Dispersive estimates and NLS on product manifolds

We prove a general dispersive estimate for a Schroedinger type equation on a product manifold, under the assumption that the equation restricted to each factor satisfies suitable dispersive estimates. Among the applications are the two-particle Schroedinger equations on Euclidean spaces, and the nonlinear Schroedinger equation on the product of two real hyperbolic spaces

The wave equation on hyperbolic spaces

In this paper, we study the dispersive properties of the wave equation associated with the shifted Laplace-Beltrami operator on real hyperbolic spaces, and deduce Strichartz estimates for a large family of admissible pairs. As an application, we obtain local well-posedness results for the nonlinear wave equation

Nonlinear Schrödinger equation on four-dimensional compact manifolds

International audienc

Italy's image as a tourism destination in the Chinese leisure travel market.

This study aims to measure the image of Italy as a tourism destination on the Chinese leisure traveller market. To this end, Echtner & Ritchie’s model (1991) is applied; however, compared to its original formulation, it is implemented with greater consideration of the experiential dimension and potential travel constraints affecting the perception of the range of tourism goods and services on offer. This enables not just a denotative, but also and above all a connotative measurement of the image, thereby reducing the risk of ambiguity in the interpretation of the most significant attributes that emerged during the analysis. Adopting a hypothetical segmentation of the market in question, it was also possible to the elements that act as encouraging and discouraging factors regarding a holiday in Italy are highlight, identifying tailor-made approaches to the construction and promotion/commercialisation of tourism products designed to be attractive to the specific segment of interest

Nonlinear Schr\"odinger equation on real hyperbolic spaces

We consider the Schr\"odinger equation with no radial assumption on real hyperbolic spaces. We obtain sharp dispersive and Strichartz estimates for a large family of admissible pairs. As a first consequence, we get strong well-posedness results for NLS. Specifically, for small intial data, we prove $L^2$ and $H^1$ global well-posedness for any subcritical nonlinearity (in contrast with the Euclidean case) and with no gauge invariance assumption on the nonlinearity $F$. On the other hand, if $F$ is gauge invariant, $L^2$ charge is conserved and hence, as in the Euclidean case, it is possible to extend local $L^2$ solutions to global ones. The corresponding argument in $H^1$ requires the conservation of energy, which holds under the stronger condition that $F$ is defocusing. Recall that global well-posedness in the gauge invariant case was already proved by Banica, Carles & Staffilani, for small radial $L^2$ data and for large radial $H^1$ data. The second important application of our global Strichartz estimates is "scattering" for NLS both in $L^2$ and in $H^1$, with no radial or gauge invariance assumption. Notice that, in the Euclidean case, this is only possible for the critical power $\gamma=1+\frac4n$ and can be false for subcritical powers while, on hyperbolic spaces, global existence and scattering of small $L^2$ solutions holds for all powers $1<\gamma\le1+\frac4n$. If we restrict to defocusing nonlinearities $F$, we can extend the $H^1$ scattering results of Banica, Carles & Staffilani to the nonradial case. Also there is no distinction anymore between short range and long range nonlinearity : the geometry of hyperbolic spaces makes every power-like nonlinearity short range.Comment: Version 1 : 18 January 2008. Version 2 : 29 February 200

Crista terminalis bridge: a rare variant mimicking right atrial mass

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Ultrasound-Guided Microinjection into the Mouse Forebrain In Utero at E9.5

In utero survival surgery in mice permits the molecular manipulation of gene expression during development. However, because the uterine wall is opaque during early embryogenesis, the ability to target specific parts of the embryo for microinjection is greatly limited. Fortunately, high-frequency ultrasound imaging permits the generation of images that can be used in real time to guide a microinjection needle into the embryonic region of interest. Here we describe the use of such imaging to guide the injection of retroviral vectors into the ventricular system of the mouse forebrain at embryonic day (E) 9.5. This method uses a laparotomy to permit access to the uterine horns, and a specially designed plate that permits host embryos to be bathed in saline while they are imaged and injected. Successful surgeries often result in most or all of the injected embryos surviving to any subsequent time point of interest (embryonically or postnatally). The principles described here can be used with slight modifications to perform injections into the amnionic fluid of E8.5 embryos (thereby permitting infection along the anterior posterior extent of the neural tube, which has not yet closed), or into the ventricular system of the brain at E10.5/11.5. Furthermore, at mid-neurogenic ages (~E13.5), ultrasound imaging can be used direct injection into specific brain regions for viral infection or cell transplantation. The use of ultrasound imaging to guide in utero injections in mice is a very powerful technique that permits the molecular and cellular manipulation of mouse embryos in ways that would otherwise be exceptionally difficult if not impossible

Wine Experiences: A Review from a Multisensory Perspective

The existing multisensory literature suggests that the combination of the different human senses in a controlled fashion during food/drink experiences can provide more enjoyment to consumers. The present research reviews recent literature relating multisensory perception with wine experiences, focusing on the interaction of the five basic senses (taste, smell, vision, touch, and sound). This is mostly being assessed from a perceptual and behavioral consumer perspective. Here, the authors report different ways in which such interactions across these senses can affect the way a wine is experienced, prior to, during, and even after tasting. The authors finish this literature review by providing some insights in the context of wine and food pairing, while also generally reflecting on potential future work. These insights may be inspirational for a diverse group of organizations working with wine. Based on such multisensory approaches, it may be possible to bring unforeseen sensations to the different wine experiences, while at the same time stressing particular sensory and/or emotional attributes