Une nouvelle définition de l'entropie dynamique des systèmes non commutatifs

An alternative definition of entropy for non-commutative systems, equivalent to the one by A. Connes, H. Narnhofer, and W. Thirring, is given. It is based on the concepts of conditional entropy, and stationary couplings with classical systems. It allows to prove that any quantum dynamical system with singular spectrum has zero entropy.     

The Hochschild class of the Chern character for semifinite spectral triples

We provide a proof of Connes’ formula for a representative of the Hochschild class of the Chern character for (p,∞)-summable spectral triples. Our proof is valid for all semifinite von Neumann algebras, and all integral p?1. We employ the minimum possible hypotheses on the spectral triples.     

Stochastic Arithmetic: s-spaces and Some Applications

It has been recently shown that computation with stochastic numbers as regard to addition and multiplication by scalars can be reduced to computation in familiar vector spaces. In this work we show how this can be used for the algebraic solution of linear systems of equations with stochastic right-hand sides. On several examples we compare the algebraic solution with the simulated solution using the CADNA package.     

New access to H-phosphonates via metal-catalyzed phosphorus-oxygen bond formation

A novel approach to H-phosphonates from hypophosphorous acid using a transfer hydrogenation process was developed. This method is atom-economical, environmentally friendly, catalytic, and efficient, leading easily to H-phosphonate monoesters or ammonium salt in moderate to good yields.     

Some refinements of Dade's projective conjecture

In this paper a further refinement of Dade's projective conjecture, due to Boltje, is presented. This new statement includes ideas first published by Isaacs and Navarro as well as the recent contractibility version of Alperin's conjecture introduced by Boltje. Leaning heavily on the work of Robinson, weaker forms of the conjecture are proved in the case of p-solvable groups.     

Molybdenum-catalyzed episulfidation of (E)-cycloalkenes with elemental sulfur

Episulfidation of (E)-cyclooctene and (E)-cyclononene was achieved with elemental sulfur by using a catalytic amount of a molybdenum oxo complex.