Solid-Liquid Phase Transfer Catalysis Without Solvent: Further Improvement in SNAr Reactions

Solid-liquid PTC without added solvent efficiently promotes SNAr reactions of a variety of anionic nucleophiles generated in situ. This methodology is applied with success to some examples concerning non-activated aromatic systems. TDA-1 is the most effective catalyst.     

Géométrie diophantienne et variétés toriques

We present some results on projective toric varieties which are relevant in diophantine geometry. We interpret and study several invariants attached to these varieties by geometrical and combinatorial terms. We also give a Bézout theorem for Chow weights of projective varieties and an application to the theorem of successive algebraic minima. These results are extracted from the two texts of Philippon and Sombra mentioned in the references at the end of this Note (both downloadable from http://fr.arxiv.org). To cite this article: P. Philippon, M. Sombra, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

An abelian analogue of Schanuel’s conjecture and applications

The Ramanujan Journal - In this article we study an abelian analogue of Schanuel’s conjecture. This conjecture falls in the realm of the generalised period conjecture of André. As shown...     

Variétés abéliennes et indépendance algébrique. I

Sans résuméLaboratoire Associé au C.N.R.S. N^o 169     

Macrocyclic Ethers by Free Radical Cyclizations

Tin hydride reduction of ω-iodo-polyoxaalkyl acrylates 1 using syringe pump addition of both reactants to a solution of AIBN in benzene at 80°C afforded the corresponding cyclic polyethers in excellent yields.     

Sur des hauteurs alternatives. I

Sans résuméCe travail a été complété au cours d'un stage de recherche à l'Université Friedrich Alexander (Erlangen) dans le cadre d'une bourse de la Fondation Alexander von Humboldt     

A Device Enhancement for the Dry Sliding Friction Coefficient Measurement Between Steel 1080 and VascoMax with Respect to Surface Roughness Changes

An enhancement of an existing tribometer device developed by Philippon et al. (Wear 257:777–784, 2004) is presented in this work. This experimental device is made up of a dynamometer ring and a specific load sensor allowing to apply an apparent normal force on specimens and to measure frictional forces respectively. A set of strain gauges are added to the upgraded dynamometer ring in this new configuration. The apparent normal force can be recorded accurately during the sliding process. The setup is adapted on a hydraulic testing machine to carry out steel-on-steel dry sliding tests. The first set of standard Steel on standard Steel specimens (XC 38 French standard steel) with two apparent normal pressures are imposed (8 and 80 MPa) as the range of sliding velocities varies from 0.12 to 3.72 m/s for the same contact conditions. The main set of experiments with low sliding velocities (varying from 0 to 3 m/s) for the Steel 1080 on Steel VascoMax are performed in the same tested setup. The recordings of normal and tangential forces leading to the friction coefficient determination are discussed. The values of dry friction coefficient μ according to the experimental parameters are in good agreement with those observed in the literature. Using this new configuration, the effects of the sliding velocity on the surface roughness changes and on the dry fiction coefficient are also investigated. Additionally the surface roughness changes are also investigated. Performing the scans with use of the scanning electron microscope in particular locations of the specimens show the roughness decrease and reveal the occurrence of the wear phenomenon. Moreover, very interesting relations between wear and sliding velocity are observed.     

A refinement of the Bernštein-Kušnirenko estimate

A theorem of Kušnirenko and Bernštein (also known as the BKK theorem) shows that the number of isolated solutions in a torus to a system of polynomial equations is bounded above by the mixed volume of the Newton polytopes of the given polynomials, and this upper bound is generically exact. We improve on this result by introducing refined combinatorial invariants of polynomials and a generalization of the mixed volume of convex bodies: the mixed integral of concave functions. The proof is based on new techniques and results from relative toric geometry.