Combinatorial approach for fast screening of functional materials

We present an integrated system with automated sample fabrication for combinatorial investigations of solution-processed organic materials. To illustrate the applicability of the system, we give examples of typical experimental results with organic electronic devices. Organic light emitting diodes (OLEDs) based on a poly-(N-vinylcarbazole) matrix system with small molecule hole-transporter N,N′-Bis(3-methylphenyl)-N,N′-diphenyl-benzidine (TPD) and electron transporter 2-(4-tert-butylphenyl)-5-(4-biphenylyl)-1,3,4-oxadiazole (PBD) were optimized. In a single experimental run, the optimum range of TPD and PBD concentrations has been determined. Furthermore, we screened the influence of a gate dielectric modification with poly(methyl silsesquioxane) in organic field effect transistors and show that the choice of the material system, which constitutes the interface between the gate dielectric and the organic semiconductor, modulates the mobility of the field-effect device by more than two orders of magnitude. Finally, we present a combinatorial study of the influence of PEDOT-PSS and P3HT-PC₆₁BM layer thickness variation in organic photo voltaic cells. To summarize, we describe the possibilities of a combinatorial tool for solution based multilayer devices comprising functional materials. The tool is applicable to a vast variety of such materials. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1587–1593, 2010     

Large deviations of Poisson shot noise processes under heavy tail semi-exponential conditions

In this note we provide a large deviation principle for Poisson shot noise processes under heavy tail semi-exponential conditions on the total shot per arrival. As in the light tail case, our result shows an insensitivity property of the model.     

The relationship between catalyst precursors and chain end groups in homogeneous propene polymerization catalysis

The chain transfer to monomer reactions promoted by primary and secondary growing chains in the propene polymerization promoted by ansa‐zirconocenes and postmetallocene precursors are studied by using DFT methods. From the theoretical results it comes out that the prevalence of propene insertion over β‐hydrogen transfer to the monomer decreases drastically in the presence of a secondary chain. Furthermore, we explained the reason why C₂‐symmetric metallocene catalysts promote the selective formation of cis but‐2‐enyls end group after a 2,1 inserted unit whereas for octahedral bis(phenoxy‐imine)titanium‐based catalysts, chain release promotes exclusively the formation of allyl terminated chain end. These results might be useful to design ligand precursors able to obtain not only high M_n PP polymers but also tuned chain end groups to build new polymer architectures. Overall, a more general picture of the enantioselectivity of the chain transfer to monomer processes is reported. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 699–708, 2010     

An addition and a correction to my paper “Differential inequalities for evolution equations”

This paper provides a generalization of the main lemma and a correct proof of an extended version of Theorem 2, in [G. Vidossich, Differential inequalities for evolution equations, Nonlinear Anal. TMA 25 (1995) 1063-1069].     

A class of 3-dimensional manifolds with bounded first eigenvalue on 1-forms

Let be the framebundle over an oriented, Riemannian surface . Denote by the first nonzero eigenvalue of the Laplace operator acting on differential forms of degree 1. We prove that for all with canonical metrics of volume 1.

     

Hölder continuity of local minimizers of vectorial integral functionals

We study the regularity of vector-valued local minimizers in $ W^{1,p}, p > 1 $, of the integral functional where is an open set in $ \mathbb{R}^N $ and f is a continuous function, convex with respect to the last variable, such that $ 0 \leq f(x,u,t)\leq C(1+t^p) $.We prove that if f = f(x, t), or f = f(x, u, t) and $ p \leq N $, then local minimizers are locally Hölder continuous for any exponent less than 1. If f = f(x, u, t) and p < N then local minimizers are Höolder continuous for every exponent less than 1 in an open set $ \Omega_0 $ such that the Hausdorff dimension of $ \Omega \backslash \Omega_0 $ is less than N–p.AMS Subject Classification: 49N60.     

Hoeffding decompositions for exchangeable sequences and chaotic representation of functionals of Dirichlet processes

Consider an exchangeable sequence $\text{X}\text{={X}{}_{\mathrm{n}}\text{:}\text{1?n<N}}$, where $\text{N∈}\text{N}\text{∪{∞}}$, and note $\text{X}{}_{\mathrm{n}}\text{=(X}{}_1\text{,…,X}{}_{\mathrm{n}}\text{)}$. We say that $\text{X}$ is Hoeffding decomposable if, for each n, every square integrable, centered and symmetric functional of $\text{X}{}_{\mathrm{n}}$ is the orthogonal sum of n U-statistics with degenerated and symmetric kernels. We state a necessary and sufficient condition for an exchangeable sequence to be Hoeffding decomposable, named weak independence. We show that a class of weakly independent sequences is given by generalized urn sequences and, specifically, by generalized Pólya urns. We point out that this yields an orthogonal decomposition of the space of square integrable functionals of Dirichlet–Ferguson processes into orthogonal subspaces of multiple integrals. Explicit formulae are provided. To cite this article: G. Peccati, C. R. Acad. Sci. Paris, Ser. I 336 (2003).