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A remark on the Strichartz inequality in one dimension. Ryan Frier, Shuanglin Shao. In this paper, we study the extremal problem for the Strichartz inequality for the Schrödinger equation on . We show that the solutions to the associated Euler-Lagrange equation are exponentially decaying in the Fourier space and thus can be …Shuanglin Shao: Snow 306: Thursday, 3/31/22: 4:00 pm: Smith Colloquium Moduli Space of Fano Varieties Yuchen Liu, Northwestern University Zoom link: https://kansas ...Photograph By:Wang Hock Weng. Lian Shan Shuang Lin Monastery is a Buddhist monastery located in Toa Payoh, Singapore. The temple was founded in 1898, but the construction of the premises only began in 1902 by Low …Shuanglin Shao's 18 research works with 438 citations and 859 reads, including: On one dimensional Quantum Zakharov system Shuanglin Shao's research while affiliated with …Shuanglin Shao. Mathematics. 2009; In this paper, we first show that there exists a maximizer for the non-endpoint Strichartz inequalities for the Schrodinger equation in all …Shuanglin Shao 2, 1. Department of Mathematics, National Tsing Hua University, Hsinchu 30013 2. Department of Mathematical Sciences, Xi'an Jiaotong-Liverpool University, SIP. …Jun 8, 2009 · Benoit Pausader, Shuanglin Shao. We prove global wellposedness and scattering for the Mass-critical homogeneous fourth-order Schrodinger equation in high dimensions n>4, for general L^2 initial data in the defocusing case, and for general initial data with Mass less than certain fraction of the Mass of the Ground State in the focusing case. Jun 26, 2007 · Authors: Shuanglin Shao Download PDF Abstract: For cylindrically symmetric functions dyadically supported on the paraboloid, we obtain a family of sharp linear and bilinear adjoint restriction estimates. Download a PDF of the paper titled A remark on the two dimensional water wave problem with surface tension, by Shuanglin Shao and Hsi-Wei Shih Download PDF Abstract: We consider the motion of a two-dimensional interface between air (above) and an irrotational, incompressible, inviscid, infinitely deep water (below), with surface tension …In this thesis we are mainly concerned with local wellposedness (LWP) problems for nonlinear evolution equations, two global results will then be a direct consequence of conservation laws. A standard scheme to prove LWP is the application of the contraction mapping principle to the corresponding integral equation in a suitable Banach function space. In this context the use of a two parameter ...Shuanglin's Blog. research and teaching related . Posted by: Shuanglin Shao | August 29, 2020 Measure and Integration theory, Lecture 3. In this section, the …Shuanglin Shao Professor in the Mathematics department at University of Kansas 17% Would take again 3.6 Level of Difficulty Rate Professor Shao I'm Professor Shao Professor Shao 's Top Tags Get ready to read Participation matters EXTRA CREDIT Tough grader Group projects Check out Similar Professors in the Mathematics Department A necessary and sufficient condition on the precompactness of extremal sequences for one-dimensional $$\alpha $$ α -Strichartz inequalities, equivalently $$\alpha $$ α -Fourier extension estimates, is established based on the profile decomposition arguments. One of our main tools is an operator-convergence dislocation property consequence which …4 ene 2021 ... Title:A remark on the Strichartz inequality in one dimension. Authors:Ryan Frier, Shuanglin Shao. Download a PDF of the paper titled A remark ...Abstract. For cylindrically symmetric functions dyadically supported on the paraboloid, we obtain a family of sharp linear and bilinear adjoint restriction estimates. As corollaries, we first extend the ranges of exponents for the classical \textit {linear or bilinear adjoint restriction conjectures} for such functions and verify the \textit ...In this thesis we are mainly concerned with local wellposedness (LWP) problems for nonlinear evolution equations, two global results will then be a direct consequence of conservation laws. A standard scheme to prove LWP is the application of the contraction mapping principle to the corresponding integral equation in a suitable …On the extremizers of an adjoint Fourier restriction inequality. Michael Christ, Shuanglin Shao. The adjoint Fourier restriction inequality for the sphere states that if then $\widehat {f\sigma}\in L^4 (\reals^3)$. We prove that all critical points of the functional $\norm {\widehat {f\sigma}}_ {L^4}/\norm {f}_ {\lt}$ are smooth; that any ...Shuanglin Shao, Linear and bilinear endpoint Strichartz estimates : Christoph Thiele: Vjekoslav Kovac, Carleson's almost everywhere convergence theorem : Nov. 28: Shuanglin Shao, Linear and bilinear endpoint Strichartz estimates : Terence Tao: Zubin Gautam, A pointwise ergodic theorem for amenable groups: Dec. 5: Zubin Gautam, A pointwise ... for all. Theorem 1.11. If is an outer measure on , the collection of -measurable sets is a algebra, and the restriction of to is a complete measure. Proof. The proof is divided into 3 Steps. Step 1. We prove that is a algebra. (a). . (b).Sakshi Telugu ePaper : Read News in Telugu from Andhra Pradesh, Telangana, Hyderabad, India and World on Politics, Entertainment, Family, Sports, Business, CricketShuanglin Shao (University of Kansas). Title: On smoothness of extremizers to an adjoint Fourier restriction inequality on S2. Abstract: The extremizers to ...Oct 19, 2023 · Shao Lan Fu 12.57 % ... Pacific Shuanglin Bio-pharmacy Co., Ltd. 3004, Sunshine City World Fincl Ctr No. 8 Changxing South Street. 030000, Taiyuan + Fall 2017, Math 500, Real Analysis Course Information. Course Coverage: This course intends to cover some basic topics of real analysis at the undergraduate level: the real number system, limits and sequences, sequences and series of functions, continuity and differentiability of functions, Riemann integrals.

Fall 2017, Math 500, Real Analysis Course Information. Course Coverage: This course intends to cover some basic topics of real analysis at the undergraduate level: the real number system, limits and sequences, sequences and series of functions, continuity and differentiability of functions, Riemann integrals.Shuanglin Shao——The entropy estimate for the res... 时间：12月12日，9:00-10:00 地点：Zoom会议，会议号：988 9149 1513，密... 人才招聘. Copyright (C)2017 ...A necessary and sufficient condition on the precompactness of extremal sequences for one-dimensional $$\\alpha $$ α -Strichartz inequalities, equivalently $$\\alpha $$ α -Fourier extension estimates, is established based on the profile decomposition arguments. One of our main tools is an operator-convergence dislocation property consequence which …32 Analyticity of extremizers to the Airy-Strichartz inequality, with Shuanglin Shao. Bulletin of the London Mathematical Society 44 (2012), no. 2, 336–352 ...1. Introduction. Breast cancer in women has become the most common cancer worldwide. There are an estimated 2.3 million new cases each year, accounting for about 11.7% of all new cancer cases. [] At present, the primary approach to treating breast cancer involves surgical resection of the lesion in conjunction with radiotherapy and …

Shuanglin Shao MathSciNet Ph.D. University of California, Los Angeles 2008 Dissertation: Restriction Estimates for Paraboloids and Cones in the Cylindrically Symmetric Case Mathematics Subject Classification: 42—Fourier analysis Advisor 1: Terence Chi-Shen Tao No students known.André Martinez, Thierry Ramond and Johannes Sjöstrand: Global existence and uniqueness results for weak solutions of the focusing mass-critical nonlinear Schrödinger equation…

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