Robust stabilization of chained systems via hybrid control

Published versio

Some unbounded functions of intermittent maps for which the central limit theorem holds

We compute some dependence coefficients for the stationary Markov chain whose transition kernel is the Perron-Frobenius operator of an expanding map $T$ of $[0, 1]$ with a neutral fixed point. We use these coefficients to prove a central limit theorem for the partial sums of $f\circ T^i$, when $f$ belongs to a large class of unbounded functions from $[0, 1]$ to ${\mathbb R}$. We also prove other limit theorems and moment inequalities.Comment: 16 page

XLIII. Extract from a memoir entitled "Considerations on colours, and several of their singular appearances." Read in the mathematical and physical class of the French National Institute, Ventose 13, an 13

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A latitude-dependent wind model for Mira's cometary head

We present a 3D numerical simulation of the recently discovered cometary structure produced as Mira travels through the galactic ISM. In our simulation, we consider that Mira ejects a steady, latitude-dependent wind, which interacts with a homogeneous, streaming environment. The axisymmetry of the problem is broken by the lack of alignment between the direction of the relative motion of the environment and the polar axis of the latitude-dependent wind. With this model, we are able to produce a cometary head with a ``double bow shock'' which agrees well with the structure of the head of Mira's comet. We therefore conclude that a time-dependence in the ejected wind is not required for reproducing the observed double bow shock.Comment: 4 pages, 4 figures, accepted for publication in ApJ

Adaptive density estimation for stationary processes

We propose an algorithm to estimate the common density $s$ of a stationary process $X_1,...,X_n$. We suppose that the process is either $\beta$ or $\tau$-mixing. We provide a model selection procedure based on a generalization of Mallows' $C_p$ and we prove oracle inequalities for the selected estimator under a few prior assumptions on the collection of models and on the mixing coefficients. We prove that our estimator is adaptive over a class of Besov spaces, namely, we prove that it achieves the same rates of convergence as in the i.i.d framework

Pbx(OH)y cluster formation and anomalous thermal behaviour in STI framework-type zeolites

For the first time, the structural investigation of a Pb-exchanged zeolite (Pb13.4(OH)10Al17.4Si54.6O144 ∙38H2O) with STI framework type, revealed a highly unusual and intriguing sudden volume increase under continuous heating. Understanding the fundamental mechanisms leading to such an unusual behaviour is essential for technological applications and interpretation of chemical bonding in zeolites. The dehydration was tracked in situ from 25 to 450 °C by single crystal X-ray diffraction, infrared and X-ray absorption spectroscopy. Further interpretation of the experimental observations was supported by ab initio molecular dynamics simulations. Initially, Pb-STI unit-cell volume contracts (ΔV = -3.5%) from 25 to 100°C. This agrees with the trend observed in STI zeolites. Surprisingly, at 125°C, the framework expanded (ΔV = +2%), adopting a configuration, which resembles that of the room temperature structure. Upon heating, the structure loses H2O but no de-hydroxylation occurred. The key mechanism leading to the sudden volume increase was found to be the formation of Pbx(OH)y clusters, which prevent the shrinking of the channels, rupture of the tetrahedral bonds and occlusion of the pores. This zeolite has therefore an increased thermal stability with respect to other STI metal-exchanged zeolites, with important consequences on its applications