Up to isometries,a deformation is a continuous function of its metric tensorAux isométries près,une déformation est une fonction continue de son tenseur métrique

If the Riemann–Christoffel tensor associated with a field of class $\text{C}{}^2$ of positive definite symmetric matrices of order three vanishes in a connected and simply connected open subset $\text{Ω?}\text{R}{}^3$, then this field is the metric tensor field associated with a deformation of class $\text{C}{}^3$ of the set $\text{Ω}$, uniquely determined up to isometries of $\text{R}{}^3$. We establish here that the mapping defined in this fashion is continuous, for ad hoc metrizable topologies. To cite this article: P.G. Ciarlet, F. Laurent, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 489–493.     

Structure of neutron-rich Be and C isotopes

The structure of neutron-rich beryllium isotopes has been investigated using different heavy-ion-induced transfer reactions. In neutron transfer reactions, the population of final states shows a strong sensitivity to the chosen core nucleus, i.e., the target nuclei ⁹Be or ¹⁰Be, respectively. Molecular rotational bands up to high excitation energies are observed with ⁹Be as the core due to its pronounced 2α-cluster structure, whereas only a few states at low excitation energies are populated with ¹⁰Be as the core. For ¹¹Be, a detailed investigation has been performed for the three states at 3.41, 3.89, and 3.96 MeV, which resulted in the most probable spin-parity assignments 3/2⁺, 5/2^?, and 3/2^?, respectively. Furthermore, we have studied particle-hole states of ¹⁶C using the ¹³C(¹²C, ⁹C)¹⁶C reaction and found 14 previously unknown states. Using the ¹²C(¹²C, ⁹C)¹⁵C reaction, five new states were observed for ¹⁵C.     

Oxygen-distribution imaging with a novel two-tracer laser-induced fluorescence technique

We introduce a new technique for imaging oxygen concentrations in fuel/air mixtures that takes advantage of the different responses of toluene and 3-pentanone to collisional quenching by molecular oxygen. Since laser-induced fluorescence signals from both tracers upon excitation at 248 nm are spectrally well separated, simultaneous detection is possible. The technique is first applied to instantaneous imaging in turbulent mixing processes of interacting seeded air and nitrogen flows. Received: 1 August 2001 / Revised version: 29 October 2001 / Published online: 29 November 2001     

Solubility parameter determination of cationic surfactants by inverse GC

Summary The solubility parameters of cationic surfactants were obtained using the inverse gas chromatographic technique. The surfactants didodecyl dimethyl ammonium bromide, dioctadecyl dimethyl ammonium bromide and dodecyl pyridinium chloride were used as stationary phase and retention data of different probe solutes were measured at different temperatures. The results were analysed by the combination of Flory-Huggins and Hildebrand theories, and the solubility parameters of the surfactants were obtained in a range of temperatures between 80–120°C.     

Arithmetic functions with linear recurrence sequences

We obtain asymptotic formulas for all the moments of certain arithmetic functions with linear recurrence sequences. We also apply our results to obtain asymptotic formulas for some mean values related to average orders of elements in finite fields.