Quasi-analytic solutions of linear parabolic equations

Uniqueness of solutions of the Cauchy problem of a parabolic equation, and the related question of analyticity with respect to time, depend on global properties of the solution. We demonstrate that if the growth of the initial function (and, if relevant, of the inhomogeneous part and its derivatives) is not too great, solutions of non-stationary parabolic equations whose coefficients belong to quasi-analytic classes are quasi-analytic with respect to all variables and hence are unique. This study is motivated by the problem of endogenous completeness in continuous-time financial markets.     

Full backward non-homogeneous semi-Markov processes for disability insurance models: A Catalunya real data application

In this paper a stochastic model for disability insurance contracts is presented. The model is based on a discrete time non-homogeneous semi-Markov process to which the backward recurrence time process is joined. This permits us to study in a more complete way the disability evolution and to face the duration problem in a more effective way. The model is applied to a sample of contracts drawn at random from a mutual insurance company.     

Effective balance equations for elastic composites subject to inhomogeneous potentials

We derive the new effective governing equations for linear elastic composites subject to a body force that admits a Helmholtz decomposition into inhomogeneous scalar and vector potentials. We assume that the microscale, representing the distance between the inclusions (or fibers) in the composite, and its size (the macroscale) are well separated. We decouple spatial variations and assume microscale periodicity of every field. Microscale variations of the potentials induce a locally unbounded body force. The problem is homogenizable, as the results, obtained via the asymptotic homogenization technique, read as a well-defined linear elastic model for composites subject to a regular effective body force. The latter comprises both macroscale variations of the potentials, and nonstandard contributions which are to be computed solving a well-posed elastic cell problem which is solely driven by microscale variations of the potentials. We compare our approach with an existing model for locally unbounded forces and provide a simplified formulation of the model which serves as a starting point for its numerical implementation. Our formulation is relevant to the study of active composites, such as electrosensitive and magnetosensitive elastomers.     

Heterogeneous enantioselective epoxidation of olefins catalysed by unsymmetrical (salen)Mn(III) complexes supported on amorphous or MCM-41 silica through a new triazine-based linker

High enantioselectivity (ee up to 84%) has been achieved in heterogeneous asymmetric epoxidation using a silica-bound unsymmetrical (salen)-manganese(III) complex; amorphous silica can be used in the same way as MCM-41, showing a positive effect in the catalyst recycling.     

Hilbert-Schmidt Hankel Operators on the Bergman Space of Planar Domains

In this paper we study the problem of the membership of H _ϕ in the Hilbert-Schmidt class, when and Ω is a planar domain. We find a necessary and sufficient condition.We apply this result to the problem of joint membership of H _φ and in the Hilbert-Schmidt class. Using the notion of Berezin Transform and a result of K. Zhu we are able to give a necessary and sufficient condition. Finally, we recover a result of Arazy, Fisher and Peetre on the case with φ holomorphic.     

Anomalous behavior of amine oxide surfactants at the air/water interface

A commonly stated requirement for the preparation of stable Langmuir monolayers of amphiphilic molecules at an air/water interface is that the surfactant must be insoluble in the subphase solution; however, a few prior studies have reported that some soluble surfactants can, under certain conditions, be compressed. The anomalous compression of soluble amphiphiles is extremely interesting and important, as it presents the possibility of greatly increasing the number of candidate compounds suitable for Langmuir monolayer studies and Langmuir-Blodgett deposition. The aim of this work was to obtain a better understanding of the factors that determine whether monolayers of a given water-soluble surfactant can be compressed. A series of amine oxide surfactants, including a novel gemini surfactant, were studied to explore the relationship between molecular structure and behavior at the air/water interface. Amine oxides are an especially interesting class of surfactants because their self-assembly in solution and at interfaces is pH-sensitive. Surface pressure-area isotherms show that the solubility of a surfactant in the subphase solution is not, in and of itself, a useful parameter in predicting whether the monolayer is compressible. Molecular modeling calculations suggest that the tendency of molecules to self-assemble plays a much more important role than solubility in this regard. The effect of pH was also investigated. We present a hypothesis that formation of dimers or small clusters of molecules at the interface inhibits the dissolution of these species into the subphase, and as a consequence the monolayer can be compressed.     

Photopolymerization in water of diacetylenes chemisorbed onto noble metal nanoparticles: a spectroscopic study

Gold and silver nanoparticles of different size, decorated by a diacetylenic monomer having a COOH anchor group, were prepared in aqueous dispersions. Topochemical polymerization of the colloidal suspensions was obtained by UV irradiation and studied by means of spectroscopic techniques (UV–visible absorption, IR and Raman spectroscopies). A variety of polymer phases were found in the case of silver nanohybrids. The main contribution for this investigation was supplied by the Raman spectra, which provide detailed information on the polymer forms and on the preferred conformation of the alkylic side chains. Copyright © 2009 John Wiley & Sons, Ltd.