Compact spreads and compact translation planes over locally compact fields

We prove that a spread S over a locally compact nondlscrete field F defines a topological translation plane if and only if the spread is compact. For F=R, this is implicit in Breuning's thesis [Bre], cf. [B 2]. For the proof, we describe the point set of the projective translation plane as a quotient space of some projective space, with identifications taking place in one hyperplane. This is new even for F=R.     

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).     

Soliton chaos and lengthscale competition in nonlinear dynamics

Perturbing soliton-bearing completely integrable dynamics can give rise to rich and fascinating behaviour. If the perturbation introduces a lengthscale which is large compared to the spatial extent of the solitons present in the system, the solitons move like particles in an effective potential. Taking into account two-soliton interaction can result in chaotic behaviour called ‘soliton chaos’. In the opposite limit of a small-lengthscale perturbation the solitons acquire a dressing which effectively shields them from the perturbation. If the resulting ‘dressed solitons’ are subject to an additional long-wavelength perturbation they move like renormalised particles. Furthermore they can scatter nearly elastically. If the perturbation contains lengthscales which are comparable to one of the soliton's typical lengthscales then lengthscale competition can occur. Neither the particle approximation nor the dressed-particle approximation for the soliton is valid and complicated spatio-temporal behaviour is observed. We illustrate this scenario by means of the perturbed nonlinear Schrödinger equation. The perturbed sine-Gordon equation and the Ablowitz-Ladik equation are also discussed.     

Rhamnosylation of lignans by a Streptomyces strain

Screening of 400 Streptomyces strains for biotransformation of the natural lignan matairesinol led to the identification of Streptomyces sp. LS136, capable of producing a single metabolite in moderate yields. Isolation and purification by preparative HPLC, followed by structural analyses by LC-MS and NMR, established the structure as matairesinol-4-O-rhamnoside. This bacterial strain was also used for rhamnosylation of the abundant natural lignans, hydroxymatairesinol and secoisolariciresinol.     

Direct fission versus sequential evaporation mechanism of sputtered caesium iodide cluster ions

A triple stage hybrid mass spectrometer was scanned for the trapping of the reaction intermediates of the over-all loss of two CsI-moieties from size-selected caesium iodide cluster ions of the general formula Cs (CsI)⁺ _n . In addition to appropriate MS/MS/MS-methods an electrically floated collision cell has been applied to trap intermediates of unimolecular and collision-induced evaporations. In comparison with other experimental findings the features of the evaporation mechanism are discussed.