Approximation and support theorem for a wave equation in two space dimensions

We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an approximation theorem, in the convergence of probability, for equations obtained by smoothing the random noise. For some particular classes of coefficients, approximation in the Lp-norm for p¿1 is also proved.

Interaction of Spiral Waves in the Complex Ginzburg-Landau Equation

Solutions of the general cubic complex Ginzburg-Landau equation comprising multiple spiral waves are considered, and laws of motion for the centers are derived. The direction of the motion changes from along the line of centers to perpendicular to the line of centers as the separation increases, with the strength of the interaction algebraic at small separations and exponentially small at large separations. The corresponding asymptotic wave number and frequency are also determined, which evolve slowly as the spirals move

Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schr odinger equation in the non-commu- tative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schröodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.

Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schrödinger equation in the non-commu- tative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schröodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.

Ingénieur pédagogique et démarche projet : facteurs clés de succès pour l'intégration des technologies dans la pratique enseignante?

Résumé: Les gouvernements des pays occidentaux ont dépensé des sommes importantes pour faciliter l'intégration des technologies de l'information et de la communication dans l'enseignement espérant trouver une solution économique à l'épineuse équation que l'on pourrait résumer par la célèbre formule " faire plus et mieux avec moins ". Cependant force est de constater que, malgré ces efforts et la très nette amélioration de la qualité de service des infrastructures, cet objectif est loin d'être atteint. Si nous pensons qu'il est illusoire d'attendre et d'espérer que la technologie peut et va, à elle seule, résoudre les problèmes de qualité de l'enseignement, nous croyons néanmoins qu'elle peut contribuer à améliorer les conditions d'apprentissage et participer de la réflexion pédagogique que tout enseignant devrait conduire avant de dispenser ses enseignements. Dans cette optique, et convaincu que la formation à distance offre des avantages non négligeables à condition de penser " autrement " l'enseignement, nous nous sommes intéressé à la problématique du développement de ce type d'applications qui se situent à la frontière entre les sciences didactiques, les sciences cognitives, et l'informatique. Ainsi, et afin de proposer une solution réaliste et simple permettant de faciliter le développement, la mise-à-jour, l'insertion et la pérennisation des applications de formation à distance, nous nous sommes impliqué dans des projets concrets. Au fil de notre expérience de terrain nous avons fait le constat que (i)la qualité des modules de formation flexible et à distance reste encore très décevante, entre autres parce que la valeur ajoutée que peut apporter l'utilisation des technologies n'est, à notre avis, pas suffisamment exploitée et que (ii)pour réussir tout projet doit, outre le fait d'apporter une réponse utile à un besoin réel, être conduit efficacement avec le soutien d'un " champion ". Dans l'idée de proposer une démarche de gestion de projet adaptée aux besoins de la formation flexible et à distance, nous nous sommes tout d'abord penché sur les caractéristiques de ce type de projet. Nous avons ensuite analysé les méthodologies de projet existantes dans l'espoir de pouvoir utiliser l'une, l'autre ou un panachage adéquat de celles qui seraient les plus proches de nos besoins. Nous avons ensuite, de manière empirique et par itérations successives, défini une démarche pragmatique de gestion de projet et contribué à l'élaboration de fiches d'aide à la décision facilitant sa mise en oeuvre. Nous décrivons certains de ses acteurs en insistant particulièrement sur l'ingénieur pédagogique que nous considérons comme l'un des facteurs clé de succès de notre démarche et dont la vocation est de l'orchestrer. Enfin, nous avons validé a posteriori notre démarche en revenant sur le déroulement de quatre projets de FFD auxquels nous avons participé et qui sont représentatifs des projets que l'on peut rencontrer dans le milieu universitaire. En conclusion nous pensons que la mise en oeuvre de notre démarche, accompagnée de la mise à disposition de fiches d'aide à la décision informatisées, constitue un atout important et devrait permettre notamment de mesurer plus aisément les impacts réels des technologies (i) sur l'évolution de la pratique des enseignants, (ii) sur l'organisation et (iii) sur la qualité de l'enseignement. Notre démarche peut aussi servir de tremplin à la mise en place d'une démarche qualité propre à la FFD. D'autres recherches liées à la réelle flexibilisation des apprentissages et aux apports des technologies pour les apprenants pourront alors être conduites sur la base de métriques qui restent à définir. Abstract: Western countries have spent substantial amount of monies to facilitate the integration of the Information and Communication Technologies (ICT) into Education hoping to find a solution to the touchy equation that can be summarized by the famous statement "do more and better with less". Despite these efforts, and notwithstanding the real improvements due to the undeniable betterment of the infrastructure and of the quality of service, this goal is far from reached. Although we think it illusive to expect technology, all by itself, to solve our economical and educational problems, we firmly take the view that it can greatly contribute not only to ameliorate learning conditions but participate to rethinking the pedagogical approach as well. Every member of our community could hence take advantage of this opportunity to reflect upon his or her strategy. In this framework, and convinced that integrating ICT into education opens a number of very interesting avenues provided we think teaching "out of the box", we got ourself interested in courseware development positioned at the intersection of didactics and pedagogical sciences, cognitive sciences and computing. Hence, and hoping to bring a realistic and simple solution that could help develop, update, integrate and sustain courseware we got involved in concrete projects. As ze gained field experience we noticed that (i)The quality of courseware is still disappointing, amongst others, because the added value that the technology can bring is not made the most of, as it could or should be and (ii)A project requires, besides bringing a useful answer to a real problem, to be efficiently managed and be "championed". Having in mind to propose a pragmatic and practical project management approach we first looked into open and distance learning characteristics. We then analyzed existing methodologies in the hope of being able to utilize one or the other or a combination to best fit our needs. In an empiric manner and proceeding by successive iterations and refinements, we defined a simple methodology and contributed to build descriptive "cards" attached to each of its phases to help decision making. We describe the different actors involved in the process insisting specifically on the pedagogical engineer, viewed as an orchestra conductor, whom we consider to be critical to ensure the success of our approach. Last but not least, we have validated a posteriori our methodology by reviewing four of the projects we participated to and that we think emblematic of the university reality. We believe that the implementation of our methodology, along with the availability of computerized cards to help project managers to take decisions, could constitute a great asset and contribute to measure the technologies' real impacts on (i) the evolution of teaching practices (ii) the organization and (iii) the quality of pedagogical approaches. Our methodology could hence be of use to help put in place an open and distance learning quality assessment. Research on the impact of technologies to learning adaptability and flexibilization could rely on adequate metrics.

Increased risk of cardiovascular disease (CVD) with age in HIV-positive men : a comparison of the D:A:D CVD risk equation and general population CVD risk equations

OBJECTIVES: The aim of the study was to statistically model the relative increased risk of cardiovascular disease (CVD) per year older in Data collection on Adverse events of anti-HIV Drugs (D:A:D) and to compare this with the relative increased risk of CVD per year older in general population risk equations. METHODS: We analysed three endpoints: myocardial infarction (MI), coronary heart disease (CHD: MI or invasive coronary procedure) and CVD (CHD or stroke). We fitted a number of parametric age effects, adjusting for known risk factors and antiretroviral therapy (ART) use. The best-fitting age effect was determined using the Akaike information criterion. We compared the ageing effect from D:A:D with that from the general population risk equations: the Framingham Heart Study, CUORE and ASSIGN risk scores. RESULTS: A total of 24 323 men were included in analyses. Crude MI, CHD and CVD event rates per 1000 person-years increased from 2.29, 3.11 and 3.65 in those aged 40-45 years to 6.53, 11.91 and 15.89 in those aged 60-65 years, respectively. The best-fitting models included inverse age for MI and age + age(2) for CHD and CVD. In D:A:D there was a slowly accelerating increased risk of CHD and CVD per year older, which appeared to be only modest yet was consistently raised compared with the risk in the general population. The relative risk of MI with age was not different between D:A:D and the general population. CONCLUSIONS: We found only limited evidence of accelerating increased risk of CVD with age in D:A:D compared with the general population. The absolute risk of CVD associated with HIV infection remains uncertain.

Local thermodynamics and the generalized Gibbs-Duhem equation in systems with long-range interactions

The local thermodynamics of a system with long-range interactions in d dimensions is studied using the mean-field approximation. Long-range interactions are introduced through pair interaction potentials that decay as a power law in the interparticle distance. We compute the local entropy, Helmholtz free energy, and grand potential per particle in the microcanonical, canonical, and grand canonical ensembles, respectively. From the local entropy per particle we obtain the local equation of state of the system by using the condition of local thermodynamic equilibrium. This local equation of state has the form of the ideal gas equation of state, but with the density depending on the potential characterizing long-range interactions. By volume integration of the relation between the different thermodynamic potentials at the local level, we find the corresponding equation satisfied by the potentials at the global level. It is shown that the potential energy enters as a thermodynamic variable that modifies the global thermodynamic potentials. As a result, we find a generalized Gibbs-Duhem equation that relates the potential energy to the temperature, pressure, and chemical potential. For the marginal case where the power of the decaying interaction potential is equal to the dimension of the space, the usual Gibbs-Duhem equation is recovered. As examples of the application of this equation, we consider spatially uniform interaction potentials and the self-gravitating gas. We also point out a close relationship with the thermodynamics of small systems.

Effective Electrodiffusion equation for non uniform nanochannels

We derive a one dimensional formulation of the Planck-Nernst-Poisson equation to describe the dynamics of of a symmetric binary electrolyte in channels whose section is of nanometric section and varies along the axial direction. The approach is in the spirit of the Fick-Jacobs di fusion equation and leads to a system of coupled equations for the partial densities which depends on the charge sitting at the walls in a non trivial fashion. We consider two kinds of non uniformities, those due to the spatial variation of charge distribution and those due to the shape variation of the pore and report one and three-dimensional solutions of the electrokinetic equations.

Predicting overall service quality: a structural equation modelling approach

In this article, the results of a modified SERVQUAL questionnaire (Parasuraman et al., 1991) are reported. The modifications consisted in substituting questionnaire items particularly suited to a specific service (banking) and context (county of Girona, Spain) for the original rather general and abstract items. These modifications led to more interpretable factors which accounted for a higher percentage of item variance. The data were submitted to various structural equation models which made it possible to conclude that the questionnaire contains items with a high measurement quality with respect to five identified dimensions of service quality which differ from those specified by Parasuraman et al. And are specific to the banking service. The two dimensions relating to the behaviour of employees have the greatest predictive power on overall quality and satisfaction ratings, which enables managers to use a low-cost reduced version of the questionnaire to monitor quality on a regular basis. It was also found that satisfaction and overall quality were perfectly correlated thus showing that customers do not perceive these concepts as being distinct

Foam-forming properties of Ilex paraguariensis (mate) saponin: foamability and foam lifetime analysis by Weibull equation

Saponins are natural soaplike foam-forming compounds widely used in foods, cosmetic and pharmaceutical preparations. In this work foamability and foam lifetime of foams obtained from Ilex paraguariensis unripe fruits were analyzed. Polysorbate 80 and sodium dodecyl sulfate were used as reference surfactants. Aiming a better data understanding a linearized 4-parameters Weibull function was proposed. The mate hydroethanolic extract (ME) and a mate saponin enriched fraction (MSF) afforded foamability and foam lifetime comparable to the synthetic surfactants. The linearization of the Weibull equation allowed the statistical comparison of foam decay curves, improving former mathematical approaches.

Solving Schrödinger equation for two dimensional potentials using supersymmetry

The formalism of supersymmetric Quantum Mechanics can be extended to arbitrary dimensions. We introduce this formalism and explore its utility to solve the Schrödinger equation for a bidimensinal potential. This potential can be applied in several systems in physical and chemistry context , for instance, it can be used to study benzene molecule.

Mathematical equation correction to spectral and transport interferences in high-resolution continuum source flame atomic absorption spectrometry: determination of lead in phosphoric acid

In this work, a new mathematical equation correction approach for overcoming spectral and transport interferences was proposed. The proposal was applied to eliminate spectral interference caused by PO molecules at the 217.0005 nm Pb line, and the transport interference caused by variations in phosphoric acid concentrations. Correction may be necessary at 217.0005 nm to account for the contribution of PO, since Atotal217.0005 nm = A Pb217.0005 nm + A PO217.0005 nm. This may be easily done by measuring other PO wavelengths (e.g. 217.0458 nm) and calculating the relative contribution of PO absorbance (A PO) to the total absorbance (Atotal) at 217.0005 nm: A Pb217.0005 nm = Atotal217.0005 nm - A PO217.0005 nm = Atotal217.0005 nm - k (A PO217.0458 nm). The correction factor k is calculated from slopes of calibration curves built up for phosphorous (P) standard solutions measured at 217.0005 and 217.0458 nm, i.e. k = (slope217.0005 nm/slope217.0458 nm). For wavelength integrated absorbance of 3 pixels, sample aspiration rate of 5.0 ml min-1, analytical curves in the 0.1 - 1.0 mg L-1 Pb range with linearity better than 0.9990 were consistently obtained. Calibration curves for P at 217.0005 and 217.0458 nm with linearity better than 0.998 were obtained. Relative standard deviations (RSD) of measurements (n = 12) in the range of 1.4 - 4.3% and 2.0 - 6.0% without and with mathematical equation correction approach were obtained respectively. The limit of detection calculated to analytical line at 217.0005 nm was 10 µg L-1 Pb. Recoveries for Pb spikes were in the 97.5 - 100% and 105 - 230% intervals with and without mathematical equation correction approach, respectively.