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We prove scattering for the defocusing fourth-order Schrödinger equation in low spatial dimensions (1 ⩽ n ⩽ 4). Inspired by the method in (Pausader 2010 Indiana Univ. Math. J. 59 791–822), we utilize a strategy from Kenig and Merle (2006 Invent. Math. 166 645–75) to compensate for the absence of a Morawetz-type estimate, then we use a new virial-type ingredient to finish the proof.Dec 13, 2018 · Shuanglin Shao Department of Mathematics, KU Snow Hall 615 Phone: Fax: 1460 Jayhawk Blvd Lawrence, KS 66045-7594 Email: Homepage: Education (785)864-4762 (785)864-5255 [email protected] www.math.ku.edu/ ̃slshao Ph.D. Mathematics, University of California, Los Angeles (UCLA), 2008. M.S. Mathematics, Beijing Normal University, 2004. Posted by: Shuanglin Shao | August 15, 2020 Lecture 1 This semester we will study the measure theory and integration theory, namely Chapters 1,2,3, and 6 in …

32 Analyticity of extremizers to the Airy-Strichartz inequality, with Shuanglin Shao. Bulletin of the London Mathematical Society 44 (2012), no. 2, 336–352 ...Authors: Shuanglin Shao. Download PDF Abstract: In this note, we show that a pair of Gaussian functions are extremisers to a bilinear Strichartz inequality, and unique up to the symmetry group of the inequality. Comments: 6 pages. The constant in defining the inverse Fourier transform is corrected;the expression of convolution of …Currently supported by the UCAS Joint Training Program, I visit Shuanglin Shao for one year (extended to two years) at Department of mathematics in University of Kansas. I have broad interests in ...We identify the compactness threshold for optimizing sequences of the Airy–Strichartz inequality as an explicit multiple of the sharp constant in the Strichartz inequality. In particular, if the sharp constant in the Airy–Strichartz inequality is strictly smaller than this multiple of the sharp constant in the Strichartz inequality, then there is an optimizer for the former inequality. Our ...

André Martinez, Thierry Ramond and Johannes Sjöstrand: Global existence and uniqueness results for weak solutions of the focusing mass-critical nonlinear Schrödinger equationSHUANGLIN SHAO Abstract. We prove that the extremizers to the Tomas-Stein inequal-ity for the one dimension sphere are smooth. This is achieved by study-ing the associated Euler-Lagrange equation. 1. Introduction To understand the Fourier transform of functions on the Euclidean space, Stein [27] proposed the restriction problem. ….

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32 Analyticity of extremizers to the Airy-Strichartz inequality, with Shuanglin Shao. Bulletin of the London Mathematical Society 44 (2012), no. 2, 336–352 ...From: Shuanglin Shao Wed, 15 Jul 2015 17:13:51 UTC (29 KB) [v2] Tue, 26 Jan 2016 19:14:09 UTC (28 KB) Full-text links: Download: Download a PDF of the paper titled On ...SHUANGLIN SHAO Abstract. In [5], when the spatial variable x is localized, Lee observed that the Schro¨dinger maximal operator eit∆f(x) enjoys certain localization property in tfor frequency localized functions. In this note, we give an alternative proof of this observation by using the method of stationary phase, and then include two

Shuanglin Shao: 306 Snow: Friday, 9/3/21: 10:00am: Graduate Student Probability Seminar Fundamentals of Continuous Stochastic Processes: Zoom ...Shuanglin's Blog. research and teaching related . Posted by: Shuanglin Shao | August 29, 2020 Measure and Integration theory, Lecture 3. In this section, the main theorem is the Carath\’eodory theorem. It enables us to construct measures from outer measures. We introduce the concept of outer measure.Dec 9, 2022 · Shuanglin Shao: 306 Snow: Thursday, 9/1/22: 4:00 pm: Graduate Student Probability Seminar Random Walk: A Modern Introduction Ray Zhang: 564 Snow: Friday, 9/2/22: 12:00 pm: GSO Seminar Intro to D-modules Christopher Wong: 256 Snow 3:00 pm: Combinatorics Seminar Counting Embeddings of Graphs in State Space Vance Gaffar, Baker University: 306 Snow

furman espn Shuanglin Shao Department of Mathematics, KU Snow Hall 615 Phone: Fax: 1460 Jayhawk Blvd Lawrence, KS 66045-7594 Email: Homepage: Education (785)864-4762 (785)864-5255 [email protected] www.math.ku.edu/ ̃slshao Ph.D. Mathematics, University of California, Los Angeles (UCLA), 2008. M.S. Mathematics, Beijing Normal University, 2004.Associate Professor, Acting Associate Chair and Director of Undergraduate Studies, Spring 2024 elida athleticslightfoot ku The purpose of the AWM is to encourage women and girls to study and to have active careers in the mathematical sciences, and to promote equal opportunity and the equal treatment of women and girls in the mathematical sciences. mary huntoon obituary The purpose of the AWM is to encourage women and girls to study and to have active careers in the mathematical sciences, and to promote equal opportunity and the equal treatment of women and girls in the mathematical sciences. thammasatjack wellernike custom football cleats Shuanglin Shao (University of Kansas) On smoothness of extremizers to an adjoint Fourier restriction inequality on S^2. Abstract. Tuesday, October 16, 4:00 p.m., VV B139. Laurent Stolovitch (University of Nice - Sophia Antipolis) Normal forms of analytic perturbations of quasihomogeneous vector fields Abstract. practice pharmacy Shuanglin Shao, mathematics; Suzanne Shontz, electrical engineering and computer science; Randy Stotler, geology; Jason Travers, special education; Yang Yi, electrical engineering and computer science; Jiso Yoon, political science; Want articles like this sent straight to your inbox? what's one useful strategy for planningrecently sold homes in tampa bay golf and country clubpathfinder wrath of the righteous traitor STATE OF NEW HAMPSHIRE CHAIRMAN Martin P. Königsberg TDD Access: Relay NH 18007352964 COMMISSIONERS Robert R. Scott Tel. (603)2712431 FAX No. 2713878 EXECUTIVE DIRECTOR Debra A. Howland Website: