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.     

Total Chemical Synthesis of an Intra‐A‐Chain Cystathionine Human Insulin Analogue with Enhanced Thermal Stability

Despite recent advances in the treatment of diabetes mellitus, storage of insulin formulations at 4 °C is still necessary to minimize chemical degradation. This is problematic in tropical regions where reliable refrigeration is not ubiquitous. Some degradation byproducts are caused by disulfide shuffling of cystine that leads to covalently bonded oligomers. Consequently we examined the utility of the non‐reducible cystine isostere, cystathionine, within the A‐chain. Reported herein is an efficient method for forming this mimic using simple monomeric building blocks. The intra‐A‐chain cystathionine insulin analogue was obtained in good overall yield, chemically characterized and demonstrated to possess native binding affinity for the insulin receptor isoform B. It was also shown to possess significantly enhanced thermal stability indicating potential application to next‐generation insulin analogues.     

Sharp error bounds for complex floating-point inversion

We study the accuracy of the classic algorithm for inverting a complex number given by its real and imaginary parts as floating-point numbers. Our analyses are done in binary floating-point arithmetic, with an unbounded exponent range and in precision p; we also assume that the basic arithmetic operations (+, ?, ×, /) are rounded to nearest, so that the roundoff unit is u = 2^?p. We bound the largest relative error in the computed inverse either in the componentwise or in the normwise sense. We prove the componentwise relative error bound 3u for the complex inversion algorithm (assuming p ≥ 4), and we show that this bound is asymptotically optimal (as p → ∞) when p is even, and sharp when using one of the basic IEEE 754 binary formats with an odd precision (p = 53, 113). This componentwise bound obviously leads to the same bound 3u for the normwise relative error. However, we prove that the smaller bound 2.707131u holds (assuming p ≥ 24) for the normwise relative error, and we illustrate the sharpness of this bound for the basic IEEE 754 binary formats (p = 24,53,113) using numerical examples.