Shuanglin shao.

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.Shuanglin's Blog. research and teaching related . Posted by: Shuanglin Shao | December 6, 2009 Kato-smoothing effect “Kato smoothing” “is ” important in dispersive PDE.“Smoothing”, as it stands, sounds like a very good word. But why is it good? How will it be used remains as vague questions to me.Authors: Soonsik Kwon, Shuanglin Shao. Download PDF Abstract: In this short note, we consider the global dynamics of the defocusing generalized KdV equations: u_t + u_{xxx} = (|u|^{p-1}u)_x. We use Tao's theorem that the energy moves faster than mass to prove a moment type dispersion estimate. As an application of the dispersion …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 ...Shuanglin Shao (IMA - University of Minnesota) On extremals to the Tomas-Stein inequality for the sphere Abstract. Tuesday, September 14, 4:00 p.m., VV B139. Alexander Nagel (UW Madison) Convolution with flag distributions on homogeneous nilpotent Lie groups Abstract. Tuesday, September 21, 4:00 p.m., VV B139. Andrej Zlatoš (UW Madison)

MathSciNet Ph.D. University of California, Los Angeles 2008 Dissertation: Restriction Estimates for Paraboloids and Cones in the Cylindrically Symmetric Case Mathematics …

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SOONSIK KWON, SHUANGLIN SHAO Abstract. We consider the global dynamics of the defocusing generalized KdV equation @tu + @3 xu = @x(jujp 1u): We use Tao’s theorem [5] that the energy moves faster than the mass to prove a moment type dispersion estimate. As an application of the dispersion esti-We study the existence of standing waves, of prescribed L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage ...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 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

Authors: Shuanglin Shao. Download PDF Abstract: In this paper, for cylindrically symmetric functions dyadically supported on the paraboloid, we obtain a family of sharp linear and linear adjoint restriction estimates.

Recently, Christ and Shao [1], [2] have proved the existence of maximizers for the adjoint Fourier restriction inequality of Stein and Tomas [5] for the sphere: (1) where is the standard unit sphere equipped with its natural surface measure σ induced by the Lebesgue measure on . Here the Fourier transform of an integrable function f supported ...

Instructor: Shuanglin Shao Office: Snow Hall 615 Email: [email protected] Office Hour: MWF: 1:00 --- 2:00 PM, or by appointment. Grade Policy.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?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 2 ene 2009 ... 2009(2009), No. 03, pp. 1-13. Maximizers for the Strichartz and the Sobolev-Strichartz inequalities for the Schrodinger equation. Shuanglin Shao.Michael Christ and Shuanglin Shao, Existence of extremals for a Fourier restriction inequality, Anal. PDE 5 (2012), no. 2, 261–312. MR 2970708, DOI 10.2140/apde.2012.5.261; Michael Christ and Shuanglin Shao, On the extremizers of an adjoint Fourier restriction inequality, Adv. Math. 230 (2012), no. 3, 957–977.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.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 …

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 ...12 feb 2021 ... In: arXiv preprint math/9704212 (1997) (cit. on p. 4). [Sha08]. Shuanglin Shao. “Maximizers for the Strichartz inequalities and the Sobolev-.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 ...Authors: Shuanglin Shao. Download a PDF of the paper titled The linear profile decomposition for the Airy equation and the existence of maximizers for the Airy Strichartz inequality, by Shuanglin Shao.Spring 2016, Math 766, Real Analysis Course Information. Course Coverage: This course is the second part of real analysis at the graduate level; the first part is Math 765.. It continues with the following topics from Chapters 7, 8, 10, 11: infinite series of functions, the Topology in the Euclidean spaces, Metric spaces, and Differentiability onJun 22, 2010 · 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 $ orm {\widehat {f\sigma}}_ {L^4}/ orm {f}_ {\lt}$ are smooth; that any ... Instructor: Shuanglin Shao Office: Snow Hall 615 Email: [email protected] Office Hour: MWF: 1:00 --- 2:00 PM, or by appointment. Grade Policy. Homework: There will be 10 homework. Each homework consists of roughly 20 problems; only 3 of them will be graded, which will be decided after you turn in homework. The lowest homework grade will be dropped.

Posted by: Shuanglin Shao | September 18, 2020 Measure and Integration theory, Lecture 7. Let be a real valued measurable function. Let .

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; In this paper, we study the extremal problem for the Strichartz inequality for the Schr\"{o}dinger equation on the $\mathbb{R} \times \mathbb{R}^2$; we provide a new proof to the ...Shuanglin Shao. Associate Professor; Contact Info. [email protected]. 785-864-4762. 627 Snow. Personal Links. Webpage Webpage; Research — Harmonic Analysis ... Associate Professor, Acting Associate Chair and Director of Undergraduate Studies, Spring 2024JIN-CHENG JIANG AND SHUANGLIN SHAO Abstract. Inthis paper, we studythe extremal problem for the Strichartz inequality for the Schr¨odinger equation on the R×R2. We show that the solutions to the associated Euler-Lagrange equation are exponentially decaying in the Fourier space and thus can be extended to be complex analytic.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 ...Analysis and Ergodic Theory Summer School, Lake Arrowhead ∗ September 17th - September 22nd 2006 Organizers: Ciprian Demeter, University of California, Los Angeles

May 1, 1964 is the birth date of Shuanglin. His age is 59. Shuanglin lives at 10041 Southwest 145th Strt, Miami, FL 33176-7088. We assume that Blanka Bello and Joseph Frank Bello were among five dwellers or residents at this place. He can be reached via e-mail [email protected]. Rent value for a two bedroom unit in the zip code 33176 is ...

SHUANGLIN SHAO; BENOIT PAUSADER. Mathematics Department, Brown University, Box 1917, Providence, Rhodes Island 02912, USA. Search for more papers by this author

Shuanglin Shao UCLA, Los Angeles, USA; Download PDF. 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 ...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. Advisor: Terence Tao.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 DepartmentInstructor: Shuanglin Shao Office: Snow Hall 615 Email: [email protected] Office Hour: Monday, Wednesday, Friday: 10 --10:50 AM; or by appointment. Grade Policy. Homework: There will be 10 homework. Each homework consists of roughly 20 problems; only 3 of them will be graded, which will be decided after you turn in homework. The lowest homework ...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 ...Shuanglin Shao 3 Research Talks 1. Beijing Conference on harmonic analysis and its applications , "On characterization of the sharp Strichartz inequalities for the Schrdinger equations"¨ , University of Chinese Academy of Sciences, Beijing, China, June 2018. 2. Special Section of nonlinear Dispersive Equations , "On characterization of 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¨oindgerBENOIT PAUSADER AND SHUANGLIN SHAO Abstract. We prove global wellposedness and scattering for the Mass-critical homogeneous fourth-order Schro¨dinger equation in …Shuanglin Shao. Associate Professor; Contact Info. [email protected]. 785-864-4762. 627 Snow. Personal Links. Webpage Webpage; Research — Harmonic Analysis ... 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 SnowAuthors: Jincheng Jiang, Shuanglin Shao, Betsy Stovall Download PDF Abstract: We establish linear profile decompositions for the fourth order Schrödinger equation and for certain fourth order perturbations of the Schrödinger equation, in dimensions greater than or equal to two.Shuanglin Shao is on Facebook. Join Facebook to connect with Shuanglin Shao and others you may know. Facebook gives people the power to share and makes the world more open and connected.

32 Analyticity of extremizers to the Airy-Strichartz inequality, with Shuanglin Shao. Bulletin of the London Mathematical Society 44 (2012), no. 2, 336–352 ...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 …Shuanglin Shao. Associate Professor; Contact Info. [email protected]. 785-864-4762. 627 Snow. Personal Links. Webpage Webpage; Research — Harmonic Analysis ...... Shuang; Lin, Shao; Hajat, Shakoor; Yang, Lianping; Huang, Cunrui; (2019) The impact of the 2016 flood event in Anhui Province, China on infectious diarrhea ...Instagram:https://instagram. arkansas cs kansasfox5news atlantameineke car care center couponsromatic period 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 ... what is the highest point in kansaskansas jayhawk basketball news Oct 18, 2020 · Posted by: Shuanglin Shao | October 18, 2020 Measure and Integration theory, Lecture 13. Lemma 3.15. (Vitali type covering lemma. Liked by Shuanglin Shao. Education UCLA Ph. D Math. 2004 - 2008. View Shuanglin's full profile See who you know in common Get introduced ... mandatos informales afirmativos Thesis advisor: Shuanglin Shao First job: Assistant Teaching Professor, Arizona State University, Tempe, AZ Website: Link. Mehmet Yenisey. Graduation date: Summer 2022 Research area: Probability Theory Thesis title: The metric geometry nature of Wasserstein spaces of probability measures: On the point of view of submetry projectionsDOI: 10.1142/S0219891610002256 Corpus ID: 14454549; THE MASS-CRITICAL FOURTH-ORDER SCHRÖDINGER EQUATION IN HIGH DIMENSIONS @article{Pausader2009THEMF, title={THE MASS-CRITICAL FOURTH-ORDER SCHR{\"O}DINGER EQUATION IN HIGH DIMENSIONS}, author={Benoit Pausader and Shuanglin Shao}, journal={Journal of Hyperbolic Differential Equations}, year={2009}, volume={07}, pages={651-705}, url={https://api ...