On eigenfunction approximations for typical non-self-adjoint Schroedinger operators

We construct efficient approximations for the eigenfunctions of non-self-adjoint Schroedinger operators in one dimension. The same ideas also apply to the study of resonances of self-adjoint Schroedinger operators which have dilation analytic potentials. In spite of the fact that such eigenfunctions can have surprisingly complicated structures with multiple local maxima, we show that a suitable adaptation of the JWKB method is able to provide accurate lobal approximations to them.Comment: 17 pages, 11 figure

La tuberculose extra-ganglionnaire de la sphere O.R.L.

La tuberculose extra ganglionnaire est une pathologie rare en ORL. Elle pourrait poser des problèmes diagnostiques surtout avec la pathologie tumorale. Nous rapportons 10 cas de localisations extra-ganglionnaires, colligés au service ORL de l\'hôpital Tahar Sfar de Mahdia entre 1988 et 2004. Il s\'agissait de 7 femmes et 3 hommes, âgés entre 19 et 77 ans (moyenne : 39 ans). La maladie a touché le cavum dans 3 cas, les glandes salivaires dans 3 cas, les amygdales palatines dans 2 cas et le larynx chez 2 patients. Le diagnostic était dans tous les cas histo-pathologique. Tous nos patients ont reçu un traitement anti-tuberculeux. L\'évolution était favorable avec un recul moyen de 11 mois. Conclusion : La tuberculose extra-ganglionnaire en ORL pose surtout des problèmes diagnostiques. Son diagnostic est le plus souvent histo-pathologique. Son traitement repose sur la himiothérapie anti-tuberculeuse. Extra-nodal tuberculosis is a rare in ENT practice. We report 10 cases of extra-ganglionic localizations of tuberculosis, treated in ENT department of the Tahar Sfar hospital of Mahdia between 1988 and 2004. They were 7 women and 3 men, aged between 19 and 77 years (average: 39 years) . The disease has touched the nasopharynx in 3 cases, the salivary glands in 3 cases, the tonsils in 2 cases and the larynx in 2 cases. The diagnosis was in all cases histo-pathological. All our patients received an anti-tubercular treatment. The evolution was favorable with 11 months average outcome. Conclusion: Extra-nodal tuberculosis in ENT poses especially diagnostic problems. Its treatment is based on anti-tubercular chemotherapy. Journal Tunisien d\'ORL et de chirurgie cervico-faciale Vol. 16 2006: pp. 36-3

On the Born-Oppenheimer approximation of diatomic molecular resonances

We give a new reduction of a general diatomic molecular Hamiltonian, without modifying it near the collision set of nuclei. The resulting effective Hamiltonian is the sum of a smooth semiclassical pseudodifferential operator (the semiclassical parameter being the inverse of the square-root of the nuclear mass), and a semibounded operator localised in the elliptic region corresponding to the nuclear collision set. We also study its behaviour on exponential weights, and give several applications where molecular resonances appear and can be well located.Comment: 22 page

Histiocytose langerhansienne multiviscerale avec atteinte auriculaire bilaterale a propos d’une observation

L’histiocytose langerhansienne multi-viscérale est une prolifération clonale des cellules de Langerhans, touchant plusieurs organes. Cette entité se voit surtout chez l’enfant. Dans ce travail, nous rappelons les aspects cliniques avec la fréquence d’atteinte oto-rhino-laryngologique, ainsi que les moyens de diagnostic et le traitement de cette affection rare. Nous présentons le cas d’un enfant âgé de 2 ans qui a été hospitalisé pour une pneumopathie interstitielle, associée à une otorrhée bilatérale. L’examen a montré un comblement des 2 conduits auditifs externes et des lésions cutanées squameuses. La biopsie a conclu à une histiocytose langerhansienne. Malgré la chimiothérapie, l’enfant est décédé après 11 mois.Mots-clés : Histiocytose langerhansienne, atteinte auriculaire

Electrocaloric effect in Ba(0.2)Ca(0.8)Ti(0.95)Ge(0.05)O(3) determined by a new pyroelectric method

The present letter explores the electrocaloric effect (ECE) in the lead free oxide Ba0.8Ca0.2Ti0.95Ge0.05O3 ceramics (BCTG). The electrocaloric responsivity (dT/dE) was determined by two different methods using the Maxwell relationship (dT/dE)~(dP/dT)_E. In a first well-known indirect method, P-E hysteresis loops were measured in a wide temperature range from which the pyroelectric coefficient p_E=(dP/dT)_E and thus (dT/dE) were determined by derivation of P(T,E) data. In the second novel method the pyroelectric coefficient p_E and consequently the electrocaloric responsivity was determined by direct measurements of the pyroelectric currents under different applied electric fields. Within the experimental error good agreement was obtained between two methods with an electrocaloric responsivity equal to 0.18 +/- 0.05 10-6 K.m.V-1 was obtained at about 410 KComment: 5 pages, 4 figure

Addressing the ‘whys’ of UK children’s YouTube use: a purposes approach

Despite the widespread use of YouTube by children, there has been limited research undertaken on the “why” questions of their use. Past theoretical approaches have framed these questions in terms of broader individual needs and their relation to media use, though this work has mainly focused on adults and adolescents. This article presents relevant findings from a mixed methods study of children’s (aged 0–16) uses of social media in the United Kingdom to consider instead the “purposes” of children’s YouTube use, drawing on: (1) an online family survey; (2) family case studies; (3) child focus groups; and (4) child telephone interviews. “Purpose” is theorized in the article in relation to the ways children themselves make sense of and articulate the reasons they use YouTube or, in the case of parents and carers, for allowing, facilitating, or encouraging their children to use YouTube. Parents tended to frame the purposes of children’s YouTube use more instrumentally, focusing on perceived educational benefits and their own convenience needs. While sharing a focus on instrumental purposes, children sometimes emphasized broader dimensions of purpose, with an increased focus on humor, sensory, and hedonic dimensions. Children’s responses also emphasized the autotelic nature of play. The study foregrounded the extent to which the purposes of others (such as commercial entities) are served by children’s YouTube use. Seven child-centered, parent-centered, and “other” purposes for children’s YouTube use are discussed: cognitive, corporeal, cultural, collaborative, creative, commercial, and convenience

Wigner's Dynamical Transition State Theory in Phase Space: Classical and Quantum

A quantum version of transition state theory based on a quantum normal form (QNF) expansion about a saddle-centre-...-centre equilibrium point is presented. A general algorithm is provided which allows one to explictly compute QNF to any desired order. This leads to an efficient procedure to compute quantum reaction rates and the associated Gamov-Siegert resonances. In the classical limit the QNF reduces to the classical normal form which leads to the recently developed phase space realisation of Wigner's transition state theory. It is shown that the phase space structures that govern the classical reaction d ynamicsform a skeleton for the quantum scattering and resonance wavefunctions which can also be computed from the QNF. Several examples are worked out explicitly to illustrate the efficiency of the procedure presented.Comment: 132 pages, 31 figures, corrected version, Nonlinearity, 21 (2008) R1-R11

Structure and dynamics of ring polymers: entanglement effects because of solution density and ring topology

The effects of entanglement in solutions and melts of unknotted ring polymers have been addressed by several theoretical and numerical studies. The system properties have been typically profiled as a function of ring contour length at fixed solution density. Here, we use a different approach to investigate numerically the equilibrium and kinetic properties of solutions of model ring polymers. Specifically, the ring contour length is maintained fixed, while the interplay of inter- and intra-chain entanglement is modulated by varying both solution density (from infinite dilution up to \approx 40 % volume occupancy) and ring topology (by considering unknotted and trefoil-knotted chains). The equilibrium metric properties of rings with either topology are found to be only weakly affected by the increase of solution density. Even at the highest density, the average ring size, shape anisotropy and length of the knotted region differ at most by 40% from those of isolated rings. Conversely, kinetics are strongly affected by the degree of inter-chain entanglement: for both unknots and trefoils the characteristic times of ring size relaxation, reorientation and diffusion change by one order of magnitude across the considered range of concentrations. Yet, significant topology-dependent differences in kinetics are observed only for very dilute solutions (much below the ring overlap threshold). For knotted rings, the slowest kinetic process is found to correspond to the diffusion of the knotted region along the ring backbone.Comment: 17 pages, 11 figure