Proof of a conjecture by Gazeau et al. using the Gould Hopper polynomials

We prove the "strong conjecture" expressed by Gazeau et al. in arXiv:1203.3936v1 [math-ph] about the coefficients of the Taylor expansion of the exponential of a polynomial. This implies the "weak conjecture" as a special case. The proof relies mainly about properties of the Gould-Hopper polynomials

Biodiversité et gestion des systèmes aquatiques continentaux

La biodiversité des eaux continentales se caractérise par une forte endémicité de nombreuses espèces résultant de la nature insulaire des milieux. Alors qu'elles n'occupent que 1-2 % des terres émergées une proportion importante de vertébrés (environ 1/3) vit dans les eaux continentales ou en dépendent étroitement pour réaliser leur cycle biologique. Certains systèmes aquatiques, comme les lacs dits anciens, sont de véritables laboratoires naturels pour étudier l'évolution, et il faut protéger ce patrimoine.Les recherches sur l'origine et la dynamique de la biodiversité aquatique (inventaire, phylogénie, biogéographie) doivent se poursuivre, notamment pour les milieux tropicaux encore mal connus. Les relations fonctionnelles entre les espèces et les écosystèmes constituent un nouveau centre d'intérêt qui nécessite à la fois de revisiter les résultats déjà obtenus, de mettre en place des recherches spécifiques, et de développer des approches expérimentales. Quelles relations existent-ils entre la biodiversité et la stabilité ou la productivité des écosystèmes par exemple ?La biodiversité est un médiateur entre les systèmes écologiques et les systèmes sociaux dont la conservation s'inscrit dans la problématique du développement durable. La valorisation économique de la biodiversité pose de nouvelles questions à l'économie de l'environnement malgré les difficultés méthodologiques rencontrées. Les questions qui intéressent les gestionnaires portent principalement sur l'état de santé des écosystèmes et les moyens de la caractériser (indicateurs biologiques par exemple). La gestion durable des ressources vivantes, et une meilleure évaluation des conséquences des introductions d'espèces (biomanipulations) constituent également des objectifs finalisés auxquels les recherches dans le domaine de la biodiversité aquatique se doivent d'apporter des éléments de réponse.As a result of their island-like nature, inland waters are usually characterised by a high level of endemicity for several animal groups. This patchy distribution also results in great genetic variability between populations. While inland waters occupy only 1-2 % of emerged lands an unusual high proportion of vertebrates (around 1/3) inhabits or is strongly dependant on inland waters to complete their biological cycle. This remarkable concentration of vertebrate biodiversity is also extremely vulnerable, given that inland water aquatic resources world-wide have undergone severe deterioration.The fragility of inland water ecosystems and their species has been recognised all over the world. These resources have been exposed to a variety of increasing pressures such as water extraction for domestic, agricultural and industrial uses, pollution (organic and inorganic), fishing, introduction of exotic species, habitat alterations in relation to water management, etc. These stressors to the inland water environments have affected, and will continue to affect life in all inland water ecosystems. One of the major causes of change in biodiversity has been, and most likely will continue to be long-term, climate change.More knowledge is needed about the identification of species, how biological diversity is distributed, and what the trends observed on the short- to long-term biodiversity changes are.In many tropical countries there are lakes and rivers lacking even the most basic research on fauna and flora. Pertinent information on biological diversity in most developing countries, when it exists, is too sparse or scattered to be of practical use. Therefore, efforts should be devoted to the development of computer data bases and information networks for the collection and storage of information dealing with the identification and distribution of freshwater biodiversity. Development of these systems would benefit from the expertise and collaboration of taxonomists all over the world.From the perspective of sustainable development, multiple-use management of aquatic ecosystems can provide the framework for achieving long-term sustainability of resources and for maintaining biodiversity. The future of biodiversity is closely linked to the management options at the watershed scale and a key issue is to promote an integrated basin management approach of aquatic. However, a wise management of aquatic systems and the conservation of their biodiversity requires not only technical inputs, but also a good knowledge of social and economic issues. Valuation is a fundamental step in informing planners and resource managers about the economic importance of biodiversity in national development objectives, and to demonstrate the importance of different areas for the biological resources they contain. Research programs have also to be intensified on the complex relationships between biodiversity and aquatic ecosystems functioning which are still poorly understood. Some major ecological issues have been identified : how is system stability and resilience affected by species diversity, and to what extent could the integrity and sustainability of ecosystems be maintained in spite of species deletions resulting from degradation of environmental conditions ? The relationship of species richness to such processes as biological productivity is still an open question.The key to successful monitoring programs is to maintain the ability to detect general changes in the status of biodiversity and to identify tools that are adequate and appropriate for assessing the effectiveness of measures taken for the conservation of biodiversity through the sustainable use of aquatic systems. A variety of indicators of biological diversity in aquatic systems have been developed and may be employed. The precautionary principle, as adopted for fisheries by FAO, emphasises growing awareness that fisheries management cannot be seen in isolation and must fit an integrated context which satisfies the requirement both for long-term resource sustainability and environmental conservation.An understanding of the effects of invading exotic organisms on freshwater systems should receive high priority in regard to their documented consequences on native biodiversity in ecosystems where they have been introduced. The knowledge required relates primarily to predictable effects of introduced species

Production of positronium chloride: A study of the charge exchange reaction between Ps and Cl−^{-}

We present cross sections for the formation of positronium chloride (PsCl) in its ground state from the charge exchange between positronium (Ps) and chloride (Cl$^-$) in the range of 10 meV - 100 eV Ps energy. We have used theoretical models based on the first Born approximation in its three-body formulation. We simulated the collisions between Ps and Cl$^-$ using ab-initio methods at both mean-field and correlated levels extrapolated to the complete basis set limit. We have investigated Ps excited states up to ${n=4}$. The results suggest that the channel Ps(${n=2}$) is of particular interest for the production of PsCl in the ground state, and shows that an accurate treatment of the electronic correlation leads to a significant change in the global shape of the PsCl production cross section with respect to the mean-field level.Comment: 13 Pages, 7 Figures, 3 Table

Detection of the tagged or untagged photons in acousto-optic imaging of thick highly scattering media by photorefractive adaptive holography

We propose an original adaptive wavefront holographic setup based on the photorefractive effect (PR), to make real-time measurements of acousto-optic signals in thick scattering media, with a high flux collection at high rates for breast tumor detection. We describe here our present state of art and understanding on the problem of breast imaging with PR detection of the acousto-optic signal

Numerical studies towards practical large-eddy simulation

Large-eddy simulation developments and validations are presented for an improved simulation of turbulent internal flows. Numerical methods are proposed according to two competing criteria: numerical qualities (precision and spectral characteristics), and adaptability to complex configurations. First, methods are tested on academic test-cases, in order to abridge with fundamental studies. Consistent results are obtained using adaptable finite volume method, with higher order advection fluxes, implicit grid filtering and "low-cost" shear-improved Smagorinsky model. This analysis particularly focuses on mean flow, fluctuations, two-point correlations and spectra. Moreover, it is shown that exponential averaging is a promising tool for LES implementation in complex geometry with deterministic unsteadiness. Finally, adaptability of the method is demonstrated by application to a configuration representative of blade-tip clearance flow in a turbomachine

Convergence of the Generalized Volume Averaging Method on a Convection-Diffusion Problem: A Spectral Perspective

A mixed formulation is proposed and analyzed mathematically for coupled convection-diffusion in heterogeneous medias. Transfer in solid parts driven by pure diffusion is coupled with convection-diffusion transfer in fluid parts. This study is carried out for translation-invariant geometries (general infinite cylinders) and unidirectional flows. This formulation brings to the fore a new convection-diffusion operator, the properties of which are mathematically studied: its symmetry is first shown using a suitable scalar product. It is proved to be self-adjoint with compact resolvent on a simple Hilbert space. Its spectrum is characterized as being composed of a double set of eigenvalues: one converging towards −∞ and the other towards +∞, thus resulting in a nonsectorial operator. The decomposition of the convection-diffusion problem into a generalized eigenvalue problem permits the reduction of the original three-dimensional problem into a two-dimensional one. Despite the operator being nonsectorial, a complete solution on the infinite cylinder, associated to a step change of the wall temperature at the origin, is exhibited with the help of the operator’s two sets of eigenvalues/eigenfunctions. On the computational point of view, a mixed variational formulation is naturally associated to the eigenvalue problem. Numerical illustrations are provided for axisymmetrical situations, the convergence of which is found to be consistent with the numerical discretization