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Existence de points fixes enlacés à une orbite périodique d'un homéomorphisme du plan
1992
Let f be an orientation-preserving homeomorphism of the plane such that f-Id is contracting. Under these hypotheses, we establish the existence, for every periodic orbit, of a fixed point which has nonzero linking number with this periodic orbit.
Quantization of Poisson Lie Groups and Applications
1996
LetG be a connected Poisson-Lie group. We discuss aspects of the question of Drinfel'd:can G be quantized? and give some answers. WhenG is semisimple (a case where the answer isyes), we introduce quantizable Poisson subalgebras ofC ∞(G), related to harmonic analysis onG; they are a generalization of F.R.T. models of quantum groups, and provide new examples of quantized Poisson algebras.
On the stability of some controlled Markov chains and its applications to stochastic approximation with Markovian dynamic
2015
We develop a practical approach to establish the stability, that is, the recurrence in a given set, of a large class of controlled Markov chains. These processes arise in various areas of applied science and encompass important numerical methods. We show in particular how individual Lyapunov functions and associated drift conditions for the parametrized family of Markov transition probabilities and the parameter update can be combined to form Lyapunov functions for the joint process, leading to the proof of the desired stability property. Of particular interest is the fact that the approach applies even in situations where the two components of the process present a time-scale separation, w…
From Feynman–Kac formulae to numerical stochastic homogenization in electrical impedance tomography
2016
In this paper, we use the theory of symmetric Dirichlet forms to derive Feynman–Kac formulae for the forward problem of electrical impedance tomography with possibly anisotropic, merely measurable conductivities corresponding to different electrode models on bounded Lipschitz domains. Subsequently, we employ these Feynman–Kac formulae to rigorously justify stochastic homogenization in the case of a stochastic boundary value problem arising from an inverse anomaly detection problem. Motivated by this theoretical result, we prove an estimate for the speed of convergence of the projected mean-square displacement of the underlying process which may serve as the theoretical foundation for the de…
Quantum-chemical determination of Born–Oppenheimer breakdown parameters for rotational constants: the open-shell species CN, CO+ and BO
2013
The quantum-chemical protocol for computing Born-Oppenheimer breakdown corrections to rotational constants in the case of diatomic molecules is extended to open-shell species. The deviation from the Born-Oppenheimer equilibrium rotational constant is obtained by considering three contributions: the adiabatic correction to the equilibrium bond distance, the electronic contribution to the moment of inertia requiring the computation of the rotational g-tensor, and the so-called Dunham correction. Values for the Born-Oppenheimer breakdown parameters of CN, CO+, and BO in their (2)sigma(+) electronic ground states are reported based on coupled-cluster calculations of the involved quantities and …
Casimir-Lifshitz force out of thermal equilibrium between dielectric gratings
2014
We calculate the Casimir-Lifshitz pressure in a system consisting of two different 1D dielectric lamellar gratings having two different temperatures and immersed in an environment having a third temperature. The calculation of the pressure is based on the knowledge of the scattering operators, deduced using the Fourier Modal Method. The behavior of the pressure is characterized in detail as a function of the three temperatures of the system as well as the geometrical parameters of the two gratings. We show that the interplay between non-equilibrium effects and geometrical periodicity offers a rich scenario for the manipulation of the force. In particular, we find regimes where the force can…
On the arithmetic and geometry of binary Hamiltonian forms
2011
Given an indefinite binary quaternionic Hermitian form $f$ with coefficients in a maximal order of a definite quaternion algebra over $\mathbb Q$, we give a precise asymptotic equivalent to the number of nonequivalent representations, satisfying some congruence properties, of the rational integers with absolute value at most $s$ by $f$, as $s$ tends to $+\infty$. We compute the volumes of hyperbolic 5-manifolds constructed by quaternions using Eisenstein series. In the Appendix, V. Emery computes these volumes using Prasad's general formula. We use hyperbolic geometry in dimension 5 to describe the reduction theory of both definite and indefinite binary quaternionic Hermitian forms.
Monte Carlo simulations of the solid-liquid transition in hard spheres and colloid-polymer mixtures
2010
Monte Carlo simulations at constant pressure are performed to study coexistence and interfacial properties of the liquid-solid transition in hard spheres and in colloid-polymer mixtures. The latter system is described as a one-component Asakura-Oosawa (AO) model where the polymer's degrees of freedom are incorporated via an attractive part in the effective potential for the colloid-colloid interactions. For the considered AO model, the polymer reservoir packing fraction is eta_p^r=0.1 and the colloid-polymer size ratio is q=sigma_p/\sigma=0.15 (with sigma_p and sigma the diameter of polymers and colloids, respectively). Inhomogeneous solid-liquid systems are prepared by placing the solid fc…
Epidemiology of congenital diaphragmatic hernia in Europe: a register-based study.
2015
INTRODUCTION: Published prevalence rates of congenital diaphragmatic hernia (CDH) vary. This study aims to describe the epidemiology of CDH using data from high-quality, population-based registers belonging to the European Surveillance of Congenital Anomalies (EUROCAT).METHODS: Cases of CDH delivered between 1980 and 2009 notified to 31 EUROCAT registers formed the population-based case series. Prevalence over time was estimated using multilevel Poisson regression, and heterogeneity between registers was evaluated from the random component of the intercept.RESULTS: There were 3373 CDH cases reported among 12 155 491 registered births. Of 3131 singleton cases, 353 (10.4%) were associated wit…
Large numbers of cold positronium atoms created in laser-selected Rydberg states using resonant charge exchange
2016
Lasers are used to control the production of highly excited positronium atoms (Ps*). The laser light excites Cs atoms to Rydberg states that have a large cross section for resonant charge-exchange collisions with cold trapped positrons. For each trial with 30 million trapped positrons, more than 700 000 of the created Ps* have trajectories near the axis of the apparatus, and are detected using Stark ionization. This number of Ps* is 500 times higher than realized in an earlier proof-of-principle demonstration (2004 Phys. Lett. B 597 257). A second charge exchange of these near-axis Ps* with trapped antiprotons could be used to produce cold antihydrogen, and this antihydrogen production is e…