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.     

Heterogeneous electron-transfer kinetics for ruthenium and ferrocene redox moieties through alkanethiol monolayers on gold

The standard heterogeneous electron-transfer rate constants between substrate gold electrodes and either ferrocene or pentaaminepyridine ruthenium redox couples attached to the electrode surface by various lengths of an alkanethiol bridge as a constituent of a mixed self-assembled monolayer were measured as a function of temperature. The ferrocene was either directly attached to the alkanethiol bridge or attached through an ester (CO(2)) linkage. For long bridge lengths (containing more than 11 methylene groups) the rate constants were measured using either chronoamperometry or cyclic voltammetry; for the shorter bridges, the indirect laser induced temperature jump technique was employed to measure the rate constants. Analysis of the distance (bridge length) dependence of the preexponential factors obtained from an Arrhenius analysis of the rate constant versus temperature data demonstrates a clear limiting behavior at a surprisingly small value of this preexponential factor (much lower than would be expected on the basis of aqueous solvent dynamics). This limit is independent of both the identity of the redox couple and the nature of the linkage of the couple to the bridge, and it is definitely different (smaller) from the limit derived from an equivalent analysis of the rate constant (versus temperature) data for the interfacial electron-transfer reaction through oligophenylenevinylene bridges between gold electrodes and ferrocene. There are a number of possible explanations for this behavior including, for example, the possible effects of bridge conformational flexibility upon the electron-transfer kinetics. Nevertheless, conventional ideas regarding electronic coupling through alkane bridges and solvent dynamics are insufficient to explain the results reported here.     

On the structure of singular sets of convex functions

Whenf is a convex function ofR ^h, andk is an integer with 0<k, then the set ^k (f)=x:dim(f(x)k may be covered by countably many manifolds of dimensionh–k and classC ² except an _h–k negligible subset.The author is supported by INdAM     

A study of the conformation of some 3,3′-bithienyl and biselenienyl derivatives by measurements of twisting powers in nematic liquid crystals and of dipole moments

The conformation of chiral 2,2′-dinitro-3,3′-bithienyl-4,4′-dicarboxylic acid (Ia), its dimethylester (Ib), and analogous selenium derivatives Ic and Id was investigated by means of induced cholesteric mesophases. A parallel investigation on the diester (Ib) and on other model 3,3′-bithienyls was carried out with dipole moment measurements. The conclusions reached with the two independent methods for derivative Ib are in excellent agreement and indicate, if a single conformation is assumed, a preferred cisoid conformation with a dihedral angle somewhat smaller than 90°. Alternatively, if the existence of both cisoid and transoid conformations having supplementary dihedral angles is assumed, the data indicate a higher population for the cisoid form.