Well-Posedness by Perturbations of Variational Problems

In this paper, we consider the extension of the notion of well-posedness by perturbations, introduced by Zolezzi for optimization problems, to other related variational problems like inclusion problems and fixed-point problems. Then, we study the conditions under which there is equivalence of the well-posedness in the above sense between different problems. Relations with the so-called diagonal well-posedness are also given. Finally, an application to staircase iteration methods is presented.     

Palladium-catalyzed pseudo-domino cyclizations: An easy entry toward polycondensed pyrrolidone derivatives

A new type I palladium-catalyzed pseudo-domino process is developed, in which a single Pd-based catalytic system promotes two mechanistically unrelated, sequential catalytic cycles in chronologically distinct order. Suitable precursors undergo an allylic alkylation and a Heck coupling in sequence, affording polycondensed pyrrolidone derivatives. Depending on the starting precursors, intra/inter or doubly intramolecular processes can be obtained. The allylic alkylation process takes place always very smoothly. On the other hand, the Heck coupling turns out to be rather difficult either when the process is intermolecular, or when an intramolecular process generates polycondensed structures featuring three fused bonds connected to a common carbon atom. In such difficult cases, use of the Herrmann-Beller phosphapalladacycle allowed to catalyze the coupling. This study demonstrates also that allylic alkylations can be catalyzed by the Herrmann-Beller phosphapalladacycle.     

An adaptive scheme for the approximation of dissipative systems

We propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally Lipschitz. Under this assumption, a regular explicit Euler scheme–with constant or decreasing step–may explode and implicit Euler schemes are CPU-time expensive. The algorithm we introduce is explicit and we prove that any weak limit of the weighted empirical measures of this scheme is a stationary distribution of the stochastic differential equation. Several examples are presented including gradient dissipative systems and Hamiltonian dissipative systems.     

Discriminant of a generic projection of a minimal normal surface singularity

Let (S,0) be a rational complex surface singularity with reduced fundamental cycle, also known as a minimal singularity. Using a fundamental result of M. Spivakovsky, we explain how to describe the equisingularity type of the discriminant curve for a generic projection of (S,0) onto $\text{(}\text{C}{}^2\text{,0)}$ from the resolution of (S,0). To cite this article: R. Bondil, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Efficient indirect electrochemical in-situ regeneration of nadh:electrochemically driven enzymatic reduction of pyruvate catalyzed by d-ldh

Using [Cp(Me)₅Rh(bipy)C1]C1 (1) as redox catalyst for the continous NADH regeneration it was possible to perform an electrochemically driven enzymatic reduction of pyruvate to D-lactate catalyzed by D-LDH at a rate of 5 turnovers per hour. This is by a factor of 20 faster than the best results obtained until now. Current yields of 50 to 70 % may be obtained.     

Proton-proton correlations at small relative momentum in neon-nucleus collisions at E/A=400 and 800 MeV

Proton-proton small angle correlations have been measured in neon-nucleus collisions, using the 4 pi detector Diogene, at 400 and 800 MeV per nucleon incident energies. Values of the size of the emitting region are obtained by comparison with the Koonin formula, taking into account the biases of the apparatus. The dependence of the density on target mass and incident energy is also analysed.     

Sensitive method of detection, quantitation and purification of peptides using pre-column derivatization with phenyl isothiocyanate

A sensitive method for the detection, quantitation and purification of peptides is described. The method is based on pre-column derivatization of peptides with phenyl isothiocyanate to form phenylthiocarbamoyl derivatives (PTC peptides). The derivatized peptides are analysed by reversed-phase high-performance liquid chromatography on a Zorbax ODS column (5 micron) and detected at 269 nm with a sensitivity limit of 1-5 pmol. The technique was utilized for the separation of a mixture of closely related synthetic peptides. The eluted PTC peptides were collected with an average recovery yield of 75% as determined by amino acid analysis. This method of separation of PTC peptides was also combined with the determination of the complete structure of recovered PTC-dynorphin A-(1-13) using the solid-phase sequenator (Sequemat). The advantages of the derivatization method are the rapidity and completeness of the reaction, the stability of the product, the sensitivity and specificity of the detection of derivatized peptides and the compatibility of the technique with subsequent analytical procedures. A particular application of this method was exemplified by the dosage of enkephalins secreted from perfused bovine adrenal glands.