Vassiliev invariants for braids on surfaces

We show that Vassiliev invariants separate braids on a closed oriented surface, and we exhibit a universal Vassiliev invariant for these braids in terms of chord diagrams labeled by elements of the fundamental group of the surface.

     

Stereoselective synthesis of trifluoromethyl-substituted 1,2-diamines by aza-Michael reaction with trans-3,3,3-trifluoro-1-nitropropene

Aza-Michael addition of optically pure 4-phenyl-2-oxazolidinone to 3,3,3-trifluoro-1-nitropropene proceeds smoothly at low temperature with a high yield. Diastereoselectivity of the addition depends on the base used and lithiated species proved to be highly efficient affording 92% de. Optically pure 1,2-diamino-3,3,3-trifluoropropane is prepared in 58% yield from the aza-Michael addition product through a three-step procedure.     

Classical and quantum aspects of multimode parametric interactions

Parametric interactions in nonlinear crystals represent a powerful tool in the optical manipulation of information, both in the classical and the quantum regime. Here, we analyze in detail classical and quantum aspects of three-and five-mode parametric interactions in x⁽²⁾ nonlinear crystals. The equations of motion are explicitly derived and then solved within the parametric approximation. We describe several applications, including holography, all-optical gates, generation of entanglement, and telecloning. Experimental results on the photon distributions and correlations of the generated beams are also reported and discussed.     

Ethyl-4,4,4-trifluoroacetoacetate (ETFAA), a powerful building block for enantiopure chirons in trifluoromethyl-β-amino acid series

Herein are studied new transformations of ethyl-4,4,4-trifluoroacetoacetate (ETFAA), giving access to a series of enantiopure chirons bearing both a trifluoromethyl group and an amino moiety. The key intermediate is obtained optically pure by a resolution procedure.     

Tribological properties of ormosil coatings

Transparent plastics are not scratch resistant. The damage leads to a loss of optical properties. Coatings prepared using either tetraethoxysilane or colloidal silica particles embedded in glymo is a way to avoid these disadvantages. Tribological experiments are carried out to better understand the surface modification due to a sliding friction. It is shown that the wear track is not directly related to usual mechanical properties such as Young's modulus and the hardness of the coating. The different stages leading to material loss are discussed in term of particle removal and debris circulation (accumulation or elimination) through the friction track. The mechanical properties of the film combined with the film to substrate adhesion are expected to play an important role as it can be deduced from results obtained as a function of the coating composition.     

Arrangements of hyperplanes with property D

We denote by the complement of the complexification of a real arrangement of hyperplanes. It is known that there is a certain technical property, called property D, on real arrangements of hyperplanes such that: if a real arrangement of hyperplanes is simplicial then has property D, and if has property D then is aK(, 1) space. Our main goal is to prove that: if has property D then is simplicial. We also prove that a quasi-simplicial arrangement is always simplicial.     

Diastereoselective ring-closing metathesis: synthesis of P-stereogenic phosphinates from prochiral phosphinic acid derivatives

[reaction: see text] The preparation of phosphorus-containing trienes featuring two diastereotopic vinyl moieties followed by a diastereoselective ring-closing metathesis is described. This methodology allowed for the synthesis of novel highly functionalized P-stereogenic heterocycles featuring both an exo- and an endocyclic double bond. An investigation into the factors influencing the diastereochemical outcome of the ring-closing metathesis is also presented, revealing that the geometry of the double bonds conjugated to phosphorus is important and that 1,3-stereoinduction is superior to 1,4-stereoinduction for these reactions.