Algebras generated by idempotents and the symbol calculus for singular integral operators

It is proved that in Banach algebras generated by two idempotents and, perhaps, by a certain flip operator the standard identity F₄ is fulfilled. The maximal ideal space of such algebras is determined and the corresponding symbol is given. By means of local techniques these results are applied to obtain a symbol calculus for singular integral operators with Carleman shift (changing the orientation) in weighted Banach spaces.     

Activation de l'oxygène moléculaire nouveaux systèmes d'hydroxylation des hydrocarbures

New oxygen-activating systems for hydroxylation of hydrocarbons in organic solvents at ambient temperature are described. These systems are composed of a transition metal and an electron donating ligand, giving a strongly polarised peroxidic form active in hydroxylation. The most active systems are FeCl₂/DH₂/AH/O₂ (DH₂ = hydrazobenzene or orthophenylene diamine, AH = carboxylic acid).     

Pyrene measurements in sooting low pressure methane flames by jet-cooled laser-induced fluorescence

This paper presents in detail the study we carried out concerning the pyrene measurement by jet-cooled laser-induced fluorescence (JCLIF) in different sooting low pressure methane flames. The aim of this paper is both to demonstrate the potentialities of this technique for the measurement of such moderately sized polycyclic aromatic hydrocarbons under sooting flame conditions and to provide new experimental data for the understanding and the development of chemical models of the soot formation processes. Several concentration profiles of pyrene measured in different sooting flame (various pressure and equivalence ratio) are presented. The validation of the JCLIF method for pyrene measurements is explained in detail as well as the calibration procedure, based on the standard addition method, which has been implemented for the quantification of the concentration profiles. Sensitivity lower than 1 ppb was obtained for the measurement of this species under sooting flame conditions.     

Viscous-fingering-like instability of cell fragments

We present a novel flow instability that can arise in thin films of cytoskeletal fluids if the friction with the substrate on which the film lies is sufficiently strong. We consider a two-dimensional, membrane-bound fragment containing actin filaments that polymerize at the edge and depolymerize in the fragment. Performing a linear stability analysis of the initial state due to perturbations of the fragment boundary, we find, in the limit of large friction, that the perturbed actin velocity and pressure fields obey the same laws governing the viscous fingering instability of an interface between immiscible fluids in a Hele-Shaw cell. A remarkable feature of this instability is that it is independent of the strength of the interaction between actin filaments and myosin motors.     

Chaotic dynamos generated by a turbulent flow of liquid sodium

We report the observation of several dynamical regimes of the magnetic field generated by a turbulent flow of liquid sodium (VKS experiment). Stationary dynamos, transitions to relaxation cycles or to intermittent bursts, and random field reversals occur in a fairly small range of parameters. Large scale dynamics of the magnetic field result from the interactions of a few modes. The low dimensional nature of these dynamics is not smeared out by the very strong turbulent fluctuations of the flow.