estimates for overdetermined Radon transforms

We prove several variations on the results of F. Ricci and G. Travaglini (2001), concerning bounds for convolution with all rotations of arc length measure on a fixed convex curve in . Estimates are obtained for averages over higher-dimensional convex (nonsmooth) hypersurfaces, smooth -dimensional surfaces, and nontranslation-invariant families of surfaces. We compare Ricci and Travaglini's approach, based on average decay of the Fourier transform, with an approach based on boundedness of Fourier integral operators, and show that essentially the same geometric condition arises in proofs using the two techniques.

     

Composition of Lie transforms with rigorous estimates and applications to Hamiltonian perturbation theory

In this paper we exhibit a rigorous perturbation theory for nearly integrable Hamiltonian systems, based on the composition of Lie Transforms. Precisely, we first study the algorithm for the composition of Lie transforms, and provide rigorous estimates for the convergence radius and the truncation errors of the series; then we use our estimates for a particular model-example, namely a system of weakly coupled harmonic oscillators having Diophantine frequencies, and work out Nekhoroshev-like exponential estimates for the stability times.     

Outer approximation algorithms for canonical DC problems

The paper discusses a general framework for outer approximation type algorithms for the canonical DC optimization problem. The algorithms rely on a polar reformulation of the problem and exploit an approximated oracle in order to check global optimality. Consequently, approximate optimality conditions are introduced and bounds on the quality of the approximate global optimal solution are obtained. A thorough analysis of properties which guarantee convergence is carried out; two families of conditions are introduced which lead to design six implementable algorithms, whose convergence can be proved within a unified framework.     

Turing vegetation patterns in a generalized hyperbolic Klausmeier model

The formation of Turing vegetation patterns in flat arid environments is investigated in the framework of a generalized version of the hyperbolic Klausmeier model. The extensions here considered involve, on the one hand, the strength of the rate at which rainfall water enters into the soil and, on the other hand, the functional dependence of the inertial times on vegetation biomass and soil water. The study aims at elucidating how the inclusion of these generalized quantities affects the onset of bifurcation of supercritical Turing patterns as well as the transient dynamics observed from an uniformly vegetated state towards a patterned state. To achieve these goals, linear and multiple-scales weakly nonlinear stability analysis are addressed, this latter being inspected in both large and small spatial domains. Analytical results are then corroborated by numerical simulations, which also serve to describe more deeply the spatio-temporal evolution of the emerging patterns as well as to characterize the different timescales involved in vegetation dynamics.     

Convex curves, Radon transforms and convolution operators defined by singular measures

Let be a convex curve in the plane and let be the arc-length measure of Let us rotate by an angle and let be the corresponding measure. Let . Then This is optimal for an arbitrary . Depending on the curvature of , this estimate can be improved by introducing mixed-norm estimates of the form where and are conjugate exponents.     

La geometria asintotica delle foglie « eccezionali » delle foliazioni di Anosov

Résumé On considère les feuilletages d'Anosov de T₁S, avec S surface hyperbolique fermée, et on étudie la géométrie asymptotique des feuilles « exceptionnelles ».

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Lavoro eseguito nell'ambito del G.N.S.A.G.A. del C.N.R. e col contributo del M.P.I. (fondi 60%).     

Heteronuclear decoupling interference during symmetry-based homonuclear recoupling in solid-state NMR

We examine the influence of continuous-wave heteronuclear decoupling on symmetry-based double-quantum homonuclear dipolar recoupling, using experimental measurements, numerical simulations, and average Hamiltonian theory. There are two distinct regimes in which the heteronuclear interference effects are minimized. The first regime utilizes a moderate homonuclear recoupling field and a strong heteronuclear decoupling field; the second regime utilizes a strong homonuclear recoupling field and a weak or absent heteronuclear decoupling field. The second regime is experimentally accessible at moderate or high magic-angle-spinning frequencies and is particularly relevant for many realistic applications of solid-state NMR recoupling experiments to organic or biological materials.     

Relevance of swelling corrections in the unscreened polyelectrolyte chain model

The origin and importance of swelling corrections in the field-theoretic model describing an isolated, unscreened polyelectrolyte chain below six dimensions are examined in detail using the renormalization theory of higher composite operators. It is shown that these corrections become relevant below an unspecified dimension $\text{d}{}^1\text{< 6}$, when the unphysical exact result $\text{v =}\text{2}\text{(d ? 2)}$ for the size exponent breaks down and the system should be described by a new model.