Partial immersions and partially free maps

In a recent paper~\cite{DDL10} we studied basic properties of partial immersions and partially free maps, a generalization of free maps introduced first by Gromov in~\cite{Gro70}. In this short note we show how to build partially free maps out of partial immersions and use this fact to prove that the partially free maps in critical dimension introduced in Theorems 1.1-1.3 of~\cite{DDL10} for three important types of distributions can actually be built out of partial immersions. Finally, we show that the canonical contact structure on \bR^{2n+1} admits partial immersions in critical dimension for every $n$.Comment: 8 pages, submitted to the proceedings of the conference DGA201

Solvability of the cohomological equation for regular vector fields on the plane

We consider planar vector field without zeroes X and study the image of the associated Lie derivative operator LX acting on the space of smooth functions. We show that the cokernel of LX is infinite-dimensional as soon as X is not topologically conjugate to a constant vector field and that, if the topology of the integral trajectories of X is ``simple enough'' (e.g. if X is polynomial) then X is transversal to a Hamiltonian foliation. We use this fact to find a large explicit subalgebra of the image of LX and to build an embedding of R^2 into R^4 which rectifies X. Finally we use this embedding to characterize the functions in the image of LX.Comment: 21 pages, 2 figure

Cryothermal Energy Ablation Of Cardiac Arrhythmias 2005: State Of The Art

At the time of antiarrhythmic surgery, cryothermal energy application by a hand-held probe was used to complement dissections and resections and permanently abolish the arrhythmogenic substrate. Over the last decade, significant engineering advances allowed percutaneous cryoablation based on catheters, apparently not very different from standard radiofrequency ablation catheters. Cryothermal energy has peculiar characteristics. In fact, it allows testing in a reversible way the effects of energy application at higher temperature, before producing a permanent lesion at –75°C. Moreover, slow formation of the lesion allows timely discontinuation of the application, as soon as inadvertent modifications of normal atrioventricular conduction are observed during ablation in the proximity of atrioventricular node and His bundle, avoiding its permanent damage. Over the last years, percutaneous cryothermal ablation has been widely used for a variety of cardiac arrhythmias. From the data gathered, it is unlikely that cryoablation will replace standard ablation in unselected cases. Nevertheless, for the above mentioned peculiarities, cryothermal ablation has proved very effective and safe for ablation of arrhythmogenic substrates close to the normal conduction pathways, becoming the first choice method to ablate anteroseptal and midseptal accessory pathways. It can be also the best treatment for ablation of the slow pathway to abolish atrioventricular node reentrant tachycardia in pediatrics or when particular anatomy of the Koch’s triangle is observed. Cryothermal ablation of the pulmonary veins for atrial fibrillation, although longer than radiofrequency ablation, is not associated with pulmonary vein stenosis and is expected to be less thrombogenic; new catheter designs for cryothermal ablation of this challenging arrhythmia are to be tested to assess their efficacy and clinical usefulness

How Galaxies Disguise Their Ages

We calculate the contribution to Balmer line indices from far ultraviolet component sources. We find that this is significant, and may lead to identification of spurious age differences of the order of a total span of $\sim 6$ Gyrs or $\sim 15$ size bursts observed a few Gyrs after star formation stops. We suggest that claims for intermediate age populations in early-type galaxies may need to be reconsidered in the light of this new evidence.Comment: Accepted by MNRA