A counter-example to the characterization of the discontinuous value function of control problems with reflectionUn contre-exemple à la caractérisation de la fonction-valeur discontinue d'un problème de contrôle réfléchi

We consider a finite horizon deterministic optimal control problem with reflection. The final cost is assumed to be merely a locally bounded function which leads to a discontinuous value function. We address the question of the characterization of the value function as the unique solution of an Hamilton–Jacobi equation with Neumann boundary conditions. We follow the discontinuous approach developed by Barles and Perthame for problems set in the whole space. We prove that the minimal and maximal discontinuous viscosity solutions of the associated Hamilton–Jacobi can be written in terms of value functions of control problems with reflection. Nethertheless, we construct a counter-example showing that the value function is not the unique solution of the equation. To cite this article: O. Ley, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 469–473.     

Methane activation on Ni(1 1 1): Effects of poisons and step defects

We have, theoretically and experimentally, investigated the dissociation of methane on the terraces and steps of a Ni(1 1 1) surface. Using Density Functional Theory (DFT) total energy calculations combined with Ultra High Vacuum (UHV) experiments, we find that the steps exhibit a higher activity than the terraces. We have, furthermore, investigated how carbon and sulfur present on the surface will deactivate the steps, leaving only the terraces active. We find the intrinsic sticking probabilities of methane on the steps and terraces at 500 K to be 2.8 × 10⁻⁷ for the steps and 2.1 × 10⁻⁹ for the terraces, in complete agreement with our calculated difference in activation energy of 17 kJ/mol.     

Homoconjugated ketones with extended unsaturation: Wavelength-selective,regioselective, diastereoselective,and enantiospecific photochemical transformations of methyl 7-oxospiro[5.5]undeca-1,3-and -2,4,-diene-2-carboxylate

The title molecules were shown to photorearrange with remarkable selectivity. Wavelength variation steers the rearrangement modes, of which the [1,2]-acyl shift was found to be largely regioselective, diastereoselective, and enantiospecific. Chemical intercorrelation of products and mechanistic studies were carried out all along. The potential significance of these photochemical processes in selective synthetic schemes is discussed.     

New reals: Can live with them,can live without them

We give a self‐contained proof of the preservation theorem for proper countable support iterations known as “tools‐preservation”, “Case A” or “first preservation theorem” in the literature. We do not assume that the forcings add reals. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Isolation of a peptide ligand for affinity purification of factor VIII using phage display

Polypeptides for use in affinity chromatography of factor VIII were identified using phage display technology. Phage libraries were designed to express polypeptide fusions containing five to seven residues flanked by two cysteines that form a disulfide bond. Individual bacteriophage were selected for the ability of these polypeptides to bind factor VIII, and then release the protein under mild elution conditions. Strong consensus sequences were observed that appear to be necessary for this reversible interaction. Chemically synthesized ligands identified by this screening were immobilized onto a chromatographic support and used for affinity purification of factor VIII from a complex feedstream. A chromatographic step was developed that provided a 10000-fold reduction in host cell proteins and DNA, while providing exceptional product recovery.