Measure valued solutions of sub-linear diffusion equations with a drift term

In this paper we study nonnegative, measure valued solutions of the initial value problem for one-dimensional drift-diffusion equations when the nonlinear diffusion is governed by an increasing $C^1$ function $\beta$ with $\lim_{r\to +\infty} \beta(r)<+\infty$. By using tools of optimal transport, we will show that this kind of problems is well posed in the class of nonnegative Borel measures with finite mass $m$ and finite quadratic momentum and it is the gradient flow of a suitable entropy functional with respect to the so called $L^2$-Wasserstein distance. Due to the degeneracy of diffusion for large densities, concentration of masses can occur, whose support is transported by the drift. We shall show that the large-time behavior of solutions depends on a critical mass ${m}_{\rm c}$, which can be explicitely characterized in terms of $\beta$ and of the drift term. If the initial mass is less then ${m}_{\rm c}$, the entropy has a unique minimizer which is absolutely continuous with respect to the Lebesgue measure. Conversely, when the total mass $m$ of the solutions is greater than the critical one, the steady state has a singular part in which the exceeding mass ${m} - {m}_{\rm c}$ is accumulated.Comment: 30 page

Gradient estimates in parabolic problems with unbounded coefficients

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Full characterization of Gaussian bipartite entangled states by a single homodyne detector

We present the full experimental reconstruction of Gaussian entangled states generated by a type--II optical parametric oscillator (OPO) below threshold. Our scheme provides the entire covariance matrix using a single homodyne detector and allows for the complete characterization of bipartite Gaussian states, including the evaluation of purity, entanglement and nonclassical photon correlations, without a priori assumptions on the state under investigation. Our results show that single homodyne schemes are convenient and robust setups for the full characterization of OPO signals and represent a tool for quantum technology based on continuous variable entanglement.Comment: 4 pages, 3 figures, slightly longer version of published PR

Joint multi-baseline SAR interferometry

We propose a technique to provide interferometry by combining multiple images of the same area. This technique differs from the multi-baseline approach in literature as (a) it exploits all the images simultaneously, (b) it performs a spectral shift preprocessing to remove most of the decorrelation, and (c) it exploits distributed targets. The technique is mainly intended for DEM generation at centimetric accuracy, as well as for differential interferometry. The problem is framed in the contest of single-input multiple-output (SIMO) channel estimation via the cross-relations (CR) technique and the resulting algorithm provides significant improvements with respect to conventional approaches based either on independent analysis of single interferograms or multi-baselines phase analysis of single pixels of current literature, for those targets that are correlated in all the images, like for long-term coherent areas, or for acquisitions taken with a short revisit time (as those gathered with future satellite constellations)

Kernel estimates for nonautonomous Kolmogorov equations with potential term

Using time dependent Lyapunov functions, we prove pointwise upper bounds for the heat kernels of some nonautonomous Kolmogorov operators with possibly unbounded drift and diffusion coefficients and a possibly unbounded potential term

Divulgação do património geológico da ilha de Santa Maria

XIV Expedição Científica do Departamento de Biologia - Santa Maria 2009.As ilhas dos Açores apresentam uma grande variedade de rochas, formas, estruturas e paisagens, que derivam, entre outros factores, da natureza dos magmas, do tipo de vulcanismo, dos condicionalismos geotectónicos intrínsecos à sua génese e em especial do seu posicionamento no Atlântico Norte, na junção tripla das placas litosféricas Euroasiática, Norte Americana e Africana (ou Núbia). Das nove ilhas que constituem o Arquipélago dos Açores, Santa Maria é a ilha mais Oriental e Meridional do território insular. [...]. Santa Maria distingue-se das restantes ilhas açorianas pelas suas características edafo-climáticas, geológicas e morfológicas. A história geológica desta ilha traduz-se numa intensa actividade vulcânica, que terá feito emergir a mesma há cerca de 10 milhões de anos, alternada com períodos de acalmia, oscilações do nível do mar concomitantes e episódios de intensa erosão. Em consequência, a ilha, que contém as formações geológicas mais antigas do arquipélago, possui actualmente formas vulcânicas muito alteradas e índices de erosão superiores aos das outras ilhas do arquipélago, apresenta significativos afloramentos de rochas sedimentares com conteúdo fóssil abundante e diversificado e expõe abundantes afloramentos de lavas submarinas (Nunes et al., 2007). Em suma: a sua localização geográfica, clima, actividade vulcânica e oscilações do nível do mar que a afectaram contribuíram, indubitavelmente, para a sua evolução e a geodiversidade que evidencia

Adding 5-hydroxytryptamine receptor type 3 antagonists may reduce drug-induced nausea in poor insight obsessive-compulsive patients taking off-label doses of selective serotonin reuptake inhibitors: a 52-week follow-up case report

Poor-insight obsessive-compulsive disorder (PI-OCD) is a severe form of OCD where the 'typically obsessive' features of intrusive, 'egodystonic' feelings and thoughts are absent. PI-OCD is difficult to treat, often requiring very high doses of serotonergic drugs as well as antipsychotic augmentation. When this occurs, unpleasant side effects as nausea are common, eventually further reducing compliance to medication and increasing the need for pharmacological alternatives. We present the case of a PI-OCD patient who developed severe nausea after response to off-label doses of the selective serotonin reuptake inhibitor (SSRI), fluoxetine. Drug choices are discussed, providing pharmacodynamic rationales and hypotheses along with reports of rating scale scores, administered within a follow-up period of 52 weeks. A slight reduction of fluoxetine dose, augmentation with mirtazapine and a switch from amisulpride to olanzapine led to resolution of nausea while preserving the anti-OCD therapeutic effect. Mirtazapine and olanzapine have already been suggested for OCD treatment, although a lack of evidence exists about their role in the course of PI-OCD. Both mirtazapine and olanzapine also act as 5-hydroxytryptamine receptor type 3 (5-HT3) blockers, making them preferred choices especially in cases of drug-induced nausea

The combination of DInSAR and facility damage data for the updating of slow-moving landslide inventory maps at medium scale

Abstract. Testing innovative procedures and techniques to update landslide inventory maps is a timely topic widely discussed in the scientific literature. In this regard remote sensing techniques – such as the Synthetic Aperture Radar Differential Interferometry (DInSAR) – can provide a valuable contribution to studies concerning slow-moving landslides in different geological contexts all over the world. In this paper, DInSAR data are firstly analysed via an innovative approach aimed at enhancing both the exploitation and the interpretation of remote sensing information; then, they are complemented with the results of an accurate analysis of survey-recorded damage to facilities due to slow-moving landslides. In particular, after being separately analysed to provide independent landslide movement indicators, the two datasets are combined in a DInSAR-Damage matrix which can be used to update the state of activity of slow-moving landslides. Moreover, together with the information provided by geomorphological maps, the two datasets are proven to be useful in detecting unmapped phenomena. The potentialities of the adopted procedure are tested in an area of southern Italy where slow-moving landslides are widespread and accurately mapped by using geomorphological criteria