Γ -Entropy Cost for Scalar Conservation Laws

We are concerned with a control problem related to the vanishing viscosity approximation to scalar conservation laws. We investigate the Γ -convergence of the control cost functional, as the viscosity coefficient tends to zero. A first-order Γ -limit is established, which characterizes the measure-valued solutions to the conservation laws as the zeros of the Γ -limit. A second-order Γ -limit is then investigated, providing a characterization of entropic solutions to conservation laws as the zeros of the Γ -limit.     

Hydrosilylation of aromatic nitriles promoted by solvated rhodium atom-derived catalysts

Rhodium metal particles, isolated as supported or unsupported powder starting from mesitylene solvated rhodium atoms, catalyse the hydrosilylation of aromatic nitriles to N,N-disilylamines in high conversion at 100°C. Different hydrosilanes (HSiMe₃, HSi(OEt)₃) can be employed. In the case of cinnamonitrile, the chemoselectivity of the reaction to 2-trimethylsilyl-3-phenylpropionitrile and (E)- and (Z)-1-di(trimethylsilyl)amino-3-phenyl-1-propene is strongly dependent on the reaction temperature. The commercial rhodium on γ-Al₂O₃ catalyst is considerably less active and selective than the analogous catalyst prepared via Metal Vapour Synthesis (MVS) probably owing to the different dimension and distribution of the metal particles in the two samples as shown by HRTEM analysis.     

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     

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     

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.

     

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.