On the Łojasiewicz numbers

Let f be a holomorphic function of two complex variables with an isolated critical point at $\text{0∈}\text{C}{}^2$. We give some necessary conditions for a rational number to be the smallest θ>0 in the ?ojasiewicz inequality |gradf(z)|?C|z|^θ for z near $\text{0∈}\text{C}{}^2$. To cite this article: E. Garc??a Barroso, A. P?oski, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Interacting electrons on a two-dimensional surface: planar vs. spherical geometries

The center-of-mass excitations are identified in the spectrum of electrons on a two-dimensional surface in the lowest Landau level. The correspondence between the quantum numbers labeling electron states on a sphere and on a plane is drawn. The excitation spectrum on a sphere with increasing radius is shown to converge to that on a plane. In particular, in the presence of a lateral confinement (i.e. for the case of quantum dots), identical series of magic states appear in both cases. Also, a class of interaction potentials which lead to the fractional quantum Hall effect in an extended system are identified.     

X-ray residual stress measurement on mechanical components with high curvature

In this paper we deal with the definition of an appropriate X-ray diffraction procedure for residual stress determination on samples with high curvature radius. We choose as the application high-strength hot worked coil springs for car suspensions (wire diameterd=12 mm). Different methods of X-ray measurement area limitation are compared, taking into account the measurement errors, for the determination of stress in one and in three directions. After the identification of the irradiated area limits for plane samples, further limits are identified due to the sample curvature (torsion bar). We describe loading devices purposely designed, constructed and calibrated. In each case, the sample is loaded so that the stress state is determined at the same time both by strain gages and by X-ray measurement.     

Whirl and critical speeds of flywheel-container systems aboard vehicles

Summary Container-flywheel systems for road vehicles can be mounted in a variety of ways on the vehicle's body, thus allowing large or small displacements. In the case of steady precession kinematic conditions are here obtained for both large and small displacements. Dynamic analysis in the small displacement case is then tested against a complete nonlinear simulation model, previously used for studies on flywheel bus dynamics. Whirling and critical speeds are obtained and discussed.

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Sommario I sistemi contenitore-volano possono essere montati sui veicoli terrestri in vari modi, tali da permettere spostamenti relativi al veicolo più o meno grandi.Nel presente lavoro viene studiata la cinematica del moto precessionale uniforme, nel caso sia di grandi sia di piccoli spostamenti.Nel caso di piccoli spostamenti si ottiene una soluzione analitica per la dinamica precessionale del sistema; viene approfondito il caso della precessione sincrona concorde con la rotazione del volano, detta «velocità critica».La soluziòne analitica è verificata per confronto con la soluzione numerica effettuata mediante un modello non lineare a sei gradi di libertà.

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A Functional Role for Aβ in Metal Homeostasis? N‐Truncation and High‐Affinity Copper Binding

Accumulation of the β‐amyloid (Aβ) peptide in extracellular senile plaques rich in copper and zinc is a defining pathological feature of Alzheimer′s disease (AD). The Aβ1–x (x=16/28/40/42) peptides have been the primary focus of Cu^II binding studies for more than 15 years; however, the N‐truncated Aβ4–42 peptide is a major Aβ isoform detected in both healthy and diseased brains, and it contains a novel N‐terminal FRH sequence. Proteins with His at the third position are known to bind Cu^II avidly, with conditional log K values at pH 7.4 in the range of 11.0–14.6, which is much higher than that determined for Aβ1–x peptides. By using Aβ4–16 as a model, it was demonstrated that its FRH sequence stoichiometrically binds Cu^II with a conditional K_d value of 3×10^?14 M at pH 7.4, and that both Aβ4–16 and Aβ4–42 possess negligible redox activity. Combined with the predominance of Aβ4–42 in the brain, our results suggest a physiological role for this isoform in metal homeostasis within the central nervous system.     

Carbon and secondary deuterium kinetic isotope effects on SN2 methyl transfer reactions

Carbon and secondary deuterium kinetic isotope effect (KIE) for three types of S_N2 methyl transfer reactions have been predicted theoretically at a DFT level in gas phase and in aqueous solution modelled by the PCM continuum solvent model. No correlation between these isotope effects and geometrical features of the corresponding transition states (TSs), force constants of the imaginary frequency or Gibbs free energies of the studied reactions has been found. These findings suggest that comparative analysis of the magnitudes of the studied KIEs should be constrained to interpretation of the TS localization on the reaction coordinate only in a series of very closely related reactions. Copyright © 2007 John Wiley & Sons, Ltd.     

Stereoselective Synthesis of [Rp]-Dinucleoside (3′,5′)-Methanephosphonates

Abstract

DBU-assisted phosphonylating properties of diastereomerically pure 5′-O-DMT- thymidine (O-2,4,6-trimetylbenzoyl methanephosphonothiate)(1) towards alcohols [1] have been used for the synthesis of [Rp]-dithymidylyl(3′,5′)-methanephosphonothiótes (2) and metanephosphonates (3). Substrates (4) and (5) have been obtained according to the previously described methods [2].     

Spectroscopic Studies of Intramolecular Proton Transfer in 2-(4-Fluorophenylamino)-5-(2,4-Dihydroxybenzeno)-1,3,4-Thiadiazole

Spectroscopic studies of the biologically active compound 2-(4-fluorophenylamino)-5-(2,4-dihydroxybenzeno)-1,3,4-thiadiazole (FABT), have been performed. Absorption studies in the UV-Vis region for FABT in polar solvents, like water or ethanol, exhibit the domination of the enol form over its keto counterpart, with a broad absorption band centered around 340 nm. In non-polar solvents such as n-heptane or heavier alkanes the 340 nm absorption band disappears and an increase of the band related to the keto form (approximately 270 nm) is observed. Fluorescence spectra (with 270 nm and 340 nm excitation energies used) show a similar dependence: for FABT in 2-propanol a peak at about 400 nm dominates over that at 330 nm while in n-heptane this relation is reversed. The solvent dependent equilibrium between the keto and enol forms is further confirmed by FTIR and Raman spectroscopies. As can be expected, this equilibrium also shows some temperature dependences. We note that the changes between the two tautomeric forms of FABT are not related to the permanent dipole moment of the solvent but rather to its dipole polarizability.