Normal form and long time analysis of splitting schemes for the linear Schrödinger equation with small potential

We consider the linear Schrödinger equation on a one dimensional torus and its time-discretization by splitting methods. Assuming a non-resonance condition on the stepsize and a small size of the potential, we show that the numerical dynamics can be reduced over exponentially long time to a collection of two dimensional symplectic systems for asymptotically large modes. For the numerical solution, this implies the long time conservation of the energies associated with the double eigenvalues of the free Schrödinger operator. The method is close to standard techniques used in finite dimensional perturbation theory, but extended here to infinite dimensional operators.     

A new synthesis of α-substituted δ-carbolines

The paper describes a new general synthesis of α-substituted δ-carbolines based on key steps such as metalation, cross-coupling and cyclization.     

Dissymmetric gold(I) N-heterocyclic carbene complexes: a key unexpected structural parameter for highly efficient catalysts in the addition of alcohols to internal alkynes

Gold(I) N-heterocyclic carbene complexes (Au-NHC) with symmetric (bis-benzyl, -propyl and -mesityl substituents) and dissymmetric (mesityl and alkyl--benzyl or propyl--substituents) NHC ligands were synthesized and tested as catalysts for the addition of methanol to 3-hexyne, as a representative internal alkyne. While symmetric ones--bis-alkyl (propyl or benzyl) or bis-mesityl systems--displayed low activity, dissymmetric Au-NHC systems with one alkyl (benzyl or propyl) and one mesityl groups on the NHC unit were unexpectedly highly active with rates and turnover numbers up to 294,000 h(-1) and 800,000 mol.mol(Au)(-1).     

Radical-scavenging capacity of phenol fractions in the brown seaweed Ascophyllum nodosum: an electrochemical approach

In this article, the radical-scavenging capacity of phenol fractions extracted from the brown seaweed Ascophyllum nodosum was assessed using in parallel colorimetric methods (ABTS and DPPH) and electrochemistry (cyclic voltammetry). Results obtained by the three methods correlated in the case of global fractions, whereas only ABTS and DPPH correlated when activities were expressed on a phenol basis. The successive fractions separated by both their average molecular size and their polarity exhibited activities largely dependant on their phenol content, suggesting that phlorotannins are the main anti-oxidant molecules in hydro-alcoholic extracts of A. nodosum. In addition, phenol fractions of relative low molecular weight were clearly more active than others. This work opens new opportunities to better evaluate the radical-scavenging potential of phenol pools in algae using both bi-parametric fractionating and electrochemistry.     

Straightforward synthesis of poly(lauryl acrylate)-b-poly(stearyl acrylate) diblock copolymers by ATRP

Lauryl (LA) and stearyl (SA) acrylates were successfully polymerized by atom transfer radical polymerization (ATRP), leading to well defined homopolymers and diblock copolymers (PDI < 1.2). Interestingly, the polymerization was very well controlled using N,N,N′,N″,N″-pentamethyldiethylenetriamine (PMDETA), a ligand which had initially been reported to be unadvisable for the polymerization of such monomers. Both kinetic studies and chain extension reactions supported our conclusions. A PLA₆₅-b-PSA₄₇ diblock copolymer was characterized by differential scanning calorimetry and dynamic thermo-mechanical analysis, revealing that both blocks exhibit side-chain crystallinity and phase segregate in the crystalline state. The diblock behaves as a brittle rigid polymer when both blocks are crystalline, as a ductile material after the melting of the PLA phase and becomes a viscous liquid when both blocks are molten. This work could be extended to the preparation of PSA-b-PLA-b-PSA bio-issued thermoplastic elastomers.     

Linéarisation et maillage des surfaces paramétrées

We propose a methodology to simplify the parameterization of a surface composed of parametric patches, typically encountered in CAD (computer aided design) environments. This new parameterization is defined via the construction of an adaptive triangulation, called support, of each patch. The adaptation is governed by the control of the gap between the initial parameterization of the patch and that of the support. This support is used to generate the mesh of the CAD surface using an indirect approach, in which the mesh is generated via the parametric domains. The support makes it possible to disconnect the mesher from the CAD system, and in this sense it constitutes a universal tool for meshing such surfaces. An application example is given to show the pertinency of our methodology.     

On the minimum dilatation of braids on punctured discs

We find the minimum dilatation of pseudo-Anosov braids on n-punctured discs for 3 ≤ n ≤ 8. This covers the results of Song-Ko-Los (n = 4) and Ham-Song (n = 5). The proof is elementary, and uses the Lefschetz formula.     

Higher dimensional tautological inequalities and applications

We study the degeneracy of holomorphic mappings tangent to holomorphic foliations on projective manifolds. Using Ahlfors currents in higher dimension, we obtain several strong degeneracy statements such as the proof of a generalized Green-Griffiths–Lang conjecture for threefolds with holomorphic foliations of codimension one.     

A general theorem of existence of quasi absolutely minimal Lipschitz extensions

In this paper we consider a wide class of generalized Lipschitz extension problems and the corresponding problem of finding absolutely minimal Lipschitz extensions. We prove that if a minimal Lipschitz extension exists, then under certain other mild conditions, a quasi absolutely minimal Lipschitz extension must exist as well. Here we use the qualifier “quasi” to indicate that the extending function in question nearly satisfies the conditions of being an absolutely minimal Lipschitz extension, up to several factors that can be made arbitrarily small.