Dynamique des applications holomorphes propres de domaines réguliers et problème de l'injectivité

Summary This paper deals with proper holomorphic self-maps of smoothly bounded pseudoconvex domains in . We study the dynamical properties of their extension to the boundary and show that their non-wandering sets are always contained in the weakly pseudoconvex part of the boundary. In the case of complete circular domains, we combine this fact with an entropy/degree argument to show that the maps are automorphisms. Some of our results remain true in      

Constructive Approximation in de Branges–Rovnyak Spaces

In most classical holomorphic function spaces on the unit disk in which the polynomials are dense, a function f can be approximated in norm by its dilates \(f_r(z):=f(rz)~(r<1)\). We show that this is not the case for the de Branges–Rovnyak spaces \(\mathcal{H}(b)\). More precisely, we exhibit a space \(\mathcal{H}(b)\) in which the polynomials are dense and a function \(f\in \mathcal{H}(b)\) such that \(\lim _{r\rightarrow 1^-}\Vert f_r\Vert _{\mathcal{H}(b)}=\infty \). On the positive side, we prove the following approximation theorem for Toeplitz operators on general de Branges–Rovnyak spaces \(\mathcal{H}(b)\). If \((h_n)\) is a sequence in \(H^\infty \) such that \(\Vert h_n\Vert _{H^\infty }\le 1\) and \(h_n(0)\rightarrow 1\), then \(\Vert T_{\overline{h}_n}f-f\Vert _{\mathcal{H}(b)}\rightarrow 0\) for all \(f\in \mathcal{H}(b)\). Using this result, we give the first constructive proof that, if b is a nonextreme point of the unit ball of \(H^\infty \), then the polynomials are dense in \(\mathcal{H}(b)\).     

Large time behavior of periodic viscosity solutions for uniformly parabolic integro-differential equations

In this paper, we study the large time behavior of solutions of a class of parabolic fully nonlinear integro-differential equations in a periodic setting. In order to do so, we first solve the ergodic problem (or cell problem), i.e. we construct solutions of the form $\lambda t + v(x).$ We then prove that solutions of the Cauchy problem look like those specific solutions as time goes to infinity. We face two key difficulties to carry out this classical program: (1) the fact that we handle the case of “mixed operators” for which the required ellipticity comes from a combination of the properties of the local and nonlocal terms and (2) the treatment of the superlinear case (in the gradient variable). Lipschitz estimates previously proved by the authors (2012) and Strong Maximum principles proved by the third author (2012) play a crucial role in the analysis.     

Weyl Laws for Partially Open Quantum Maps

We study a toy model for “partially open” wave-mechanical system, like for instance a dielectric micro-cavity, in the semiclassical limit where ray dynamics is applicable. Our model is a quantized map on the 2-dimensional torus, with an additional damping at each time step, resulting in a subunitary propagator, or “damped quantum map”. We obtain analogues of Weyl’s laws for such maps in the semiclassical limit, and draw some more precise estimates when the classical dynamics is chaotic. Submitted: October 16, 2008. Accepted: April 3, 2009.     

The Transient Acceleration from Time-Dependent Interacting Dark Energy Models

The transient acceleration which the current cosmic acceleration is not eternal is possible by introducing the interaction between dark matter and dark energy. If the energy transfer is from dark energy to dark matter, then it is possible to realize the transient acceleration. We study the possibility of transient acceleration by considering two time-dependent phenomenological interaction forms so that the energy transfer increases as the universe evolves. Starting from a simple and extending to a more complicated ansatz, we obtain analytical expressions for the evolutions of the deceleration and the various energy density parameters. We find the ranges of the parameters in the models for a transient acceleration.     

Influence of NaClO3 on the rheological behaviour of a micellar solution of CPCl

It is now well know that a small addition of salt to a micellar solution often increases the zero-shear viscosity η₀ of the solution, the understanding of the behaviour at high salt content is more questionable. In this situation, addition of more salt induces a decrease of η₀. In this experimental work we investigate the linear and non-linear rheological behaviour of a new micellar system: CPCl (surfactant)/NaClO₃ (salt). Studies of the evolution of η₀ as well as G₀ (the elastic modulus) or τ_R (the relaxation time) are in agreement with the hypothesis of a diminution of the mean micellar length when, after the maximum η₀, the salt content increases. In the non-linear behaviour (non-Newtonian viscosity) the evolution of γ˙ _c, (which defines the occurrence of the shear thinning) with salt concentration C_S is also in agreement with such a hypothesis. Received: 29 March 1999/Accepted: 20 March 2000     

Synthesis and barrier properties of poly(ε-caprolactone)-layered silicate nanocomposites

A new polymer-ceramic nanocomposite has been synthesized consisting of well-dispersed, two-dimensional layers of an organically modified mica-type silicate (MTS) within a degradable poly(ε-caprolactone) matrix. A protonated amino acid derivative of MTS was used to promote delamination/dispersion of the host layers and initiate ring-opening polymerization of ε-caprolactone monomer, resulting in poly(ε-caprolactone) chains that are ionically bound to the silicate layers. The polymer chains can be released from the silicate surface by a reverse ion-exchange reaction and were shown to be spectroscopically similar to pure poly(ε-caprolactone). Thick films of the polymer nanocomposite exhibit a significant reduction in water vapor permeability that shows a linear dependence on silicate content. The permeability of nanocomposite containing as low as 4.8% silicate by volume was reduced by nearly an order of magnitude compared to pure poly(ε-caprolactone). © 1995 John Wiley & Sons, Inc.     

On the characterization of disordered and heterogeneous carbonaceous materials by Raman spectroscopy

The applicability of Raman spectroscopy to characterize disordered and heterogeneous carbonaceous materials (CM) is discussed, by considering both natural and synthetic CM. First, different analytical mismatches during the measurement are discussed and technical indications are provided in order to eliminate them. Second, the accuracy and relevance of the different parameters obtained by the decomposition of spectra by conventional fitting procedure, is reviewed. Lastly, a new Raman technique (Raman area mode microspectroscopy) giving an homogeneous repartition of power within a large laser beam is presented, this technique being powerful to study strongly heterogeneous CM and/or photosensitive samples.     

Chemical composition and insecticidal activity of the essential oil from Helichrysum faradifani endemic to Madagascar

Helichrysum faradifani (Asteraceae) is a perennial shrub growing in rocky and sandy places of Madagascar. The plant is used in the Malagasy traditional medicine as a wound-healing agent, disinfectant and for the treatment of syphilis, diarrhea, cough and headache. In the present work, we analysed the chemical composition of the essential oil distilled from the aerial parts of H. faradifani by GC-MS and evaluated its insecticidal activity against 2nd, 3rd and 4th instar larvae of the lymphatic filariasis vector Culex quinquefasciatus by acute toxicity assays. The most sensitive were 2nd instar (LC₅₀ = 85.7 μL L^?1) larvae. For the 3rd and 4th instar larvae, the estimated LC₅₀ were 156.8 and 134.1 μL L^?1, respectively. Monoterpene hydrocarbons (51.6%) were the major fraction of the essential oil, with the bicyclic α-fenchene (35.6%) as the predominant component. Sesquiterpene hydrocarbons (34.0%) were the second major group characterising the oil, with γ-curcumene (17.7%) as the most abundant component.     

Multi‐stage high order semi‐Lagrangian schemes for incompressible flows in Cartesian geometries

Efficient transport algorithms are essential to the numerical resolution of incompressible fluid‐flow problems. Semi‐Lagrangian methods are widely used in grid based methods to achieve this aim. The accuracy of the interpolation strategy then determines the properties of the scheme. We introduce a simple multi‐stage procedure, which can easily be used to increase the order of accuracy of a code based on multilinear interpolations. This approach is an extension of a corrective algorithm introduced by Dupont & Liu (2003, 2007). This multi‐stage procedure can be easily implemented in existing parallel codes using a domain decomposition strategy, as the communication pattern is identical to that of the multilinear scheme. We show how a combination of a forward and backward error correction can provide a third‐order accurate scheme, thus significantly reducing diffusive effects while retaining a non‐dispersive leading error term. Copyright © 2016 John Wiley & Sons, Ltd.