Existence globale pour l'équation de Smoluchowski continue non homogène et comportement asymptotique des solutions

We prove global existence of solutions to the continuous nonhomogeneous Smoluchowski equation for coagulation rates satisfying a more general structure condition than the Galkin–Tupchiev monotony hypothesis considered in (Ph. Laurençot, S. Mischler, Arch. Rational Mech. Anal. 162 (1) (2002) 45–99). The Smoluchowski coagulation rate fulfils this condition as well as some rates which vanish on the diagonal. Under the condition of positivity of the coagulation rate outside of the diagonal we prove that solutions tend to 0 in the large time asymptotic. These results depend on a new estimate from below for the dissipation rate of the L^p-norm, p>1. To cite this article: S. Mischler, M. Rodriguez Ricard, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

A note about the Gaussian property of the Brownian bridge

The Gaussian property of the Brownian bridge is characterized as an application of Ramachandran's theorem in terms of the independence of the random variables that appear in the Karhunen-Loéve expansion of the process. A reference about the construction of the Brownian bridge by means of functional transformations is also included.     

Cartesian currents,weak diffeomorphisms and existence theorems in nonlinear elasticity

Summary In this paper we introduce some new classes of functions, among these a class of weak diffeomorphisms. In these classes we prove by direct methods the existence of minimizers for several kinds of variational integrals. In particular, we prove the existence of one-to-one orientation-preserving maps that minimize suitable energies associated with hyperelastic materials. The minimizers are also proved to satisfy equilibrium equations. Finally radial deformations are discussed in connection with cavitation.     

Multilayered Cu–Ti deposition on silicon substrates for chemiresistor applications

Abstract

On the perspective to develop CuO–TiO₂ MOS, multilayered Cu and Ti thin layers were alternatively deposited on silicon wafers using 25?keV Ar?+?ion beam sputtering and, subsequently, oxidized by thermal annealing in air at 400?°C for 24?h. The deposited films have variable ratios of the Cu and Ti % at. One of the main goal is to obtain such multilayers avoiding the presence of Cu–Ti–O compounds. The samples were characterized in terms of composition (by RBS and SIMS analyses) and morphology (by AFM and SEM investigations). In particular, SIMS maps allows to observe the spatial distribution and thickness of each phase of the Cu/Ti multilayers, and further to observe Cu diffusion and mixing with Ti, as well as phase separation of CuO and TiO₂ in the samples. The reasons of this effect represent an open issue that has to investigated, in order to improve the MOS fabrication.     

Reverse micellar aggregates: effect on ketone reduction. 2. Surfactant role

Kinetics of the reduction of 3-chloroacetophenone (CAF) with sodium borohydride (NaBH(4)) were followed by UV-vis spectroscopy at 27.0 degrees C in different reverse micellar media, toluene/BHDC/water and toluene/AOT/water, and compared with results in an isooctane/AOT/water reverse micellar system. AOT is sodium 1,4-bis-2-ethylhexylsulfosuccinate, and BHDC is benzyl-n-hexadecyl dimethylammonium chloride. The kinetic profiles were investigated as a function of variables such as surfactant and NaBH(4) concentration and the amount of water dispersed in the reverse micelles, W(0) = [H(2)O]/[surfactant]. In all cases, the first-order rate constant, k(obs), increases with the concentration of surfactant as a consequence of incorporating the substrate into the interface of the reverse micelles where the reaction takes place. The reaction is faster at the cationic interface than at the anionic one probably because the negative ion BH(4)(-) is part of the cationic interface. The effect of the external solvent on the reaction shows that reduction is favored in the isooctane/AOT/water reverse micellar system than that with an aromatic solvent. This is probably due to BH(4)(-) being more in the water pool of the toluene/AOT/water reverse micellar system. The kinetic profile upon water addition depends largely on the type of interface. In the BHDC system, k(obs) increases with W(0) in the whole range studied while in AOT the kinetic profile has a maximum at W(0) approximately 5, probably reflecting the fact that BH(4)(-) is part of the cationic interface while, in the anionic one, there is a strong interaction between water and the polar headgroup of AOT below W(0) = 5 and, above that, BH(4)(-) is repelled from the interface once the water pool has formed. Application of a kinetic model based on the pseudophase formalism, which considers the distribution of the ketone between the continuous medium and the interface and assumes that reaction takes place only at the interface, has enabled us to estimate rate constants at the interface of the reverse micellar systems. At W(0) < 10, it was considered that NaBH(4) is wholly at the interface and, at W(0) >/= 10, where there are free water molecules, also the partitioning between the interface and the water pool was taken into account. The results were used to evaluate CAF and NaBH(4) distribution constants between the different pseudophases as well as the second-order reaction rate constant of the reduction reaction in the micellar interface.     

A family of alkynylgold(III) complexes [AuI(mu-{CH2}2PPh2)2Au(III)(C triple bond CR)2] (R = Ph, tBu, Me3Si): facile and reversible comproportionation of gold(I)/gold(III) to digold(II)

The symmetric digold(II)dichloride bis(ylide) complex [Au2Cl2(mu-{CH2}2PPh2)2] reacts with acetylides to form the asymmetric heterovalent gold(I)/gold(III) complexes [AuI(mu-{CH2}2PPh2)2AuIII(CCR)2] [R = Ph, tBu, and SiMe3], the phenyl analogue of which was characterized by X-ray crystallography. These compounds represent the first examples of gold(III) complexes containing two acetylide ligands. [AuI(mu-{CH2}2PPh2)2AuIII(CCPh)2] undergoes a reversible comproportionation reaction upon treatment with [Ag(ClO4)tht] to give the symmetric digold(II) cationic complex [Au2(tht)2(mu-{CH2}2PPh2)2](ClO4)2. If this complex is treated with phenylacetylene in the presence of base, the heterovalent gold(I)/gold(III) complex is re-formed. This reversible interconversion between binuclear gold(I)/gold(III) and digold(II) bis(ylide) complexes is unprecedented.     

The hydroazocine route to highly functionalized pyrrolizidines

Studies of the preparation of 1,8-dihydroazocines and transannular cyclization of hydroazocines to produce functionalized pyrrolizidines are described. Results are presented which demonstrate that unsymmetrically substituted acetylenes bearing at least one electron withdrawing groups undergo efficient cycloaddition to 1 - β - styryl - 1,2 - dihydropyridine producing in a regio-selective fashion 3,4 - disubstituted - 1,8 - dihydroazocines. The dihydroazocines generated in this manner can be converted to 1 - formyl - Δ^4,5 - epoxyazocines which undergo interesting rearrangement reactions to form pyrrolizidines when subjected to methoxide deformylation followed by acid treatment. In addition, 1,6,7,8 - tetrahydroazocines can be converted to pyrrolizidines under bromination conditions. The intriguing chemical process which occur under the conditions outlined above are described.     

The di-π-methane rearrangement : The effect of 1,4-diene structure and conformation on the reaction efficiency and stereochemistry

The photochemistry of the stereoisomeric 1,3-dimethyl-3(2-phenylethenyl)cyclohexenes has been explored Direct irradiation of the cis- and trans-β-styrylcyclohexenes leads to di-π-methane rearrangement, producing the endo- and exo-3,7-dimethyl-8-phenybicyclo[5.1.0]oct-2-enes, and cis -trans isomerization, interconverting the 1,4-diene containing substrates. Triplet sensitized photolysis of both substituted cyclohexenes leads exclusively to cis-trans isomerization. Results from low conversion direct irradiations of the cis- and trans-β-styrylcyclohexenes indicate that the singlet rearrangements are stereospecific, and lead to formation of the 8-exo and 8-endo-phenylbicyclic octenes, respectively. The relationship between di-π-methane structure and triplet reaction efficiency, and the effect of conformation on the rearrangement stereochemistry are discussed.     

Vilsmeier formylation of 5,10,15-triphenylcorrole: expected and unusual products

5,10,15-Triphenylcorrole (1) reacts with the Vilsmeier reagent (POCl(3)/DMF) to give the corresponding 3-formyl derivative 3 as the major product. The regioselectivity of the reaction was proven by X-ray crystallography and only traces of the 2-formyl isomer were observed. A more polar product is also observed and this compound becomes the major product when an excess of DMF is used for the preparation of the Vilsmeier reagent, while the formation of the 3-formyl isomer is almost completely suppressed. X-ray crystallography allowed us to identify this compound as the fully substituted N-ethane bridged derivative 4, formed from the attack of the Vilsmeier reagent at the inner core of the macrocycle. This compound is unique among porphyrinoid macrocycles, and further confirms the peculiarity of corrole chemistry.