Stochastic signal analysis: Numerical representation and applications to system theory

Alternative procedures for representing a stochastic signal as a denumerable series with uncorrelated terms are developed. The study includes considerations about parametric rescaling and its repercussions on the orthogonal expansion, as well as numerical techniques for approaching such an expansion. In addition, applications to the Gaussian characterization of stochastic signals, filtering and stochastic modelling are treated.     

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.     

Photochemistry of iminium salts : Electron transfer mechanisms for singlet quenching and photoaddition of n-electron donating alcohols and ethers

Several aspects of past and current studies in the area of iminium salt photochemistry are discussed. Investigations of olefin-iminium salt photoaddition and photocyclization reactions are reviewed and conclusions about electron-transfer pathways for fluorescence quenching and reaction are discussed. The results of recent studies of alcohol and ether photoaddition to 2-phenyl-1-pyrrolinium salts are presented. These C-C bond forming processes occur in moderate yields to produce β-amino alcohol or ether products. In addition, alcohols and ethers serve as efficient quenchers of pyrrolinium salt fluorescence. Rate constants for quenching appear to be dependent upon both the oxidation potential of the alcohols and ethers and the availability of C-H bond α to oxygen. This data along with deuterium isotope effects on quenching combine to suggest a common mechanism for both fluorescence quenching and photoaddition. The nature of this mechanism is tested using the comparative quenching effeciencies of the tertiary alcohols t-butyl alcohol and 1,2,2-trimethyl-1-cyclopropanol. The latter alcohol having a weak C-C bond adjacent to the hydroxyl function quenches the fluorescence of 2-phenyl-1-pyrrolium salts at a rate two orders of magnitude greater than for t-butyl alcohol. The observations made are interpreted in terms of a sequential electron-proton transfer mechanism for quenching and photoaddition. Lastly, the relationship of iminium salt photochemical studies to other investigations of electron-transfer photochemistry is discussed.     

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.