The Generalized Multifractional Field: A Nice Tool for the Study of the Generalized Multifractional Brownian Motion

The Generalized Multifractional Brownian Motion (GMBM) is a continuous Gaussian process {X(t)}_{t ? [0,1]}\{X(t)\}_{t\in [0,1]} that extends the classical Fractional Brownian Motion (FBM) and the Multifractional Brownian Motion (MBM) [15, 4, 1, 1]. Its main interest is that, its Hölder regularity can change widely from point to point. In this article we introduce the Generalized Multifractional Field (GMF), a continuous Gaussian field {Y(x,y)}_{(x,y) ? [0,1] ²}\{Y(x,y)\}_{(x,y)\in [0,1]^{\,2}} that satisfies for every tt, X(t)=Y(t,t)X(t)=Y(t,t). Then, we give a wavelet decomposition of YY and using this nice decomposition, we show that YY is b\beta-Hölder in yy, uniformly in xx. Generally speaking this result seems to be quite important for the study of the GMBM. In this article, it will allow us to determine, without any restriction, its pointwise, almost sure, Hölder exponent and to prove that two GMBM's with the same Hölder regularity differ by a "smoother' process.     

Contrast harmonic imaging

The behavior of ultrasound contrast agents depends highly on the acoustic pressure of the insonified ultrasound wave. For low pressure the expansion and compression is linear to the pressure, for medium acoustic pressure nonlinear behavior starts to occur and for high pressures, but still in the diagnostic range transient scattering can be noticed, resulting in an enhanced scattering followed by a disappearance of the bubble. The nonlinear and transient regime can be utilized for imaging of the contrast agent in or nearby tissue. The magnitude of the nonlinear signal from the contrast has to compete with the nonlinear component of the ultrasound wave, which is generated during propagation. It is shown that contrast is superior to tissue when using low frequencies and imaging the third or fourth harmonic of the transmitted frequency.     

Le théorème ergodique pour les opérateurs positifs sur les espaces Lp (1<p<∞) revisitéErgodic theorem for positive operators on Lp-spaces Lp (1<p<∞) revisited

We consider positive linear operators on L_p-spaces (1<p<∞), (A(L_p⁺)?L_p⁺), satisfying the inequality A^m+n<A^m+Aⁿ for all $\text{m,n∈}\text{N}\text{.}$ We describe the structure of these operators (Theorem 1). As a consequence we obtain for all f∈L^p,Aⁿf converges a.e. The last statement contains the theorem of a.e. convergence of Cesaro averages for positive mean bounded operators. To cite this article: A. Brunel, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 205–207.     

Stability of divalent europium in an ionic liquid: spectroscopic investigations in 1-methyl-3-butylimidazolium hexafluorophosphate

In this work, devoted to 1-methyl-3-butylimidazolium hexafluorophosphate ionic liquid (BumimPF(6)), the importance of the purity of the solvent for spectroscopic investigations is highlighted. Results from small angle X-ray scattering indicate that the pure solvent exhibits a local organization. Europium(II), which appears to be unusually stable in BumimPF(6), is characterized by spectroscopic techniques (absorption, luminescence). Solvation of Eu(II) in BumimPF(6) and complexation effects in the presence of the crown ether 15C5 solubilized in the ionic liquid are discussed.     

Determination of critical micelle concentration of surfactants using a near-infrared hydrophobicity probe

A near-infrared (NIR) dye has been used for the determination of critical micelle concentrations (CMC) of surfactants. This NIR dye displays significant changes in its absorption spectra dependent on the hydrophobicity of the microenvironment around the dye molecule. The absorption spectra of this NIR dye show two distinct maxima which can be used in determining hydrophobicity. The NIR hydrophobicity probe detects the changes in the microenvironment hydrophobicity accompanying micelle formation. The determined CMC values are in good agreement with values obtained using other techniques. The major advantage of this NIR method lies in the inherently low interference of the NIR spectral region.     

Electric dipole moments and conformations of isolated peptides

The electric dipole moments of the isolated amino acid tryptophan and small glycine-based peptides (WG_n, n = 1-5, W = tryptophan, G = glycine) have been measured by deflection of a molecular beam in an inhomogeneous electric field. The measurements are compared to the results of ab initio calculations and Monte-Carlo simulations. The conformation and the flexibility of the peptides, at different temperatures, are discussed. The WG_n peptides are much more floppy than an isolated tryptophan, even a single glycine is enough to make the peptide floppy on the timescale of the electric deflection measurements. Received 4 January 2002 Published online 13 September 2002     

Hétérocycles dioxinniques. Nouvelle méthode de synthèse des benzo (4H) dioxinnes-1,3

The condensation reactions between variously substituted phenols and paraformaldehyde were carried out in the presence of ion exchangers used as catalysts. The control of the hydration rate of the reaction medium afforded the selective formation of the corresponding 4H-benzo1,3-dioxins.     

Measurement of quantum states and the Wigner function

In quantum mechanics, the state of an individual particle (or system) is unobservable, i.e., it cannot be determined experimentally, even in principle. However, the notion of measuring a state is meaningful if it refers to anensemble of similarly prepared particles, i.e., the question may be addressed: Is it possible to determine experimentally the state operator (density matrix) into which a given preparation procedure puts particles. After reviewing the previous work on this problem, we give simple procedures, in the line of Lamb's operational interpretation of quantum mechanics, for measuring a translational state operator (whether pure or mixed), via its Wigner function. These procedures closely parallel methods that might be used in classical mechanics to determine a true phase space probability distribution; thus, the Wigner function simulates such a distribution not only formally, but operationally also.

E. P. Wigner⁽¹⁾

     

From equilibrium spin models to probabilistic cellular automata

The general equivalence betweenD-dimensional probabilistic cellular automata (PCA) and (D+1)-dimensional equilibrium spin models satisfying a disorder condition is first described in a pedagogical way and then used to analyze the phase diagrams, the critical behavior, and the universality classes of some automata. Diagrammatic representations of time-dependent correlation functions of PCA are introduced. Two important classes of PCA are singled out for which these correlation functions simplify: (1) Quasi-Hamiltonian automata, which have a current-carrying steady state, and for which some correlation functions are those of aD-dimensional static model. PCA satisfying the detailed balance condition appear as a particular case of these rules for which the current vanishes. (2) Linear (and more generally affine) PCA for which the diagrammatics reduces to a random walk problem closely related to (D+1)-dimensional directed SAWs: both problems display a critical behavior with mean-field exponents in any dimension. The correlation length and effective velocity of propagation of excitations can be calculated for affine PCA, as is shown on an explicitD=1 example. We conclude with some remarks on nonlinear PCA, for which the diagrammatics is related to reaction-diffusion processes, and which belong in some cases to the universality class of Reggeon field theory.