Un problème d'optimisation de forme pour la contrôlabilité exacte de l'équation des ondes 2D

We consider the wave equation defined on $\Omega ?{\mathbb{R}}^2$ and $\omega ?\Omega$. We designate by $v_{\omega }$ the distributed control of minimal $L^2(\omega \times (0,T))$ norm obtained with the Hilbert Uniqueness Method which stabilizes the system at time $T>0$. This Note addresses the question of the optimal position of ω in order to minimize $J:\omega \to 6v_{\omega }{6}_{L^2(\omega \times (0,T))}$. Assuming $\omega \in C^{1,1}(\Omega )$, we express the shape derivative of J as a curvilinear integral on ?ω (independently of any adjoint solution) leading to a descent algorithm. A numerical application is given. To cite this article: A. Münch, C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

Surface structure of (10(-)10) and (11(-)20) surfaces of ZnO with density functional theory and atomistic simulation

We have calculated the stability of two of the low-index surfaces known to dominate the morphology of ZnO as a function of stoichiometry. These two surfaces are (10(-)10) and (11(-)20). In each case, two terminations only are stable for a significant range of oxygen and hydrogen chemical potential: the pure stoichiometric surface and a surface covered in a monolayer of water. The mode by which the water adsorbs is however different for the two surfaces considered. On the (10(-)10) surface the close proximity of the water molecules means hydrogen bonding can occur between adjacent chemiabsorbed water molecules and hence there is little difference in the stability of the hydrated and hydroxylated surface, and in fact the most stable surface occurs with a combination of dissociated and undissociated water adsorption. In the case of the (11(-)20) surface, it is only when full dissociation has occurred that a hydrogen-bonding network can form. Our results also show good agreement between DFT and atomistic simulations, suggesting that potential based methods can usefully be applied to ZnO.     

Huge excitonic effects in layered hexagonal boron nitride

The all-electron GW approximation energy band gap of bulk hexagonal boron nitride is shown to be of indirect type. The resulting computed in-plane polarized optical spectrum, obtained by solving the Bethe-Salpeter equation for the electron-hole two-particle Green function, is in excellent agreement with experiment and has a strong anisotropy compared to out-of-plane polarized spectrum. A detailed analysis of the excitonic structures within the band gap shows that the low-lying excitons belong to the Frenkel class and are tightly confined within the layers. The calculated exciton binding energy is much larger than that obtained by Watanabe et al. [Nat. Mater. 3, 404 (2004).] based on a Wannier model assuming h-BN to be a direct-band-gap semiconductor.     

Chlorofluoroiodomethane as a potential candidate for parity violation measurements

CHFClI is among the more favorable molecules for parity violation (PV) measurements in molecules. Despite the fact that calculated PV effects are two orders of magnitude smaller than in some organometallic compounds, CHFClI displays interesting features which could make possible a new experimental PV test on this molecule. Indeed, ultrahigh resolution spectroscopy using an ultrastable CO(2) laser is favored by several intrinsic properties of this molecule. For example, the high vapor pressure of CHFClI allows investigation by supersonic beam spectroscopy. Indeed, the spectroscopic constants have been accurately determined by microwave and millimetre wave spectroscopy. This is important for the subsequent selection of an appropriate absorption band of CHFClI that could be brought to co?ncide with the absorption of CO(2). Partially resolved (+)- and (-)-CHFClI enantiomers with respectively 63.3 and 20.5% ee's have been recently prepared and analyzed by molecular recognition using chiral hosts called cryptophanes. Finally, the S-(+)/R-(-) absolute configuration was ascertained by vibrational circular dichro?sm (VCD) in the gas phase.     

Bounded type Siegel disks of finite type maps with few singular values

Let U be an open subset of the Riemann sphere \(\hat {\mathbb{C}}\). We give sufficient conditions for which a finite type map f: U → \(\hat {\mathbb{C}}\) with at most three singular values has a Siegel disk compactly contained in U and whose boundary is a quasicircle containing a unique critical point. The main tool is quasiconformal surgery à la Douady-Ghys-Herman-?wi?tek. We also give sufficient conditions for which, instead, Δ has not compact closure in U. The main tool is the Schwarzian derivative and area inequalities à la Graczyk-?wi?tek.     

France: genetics education for non-genetics health care providers

OBJECTIVE: This paper explores the treatment of medical genetics in undergraduate medical education, specialists' training and continuing medical education (CME) for general practitioners, specialists, nurses and midwives. METHODS: We conducted a qualitative survey of websites, published or unpublished documents, telephone interviews and mailed questionnaires. RESULTS: Genetics is a medical specialty in France, and the small number of university professors in genetics are in charge of the genetic component of medical training of all future practitioners. The study was complicated by the ongoing waves of reforms in the French health and educational systems and by the autonomy of the faculties. Specialist training and CME in genetics is heterogeneous and not organised as a priority. CONCLUSIONS: Specialist education and CME in genetics of non-geneticist health care providers needs to be adapted to the fast ongoing developments of this field of knowledge.     

On solving integral equations using Markov chain Monte Carlo methods

In this paper, we propose an original approach to the solution of Fredholm equations of the second kind. We interpret the standard Von Neumann expansion of the solution as an expectation with respect to a probability distribution defined on a union of subspaces of variable dimension. Based on this representation, it is possible to use trans-dimensional Markov chain Monte Carlo (MCMC) methods such as Reversible Jump MCMC to approximate the solution numerically. This can be an attractive alternative to standard Sequential Importance Sampling (SIS) methods routinely used in this context. To motivate our approach, we sketch an application to value function estimation for a Markov decision process. Two computational examples are also provided.