Prographes sylvestres et groupes profinis presque libres

In this article we want to give an analogous in the profinite case to the following theorem: an abstract group is free if and only if it acts freely on a tree. In a first time we define a combinatory object, the protrees, which are particular inductive systems extracted from projective systems of graphs. Then we define a notion of profinite action. These objects allow us to give the following analogous: a profinite group contains a dense abstract free subgroup if and only if it acts profreely on a protree.     

Clusters dissolution of Yb3+ in codoped SiO2-Al2O3-P2O5 glass fiber and its relevance to photodarkening

Using a combination of pulse electron paramagnetic resonance and photoluminescence spectroscopy, we demonstrate the major role of phosphorous rather than aluminium in the rare-earth dissolution process, an essential advance in telecommunication and solid laser fields. Our results also provide new insight into the micro-structural origin of the photodarkening process occurring in Yb doped fiber.     

Using conformationally locked nucleosides to calibrate the anomeric effect: Implications for glycosyl bond stability

Steric and electronic parameters, such as the anomeric effect (AE) and gauche effect play significant roles in steering the North⇆South equilibrium of nucleosides in solution.Two isomeric oxa-bicyclo[3.1.0]hexane nucleosides that are conformationally locked in either the North or the South conformation of the pseudorotational cycle were designed to study the consequences of having the AE operational or not, independent of other parameters. The rigidity of the system allowed the orientation of the orbitals involved to be set in ‘fixed’ relationships, either antiperiplanar where the AE is permanently ‘on’, or gauche where the AE is impaired. The consequences of these two alternatives were subjected to high-level calculations and measured experimentally by X-ray crystallography, hydrolytic stability of the glycosyl bond, and pK_a values.     

Ultrasonic transient bounded-beam propagation in a solid cylinder waveguide embedded in a solid medium

A semianalytical solution alternative and complementary to modal technique is presented to predict and interpret the ultrasonic pulsed-bounded-beam propagation in a solid cylinder embedded in a solid matrix. The spectral response to an inside axisymmetric velocity source of longitudinal and transversal cylindrical waves is derived from Debye series expansion of the embedded cylinder generalized cylindrical reflection/transmission coefficients. So, the transient guided wave response, synthesized by inverse double Fourier-Bessel transform, is expressed as a combination of the infinite medium contribution, longitudinal, transversal, and coupled longitudinal and transversal waveguide sidewall interactions. Simulated (f, 1/lambdaz) diagrams show the influence of the number of waveguide sidewall interactions to progressively recover dispersion curves. Besides, they show the embedding material filters specific signal portions by concentrating the propagating signal in regions where phase velocity is closer to phase velocity in steel. Then, simulated time waveforms using broadband high-frequency excitation show that signal leading portions exhibit a similar periodical pattern, for both free and embedded waveguides. Debye series-based interpretation shows that double longitudinal/transversal and transversal/longitudinal conversions govern the time waveform leading portion as well as the radiation attenuation in the surrounding cement grout. Finally, a methodology is deduced to minimize the radiation attenuation for the long-range inspection of embedded cylinders.     

Long-wavelength dispersion of acoustic waves in transversely inhomogeneous anisotropic plates

Long-wavelength onset of the fundamental branches is described for a free anisotropic plate with arbitrary through-plate variation of material properties. Main attention is given to the flexural branch. Closed-form expressions for the leading-order dispersion coefficient of the velocity and displacement are derived for a generic case and exemplified for the various types of either continuous, or discrete, or periodic inhomogeneity and for the monoclinic symmetry. The relevance of the static averaging is examined in detail. The bounds for the slope of the flexural velocity branch are established. The upper fundamental branches are considered for the case when these are uncoupled inplane and shear horizontal ones.     

Correlation between boson peak and anomalous elastic behavior in GeO2 glass: an in situ Raman scattering study under high-pressure

We present low-frequency Raman scattering of pure GeO(2) glass under pressure up to 4 GPa, corresponding to an elastic transformation. Intensity variation and frequency shift of the boson peak are analysed and compared to the Debye model. The decrease of the boson peak intensity scaled by the Debye energy is correlated to the elastic anomalous properties under pressure up to 1.5 GPa, and interpreted as an elastic homogenisation process at the local scale. We emphasize similarities between a-GeO(2) and a-SiO(2) behavior under pressure, and compare our results to other experiments, numerical studies, and predictions of several models concerning amorphous systems.     

Solution- and solid-state conformations of C(α)-alkyl analogues of methylphenidate (Ritalin) salts: avoidance of gauche(+)gauche(-) interactions

Alkyl analogues of methylphenidate (Ritalin) salts are slow onset, long duration dopamine reuptake inhibitors with a potential use as a cocaine abuse pharmacotherapy. X-ray crystallographic studies and nuclear magnetic resonance (NMR) investigations strongly suggest that avoidance of sterically unfavorable gauche(-)gauche(+) orientations effectively influences both the C(α)-alkyl side chain conformation and the formation of a predominant rotamer about the CH-CH bond ligating piperidine and C(Ar)R moieties. The favored CH-CH rotamer in D(2)O and in CD(2)Cl(2) of the pharmacologically interesting i-Bu and CH(2)-cyc-Pnt (RS,RS)-salts has the same antiperiplanar arrangement that was found in the crystal structures, although there clearly is a fast equilibrium involving smaller amounts of synclinal partners. While the rotamer in the (RS,SR)-i-Bu HCl crystal structure exhibits a synclinal orientation for the vicinal pair of adjacent methine protons, the weighted time-averaged arrangement for these protons becomes almost completely antiperiplanar when the crystals are dissolved in D(2)O. Increased steric congestion around the CH-CH bond in the analogous N-methyl tertiary ammonium salts seems to augment the quantity of the preferred rotamer within the mixture. The stereochemistry of the species observed via NMR seems to arise from specific combinations of N-methyl orientation and avoidance of sterically unfavorable gauche(-)gauche(+) arrangements.     

Analysis of the dispersion spectrum of fluid-loaded anisotropic plates: leaky-wave branches

The supersonic complex-velocity versus real-frequency dispersion spectrum of the leaky waves in fluid-loaded anisotropic plates is discussed. Utilizing the sextic plate formalism provides approximate solutions for leaky-wave velocity in a form that reveals their basic features, such as the unique correspondence of the signs of its imaginary part and of the free-plate group velocity, the relation between the leakage and the rate of frequency dispersion, and the principal trends at low, high and near-cutoff frequencies in arbitrary anisotropic plates. A particular thrust of the study is the derivation of closed-form asymptotics for the fundamental leaky-wave velocity branch(es) at low frequency and for the continuum of leaky-wave branches near the fluid-coupled and fluid-uncoupled thickness resonances. Conditions for the asymptotics accuracy are analysed, and a comparison between an analytical approximation and exact numerical curves is presented for various cases.