a full charge, with a new battery load of 50% of the previous battery pack. The new technology allows fast charging, thus solving the problem linked due to the long periods requested to charge of the conventional batteries. For example during public transport service, the minibus can be charged with only twenty minutes, allowing such operation at the terminus while waiting for the passengers. A "depleting" strategy can be applied in order to allow the minibus to be operating all the day with several charges at the stops. In this paper, the performance of a retrofitted minibus in comparison with the same minibus equipped with old generation batteries are reported. The economic benefits for the retrofitted minibus in comparison with a new minibus purchased from factories are also reported

Euler angles for G2

We provide a simple parametrization for the group G2, which is analogous to the Euler parametrization for SU(2). We show how to obtain the general element of the group in a form emphasizing the structure of the fibration of G2 with fiber SO(4) and base H, the variety of quaternionic subalgebras of octonions. In particular this allows us to obtain a simple expression for the Haar measure on G2. Moreover, as a by-product it yields a concrete realization and an Einstein metric for H.Comment: 21 pages, 2 figures, some misprints correcte