Support problem for the intermediate Jacobians of l-adic representations

We consider the support problem of Erdös in the context of l-adic representations of the absolute Galois group of a number field. Main applications of the results of the paper concern Galois cohomology of the Tate module of abelian varieties with real and complex multiplications, the algebraic K-theory groups of number fields and the integral homology of the general linear group of rings of integers. We answer the question of Corrales-Rodrigáñez and Schoof concerning the support problem for higher dimensional abelian varieties.     

Chern numbers for two families of noncommutative Hopf fibrations

We consider noncommutative line bundles associated with the Hopf fibrations of SU_q(2) over all Podle? spheres and with a locally trivial Hopf fibration of S³_pq. These bundles are given as finitely generated projective modules associated via 1-dimensional representations of U(1) with Galois-type extensions encoding the principal fibrations of SU_q(2) and S³_pq. We show that the Chern numbers of these modules coincide with the winding numbers of representations defining them. To cite this article: P.M. Hajac et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

On characterization of Poisson and Jacobi structures

We characterize Poisson and Jacobi structures by means of complete lifts of the corresponding tensors: the lifts have to be related to canonical structures by morphisms of corresponding vector bundles. Similar results hold for generalized Poisson and Jacobi structures (canonical structures) associated with Lie algebroids and Jacobi algebroids.     

The capacity of parabolic julia sets

Supported by SFB 170 “Geometrie und Analysis” at the University of G?ttingen     

Surface status and size influences of nickel nanoparticles on sulfur compound adsorption

Metallic nickel nanoparticles were incorporated on mesoporous silica to remove sulfur compounds in diesel selectively. In the first method, nickel nanoparticles were formed on mesoporous silica SBA-15 by impregnation and subsequent reduction of nickel nitrate. The sulfur adsorption capacity was strongly dependent on the nickel loading and the average nickel particle size. In the second method, nickel nanoparticles were synthesized in solution in the presence of a capping agent and then incorporated in mesoporous silica MCF by sonication. Although these particles maintain their sizes on the MCF surface after heat treatment, capping agent remaining on the Ni particle surface might interfere the adsorption of sulfur compounds.     

Low-Temperature Anti-Stokes Luminescence in Zn1-xMgxSe Mixed Crystals

Investigations of photoluminescence and Raman scattering in the ternary Zn_1-xMg_xSe compounds at 4.2 K were performed both in the Stokes and anti-Stokes regions using cw laser excitation with various wavelengths within the transparency band of the crystals. The anti-Stokes luminescence was observed for the first time in the ternary Zn_1-xMg_xSe compounds. We have found variations in the shape and position of the Stokes and anti-Stokes luminescence bands with an increase in the band gap energy, which depends on magnesium content. We assume that the anti-Stokes emission is generated by two-step excitation via deep-level centers. It is shown that the low-temperature anti-Stokes photoluminescence can probe the spatial distribution profiles of impurities in the bulk of crystals.     

Structure and polarity of 8CB films evaporated onto solid substrates

Brewster-angle reflection ellipsometry and surface optical second harmonic generation were used to study the growth of 4'-n-octyl-4-cyanobiphenyl (8CB) films evaporated in air onto polymeric and quartz glass substrates. The layer-by-layer growth of the films terminates after formation of two distinctive interfacial layers. Both of these two layers are polar and tilted. In the first layer the molecules lie nearly flat on the surface, while in the second layer they point on average about 50° toward the surface normal. The dipole moment of the second layer has a lower magnitude and an opposite direction with respect to the dipole moment of the first layer.     

Surface Nucleation Kinetics on Active Centers from Supersaturated Vapor

The formation of nuclei from a supersaturated vapor on a surface with active centers is treated within standard self-consistent classical model with exhaustion of active centers. Basic characteristics of nucleation process (total number of nuclei, nucleation rate, time lag and size distribution of nuclei) are determined by numerical solution of kinetic equations. It is shown that standard approach to nucleation on active centers based on Avrami model coincides with our approach in the values of time lag of nucleation process, but it differs in the total number of nuclei.     

Families of Line-Graphs and Their Quantization

Any directed graph G with N vertices and J edges has an associated line-graph L(G) where the J edges form the vertices of L(G). We show that the non-zero eigenvalues of the adjacency matrices are the same for all graphs of such a family L ⁿ (G). We give necessary and sufficient conditions for a line-graph to be quantisable and demonstrate that the spectra of associated quantum propagators follow the predictions of random matrices under very general conditions. Line-graphs may therefore serve as models to study the semiclassical limit (of large matrix size) of a quantum dynamics on graphs with fixed classical behaviour.