1,721,056 research outputs found
The Geodesics for Poincaré’s Half-Plane: a Nonstandard Derivation
No full textConstants of motion in Mechanics are usually inferred from groups of symmetry transformations of the given system, as, for example, a Lagrangian function that is time-invariant implies the conservation of energy. Here we wish to show that useful properties of a mechanical system can sometimes be deduced from a family of Noether-like transformations that are not inspired by any symmetry whatsoever. The sample system we concentrate on is the Lagrangian interpretation of Poincaré’s half plane of hyperbolic geometry, and the properties we will derive in a new way are the shape and the time parameterization of its geodesics
Regularity at the boundary for on q-pseudoconvex domains
No full textSolvability for /9 with regularity at the boundary of a domain
f/CC C n for forms of any degree k > 1 was characterized by pseudoconvexity of
0[2 in [ 16]. It is proved here that q-pseudoconvexity suffices to guarantee solvability
of forms of degree k _> q + 1. The method relies on the L 2 estimates in and
on their Sobolev version
Complete integrability for Hamiltonian systems with a cone potential
No full textIt is known that, if a point in R^n is driven by a bounded below potential V, whose gradient is always in a closed convex cone which contains no lines, then the velocity has a finite limit as time goes to +infinity. The components of the asymptotic velocity, as functions of the initial data, are trivially constants of motion. We find sufficient conditions for these functions to be C^k (2<k<infinity) first integrals, independent and pairwise in involution. In this way we construct a large class of completely integrable systems. We can deal with very different asymptotic behaviours of the potential and we have persistence of the integrability under any small perturbation of the potential in an arbitrary compact set
Time reversibility and energy conservation for Lagrangian systems with nonlinear nonholonomic constraints
No full textSeparate holomorphic extension of CR functions.
No full textWe consider a real analytic foliation of Cn by complex analytic manifolds of
dimension m issued transversally from a CR generic submanifold M ⊂ Cn of codimension
m. We prove that a continuous CR function f on M which has separate holomorphic
extension along each leaf, is holomorphic. When the leaves are cartesian straight planes, separate
holomorphic extension along suitable selections of these planes suffices and f turns
out to be holomorphic in a neighbourhood of their union. If M is a hypersurface we can also
specify the side of the extension, regardless the leaves are straight or not
A class of integrable Hamiltonian systems including scattering of particles on the line with repulsive interactions.
No full textThe main purpose of this paper is to introduce a new class of Hamiltonian scattering systems of the cone potential type that can be integrated via the asymptotic velocity. For a large subclass, the asymptotic data of the trajectories define a global canonical diffeomorphism \A that brings the system into the normal form , .
The integrability theory applies for example to a system of particles on the line interacting pairwise through rather general repulsive potentials. The inverse -power potential for arbitrary~ is included, the reduction to normal form being carried out for the exponents~. In particular, the Calogero system is obtained for~. The treatment covers also the nonperiodic Toda lattice.
The cone potentials that we allow can undergo small perturbations in any arbitrary compact set without losing the integrability and the reduction to normal form
Treatment of varicocele in pediatric patients with controindication for open surgery with transfemoral retrograde sclero-embolization under local anesthesia
No full textThe author describe an alternative approach for the treatment of varicocele by scleroembolization of spermatic vein
COMPACTNESS ESTIMATES FOR square(b) ON A CR MANIFOLD
No full textThis paper aims to state compactness estimates for the Kohn-Laplacian on an abstract CR manifold in full generality. The approach consists of a tangential basic estimate in the formulation given by the first author in his thesis, which refines former work by Nicoara. It has been proved by Raich that on a CR manifold of dimension 2n - 1 which is compact pseudoconvex of hypersurface type embedded in the complex Euclidean space and orientable, the property named "(CR - P-q)" for 1 <= q <= n-1/2, a generalization of the one introduced by Catlin, implies compactness estimates for the Kohn-Laplacian square(b) in any degree k satisfying q <= k <= n - 1 - q. The same result is stated by Straube without the assumption of orientability. We regain these results by a simplified method and extend the conclusions to CR manifolds which are not necessarily embedded nor orientable. In this general setting, we also prove compactness estimates in degree k = 0 and k = n - 1 under the assumption of (CR - P-1) and, when n=2, of closed range for partial derivative(b). For n >= 3, this refines former work by Raich and Straube and separately by Straube
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