Shuanglin shao.

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 areHis research mentor is Shuanglin Shao, associate professor of mathematics. MathUGRAs are awarded to students conducting semester-long independent projects culminating in an oral presentation or written work, demonstrating the student’s own development of a topic in mathematics and its applications. Recipients of the award are …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 University of Kansas prohibits discrimination on the basis of race, color, ethnicity, religion, sex, national origin, age, ancestry, disability, status as a veteran, sexual orientation, marital status, parental status, gender identity, gender expression, and genetic information in the university's programs and activities.

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. 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 theDownload 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. 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 · DOWNLOAD PDF + SAVE TO MY LIBRARY. Anal. PDE 2(1): 83-117 (2009). DOI: 10.2140/apde.2009.2.83. ARTICLE MENU. ABOUT; FIRST PAGE; CITED BY ...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.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 ...From: Shuanglin Shao Wed, 15 Jul 2015 17:13:51 UTC (29 KB) [v2] Tue, 26 Jan 2016 19:14:09 UTC (28 KB) Full-text links: Download: Download a PDF of the paper titled On ...

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.

Figure 1. Riesz diagram for theGk-symmetric restriction problem to S d−1. Estimates in the orange region follow from the Tomas–Stein inequality, estimates in the yellow region follow from Corollary 1.5, and in light of Theorem 1.3 no estimates are possible within the grey region. The possibility of estimates in the red region remains an open problem.

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

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; In this paper, we establish the linear profile decomposition for the one-dimensional fourth order Schrödinger equation where μ⩾0. As an application, we establish a dichotomy ...André Martinez, Thierry Ramond and Johannes Sjöstrand: Global existence and uniqueness results for weak solutions of the focusing mass-critical nonlinear Schrödinger equationInstructor: Shuanglin Shao Office: Snow Hall 615 Email: [email protected] Office Hour: MWF: 1-2 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.Tue, 06/06/2017. LAWRENCE — Chancellor Bernadette Gray-Little has approved promotion and the award of tenure where indicated for 62 individuals at the University of Kansas Lawrence and Edwards campuses and 77 individuals at the KU Medical Center campuses. Chancellor Gray-Little, along with Provost and Executive Vice Chancellor Neeli Bendapudi ...

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 …

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.Fall 2013, Math 647, An Introduction to PDE Course Information. Course Coverage: This course intends to cover some basic topics of partial differential equations: the introduction of the wave equation, the diffusion equation, and the Laplace equation in the one, two and three dimensional spaces.a nalysis & pde msp volume 9 no. 2 2016 jin-cheng jiang and shuanglin shao on characterization of the sharp strichartz inequality for the schrÖdinger equationInstructor: 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 ...Shuanglin Shao: 306 Snow: Friday, 9/3/21: 10:00am: Graduate Student Probability Seminar Fundamentals of Continuous Stochastic Processes: Zoom ...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 ...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-

356 JIN-CHENG JIANG AND SHUANGLIN SHAO made for log f2. Then, up to a multiple of 2ˇ, log f2.a/Dlog f.a/Clog f.a/: After restriction to R2, f satisfies(7)for x, y, wand z satisfying(8). So, by taking r sufficiently small, log f.x/Clog f.y/Dlog f.w/Clog f.z/ for x, y, w, z 2B.a;r/ˆR2 related as in(8). Since log f is twice differentiable, it ...

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 ...

BEPC-BES-III. Author Identifier: Shao.Li.Li.1. Master Advisor: Yue Kun Heng ... Shuang-Lin Li. ,. Wei-Yue Liu. et al. (Aug, 2020). Published in: Nature Phys. 16 ...28 dic 2009 ... Abstract. This is an joint work with Benoit Pausader (Brown University) and Shuanglin Shao. (University of Minnesota) In this work, ...Shuanglin Shao 2, 1. Department of Mathematics, National Tsing Hua University, Hsinchu 30013 2. Department of Mathematical Sciences, Xi'an Jiaotong-Liverpool ...Shuanglin Shao. Shuanglin Shao. Associate Professor. Contact Info. [email protected] · 785-864-4762. 627 Snow. Personal Links. Webpage Webpage. Research —.Shuanglin Shao. Mathematics. 2007; For cylindrically symmetric functions dyadically supported on the paraboloid, we obtain a family of sharp linear and bilinear ...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.Instructor: Shuanglin Shao Office: Snow Hall 615 Email: [email protected] Office Hour: M, W: 9:30-10:30 AM or by appointment. Grade Policy. Homework: There will be 5 homework. Midterm: There will one midterm of 50 minutes in class. Final Exam: There is a comprehensive final exam in class. The time ...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 $\mathbb{R}^2$. 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 …Instructor: Shuanglin Shao Office: Snow Hall 615 Email: [email protected] Office Hour: MWF: 1-2 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.Home About Select to follow link Department of Mathematics History (1866-1970) Employment

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. 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.CBMS regional conference series in mathematics, July 2006. Softcover, 373 pages. ISBN-10: 0-8218-4143-2, ISBN-13: 978-0-8218-4143-3. These lecture notes try (perhaps ambitiously) to introduce the reader to techniques in analyzing solutions to nonlinear wave, Schrödinger, and KdV equations, in as self-contained a manner as …Aug 29, 2020 · 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). Instagram:https://instagram. revolution hip hopjosh smith kansasterarria summonerspeaking ethically Shuanglin Shao Regularity of solutions to the Schrodinger equation: Nov. 15: Michael VanValkenburgh Glancing Rays: Friedlander's Example: Michael VanValkenburgh: Shuanglin Shao Regularity of solutions to the Schrodinger equation: Nov. 22: Andrea Nahmod Bilinear Pseudodifferential Operators: Christoph Thiele: Shuanglin Shao chase simpson baseballwsu stadium capacity 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¨oindgerPacific 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 ... 7online breaking news 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 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.