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.     

Small silver particles in glass surface layers produced by sodium-silver ion exchange — their concentration and size depth profile

Small spherical silver particles in a surface layer of commercial flat glass were produced by means of sodium-silver ion exchange. In each volume element of the layer there is a Gaussian distribution of the particle diameters. The mean diameter increases with penetration depth. Within one individual sample it can vary from 4.5 nm immediately at the glass surface up to more than 50 nm at the end of the layer. Due to a special preparation technique the results were gained by microspectrophotometric measurements as well as by investigations carried out with the transmission electron microscope and the electron-probe microanalyzer on one and the same sample always as function of the penetration depth.     

Timelike Compton scattering: exclusive photoproduction of lepton pairs

We investigate the exclusive photoproduction of a heavy timelike photon which decays into a lepton pair, . This can be seen as the analog of deeply virtual Compton scattering, and we argue that the two processes are complementary for studying generalized parton distributions in the nucleon. In an unpolarized experiment the angular distribution of the leptons readily provides access to the real part of the Compton amplitude. We estimate the possible size of this effect in kinematics where the Compton process should be dominated by quark exchange. Received: 9 October 2001 / Published online: 5 April 2002     

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.     

Quantification of mass flow effects in capillary SFC

A model for restrictor flow produces accurate predictions of flow that can be used to optimize restrictor design. The relative amplitudes of restrictor and other flows and their effect on efficiency are discussed.     

The speed of biased random walk on percolation clusters

 We consider biased random walk on supercritical percolation clusters in ℤ². We show that the random walk is transient and that there are two speed regimes: If the bias is large enough, the random walk has speed zero, while if the bias is small enough, the speed of the random walk is positive. Received: 20 November 2002 / Revised version: 17 January 2003 Published online: 15 April 2003 Research supported by Microsoft Research graduate fellowship. Research partially supported by the DFG under grant SPP 1033. Research partially supported by NSF grant #DMS-0104073 and by a Miller Professorship at UC Berkeley. Mathematics Subject Classification (2000): 60K37; 60K35; 60G50 Key words or phrases: Percolation – Random walk     

The potential role of ultrasound in differentiating solid and cystic swellings of the true vocal fold

This study was designed to investigate the potential role of ultrasound in the diagnosis of cysts of the true vocal fold. Materials and Methods: Grayscale ultrasound of the larynx was carried out in 29 patients with a swelling of the true vocal fold and dysphonia. The findings were then compared with those at subsequent microlaryngoscopy, in the majority of cases. Results and Conclusions: Whereas preoperative laryngeal ultrasound correctly predicted the surgical findings of a cystic lesion in only 5 of 11 cases, it correctly identified that no cyst was present in 15 of 16 instances when this had been queried. This study suggests that ultrasound may have some role in investigation of unilateral vocal fold pathology, but that further fine-tuning of the technique may be necessary.