Convexes divisibles III

Let Δ₀ be a group of finite type and FΔ₀⊂Hom(Δ₀,PGL(Rm)) be the subset of faithful representations for which there exists a properly convex Δ₀-invariant open subset Ω in P(Rm) such that the quotient Δ₀\Ω is compact. Koszul has proved in [J.L. Koszul, Déformation des connexions localement plates, Ann. Inst. Fourier 18 (1968) 103-114] that this subset FΔ₀ is open. We describe the closure of FΔ₀. As a consequence, we show that this subset FΔ₀ is closed if and only if the virtual center of Δ₀ is trivial. This condition is satisfied if and only if FΔ₀ contains a strongly¹ irreducible representation.     

On-line extraction and determination of carbofuran in raw milk by direct HPLC injection on an ISRP column

Summary A method has been developed for extraction and determination of carbofuran in milk. The method involved direct injection of raw milk on to a human serum albumin dimethyloctyl-silica gel (HSA-C₈) column and the use of 80:20 (v/v) 0.01 M phosphate buffer pH 5.5-acetonitrile as mobile phase. UV spectrophotometric detection was performed at 220 nm. Identification was based on retention time. Quantification was performed by automatic peak-area determination and was calibrated by use of an external standard.     

Transparent boundary conditions for a class of boundary value problems in some ramified domains with a fractal boundary

We consider some boundary value problems in self-similar ramified domains, with Laplace and Helmholtz equations. We discuss transparent boundary conditions. These conditions permit computing the restriction of the solutions to domains obtained by stopping the geometric construction after a finite number of steps. To cite this article: Y. Achdou et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Activity evaluation of carbon paste electrodes loaded with pt nanoparticles prepared in different radiolytic conditions

Three Pt-based catalysts prepared in different radiolytic conditions and supported on graphite powder were packed into a carbon paste electrode configuration. They were compared to each other, to the commercial (Pt) deposited on activated carbon powder (Johnson Matthey) and to pure Vulcan XC-72 for their respective abilities toward the hydrogen evolution reaction (HER). The Tafel parameters were determined for all these electrodes. From the I–V curves and their quantitative treatment, the following order of activity emerged unambiguously and reads: (PtCO)₂ (fcc structure) > (PtCO)₁ (Chini cluster) > (Pt)_neat > (Pt)_JM (Johnson Matthey) ≫ (Vulcan XC-72). As expected, all the Pt-loaded electrodes were more efficient than Vulcan XC-72. The classification appears to be linked with the mean nanoparticle size, and for comparable sizes, with the surface morphology of the materials. The results and the stability of the electrodes suggest that the small particle sizes and the good dispersity on the carbon support were maintained during the HER.     

Autour de la conjecture de L. Markus sur les variétés affines

Summary For any subgroupG of (n), we introduce some integer discGn called thediscompacity ofG. This number measures to what extent the closure ofG is not compact. The Markus' conjecture says that a compact affinely flat unimodular manifold is complete. Our main result (called the discompact theorem) is that this conjecture is true under the assumption that the linear holonomy i.e. the parallel transport has discompacity 1. Because discSO(n–1, 1)=1, this ensures that a compact flat Lorentz manifoldM is geodesically complete. Hence, by a previous result of W. Goldman and Y. Kamishima [GK], such aM is, up to finite covering, a solvmanifold. This achieves the proof of a Bieberbach's theorem for compact Lorentz flat manifolds.     

The crystal structure of bis(triphenylphosphine)-(η-cyclohexa-1,3-diene)rhenium trihydride

Bis(triphenylphosphine)(η-cyclohexa-1,3-diene)rhenium trihydride, (Ph₃P)₂(η-C₆H₈)ReH₃ (I) crystallises in the space group C2/c with cell dimensions a 22.76(2), b 10.14(1) c 29.813(6) Å, β 97.69(8)°. The final refinement of 126 variables using 1580 non-zero reflections resulted in a final R value of 0.064. In spite of uncertainties in some of the atomic positions, the structure of I is compatible with a trihydrido diene compound with a distorted pentagonal bipyramidal configuration, rather than with a dihydrido cyclohexenyl compound having an “agostic” CH ? Re interaction. The factors which govern the structure of the complexes (Ph₃P)₂(η-1,3-diene)ReH₃ are discussed.     

Nucleosides and Nucleotides. Part 21. Synthesis of a Tridecanucleoside Dodecaphosphate Incorporating the Unnatural Base 2 (1 H)-Pyridone

The modified nucleoside Π_d (1) was used in the synthesis of the oligonucleotide d (TpTpΠpCpGpTpCpApApApApTpC). Diester methodology being unsatisfactory, the triester synthesis was investigated with the unnatural nucleoside. An improved method of nucleoside phosphorylation was developed for the synthesis of the fully-protected nucleotide 2e. This molecule could be cleanly and selectively deprotected, and allowed the efficient synthesis of the desired oligonucleotide.     

Enzymatic synthesis of neopentylpolyol esters in organic media

Utilization of lipases for synthesis of esters of hydrophilic polyols has been investigated. The choice of a suitable solvent is crucial in this type of reaction. An interesting case is fatty acid esters from neopentylpolyols, such as trimethylolpropane, which are of great interest as high temperature lubricants. Enzymatic synthesis of trimethylolpropane tricaprylate was studied as an alternative to chemical manufacturing. Triester production occurred only if the water produced by esterification was continuously removed from the medium. In these condition, kinetics of appearance and transformation of mono-, di- and triesters were determined in order to define optimal conditions.