Shuanglin shao.

Shuanglin Shao 3, and Monica Visan 1, 1. Mathematics Department, University of California, Los Angeles, Box 951555, Los Angeles, CA 90095 2. Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, 335 Gwahangno, Yuseong-gu, Daejeon, Korea 305-701 ...The adjoint Fourier restriction inequality of Tomas and Stein states that the mapping f↦fσ̂ is bounded from L2(S2) to L4(ℝ3). We prove that there exist functions that extremize this inequality, and that any extremizing sequence of nonnegative functions has a subsequence that converges to an extremizer.808 Yong Ding, Chin-Cheng Lin & Shuanglin Shao. Corollary 1.7. If Cl e L°°(Kn) X L"(5n~'), q > 2(n - 1 )/n, satisfies (1.1) and the Ll -Dini condition (1.2) ...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 …

Joint with Jin-Cheng Jiang, Shuanglin Shao. Blowup behaviour for the nonlinear Klein--Gordon equation. arXiv. Joint with Rowan Killip, Monica Visan. Math. Ann. 358 (2014), no. 1-2, 289-350. Uniform estimates for the X-ray transform restricted to polynomial curves. arXiv. Joint with Spyridon Dendrinos. J. Funct. Anal., 262 (2012), 4986-5020. 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.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 ...

10 oct 2015 ... Shuanglin Shao's user avatar. Shuanglin ShaoShuanglin Shao. 111 bronze badge. Add a comment |. You must log in to answer this question. Not the ...Shuanglin Shao 2, 1. Department of Mathematics, National Tsing Hua University, Hsinchu 30013 2. Department of Mathematical Sciences, Xi'an Jiaotong-Liverpool University, SIP. …

Shuanglin Shao 2, 1. Department of Mathematics, National Tsing Hua University, Hsinchu 30013 2. Department of Mathematical Sciences, Xi'an Jiaotong-Liverpool University, SIP. Suzhou, Jiangsu, 215123 Received: April 2015 Revised: April 2016 Published: May 2017 Abstract Related Papers Cited by ...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. 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 Shuanglin Shao (Department of Mathematics, Kansas University, Lawrence, Ks., U.S.A.) Abstract In this paper, we study the extremal problem for the …From: Shuanglin Shao [v1] Mon, 8 Oct 2007 05:42:33 UTC (11 KB) Fri, 20 Jun 2008 05:30:27 UTC (9 KB) Full-text links: Download: Download a PDF of the paper titled A note on the cone restriction conjecture in the cylindrically symmetric case, by Shuanglin Shao. PDF; PostScript; Other formats Current browse context: ...

Guixiang XU, Professor | Cited by 1,044 | of Beijing Normal University, Beijing (bnu) | Read 59 publications | Contact Guixiang XU

4 RYAN FRIER AND SHUANGLIN SHAO prove that they are exponentially affine functions. In [2], Charalambides generalizes the analysis in [4] to some general hyper-surfaces in Rn that in-clude the sphere, paraboloids and cones as special examples and proves that the solutions are exponentially affine functions. In [2, 4], the functions are

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 ...Associate Professor, Acting Associate Chair and Director of Undergraduate Studies, Spring 2024 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.SHUANGLIN SHAO Abstract. We prove that the extremizers to the Tomas-Stein inequality for the one dimension sphere are smooth. This is achieved by studying the associated generalized Euler-Lagrange equa-tion. 1. Introduction To understand the Fourier transform of functions on the Euclidean space, Stein [31] proposed the restriction problem.Download a PDF of the paper titled Maximizers for the Strichartz inequalities and the Sobolev-Strichartz inequalities for the Schr\"odinger equation, by Shuanglin Shao Download PDF Abstract: In this paper, we first show that there exists a maximizer for the non-endpoint Strichartz inequalities for the Schrödinger equation in all dimensions ...Shao Shuanglin Restriction theorem in dimension 2: John Bueti : Zubin Gautam Classification of ergodic transformations with pure-point spectrum: May 02: Steve O'Dell The Aharonov Bohm effect and time-dependent scattering theory: Joe Viola : Shao Shuanglin Restriction Theoem in Dimension 2: May 09: Steve O'Dell

Shuanglin Shao Department of Mathematics University of Kansas 615 Snow Hall 1460 Jayhawk Blvd Lawrence, KS 66045-7594 Email:slshao_at_ku.edu Tel: +1-(785)864-4762 Fax:+1-(785)864-5255 Curriculum Vitae (PDF) Research Paper and Preprints Teaching Fall 2011, Math 290 Spring 2012, Math 500 FallSHUANGLIN 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 twoDec 10, 2021 · Shuanglin Shao: 306 Snow: Friday, 9/3/21: 10:00am: Graduate Student Probability Seminar Fundamentals of Continuous Stochastic Processes: Zoom ... Yifei WU | Cited by 872 | of Tianjin University, Tianjin (tju) | Read 60 publications | Contact Yifei WUSHUANGLIN SHAO (Communicated by Hart F. Smith) Abstract. In this paper, we present two arguments showing that the classi-cal linear adjoint cone restriction conjecture holds for the class of functions supported on the cone and invariant under spatial rotation in all dimensions. The first is based on a dyadic restriction estimate, while the ...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.

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SHUANGLIN SHAO (Communicated by Hart F. Smith) Abstract. In this paper, we present two arguments showing that the classi-cal linear adjoint cone restriction conjecture holds for the class of functions supported on the cone and invariant under spatial rotation in all dimensions. The first is based on a dyadic restriction estimate, while the ...Shuanglin Shao (KU) Department of Mathematics. 138 Cardwell Hall. 1228 N Martin Luther King Jr Drive, Manhattan, KS 66506 . 785-532-6750 | 785-532-0546 fax | math ... Shuanglin Shao and Monica Visan. 2012, 32(1): 191-221. doi: 10.3934/dcds.2012.32.191. Abstract(4512) PDF(146) Cited by(25). We consider the mass-critical ...Abstract: Unconventional superconductors have Cooper pairs with lower symmetries than in conventional superconductors. In most unconventional superconductors, ...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. If you have additional information or corrections ...SHUANGLIN SHAO Abstract. In this paper, we show that a pair of Gaussian functions are extremisers to a bilinear Strichartz inequality on R×R2, and unique up to the symmetry group of the inequality. 1. Introduction We consider the free Schr¨odinger equation i∂tu+∆u = …

Shuanglin Shao (Institute for Mathematics and its Applications, University of Minnesota, Minneapolis) Yifei Wu (Department of Mathematics, South China University of Technology, Guangzhou, Guangdong, China) Guixiang Xu (Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing, China) Keywords

Shuanglin Shao (KU) Contact: Virginia Naibo. [email protected]. Department of Mathematics. 138 Cardwell Hall. 1228 N Martin Luther King Jr Drive, Manhattan, KS 66506 . 785-532-6750 | 785-532-0546 fax | [email protected]. Undergraduate [email protected] . Graduate [email protected]. Contact Us;

Shuanglin Shao We prove that the extremizers to the Tomas-Stein inequality for the one dimension sphere are smooth. This is achieved by studying the associated Euler-Lagrange equation.Shuanglin Shao. Community member details; Affiliation: Faculty: Title: Associate Professor: Department: Mathematics: Address: 1445 Jayhawk Boulevard Room 627: Email: [email protected]: Contact Information Technology | [email protected] | 785-864-8080. This directory is a public record. It is a violation of Kansas State Law to knowingly give, sell or ...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.Shuanglin Shao (KU). Department of Mathematics · 138 Cardwell Hall · 1228 N Martin Luther King Jr Drive, Manhattan, KS 66506 · 785-532-6750 | 785-532-0546 fax ...Aug 31, 2008 · Download a PDF of the paper titled Maximizers for the Strichartz inequalities and the Sobolev-Strichartz inequalities for the Schr\"odinger equation, by Shuanglin Shao Download PDF Abstract: In this paper, we first show that there exists a maximizer for the non-endpoint Strichartz inequalities for the Schrödinger equation in all dimensions ... 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 (Communicated by Hart F. Smith) Abstract. In this paper, we present two arguments showing that the classi-cal linear adjoint cone restriction conjecture holds for the class of functions supported on the cone and invariant under spatial rotation in all dimensions. The first is based on a dyadic restriction estimate, while the ...SHUANGLIN SHAO Abstract. In this paper, we first show that there exists a maximizer for the non-endpoint Strichartz inequalities for the Schr¨odinger equation in all dimensions based on the recent linear profile decomposition result. We then present a new proof of the linear profile decomposition for the Schr¨oindgerSHUANGLIN SHAO Abstract. In this paper, we first show that there exists a maximizer for the non-endpoint Strichartz inequalities for the Schr¨odinger equation in all dimensions based on the recent linear profile decomposition result. We then present a new proof of the linear profile decomposition for the Schr¨oindgerOn 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 $ orm {\widehat {f\sigma}}_ {L^4}/ orm {f}_ {\lt}$ are smooth; that any ...6 benoit pausader and shuanglin shao with the usual modification when p or q is infinite, and for I ⊂ R an interval, we let L p ( I, L q ) be the set of r estriction to I of functions in L p ...

Shao, Shuanglin University of Kansas, Lawrence, KS, United States. Search grants from Shuanglin Shao Search grants from University of Kansas Center for Research Inc. Share this grant: : : Abstract; Funding; Institution; Comments; Recent in Grantomics: University of Virginia vs. funders. Who wins? ...SHUANGLIN SHAO; BENOIT PAUSADER. Mathematics Department, Brown University, Box 1917, Providence, Rhodes Island 02912, USA. Search for more papers by this authorInstructor: Shuanglin Shao Office: Snow Hall 615 Email: [email protected] Office Hour: M, W, F: 2-3 PM or by appointment. Grade Policy. Homework: There will be 10 homework. Each homework consists of roughly 10 problems; only 3 of them will be graded, which will be decided after you turn in homework. The lowest homework grade will be dropped.I would also like to thank Donghao Wang and Ruixiang Zhang for helpful discussion on Proposition 5.3. I would like to thank the anonymous referees for the thorough reading and for many writing suggestions that improved the presentation of this paper. I would like to also thank Susan Ruff and Shuanglin Shao for their writing advice.Instagram:https://instagram. ku study abroad officepositively reinforcedcraigslist cars in western massswot analysis overview SHUANGLIN SHAO (Communicated by Hart F. Smith) Abstract. In this paper, we present two arguments showing that the classi-cal linear adjoint cone restriction conjecture holds for the class of functions supported on the cone and invariant under spatial rotation in all dimensions. The first is based on a dyadic restriction estimate, while the ... dru proxquiz 8 1 graphing quadratic equations May 19, 2022 · Shuanglin Shao (Department of Mathematics, Kansas University, Lawrence, Ks., U.S.A.) Abstract In this paper, we study the extremal problem for the Strichartz inequality for the Schrödinger equation on $\mathbb{R}^2$. 2019 gmc acadia remote battery We prove that there exists an extremal function to the Airy Strichartz inequality, $e^{-t\partial_x^3}: L^2(\mathbb{R})\to L^8_{t,x}(\mathbb{R}^2)$ by using the ...5 jul 2021 ... CHANG Zhiqiao, XIN Jie, SHI Xin, HUANG Shuanglin, SHAO Jiani. Analysis on the development of core positioning parameters of GPS navigation ...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.