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.     

Efficient preparation of carbohydrate- and related polyol-amphiphiles by hydrazone ligation

The hydrazone ligation can be used to couple clustered-glycosides or glycomimetics functionalized with a hydrazino group with lipophilic glyoxylyl acid derivatives to give the corresponding amphiphiles in high yield and purity.     

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.     

Discussion of “Second order topological sensitivity analysis” by J. Rocha de Faria et al.

The aim of this discussion is to expose incorrect results in a previous IJSS article.     

Study of thermal aging effect on space charge in poly(methyl methacrylate)

Charges evolution in poly(methyl methacrylate) (PMMA) samples under thermal aging effect has been studied by means of two complementary techniques, thermal step method (TSM) and thermally stimulated depolarization current (TSDC). For the first method, measurements reveal that injected charges, whose quantity is found depending on the number of applied temperature cycles, remain close to the surface sample. TSDC measurements have been carried out for different temperatures ranging from 25 °C to 140 °C. Three distinguishable dipolar relaxations (β₁, β₂ and α) have been highlighted. In the same way, the presence of polarization and injected charges has been confirmed. In support of electric characterization, X-ray reflectometry has been used. The obtained results equally emphasized the thermal aging effect on the material.     

Photochemical expulsion of the neutral monodentate ligand L in Ru(terpy*)(diimine)(L)2+: a dramatic effect of the steric properties of the spectator diimine ligand

A series of photoreactive complexes of the type Ru(terpy*)(N-N)(L)(2+), where terpy* is 4'-(3,5-ditertiobutylphenyl)-2,2':6',2' '-terpyridine, N-N is the bidentate chelate phen or dmp (phen = 1,10-phenanthroline, dmp = 2,9-dimethyl-1,10-phenanthroline), and L is the monodentate ligand dms, MeBN, or MeOBN (dms = dimethyl sulfide, MeBN = 2,6-dimethyl benzonitrile, MeOBN = 2,6-dimethoxybenzonitrile), has been synthesized and fully characterized by proton NMR spectroscopy, electrospray mass spectrometry, and UV-vis spectroscopy. The X-ray structures of four complexes were also obtained. In neat pyridine, the quantum yields for the photosubsitution of L by pyridine were measured and showed dramatic variations depending on the steric interactions between the spectator bidentate ligand and the leaving monodentate ligand L. The use of dmp instead of phen multiplied the photosubstitution efficiency by a factor of 20-50, depending on L. This effect could be qualitatively correlated to the distortions observed in the X-ray structures of the corresponding complexes. The highly distorted structure of Ru(terpy)(dmp)(dms)(PF(6))(2) showed a very high photosubsitution quantum yield phi = 0.36 in neat pyridine. The high photoreactivity of some of the compounds makes them particularly promising as components of future light-driven molecular machines.