We consider the cubic Nonlinear Schrodinger Equation in one space dimension, either focusing or defocusing. We prove that the solutions satisfy a-priori local in time H^s bounds in terms of the H^s size of the initial data for s greater than or equal to -1/6.

The aim of these notes is to describe some recent results concerning dispersive estimates for principally normal pseudodifferential operators. The main motivation for this comes from unique continuation problems. Such estimates can be used to prove Carleman inequalities, which in turn yield unique continuation results for various partial differential operators with rough potentials.

We consider the cubic Nonlinear Schroedinger Equation (NLS) in one space dimension, either focusing or defocusing. We prove that the solutions satisfy a-priori local in time Hs bounds in terms of the Hs size of the initial data for s >=-1/4 . This improves earlier results of Christ-Colliander-Tao [2] and of the authors [12]. The new ingredients are a localization in space and local energy decay, which we hope to be of independent interest.

This work is devoted to the strong unique continuation problem for second order parabolic equations with nonsmooth coefficients. Introduction and bibliography have been revised.

We obtain L^p eigenfunction bounds for the harmonic oscillator in R^n and for other related operators, improving earlier results of Thangavelu and Karadzhov. We also construct suitable counterexamples which show that our estimates are sharp.

We establish asymptotic bounds on the L^p norms of spectrally localized functions in the case of two-dimensional Dirichlet forms with coefficients of Lipschitz regularity. These bounds are new for the range p>6. A key step in the proof is bounding the rate at which energy spreads for solutions to hyperbolic equations with Lipschitz coefficients.

We establish L^p bounds on L^2 normalized spectral clusters for self-adjoint elliptic Dirichlet forms with Lipschitz coefficients. In two dimensions we obtain best possible bounds for all p between $2 and infinity, up to logarithmic losses for $6

© 2018 The Authors. Cancer published by Wiley Periodicals, Inc. on behalf of American Cancer Society. BACKGROUND: Antibodies targeting the programmed death-ligand 1 (PD-L1)/programmed cell death protein 1 (PD-1) checkpoint may cause adverse events (AEs) that are linked to the mechanism of action of this therapeutic class and unique from those observed with conventional chemotherapy. METHODS: Patients with advanced solid tumors who were enrolled in the phase 1 JAVELIN Solid Tumor (1650 patients) and phase 2 JAVELIN Merkel 200 (88 patients) trials received avelumab, a human anti–PD-L1 IgG1 antibody at a dose of 10 mg/kg every 2 weeks. Treatment-related AEs (TRAEs) were graded using the National Cancer Institute Common Terminology Criteria for Adverse Events (version 4.0). In post hoc analyses, immune-related AEs (irAEs) were identified via an expanded AE list and medical review, and infusion-related reactions (IRRs) occurring ≤2 days after infusion and symptoms occurring ≤1 day after infusion and resolving ≤2 days after onset were identified based on prespecified Medical Dictionary for Regulatory Activities (MedDRA) terms. RESULTS: Of the 1738 patients analyzed, grade ≥3 TRAEs occurred in 177 (10.2%); the most common were fatigue (17 patients; 1.0%) and IRR (10 patients; 0.6%). TRAEs led to discontinuation in 107 patients (6.2%) and death in 4 patients (0.2%). Grade ≥3 irAEs occurred in 39 patients (2.2%) and led to discontinuation in 34 patients (2.0%). IRRs or related symptoms occurred in 439 patients (25.3%; grade 3 in 0.5% [9 patients] and grade 4 in 0.2% [3 patients]). An IRR occurred at the time of first infusion in 79.5% of 439 patients who had an IRR, within the first 4 doses in 98.6% of 439 patients who had an IRR, and led to discontinuation in 35 patients (2.0%). CONCLUSIONS: Avelumab generally was found to be well tolerated and to have a manageable safety profile. A minority of patients experienced grade ≥3 TRAEs or irAEs, and discontinuation was uncommon. IRRs occurred mainly at the time of first infusion, and repeated events were infrequent. Cancer 2018;124:2010-7. © 2018 The Authors. Cancer published by Wiley Periodicals, Inc. on behalf of American Cancer Society. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.

Using a sample of 232×106 Υ(4S)→BB̄ events collected with the BABAR detector at the PEP-II B Factory in 1999-2004, we study B-→D0K*(892)- decays where K*-→KS0π- and D0→K-π+, K-π+π0, K-π+π+π- (non-CP final states); K+K-, π+π- (CP+ eigenstates); KS0π0, KS0, and KS0ω (CP- eigenstates). We measure four observables that are sensitive to the angle γ of the CKM unitarity triangle; the partial-rate charge asymmetries ACP± and the ratios of the B-decay branching fraction in CP± and non-CP decays RCP±: ACP+=-0.08±0.19(stat)±0.08(syst), ACP-=-0.26±0.40(stat)±0.12(syst), RCP+=1.96±0.40(stat) ±0.11(syst), and RCP-=0.65±0.26(stat)±0.08(syst). © 2005 The American Physical Society.