An approach to triquinane synthesis using the Pauson-Khand reaction

Tricyclic skeletons have been generated from acyclic enyne precursors by using an intramolecular Pauson-Khand reaction in combination with aldol, Michael and alkylation reactions.     

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.     

Structures de Hodge mixtes et faisceaux réflexifs semistablesMixed Hodge structures and semistable reflexive sheaves

Let X be a smooth projective variety over an algebraically closed field of characteristic 0. We prove that the category of μ-semistable reflexive sheaves of slope μ equivariant for the action of some group on X is Abelian. The same claim for $\text{X=}\text{P}{}^2{}_{\mathrm{<mtext>C</mtext>}}$ and a stronger semistability condition gives us a geometric proof of the fact that the category of mixed Hodge structures is Abelian. To cite this article: O. Penacchio, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 475–480.     

A new insight into the understanding of the collapsed form of poly(N-isopropylacrylamide) molecules

Possible collapsed forms of poly(N-isopropylacrylamide) molecules are reviewed on the basis of first principle calculations. Various configurations and associated conformations are detailed. The calculated optimized structures exhibit different possibilities of creating networks of intra-molecular bonds of the hydrogen type. We show that the most remarkable one is able to form a local, self-saturated and well ordered helix. We also indicate in which direction the synthesis of the molecule should be oriented to improve its global behavior in term of hydrophobic/hydrophilic behavior.     

Random Classical Fidelity

We introduce a random perturbed version of the classical fidelity and we show that it converges with the same rate of decay of correlations, but not uniformly in the noise. This makes the classical fidelity unstable in the zero-noise limit.