Aug 15, 2020 · This semester we will study the measure theory and integration theory, namely Chapters 1,2,3, and 6 in Folland's real analysis book. The development of measure theory has a long history starting with Weierstrass's construction of a nowhere differential but continuous function. Page xii: Shaunglin should be Shuanglin. Page xiv: should be throughout the text (e.g. on pages 33, 34). Frechet should be Fréchet. Page xv: Frechet should be Fréchet. Page 1: “is still its infancy” should be “is still in its infancy”. Page 2: “A Study in Scarlet” should be “A Scandal in Bohemia”.Shuanglin Shao. Associate Professor; Contact Info. [email protected]. 785-864-4762. 627 Snow. Personal Links. Webpage Webpage; Research — Harmonic Analysis ... Shuanglin Shao 3 Research Talks 1. Short course, "An introduction to Fourier Analysis", Huazhong University of Science and Technology, Wuhan, China, July 2017. 2. Department Colloquium, "On characterization of the sharp Strichartz inequality for the Schrödinger equa-tion", National Cheng-Kung University, Taiwan June, 2016. 3.Authors: 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. Department of Mathematics University of Kansas 615 Snow Hall 1460 Jayhawk Blvd Lawrence, KS 66045-7594 Email:slshao_at_ku.edu Tel: +1-(785)864-4762Christ, Michael and Shao, Shuanglin. On the extremizers of an adjoint Fourier restriction inequality , Advances in Math. 230 (2012), 957-977. Bennett, Jonathan and Carbery, Anthony and Christ, Michael and Tao, Terence.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 ...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 ... 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 on 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; BENOIT PAUSADER. Mathematics Department, Brown University, Box 1917, Providence, Rhodes Island 02912, USA. Search for more papers by this authorShuanglin 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 ...Authors: Jin-Cheng Jiang, Shuanglin Shao. Download PDF Abstract: In this paper, we study the extremal problem for the Strichartz inequality for the Schrödinger equation on the $\mathbb{R} \times \mathbb{R}^2$; we provide a new proof to the characterization of the extremal functions.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 ...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.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 ...Shuanglin Shao Affiliation Mathematics Field of Study Analysis From 9/2008 – 8/2009 Shuanglin Shao works in harmonic analysis and partial differential equations. He is interested in establishing the profile decomposition result for the Airy equation, and the problem of pointwise convergence of solutions to the Schrödinger equation. Dates at IAS In this paper we study the existence of maximizers for two families of interpolation inequalities, namely a generalized Gagliardo–Nirenberg inequality and a new inequality involving the Riesz energy. Two basic tools in our argument are a generalization of Lieb’s Translation Lemma and a Riesz energy version of the Brézis–Lieb lemma.Posted by: Shuanglin Shao | September 18, 2020 Measure and Integration theory, Lecture 7. Let be a real valued measurable function. Let .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;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 …Dec 10, 2021 · Shuanglin Shao: 306 Snow: Friday, 9/3/21: 10:00am: Graduate Student Probability Seminar Fundamentals of Continuous Stochastic Processes: Zoom ... 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. 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. Associate Professor; Contact Info. [email protected]. 785-864-4762. 627 Snow. Personal Links. Webpage Webpage; Research — Harmonic Analysis ...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.Posted by: Shuanglin Shao | September 18, 2020 Measure and Integration theory, Lecture 7. Let be a real valued measurable function. Let .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 ...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 DepartmentShuanglin Shao. Associate Professor; Contact Info. [email protected]. 785-864-4762. 627 Snow. Personal Links. Webpage Webpage; Research — Harmonic Analysis ...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. Comments: 11 pages. We rewrite some of the introduction part and correct Lemma 3.2 and proposition 3.6.BENOIT PAUSADER AND SHUANGLIN SHAO Abstract. We prove global wellposedness and scattering for the Mass-critical homogeneous fourth-order Schro¨dinger equation in …Sep 23, 2014 · We study the existence of standing waves, of prescribed L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage ... Shuanglin was born in May 1, 1964 Shuanglin has 4 phone numbers Shuanglin has 3 relatives Shuanglin has 9 past addresses Shuanglin has 2 emails Shuanglin has 3 associates by phone number Shuanglin has 172 associates by address Shuanglin is married Shuanglin’s home type is Single Family Dwelling Unit The property where Shuanglin lives was built in 1999 Shuanglin has resided at the current ...Shuanglin Shao · Renming Song · Zhiqiang Cai · Shizan Fang · Hongjun Gao · Jianhua Huang · Peter Kloeden · Jicheng Liu · Xu Sun · Yanbin Tang · Fuke Wu.anski for helpful discussions, and Shuanglin Shao for corrections. 2. Reviewof H1 theory In solving (1) we first make a well-known reduction. For smooth solu-tions to (1), the mean u = u(t) := Z Ω u(t,x) dx is easily seen by integration by parts to be an invariant of the flow (this is just conservation of momentum), thus u = u0. By making theOct 8, 2007 · Download a PDF of the paper titled A note on the cone restriction conjecture in the cylindrically symmetric case, by Shuanglin Shao Download PDF Abstract: In this note, we present two arguments showing that the classical \textit{linear adjoint cone restriction conjecture} holds for the class of functions supported on the cone and invariant ... Oct 12, 2022 · 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 ... 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 projectionsShuanglin 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 (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 ... 21 mar 2023 ... Party Secretary, Chairman Shao Yuhui and his party visited EDRI ... Add：Chengdu country shuanglin road 251 Fax：028-84333172 Postcode：610021.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: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 FallShao showed that when (α,d) = (2,2), then extremizers must be analytic, and used the functional equations in Foschi’s paper [10] to give an alternative proof to show that extremizers are Guassians. The second author and Shao showed that extremizers must be Gaussians for the case when (α,d) = (2,1) in [11] as well.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 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 Fall Shuanglin Shao [*] [[Shuanglin Shao (Ph.D. University of California, Los Angeles 2008)|]] Paul Anthony Smith [*] [[Paul Anthony Smith (Ph.D. University ...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 ... The first deals with multilinear determinant functionals and is essentially a minor adaptation of the main theorem of [27], which establishes the connection between the Oberlin-type rectangle ...Instructor: Shuanglin Shao Office: Snow Hall 615 Email: [email protected] Office Hour: MWF: 1:00 --- 2:00 PM, or by appointment. Grade Policy. Aug 31, 2008 · 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 Download PDF Epub 2022 Dec 24. Authors. Shuanglin Liao , Yao Lin , Lizhen Liu , Shuai Yang , YingYing Lin , Junbing He , Yiming Shao ... Shao. Affiliations. 1 The Intensive Care ...Guixiang XU, Professor | Cited by 1,044 | of Beijing Normal University, Beijing (bnu) | Read 59 publications | Contact Guixiang XUInstructor: 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 ...Smith Colloquium Fall 2022; Date: Speaker, Title: Local Host: October 27: Joseph Auslander Professor Emeritus, University of Maryland The Galois Theory of Minimal FlowsAuthors: 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 Download PDFby Shuanglin Shao PDF Proc. Amer. Math. Soc. 137 (2009), 135-143 Request permission Abstract: In this paper, we present two arguments showing that the classical 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 ... 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 ...32 Analyticity of extremizers to the Airy-Strichartz inequality, with Shuanglin Shao. Bulletin of the London Mathematical Society 44 (2012), no. 2, 336–352 ...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. Mathematics. 2010; In [5], when the spatial variable x is localized, Lee observed that the Schrödinger maximal operator eit∆f(x) enjoys certain localization property in t for frequency localized functions. In this … Expand. Highly Influenced. PDF. 9 …Shuanglin Shao works in harmonic analysis and partial differential equations. He is interested in establishing the profile decomposition result for the Airy equation, and the …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 SHUANGLIN SHAO Abstract. Please send me an email if you nd mistakes. Thanks. 1. P151. # 19.1 Proof. (a). (b). The function is uniformly continuous on [0;ˇ] by Theorem 19.2 because it is continuous on [0;ˇ]. (c). This function is uniformly continuous on (0;1) by Theorem 19.5 because it can be extended to be a continuous function on [0;1]. The ...Instructor: 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.In this paper we study the existence of maximizers for two families of interpolation inequalities, namely a generalized Gagliardo–Nirenberg inequality and a new inequality involving the Riesz energy. Two basic tools in our argument are a generalization of Lieb’s Translation Lemma and a Riesz energy version of the Brézis–Lieb lemma.On Marcinkiewicz integral with variable kernels (with Yong Ding and Shuanglin Shao), Indiana Univ. Math. J. 53 (2004), 805-822. Parseval's formula for ...Jun 8, 2009 · 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 ... 1 ago 2023 ... Shuanglin Shao (KU). Department of Mathematics · 138 Cardwell Hall · 1228 N Martin Luther King Jr Drive, Manhattan, KS 66506 · 785-532-6750 | ...Shuanglin Shao. Mathematics. 2010; In [5], when the spatial variable x is localized, Lee observed that the Schrödinger maximal operator eit∆f(x) enjoys certain ... 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 ...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 | [email protected]. Undergraduate [email protected] . Graduate [email protected]. Contact Us; Emergency; Statements and Disclosures;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 $\mathbb{R}^2$.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. 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 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 ... 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 ...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. In this paper we study the existence of maximizers for two families of interpolation inequalities, namely a generalized Gagliardo–Nirenberg inequality and a new inequality involving the Riesz energy. Two basic tools in our argument are a generalization of Lieb’s Translation Lemma and a Riesz energy version of the Brézis–Lieb lemma.Posted by: Shuanglin Shao | September 18, 2020 Measure and Integration theory, Lecture 7. Let be a real valued measurable function. Let . 30 nov 2017 ... From: Shuanglin Shao [view email] [v1] Thu, 30 Nov 2017 21:38:36 UTC (17 KB). Full-text links: Access Paper: Download a PDF of the paper ...Enter the email address you signed up with and we'll email you a reset link.2 ene 2009 ... A restriction theorem for the Fourier transform. Bull. Amer. Math. Soc., 81:477–. 478, 1975. Shuanglin Shao. Department of Mathematics, ...Abstract: Unconventional superconductors have Cooper pairs with lower symmetries than in conventional superconductors. In most unconventional superconductors, ...Shuanglin Shao Affiliation Mathematics Field of Study Analysis From 9/2008 – 8/2009 Shuanglin Shao works in harmonic analysis and partial differential equations. He is interested in establishing the profile decomposition result for the Airy equation, and the problem of pointwise convergence of solutions to the Schrödinger equation. Dates at IAS 15 abr 2019 ... A remark on the two dimensional water wave problem with surface tension. Author links open overlay panel. Shuanglin Shao a , Hsi-Wei Shih b.Shuanglin Shao is really nice guy. However, he relies heavily on the book during lectures even going so far as to take a book from a student to complete an example problem, after directly copying from his notes. His quizzes and tests are incredibly difficult and are mainly proofs. If you can avoid him, do.12 feb 2021 ... In: arXiv preprint math/9704212 (1997) (cit. on p. 4). [Sha08]. Shuanglin Shao. “Maximizers for the Strichartz inequalities and the Sobolev-.Zican Zha查子灿. Faculty Jinhui Tang 唐金辉 Lab LeaderProfessor Zechao Li 李泽超 Professor Jinshan Pan 潘金山 Professor Xiangbo Shu 舒祥波 Professor Jiangxin Dong 董姜鑫 Professor Xinguang Xiang 项欣光 Associate Professor Yunlian Su….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-Shuanglin Shao. Associate Professor; Contact Info. [email protected]. 785-86, anski for helpful discussions, and Shuanglin Shao for c, Spring 2016, Math 766, Real Analysis Course Information. Course Coverage: This course is the second pa, Shuanglin Shao: 306 Snow: Thursday, 9/1/22: 4:00 pm: Graduate Student Probability Seminar Ran, Shuanglin Shao · Renming Song · Zhiqiang Cai · Shizan Fang · Hon, by Shuanglin Shao PDF Proc. Amer. Math. Soc. 137 (2009), 135-143 Request permission Abstract: In this paper, we pr, Shuanglin Shao. Associate Professor; Contact Info. slshao@, From: Shuanglin Shao [v1] Sun, 31 Aug 2008 20:47:08 UTC (26 K, SHUANGLIN SHAO (Communicated by Hart F. Smith) Abstrac, We establish the linear profile decomposition for the Airy equati, SHUANGLIN SHAO AND HSI-WEI SHIH Abstract. We consider the motion o, Shuanglin Shao. Associate Professor; Contact Info. [email protected]., Authors: Shuanglin Shao. Download PDF Abstract: In , Benoit Pausader, Shuanglin Shao. We prove global wellpose, Associate Professor, Acting Associate Chair and Director of U, 1. Introduction. Breast cancer in women has become the most co, View public records and voter registration of Shuanglin Hao born 1, ... Shuang; Lin, Shao; Hajat, Shakoor; Yang, Lianpin.