Multilinear eigenfunction estimates and global existence for the three dimensional nonlinear Schrödinger equations

We study nonlinear Schrödinger equations, posed on a three dimensional Riemannian manifold M. We prove global existence of strong H¹ solutions on M=S³ and M=S²×S¹ as far as the nonlinearity is defocusing and sub-quintic and thus we extend results of Ginibre, Velo and Bourgain who treated the cases of the Euclidean space R³ and the torus T³=R³/Z³ respectively. The main ingredient in our argument is a new set of multilinear estimates for spherical harmonics.     

A global algorithm to estimate the expectations of the components of an observed univariate mixture

This paper deals with the unsupervised classification of univariate observations. Given a set of observations originating from a K-component mixture, we focus on the estimation of the component expectations. We propose an algorithm based on the minimization of the “K-product” (KP) criterion we introduced in a previous work. We show that the global minimum of this criterion can be reached by first solving a linear system then calculating the roots of some polynomial of order K. The KP global minimum provides a first raw estimate of the component expectations, then a nearest-neighbour classification enables to refine this estimation. Our method’s relevance is finally illustrated through simulations of various mixtures. When the mixture components do not strongly overlap, the KP algorithm provides better estimates than the Expectation-Maximization algorithm.     

A laser Doppler anemometry technique for Reynolds stresses measurement

A technique is described for the measurement of all components of mean velocity and Reynolds stresses, in a complex turbulent flow where achieving coincidence data acquisition is difficult. The method is based on data recorded using four orientations of the laser probe. It is shown that the measurement errors are not the same for all the components of the Reynolds tensor, but they are sufficiently small to give a good accuracy. An application to a turbomachinery flow is given to illustrate the method.     

Property (<Emphasis Type="Italic">T</Emphasis>) and rigidity for actions on Banach spaces

We study property (T) and the fixed-point property for actions on L ^p and other Banach spaces. We show that property (T) holds when L ² is replaced by L ^p (and even a subspace/quotient of L ^p ), and that in fact it is independent of 1≤p<∞. We show that the fixed-point property for L ^p follows from property (T) when 1<p< 2+ε. For simple Lie groups and their lattices, we prove that the fixed-point property for L ^p holds for any 1< p<∞ if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices in products of general groups on superreflexive spaces. Bader partially supported by ISF grant 100146; Furman partially supported by NSF grants DMS-0094245 and DMS-0604611; Gelander partially supported by NSF grant DMS-0404557 and BSF grant 2004010; Monod partially supported by FNS (CH) and NSF (US).     

Homologies d'algèbres Artin–Schelter régulières cubiques

Hochschild homology of cubic Artin–Schelter regular algebras of type A with generic coefficients is computed. We follow the method used by Van den Bergh (K-Theory 8 (1994) 213–230) in the quadratic case, by considering these algebras as deformations of a polynomial algebra, with remarkable Poisson brackets. A new quasi-isomorphism is introduced. De Rham cohomology, cyclic and periodic cyclic homologies, and Hochschild cohomology are also computed. To cite this article: N. Marconnet, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Magnetic resonance imaging and pulsed Doppler sonography of poststenotic jets: Correlation between signal void and flow velocity distribution

To correlate the appearance of poststenotic jets on gradient echo images with features of localized Doppler spectra of the jets, we studied an in vitro model of steady flow-through stenoses of 86, 96, and 99% area reduction. As fluids, water and a 40% glycerol solution in water were used. MRI was performed with a 1.5 T whole body imager and gradient echo images were obtained in planes parallel to the direction of flow. Doppler spectra were acquired separately from the MR measurements at 1 cm intervals for a distance of 10 cm downstream from the stenosis. Poststenotic signal void was observed for water and for the 40% glycerol solution only if the mean velocity within the stenosis exceeded a limit of 50–60 cm/sec. On the MR images, the jets could be divided into two segments: A proximal jet segment of uniform width equal to the diameter of the stenosis, followed by a distal jet segment which was characterized by broadening and then dissipating signal void. Except for the 99% stenosis, a high signal intensity core was present within the proximal jet segment. In the proximal jet segment, the Doppler measurements showed a low temporal fluctuation of the maximal flow velocity and only little flow opposite to the main flow direction. In the distal jet segment, the velocity fluctuation and the intensity of reverse flow increased sharply. The high signal intensity core of the jet was associated with a poststenotic zone of constant maximal flow velocity. The results demonstrate a close relationship between characteristic features of poststenotic jets in MRI and pulsed Doppler sonography.