NP-hardness results for the aggregation of linear orders into median orders

Given a collection Π of individual preferences defined on a same finite set of candidates, we consider the problem of aggregating them into a collective preference minimizing the number of disagreements with respect to Π and verifying some structural properties. We study the complexity of this problem when the individual preferences belong to any set containing linear orders and when the collective preference must verify different properties, for instance transitivity. We show that the considered aggregation problems are NP-hard for different types of collective preferences (including linear orders, acyclic relations, complete preorders, interval orders, semiorders, quasi-orders or weak orders), if the number of individual preferences is sufficiently large.     

Pressure-induced structural transformations of the Zintl phase sodium silicide

The high-pressure behaviour of NaSi has been studied using Raman spectroscopy and angle-dispersive synchrotron X-ray diffraction to observe the onset of structural phase transformations and potential oligomerisation into anionic Si nanoclusters with extended dimensionality. Our studies reveal a first structural transformation occurring at 8–10 GPa, followed by irreversible amorphisation above 15 GPa, suggesting the formation of Si–Si bonds with oxidation of the Si⁻ species and reduction of Na⁺ to metallic sodium. We have combined our experimental studies with DFT calculations to assist in the analysis of the structural behaviour of NaSi at high pressure.     

Resolution of singularities of threefolds in positive characteristic II

Together with [Vincent Cossart, Olivier Piltant, Resolution of singularities of threefolds in positive characteristic. I. Reduction to local uniformization on Artin–Schreier and purely inseparable coverings, J. Algebra 320 (3) (2008) 1051–1082], this article gives a complete proof of desingularization of quasiprojective varieties of dimensional 3 on fields which are differentially finite over perfect fields.     

Zement

Ohne Zusammenfassung     

Alpha effect in helically forced turbulence

The effect on large-scale dynamics of small-scale helicity injection in three-dimensional resistive magnetohydrodynamic turbulence is investigated for a weak initial magnetic field. The magnetic configuration of α² dynamo prototype flows is such that, generally, the energy concentrates on one large-scale mode. However, we obtain that alpha effect is not limited to the dominant mode and that a non-local equation (in Fourier space) is more appropriate to describe it. It gives some insights into the non-local theory of Pouquet et al. [J. Fluid Mech. 77 (1976) 321] where the inverse cascade results from a competition between the helicity and Alfvén effects.     

Self-interacting diffusions

 This paper is concerned with a general class of self-interacting diffusions {X _t } _{t ≥0} living on a compact Riemannian manifold M. These are solutions to stochastic differential equations of the form : dX _t = Brownian increments + drift term depending on X _t and μ _t , the normalized occupation measure of the process. It is proved that the asymptotic behavior of {μ _t } can be precisely related to the asymptotic behavior of a deterministic dynamical semi-flow Φ = {Φ _t } _{t ≥0} defined on the space of the Borel probability measures on M. In particular, the limit sets of {μ _t } are proved to be almost surely attractor free sets for Φ. These results are applied to several examples of self-attracting/repelling diffusions on the n-sphere. For instance, in the case of self-attracting diffusions, our results apply to prove that {μ _t } can either converge toward the normalized Riemannian measure, or to a gaussian measure, depending on the value of a parameter measuring the strength of the attraction. Received: 21 July 2000 / Revised version: 12 December 2000 / Published online: 15 October 2001     

A mathematical model for the transient evolution of a resonant tunneling diodeModélisation d'une diode à effet tunnel résonant en régime transitoire

A mathematical model of quantum transient transport is derived and analyzed. The model describes the evolution of electrons injected into the “device” by reservoirs having a stationary statistics. The electrostatic potential in the device is modified by electron presence through electrostatic interaction. The wave functions are computed in the device region and satisfy non homogeneous open boundary conditions at the device edges. A priori estimates are deduced from the “dissipative properies” of the boundary conditions and from the repulsive character of the electrostatic interaction. To cite this article: N. Ben Abdallah, O. Pinaud, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 283–288.     

Activation of oxaziridines by lewis acids: application in enantioselective sulfoxidation

The preparation of new and easily accessible chiral N-alkyloxaziridines for asymmetric sulfides oxidation was investigated. Most significantly, we report here that inert N-alkyloxaziridines can be activated by Lewis acids to achieve a fast, selective, and efficient oxygen atom transfer to sulfides. Asymmetric sulfoxidation by three new chiral oxaziridines (two of them were structurally characterized by X-ray analysis) afforded enantioselectivities ranging from 22% to 63% ee with the simplest aryl alkyl sulfides.