Precise Synthesis and Thin Film Self-Assembly of PLLA-b-PS Bottlebrush Block Copolymers

The ability of bottlebrush block copolymers (BBCPs) to self-assemble into ordered large periodic structures could greatly expand the scope of photonic and membrane technologies. In this paper, we describe a two-step synthesis of poly(l-lactide)-b-polystyrene (PLLA-b-PS) BBCPs and their rapid thin-film self-assembly. PLLA chains were grown from exo-5-norbornene-2-methanol via ring-opening polymerization (ROP) of l-lactide to produce norbornene-terminated PLLA. Norbonene-terminated PS was prepared using anionic polymerization followed by a termination reaction with exo-5-norbornene-2-carbonyl chloride. PLLA-b-PS BBCPs were prepared from these two norbornenyl macromonomers by a one-pot sequential ring opening metathesis polymerization (ROMP). PLLA-b-PS BBCPs thin-films exhibited cylindrical and lamellar morphologies depending on the relative block volume fractions, with domain sizes of 46–58 nm and periodicities of 70–102 nm. Additionally, nanoporous templates were produced by the selective etching of PLLA blocks from ordered structures. The findings described in this work provide further insight into the controlled synthesis of BBCPs leading to various possible morphologies for applications requiring large periodicities. Moreover, the rapid thin film patterning strategy demonstrated (>5 min) highlights the advantages of using PLLA-b-PS BBCP materials beyond their linear BCP analogues in terms of both dimensions achievable and reduced processing time.     

Remarks on exact controllability for Stokes and Navier–Stokes systems

This Note deals with the controllability of Stokes and Navier–Stokes systems with distributed controls with support in possibly small subdomains. We first present a new global Carleman inequality for the solutions to Stokes-like systems that leads to the null controllability at any time T>0. Then, we present a local result concerning exact controllability to trajectories of the Navier–Stokes system. To cite this article: E. Fernández-Cara et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Synthesis of 2-pyrone-4-carboxaldehydes from acetylene dicarboxaldehyde monoacetal

Reaction of acetylene dicarboxaldehyde monoacetal with substituted Meldrum’s acid leads good yields in 2-pyranones-4-carboxaldehydes substituted in position 3.     

High-frequency magnetoimpedance in nanocomposites

The transmission of millimeter-range electromagnetic waves (30–50 GHz) through a magnetic nanocomposite thin film exhibiting tunnel magnetoresistance (TMR) is calculated. The relative change of transmission coefficient in an applied magnetic field due to the magnetorefractive effect is approximately linear with TMR and strongly depends on nanocomposite resistivity and film thickness. The obtained results are in a good agreement with experiment.     

Approche non paramétrique du filtrage de système non linéaire à temps discret et à paramètres inconnus

Particle filters are presently among the most powerful tools for filtering discrete time non linear systems. However the presence of unknown parameters in the system equations makes their use more complex and can even impair their convergence properties. This Note shows how an on-line consistent estimation of these parameters can be obtained simultaneously to that of the state variables to be filtered. This approach relies upon a kernel-based non parametric estimation of conditional probability densities from successive Monte Carlo generations of system particles. To cite this article: V. Rossi, J.-P. Vila, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

On the Curvature of the Central Path of Linear Programming Theory

We prove a linear bound on the average total curvature of the central path of linear programming theory in terms of the number of independent variables of the primal problem, and independent of the number of constraints.     

Conversations on mind, matter, and mathematics

Conclusion  The debate between Jean-Pierre Changeux and Alain Connes is one of the most, interesting to take place in recent years. It re-frames in a very up-to-date context a whole series of traditional and difficult questions from the standpoint of the knowledge and experience of two of the leading protagonists of contemporary science. To the choice presented by the neurobiologist between a Platonist ontology and a neurocognitive psychology of mathematical activity, the mathematician replies with a conception that is objective (neither ontological nor psychological) of the thoroughly consistent universe of mathematical idealities. It is indeed in this three-sided arena that the major difficulties play themselves out. One of the great virtues of the book is to cast a spotlight on this confrontation.     

Mesures de Monge-Ampère et mesures pluriharmoniques

Sans résumé     

K-Dependence and temperature dependence of N2-, H2-, and He-broadening coefficients for the J = 12-11 transition of acetonitrile CH3CN located near 220.7 GHz

Extensive experiments on the K = 3 component of the J = 12-11 rotational transition of acetonitrile CH₃C¹⁴N, located near 220.7 GHz, were performed at different temperatures in the range 235-350 K. They allow determining the N₂-, H₂-, and He-broadening coefficients, as well as their temperature dependences. More specific measurements on all the K-components of the involved transition perturbed by N₂ at 303 K allow to point out a clear decreasing of the broadening coefficient with increasing K. Narrowing effects are clearly observed, and experimental lines were analysed both with Voigt and speed dependent Voigt profiles; but no exhaustive lineshape study was carried out. All the experimental parameters are compared with results derived from a semiclassical calculation of collisional interactions, including electrostatic, induction, and dispersion energy contributions.