ALMOST SURE POINTWISE CONVERGENCE OF THE CUBIC NONLINEAR SCHRODINGER EQUATION ON ̈ T 2

We revisit a result from “Pointwise convergence of the Schr ̈odinger flow, E. Compaan, R. Luc`a, G. Staffilani, International Mathematics Research Notices, 2021 (1), 596-647” regarding the pointwise convergence of solutions to the periodic cubic nonlinear Schr ̈odinger equation in dimension d = 2

Invariant measures for the dnls equation

We describe invariant measures associated to the integrals of motion of the periodic derivative nonlinear Schr\"odinger equation (DNLS) constructed in \cite{MR3518561, Genovese2018}. The construction works for small $L^2$ data. The measures are absolutely continuous with respect to suitable weighted Gaussian measures supported on Sobolev spaces of increasing regularity. These results have been obtained in collaboration with Giuseppe Genovese (University of Z\"urich) and Daniele Valeri (University of Glasgow)

Convergence over fractals for the Schrödinger equation

We consider a fractal refinement of the Carleson problem for the Schrödinger equation, that is to identify the minimal regularity needed by the solutions to converge pointwise to their initial data almost everywhere with respect to the $\alpha$-Hausdorff measure ($\alpha$-a.e.). We extend to the fractal setting ($\alpha < n$) a recent counterexample of Bourgain \cite{Bourgain2016}, which is sharp in the Lebesque measure setting ($\alpha = n$). In doing so we recover the necessary condition from \cite{zbMATH07036806} for pointwise convergence~$\alpha$-a.e. and we extend it to the range $n/2<\alpha \leq (3n+1)/4$.Ikerbasqu

Quasi-invariance of low regularity Gaussian measures under the gauge map of the periodic derivative NLS

The periodic DNLS gauge is an anticipative map with singular generator which revealed crucial in the study of the periodic derivative NLS. We prove quasi-invariance of the Gaussian measure on L2(T) with covariance [1+(−Δ)s]−1 under these transformations for any [Formula presented]. This extends previous achievements by Nahmod, Ray-Bellet, Sheffield and Staffilani (2011) and Genovese, Lucà and Valeri (2018), who proved the result for integer values of the regularity parameter s

Adjuvant vaginal interventional radiotherapy in early-stage non-endometrioid carcinoma of corpus uteri: a systematic review

Purpose: This systematic review focused on rare histological types of corpus uteri malignancy, including uterine carcinosarcoma (UCS), uterine clear cell carcinoma (UCCC), and uterine papillary serous carcinoma (UPSC), and it is proposed to assist with clinical decision-making. Adjuvant treatment decisions must be made based on available evidences. We mainly investigated the role of vaginal interventional radiotherapy (VIRt) in UCS, UCCC, and UPSC managements. Material and methods: A systematic research using PubMed and Cochrane library was conducted to identify full articles evaluating the efficacy of VIRt in early-stage UPSC, UCCC, and UCS. A search in ClinicalTrials.gov was performed in order to detect ongoing or recently completed trials as well as in PROSPERO for ongoing or recently completed systematic reviews. Survival outcomes and toxicity rates were obtained. Results: All studies were retrospective. For UCS, the number of evaluated patients was 432. The 2- to 5-year aver- age local control (LC) was 91% (range, 74.2-96%), disease-free survival (DFS) 88% (range, 82-94%), overall survival (OS) 79% (range, 53.8-84.3%), the average 5-year cancer-specific survival (CSS) was 70% (range, 70-94%), and G3-G4 toxicity was 0%. For UCCC, the number of investigated patients was 335 (UCCC – 124, mixed – 211), with an average 5-year LC of 100%, DFS of 83% (range, 82-90%), OS of 93% (range, 83-100%), and G3-G4 toxicity of 0%. For UPSC, the number of examined patients was 1,092 (UPSC – 866, mixed – 226). The average 5-year LC was 97% (range, 87.1-100%), DFS 84% (range, 74.7-95.6%), OS 93% (range, 71.9-100%), CSS 89% (range, 78.9-94%), and G3-G4 toxicity was 0%. Conclusions: These data suggest that in adequately selected early-stage UPSC and UCCC patients, VIRt alone may be suitable in women who underwent surgical staging and received adjuvant chemotherapy. In early-stage UCS, a multidisciplinary therapeutic approach has to be planned, considering high-rate of pelvic and distant relapses

Retrospective Investigation of an Influenza A/H1N1pdm Outbreak in an Italian Military Ship Cruising in the Mediterranean Sea, May-September 2009

BACKGROUND: Clinical surveillance may have underestimated the real extent of the spread of the new strain of influenza A/H1N1, which surfaced in April 2009 originating the first influenza pandemic of the 21(st) century. Here we report a serological investigation on an influenza A/H1N1pdm outbreak in an Italian military ship while cruising in the Mediterranean Sea (May 24-September 6, 2009). METHODS: The contemporary presence of HAI and CF antibodies was used to retrospectively estimate the extent of influenza A/H1N1pdm spread across the crew members (median age: 29 years). FINDINGS: During the cruise, 2 crew members fulfilled the surveillance case definition for influenza, but only one was laboratory confirmed by influenza A/H1N1pdm-specific RT-PCR; 52 reported acute respiratory illness (ARI) episodes, and 183 reported no ARI episodes. Overall, among the 211 crew member for whom a valid serological result was available, 39.3% tested seropositive for influenza A/H1N1pdm. The proportion of seropositives was significantly associated with more crowded living quarters and tended to be higher in those aged <40 and in those reporting ARI or suspected/confirmed influenza A/H1N1pdm compared to the asymptomatic individuals. No association was found with previous seasonal influenza vaccination. CONCLUSIONS: These findings underline the risk for rapid spread of novel strains of influenza A in confined environment, such as military ships, where crowding, rigorous working environment, physiologic stress occur. The high proportion of asymptomatic infections in this ship-borne outbreak supports the concept that serological surveillance in such semi-closed communities is essential to appreciate the real extent of influenza A/H1N1pdm spread and can constitute, since the early stage of a pandemic, an useful model to predict the public health impact of pandemic influenza and to establish proportionate and effective countermeasures

Management of Asymptomatic Sporadic Non-Functioning Pancreatic Neuroendocrine Neoplasms No Larger Than 2 Cm: Interim Analysis of Prospective ASPEN Trial

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