Functionalisation of free amino groups of lysine dendrigraft (DGL) polymers

Lysine dendrigraft polymers (DGL) are promising candidates as carriers for targeted drug/gene delivery and bio-imaging, as such deserving extensive chemical functionalisation studies. We describe here examples of complete grafting of DGL amino groups by various substituents: hydrophobic amino acids (Ala, Val, Leu), dicarboxylic acids (succinic, Asp), guanidyl and saccharides (Gal), by means of straightforward coupling reactions, thus opening to versatile tuning of DGL properties (hydrophobicity, nucleophilicity, electric charge…). DGL functionalisation by lactose (when carried out so as to avoid borate ester formation between sugars) however yields partially grafted DGL; besides, partial grafting can be achieved by tuning the reagent/DGL stoichiometric ratio.     

Confidence intervals for the Hurst parameter of a fractional Brownian motion based on finite sample size

In this paper, we show how concentration inequalities for Gaussian quadratic form can be used to propose confidence intervals of the Hurst index parametrizing a fractional Brownian motion. Both cases where the scaling parameter of the fractional Brownian motion is known or unknown are investigated. These intervals are obtained by observing a single discretized sample path of a fractional Brownian motion and without any assumption on the Hurst parameter H.     

Direct numerical simulation and global stability analysis of three-dimensional instabilities in a lid-driven cavity

The first bifurcation in a lid-driven cavity characterized by three-dimensional Taylor–Görtler-Like instabilities is investigated for a cubical cavity with spanwise periodic boundary conditions at Re=1000. The modes predicted by a global linear stability analysis are compared to the results of a direct numerical simulation. The amplification rate, and the shape of the three-dimensional perturbation fields from the direct numerical simulation are in very good agreement with the characteristics of the steady S1 mode from the stability analysis, showing that this mode dominates the other unstable unsteady modes. To cite this article: J. Chicheportiche et al., C. R. Mecanique 336 (2008).     

On the cohomological equation for interval exchange maps

We exhibit an explicit full measure class of minimal interval exchange maps T for which the cohomological equation Ψ?Ψ°T=Φ has a bounded solution Ψ provided that the datum Φ belongs to a finite codimension subspace of the space of functions having on each interval a derivative of bounded variation.The class of interval exchange maps is characterized in terms of a diophantine condition of “Roth type” imposed to an acceleration of the Rauzy–Veech–Zorich continued fraction expansion associated to T. To cite this article: S. Marmi et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Dimension Free and Infinite Variance Tail Estimates on Poisson Space

Concentration inequalities are obtained on Poisson space, for random functionals with finite or infinite variance. In particular, dimension free tail estimates and exponential integrability results are given for the Euclidean norm of vectors of independent functionals. In the finite variance case these results are applied to infinitely divisible random variables such as quadratic Wiener functionals, including Lévy’s stochastic area and the square norm of Brownian paths. In the infinite variance case, various tail estimates such as stable ones are also presented.      

Convergence in variation of the laws of multiple stable integrals

Multiple stable integrals generalize Wiener–Itô integrals, their construction being based upon a generalized LePage representation. This approach allows one to study their behaviour. We are interested in this Note in the continuity for total variation norm of the laws of these integrals I_d(f) with respect to f. To cite this article: J.-C. Breton, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Peptide synthesis in room temperature ionic liquids

We demonstrate that chemical peptide coupling using modern coupling agents is efficient in rt ionic liquids. This new approach presents some advantages, especially in the case of hindered amino acids, which are not easy to couple under standard conditions, since high purities for the crude peptides were observed with respect to coupling in classical solvents.     

Functional Erdös-Rényi laws for processes indexed by sets

We consider a process X(A) indexed by some sets A∈A, where A is a collection of sets. We prove a functional form of the Erdös-Rényi laws. The result may be specialized to get back and sometimes improve previous versions of the classical Erdös-Rényi laws.