Approximation locale précisée dans des problèmes multi-échelles avec défauts localisés

We proceed here with our systematic study, initiated in [3], of multiscale problems with defects, within the context of homogenization theory. The case under consideration here is that of a diffusion equation with a diffusion coefficient of the form of a periodic function perturbed by an $L^r({\mathbb{R}}^d)$, $1<r<+\infty$, function modelling a localized defect. We outline the proof of the following approximation result: the corrector function, the existence of which has been established in [3], [4], allows us to approximate the solution to the original multiscale equation with essentially the same accuracy as in the purely periodic case. The rates of convergence may however vary, and are made precise, depending upon the $L^r$ integrability of the defect. The generalization to an abstract setting is mentioned. Our proof exactly follows, step by step, the pattern of the original proof of Avellaneda and Lin in [1] in the periodic case, extended in the works of Kenig and collaborators [12], and borrows a lot from it. The details of the results announced in this Note are given in our publications [2], [11].     

Mesoporous carbon supported ultrasmall palladium particles as highly active catalyst for Suzuki‐Miyaura reaction

A fast and efficient eco‐friendly two‐step preparation of a palladium‐containing mesoporous carbon catalyst ( C1 ) from green and readily available carbon precursors (phloroglucinol and glyoxal), a porogen template (pluronic F‐127) and PdCl₂ is described. Catalyst C1 contains ultra‐small Pd nanoparticles (1.2 nm) uniformly dispersed in the carbon network and shows an outstanding activity for Suzuki‐Miyaura reactions in pure water: extremely low amounts of palladium (10 μequiv. in most cases) are sufficient to afford almost palladium‐free products (containing <0.25 ppm of precious metal without further purification steps).     

Etude rovibrationnelle de la bande parallèle à structure perpendiculaire v 4 + v 6 de CH3 35Cl

La bande infrarouge v ₄ ^±1 + v ₆ ^?1 de CH₃ ³⁵Cl, centrée vers 4051 cm^-1, a été analysée sur un spectre de 0,0075 cm^-1 de résolution. On a mis en évidence une résonance l vibrationnelle de couplage R = -2,5 cm^-1, et une résonance anharmonique de couplage W _F ～4,86 cm^-1 avec la bande 4v ₆ ⁰ centrée vers 4049 cm^-1; par suite de la proximité des deux centres de bande, cette résonance est forte et fait apparaître la sous-bande K = 0 de 4v ₆ ⁰. Un calcul de moindres carrés sur 813 raies a donné un écart standard de 0,020 cm^-1, de petites anomalies rotationnelles restant à élucider.     

A Convenient Access to Chiral Sulfonic Acids

Neomenthyl and trans myrtanyl sulfonic acids are obtained, free from inorganic salts, starting from the corresponding chiral alcohols.     

SYNTHESIS OF TWO STABLE DIPHOSPHENES WITH A NEW STABILIZING SUBSTITUENT

Abstract

Two new diphosphenes 7 and 10 have been synthesized by action of DBU on trichlorogermylphosphines 4 and 8; this route involves the intermediate formation of chlorophosphines 5 and 9. Diphosphenes 7 and 10 are stabilized by the 2,6-bis(trifuoromethyl)phenyl group which presents both steric and electronic effects and is used for the first time in phosphorus chemistry.     

A Class of Non-associated Materials: n-Monotone Materials—Hooke’s Law of Elasticity Revisited

Generalized Standard Materials are governed by maximal cyclically monotone operators and modeled by convex potentials. Géry de Saxcé’s Implicit Standard Materials are modeled by biconvex bipotentials. We analyze the intermediate class of n-monotone materials governed by maximal n-monotone operators and modeled by Fitzpatrick’s functions. Revisiting the model of elastic materials initiated by Robert Hooke, and insisting on the linearity, coaxiality and monotonicity properties of the constitutive law, we illustrate that Fitzpatrick’s representation of n-monotone operators coming from convex analysis provides a constructive method to discover the best bipotential modeling a n-monotone material. Giving up the symmetry of the linear constitutive laws, we find out that n-monotonicity is a relevant criterion for the materials characterization and classification.     

Organic Syntheses Without Solvent: Preparation of Alkoxyphthalimides and of Alkoxylamines

Alkoxyphthalimides are prepared by alkylation of N-hydroxyphthalimide under solid-liquid phase transfer catalysis without solvent. When conversion of alkoxyphthalimides into alkoxylamines is nearly complete, neat hydrazine hydrate is added at room temperature.     

Synthesis of NMP/RAFT inifers and preparation of block copolymers

Two different initiator/transfer agents (inifers) containing an alkoxyamine and a dithiobenzoate were synthetized and used to trigger out either reversible addition‐fragmentation chain transfer (RAFT) polymerization or nitroxide‐mediated polymerization (NMP). α‐Dithiobenzoate‐ω‐alkoxyamine‐difunctional polymers were produced in both cases which were subsequently used as precursors in the formation of block copolymers. This synthetic approach was applied to N‐isopropylacrylamide (NIPAM) or polyethylene oxide methacrylate (EOMA) to form α,ω‐heterodifunctional homopolymers via RAFT at 60°C which were chain extended with styrene by activating the alkoxyamine moiety at 120°C. Under such temperature conditions, it is proposed that a tandem NMP/RAFT polymerization is initiated producing a simultaneous growth of polystyrene blocks at both chain‐ends. Self‐assembled nanostructures of these amphiphilic block copolymers were evidenced by scanning electron microscopy. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012