Stable standing waves for a class of nonlinear Schroedinger-Poisson equations

We prove the existence of orbitally stable standing waves with prescribed $L^2$-norm for the following Schr\"odinger-Poisson type equation \label{intro} %{%{ll} i\psi_{t}+ \Delta \psi - (|x|^{-1}*|\psi|^{2}) \psi+|\psi|^{p-2}\psi=0 \text{in} \R^{3}, %-\Delta\phi= |\psi|^{2}& \text{in} \R^{3},%. when $p\in \{8/3\}\cup (3,10/3)$. In the case $3<p<10/3$ we prove the existence and stability only for sufficiently large $L^2$-norm. In case $p=8/3$ our approach recovers the result of Sanchez and Soler \cite{SS} %concerning the existence and stability for sufficiently small charges. The main point is the analysis of the compactness of minimizing sequences for the related constrained minimization problem. In a final section a further application to the Schr\"odinger equation involving the biharmonic operator is given

Mapping Cortical Degeneration in ALS with Magnetization Transfer Ratio and Voxel-Based Morphometry

Pathological and imaging data indicate that amyotrophic lateral sclerosis (ALS) is a multisystem disease involving several cerebral cortical areas. Advanced quantitative magnetic resonance imaging (MRI) techniques enable to explore in vivo the volume and microstructure of the cerebral cortex in ALS. We studied with a combined voxel-based morphometry (VBM) and magnetization transfer (MT) imaging approach the capability of MRI to identify the cortical areas affected by neurodegeneration in ALS patients. Eighteen ALS patients and 18 age-matched healthy controls were examined on a 1.5T scanner using a high-resolution 3D T1 weighted spoiled gradient recalled sequence with and without MT saturation pulse. A voxel-based analysis (VBA) was adopted in order to automatically compute the regional atrophy and MT ratio (MTr) changes of the entire cerebral cortex. By using a multimodal image analysis MTr was adjusted for local gray matter (GM) atrophy to investigate if MTr changes can be independent of atrophy of the cerebral cortex. VBA revealed several clusters of combined GM atrophy and MTr decrease in motor-related areas and extra-motor frontotemporal cortex. The multimodal image analysis identified areas of isolated MTr decrease in premotor and extra-motor frontotemporal areas. VBM and MTr are capable to detect the distribution of neurodegenerative alterations in the cortical GM of ALS patients, supporting the hypothesis of a multi-systemic involvement in ALS. MT imaging changes exist beyond volume loss in frontotemporal cortices

Study of shape coexistence in the 188Hg isotope

Shape coexistence is a striking phenomenon that has attracted a large community and has been evidenced in many nuclear species where structures belonging to different deformations are observed coexisting within a typical energy range of nuclear excitation. Along the Z=80 isotopic chain, the 188Hg nucleus is the border-line where the presence of this phenomenon is foreseen but has not been confirmed yet. For this reason, this nucleus has been studied in a two-steps experiment performed at the Laboratori Nazionali di Legnaro in order to measure the lifetimes of the low-lying states of the 188Hg