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).     

Toggling enantioselective catalysis--a promising paradigm in the development of more efficient and versatile enantioselective synthetic methodologies

The increasingly needed synthesis of both enantiomers of a chiral compound usually requires the use of both enantiomers of a chiral catalyst. Several of the usually employed chiral ligands are naturally available in only one enantiomeric form, the antipode often being of labor-intensive preparation. Enantiodivergent asymmetric catalysis has accrued in importance in this regard, in that it allows expeditious access to both enantiomers of a product without any direct modification on the chemical structure of the chiral promoter. Various promising examples will be discussed throughout the review. If available or envisageable, a mechanistic rationale for the observed enantioinversion will be outlined.     

Chemometric investigation of the efficiency of different TiO<Subscript>2</Subscript>-based catalysts as principal components of TOC photochemical sensors under development

There is an increasing demand for measurement of organic carbon in solutions both in industry and in environmental research for the purpose of continuous water-quality monitoring. Practically all the methods used are based on a catalytic system in which metal oxides play a major role. The development of a new TOC/DOC measurement system, in our work, uses a mixed anatase-rutile form of TiO(2 )as catalyst of the mineralisation process, and direct measurement of the CO(2) produced, by a gaseous diffusion electrode. The entire research is based on heterogeneous catalysis using an immobilised catalyst, which can offer considerable advantages over other methods of catalysis. Four different catalytic systems were analysed. Three involved thermal immobilisation of TiO(2) on glass supports (glass spheres and glassy particulates) or on an Al metal grid. One further system consisted of direct oxidation of a Ti grid at high temperatures. The system was illuminated using a 350 nm UV source (350 mW cm(-2)) contained in a home-made measurement cell. Five molecules-malic acid, pentachlorophenol, sodium dodecylsulfate, hydroquinone, and citric acid-which were deemed to be representative and had been investigated in several previous studies, were used as photodegradation targets. However, it was not possible to obtain a direct expression of "catalytic efficiency" simply by reading the data obtained, nor any indirect molecular "recalcitrancy" scale. Chemometric analysis, by principal components analysis, allows the five used catalytic systems to be easily compared each other and a single PC component is able to perform classification.