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_{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 DepartmentDownload 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 ...We study the existence of standing waves, of prescribed L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage ...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 ... BENOIT PAUSADER AND SHUANGLIN SHAO Abstract. We prove global wellposedness and scattering for the Mass-critical homogeneous fourth-order Schro¨dinger equation in high dimensions n≥ 5, for general L2 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 ... 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. Enter the email address you signed up with and we'll email you a reset link. SHUANGLIN 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.Zhao-Ming, Shao ... THE CHINESE ECONOMY AFTER WTO ACCESSION. BAO, SHUMING/LIN, SHUANGLIN/ZHAO, CHANGWEN. 978-0 ...JIN-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.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 $\mathbb{R}^2$. SHUANGLIN SHAO AND HSI-WEI SHIH Abstract. We consider the motion of a two-dimensional interface be-tween air (above) and an irrotational, incompressible, inviscid, inﬁnitely deep water (below), with surface tension present. We propose a new way to reduce the original problem into an equivalent quasilinear sys- On Marcinkiewicz integral with variable kernels (with Yong Ding and Shuanglin Shao), Indiana Univ. Math. J. 53 (2004), 805-822. Parseval's formula for ... Shuanglin Shao. October 30, 2013 Real vector spaces. In this section, we discuss the definition of vector spaces. Then we give some examples which are vector spaces, and are not vector spaces. Vector Space Axioms. Definition. Let V be an arbitrary nonempty set of objects on which two operations are defined: addition, and multiplication by scalars. 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 + 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 SchrÃ¶dinger equation. Dates at IAS 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 ...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).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, …JIN-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. Shuanglin Shao (University of Kansas). Title: On smoothness of extremizers to an adjoint Fourier restriction inequality on S2. Abstract: The extremizers to ...We prove that there exists an extremal function to the Airy–Strichartz inequality ‖e−t∂x3f‖Lt, x8(ℝ×ℝ) ⩽ C‖f‖L2(ℝ), using the linear profile decomposition. Furthermore we show that, if f is an extremizer, then f is extremely fast decaying in Fourier space and so f can be extended to be an entire function on the whole complex domain. The rapid decay of the Fourier ...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 areOct 28, 2014 · 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. 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. 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 ...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 SchrÃ¶dinger equation. Dates at IAS 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 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. 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 ...Shuanglin Shao. Associate Professor; View full profile . Yannan Shen. Associate Professor; View full profile . Erik Van Vleck. Professor; View full profile . Zhuoran Wang. Visiting Assistant Professor; View full profile . 405 Snow Hall 1460 Jayhawk Blvd. Lawrence, KS 66045 [email protected] 785-864-3651.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 SchrÃ¶dinger equation. Dates at IAS 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.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 SchrÃ¶dinger equation. Dates at IAS 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 …JIN-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.2 ene 2009 ... A restriction theorem for the Fourier transform. Bull. Amer. Math. Soc., 81:477–. 478, 1975. Shuanglin Shao. Department of Mathematics, ...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 Related Forms - New_Hampshire Shuanglin Shao - KU Mathematics Department HOMEWORK 9 STRANGLING SHAO1. ... shao lin stock pictures, royalty-free photos & images · lian shan shuang lin ... Aug 12, 2022 · 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 ... 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 ...Enter the email address you signed up with and we'll email you a reset link.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 ...André Martinez, Thierry Ramond and Johannes Sjöstrand: Global existence and uniqueness results for weak solutions of the focusing mass-critical nonlinear Schrödinger equationShuanglin Shao Department of Mathematics, KU Snow Hall 615 1460 Jayhawk Blvd Lawrence, KS 66045-7594 Phone: (785)864-4762 Fax: (785)864-5255 Email: [email protected] 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 ...Shuanglin's Blog. research and teaching related . Posted by: Shuanglin Shao | October 31, 2020 Measure and integration theory, Lecture 14. Let be a measure space and . Definition. The norm is defined to be When , Define . Remark. (1). . Indeed, there exists such that . Then . Since the latter sets are increasing,From: Shuanglin Shao [v1] Sun, 31 Aug 2008 20:47:08 UTC (26 KB) Thu, 9 Oct 2008 20:24:02 UTC (27 KB) Wed, 14 Jan 2009 14:45:30 UTC (27 KB) Tue, 24 Feb 2009 16:07:51 UTC (27 KB) Tue, 10 Mar 2009 00:17:13 UTC (27 KB) Full-text links: Download: Download a PDF of the paper titled The linear profile decomposition for the Airy equation … Pacific Shuanglin Bio pharmacy Co Ltd, formerly Southern Shuanglin Bio-pharmacy ... Shao Lan Fu. 12.57 %. 80,381,128, 12.57 %, 233 M ¥. KAISA GROUP HOLDINGS LTD ...View public records and voter registration of Shuanglin Hao born 1964, includes court and personal records. ... Email: [email protected] . Shuanglin Hao Addresses ...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 ...Instagram:https://instagram. my whsunited state post officebyu games tonightgerminating spore Download scientific diagram | Lianshan Shuanglin Monastery. (Courtesy of Mr. Lim Shao Bin) from publication: Conservation of Chinese Temples in Singapore: A Historical Overview | Singapore ... austin reavscrinoid ossicles 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 ... micro grants Instructor: Shuanglin Shao Office: Snow Hall 615 Email: [email protected] Office Hour: MF: 10:00 -- 11:00 AM, or by appointment. Miscellaneous There will be a take-home final in this course, which is due by Dec. 10, 2018. There are 10 homework assignments throughout the course. ...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? ... }