Postpolymerization modification of reactive polymers derived from vinylcyclopropane. III. Polymer sequential functionalization using a combination of amines with alkoxyamines,hydrazides, isocyanates,or acyl halides

A new 1,1‐disubstituted‐2‐vinylcyclopropane monomer bearing a ketone and a pentafluorophenyl ester was synthesized and successfully polymerized to yield a polymer with two side chain moieties readily available for post‐polymerization modification. After a quantitative modification of the pentafluorophenyl moiety with amines, a subsequent second functionalization reaction was successfully performed on the ketone moiety leading to a double side‐chain functionalized polymer using two different routes. The first route utilized hydrazide and hydroxylamine derivatives leading to a ketone conversion of 25 to 85%. In the second route, the ketone moiety was first reduced to alcohol (reduction conversion up to 100%) and then converted into the corresponding ester or urethane using acyl halides or isocyanates, respectively, with a conversion ratio of up to 90%. A library of functionalized polymers was synthesized to confirm the effectiveness of this approach. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 2841–2849     

A Fixed-Point Theorem and Equilibria of Abstract Economies with Weakly Upper Semicontinuous Set-Valued Maps

The main purpose of this paper is to introduce the notion of weakly upper semicontinuous set-valued maps and to establish a new fixed-point theorem. The set-valued maps with an approximating upper semicontinuous selection property are also defined. Next, we use our fixed-point result to obtain equilibrium existence in abstract economies with two constraints, which provide a natural scenario for potential applications of our approach to general equilibrium theory. In this regard, we set models of economies with asymmetric informed agents, who are able to improve their initial information through market signals. These economies offer examples in which the informational feasibility requirement represents an additional constraint.     

Non‐Linear Signal Detection Improvement by Radiation Damping in Single‐Pulse NMR Spectra

When NMR lines overlap and at least one of them is affected by radiation damping, the resonance line shapes of all lines are no longer Lorentzian. We report the appearance of narrow signal distortions, which resemble hole‐burnt spectra. This new experimental phenomenon facilitates the detection of tiny signals hidden below the main resonance. Theoretical analysis based on modified Maxwell–Bloch equations shows that the presence of strong transverse magnetization creates a feedback through the coil, which influences the magnetization of all spins with overlapping resonance lines. In the time domain this leads to cross‐precession terms between magnetization densities, which ultimately cause non‐linear behavior. Numerical simulations corroborate this interpretation.     

Structure of the set of equilibrated loads in nonlinear elasticity and applications to existence and nonexistence

In this paper, we point out and use the geometrical structure of the set of equilibrated loads in nonlinear elasticity, for existence theorems for various nonlinear traction problems, and for nonexistence results in linearized elasticity.

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Résumé Dans cet article, on met en évidence la structure géométrique de l'ensemble des charges équilibrées en élasticité non linéaire, et on utilise cette structure pour montrer divers théorèmes d'existence pour des problèmes de traction non linéaires, ainsi que des résultats de non existence pour l'élasticité linéarisée.

     

Déformation cumulée tensorielle dans le référentiel en rotation logarithmiqueCumulated tensorial strain measure in the logarithmic rotating frame.

The time integration of strain rate tensor $\stackrel{?}{\mathit{D}}$ is a central problem in large transformations even if it is often an underlying one. The cumulated tensorial strains, obtained by the time integration of strain rate tensor $\stackrel{?}{\mathit{D}}$, allow the tackling of this problem from a geometrical point of view, and independently of material behaviour considerations. The time integration here takes place in the local objective frame defined by the logarithmic spin proposed by Lehmann et al. and Xiao et al. The numerical results obtained in a closed deformation path are presented here. The advantages and drawbacks of this novel integration for the development of behaviour laws are described. To cite this article: V. Mora et al., C. R. Mecanique 332 (2004).     

A Renewal Theorem for Strongly Ergodic Markov Chains in Dimension <Emphasis Type="Italic">d</Emphasis> ≥ 3 and Centered Case

In dimension d ≥ 3, we present a general assumption under which the renewal theorem established by Spitzer (1964) for i.i.d. sequences of centered nonlattice r.v. holds true. Next we appeal to an operator-type procedure to investigate the Markov case. Such a spectral approach has been already developed by Babillot (Ann Inst Henri Poincaré, Sect B, Tome 24(4):507–569, 1988), but the weak perturbation theorem of Keller and Liverani (Ann Sc Norm Super Pisa CI Sci XXVIII(4):141–152, 1999) enables us to greatly weaken the moment conditions of Babillot (Ann Inst Henri Poincaré, Sect B, Tome 24(4):507–569, 1988). Our applications concern the v-geometrically ergodic Markov chains, the ρ-mixing Markov chains, and the iterative Lipschitz models, for which the renewal theorem of the i.i.d. case extends under the (almost) expected moment condition.