A robust and efficient adaptive reweighted estimator of multivariate location and scatter

This article proposes a reweighted estimator of multivariate location and scatter, with weights adaptively computed from the data. Its breakdown point and asymptotic behavior under elliptical distributions are established. This adaptive estimator is able to attain simultaneously the maximum possible breakdown point for affine equivariant estimators and full asymptotic efficiency at the multivariate normal distribution. For the special case of hard-rejection weights and the MCD as initial estimator, it is shown to be more efficient than its non-adaptive counterpart for a broad range of heavy-tailed elliptical distributions. A Monte Carlo study shows that the adaptive estimator is as robust as its non-adaptive relative for several types of bias-inducing contaminations, while it is remarkably more efficient under normality for sample sizes as small as 200.     

Algebras of Random Operators Associated to Delone Dynamical Systems

We carry out a careful study of operator algebras associated with Delone dynamical systems. A von Neumann algebra is defined using noncommutative integration theory. Features of these algebras and the operators they contain are discussed. We restrict our attention to a certain C ^*-subalgebra to discuss a Shubin trace formula.     

Derivation of the k–ε model for locally homogeneous turbulence by homogenization techniques

We derive the incompressible and compressible k–ε model for locally homogeneous turbulence. The model is rigorously derived on formal mathematical grounds using the MPP modelling technique. This lets us calculate by either analytical or numerical means the closure constants of the model. To cite this article: T. Chacón Rebollo, D. Franco Coronil, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Etude des ondes rampantes sur un corps convexe vérifiant une condition ďimpédance par une méthode de développement asymptotique

We study the creeping waves propagating on a convex object, whose surface impedance is Z. To this end, we seek, by using an asymptotic expansion method, a solution of Maxwell equations, propagating along a geode sic, and satisfying Silver-Müller radiation condition at infinity, and the impedance boundary condition at the surface of the body. By using a geodesic coordinate system suited to the problem, we obtain a closed form solution. The electric and magnetic fields are given in term of the components of these fields along the binormal to the geodesic. We show that two types of creeping waves exist: the electric (resp. magnetic) type, with a non zero binormal component of the electric (resp magnetic) field. They are uncoupled, except in the vicinity of Z = 1, where a rotation of the polarization, similar to Rytov’s law, is evidenced.     

Analysis of aperture-coupled microstrip antenna using thesegmentation method

The authors present an original analysis of an aperture-coupled microstrip antenna. The theory is based on the segmentation method, which considers the patch as a multiport network whose impedance matrix is deduced from a hybrid matrix, and the use of analytical expressions of the cavity admittance at the slot centre. The theory is presented for the first time, and the theoretical results are in good agreement with previous published measurements     

Energy Conserving, Liouville, and Symplectic Integrators

In this paper, we construct an integrator that converves volume in phase space. We compare the results obtained using this method and a symplectic integrator. The results of our experiments do not reveal any superiority of the symplectic over strictly volume-preserving integrators. We also investigate the effect of numerically conserving energy in a numerical process by rescaling velocities to keep energy constant at every step. Our results for Henon-Heiles problem show that keeping energy constant in this way destroys ergodicity and forces the solution onto a periodic orbit.     

Part II: An example of the use of the comsis software: simulation of an optical network which uses wavelength multiplexing,fsk modulation format and direct detection

This second article deals with using the Comsis software for a particular application. Simulation is used to determine the maximum channel density in presence of crosstalk. In a first part, the modelling of the system is described. The simulation parameters of different optical elements are given. The results show that in the case of channels modulated at 500 Mbitls using fsk modulation format, and a direct detection operation at 1,5 μm, a minimum spacing of 6 GHz can be obtained with a 2 dB penalty. Thus if only the bandwidth of the erbium doped fibre amplifier is taken into account, the maximum number of channels which can be used is 250. However if the fsr (free spectral range) of optical filter is taken into account, the maximun number of channels is limited to 30.     

Projectivep-algebras

Presented by R. Freese.     

Canonical methods for Hamiltonian systems: numerical experiments

A Hamiltonian system possesses dynamics (e.g. preservation of volume in phase space and symplectic structure) that call for special numerical integrators, namely canonical methods. Recent research on this aspect have shown that canonical numerical integrators may be needed for Hamiltonian systems. In this paper, we focus on numerical experiments that compare canonical and non-canonical numerical integrators. Test problems are taken from different areas in physical sciences. These experiments help to buttress the claims that canonical numerical integrators give results that mimic the qualitative behavior of the original system and that canonical numerical integrators are suitable for long time integrations. Our experiments indicate that higher-order canonical methods allow for larger timestep than lower-order canonical methods.     

Topochemically Controlled Redox Reactions in the System In/Sn/Cl

The difference in reactivity of the two modifications of InCl in solid state reactions with SnCl₂ is discussed. It is explained on the basis of semi‐empirical and ab initio calculations giving the density of states diagrams of InCl and the energies of possible disproportionation reactions. Their general features are discussed on the basis of a simple bonding picture for open‐packed structures involving inert pair elements. A detailed analysis of the DOS distribution allows to pinpoint the observed redox instability to a specific structural feature of α‐InCl.