Short-range order and F ion diffusion inside the Pb1 − xAlxF2 + x solid solution Part II: Al NMR investigation and proposal of clustering process

A ²⁷Al nuclear magnetic resonance (NMR) investigation at room temperature of the Pb_{1 − x}Al_xF_{2 + x} (0 ≤ x ≤ 0.12) solid solution and of the ordered Pb₉Al₂F₂₄ phase is carried out. Two different types of aluminium ions are identified and their ratio is determined as a function of x. A clustering process based on the formation of column clusters, more and more extended when x increases, is proposed on the basis of results issued from the ¹⁹F (Part I) and ²⁷Al NMR investigations.     

On the relation between protonium level shifts and nucleon-antinucleon scattering amplitudes

We study the Coulomb and threshold corrections to the low-energy scattering parameters for the proton-antiproton system, with numerical examples based on current optical models. Some commonly used expressions are shown to be inconsistent with our results. We check that the Trueman formula is valid for the level shifts of protonium, provided one takes properly into account the Coulomb corrections to the scattering lengths and volumes.     

Cohomologie des groupes et corps d'invariants multiplieatifs

Sans résumé     

Vowel Intelligibility in Classical Singing

Vowel intelligibility during singing is an important aspect of communication during performance. The intelligibility of isolated vowels sung by Western classically trained singers has been found to be relatively low, in fact, decreasing as pitch rises, and it is lower for women than for men. The lack of contextual cues significantly deteriorates vowel intelligibility. It was postulated in this study that the reduced intelligibility of isolated sung vowels may be partly from the vowels used by the singers in their daily vocalises. More specifically, if classically trained singers sang only a few American English vowels during their vocalises, their intelligibility for American English vowels would be less than for those classically trained singers who usually vocalize on most American English vowels. In this study, there were 21 subjects (15 women, 6 men), all Western classically trained performers as well as teachers of classical singing. They sang 11 words containing 11 different American English vowels, singing on two pitches a musical fifth apart. Subjects were divided into two groups, those who normally vocalize on 4, 5, or 6 vowels, and those who sing all 11 vowels during their daily vocalises. The sung words were cropped to isolate the vowels, and listening tapes were created. Two listening groups, four singing teachers and five speech-language pathologists, were asked to identify the vowels intended by the singers. Results suggest that singing fewer vowels during daily vocalises does not decrease intelligibility compared with singing the 11 American English vowels. Also, in general, vowel intelligibility was lower with the higher pitch, and vowels sung by the women were less intelligible than those sung by the men. Identification accuracy was about the same for the singing teacher listeners and the speech-language pathologist listeners except for the lower pitch, where the singing teachers were more accurate.     

Convex Sobolev inequalities and spectral gap

This Note is devoted to the proof of convex Sobolev (or generalized Poincaré) inequalities which interpolate between spectral gap (or Poincaré) inequalities and logarithmic Sobolev inequalities. We extend to the whole family of convex Sobolev inequalities results which have recently been obtained by Cattiaux, and Carlen and Loss for logarithmic Sobolev inequalities. Under local conditions on the density of the measure with respect to a reference measure, we prove that spectral gap inequalities imply all convex Sobolev inequalities including in the limit case corresponding to the logarithmic Sobolev inequalities. To cite this article: J.-P. Bartier, J. Dolbeault, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Convergence in probability for perturbed stochastic integral equations

Summary In this work, one considers two stochastic integral equations indexed by some parameter and one studies the contiguity of their solutions when the parameter converges to some ₀. Two types of behaviour are described; they lead to the notion of regular and singular perturbations. The method which is used also enables a study of the rate of convergence. Applications to time discretization of equations are given.     

Stabilizing an uncertain production system

Consider a production system that consists ofm machines each of which can produce parts ofn types. When machinek is used, it produces a part of typei with probabilityp _ki . Requests arrive for parts, one at a time. With probability _i an arriving request is for a part of typei. The requests must be served without waiting. Thus, if a requested part is not available, it must be produced. We find necessary and sufficient conditions for the existence of a strategy (a choice of the machines to be used) which makes the inventory of parts stable and we provide such a strategy.Two variations of this model are also considered: the case of batch arrivals of requests, and that of a system where the requests can be queued.