Behaviour of Pluronic P84 block copolymer micelles above the gelification temperature as probed by positron annihilation lifetime spectroscopy

The new method based on positron annihilation lifetime spectroscopy (PALS) to determine both the mean core radius, R(core), and aggregation number, N(ag), of micelles is applied to the study of aqueous solutions of the triblock Pluronic P84 copolymer as a function of temperature (T), beyond the gelification point (334 K). Two long-lived components appear in the PALS spectra, ascribed to triplet positronium in the water bulk (o-Ps(aq)) and in the organic core of the micelles (o-Ps(org)). Of the various fitting parameters, only the lifetime of the latter species, tau4, and the micellar parameters, R(core) and N(ag), disclose the occurrence of gelification by first increasing up to 334 K, then decreasing. By contrast to what is known in case of phase transition, none of the parameters shows any abrupt change at 334 K, whereas the macroscopic viscosity of the solutions suffers a drastic increase. This is attributed to the fact that positronium is sensitive to the microviscosity of the solutions. At the transition point, the properties of the polyoxipropylene aggregates forming the organic core of the P84 micelles are not greatly affected. Furthermore, the fact that the experimental N(ag) values coincide with those calculated for spheres, from the R(core) values, indicates that the shape of the P84 cores does not change significantly after gelification. The onset of gelification results from a decrease in the hydrogen bonding interactions in the solution with an ensuing relative increase in the interactions between the polyoxipropylene (PPO) groups, initially forming the corona of the P84 micelles, in an intermicellar mode. This increased solicitation of the PPO groups outside their initial location would result in depletion in the number of surfactant molecules forming the micelles, viz. a decrease in both R(core) and N(ag) above 334 K. From the data, additional information can be gained regarding the local viscosity and surface tension in the micellar cores.     

Potassium Fluoride on Alumina: A Convenient Synthesis of O-Alkyl Methyldithiocarbonates. Pyrolysis of O-Benzyl-S-Methyldithiocarbonates

Xanthates were easily prepared by adsorption of alcohol on KF-Al₂O₃ followed by treatment of carbon disulfide and iodomethane at room temperature. Pyrolysis of benzyl xanthate affords to a complex mixture of products. A radical process was proposed to explain the nature of products obtained.     

Solvent-Free Condensation of Methyl Pyridinium and Quinolinium Salts with Aldehydes Catalyzed by DBU

Methylpyridinium and methylquinolinium salts were condensed under solvent-free conditions with aromatic aldehydes in the presence of 1,8-diazabicyclo[5.4.]undec-7-ene (DBU) as catalyst, by grinding at room temperature. The products are dyes or useful intermediates. The DBU can be easily recycled and reused.     

Prolongement d'un courant négatif plurisousharmonique avec condition sur les tranches

In this Note, we prove a theorem on the extension of a negative (or positive) plurisubharmonic current T (i.e. such that $d{d}^{c}T?0$) with condition on the slices with respect to some coordinates. This theorem generalizes a result proved by El Mir–Ben Messaoud relative to d-closed positive currents with a condition on slices. The method consists first of proving a Chern–Levine–Nirenberg inequality for a positive (or negative) psh current, which is a generalization of results obtained by Bedford–Taylor, Demailly and Sibony for d-closed positive currents. Also we prove an Oka type inequality for positive psh currents, thereby generalizing former results by Ben Messaoud–El Mir concerning positive currents with a negative $d{d}^c$. To cite this article: M. Toujani, H. Ben Messaoud, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Opérateur de Monge-Ampère et Tranchage des Courants Positifs Fermés

Sans résumé

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Directional Lipschitzness of Minimal Time Functions in Hausdorff Topological Vector Spaces

In a general Hausdorff topological vector space E, we associate to a given nonempty closed set S???E and a bounded closed set Ω???E, the minimal time function T _S,Ω defined by $T_{S,\Omega}(x):= \inf \{ t> 0: S\cap (x+t\Omega)\not = \emptyset\}$ . The study of this function has been the subject of various recent works (see Bounkhel (2012, submitted, 2013, accepted); Colombo and Wolenski (J Global Optim 28:269–282, 2004, J Convex Anal 11:335–361, 2004); He and Ng (J Math Anal Appl 321:896–910, 2006); Jiang and He (J Math Anal Appl 358:410–418, 2009); Mordukhovich and Nam (J Global Optim 46(4):615–633, 2010) and the references therein). The main objective of this work is in this vein. We characterize, for a given Ω, the class of all closed sets S in E for which T _S,Ω is directionally Lipschitz in the sense of Rockafellar (Proc Lond Math Soc 39:331–355, 1979). Those sets S are called Ω-epi-Lipschitz. This class of sets covers three important classes of sets: epi-Lipschitz sets introduced in Rockafellar (Proc Lond Math Soc 39:331–355, 1979), compactly epi-Lipschitz sets introduced in Borwein and Strojwas (Part I: Theory, Canad J Math No. 2:431–452, 1986), and K-directional Lipschitz sets introduced recently in Correa et al. (SIAM J Optim 20(4):1766–1785, 2010). Various characterizations of this class have been established. In particular, we characterize the Ω-epi-Lipschitz sets by the nonemptiness of a new tangent cone, called Ω-hypertangent cone. As for epi-Lipschitz sets in Rockafellar (Canad J Math 39:257–280, 1980) we characterize the new class of Ω-epi-Lipschitz sets with the help of other cones. The spacial case of closed convex sets is also studied. Our main results extend various existing results proved in Borwein et al. (J Convex Anal 7:375–393, 2000), Correa et al. (SIAM J Optim 20(4):1766–1785, 2010) from Banach spaces and normed spaces to Hausdorff topological vector spaces.     

Théorèmes d'existence pour des inclusions différentielles du second ordre

We prove several existence theorems for second order differential inclusions of the form $\text{x}\text{?}\text{(t)∈K(x(t))}$, $\text{x}\text{?}\text{(t)∈?N(K(x(t));}\text{x}\text{?}\text{(t))+F(t,}\text{x}\text{?}\text{(t)),}$ when K and F are set-valued mappings taking nonconvex and convex values, respectively, in a Hilbert space H. To cite this article: M. Bounkhel, D. Laouir-Azzam, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

On the finite element approximation of elliptic QVIs with noncoercive operators

In this paper, we extend the approach developed by the author for the standard finite element method in the L^∞‐norm of the noncoercive variational inequalities (VI) (Numer Funct Anal Optim.2015;36:1107‐1121.) to impulse control quasi‐variational inequality (QVI). We derive the optimal error estimate, combining the so‐called Bensoussan‐Lions Algorithm and the concept of subsolutions for VIs.